mark ortiz chassis newsletter

mark ortiz chassis newsletter
MARK ORTIZ CHASSIS NEWSLETTER
ÍNDICE DE LOS ARTÍCULOS PUBLICADOS
2000.5 – Rear sway bars; Effects of wheel and axle offsets; Making handling more consistent; Relationship of gear ratio and RPM
2000.6 – Effects of rear spring split; Using brake floaters
2000.7 – Brake failure in pavement Late Models; Polar moment of inertia (yaw inertia)
2000.8 – Shock dynamics – What the shock dyno does and doesn’t tell you; Effects of gas pressure; Control ratio; Natural frequency,
damping strength, and roadholding
2000.9 – How to string a car for 4-wheel alignment; Effects of caster
2000.10 – Checking rear axles for straightness; Torque arms versus pull bars
2000.11 – Suggested off-season reading
2000.12 – Springs, roll, and cornering balance; Shorty Panhard bars versus long ones
2001.1 – Wind tunnel testing for short track cars; Rear caster; Stacked coilover springs
2001.2 – Required frame stiffness; Making ballast weights
2001.3 – Safety issues – The HANS device; Soft wall design requirements
2001.4 – 5th coil location and rate; Soft wall update; Soft noses on cars
2001.5 – Chrome moly in stock cars; Rear stagger versus cross
2001.6 – Weight transfer in winged-over sprint cars, with discussion of the various components of weight transfer (wheel load transfer)
2001.7 – Chassis troubleshooting chart, with discussion of the 5 phases of the cornering process and assumptions on which the
troubleshooting chart is based
2001.8 – Things that make spring changes work backwards
2001.9 – Stock car safety issues, including discussion of NASCAR’s Earnhardt Report; Tire data – its availability and its limitations
2001.10 – Balancing the car with camber and tire pressure
2001.11 – The big tracks and their big wrecks; Factors in spring selection
2002.1 – Suspension natural frequencies
2002.2 – Winston Cup harness installation; Things that make spring changes work backwards, revisited; Basic shock questions
2002.3 – Update/correction on Winston Cup harness installation; Racing front-drive cars
2002.4 – Quads on pavement
2002.5 – Suspension frequencies revisited; Quads on pavement revisited; Space frame or monocoque?; Tire care
2002.6 – Oil accidentally or deliberately applied to tires; Diagonal percentage and tire stagger for road racers; Narrower rear track than
front
2002.7 – Braking/downshifting technique
2002.8 – Steering geometry variables; Importance of steering rack placement; Bump steer as Ackermann modification?; Relationship o
horsepower and engine torque to acceleration and axle torque
2002.9 – Additional remarks on bump steer and horsepower/torque; Finding centers of gravity for whole car, unsprung masses, and
sprung mass
2002.10 – Effects of wheelbase, CG height, and static rear percentage on traction and corner exit behavior
2002.11 – Push rods, pull rods, or both; More on trail and steering feel; Kart scaling; Another tire care tip
2002.12 – Ackermann effect, with recommendations for autocross and hillclimbing; Torque and power distribution with various types of
differentials
2002.12 – Analyzing shock traces
2003.1 – Shocks wanted for research; Tire warmers found; Spring placement on triangulated 4-link rear axle; Roll center with a j-bar
2003.2 – Shock research update; More on rear wheel placement and traction, including discussion of gyroscopic precession
2003.3 – Tire warmers less expensive than I though; Independent rear suspension for dirt racing?
2003.4 – Special issue on shock and spring forces and their effects on tire loading
2003.7 – Right rear spring stiffest, on a Cup car? Pushrod angle, motion ratio, wheel rates, and roll angle
2003.8 – Load transfer basics
2003.9 – Shock research update – end-of-stroke phenomena due to fluid compressibility, as opposed to acceleration sensitivity
2003.11 – Weight distribution and tire size; Car width versus drag
2003.12 – More on racing front-drive cars, and on load transfer; Single or dual rear brakes for FSAE?
2004.1 – Reverse Ackermann or toe-in on ovals; Setting up road racing cars that are heavier on one side than the other; Independent
or beam axle front suspension for ovals?
2004.3 – Types of differentials and their effects on car behavior
2004.4 – Effect of brake caliper mounting position; More on weight distribution; Spring splits with big bars
2004.5 – Correction to April remarks on caliper mounting (archived April issue incorporates the correction); New Nextel Cup tire and
implications for control arm geometry; control arm angles in F1; Arm angles in triangulated 4-bar beam axle rear suspension
2004.6 – More on F1 control arm angles, with discussion of “lateral anti” concept and shortcomings of using force line intersection as
roll center; Use of clutch when downshifting
2004.7 – Setup for lower grip; Lowering blocks on truck arms; Ohlins high-frequency shock piston; Which front shock to soften for
improved exit; soft links on sway bars
2004.8 – Further discussion of roll center assignment based on lateral anti, with discussion of lateral migration of the roll center as
traditionally defined
2004.9 – Tire load sensitivity and weight transfer in trailbraking; Why are wide tires better?; Relative importance of front/rear weight
distribution versus yaw inertia; Roll and ride spring preload in monoshock suspensions; Why so few rear monoshock suspensions?
2004.12 – Roll center below ground; Roll moments from longitudinal anti
2005.1 – Steering axis inclination and scrub radius
2005.3 – Finer points of anti-roll bars on stock cars
2005.5 – Can an oval track car have too much left percentage?
2005.7 – Dynamics of three-wheeled vehicles
2005.9 – Load transfer case with added rear ride compression
2005.11 – Optimizing engine-over-drive-wheels cars
2006.1 – Tires in the snow
2006.2 – Roll axis inclination
2006.3 – Worm gear vs. clutch pack differentials
2006.4 – Springs, bars, and load transfer
2006.5 – Rear percentage or polar moment?
2006.6 – Effects of spring rates and damper settings during cornering
2006.7 – Beam axle front suspension pros, cons, and design issues
2006.8 – Effects of Panhard bar fore-aft location, slope, and offset
2006.9 – Roll center in trailing arm front suspension; More on roll axis and related analytical topics
2006.10 – Twist beams and jointed De Dion tubes
2006.11 – Stiff rebound damping
2006.12 – Coil binding setups in stock cars – friend or foe?; Falling force shocks
2007.1 – Tall vs. short sidewalls
2007.2 – Modern driveshaft joints vs. rubber doughnuts; Zero-droop setups
2007.3 – Diamond layout
2007.4 – Roll steer and anti-squat/anti-lift in strut suspension
2007.5 – Roll axis for live rear axle road/hillclimb car; Roll axis of the axle
2007.6 – Another triangulated four-link axle; Large vs. small tire and wheel diameter
2007.7 – More thoughts on zero-droop setups, and related oval track spring split issues; High or low panhard bar
2007.8 – Is it bad to lift a wheel?; Hollow vs. solid anti-roll bars
2007.9 – Droop-limited rear suspension; Satchell link rear suspension; A word from the inventor
2007.10 – What exactly are shaker rigs for?
2007.11 – On the march again; Radial tire camber; A radical radial notion
2007.12 – Ins and outs of toe and ackermann
2008.1 – More exotic vehicle layout ideas
2008.3 – Another exotic car layout
2008.4 – Late Corvair rear suspension
2008.5 – Another pony car suspension from the 60′s; Really quick steering
2008.6 – Why not go for 100% camber recovery?; Gyros for roll stability
2008.7 – Front to rear track ratio
2008.8 – Dirty tricks; Porsche 993 rear suspension
2008.9 – Monoshock suspensions; Z-bars; Stock car front ends with bump rubbers
2008.10 – Differentials and yaw control
2008.12 – Controlling AWD front/rear torque split on a budget; Is there such a thing as too big (in tires, that is)?
2009.1 – Damping ratio
2009.3 – Trailing arms with torsional rubber springing; Ride and roll rates with monoshocks
2009.4 – “Minding Your Anti” video now on DVD; Raised lower control arms on 2009 F1 cars; Pullrod suspensions in F1; Rate and
length numbers on torsion bars
2009.5 – The anti controversy
2009.7 – The unsprung component in load transfer
2009.8 – Chasing a push
2009.9 – Leading and trailing wheels for oval track
2010.1 – Use ride height to tune cornering balance, or anti-roll bars?; Roll center and anti-lift in triangulated 4-link beam axle;
Measuring grip
2010.2 – Effect of changing location of just the wheel center; Effects of droop limiting
2010.3 – Old-school rocker suspension; De Dion tube design and location; Lateral location of live axle
2010.4 – Banked turn puzzle; Reverse-cant rear leaf springs
2010.5 – Selecting rear end ratio; Torque tube for front engine IRS car
2010.6 – Torsion bar tube height; Twin I beam suspension, Relationship of tire size and weight distribution
2010.7 – Tuning transient behavior of front-wheel-drive autocross car
2010.8 – When lots of front roll stiffness helps, and when it doesn’t
2010.9 – When one is a very small animal: Considering an RC car
2010.10 – Roll center theory
2010.11 – High and low speed balance, and torque arm length
2010.12 – Hybrid or semi-independent suspensions
2011.1 – Coil bind and bump stop setups in stock cars
2011.2 – Sway bar/spring rate equivalency; What wheel rate for damper calculations?
2011.3 – Followup information to January issue on stock car anti-roll bar preload and related asymmetries; Followup question to the
February issue on anti-roll bars
2011.4 – Negative camber only on the front wheels, or more on the fronts than on the rears, on some cars; Roll center/front view
geometry with dual ball joints
2011.5 – Why use sway bars at all?
2011.6 – Effects of caster and scrub radius; Camber gain recommendations
2011.7 – Mumford Linkage; Toe out for turn in
2011.8 – Toe, Ackermann, cornering force, turn-in and related puzzles
2011.9 – Anti-roll bars on Formula Vees revisited; General advice on setting dampers
2011.10 – The DeltaWing car
2011.11 – First-generation Mazda RX7 four-link; Unified theory of suspension setup for particular track?
2011.12 – More/less anti-squat – or what? – to fix wheelspin/rear tire wear
2012.1 – Equal wheel rates left/right, or equal frequencies?; Two-wheeler that doesn’t lean, but shifts weight laterally?
2012.2 – Anti-dive, and the Lotus reactive ride height system
2012.3 – More on reactive anti-dive; Forces on control arms when cornering
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
PRESENTED FREE OF CHARGE
AS A SERVICE TO THE
MOTORSPORTS COMMUNITY
May 2000
WELCOME
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Selected questions will be presented, at my discretion. Readers are invited to
submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083; by phone at 704-933-8876;
by e-mail to: markortiz@vnet.net
Mark Ortiz
We are nearing completion on a street stock 79 Camaro to run on ½ mile asphalt track with 10
degree banking in looong corners. We are considering trying a rear sway bar. We’re being told to
toss it, but I can’t help thinking there’s something there if we’re willing to work on it. Any thoughts
on what we might expect to encounter if we try running it?
Go ahead and try it.
If it is simply added with no other changes, a rear anti-roll bar will loosen the car. Used with
softer springs to get similar overall roll resistance, it will result in a softer wheel rate in pitch
and heave.
Be aware that your setup will require different springs than other people’s. Of course, if you’re
running a rear anti-roll bar, you’ve moved beyond tuning by imitation anyway.
On a street stock, which usually cannot run jacking screws, anti-roll bars with drop links offer a
way to adjust wedge and tilt (by changing link length), provided that bar preloading is not
prohibited. Having bars at both ends expands the scope of such adjustments. You also have the
ability to quickly loosen or tighten the car by disconnecting a bar.
All the tech books and articles I’ve seen tell you to kick out the left rear tire and tuck in the right rear
tire to tighten a dirt car and give it better forward bite. This is commonly done for a dry slick track. I
understand why the right rear bites better but how can moving the left rear out from the car give you
better forward bite? You are taking weight off of it when you do this.
The reason rear wheel lateral positioning works as it does relates to the line of action of the
forward thrust of the tire, rather than the load on the tire.
To illustrate, imagine your car was nose-heavy enough so you could take off one rear wheel
and drive it as a tricycle. If you had only the left rear wheel, the car would try to turn right
under power because all the thrust would be acting left of the center of mass. If you ran only a
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right rear instead, it would try to turn left under power. (Motorcycle sidecar rigs really display
this effect.)
With two rear wheels, moving either or both of them left or right has a similar effect, only
more subdued .
Moving both rear wheels to the left, then, makes the car try to turn right more (or left less)
under power. Exiting a left turn, this tightens the car. Consequently, the rear tires don’t have to
use as much of their grip for cornering and have more available for propulsion.
Toeing both rear wheels leftward (leading the right rear, with a beam axle) has a similar effect,
and doesn’t cost you left percentage.
How do you make a car less sensitive to track variations? On a dirt track modified, I am constantly
having to adjust for track changes and many times am one notch behind the track. Is this the sport in
it or is there a technical solution?
Here are two tools to help control variation in a car’s balance as grip varies:
1) Static diagonal percentage / roll resistance distribution. If the car is close to right in
average conditions but goes loose on slick and tight on tacky, add diagonal and use
more rear roll resistance and/or less front. Idea here is to increase dynamic (running)
diagonal at moderate lateral acceleration (low grip) yet decrease it at high lateral
acceleration (high grip). For a car that goes tight on slick, reverse this strategy.
2) Tire stagger. Tire stagger has more effect as grip increases. Therefore, if the car has
little or no rear stagger – meaning stagger effect is tightening the car – the car will feel
this effect more when grip is good, and act tighter. As grip diminishes, the locked axle
push effect decreases and the car goes toward loose. If the car runs generous stagger,
you see an opposite effect. Of course, changes in stagger require compensating changes
elsewhere in the setup, and in some cases the tire sizes you’d like aren’t obtainable –
but at any rate that’s how it works.
If I change from 6.26 final drive to a 6.56 final drive, how much RPM gain can I expect, and will the
lap times be faster or slower? I have good bite, but am getting beat out of the corners. Currently
turning 6200 – 406 engine, 87” rear tires, 1/3 to 3/8 mile dirt track.
You’ll be around 6500 at equal speed. If you’re above that, it’s because you’re going faster!
Assuming that 406 can survive, you should gain some speed.
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
PRESENTED FREE OF CHARGE
AS A SERVICE TO THE
MOTORSPORTS COMMUNITY
June 2000
WELCOME
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Selected questions will be presented, at my discretion. Readers are invited to
submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083; by phone at 704-933-8876;
by e-mail to: markortiz@vnet.net
Mark Ortiz
We race on 1/3 mile high-banked and ½ mile flat asphalt tracks. Car is Chevy metric with rear
weight jacks, 3200# minimum, stock lower and upper A-frames, stock 4-link rear end with Ford 9”
axle, coil springs all around.
Without really getting into specific spring rates, my question has to do with the relative stiffness of
the rear springs. Isn’t it a generally accepted principle that the LR spring is stiffer than the RR
spring, by 25 pounds or so?
I thought that on dirt the opposite was true, but on asphalt the LR is the stiffer spring.
Comments? What characteristics would a stiffer RR produce?
Actually, stiffer LR is more common on both dirt and pavement.
Let’s assume we’re comparing setups using the same pair of springs, and just swapping them
side to side.
On a truly flat track (no banking at all), mid-turn behavior should be about the same either
way. The steeper the banking, the more the right-stiff split will loosen the car mid-turn.
In general, the right-stiff split will loosen exit on any track. Steeper banking will intensify the
effect. This assumes that the rear suspension compresses under power. Rear anti-squat will
reduce the effect. If anti-squat is great enough so the rear end rises under power, the effect
reverses.
The right-stiff split will tighten entry on a flat track, assuming that the rear lifts in braking and
that the car has a reasonable amount of front brake. Extreme amounts of anti-lift or rear brake
can cause the effect to reverse. Steeper banking will diminish the normal effect and can reverse
it in extreme cases.
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I have seen brake floaters being used in several ways. Some use a floater only on the right side. I’ve
also seen them with the floater rods mounted on the top or mounted on the bottom of the right side.
What would be the proper position of the rods, and should you have them on both left and right
sides?
There is really no right or wrong way to set up brake floaters – just predictable effects.
Most often, brake floaters are set up to produce pro-lift. For links above the axle running
forward, this means the forward end of the link is above the rear end. For a link below the axle,
the link runs downhill toward the front or uphill toward the rear.
Floaters can also be set up for anti-lift, which really makes more sense for shortening braking
distances as it lowers rather than raises the center of gravity. Pro-lift has the advantage of
allowing you to use lots of rear brake without wheel hop. In some cases, rear lift is used to
promote rear steer effects.
When a floater is used on the right only, it is usually intended to give more pro-lift on the right,
de-wedging the car and loosening entry. (Note that de-wedging the car can tighten entry
instead if the car has a lot of rear brake.) The left brake torque reacts through whatever means
are provided to resist it at the axle housing.
It is possible, especially with telescoping links on the axle, to get almost any desired properties
using only one floater. The one thing you can’t do is separately tune engine braking torque
reaction and left brake torque reaction.
I think two floaters are worth having, since the added expense is pretty small. But a car with
one can be made to do most of the same things.
CORRECTION
Last month’s newsletter contained a statement in the response to a question about rear wheel
offset/lateral position that read: “If you had only one rear wheel, the car would try to turn right under
power…” That should have been: “If you had only the left rear wheel, the car would try to turn right
under power…”
My apologies for any confusion this may have created.
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
PRESENTED FREE OF CHARGE
AS A SERVICE TO THE
MOTORSPORTS COMMUNITY
July 2000
WELCOME
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Selected questions will be presented, at my discretion. Readers are invited to
submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083; by phone at 704-933-8876;
by e-mail to: markortiz@vnet.net
Mark Ortiz
BRAKE FAILURE IN PAVEMENT LATE MODELS
I’ve been getting both questions and comments from various people about brake failures in pavement
Late Models. It appears that brakes on these cars go away a lot, especially the fronts. These failures
occur when the car is running under green for long periods, and also following restarts after red
flags. Very often, the car doesn’t lose brakes entirely. It just loses the fronts, sometimes gradually,
sometimes suddenly, and spins on entry.
Although pads and rotors can fail from extreme heat, it appears that the majority of problems in these
cars are related to fluid boiling in the front calipers. This is certainly the case when the front brakes
suddenly don’t work following a red-flag heat soak.
Better ducting helps, especially under green-flag conditions. Juggling weight distribution and brake
balance to make the rears do more of the work helps a little. Making sure the fluid is fresh is
essential. But the clients who say they’ve really licked the problem are using both heat-shielded
calipers and/or reduced-conductivity pistons, and brake fluid recirculating systems. In general,
applying these measures on just the front brakes seems to be sufficient. This will of course depend
somewhat on brake bias.
POLAR MOMENT OF INERTIA (YAW INERTIA)
Mark, one of my racing buddies used the term “polar moment of inertia” in a conversation we were
having the other day. I have heard this expression before, but do not understand what it is. Could you
explain what it is, and what effect it has on race cars – also, can you measure it somehow, and how
does it relate to suspension design and/or coilover placement?
The way racers use the term, it means polar moment of inertia in yaw. A car also has a polar
moment of inertia in roll, and in pitch.
Yaw is rotational, or angular, motion about a vertical axis (i.e. rotation as seen from above, or
rotation that changes the direction the car points). To take a turn, we must accelerate the car in
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yaw in the direction of the turn during entry, then decelerate it in yaw (accelerate it in the
direction opposite the turn) during exit. We must start it rotating to make it turn, then stop the
rotation to make it go straight again.
The car acts as a giant flywheel – its inertia opposes these accelerations. When it’s running
straight, it doesn’t want to start rotating. Once it’s rotating, it wants to keep rotating. This effect
tightens entry and loosens exit.
The polar moment of inertia is the magnitude of this inertial effect. We increase it by moving
masses away from the center of gravity. We decrease it by centralizing masses. A mid-engine
car, like an Indy car, has a small polar moment of inertia in yaw. A stock car with the engine
between the front wheels and 200 pounds of ballast, the battery, and the fuel load behind the
rear axle has a large polar moment of inertia in yaw. So does a VW beetle, an Audi front-drive
sedan, or a Porsche 911, with the engine outside the wheelbase.
Most people don’t try to measure yaw inertia. GM built a giant turntable fixture to measure it.
You can mathematically estimate it by breaking the car down into components, weighing these
or calculating their mass, and multiplying the masses by the square of their distance from the
CG. Most of us don’t bother. For a pure racing car, we just try to put all the heavy stuff as close
to the middle, or the expected CG, as possible.
For a production-based car, we often face the issue as a choice between placing components or
ballast toward the rear bumper to get more rear percentage, or more centrally to reduce yaw
inertia. In such cases I usually go for the rear percentage, especially for oval track applications.
An exception would be where you can get more than enough rear percentage, and still fall short
of legal minimum weight. Then it makes sense to centralize the ballast.
On an oval track car, we can use asymmetrical setups to make the car enter and exit as loose or
tight as we want, even if the car has a lot of yaw inertia. Also, we don’t encounter such abrupt
changes of direction on an oval as we see in a chicane or sharp turn on a road course.
Consequently, minimizing yaw inertia is more important in road racing than on oval tracks.
Both large and small polar moments of inertia are mixed blessings for any car. A car with a
small polar moment and a short wheelbase will be twitchy (e.g. older Toyota MR2), unless it’s
set up very tight (e.g. Pontiac Fiero). When such a car encounters a slippery patch in mid-turn,
it will do a big wiggle and possibly spin, whereas a car with more yaw inertia will be more
stable.
So a car with a small polar moment should have a long wheelbase if possible. Suspension
geometry requirements don’t really change with yaw inertia. Moving coilovers toward the
center of the car reduces yaw inertia, but not a lot since coilovers aren’t very heavy.
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
PRESENTED FREE OF CHARGE
AS A SERVICE TO THE
MOTORSPORTS COMMUNITY
August 2000
WELCOME
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Selected questions will be presented, at my discretion. Readers are invited to
submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083; by phone at 704-933-8876;
by e-mail to: markortiz@vnet.net
Mark Ortiz
“THE SHOCK DYNO LIES!”
How come if I dyno a Bilstein shock (Roehrig dyno, using their software), and then duplicate the
graph exactly on an Ohlins, the shock feels completely different to the driver? I mean different as in
no side bite, and no forward bite – but the driver says the car doesn’t feel any stiffer.
Also, if I vary the gas pressure, the dyno displays the same graph, but the driver can feel a difference
in the shock. Why?
At what point in rebound/compression valving split will jacking occur? We valved an Ohlins to be
exactly like our Bilsteins, and the Ohlins ratcheted down in the turn until it bottomed out and almost
scared the driver to death.
How do I match the shocks to the track surface for maximum compliance and therefore maximum
forward bite? The tires of the winning car in the 100 lap day show seemed to just roll over the
washboard surface, and on all the other cars you could see the tires bouncing up and down.
The tracks get rough, and because the roughness is caused by the same type of vehicle, the roughness
always has the same look. I would think that since the pattern of 3” to 4” holes and bumps is always
similar, the “perfect” spring frequency and shock valving could be found. How do I test for this?
The shock dyno doesn’t lie, but it doesn’t tell the whole truth.
First of all, I believe your dyno cycles the shock through a 2” stroke, normally near mid-travel,
at 100 cycles/min (1.67 Hz). This gives a peak velocity at mid-stroke of just over 10 in/sec. A
rough dirt track may give you shaft speeds above that.
Your dyno only generates simple harmonic motion. Other companies make more expensive
dynos that can generate approximately square-wave (very high acceleration) motion, or can
reproduce on-track motions recorded by electronic data acquisition. These modes of testing
have value because shocks are sensitive to acceleration as well as velocity.
Your software can be programmed to show you various outputs. Many people look only at one
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end of the stroke, most often the extended end (rebound valving closing, compression valving
opening). It helps to look at both ends. A plot showing both ends of the stroke, force versus
absolute velocity, will have two points or noses at the left side, and four traces. I have seen
instances where looking at the full stroke showed me acceleration sensitivities that I never
would have known about if I had only looked at the extended end of the stroke.
The usual thing the program does with the gas force is to re-zero the load readout after
stopping momentarily at mid-stroke and reading the gas force. However, the program should
tell you, as a numerical readout, what that gas force is. It will vary with the pressure you put in
at build, and also with the volume of the gas, which you control by varying the floating
piston’s position at build or the oil volume you pour in.
You don’t always get the same trace with different gas pressures, even with re-zeroing. More
gas pressure actually increases rebound damping force (with gas force omitted), due to reduced
nucleate boiling (incipient cavitation) on the downstream side of the piston. This effect is
greatest at high velocity, with a stiff rebound stack, low gas pressures, and hot oil. The effect is
least – sometimes unnoticeable – at low velocity, with a soft rebound stack, high gas pressures,
and cooler oil.
Valving split is sometimes expressed in terms of control ratio – the ratio between rebound and
compression damping, at a particular shaft speed. As a rule of thumb, a control ratio of 1.3 to
2.5 is pretty normal; <1.3 is somewhat bump-stiff; >4.0 is likely to jack down. Jacking is also
promoted by stiffer dampers, softer springs, or a bumpier track.
Tuning for a particular disturbance frequency is mainly a matter of making sure your natural
frequencies don’t match the excitation frequency. Since your unsprung masses and tires are
similar to the other cars’, this means using spring rates that don’t match theirs, or using stiffer
damping. Sometimes it helps to stiffen just rebound, but if you’re jacking down to the bump
stops you may be too far down that path now. Soft damping gives better roadholding, except
when the bumps excite the system at one of its natural frequencies. Stiff damping raises natural
frequencies, and also makes the system less frequency-sensitive.
You can also raise natural frequency by using somewhat stiffer springs than your competitors.
In the days of cart-sprung cars with primitive dampers, this was a major reason people sprung
race cars stiffly. Another approach is to run substantially softer instead. With everybody so soft
nowadays, that can be difficult, but if you add a sway bar and good bump rubbers it can work.
Finding a good combination is mainly cut-and-try at the track. Electronic data acquisition can
be a big help. I have an associate who specializes in that. His name is John Chapman. He’s in
Charlotte at 704-549-1309, e-mail jchap56756@aol.com. For shock dyno and build service, I
recommend Scott Munksgard at Munksgard Technical Services in Concord, NC at 704-7822611, e-mail MTSdyno@aol.com. He custom-builds Bilstein, Ohlins, Penske, and Carrera
shocks, and sells AFCO and Pro shocks and Afcoil and Hypercoil springs.
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MOTORSPORTS COMMUNITY
September 2000
WELCOME
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Selected questions will be presented, at my discretion. Readers are invited to
submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083; by phone at 704-933-8876;
by e-mail to: markortiz@vnet.net
Mark Ortiz
WHEEL ALIGNMENT
I run an open-wheel mod (2400 lbs, asphalt). When squaring the chassis, is it best to align the right
front to the right rear, or the left front to the left rear, and why? Our car is one inch wider in the front.
You really shouldn’t use the front wheels as a reference at all. If you change your front end
settings, your wheel offsets, or your axle lateral position, you’ve lost the ability to recover your
rear wheel alignment setting. Not good.
Instead, you need a way to align your rear wheels with respect to the frame. Preferably, you
should directly measure the alignment of both wheels – not one wheel, not the axle. That way,
you are never caught out by a bent axle.
To do this with string, you need to make yourself a set of stringing bars which let you run two
parallel strings down both sides of the car. I buy two pieces of aluminum angle, clamp them
together to form a “T”, and match-file notches in the edges at the base of the “T”. The spacing
of the notches needs to be slightly greater than the width of the car.
I set the bars on jack stands in front of and behind the car so the strings are about hub height,
weight each end of each string with a nut, bolt, and pair of washers to hold them taut, make
sure they lie in the filed notches so they’re parallel, and measure from the strings to the wheel
rims.
On an asymmetrical oval track car, you have to pick a method of positioning the parallel
strings relative to the frame – i.e. you have to decide what you call “straight ahead”. I like to do
this by measurement from two marked positions on a frame rail, preferably the left one since it
gets bent less often. I pay attention to any existing marks or methods, and try to make my
definition of “straight ahead” consistent with those.
Once you’ve gotten to this point, you have a way of checking alignment of all four wheels that
will not be thrown off by changes to front end settings, wheel offsets, axle position, or other
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tuning variables. One other advantage: if you ever race cars with independent rear suspension,
you’ll be right at home.
Having said all this, I can tell you one thing about how the two methods you mention compare
to each other for your car – assuming the axle is straight, and assuming you don’t change
anything else on the car. If you string on the left, the car will end up with more right rear lead
than if you string on the right. That will tighten the car under power. Effect when braking
depends on brake bias, driving style, and nuances of language. Many people report a looser car,
especially those who mainly slow the car with the rear wheels.
If your car were wider in back than in front, you would get more right rear lead by stringing on
the right instead.
Some people consider me an old lady on this wheel alignment stuff, but cars are extremely
sensitive to rear wheel alignment. Undetected rear wheel alignment problems are a leading
cause of mysterious handling quirks.
CASTER
We run asphalt tracks, 1/3 to ½ mile, with a 2800# car. I am looking for a little more front end bite to
be able to “cut under” a competitor, starting at the center and coming out of the turn.
The very first inch of contact on the inside and outside of the RF tire seem to run 10 to 12 degrees
hotter than the rest of the tire (157/145/155). We run caster settings of 1.5 degrees left/3.5 degrees
right. Would raising the caster to 2.0/5.5 help? The driver steers the front wheels about 5 to 6
degrees to take these turns. Will we get too much caster-induced camber?
I’d try more caster. You don’t need 3 ½ degrees split, unless you like the steering to pull left,
which has nothing to do with making the front tires stick. I’d try 5 degrees both sides, or use
whatever split the driver is comfortable with.
Based on your tire temperatures, the RF could use some more air. As for camber, many people
will tell you that near-equal right and left shoulder temps mean your cornering camber is
perfect. However, clients of mine who have measured tire temperatures while the car is running
say that, as a rule of thumb, when the left and right shoulders of an oval track car’s RF tire read
similar in the turns, the left shoulder reads about 10 degrees hotter than the right in the pits
after a run. So I don’t think you’ll end up with excessive camber. The car may even want a
little more static camber. Try leaving it unchanged, and see what temps you get with more
caster and more air.
Changing caster always changes bump steer, so you will need to check that.
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
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October 2000
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
CHECKING REAR AXLES
Last month’s piece on stringing cars to measure wheel alignment on the vehicle has proven very
popular, and has also engendered further discussion. One topic that’s come up has been how to check
a rear axle before installing it. Here’s a good method. You need a pair of v-block stands to support
the axle, and a bump steer gauge with two dial indicators or the digital equivalent.
Install the bump steer plate where one wheel would mount. Position the indicators against the plate
as you would when measuring bump steer, and zero the indicators. While you hold the bump steer
plate so it can’t rotate, have a helper rotate the axle housing, while you watch the dial indicators.
Start at zero degrees pinion angle, or a pinion angle of your choice, and record readings at 90 degree
intervals. Repeat for the other wheel. Compare the difference in indicator readings at positions 180
degrees opposite, then DIVIDE BY TWO to get camber and toe in inches at indicator span.
Many people use a somewhat similar method, turning the housing with the axle resting on its wheels,
and just measure wheel-to-wheel toe, using a tape or a trammel bar. The problem with this is that
both snouts can be cocked the same direction, and if you only measure wheel-to-wheel you won’t
pick that up. If you place a stationary object next to each tire, you can see any large individual wheel
misalignment. An axle with both wheels aimed to the right, or both aimed left, can be made to work
acceptably if you string the car as described in last month’s issue. But if you just check wheel-towheel toe, then align the axle to the frame, you can get unexplained handling problems.
Since nothing is perfect in the real world, the question arises of what constitutes an acceptable axle.
The answer is that a bit of overall toe-in is acceptable, perhaps even desirable. Toe-in adds drag, but
stabilizes the car under power. Any amount of toe-out is unacceptable. Toe-out makes a car loose
and directionally unstable under power. It is possible to use toe-out as a crutch to make a spool work
on a road course, but this is a desperation measure.
Camber can be used to improve cornering. For road racing, we generally want a little negative
camber on both wheels. Sometimes we may want more camber on one wheel than the other, for
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courses that are predominantly right or left. For oval track, we want positive camber on the left and
negative on the right. On oval track cars, camber comes from both the axle and from tire stagger.
With a track of 60”, each inch of stagger adds about .15 degree of camber, negative on the right,
positive on the left.
How much camber you can run will be limited either by the rules or by component life. On fullfloater axles, with standard shafts and drive flanges, a prudent limit is .75 degree at the axle, plus
whatever you get from tire stagger. This would correspond to a maximum camber reading of about
.013” per inch of indicator span when checking the axle as described above. You can push this limit,
depending on how much torque you are transmitting through the splines, at what wheel rpm, for how
long. Axles with convex splines are available for more aggressive angles. In general, non-fullfloating axles will not accept as much toe or camber as full-floaters. You only have one set of splines
to work with, at the inboard end of the shaft. Cocking the bearing at the outboard end just gets you
bearing failures.
TORQUE ARM OR PULL BAR?
Will a torque arm give more forward bite than a pull bar?
Not necessarily. All either system does is generate an anti-squat jacking force, which only
helps a little anyway. Either layout can be made to produce any amount of anti-squat desired.
One advantage of pull bars is that they can be made short enough to go behind the driver,
although many you see are too long for that. If you mount the pull bar left of center, its lift
force adds wedge under power. In most classes where torque arms are legal, you can’t fit an
adequately long one behind the driver. Another advantage for the pull bar is that you usually
save some overall and unsprung weight.
In general, torque arms provide better damping of axle rotation. Their shocks act at a greater
distance from the axle. Also, in most existing cars, torque arm layouts provide more anti-squat,
and the anti-squat changes less with ride height. This doesn’t always have to be the case,
however. Actual geometry of the particular layout is very important.
One interesting possibility with torque arms is to use two springs or coilovers - one ahead, one
further back on the arm. You then use a conventional single spring for the rear one, and a
conventional spring stacked with a very light “tender spring” for the front position. This makes
the arm act short when grip is poor and axle torque is low, and effectively lengthen as axle
torque increases. Most of the damping should be at the front spring, or forward of it. It
probably is also possible to get a similar effect using two pull bars, or even a pull bar and a
torque arm together. Bottom line: you can get good results with either layout, and both hold
unrealized potential for those who are willing to reason from first principles and innovate.
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November 2000
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
WINTER READING MATERIAL
As the racing season winds down, I’m getting lots of requests for recommendations for off-season
reading. Therefore, I have decided to devote this issue of the newsletter to sources of information to
help readers advance their self-education.
Please note that it is impossible to include all works of value in a brief list. Omission of a work does
not imply condemnation. Likewise, inclusion of a work does not imply infallible accuracy, although
I am making an effort to recommend documents that are largely accurate and widely well-regarded.
Let’s start with some of the best general-purpose texts on vehicle dynamics.
Race Car Vehicle Dynamics by William & Douglas Milliken, SAE, 1995: Widely considered the
standard reference work on the subject. Some portions are by other authors. Some chapters are
highly mathematical; others are more conversational. Includes a chapter on the history of vehicle
dynamics. Authors operate Milliken Research Associates, Inc. in Williamsville (Buffalo area), NY.
Tires, Suspension, and Handling by John Dixon, SAE, 1996: Another excellent reference. Good
discussions of tire and suspension characteristics. Author is Senior Lecturer in Engineering
Mechanics at The Open University, Great Britain.
Fundamentals of Vehicle Dynamics by Thomas Gillespie, SAE, 1992: A somewhat shorter and very
readable vehicle dynamics text. Author teaches vehicle dynamics at University of Michigan and Ford
Motor Company.
Car Suspension and Handling by Donald Bastow and Geoffrey Howard, SAE, 1993: Third edition of
a work first published in 1980. More conversational than the above books, with a large appendix
devoted to calculations. Authors are engineers with long and varied experience in the English
automotive industry.
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A couple of sources specifically on dampers (shock absorbers) deserve mention.
The Shock Absorber Handbook by John Dixon, SAE, 1999: Not really my idea of a handbook. More
of an engineering text on dampers. Good coverage of principles and history of damper design and
ride tuning theory. Not much on use of dampers as a tool to control transient behavior of race cars.
For a good discussion of how to use low-speed damping to influence transient handling, plus a good
brief overview of damper function, see a pair of articles in the March and April 1996 Sportscar,
entitled Damper Physics: The Black Art of Adjustable Shock Absorbers, by Neil Roberts. These
articles, minus illustrations, can also be read and downloaded for free at www.gtf1.com under the
titles of Racing Dampers 201 & 202.
On aerodynamics, a couple of good ones are:
Competition Car Downforce by Simon McBeath, Haynes/Foulis, 1998: A fairly brief, highly
readable work specifically dealing with downforce – therefore readily applicable to racing.
Aerodynamics of Road Vehicles, ed. by Wolf-Heinrich Hucho, SAE, 1998: Compendium of papers
and articles by a variety of authors on aerodynamics. Fourth edition, originally published in
Germany. Good general-purpose text on the subject, including lift/downforce, drag, and directional
stability.
Some lesser-known magazines I like include:
Racecar Engineering and Race Tech, published in England, both available by subscription in the US
from EWA Magazines, 205 US Hwy. 22, Green Brook, NJ 08812, phone 1-800-392-4454, web site
www.ewacars.com. More technical depth than most US car magazines.
Grassroots Motorsports, available from Motorsport Marketing, 555 West Granada Blvd., Suite B-9,
Ormond Beach, FL 32174, phone (904) 673-4148, web site www.grmotorsports.com. Good
coverage of amateur road racing, autocross, and vintage racing.
Speedway Illustrated, P.O. Box 37574, Boone, IA 50037, phone 1-888-837-3684, web site
www.speedwayillustrated.com. New magazine from former Stock Car Racing editor Dick Berggren.
For a good catalog of automotive books, contact Classic Motorbooks at www.motorbooks.com or 1800-826-6600. SAE sells books at www.sae.org/BOOKSTORE or (724) 776-4970.
I have published 6 articles in Racecar Engineering. These comprise a 2-part series on suspension
interconnection and a 4-part series on asymmetrical cars. I have photocopies available at $2/article,
check or money order to me (postage included; NC residents please add 6% sales tax).
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December 2000
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC 28083;
by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my posts on
the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to check out these
sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
SPRINGS, ROLL, AND CORNERING BALANCE
As I understand it, the stiffer the coil spring, the more weight is put on that corner, therefore planting
the tire more. My question is, what is the difference between the stiffer coil vs.body roll? Example: A
stiffer RF coil should put more weight on that tire, giving it more bite – therefore making the car steer
better. However, you hear all the time about NASCAR teams taking spring rubbers out of the RF when
they are tight to allow the chassis to roll over on the RF, making it turn. Is it because this allows the
LR to lift, which makes it turn? Please explain, in simple terms.
Stiffening the right front spring, or adding preload to it, does load that tire more, and does make
it produce more cornering force, in a left turn.
However, this comes at the expense of left front tire loading. The spring change can’t change the
total load on the front wheel pair, only the distribution of that total between the right front and
left front. The spring change also can’t change the total load on the rear wheel pair, the right
wheel pair, or the left wheel pair, only the diagonally opposite wheel pairs.
So rear wheel loads when cornering are also affected by the front springs. The total rear wheel
load doesn’t change, but its right/left distribution changes, oppositely to the front wheels.
This means that with a stiffer RF spring, the front tires are loaded more unequally when
cornering, and the rears are loaded more equally, than with a softer RF spring.
Now here’s the key: When you concentrate the load on the outside tire, you lose more cornering
power on the inside tire than you gain on the outside one. This is because grip from a tire
increases with load, but at a DECREASING RATE.
Therefore, when you load the fronts more unequally and the rears more equally, that hurts
available cornering force at the front and improves available cornering force at the rear: tighter
car. That’s the condition with the spring rubber in the RF. Take the rubber out, and you load the
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fronts more equally than before, and the rears more unequally. That helps stick the front, at the
expense of the rear: looser car.
It works this way on dirt too, contrary to what some people will tell you.
SHORTY PANHARD BARS VS. LONG ONES
Can you help me understand the advantages and/or differences of the shorty Panhard bar (left chassis
to left diff.) versus a long Panhard bar, for a dirt modified or Late Model? I know the shorter bars are
more aggressive and plant the left rear more. Some say they’re harder to drive. Generally speaking,
what changes are needed when changing between these types of bars?
The shorty bar, especially when steeply inclined, jacks the left rear corner of the frame up in
response to left-turn cornering force.
Since its angle increases as the car rolls and jacks, the effect increases exponentially as cornering
force increases. The angle also varies a lot as the car goes over bumps, so the chassis becomes
highly bump-sensitive.
Consequently, the shorty bar is at its worst on a rough, tacky, variable track, and at its best on a
smooth, slick, highly consistent track.
Despite the popularity of shorty bars, I question their merit, because you can get as much
dynamic diagonal as you want by other means, without the inconsistent behavior. I think a long
bar is a clear advantage if the track changes and has bumps, as most tracks do. I doubt that a long
bar is even a disadvantage on a smooth dry-slick track, if you set it up right.
Some people believe that the jacking force adds to the overall loading of the axle or tires. This
doesn’t really occur. The suspension can’t push down any harder on the axle than the car pushes
down on the suspension (if we ignore the weight of the suspension parts). Raising the rear of the
car, even with cornering-induced jacking, doesn’t increase total rear wheel load. Raising the left
rear does increase diagonal percentage. This makes the rear stick better, at the expense of the
front.
Things a long bar calls for, compared to a shorty bar on the same car, include some combination
of the following:
1)
2)
3)
4)
More static diagonal
Lower Panhard bar height
Softer rear springs
Stiffer front springs
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CHASSIS NEWSLETTER
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January 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
WIND TUNNEL TESTING FOR SHORT TRACK CARS
Many classes in short track racing involve cars that are aerodynamically very similar to each other,
due both to tight bodywork rules and to copycat engineering. Most of these classes of cars are never
tested scientifically to evaluate and improve their aerodynamic properties. This is due in
considerable measure to the fact that wind tunnel time is expensive, and also to the fact that most
short track racers don’t know where to look for a wind tunnel that would have the time or inclination
to work with them.
There is now a wind tunnel that is actually looking for short track cars to test. It’s the tunnel at
Langley, VA, which was originally built in the 1930’s by NACA for running full-scale tests on
fighters and similar-size aircraft. The tunnel is now leased to Old Dominion University. They have
so far tested a DIRT modified, and are looking to test other types of dirt and pavement cars.
The DIRT mod test is described in a recent SAE paper by Drew Landman and Eric Koster. Among
other things, the test revealed that the car generated net lift at the front axle, despite having a
“snowplow” front end. This was of great interest to the team running the car, as they had been trying
all sorts of chassis tweaks to cure an entry push.
This testing service is not free. In fact, it costs $1400/hour. For a one-day session long enough to do
any good, you’re looking at eight to ten thousand dollars. However, the payoffs are potentially
enormous. Adding downforce can dramatically improve lap time. Small changes in the average
pressures on the top or bottom side of a car can generate hundreds of pounds of vertical force,
because the car’s plan view area is so large.
The similarity of the cars in many classes means that racers can form groups to share the costs,
provide one or more representative cars for test, and share the knowledge gained. If racers can get
their friends – or maybe their car builders -- interested, there is a good chance that participants can
make considerable gains at reasonable cost. I have volunteered to serve as a coordinator and compile
lists of interested racers by car class. E-mail or phone me if you might want to pursue this.
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REAR CASTER
What is rear caster, and how does it affect the handling of a vehicle?
The term “rear caster” is normally applied to the side view inclination of the rear upright in an
independent rear suspension. The concept is not applicable to beam axle rears. The upright
often will not have an identifiable steering axis, but it should have some agreed features by
which we can measure its inclination on a particular car.
We ordinarily don’t have a steering mechanism at the rear, but we have one or more links per
wheel that provide toe location and give the suspension its bump steer properties. So on many
cars setting rear caster is our main way of adjusting rear bump steer. Sometimes there is a
factory-recommended spec, but it is best to establish the desired rear caster setting by dialing in
rear bump steer properties using a bump steer gauge, then measuring what upright angle or rear
caster we have when the bump steer is the way we want it. Measuring this angle then becomes
a quick way to recover the setting without going through the whole bump steering process.
In general, tilting the upright back at the top (adding caster) adds roll understeer – makes the
wheel toe in in bump and toe out in droop. Tilting the upright forward at the top does the
opposite. In some designs rear caster has no effect at all, even though you can adjust it. This is
uncommon nowadays since it is useful to be able to tune rear bump steer. On some other cars,
you can’t adjust rear caster but you can adjust bump steer with shims on the toe control link.
STACKED COILOVER SPRINGS
Why do people use two springs of different rates stacked on top of each other on a coilover?How do
you figure the rate of a combination like that?
The usual reason for stacking a soft coil spring on top of a firmer one is to get a stepped rising
rate. One spring, usually the softer one, coil-binds before the coilover bottoms. With one spring
coil-bound, the rate of the combination is the rate of the spring that can still move.
The rate of two stacked coils is less than the rate of either one alone. If we call the rates of the
two individual springs A and B, and the rate of the combination C, then C = (AB)/(A+B).
In many cases, neither spring is coil-bound at static ride height. The idea is to get a rising
spring rate to avoid bottoming or to cope with increased aerodynamic downforce at higher
speeds. In other cases, the softer spring is so soft that it is coil-bound in normal operation and
only serves to take up clearance at full droop. This is sometimes called a tender spring. Finally,
it is also possible to use a special stop that causes the assembly to go stiffer in extension rather
than compression. This is most often used on the left front on dirt cars, to tighten exit.
The Mark Ortiz Automotive
CHASSIS NEWSLETTER
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February 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
REQUIRED FRAME STIFFNESS
Is there a way of calculating how much torsional stiffness a car’s frame needs to have?
In road car engineering, it is customary to calculate a torsional natural frequency for the sprung
structure, and compare this to the damped natural frequencies of the front and rear suspension
in roll and warp. What this calculation tells you is whether you have enough stiffness to make
the dampers (shocks) work as intended.
Any good race car should exceed this minimum by a substantial margin. I have never
attempted to calculate or measure torsional natural frequency for a race car, and I doubt that
anybody else does. Natural frequency depends not only on torsional stiffness, but also the mass
of the sprung structure, and even the placement of major masses within the structure.
Measuring just the torsional stiffness of the frame is fairly common. This involves anchoring
one end of the frame, typically at spring or rocker mounting points, and twisting the other end
with a lever and a jack at the spring or rocker mounts. People don’t try to reduce this measured
stiffness to a calculated minimum; more is better.
There are some broad rules regarding how stiff is “stiff enough”.
1) The stiffer the suspension’s wheel rate in roll and warp, the stiffer the frame needs to
be. Cars with beam axles at both ends typically have the softest wheel rates in roll and
warp, and require the least torsional frame stiffness.
2) The stiffer the frame is, the more responsive the car is to tuning via roll resistance
distribution. A flexible car does respond to roll resistance variation, but it takes a bigger
change in roll resistance to get a given increment of cornering balance adjustment.
3) A car that relies on unequal front and rear roll resistance (one that corners on three
wheels, or nearly so) needs a stiff structure more than one that has similar roll
resistance front and rear.
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4) A flexible car is more difficult to mess up with adjustments. It’s also more difficult to
fix with adjustments.
5) Stiff cars need smoother drivers. Jerky drivers often prefer more flexible cars.
Torsional stiffness of the whole frame, with loads applied at the spring or rocker mounts, isn’t
the only kind of rigidity that matters. All the load points that absorb forces from the suspension
and steering need to be as rigid as possible. We can set forth a few general rules to help assure
this:
1) Triangulate the frame as well as possible.
2) Feed loads, especially suspension loads, into the structure at tube junctions, not in the
middle of a span.
3) Design brackets to minimize local torsion and bending loads. Make forces pass right
through tube centerline intersections when possible.
4) When you cannot avoid feeding a load into a span, or when you are using stressed
panels, design brackets so they spread the load so you minimize localized deflection.
5) Mount spherical joints and rod ends in double shear (plates on both sides) whenever
possible.
MAKING BALLAST WEIGHTS
What does lead weigh per cubic inch? I want to make ballast weights using lead-filled 3”x3” or
4”x4” square tubing, weighing 25 and 50 pounds, and I need to know how long to make them.
Lead weighs about .41 lb./cu.in. in pure form – let’s say about .40 if you’re melting down
wheel weights. If you use .125” wall tubing, 3”x3” weighs .39 lb./in. and 4”x4” weighs .53
lb./in. Internal cross-sectional areas are about 7.56 sq.in. for the 3”x3” and 14.06 sq.in. for the
4”x4”.
So one inch of 3”x3” filled with lead weighs about 3.41 lb., and one inch of 4”x4” weighs
about 6.15 lb.
Therefore, a 25 lb. weight using the 3”x3” would be 7.33” long, and a 50 lb. one would be
14.66”. Using the 4”x4”, you’d need about 4.07” for a 25 lb. or 8.13” for 50 lb.
Mounting holes, mounting hardware, voids in the lead fill, and using other wall thicknesses
may cause minor variations from these theoretical numbers. If you make the weights a little on
the large side, you can lighten them more easily than you can add material.
CAUTION: Lead is toxic. Any time you melt lead, be sure to provide good ventilation, and
avoid inhaling fumes.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
SAFETY ISSUES
With the deaths of Dale Earnhardt and three other national-level NASCAR drivers in the last 12
months, all from basal skull fractures in frontal impacts with walls, much attention is suddenly being
paid to this type of injury, and this type of impact. I would like to offer my own thoughts on the
matter.
THE HANS DEVICE
The HANS (head and neck support) device has been around for some 20 years in various forms. It
has had trouble gaining acceptance for reasons of bulk, mobility restriction, and appearance. There is
little doubt that it will prevent basal skull fractures in frontal impacts, and NASCAR drivers are
suddenly ordering the device in much larger numbers.
I do not doubt the device’s effectiveness. However, it should be pointed out that there is only a
certain range of impact severity where it really helps. (Impact severity depends on magnitude,
duration, and number of accelerations.) Below a certain threshold of impact severity, the driver will
survive without the HANS. Above a higher threshold, the HANS will save the skull and neck, but
the driver will be killed anyway by other internal injuries. Therefore, the HANS may be part of the
answer, but there is also a need to reduce impact severity in frontal contact with the wall.
SOFT WALLS
The need to reduce impact severity in frontal collisions with walls has led to various ideas for
cushions for concrete retaining walls. Some tracks in the northeastern US are using blocks of
styrofoam (styrene foam). NASCAR has done a few experiments with encapsulated styrofoam, as
used for marine dock bumpers. I do not claim to be an expert on impact absorption devices, but I
would like to make some general observations on what is required of such a system.
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First, the cushioning system must preserve the good points of a simple concrete wall as much as
possible. The uncushioned wall performs very well in glancing impacts, which are in fact the vast
majority. The car slides along the wall, loses speed gently, and either comes to rest or continues
around the track. It is vital that any cushion present a hard, smooth, continuous surface in a glancing
impact, and not snag the car.
Second, on frontal impact the cushion must yield in a controlled manner, and not spring back
immediately.
These two objectives are absolutely crucial. Additionally, it is helpful if the cushion can recover its
shape and absorb more than one impact. It should be replaceable quickly, in sections, when it cannot
recover. It should do its job without making a mess. It should be as compact as possible, though
there is an inevitable tradeoff here between compactness and impact absorption. It is desirable that
the cushion be non-flammable, though this is a secondary consideration. Cost is inevitably a factor.
Finally, it is a good thing if the cushion can be made of reused or recycled materials.
I have no patents on wall cushions, and I am not promoting anybody else’s system, but there are
some particular design features that can help accomplish the objectives described above.
The cushion needs to have a metal, plastic, or composite facing. This should probably be part of the
individual segment of the cushion, for easy replacement of both the facing and whatever is behind it.
To avoid the problem of a car deforming one segment and being snagged by the next segment, the
facing of each segment should overlap the facing of the next segment, in the direction of vehicle
travel.
Behind the facing, there must be some kind of deformable structure to absorb impact. Possibilities
here include cellular or foam structures, telescoping hydraulic units, and bladders containing air or
water, with blowoff valves.
One approach might be to mold cushion segments in one piece, with a relatively thick facing and a
thinner-walled honeycomb crush structure behind that. A possible material would be polyethylene,
sourced from recycled milk jugs. This would gently recover its shape after impact, if the damage is
not too severe. When the segment is too severely crushed for that, it would be replaced, and
recycled.
Bladders, made of reinforced rubber as in fuel cells, could be refilled with air or water after an
impact and be ready for another. Water exiting through blowoffs absorbs impacts very nicely. The
principle has been used for vehicle bumpers. The water would wet down the track, but absorbent
compounds used for other spills, or simple evaporation, might cope with that. Alternatively, air-filled
bladders could be restored to shape with a pressure hose. Foams such as those used for earplugs and
cockpit padding can also be used in bladders.
To fasten segments to the wall, one solution is cables through the wall, with fork clips.
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April 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
5TH COIL LOCATION AND RATE
I’m running a dirt Late Model with a torque arm.The car is good overall but could use some more
forward bite on slick corners. I have gotten a lot of different opinions about how to set up my torque
arm and 5th coil. Please explain what moving the 5th coil mount forward or backward on the torque
arm does to forward bite, and what softening or stiffening the spring does to forward bite.
First of all, there’s a reason you’re getting conflicting information on the effects of torque arm
length and spring rate on “forward bite” (forward acceleration capability, propulsive traction,
ability to put power down): the effects are mainly imaginary. There are real effects, but they
don’t amount to much where the tires meet the track.
The shorter the torque arm length is, the more upward jacking effect it has. Contrary to what
people will tell you, this in itself does not increase the loading on the axle. It just makes a
portion of the load go through the fifth coil and a correspondingly smaller portion go through
the right and left rear springs. It does lift the car, however, and there is a small but real effect
due to that. The higher sprung mass CG causes slightly more load transfer to the rear wheels.
Therefore, you should run the torque arm as short as you can without encountering wheel hop.
When the arm is short enough to cause the rear of the car to rise rather than squat when you get
on the power (geometry of your axle locating linkages also affects this), the effect of rear
wheel rate split is reversed. This means that softening the left rear spring adds wedge under
power and tightens exit, whereas with a suspension that squats in forward acceleration you
tighten exit by softening the right rear and/or stiffening the left rear. Effect of front spring split
on exit is the same either way: stiffer left front for tighter exit.
The spring on the torque arm doesn’t affect how much the car lifts. It just affects how much the
axle rotates. This cushions the application of torque to the wheels. Whether this really does
anything is questionable. I’ve had a client who did blind back-to-back tests with different
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spring rates, and no spring at all, on a torque link (not a torque arm, but the effect is similar).
Neither the driver nor the stopwatch could detect any difference between different spring rates,
or the rigid link. It may be that the spring makes some difference in a very jerky application of
power.
We can also say for sure that if the spring is too light, the axle will rotate too much and you
will destroy U-joints or other parts. The minimum spring rate required to prevent this increases
a lot as you shorten the arm. It varies inversely with the square of the arm length (measured
from axle center to spring center), plus a bit. That is, the rate required with a 30” arm is MORE
THAN 42/32 = 1.78 times as great as with a 40” arm. If the car didn’t lift more with the shorter
arm, the factor would be exactly 1.78. But it does lift more. How much more depends on the
rest of the system, but it’s safe to say you would need at least 2 times the spring rate.
There are all kinds of interesting possibilities with torque arms and torque links, involving
offset links and arms, multiple links and arms, multiple springs, snubbers, dampers, and so on.
However, these are beyond the scope of your question, and involve fabrication and advanced
setup knowledge. I am interested in working with car owners or builders who would like to
pursue such possibilities.
SOFT WALL UPDATE
Last month I offered some general remarks about soft wall technology. I was gratified to read on
Jayski that Petty Enterprises tested a segmented, molded plastic wall cushion during March. They
instrumented a couple of Adam’s old cars with a recording accelerometer and crashed them into a
wall with and without the cushion. Reportedly, the cushion, which is about 2 feet thick, reduced peak
acceleration from 100 g to 40 g. I didn’t have anything to do with this, and I don’t have any more
specifics on the system they used, but that’s definitely enough difference to save a life. If the system
performs well in glancing impacts, and is reasonably priced, this looks very promising.
SOFT NOSES
Another subject of recent interest is deformability of the front ends on stock cars. People have
expressed concern that front clips have become too crush-resistant in the search for torsional
stiffness. This may be true, but there are ways to make a front clip torsionally stiff without making it
so hard in a crash. A real space-frame front clip, in mild steel, with triangulation that doesn’t run so
nearly lengthwise, and no boiler-plate frame rails, would help – if it were legal. Also, I think the
nose structure forward of the frame could be made to absorb more energy. Right now, it collapses
very easily, and then the deformation stops or slows abruptly once it reaches the frame. More sheet
metal, honeycomb, and/or plastic crush structure inside the nose molding could help a lot, and this
could be added to existing cars. The energy-absorbing nose cones in CART show what can be done.
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May 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering answers to
chassis questions. Readers may submit questions by mail to: 155 Wankel Dr., Kannapolis, NC
28083; by phone at 704-933-8876; by e-mail to: markortiz@vnet.net. Topics are also drawn from my
posts on the tech forums at www.racecartech.com and www.rpmnet.com. Readers are invited to
check out these sites, and to subscribe to this newsletter by e-mail.
Mark Ortiz
CHROME MOLY IN STOCK CARS
Recent discussions of frontal impact deaths in stock cars have produced allegations that some of the
more advanced teams in Winston Cup, which build their own chassis, are now using chrome-moly
(4130) steel in their frames, supposedly including even the large rectangular main rails. I have no
way of verifying these reports, but I have noticed that various other classes in racing are allowing
thinner-walled tubing in roll cages when 4130 is used. I am told the material is making major inroads
in dirt Late Model construction as a result of this, as it allows considerably lighter cars.
Most stock car classes, including Winston Cup, neither require 4130 nor give it a wall thickness
break. Therefore, there is no weight saving to be had from it. The reported reason for using it in Cup
cars is to gain stiffness.
These developments prompt me to offer some information about what 4130 will and won’t do for a
car, and some of the less-recognized properties of the material. All this information has been
published before. I would particularly like to tip my hat to Carroll Smith, whose book Engineer to
Win offers considerable insight into this and other materials-related matters.
STIFFNESS
First thing we need to emphasize, and this will come as a shock to many racers, is that 4130 offers no
significant stiffness advantage over mild steel! The gain is 1% or less. That’s assuming equal wall
thickness and weight, and identical design. If the frame is built with lighter gauge tubing to save
weight, it will actually flex MORE.
Note that stiffness means resistance to deflection under load, short of the point of permanent
deformation. Stiffnesses of all steels are remarkably similar. The best spring steels are less than 3%
stiffer than mild steel, and 4130 as normally used in frames is actually closer to mild steel than to
spring steel. Resistance to permanent deformation is called strength, and that’s where chrome-moly
offers potential gains. In normal use, a car frame is a stiffness-limited structure, and therefore does
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not gain performance significantly from the use of 4130, unless the rules allow us a frame or cage
weight reduction. This applies until we crash the car. At that point, we suddenly have a strengthlimited structure.
STRENGTH
Steels may be very similar in stiffness, but they differ dramatically in strength. Strength can be
expressed in terms of ultimate tensile strength, yield strength, and impact strength. Ultimate tensile
strength refers to tension load required to pull the material completely apart. Yield strength refers to
tension load required to permanently deform the material. Both ultimate tensile strength and yield
strength are measured by applying a gradually increasing load to the material. Impact strength, on
the other hand, is measured by striking a sudden blow, of known magnitude. If the material deforms,
but doesn’t fracture, it passes. If it actually breaks, it fails.
The distinctions between these different kinds of strength are of great importance in race car
construction. For portions of the structure that are close to the driver, we mainly want to prevent the
wall, track surface, or whatever the car hits, from intruding into the cockpit. This means we want
yield strength. A little deformation may cushion an impact, but we don’t have room for large
deformations. For portions further from the driver, we want a structure that deforms in a controlled
manner, preferably outer portions first, absorbing energy as it crumples. To achieve this, we need
graduated yield strength – more as the deformation approaches the driver. In both cases, we need
impact strength; the structure can only do its job if it doesn’t come apart on impact.
Mild steel does not respond to heat treatment; its carbon content is too low. Consequently, its
properties remain about the same no matter how we weld it, heat it, or cool it. It never becomes
brittle, as long as we don’t introduce impurities while welding. Its yield strength is moderate, but its
impact strength is good. In a crash, it deforms and absorbs energy, while resisting being torn apart or
fracturing. This makes mild steel a good choice for most portions of a stock car frame. There is no
significant stiffness penalty compared to 4130, and greater deformability when the car takes a hit.
Therefore, there may be a case for using 4130 for the cage in the driver’s compartment of a stock
car, but not for the front or rear clips.
4130, on the other hand, will harden when heated above its critical temperature and cooled rapidly.
Cooled slowly, it remains soft. In the hardened condition, 4130 has great tensile and yield strength,
but POOR IMPACT STRENGTH. It’s hard and strong, but brittle. 4130 tubing, as supplied, is not in
the hardened condition. It’s cold drawn and normalized – fairly soft. In this condition, it will usually
bend on impact and not fracture, just like mild steel, and it is somewhat stronger. But when we TIG
weld 4130, we get a hard zone, not at the weld but half an inch or a little more from the weld. This
happens because this region is heated enough to produce hardening, and is close enough to cool
metal to be cooled abruptly after welding. The result of this is the failure pattern commonly seen in
crashed 4130 frames: the tubes bend, the frame diamonds and twists, but there are some fractures
near the welds. Not at the welds, but an inch or less from them.
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Most people who build 4130 frames simply live with this. But there is a solution. After welding, heat
the joint and the nearby metal to a dull cherry red with an oxy-acetylene torch, and allow to air-cool
slowly. In warm ambient temperatures, just letting the area cool naturally is often sufficient. In
colder ambient temperatures, or for insurance, a sheet metal or foil shield loosely fitted around the
joint will slow the cooling sufficiently to avoid hardening.
Another approach, seldom considered nowadays, is to gas weld the joint instead. 4130 tubing was
originally invented about 75 years ago for the aircraft industry. TIG welding was unknown. Aircraft
structures were gas welded. Gas welding heats the metal surrounding the weld more than TIG
welding does. This compounds distortion problems, but it does alleviate the problem of having very
hot metal near cool metal that can quench it. In many cases, this will automatically eliminate the
brittle zone.
REAR STAGGER VERSUS STATIC CROSS
We run a Late Model on pavement and have a question about the relationship of cross weight to
stagger. In 1999, we used about 1.25 inches of rear stagger with 54% cross. In 2000, we increased
our stagger to 2 inches, thus having to jack more cross into the car to keep it the same. How do you
know when you have hit this balance right? I hear guys talking at the track about how much stagger
they run, and it seems to vary widely.
Stagger loosens the car through the entire turn. Most people report the biggest effect on exit, at
least on pavement. Stagger has greatest effect when the rear tires are loaded the most, but the
effect goes away when the wheels spin.
Static cross has more effect when cornering force is moderate, meaning it does affect entry and
exit more than mid-turn. Springs, conversely, affect mid-turn the most. Static cross tightens the
car, except that the effect can reverse on entry if you slow the car mainly with the rear wheels.
Stagger has more effect when grip is good. Static cross has more effect when grip is poor. So
the way you blend stagger and cross affects how the car’s balance varies as track conditions
change. A car with modest stagger and modest cross will go loose on slick more than the same
car with more stagger and more cross.
So usually, consistency improves with more stagger and cross. The penalty comes in tire drag,
especially down the straights, which increases as you add stagger.
2001 CONSULTING RATES
Hourly: $40/hour. Monthly retainer: $240/month. Season retainer: $1200/year. Retainer option gets
you unlimited phone time, plus e-mail within reason. Payment is by check or money order. I am also
available to join your team for tests or races on an hourly + cost + per diem basis.
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June 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Topics and questions are also drawn from my posts on the tech forum
at www.racecartech.com , where readers can see chassis consulting done for free. Readers are
invited to subscribe to this newsletter by e-mail.
WEIGHT TRANSFER IN WINGED-OVER SPRINT CARS
I see winged sprint cars rolling to the left in left turns when cornering on dirt. How does this
happen? What is going on with the wheel loads when the car does this? How does this behavior
impact the car’s response to spring or torsion bar changes?
Roll and load transfer in winged sprint cars make a very interesting analysis exercise, and a very
good lesson in the distinction between roll and wheel load transfer (“weight transfer”). When
equipped with a high wing with big side plates, a sprint car can transfer wheel load rightward while
rolling leftward. Or, on a very slippery surface, the car theoretically could actually transfer wheel
load leftward, though this would be unusual.
Disregarding aerodynamic forces for the moment, total wheel load transfer in any car is simply the
car’s weight, times lateral acceleration in g’s, times its overall CG height, divided by track. This is
the number of pounds by which the inside wheel pair loading is reduced, and the identical number of
pounds by which the outside wheel pair loading is increased.
To estimate front and rear wheel load changes, this total load transfer is customarily broken down
into the following components:
1) Load transfer of the front and rear unsprung masses. These act independently at the front and
rear, and act through the tires but not through the suspension. The rear unsprung mass load
transfer is substantial when the car has a live axle. Each of the two unsprung masses has its own
center of mass, or center of gravity, approximately at hub height.
2) Geometric load transfer (sprung mass load transfer through the suspension members). For the
front or rear wheel pair, this component is equal to the pounds of sprung weight at that end of the
car, times lateral acceleration in g’s, times roll center height at that end of the car, divided by
track width at that end of the car.
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For a car with high roll centers, such as a sprint car, this component is the largest one. For a car
with low roll centers at both ends, such as a car with four-wheel independent suspension, this
component is small. For a stock car or IMCA-style modified or dirt Late Model, with
independent front suspension and a live axle in back, this component is small at the front and
large at the rear. For a roll center below ground level, this component is negative (leftward, in a
left turn).
3) Elastic load transfer (sprung mass load transfer through the springs, including anti-roll bars or
other roll-resisting interconnective springs if present). To calculate this component, we need to
know the wheel rate in roll for each wheel, and the wheel’s distance, laterally, from the sprung
mass CG plane (the longitudinal, vertical, plane containing the sprung mass CG). Using these
wheel rates and moment arms, we calculate the elastic (spring-derived) roll resistance, or angular
anti-roll rate, for each end of the car, in lb-in per degree of roll. Adding the front and rear angular
anti-roll rates, we have the angular anti-roll rate for the whole car.
That angular anti-roll rate resists the sprung mass roll moment about the roll axis. This roll
moment is equal to the sprung weight, times lateral acceleration in g’s, times the moment arm of
the sprung mass CG about the roll axis. (This is measured perpendicular to the roll axis in side
view, not vertically in side view or diagonally in three dimensions.)
If we divide the roll moment (lb-in) by the overall elastic anti-roll rate (lb-in/deg), we get the
amount of roll (deg). Working backwards, we divide the front and rear elastic anti-roll rates
(lb-in/deg) by the roll (deg) to get the elastic anti-roll moments for the front and rear wheel pairs
(lb-in). We then divide the wheel pair elastic anti-roll moment (lb-in) by the wheel pair track (in)
and we have the elastic component of the load transfer (lb) at each wheel of the pair.
Sprint cars have a soft wheel rate in roll, and a small moment arm from sprung mass CG to roll
axis. Therefore, their elastic load transfer is a fairly small component. Their roll angles can be
considerable, despite the high roll axis, due to the soft springing. Any force acting at a large
distance from the roll axis can roll a sprint car a lot, without creating a lot of wheel load change.
If you have a sprint car on wheel scales, and you push laterally on the roll cage, you can easily
rock the car, while the wheel scale readings change relatively little, compared to rocking a stock
car or a road racing car the same amount (which would also take a much stronger push).
In a car with a low roll axis, elastic load transfer is the largest component. In a stock car, elastic
load transfer is the largest component at the front, and relatively small at the rear.
4) Load transfer due to lateral CG movement. This component is very small in cars, but can be
highly significant in heavy trucks and other tall vehicles, especially when the cargo can shift or
slosh.
These four components comprise the factors in lateral load transfer, assuming a flat (unbanked) turn,
constant speed, constant turn radius, and rigid tires – and ignoring aerodynamic influences. This is of
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course a simplified model – complex enough already though, right?
When the car is not in steady state cornering, there are additional factors. Actual cornering involves
longitudinal accelerations as well as lateral ones. These effects are highly significant, especially in
oval track racing. But for simplicity, let’s just consider the effect of lateral acceleration increasing on
entry and decreasing on exit.
When the lateral acceleration is changing, the car’s roll angle will be changing. That is, the car has a
roll velocity, not just a roll position. The suspension is in motion. This is called a transient condition.
In transient cornering, we have additional load transfer factors:
5) Frictional load transfer. This includes forces generated by the shocks and also any other
friction in the suspension. These frictions create front or rear frictional moments that act in
parallel with the elastic moments, and may either add to the elastic moments or subtract from
them. In general, frictional moments add to elastic moments any time the suspension is moving
away from static position, and subtract from elastic moments when the suspension is moving
toward static position. Hydraulic forces are velocity dependent. Dry friction forces are more or
less independent of velocity.
6) Minor inertial effects. These arise from accelerations (changes of velocity) of the various
elements of the car, particularly the sprung mass in roll. Properly understood, the centrifugal
force and all other forces the tires have to overcome when cornering are also inertial effects. Roll
inertia is minor compared to these. However, it can have significant effects in cars that roll a lot,
in sudden maneuvers. Roll inertia explains why a vehicle may corner in a stable slide on a
skidpad, yet overturn in a lane change or slalom test.
Breaking down the components of roll resistance like this allows us to predict the effects of changes
to the various design and tuning factors that govern these components, in a sprint car or any other.
Now let’s look at the forces from the wings. On a sprint car, we actually have two wings, but the rear
one generates the most significant forces; it’s big, and it’s far enough from the bodywork to get
ample airflow. It’s also up high, and has big side plates. These are the factors that allow it to roll the
car leftward, when the car is passing through the air at an angle (i.e., is in aerodynamic yaw).
Each wing generates a downward force. This acts approximately in the CG plane, or a little more
strongly on the left wheels than the rights. It loads all four wheels. This increases the longitudinal
and lateral forces available from all the tires, which of course is why people use wings. This, in turn,
increases all accelerations generated by tire forces.
The downward forces from the wings, in themselves, have little effect on roll or amount of lateral
load transfer. The added tire forces affect roll, but if anything they increase the tendency to roll
rightward.
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The wings also generate a rearward drag force. This unloads the front tires and loads the rears, and
causes some rearward pitch.
Finally, the wings, especially the side plates on the main one, generate a leftward drag force when
the car is in aerodynamic yaw. That’s what rolls the car left. This force is small compared to the
leftward force from the tires or the rightward inertia force (centrifugal force) at the sprung mass CG,
but it acts on a huge moment arm about the roll axis. It’s like your hand on the roll cage in the earlier
example of easily rocking a sprint car on wheel scales without affecting the scale readings a great
deal, compared to other kinds of cars.
In round numbers, a sprint car’s roll axis is about a foot above the ground, the overall and sprung
mass CG’s are about a foot and a half above the ground, and the wing is about 6 feet up.
So the car sees a net leftward load transfer if the side force at the wing is more than ¼ as great as the
centrifugal inertia force at the CG. This means the wing has to make ¼ of the lateral force. It has to
make 1/3 as much force from air as the tires make with four sticky rubber footprints on the ground,
aided by downforce. That’s not impossible, but it takes a lot of air speed and a very slippery track.
However, the car will roll leftward if the side force at the wing is more than about 1/10 as great as
the centrifugal inertia of the sprung mass only. This is a much easier condition to achieve.
In this state, the elastic component of the load transfer is negative (leftward), but the geometric load
transfer is still positive (rightward) and is greater than the elastic load transfer. The unsprung mass
load transfer is still positive (rightward). The load transfer due to sprung mass CG movement is
negative (leftward), but very small. Thus, the big components of the load transfer are not reversed,
just the small ones. The car is transfering wheel load rightward despite rolling leftward.
Since the elastic load transfer is reversed, the usual effect of spring changes is also reversed. More
rear spring adds wedge when cornering and tightens the car.
Effect of roll center height is as usual. Raising the front roll center tightens the car; raising the rear
roll center makes it looser.
Effect of static cross (diagonal percentage) is as usual. More load on the right front and left rear
tightens the car, except perhaps on entry when slowing mainly with the rear wheels .
Shock tuning, assuming the track is smooth enough for low speed damping of roll motion to matter,
works backwards. To add wedge on entry, add RR rebound damping or LR compression damping, or
reduce RF rebound or LF compression. To add wedge on exit, add RF compression or LF rebound,
or reduce RR compression or LR rebound.
Bump rubbers on the RF or LR tighten the car, when the car is leaning on the rubber.
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CHASSIS NEWSLETTER
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July 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Topics and questions are also drawn from my posts on the tech forum
at www.racecartech.com , where readers can see chassis consulting done for free. Readers are
invited to subscribe to this newsletter by e-mail.
CHASSIS TROUBLESHOOTING GUIDE
From time to time, people ask me to write a simplified chassis troubleshooting guide, as some other
writers and car builders have done. I have shied away from this because so many things can alter the
way chassis variables work. For example, changes to the left springs of an oval track car work one
way in steady-state cornering on a flat track, and the opposite way in steady-state cornering on a
steep banking. Rear spring split works one way if the rear suspension squats under power, and the
opposite way if it lifts. Anything that adds diagonal percentage tightens the car (adds understeer),
except on entry when the car is mainly being slowed by the back wheels, if the retarding force is
strong and cornering force is moderate. So I always ask a client about the car, the track, and the
driver’s style before trying to solve problems (although in some instances a question does have a
quick, simple answer).
However, it is possible to create a simple troubleshooting guide for a certain set of conditions and
assumptions. I will offer such a guide here, but I want to be very explicit about the assumptions:
1) The inside suspension is assumed to extend rather than compress in steady-state cornering. That
is, the turn is assumed to be fairly flat, grip is assumed to be fairly good, and relationship
between ride and roll rates is assumed to be fairly conventional. This will make the guide
applicable to relatively flat ovals. It will also be applicable to most road course corners, but I will
assume for this discussion that we are examining a left turn. Road racers will have to “think
mirror image” when applying the rules to right turns.
2) The suspension is assumed to be free of large jacking forces. In braking, the front suspension
compresses and the rear suspension extends. Under power, the front suspension extends and the
rear suspension compresses.
3) The front brakes are assumed to do at least half of the braking. The driver is not assumed to be
tossing the tail out with the brakes.
4) The surface is assumed to be smooth enough so that sprung mass motion creates most of the
shock movement, rather than bumps. This means we are looking at low-speed damping.
We will need to break the turn down into five portions, rather than the customary three:
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Early entry: Braking is hard, and brake application is either steady or increasing. Cornering force is
present, and increasing, but still moderate compared to rearward force from braking. This phase of
the cornering process may not exist in many corners on a road course, or a severely paperclip-shaped
oval. In such cases, the driver will do the hard braking in a straight line, and start to ease out of the
brakes as he/she begins to turn in. But on most ovals, this phase will usually be present. I quite often
see oval track drivers turn before they lift, or about the same time. This phase may also be present in
road course corners that are fast, last a long time, or require an in-fast-out-slow line.
In this phase, roll position is rightward from static (left turn, remember), and increasing. Roll
velocity is rightward, and increasing. Pitch position is forward from static, and increasing. Pitch
velocity is forward, and may be increasing or decreasing.
The most active corners of the car are the right front and the left rear. The right front suspension’s
position is compressed from static, and its velocity is in the compression direction. The left rear
suspension’s position is extended from static, and its velocity is in the extension direction.
Late entry: Braking is diminishing, and ends at the completion of this phase. With a capable driver,
cornering force should build as braking force diminishes.
Roll position is rightward from static, and increasing. Roll velocity is rightward, and may be
increasing or decreasing early in this phase. Late in this phase, roll velocity will be rightward and
decreasing. Pitch position is forward from static, and decreasing (because braking is diminishing).
Pitch velocity is rearward.
The most active corner in terms of position is the right front. It will generally see its greatest
compression somewhere early in the late entry phase. (This varies depending on several factors,
including anti-dive, anti-roll, and roll rate/ride rate relationship.) The left rear is also active in terms
of position. It will see its greatest extension. The most active corners in terms of velocity are the left
front and right rear. The left front is extending; the right rear is compressing.
Mid-turn: Braking has ended. The driver feeds in at least enough power to overcome drag. The car
either holds steady speed or gently begins to gain speed. The car is approximately in steady-state
cornering. Forward acceleration is negligible. Lateral acceleration is at its maximum. Duration of
this phase may be considerable with a smooth driver in a long turn, or it may be negligible if the turn
is brief or the driver is abrupt.
Roll position is rightward from static, and stable. Roll velocity is near zero. If the mid-turn phase
lasts a noticeable length of time and steady-state cornering is closely approximated, pitch position
will be close to static, and pitch velocity will be near zero.
If steady-state cornering is approximated, all corners of the suspension are active in terms of
position, and none are active in terms of velocity. The more the turn is banked, the more the rights
are compressed and the less the lefts are extended. In corners around 15 degrees, the lefts neither
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compress nor extend much, and at steeper angles the lefts compress. As stated earlier, we are not
considering such cases here.
The car is sensitive to all of its springs, especially the rights, and none of its shocks.
Early exit: The driver begins to increase power application and allow the car to widen its arc.
Lateral acceleration diminishes and forward acceleration increases.
Roll position is rightward from static, and decreasing. Roll velocity is leftward, and increasing. Pitch
position is rearward from static, and increasing. Pitch velocity is rearward.
The most active corner in terms of position is the right rear. It will see its greatest compression
during this phase. The left front is also active in terms of position. It will see its greatest extension. In
terms of velocity, the most active corners are the right front and left rear. The right front is extending
(de-compressing); the left rear is compressing (de-extending).
Late exit: Similar to early exit, except that forward acceleration is now the dominant factor and
lateral acceleration is fading into insignificance. Lateral acceleration will be zero at the conclusion of
this phase, or very nearly zero, and forward acceleration will be at its maximum.
Roll position is rightward from static, less than before, and diminishing. At the conclusion of this
phase, roll position reaches approximately static (car is going straight). Roll velocity is leftward, and
decreasing. Pitch position is rearward from static, and increasing. Pitch velocity is rearward.
The most active corners in terms of position are still the right rear and left front, but the relative
significance of right rear compression is diminishing. At some point in this phase, right front and left
rear positions reverse from earlier phases: the right front goes into an extended position and the left
rear goes into a compressed position. This means that spring changes on these two corners work
backwards from the way they worked in previous phases. The most active corners in terms of
velocity are still the right front and left rear.
We pay attention to suspension position because it is the key to spring tuning. We pay attention to
suspension velocity because it is the key to shock tuning. Note that early and late exit are similar in
terms of suspension velocity, but qualitatively different in terms of suspension position.
Now that we know what the suspension is doing in the turn, we are in a position to predict the effects
of spring and shock changes. Remember that the rules which follow are only as good as your
situation’s match-up to the one we’re modeling here. If your rear suspension lifts under power or
compresses in braking, or you run on steep banking, the rules change.
I am also including rules relating to other tuning variables such as tire stagger, brake bias, and so on.
I have tried to keep the chart to a single page, with reasonable size print, so it is a useful basic guide
but cannot be a comprehensive reference work.
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CHASSIS TROUBLESHOOTING CHART
CAUTION: See the rest of this publication for important information on applicability of these rules.
Tuning factors listed are the most influential ones for the phase of cornering specified,
but are not the only influential ones.
TO TIGHTEN LOOSE CAR
TO LOOSEN TIGHT CAR
Early
Entry
Stiffer right springs, especially RF
Softer left springs, especially LR
Stiffer RF compression damping
Softer LR extension damping
More front brake
Less front and rear tire stagger
More static diagonal percentage
Softer right springs, especially RF
Stiffer left springs, especially LR
Softer RF compression damping
Stiffer LR extension damping
More rear brake
More front and rear tire stagger
Less static diagonal percentage
Late
Entry
Stiffer RF spring
Softer LR spring
Stiffer LF extension damping
Softer RR compression damping
More front brake
Less front and rear tire stagger
Higher front/lower rear roll center
Stiffer front/softer rear anti-roll bar(s)
More static diagonal percentage
Softer RF spring
Stiffer LR spring
Softer LF extension damping
Stiffer RR compression damping
More rear brake
More front and rear tire stagger
Lower front/higher rear roll center
Softer front/stiffer rear anti-roll bar(s)
Less static diagonal percentage
Midturn
Stiffer front springs, especially RF
Softer rear springs, especially RR
Stiffer front/softer rear anti-roll bar(s)
Higher front/lower rear roll center
Less rear tire stagger
More static diagonal percentage
Softer front springs, especially RF
Stiffer rear springs, especially RR
Softer front/stiffer rear anti-roll bar(s)
Lower front/higher rear roll center
More rear tire stagger
Less static diagonal percentage
Early
Exit
Softer RR spring
Stiffer LF spring
Softer RF extension damping
Stiffer LR compression damping
Less rear tire stagger
Higher front/lower rear roll center
Stiffer front/softer rear anti-roll bar(s)
Aim rear wheels leftward
More static diagonal percentage
Stiffer RR spring
Softer LF spring
Stiffer RF extension damping
Softer LR compression damping
More rear tire stagger
Lower front/higher rear roll center
Softer front/stiffer rear anti-roll bar(s)
Aim rear wheels rightward
Less static diagonal percentage
Late
Exit
Softer right springs, especially RR
Stiffer left springs, especially LF
Softer RF extension damping
Stiffer LR compression damping
Less rear tire stagger
Aim rear wheels leftward
More static diagonal percentage
Stiffer right springs, especially RR
Softer left springs, especially LF
Stiffer RF extension damping
Softer LR compression damping
More rear tire stagger
Aim rear wheels rightward
Less static diagonal percentage
For help with cars or situations not covered here, call Mark Ortiz at 704-933-8876 or e-mail markortiz@vnet.net.
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CHASSIS NEWSLETTER
PRESENTED FREE OF CHARGE
AS A SERVICE TO THE
MOTORSPORTS COMMUNITY
August 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Topics and questions are also drawn from my posts on the tech forum
at www.racecartech.com , where readers can see chassis consulting done for free. Readers are
invited to subscribe to this newsletter by e-mail.
COMPUTER PROBLEMS AT RACECARTECH
The tech forum mentioned above at www.racecartech.com has been down for about two weeks at
this writing. Some people are under the impression that I own the site, but actually I just post there
regularly. The timing of the problem leads me to suspect it may be related to a reported long-running
tunnel fire in Baltimore which has damaged fiber optic cables. One would think the internet would
have enough circuit redundancy to make damage to one cable inconsequential, but news reports are
saying this fire has massively disrupted internet communications. Whether this is the problem or not,
the forum will hopefully be up and running again soon. Meanwhile, my services remain available
privately, as always.
THINGS THAT MAKE SPRING CHANGES WORK BACKWARDS
Last month I presented a chassis troubleshooting chart. I took care to point out that the
recommendations in that chart apply only for a certain set of assumptions, including a fairly flat
track and suspension with no large jacking forces. This month I’m going to supplement last month’s
information by discussing some factors that make spring changes work differently.
TRACK BANKING
In a flat turn, on most cars the inside suspension (left side, for a left turn) extends and the outside
compresses. As the track banking gets steeper, the inside suspension extends less and the outside
suspension compresses more. The car still rolls outward, but the entire chassis is pressed down due
to the banking. Steep bankings are generally only encountered on oval tracks, so we will be
discussing left-turn situations here.
Beyond a certain banking angle, the left suspension no longer extends, but compresses instead. This
reverses the effect of left side spring changes: stiffer left front reduces instantaneous diagonal
percentage and loosens the car, while a stiffer left rear adds instantaneous diagonal and tightens the
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car, in steady-state cornering. Right spring changes still work the same as on a flat track, except they
have greater effect, due to the greater deflection.
I like to speak of a critical angle for track banking. This refers to the angle at which the left
suspension neither compresses nor extends in steady-state cornering. The critical banking angle
varies with springs, anti-roll bars, suspension geometry, aerodynamics, and amount of grip. It is
usually somewhat different for the front and rear of the car. As a rule of thumb, critical banking
angle for stock cars on asphalt is around 15 degrees.
The slipperier the surface, the smaller the critical banking angle. Or more accurately, the slipperier
the track/tire combination, the smaller the critical banking angle.
The less the car relies on its springs for its roll resistance, the less the critical banking angle. If you
increase the anti-roll bar stiffness and decrease the spring stiffness, that makes the car corner at a
lower ride height on the banking, and reduces the critical banking angle. This has been a major issue
in Winston Cup lately. Some teams have tried outrageously soft springs on the front, with very stiff
bars, to make the car corner lower on relatively flat tracks. This was the reason for the bump rubbers
which NASCAR recently outlawed.
Raising the roll center on a beam axle, and softening the springs, also reduces the critical banking
angle. Raising the roll center on an independent suspension can have a similar effect, although we
may also encounter jacking effects that can reduce or reverse this. On beam axles, we can have
jacking effects that are separable from roll resistance. For example, if we raise the left end of an
“across-the-car” (or long) Panhard bar, and lower right end an equal amount, we make the car jack
up in a left turn, with little effect on the roll center. Such a change increases the critical banking
angle.
It is difficult to calculate the critical banking angle precisely, but it is quite easy to know when we’re
there if we have electronic data acquisition. When we are close to the critical banking angle, the ride
height traces from the left wheels will correlate heavily with longitudinal acceleration, throttle
position, and brake pressure, and will be largely insensitive to lateral acceleration. In this situation,
the car’s steady-state cornering balance is insensitive to left spring changes, but left spring changes
do affect its entry and exit characteristics. This means we can tune mid-turn properties with the right
springs, and tune entry and exit with the lefts.
LARGE JACKING FORCES
Note that steep bankings reverse the effect of left spring changes because they reverse the usual
direction of suspension motion on the left side of the car. It is a basic rule that anything that reverses
the usual direction of suspension motion at a particular corner of the car reverses the effect of spring
changes at that corner. The other very common cause of reversed suspension motion is large jacking
forces: forces that try to extend or compress the suspension when the tire generates horizontal forces.
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Designers deliberately build jacking properties into suspensions to resist roll and pitch, and to raise
the center of gravity under power, which increases load transfer to the rear wheels.
At the front end, we call upward jacking forces (ones that try to extend the suspension) in braking
anti-dive. At the rear, we call downward jacking forces (ones tending to compress the suspension) in
braking anti-lift. In rear-wheel-drive cars, upward rear suspension jacking forces under power are
called anti-squat. It is also possible to have front anti-lift under power when the front wheels are
driven.
The front suspension is said to have 100% anti-dive if the jacking force is exactly sufficient to
prevent the suspension from compressing under braking. Most cars have less anti-dive than this, and
many have none at all. When the anti-dive is zero, jacking forces are absent in braking, and the
forces tending to compress the front suspension are resisted entirely by the springs. If downward
jacking forces are produced in braking, anti-dive is said to be negative. Negative anti-dive is also
referred to as pro-dive.
If a car has exactly 100% anti-dive at the front, the left and right front suspensions neither compress
nor extend in braking, regardless of spring rates. This means that, in pure braking, front spring
choices have no effect on instantaneous diagonal percentage. If anti-dive exceeds 100%, the front of
the car actually lifts in braking, and instantaneous diagonal percentage increases if we soften the
right front spring or stiffen the left front – opposite of the usual.
Note that these are mainly hypothetical cases, since most cars have far less than 100% anti-dive.
Most stock cars nowadays have moderate anti-dive at static, and lose anti-dive rapidly as the
suspension compresses, sometimes going to pro-dive. When a car has pro-dive, front spring changes
affect entry balance in the usual way, only their effect is greater. When a car has moderate anti-dive,
front spring changes affect entry balance in the usual way, only their effect is less. These comments
also apply to individual corners of the car: when we have pro-dive on the right front and anti-dive on
the left front, entry is highly sensitive to right front spring changes, and much less sensitive to left
front spring changes.
Similar effects occur at the rear in braking. If the car has 100% anti-lift, the rear suspension neither
extends nor compresses in braking, and spring choices have no effect on instantaneous diagonal
percentage in pure braking. Of course, to meaningfully say that the car is loose or tight, we must
have some cornering, and therefore some roll, along with our braking, and front and rear springs will
have effects on instantaneous diagonal percentage due to their effect on front and rear roll resistance,
even in the case of a car with 100% anti-dive and 100% anti-lift at all four corners.
Unlike 100% anti-dive, 100% anti-lift (or more) is common in road cars, or in production-based road
racing sedans and sports cars. Cars that react rear brake torque through a simple trailing arm or semitrailing arm generally have more than 100% anti-lift. Examples include C2 and C3 Corvettes, many
BMW’s, Porsche 911’s and 356’s, and all but the first Mazda RX-7’s. Some dirt modifieds and Late
Models also have more than 100% anti-lift, though others have pro-lift. Anti-lift exceeding 100%
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will be evident in data acquisition outputs or trackside observation: the rear will drop rather than rise
when the car slows. The anti-lift effects may be different for engine braking than for actual brake
forces, and a car can have anti-lift on decel yet have pro-lift on the brakes. A typical dirt car 4-bar
rear with a torque arm, and calipers on the birdcages, usually exhibits this mix of properties. Most
trailing arm independent rears are the opposite: pro-lift on decel, anti-lift on the brakes.
Under power, the right and left rear suspensions may either extend or compress. In addition, live
axle suspensions transmit driveshaft torque, which tends to extend the left rear suspension and
compress the right rear, adding instantaneous diagonal percentage. The effect on suspension position
is called torque roll; the effect on wheel loads is called torque wedge.
If the rear suspension as a whole neither compresses nor extends under power, that is 100% antisquat. In this case, rear spring changes have little effect on wheel loads in pure forward acceleration,
except that in live axle rears, torque roll and torque wedge still occur unless the suspension is
carefully designed to eliminate this. Softening either rear spring, or both, increases torque roll and
torque wedge, regardless of overall anti-squat.
Stiffening the front anti-roll bar decreases torque roll but increases torque wedge. Stiffening the left
front spring likewise decreases torque roll but increases torque wedge. Stiffening the right front
spring also decreases torque roll and increases the torque-related component of wedge change.
However, in most cases the unloading of the front end under power extends the right front
suspension more than torque roll compresses it, so the net effect of a stiffer right front spring is to
de-wedge the car in pure forward acceleration.
We can also speak of anti-squat effects at each rear wheel individually, even in live axles, and we
may include driveshaft torque effects when considering these, or not – as long as we don’t forget that
the driveshaft torque is there. When either rear spring extends under power rather than compressing,
the effect of spring changes at that corner of the car is reversed. A common instance of this occurs
on the left rear of typical 4-bar dirt Late Models, where a softer LR spring will tighten exit.
INTERACTION OF THESE EFFECTS
As if we didn’t have enough complexity just considering these effects in isolation, in the real world
we often have banking effects and jacking effects acting together. Without electronic data
acquisition, it may be difficult to know or predict whether, or when, a particular corner of the car
compresses or extends. However, we do know this much: if the actual direction of suspension
motion is opposite to what we’d get on a flat track with small jacking forces, effects of spring
changes will be opposite too. If motions are bigger, effects of spring changes are bigger. If little
motion occurs, spring rate will have little effect.
With electronic data acquisition, we can use these principles to predict effects of spring changes in
particular parts of the turn, even with complex jacking/banking combinations. And even if we don’t
have electronic data acquisition, these principles can still help us make sense of our observations.
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September 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net.
BAD NEWS, AND GOOD NEWS
The tech forum at www.racecartech.com, arguably the hottest chassis forum on the internet, has now
been down for a month and a half. Over the past year or more, I have answered questions for free on
this forum, and have gotten quite a few paying clients as a result. Since people have come to think of
that site as the place to find me, I would prefer to stay there. But if it stays down much longer, I’m
going to have to start my own message board, or possibly find another one to hang out on. I have emailed the owners of the racecartech site, asking them what we should expect. I have received no
answer. Stay tuned. Meanwhile, I am definitely still in the consulting business, though the
“economic slowdown” has hit me hard.
On a brighter note, I have recently come to an agreement with Racecar Engineering magazine to
publish a monthly column based on this newsletter. For those unfamiliar with that magazine, it is
published in England and features deeper and better tech articles than the car magazines at your local
supermarket. Subscriptions for the US, Canada, and Mexico are handled by EWA Magazines, 205
US Hwy. 22, Green Brook, NJ 08812; phone 1-800-392-4454; website www.ewacars.com.
STOCK CAR SAFETY ISSUES
The month of August has seen the release of NASCAR’s report on the death of Dale Earnhardt, and
the first public demonstration of the Humpy Bumper. There was also one independent study released
which advocated crush structures in stock car noses.
On the whole, I find NASCAR’s official conclusions, as presented by Dr. James Raddin, to be
logical and consistent with the physical evidence as presented. The only real room for doubt lies in
the difficulty of verifying that physical evidence, particularly in view of the long delay before the
separated belt was announced, the rescue worker’s insistence that the belt was not separated, and the
refusal to allow public access to the autopsy photos.
Concerning the belt, I agree that it was installed improperly, if the illustrations we’ve seen are
correct. I also agree that the shoulder harness was installed with an inordinately long run to the
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anchor point. I agree that the lap belt’s mounting could cause failure, at approximately the point
where the belt passed through the hole in the seat, which is also where the adjuster was. But we are
being asked to believe that this happened during the crash; that the separated portion of the belt was
displaced 4 to 8 inches after the crash (therefore more than that during the crash); that the driver
moved far enough to severely deform the steering wheel and break 8 ribs and his sternum against it and that somehow the harness was still tight enough to make it hard to release the buckle, and the
separated belt was somehow invisible to everybody until some days after the accident. Maybe I’m
missing something, but I don’t see how that’s physically possible. I can see how the belt could have
separated, but I don’t see how it could have done so without the separation being immediately
apparent.
Looking at published photographs of the belt, I agree that it appears to have been pulled apart, not
cut. However, this appears to have happened in two stages, not all at once. I say this because the
bottom third of the break has a different appearance than the top two thirds. The bottom third of the
break appears to have been initially torn over a sharp edge, such as the adjuster, and operated in this
condition for a while, with the tear slowly growing. If this were not so, the fibers on the left (in the
photo), or working, segment would not be bent back and flattened the way they are, and the edge of
the right, or unstressed tail, segment would not be so cleanly cut. The entire break would be ragged,
without the fibers being bent back and flattened, like the top two thirds.
Here’s a possible explanation: the belt did fail, or was in the process of failing, due to improper
installation, but not to the point of complete separation. It stretched more than one would normally
expect, and the shoulder straps did too. But the belt still held together. Then some time after the
crash, somebody discovered the damage to the belt, and somebody pulled it apart the rest of the way.
I realize the enormity of this suggestion, and I realize that there is no direct proof that this occurred.
However, this theory would explain the initial absence of any mention of the belt failure, and the 5day delay in announcing it. I have heard no other plausible explanation of these things.
This theory does require a concerted attempt to deceive the public, and this would require a motive.
Such a motive is not hard to discern, however. The Earnhardt crash was the fourth in a string of
similar ones, resulting in similar fatal injuries. Without belt failure as an issue, the focus inevitably
shifts to car and wall construction. Changing cars and walls costs big money, and is fraught with the
perils of developing new technology, which may not always work as intended. Remember that the
France family owns big interests in a number of tracks, as well as a controlling interest in NASCAR.
With the belt failure controversy raging, the waters are muddied sufficiently that changes to cars and
walls can be deferred for some time – perhaps indefinitely.
I do not prefer conspiracy theories over simpler, less dramatic explanations. But I will believe in a
conspiracy more readily than I will believe in a miracle. And what we’re seeing with this belt issue
appears to me to be unexplainable except as a conspiracy or a miracle. I await the explanations of
those who think otherwise.
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NASCAR’s position on crush structures in the nose is that there may be “unintended consequences”
in the form of cars moving each other around more when light contact occurs. This concern is not
entirely unwarranted, but I certainly think the concept of energy-absorbing noses should be tested,
not merely dismissed.
Also, it is my understanding that the object of nudging another car is to move it, at least when the
nudge is deliberate. In the case of purely accidental contact, we are faced with the classic design
tradeoff that we always encounter when designing any kind of cushioning system in a finite space:
softer is better for light forces, but a soft cushion bottoms out when forces are greater. This dilemma
is the same one we face with seat pads, roll bar pads, and even vehicle suspension systems.
I was not present for the demonstration of the Humpy Bumper, the carbon fiber structure designed to
fit inside stock car noses. Published reports say a test car was driven into a wall at an angle, with an
impact speed of 40 mph. I am not clear whether that is the car’s speed, or the component of its
velocity perpendicular to the wall, or the reduction of its velocity during impact. The last of these is
the one that would create a similar condition to the Earnhardt crash. The car’s velocity decreased 42
to 44 mph during the two impacts combined, from an initial speed of around 160 mph.. Reportedly,
the test car’s nose crushed visibly less than would normally be expected, and the car bounced off the
wall, requiring some reporters to move fast to evade it.
I am not certain how much to make of this one instance, but it is not desirable for an energyabsorbing structure to be resilient: it should not spring back. It should crumple, and stay squashed.
For reasons of both cost and non-resilience, I would suggest looking hard at crush structures of mild
steel, aluminum, or plastic such as ABS or polyethylene. How about “egg-crate” radiator ducts, with
internal vanes forming a crush structure while also maintaining orderly air flow to the radiator?
The independent report that suggested crush structures proposed styrene foam, encapsulated in sheet
aluminum. This has possibilities, especially in the fenders, ahead of the wheels and alongside the
radiator duct. Aluminum honeycomb or egg-crate has potential in that area as well.
Whatever material is used, the structure should incorporate graduated rigidity or yield strength. The
portions closest to the nose molding should deform easily, and the structure should offer
progressively greater resistance as deformation moves further inboard. This increase in resistance
should be as gradual and stepless as possible. With an egg-crate structure, this is easily achieved by
using more panels, and/or thicker material, for the inboard portions.
I sent copies of my April newsletter, which addressed adding crush structures to both noses and
walls, to Mike Helton and Gary Nelson. NASCAR sent them back, with a letter saying that their
policy is to not accept any unsolicited suggestions! Remember that next time you see a NASCAR
representative on TV saying they are receiving new ideas all the time. No doubt they are receiving
them, but this evidently doesn’t mean they read them.
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Lest any one suppose that I am unconditionally critical of NASCAR, I do think they are making
good decisions in establishing a new safety research center in Conover, NC, and putting impact data
recorders in the cars. Hopefully, crush structures will be among the items investigated.
TIRE DATA
Why is it so difficult to find data for mathematical modeling of tire properties? Do tire companies
have the ability to test the forces a tire generates at various slip angles, loads, camber angles, and so
on? If so, why don’t they make this information public?
Tire companies do have machines that can test a tire against a simulated road surface, at
controlled normal force (vertical load), camber angle, and slip angle, and measure the drag and
lateral forces the tire generates. Sometimes they also contract out this work to a laboratory like
Calspan, where much of the equipment used for this was first developed.
The machines use a large wheel or a very strong belt to simulate the road surface. This of
course most closely simulates pavement, not dirt. Early machines also were built that rolled the
tire along the ground, attached to a heavy truck.
The indoor machines with simulated road surfaces were developed to produce more accurate
and repeatable measurements. The fact that this was necessary tells us something important
about tire behavior: in the real world, what occurs doesn’t just depend on the tire. It depends at
least as much on the road surface and the weather. Therefore, tire data are only meaningful
when taken under very carefully controlled conditions. To model tire behavior accurately for
the real world, testing needs to be done under a variety of carefully controlled conditions, and
the effects of these changes have to be included in the report.
As if this weren’t enough, tires themselves are highly variable in their behavior. Their
properties vary with age, heat cycling (itself sensitive to amount and speed of temperature
change), wear, inflation pressure, tire temperature, air temperature, road temperature, air flow
to the tire, vehicle speed, combination of loadings in multiple directions, manufacturing
variations, rim width, and other factors. The tire even has different properties as it proceeds
through a turn, because it rapidly heats up. It heats faster at a high road speed than at a low
road speed.
Any attempt to test and analyze how these factors play off against each other results in a
voluminous report. The best we can do for purposes of mathematical simulation is to assume a
simplified tire model, preferably averaged from such a report, that we can use for comparative
calculations when varying other factors. If we are dealing with incremental changes to the car,
on known tracks, with many runs already logged, as in F1, then reasonably accurate lap time
prediction is possible. If we are trying to predict less familiar situations, accuracy available
from the simulation inevitably diminishes.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net.
RACECARTECH DIES (I THINK)
The owners of www.racecartech.com , where I used to give free advice, have announced that they
are closing the site due to unprofitability, effective Sept. 30. I would take this as final word, only a
client of mine has recently expressed interest in possibly taking over the site. By next month I’ll
know if anything is going to come of this.
BALANCING THE CAR WITH CAMBER AND TIRE PRESSURE
Thanks for your July newsletter – the troubleshooting guide is very meaningful, even for a road
racer such as myself. Could you comment on how camber and tire pressure might be used to address
tight and loose conditions?
A tire has a preferred camber and pressure. If you go either direction from the optimum, you
lose grip. Therefore, if you deliberately depart from best camber and pressure, you are
throwing grip away. Ordinarily, you don’t want to do that. It’s better to balance the car by
managing wheel loads, because that way you are redistributing the available “grip budget”
rather than throwing some away at the end that sticks better.
Okay, that’s the basic answer. But beyond that, there are complex and fascinating nuances.
To begin with, optimum camber and pressure for longitudinal acceleration (braking and
propulsion) are different than for lateral acceleration (cornering). For longitudinal forces, we
want the tire at zero degrees camber – straight up. For cornering, we want it leaning slightly
into the turn if possible. The optimum pressure for longitudinal acceleration will generally be
less than for lateral. So we have to compromise.
The compromise we strike has some effect on the tire’s behavior in various parts of the turn.
With a less aggressive camber setting, we may improve the tire’s grip in early entry and late
exit, when longitudinal forces are great and lateral ones are moderate, and reduce its grip in the
middle of the turn. We can also do this with a moderate pressure reduction.
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Reducing pressure will, in some cases, make the tire work better in the first part of a turn at the
expense of the latter part, particularly on ovals. This happens because with lower pressure, the
contact patch is longer. The rearmost portion of the contact patch has a form of interaction with
the road surface which is characterized by cyclical sliding and reattachment. This builds huge
amounts of heat in the outer layer of the tread rubber. Surface temperatures in normal racing
use can exceed 400 deg. F. at corner exit, in a tire that shows half that temperature when we
measure it after a run. This means the rubber temperature is well above optimum in the last part
of a turn.
At lower pressure, the tire heats faster as it corners. Therefore, slightly lower pressure may
improve grip early in the turn, and reduce grip through the last 2/3 of the turn. Lower pressure
will also usually help the tire early in a run, at the expense of the rest of the run.
There is some difference between oval applications and road racing applications or street or
autocross use. In oval racing, especially ovals of a mile or more, the turns are big and last a
long time. On a 1.5 mile track, a 180 mph lap takes 30 seconds. The turns are around half the
lap distance, and are taken at somewhat lower speed than the straights. This translates to
sustained cornering for up to ten seconds, depending on the track and where we define the
beginning and end of the cornering process to be. Steering inputs are small and gentle. This
means that tire heating during the turn is a major factor, and tire rigidity on turn-in is not very
important. Consequently, the driver may report better front grip on entry with slightly reduced
front pressure on an oval. Conversely, when turns are tight and last only a second or so,
steering inputs are large and abrupt, tire heating is less of a factor, and tire rigidity counts more.
In such situations, turn-in may be improved with higher front pressures than optimum for
steady-state cornering.
One problem with using these principles to tune the car is that we don’t really have very
precise control over tire pressure. If the front tires are a little on the soft side and the rears are
ideal when the sun is behind clouds, what happens when the sun comes out? What happens
when the driver presses a little harder and the tires heat up? The fronts will optimize, and the
rears will have too much pressure. The car will get looser. Tuning a race car with tire pressures
makes it inconsistent. Therefore, when possible I try to make the fronts and rears optimize
together, and be too soft or too hard together as conditions vary.
You hear a lot about tuning tire spring rates with pressures. This is mostly smoke, especially in
cars with compliant suspensions, such as stock cars. Contact patch length, contact patch
loading distribution, and tire heat buildup are the big factors that change when we vary
pressure. When a team adds or subtracts a pound on one tire on a pit stop, they are mainly
throwing away a little grip on that corner to balance the car. Often they can either add or
reduce pressure to kill the grip, but the effect comes later in the run, and later in the turn, if
underinflation is chosen, and earlier if overinflation is used. Using tire pressure instead of
suspension adjustment during a race makes sense because balance is so important, and
adjusting suspension during a pit stop costs time and track position.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
LIFE AFTER RACECARTECH
Since the Racecartech site has closed, I am making occasional posts at www.rpmnet.com and the
Weekend Auto Racers forum at http://netpaths.com/cgi-bin/tech.pl.
THE BIG TRACKS AND THEIR BIG WRECKS
There is now widespread recognition of the prevalence of huge, multi-car wrecks at almost every
race at Daytona and Talladega. Most observers agree that this relates to the large packs of cars
running close together at high speeds. New rules against putting the left wheels on the apron to pass
have not solved the problem. Restrictor plates on the engines, aerodynamic drag-inducing additions
to bodies, and restrictions on spring and damper calibration have all been instituted with minimal
impact on the problem.
I wish I had a simple solution myself, but I don’t. I do, however, have some thoughts on the
fundamental causes of the problem.
There is an “elephant at the dinner table” here – a problem that really should be clear to everybody,
but that nobody wants to mention. That problem is the design of these tracks: they are 2 ½ miles or
longer, with bankings of 30 degrees or more. This means that unless the cars can do well over 200
mph, they can run wide open all the way around the track. If they run fast enough to be grip-limited
in the turns, they become really hard to contain when they get out of control, and impacts occur at
pretty ferocious speeds. Concern about these factors is what has led to all the efforts to slow the cars.
But now that the cars can run wide open all the way around the track, drafting becomes the key to
victory, just as it is in that other power-limited sport, bicycle racing. Bicycle racing is also subject to
massive pileups, for very similar reasons. This fact should tell us something about the prospects for
eliminating the pileups by slowing the cars. Slowing the cars further may reduce injuries and deaths
somewhat, but the pileups will still occur.
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It has been suggested that smaller engines be used rather than restrictor plates. This might improve
the throttle response of the engines, but it will not change the fact that they will be running at full
power except when drafting another car. We might expect a bit more passing, but these races already
have an abundance of passing.
As long as there are no turns small or flat enough to slow the cars, there is no way out of the
dilemma. Either the cars will run in huge drafting packs, or they will run so fast that they will be
excessively dangerous to drivers and spectators when they crash, even though they will probably
crash in smaller numbers at a time.
The only avenue that might offer some promise is to reduce the grip of the tires sufficiently so that
even with modest power, the cars will have to slow significantly for the turns. Trouble is, that would
require a pretty significant grip reduction. I hesitate to advocate making the cars really slidey when
the wind already moves them around so much, and when they already take forever to stop following
loss of control.
SELECTING SPRINGS
When a new car is built, is there a way to calculate best spring rates to try first, and thereby
minimize testing?
There is no method that works for all types of car. Spring rates are only one of many tuning
and design variables, and all these variables interact with each other. You can measure some of
these factors; others you can only guess at. With more resources, you can measure more, and
guess at fewer. For example, with wind tunnel testing, aerodynamic effects become much less
of a guess. The track or road conditions are another important variable. Any given car will
want different setups, including springs, for different conditions.
A common method is to simply borrow a spring combination from a car that is estimated to be
similar, and test from there. Many race cars are built to existing class rules and are similar to
ones already running, with small variations. When using this method or any other, it is vital to
go by wheel rate, the rate at the wheel. Many suspensions have one wheel rate in ride and
another in roll, and you need to look at both.
In oval track racing especially, many different spring combinations can be made to work fairly
decently, because we can vary diagonal percentage, stagger, and other factors to suit the
springs. Even in road racing and figure 8 racing, the car can be adjusted to suit various spring
packages by varying roll center heights, anti-roll bars, and aerodynamic surfaces. In many
cases, the difference between a superior spring package and an inferior one will be seen in the
car’s transient behavior, and its response to varying conditions.
That said, we can state some definite rules for the ways spring choices relate to other factors.
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RELATIONSHIPS BETWEEN SPRING CHOICES AND OTHER FACTORS
OTHER FACTORS REMAINING EQUAL:
Stiffer springs at one end of the car call for stiffer springs at the other end.
Wider or stickier tires at one end of the car call for stiffer springs at that end and/or softer ones at the other
end.
Rougher surfaces call for softer springs, with higher ride heights. This assumes that suspension travel is
available to do this. If bottoming is a problem, stiffer springs may be needed to overcome that.
More aerodynamic downforce calls for stiffer springs.
A stiffer anti-roll bar calls for softer springs at that end of the car, and/or stiffer springs at the opposite end.
To correct an understeering car (tight condition), use stiffer rear springs and/or softer fronts.
To correct an oversteering car (loose condition), use softer rear springs and/or stiffer fronts.
More diagonal percentage calls for softer front springs and/or stiffer rears.
More rear tire stagger calls for softer rear springs and/or stiffer fronts.
A lower roll center at one end of the car calls for stiffer springs at that end. A lower roll axis calls for stiffer
springs at both ends.
More weight at one end of the car calls for softer springs at that end and/or stiffer springs at the opposite end,
to preserve similar cornering balance. This requirement is at odds with the need to add spring rate
proportionally to weight, to preserve similar ride characteristics. In some cases it will not matter whether
similar ride characteristics are preserved. In other cases, we may want to work with anti-roll bars and
suspension geometry as well as springs, to reduce relative roll resistance at the end that’s seeing the weight
increase.
On banked ovals, there is a critical angle of banking, at which the left suspension neither compresses nor
extends in steady-state cornering. For typical stock car chassis on asphalt, the critical angle will be around 15
degrees. On dirt, the critical angle will be somewhat smaller than this. Below the critical angle, left side spring
changes have effects as described above. Near the critical angle, left spring changes have little effect on
steady-state cornering balance. Above the critical angle, effects of left spring changes on steady-state
cornering balance work backwards: a stiffer left front loosens the car; a stiffer left rear tightens the car.
On ovals, assuming the car does not generate large jacking forces (true for most pavement cars, but not for
some dirt cars), and assuming that the car is not slowed primarily by the rear wheels, stiffer left springs and/or
softer rights loosen the car when braking and turning left together (entry), and tighten it when turning left and
applying substantial power (exit). Conversely, stiffening the rights tightens entry and loosens exit.
Anything that reverses direction of suspension position change reverses effects of spring changes.
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December 2001
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
ANALYZING SHOCK TRACES
I am an aspiring race engineer – currently work for a professional sports car team – as well as a
mechanical engineering student. I am learning to use data acquisition. I was hoping you could give
me some insight into reading the shock velocity traces from the data system. Should they be
compared to the dyno charts to make sure they are operating in the correct range? What can be
deduced as far as oversteer/understeer characteristics?
This is a fairly complex subject, and one that has seen its share of hype and mystification,
particularly in stock car racing. A few years ago, shock technology went through a “trick of the
week” phase. Teams suddenly discovered that it was worth paying attention to, and shocks
went from almost a non-factor to a perceived panacea practically overnight. Suddenly people
were trying to fix every problem with shocks. This is a wrong approach. The first thing to
remember about shocks is that they are only one element of the total package, not a holy grail.
The second thing to remember is that you need a rapid sampling rate to get shock traces that
are accurate enough to be meaningful. Once you have a good shock position trace, it can look
quite different depending on how you filter it. This is because shock velocities and
accelerations undergo dramatic, continual change, especially on a bumpy surface. What
sampling rate is good enough? Opinions vary, but anything under 100/sec is definitely too
slow. 250/sec is a common general-purpose recommendation. 500/sec is fast.
Sampling rate makes more difference on a rough surface than on a smooth one. This is also
true of filtering. Sampling rate also becomes more critical if you want to differentiate the
position trace to obtain a velocity trace, and even more if you want to differentiate the velocity
trace and look at acceleration. Inaccurate information can be worse than none at all.
The shock traces, taken alone, actually tell you more about the track and the rest of the setup
than they do about the shocks themselves, at least in normal circumstances. The wheel motion
will be reduced some as you stiffen up the damping, but ordinarily the track surface and the
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spring rates mainly determine how the wheels move. (An exception occurs when a shock is
grossly undervalved or overvalved, or is leaking, sticking, or otherwise malfunctioning.) The
shock valving determines the forces the shock generates when it goes through those motions,
and those forces affect wheel loadings.
To know the force a shock is generating at a particular instant, you need to know the
instantaneous velocity, which you get from on-car data, and the force the shock can be
expected to generate at that velocity, which you get from shock dyno data.
Shocks are also acceleration-sensitive. The degree of acceleration sensitivity can vary widely.
To get the best assessment of what forces the shock is producing at a particular point on the
track, we need to reproduce both the velocity and the acceleration on the shock dyno. To do
this requires a high-cost shock dyno that can be programmed to either produce a particular
acceleration, or to play back motion recorded on-car. This means the dyno must be controlled
fully electronically – usually with with high-powered hydraulics providing the actual force –
rather than the more common variety with a scotch yoke drive that always produces a
sinusoidal motion.
If we don’t have access to such a dyno, we can at least get some idea of whether we have a
highly acceleration-sensitive shock by looking at a full-cycle trace from a sinusoidal dyno. In a
plot where absolute velocity is the horizontal coordinate and force is the vertical coordinate, a
full cycle trace will have two points or noses at the left (zero velocity) edge of the graph. These
represent the “turn-around” points in the cycle – full compression, and full extension. If the
two noses have dramatically different shapes, the shock is probably displaying acceleration
sensitivity, particularly if all shocks of the same design show this pattern. If just one shock
shows such a pattern, that suggests a malfunction on that individual unit.
Another way to get some indication of a shock’s acceleration sensitivity is to look at its
construction. If the valving includes relatively massive chunks of metal that see big
accelerations when the unsprung mass does, that’s a strong indication that the valving will be
acceleration-sensitive. Examples include: dual-tube shocks with foot valves having coil-springloaded discs or spools, where the shock body is down or moves with the wheel; and gas shocks
with coil-spring-loaded discs or spools on the piston, where the shock body is up or the piston
moves with the wheel. Deflective-disc valving has minimal acceleration sensitivity.
Acceleration sensitivity is not necessarily a performance disadvantage. It may even be helpful
in some instances. However, it does complicate the process of inferring shock forces from oncar traces, based on sinusoidal dyno testing.
Merely knowing whether the shock is highly acceleration-sensitive does not allow us to know
actual forces in combinations of acceleration and velocity that our dyno can’t reproduce, but it
does at least let us make informed guesses as to whether we can assume dyno data to be
representative for a specific instant picked from an on-car trace.
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Fortunately, we can accomplish a lot without knowing exact shock forces. Provided we know
what portion of the valving is active at the instant in question, we can at least qualitatively
predict what will happen to our wheel loadings if we soften or stiffen that portion of the
valving. And from that, we can predict whether such a change will move the car toward
oversteer or toward understeer (loosen it or tighten it) at that point in the lap.
To meaningfully discuss such predictions, we have to break track surfaces down into rough
ones and smooth ones. Rough surfaces are ones where there are enough bumps so that the
bumps cause most of the suspension movement. Smooth surfaces are ones that are smooth
enough so that most suspension movement is caused by sprung mass motion. Shock velocities
will be much greater, and will change much more, on a rough surface than on a smooth one.
On a rough surface, damping affects tire loads in two basic ways. First, the amount of damping
affects the wheel’s ability to ride the bumps with minimum load variation at the contact patch,
and minimum non-contact (airborne) time. Second, the balance between compression (bump)
damping and extension (rebound) damping affects the suspension’s tendency to jack up or
down when riding a series of bumps. Jacking down is by far the more common of these two
possibilities.
Looking at the first of these issues, the suspension behaves better over bumps when lightly
damped except when the bumps excite the suspension at the unsprung mass natural frequency,
or a simple multiple or fraction (harmonic) of that frequency. In such instances, the suspension
performs better if stiffly damped. Excitation at a vulnerable frequency is the worst-case
situation, the scenario most likely to send the car out of control due to being upset by bumps.
Therefore, there is a strong case for erring on the stiff side when in doubt; the car will be worse
on “friendly-frequency” bumps, but will be less upset by the patches to which it is most
vulnerable.
Looking at the second issue, if all four corners of the car jack down a bit, this may have little
effect on cornering balance. However, if only one wheel jacks its suspension down, or if three
do and one doesn’t, or if two diagonally opposite wheels do and the other two don’t, then the
jacking will change the car’s instantaneous diagonal percentage (percentage of tire loading on
the outside front and inside rear, or right front and left rear for oval track). If instantaneous
diagonal is increased, that moves the car toward understeer (tightens it); if instantaneous
diagonal is decreased, that moves the car toward oversteer (loosens it).
On bumpy surfaces, medium to high speed valving is at work. On smooth surfaces, only lowspeed valving is relevant. These terms are relative. On a stiffly suspended car, as in F1 or
CART, “low speed” might mean below 1 in/sec (.025 m/sec). In stock cars or moderate
downforce sports cars, “low speed” is commonly taken to mean below 2 in/sec (.05 m/sec). In
passenger cars or off-road cars, “low speed” can be a lot higher. In any of these contexts, low
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speed damping means the velocity range that can be attained by driving the car violently on a
smooth surface. Usually, low speed damping is governed by bleeds and preloads in the valving.
On a surface smooth enough to allow sprung mass motion to be the main input, we can control
corner entry and exit oversteer/understeer properties with the low-speed damping. The basic
rules for this are:
1. Whenever a damper’s velocity is in the extension direction, stiffer extension (rebound)
valving reduces load on that tire and the diagonally opposite one, and increases load on
the other two tires.
2. Whenever a damper’s velocity is in the compression direction, stiffer compression
(bump) valving increases load on that wheel and the diagonally opposite one, and
decreases load on the other two.
3. We get the greatest effect from changing the shocks that are have the highest velocity at
the instant or point on the track that we seek to affect.
4. Effects on oversteer/understeer balance can be predicted by examining the effect on
instantaneous diagonal percentage; more diagonal = tighter car.
We can write troubleshooting charts for various types of cars and tracks, and these can get
quite long and complex. However, the four principles above can be used for all cars, and with
data acquisition, you don’t have to infer or guess at shock velocities.
So, returning to your question regarding whether we can deduce oversteer or understeer from
shock velocity, the answer is that we cannot, but knowing shock velocity can help us predict
changes to balance that will result from changes in valving. We determine the presence of
understeer or oversteer by examining steering position, or a calculated speed-corrected steer
channel. We also make sure we talk to the driver, because what really counts is whether the car
is looser or tighter than the driver wants it. Also, a tight car can exhibit oversteer if the driver is
purposely driving it loose to make it turn. Data acquisition is a tool to supplement human
senses and brains, not a substitute for them.
As to what we compare to dyno traces or tabular charts, comparison to dyno data is done to
infer forces, as noted above. We compare our dyno data to the manufacturer’s if we have data
from the manufacturer for the build spec we’re using. We also compare our dyno traces to
traces from shocks in our own inventory with identical build specs. We use these comparisons
to make sure we don’t have leakage or sticking, and to make sure we really built what we
thought we built. It’s surprisingly easy to include an extra disc, or leave one out, or grab the
wrong diameter or thickness.
Finally, we compare dyno data for different shocks to evaluate the effect of a change to the
build spec – to see what velocity range it affected and how much. We then compare this to the
on-car velocity data to predict the handling effect of the build spec change, applying the four
rules listed above.
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January 2002
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
SUSPENSION NATURAL FREQUENCIES
What suspension frequency should I be looking for in a formula car? Should the front and rear
suspension have equal or similar frequency?
For readers less familiar with the subject, this question concerns the sprung mass natural
frequency in ride, for the front and rear wheel pair systems. Natural frequency is a measure of
how stiff the suspension is, which expresses stiffness in a way that is independent of the
vehicle size or weight. That is, a given frequency feels comparably stiff whether the car is big
and heavy or small and light, unlike a given spring rate or wheel rate. If the car is twice as
heavy and the wheel rate is also twice as stiff, the natural frequency is the same.
A natural frequency is a vibration frequency at which a system will vibrate or oscillate when
displaced from its static position, and released. For a simple system consisting of a mass
supported by a spring:
f = .159 (S/m)1/2
where
f = natural frequency in Hertz (Hz), or oscillations per second.
S = spring rate, in Newtons/meter (N/m).
m = mass supported by the spring, in kilograms (Kg).
The quantity S/m is the inverse of m/S, which is the static deflection – the amount of spring
compression at static condition. We may say that the natural frequency is inversely
proportional to the square root of the static deflection. We may also say that the static
deflection is inversely proportional to the spring rate, for a given mass. Therefore, natural
frequency is proportional to the square root of spring rate, other factors held constant. So if we
put springs with twice the rate on a car, the front and rear natural frequencies increase by a
factor of the square root of 2.
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The simple formula above is not really a very good approximation of an automobile
suspension, especially a racing vehicle with stiff springs, stiff damping, and aerodynamic
downforce. The tire is compliant, and its compliance is in series with the wheel rate. This
makes the system softer, and the natural frequency lower, than if the tire were rigid. This is
true for all cars, but it assumes particular significance when the suspension is stiff and the tire
compliance is a large percentage of the total. If we know a spring rate for the tire, and the
wheel rate from the suspension, the rate of the system is:
1/Sc = 1/Ss + 1/St , or Sc = (Ss St) / (Ss + St)
where
Sc = spring rate of the combination.
Ss = wheel rate of the suspension.
St = spring rate of the tire.
So if the tire is as compliant as the suspension, the frequency is only about .71 times what it
would be if the tire were rigid.
Note that the above formulas assume a constant spring rate. In actual cars, we often have a
rising wheel rate. This means that the frequency varies depending on suspension position.
Some authors have suggested that natural frequency diminishes as downforce increases,
because deflection increases. This is a misconception. Natural frequency is sensitive to the
relationship between weight (mass times gravity) and effective wheel rate, and nothing else.
This does not mean that rising-rate suspension is bad.
We have so far been talking about undamped natural frequency. Damping a system raises its
natural frequency. To calculate a damped natural frequency, we need a constant spring rate,
and a constant damping coefficient. In actual cars, damping coefficient is not constant, so any
value we use for calculations has to be an approximation based on shock dyno outputs for
velocities in the range we are trying to model. Stiff damping can raise frequency by as much as
30%, compared to the same system completely undamped.
As if this were not enough complexity, a suspension system will usually have different wheel
rates when absorbing a one-wheel bump (combined roll and ride, or oppositional and
synchronous motion) than when absorbing a two-wheel bump (pure ride or synchronous
motion). The unsprung masses also have their own natural frequencies, much higher than the
sprung mass frequencies, and these also vary depending on whether the wheels are moving
synchronously or oppositionally.
In passenger cars, we have additional natural frequencies for masses flexibly attached to the
main sprung mass, such as the engine on its mounts and the driver on a springy seat. These can
be tuned to interfere with the ride motions of the sprung structure, and some useful ride
damping can be achieved this way. Conversely, if these frequencies reinforce, ride quality will
be adversely affected.
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Passenger car engineers also look at “bounce” frequency (front and rear suspensions moving in
the same direction, or basically in heave, approximating car behavior when both ends are
excited together, as when traversing long humps and dips) and “pitch” frequency (car
oscillating about a node near its middle, front and rear suspensions moving opposite directions,
relevant to excitation by a short bump struck by first the front wheels and then the rears).
Despite all this, we can actually tell quite a bit about a car’s characteristics by just looking at
the front and rear undamped frequencies, calculated using the front and rear portions of the
sprung mass and the combined wheel rates for the front and rear wheel pairs. As previously
noted, these will be inversely proportional to the square root of the static deflection for the
front and rear. With asymmetrical cars, that would be an average of left and right static
deflections, for the front and rear.
The equations given earlier are for frequency in Hertz, which is cycles or oscillations per
second. It has also been customary, especially in countries using English units, to express
suspension frequencies in oscillations or cycles per minute (opm or cpm). This figure will of
course be 60 times the frequency in Hertz. It may also be calculated from static deflection in
inches as follows:
F = 188 / (x1/2)
where
F = frequency in opm or cpm
x = static deflection in inches
Note that static deflection is calculated from the point where the spring is completely unloaded,
which may be different from full droop on the suspension if the spring is loose or preloaded at
full droop. When wheel rate is not constant, the only way to obtain valid static deflection for
frequency calculation is to determine the instantaneous wheel rate at static ride height and
divide by sprung weight.
Ranges of frequencies commonly found in different types of vehicles are:
Very soft passenger car: 0.5 to 0.8 Hz (30 to 50 opm)
More sporting passenger car: 1.0 to 1.3 Hz (60 to 80 opm)
Modern sports car: 1.1 to 1.5 Hz (70 to 90 opm)
Pavement race car with modest downforce: 1.5 to 2.0 Hz (90 to 120 opm)
Modern race car with ample downforce and ground effect: 5.0 Hz (300 opm) or more
As to the relationship between front and rear frequencies, the traditional answer from
passenger car engineering is that the front static deflection should be about 30% greater than
the rear. This would mean that the ratio of front frequency to rear frequency would be around
.88. Such a relationship makes the front end and the rear end roughly go up and down together
on the first bounce after a short disturbance, while allowing the car to ride long disturbances
with a minimum of pitch. It also allows for some passengers and luggage in the rear.
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This approach presents problems in rear-engine cars, however, and even in front-engine cars
with aerodynamics that are sensitive to front ride height. The main difficulty is that front ride
height changes too much in braking and forward acceleration. With tail-heavy cars, a very stiff
front anti-roll bar is usually required if front roll resistance is to be adequate to assure proper
load transfer allocation with soft front springs. In braking and under power, the front end will
rise and fall dramatically, and if we have a front valance skirt, a front splitter, or a front wing,
aerodynamic properties will be too sensitive to braking, power application, and disturbances
from the track surface.
Consequently, race cars often have higher natural frequencies in front than in back. Front to
rear frequency ratios may reach 1.5 or greater. This actually represents a return to the
frequency relationships of the early 1930’s, when cars had beam axles and longitudinal leaf
springs, anti-roll bars were uncommon, and the front springs were spaced closer than rears for
reasons of steering clearance. With these characteristics, and 50% or greater static rear
percentage, the car will oversteer unless the front springs are a good deal stiffer than the rears.
It turns out that having the front frequency a lot higher than the rear is a good second choice in
terms of ride, if it is impractical to make the front a bit softer. If you make the front and rear
frequencies similar, or the rear a little softer than the front, the car pitches excessively on short
bumps, although it rides long disturbances very nicely.
All of this is more important in softly damped passenger cars, and softly sprung and damped
dirt cars, than in firmly damped pavement race cars. With firm damping, the first and second
oscillations after a disturbance are not much of a concern, as the damping suppresses them in
any case. Consequently, many race engineers pay little attention to frequency relationships
unless the car exhibits ride motions bad enough to hurt lap time or make the driver complain.
Choice of frequencies then comes down to factors other than ride motion. There is no perfect
set of springs for all tracks, as shown by the fact that almost everybody uses different
combinations depending on where they’re running. The most fundamental tradeoff is between
ability to ride bumps (softer is better) and ability to limit ground clearance changes, reduce CG
height, and control camber (stiffer is better). The bumpier the track, the softer and higher we
have to run the car. The smoother the track, the more sensitive the car is to ground effects, the
more sensitive the ground effects are to pitch and roll, and the more downforce the car
generates, the stiffer we have to make the springs. On ovals, steeper banking calls for stiffer
springs. In general, we can use softer springs if the car provides roll or pitch resistance from
geometry or interconnective springs such as anti-roll bars. So we are faced with a complex
compromise, which cannot be reduced to a simple formula, or even a simple rule about
frequency relationships.
Finally, in production cars, we may stiffen up the springs just to crutch bad geometry or limit
the antics of leaf-sprung axles. As Colin Chapman reportedly once said, “Any suspension will
work if you don’t let it.”
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
WINSTON CUP HARNESS INSTALLATION
NASCAR has announced that they are now going to require that safety harnesses be installed
according to the harness manufacturer’s instructions. Harness manufacturers, without exception,
recommend that lap belts go downward or slightly rearward to their anchor points, and that all belts
have as short a run as possible, and not be bent around any sharp edges.
As a consequence of my now being a columnist for Racecar Engineering, I got to visit Richard
Childress Racing as part of the annual UAW-GM media tour. (Actually, Paul Van Valkenburgh was
the magazine’s designated representative, but he had to go to Atlanta the last day of the tour, so I
snagged his seat on the bus.)
The folks at Childress gave us a really nice meal and presentation, after which they formally
unveiled their new paint schemes, apparently on new cars. Following that, they let all of us check out
the cars up close, and interview the drivers and other personnel.
Late during this period I was looking at Kevin Harvick’s car. I noticed that the belts were mounted
just like they used to be in Dale Earnhardt’s cars: lap belt mounts almost straight back from the seat
holes; shoulder harness run over a bar at shoulder height and then another foot and a half or so down
to an anchor point around kidney level.
It occurred to me that maybe I was looking at an older show car, used to display the paint scheme.
Yet the car appeared new. The lower seatback mount, a square steel tube a bit above the floor, which
held the seat in place and carried the lap belt mounts, was unpainted, and definitely appeared to be
brand new.
Following Dale Earnhardt’s death, the belt mounting issue assumed great significance, and this is of
course the reason for the new rule. It was a point of public contention whether the Childress
organization had been informed that there was a problem with their belt installation. I don’t recall
anybody saying that the installation was correct, or superior to the recommended geometry. The only
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controversy was whether the incorrect installation had been brought to the team’s attention. Surely
they can’t claim ignorance now.
I will be watching the press for mention of this matter in upcoming Daytona coverage. I also invite
anybody from RCR who may see my remarks to comment.
THINGS THAT MAKE SPRING CHANGES WORK BACKWARDS, REVISITED
In the August 2001 issue of this newsletter, I pointed out that on oval tracks there is a critical angle
of track banking for a particular end of a particular car, at which the left side suspension no longer
extends as the car rolls. At this banking angle, the car becomes insensitive to left spring changes.
Beyond this banking angle, the effect of left spring changes reverses.
It has recently come to my attention that in beam axle suspensions, there will be a range of banking
angles within which the left suspension will extend, as measured at the wheel – yet the left spring
will compress! This is possible because the spring is inboard of the tire. It is possible that a node, or
point of zero motion, may exist between the wheel and the spring.
For example, suppose the springs are exactly ½ the track width apart, and suppose that the
suspension is in a condition of 1” per wheel of roll (about 2 degrees) and 3/4” of “squash” or ride
compression due to track banking. The right wheel then has 1 3/4” of compression, and the left
wheel has 1/4” extension. The left spring, however, has 1/4” compression. The right spring has
1 ¼” compression. A node, or point of zero displacement, exists midway between the left tire center
plane and the left spring.
If this is the rear suspension, and the front suspension is an independent system in the same state of
roll and ride, we have a situation where stiffening either left spring tightens the car (adds
understeer). Fortunately, such conditions will mainly be encountered close to the critical angle,
where sensitivity to left spring changes is fairly small in any case. It is possible, however, that
substantial reverse sensitivity to left spring changes may be encountered when compression at the
left rear wheel is small.
For those with good simulation software or data acquisition, questions of whether a spring is
compressed or extended from static at a particular point in the lap are more easily resolved. For those
of us who rely largely on our butts and our brains, qualitatively understanding physical principles is
the only way to make sense of our observations. And even for those with electronic help, qualitative
insight is part of making sense of the data.
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SOME BASIC SHOCK QUESTIONS
Mark, could you help me understand some things about shocks?
 What is hysteresis?
 What is the difference between force and absolute velocity?
 What are they referring to when they talk about compression open, compression closed,
rebound open, and rebound closed?
 Why does a shock cycle have 4 strokes instead of just one compression and one rebound
stroke?
Webster’s defines hysteresis as “a retardation of the effect when forces acting upon a body are
changed (as from viscous or internal friction)”. Applied to a damper, this means the damping
force or work.
Most of us have a pretty good idea what a force is. Webster’s definition is “an agency or
influence that if applied to a free body results chiefly in acceleration of the body and
sometimes in elastic deformation and other effects”. In the case of a shock, the force we
measure is the force acting at the damper shaft. The force can act in two directions: extension
or compression.
Shocks generate two kinds of forces: damping forces and gas spring forces. Gas spring forces
are always in the extension direction. Damping forces are always opposite to the direction of
motion.
Velocity, in physics and engineering, means the rate and direction of position change. With a
shock, we have a simple case where motion is either in the extension or the compression
direction. We can therefore express a velocity simply as a magnitude (inches or millimeters per
second) with a positive or negative sign to denote direction.
The absolute value of a number is the greater of the number and its opposite (or additive
inverse). The absolute value of 4 is 4; the absolute value of –4 is also 4. The absolute velocity
of a shock shaft is the magnitude of its rate of position change, irrespective of the direction. If
the velocity is 5 in/sec in extension, the absolute velocity is 5 in/sec. If the velocity is 5 in/sec
in compression, that is also an absolute velocity of 5 in/sec. Absolute velocity is therefore just a
fancy way of saying shaft speed.
The earliest shock dynos were purely mechanical devices (except for the electric motor) that
generated a plot of force (on the vertical axis) versus position (horizontal axis). The resulting
curve would be a loop. Modern dynos can also produce such a plot. Such a loop is sometimes
called a hysteresis loop. The area enclosed by the loop corresponds to the mechanical work
done upon the shock by the dyno during one cycle. This mechanical work in turn corresponds
to the watt-hours of electricity used by the dyno to produce the movement, and the heat energy
that warms up the shock as we work it.
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Modern shock dynos can calculate velocity from position. With most dynos, the shock is
worked through a two inch stroke at 100 cycles per minute. This gives a peak velocity at midstroke of just over 10 in/sec, and a velocity at any other point in the cycle that can be directly
calculated by multiplying the peak velocity by the sine of the crank angle.
The dyno can therefore display force versus velocity, in a number of different formats. The
most popular format is force (on the vertical axis) versus absolute velocity (on the horizontal
axis). This means that force is displayed as a negative or positive value, but absolute velocity is
always positive. The axes take the form of a letter T rotated 90 degrees to the left. The
horizontal axis extends across the middle of the screen or page, with zero at the left. The
vertical axis runs along the left edge of the screen or page, with zero in the middle.
Force during the extension (rebound) stroke is customarily displayed as negative; force during
the compression (bump or jounce) stroke is positive. Note that damping force always acts in
opposition to motion, so the compression damping force actually acts in the extension
direction, and extension damping force actually acts in the compression direction.
One cycle of the dyno does have just one compression stroke and one extension stroke. But on
the type of plot described above, this produces four traces. On the compression stroke, the
absolute velocity starts at zero, builds to just over 10 in/sec at mid-stroke, then decreases to
zero again at the end of the stroke. Commonly, the absolute velocity scale reads up to ten.
Higher values are off the screen or page. So the trace for this stroke starts at the left, runs
across the screen or page and off the right edge briefly (at mid-stroke), then comes back to the
left and ends at zero. The height of the trace at any given point corresponds to the force at that
point in the stroke. A similar process occurs during the extension stroke, generating two more
traces, running mostly below the horizontal axis.
During the first half of the compression stroke, the velocity is increasing, so the valves are
opening. This is referred to as the compression, opening (not open) phase of the cycle. The
second half of the compression stroke is the compression, closing phase. Correspondingly, the
first half of the extension stroke is the extension, opening phase, and the second half is the
extension, closing phase. Each of these phases corresponds to one of the four traces on the
graph.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
MORE ON BELT MOUNTING
Regular readers will recall that last month I mentioned seeing improperly mounted lap and shoulder
belts on a car displayed to the press at Richard Childress Racing. I have recently talked with Brian
Butler of Butler Built seats, who custom-builds seats for RCR and supervises their installation. He
tells me that all actual race cars he has worked on lately at RCR have the belts mounted correctly,
and we agreed on what “correctly” meant. Brian was sure I had seen a show car that did not reflect
actual current race car practice. I am relieved to hear that. I like being proven wrong on something
like this.
RACING FRONT-DRIVE CARS
I have had a number of inquiries lately from people racing front-wheel-drive cars, asking about
literature or information sources about setting up front-drive cars. It appears there is a distinct lack of
literature currently in print on this subject, at least beyond manuals dealing with particular cars, and
brief passages in general chassis books. So I’m going to offer some comments on the characteristics
of front-drive cars in racing and high-performance applications.
The idea of racing a front-drive car is a bit like the idea of teaching an elephant to dance. It can be
done, and people do it, but the basic anatomy of the critter involved is not particularly conducive to
the activity. If we drive only two wheels of a car, they really should be the rears, for a number of
reasons. The most obvious reason is that under forward acceleration, and when going uphill, tire
loading transfers from the front wheels to the rears.
A slightly less obvious reason is that we have better control of the car when we can control the front
wheels with the steering wheel and the rear wheels with the throttle. With front wheel drive, the only
thing we can use to influence the rear wheels is the brakes. Some drivers become fairly adept at left
foot braking and using the hand brake to slide the rear end of a front-drive car, but this is
fundamentally awkward compared to throttle-steering. Active yaw control, which selectively applies
individual brakes according to a computer’s interpretation of car behavior and driver intent, also
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offers some promise, but it is essentially a band-aid. For racing, any use of the brakes to control the
car’s balance or yaw behavior is definitely a last-resort approach (except perhaps when trail-braking
on entry), because it works the tires against each other and dissipates speed. Even the best electronics
are better added to a chassis with good fundamental dynamics.
For these reasons, nobody builds race cars with front wheel drive nowadays, if they have free choice
of layout. However, front wheel drive shows up on the race track in production classes, and
production-based classes, because it is popular for passenger cars.
Let’s examine the reasons for this popularity.
Front wheel drive, with front engine, is one of four possibilities in a four wheeled, two-wheel-drive
vehicle, the others being rear engine/rear drive, front engine/rear drive, and rear engine/front drive.
This last option is never used, although Buckminster Fuller designed a rear-engine/front-drive car
(with rear steering!) in the 1930’s. One example was actually built. It ran, but its handling properties
did not attract imitators.
Front engine/front drive and rear engine/rear drive are commonly referred to as engine-over-drivewheels layouts. Both layouts concentrate the entire powertrain at one end of the car. This saves
weight and space. It also puts well over 50% of the car’s weight on the drive wheels – usually
somewhere between 55 and 67 percent. This is good for propulsive traction. However, it is at best a
mixed blessing in terms of cornering behavior. Due to tire load sensitivity – the decrease in
coefficient of friction as loading increases, which we have discussed in previous issues – nose-heavy
cars tend to understeer in steady-state cornering, and tail-heavy ones tend to oversteer. The car tries
to leave the desired path heavy-end-first.
If we are faced with a choice between heavy understeer and heavy oversteer, understeer is clearly the
safer choice. This is one reason why rear-engine/rear-drive layouts have fallen from favor for
passenger cars. Another reason is the simple fact that luggage or cargo space in the rear of a vehicle
is more useful than luggage or cargo space in the nose, because the space can be filled or over-filled,
and the lid left partly open, for short hauls with big loads. The rear seat can be made to fold to
accommodate long objects.
Additionally, a nose-heavy car has better directional stability in crosswinds than a tail-heavy one,
other things being equal. This is highly significant for a light sedan that spends much of its life on
freeways. Tail-heavy cars can be made adequately stable in crosswinds, but this requires careful
attention to aerodynamics, and places added constraints on styling.
These practical and safety-related concerns have driven the trend to front-engine/front-drive cars. I
personally think that the rear engine/rear drive option has an unrecognized future, for cars with back
seats, intended for drivers who place priority on performance. Existing front-drive powertrains,
especially the larger V6 and V8 variety, could be adapted to such cars, placing the engine slightly
ahead of the rear axle line, with a relatively long wheelbase. In other words, we are envisioning a
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stretched, larger-engined version of the Toyota MR2/Pontiac Fiero/Fiat X1/9 concept. However,
such a layout would not match the practicality of a front-engine car for hauling bulky loads, and
would probably have somewhat more interior noise. So front-engine/front-drive cars are here to stay,
and will surely command a large share of the passenger car market for the foreseeable future.
I mentioned the tendency for a car to try to leave the desired path heavy-end-first. We have two
principal tools we can use to control this tendency: use bigger and/or stickier tires at the heavy end of
the car; and/or put most of the roll resistance at the light end. We can also play with secondary
factors such as toe, camber, and tire inflation. Finally, we can simply reduce the nose-heaviness or
tail-heaviness, by moving the engine toward the center of the car, or by moving heavy components to
the light end as much as possible.
In rear-engine/rear-drive cars, it is common nowadays to use larger tires in back. The reliability of
modern tires, the increased availability of road service, and the advent of space-saver spare tires have
paved the way for this trend. When front-engine/front-drive cars pushed rear-engine/rear-drive cars
out of the passenger car market, most manufacturers considered it essential to have a full-size spare
that could be used at any corner of the car. This is still a practical advantage, but not the necessity
that it once was.
It is also common in rear-engine cars to mitigate some of the tail-heaviness by using a mid-engine
layout. Even if the tail-heaviness is modest, drive traction will be quite good, thanks to the rearward
load transfer under power.
With front drive, this load transfer works against us. Consequently, we are faced with a dilemma:
maximize front-heaviness so we can put power down, or minimize front-heaviness so we can corner.
There is no way to achieve one objective without compromising the other. This is also true with tailheaviness in rear-drive cars, but the compromise is less excruciating thanks to the help we get from
rearward load transfer.
If we were designing for an imaginary set of rules that required us to use front wheel drive, but
allowed us ample freedom otherwise, we might make the car extremely nose-heavy, use big tires in
front and smaller ones in back, and be sure to provide power steering and huge front brakes. We
would also make the wheelbase really long. This would be a funny-looking car, and less enjoyable to
drive than a rear-drive racing car, but that would be the way to go fastest with front drive.
In real-world classes where front-drive cars compete, we are usually constrained by tire rules and
limitations on modifying stock body configurations. Production front-drive cars invariably use the
same size tires at both ends – partly for practicality, partly to provide for the occasional heavy load
in the rear. Road-racing and oval-track front-drive cars consequently use equal-size tires all around,
although big fronts and little rears are seen in drag racing.
We are also usually required to keep most of the stock body/frame structure and suspension, and
prohibited from moving the engine. Our control of front/rear weight distribution is then limited to
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moving minor components, and placing ballast if we run any. To the extent that we can choose our
CG location, the principles we want to follow with front wheel drive are these:
 If the track has high-speed turns; if a large portion of the lap is spent cornering; if grip is
ample; if power is modest – try to move weight rearward.
 If the track has slow turns followed by straightaways; if a small portion of the lap is spent
cornering; if grip is modest; if power is ample – try to move weight forward.
 For drag racing, standing starts, or hill climbing, try to move weight forward.
 If braking is especially important, try to move weight rearward.
 In all cases, try to place weight as low in the car as possible.
Regarding suspension setup, we are forced to work around the fact that the front wheels limit the car.
If the car were not nose-heavy, it might make sense to give the front and rear suspension systems
similar roll resistance, and try to work all four tires. A front-drive car done this way (if it were
possible, which would only occur if we had lots of ballast to work with) would have very poor
forward bite. Since a front-drive car is necessarily nose-heavy, it must be set up to work the front
tires as evenly as possible. That means it must corner with the inside rear tire very lightly loaded or
airborne. We trade away lateral grip at the rear to gain more at the front, where we need it.
We also gain drive traction on the inside front wheel. This is important in a front-drive car, because
we cannot use limited-slip differentials that lock too firmly or abruptly, unless the driver has great
tolerance for steering fight.
It is important to note that once the inside rear wheel is airborne, the rear suspension has contributed
all the anti-roll moment it can, and any further roll resistance has to come from the front. Up to the
point of rear wheel lift, rear load transfer builds faster than front load transfer. Beyond that point,
rear load transfer is 100%, and front load transfer builds rapidly. So does roll angle. So does
understeer.
As a general rule, to get a car that has good consistency as grip varies, we want the inside rear wheel
to lift just a little in steady-state cornering, when grip is good. If it lifts more than that, we are likely
to have a relatively loose car when grip is poor and a much tighter car when grip is good.
Many front-drive cars use MacPherson strut front suspensions. Most of these suspensions, especially
when lowered for racing, have camber properties that produce little camber change in ride and
substantial camber change in roll. This means we can improve the cornering camber on those
overworked front tires by providing ample wheel rates in roll. On the other hand, allowing soft
action in ride will not compromise camber control very much at all. This argues for fairly stiff antiroll bars, even at the front, and relatively soft springs. That is, the front needs to be stiff in roll, and
the rear needs to be stiffer yet, by a sufficient amount to make the inside rear wheel lift just a little
when grip is good. In the real world, available suspension travel and rules regarding anti-roll bars
and their mounting may constrain this approach, but the idea is to get the desired roll stiffness
distribution, and do it with bars as much as possible.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
QUADS ON PAVEMENT
I am a student at the University of Ulster in Northern Ireland studying Mechanical Engineering. I
am currently working on a project which involves designing a suspension for a purpose-built road
going quad [quadricycle].
I am sure you are familiar with quads. The quad I am working on is similar to existing quads.
However, it will be approved to go on the road, and it will handle better on the road than current
quads, which are designed exclusively for off-road conditions.
Current sports quads have a single swing-arm at the rear which connects to a solid rear axle. This
has long travel, and a relatively soft suspension. Re-bound is slow on these quads. At the front, a
double wishbone set-up is used on each side. A similar long shock is used, however re-bound is
slightly faster. The suspension set-up is mainly for high jumps and being used on rough terrain.
When this set-up is used on the road it produces a very soft ride. There is too much pitch during
retardation and acceleration, and sufficient roll to lift the inside rear tyre, almost without fail, when
there is even a slight change in direction. This wheel lifting problem is also attributed to the solid
rear axle and single swing-arm set-up.
The quad I am developing has no differential, and is driven by the rear wheels. This can make
acceleration from tight corners at slow speed very difficult. You can't put the power on until you are
in a straight line. Can suspension set-up affect this? Often, the front wheels lift completely when
the power is being applied. This results in massive understeer.
What would you suggest to be a cheap and effective method to design a new suspension set-up for a
quad bike for the road? It should solve the following problems:
1) High levels of pitch and roll on hard surfaces.
2) Inside rear wheel lifting during cornering.
3) Understeer when applying power.
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I don't know what laws you have in Northern Ireland that would allow licensing a quad for the street,
but you definitely couldn't do that over here. Anything with an engine and four wheels is considered
a car in the US, and has to comply with windshield, side impact, and other standards that a quad has
no hope of meeting.
It would be legal to race quads on pavement almost anywhere in the world. As far as I know nobody
has tried it, probably due to the vehicles' poor handling properties on pavement, which you have
observed.
The ride and handling problems you describe are largely inherent in the layout of the vehicle. To get
away from them, you would need a rear suspension with a wheel rate in roll comparable to the front,
a differential, and a much lower CG and/or longer wheelbase and wider track. You could
conceivably design such a vehicle, and still have the rider sit astride it instead of in it, but there
would be safety and aerodynamic penalties, with the only advantage being that using body english
would be somewhat easier. For good results, a pavement quad would have to look dramatically
different from a dirt one. You can't just doctor the links and springs.
What you can do with the links and springs, keeping the existing layout, is make the front
suspension very stiff in roll like the rear, and stiffen the wheel rate in pitch. If you do this with
interconnective springing (anti-roll bars, anti-pitch bars, diagonal bars, or equivalent devices), it is
still possible to keep the wheel rate in heave fairly soft. You would then essentially have a suspended
go-kart with a motorcycle-style operator position. This will give you a vehicle that will bicycle, or
flip, instead of tricycle, and will pitch less on its suspension due to longitudinal accelerations.
However, there will be more sprung mass pitch due to bumps. The tendency to overturn -- laterally
in cornering, rearward in forward acceleration, forward in rearward acceleration -- can only be
controlled by the suspension up to the point of wheel lift. Beyond that, it's purely a matter of where
the center of gravity resides relative to the four contact patches. To change that, you have to
fundamentally redesign the vehicle.
The whole logic of the quad is that it gives you a very short, narrow package, allowing the machine
to operate on many trails that would otherwise require a motorcycle or a mule. If you make the track
and wheelbase sufficient to work well on pavement, you throw away the main advantage of the
motorcycle riding position.
I have mentally toyed with an idea that poses some similar problems. I am a bicyclist, and I have
noticed that the world could use a human-powered on-road vehicle that will work decently in snowy,
icy conditions, and also on dry pavement. Such a vehicle would probably need four wheels, and
would have to be narrow enough to allow cars to pass, and preferably narrow enough to fit through a
door and be brought in the house like a bicycle. The realities of operation in snowy conditions would
require a conventional riding position; a recumbent would expose the rider to cold, dirty baths of
snow, ice, water, and slush thrown by passing vehicles, and would be too hard for motorists to see.
The rider would have to sit slightly higher than on a bike, for reasons of pedal-to-ground clearance.
The rider's legs must be straight enough to give good pedaling efficiency. So this would be a really
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tall, narrow device, with a really high CG -- even worse than what you're contemplating. Pitch
stability would not be a big problem, due to the modest power, but roll stability would be a major
issue.
In the UK, some people build high-tech pedal-driven tricycles, and even race them. These vehicles
are almost never seen on my side of the Atlantic. They obviously have the same stability problem
that has caused quads to replace trikes in the ATV market, only even worse. The riders coast through
turns with a knee hooked over the top tube, hanging off the inside of the trike like a sidecar monkey
-- and cornering speed is still limited mainly by overturning rather than grip.
I think the best approach to a tall, narrow vehicle with more than two wheels would be to give up on
trying to make the vehicle corner flat like a car, and instead make the suspension extremely soft in
roll. The rider would then lean the vehicle into the turns like a two-wheeler. The suspension would
resist this, but only gently, up to perhaps 20 degrees of lean. The rider would also have to hang off
the inside of the vehicle to corner hard on pavement. One thing that works in our favor with human
power is that the rider is the majority of the mass, making the CG highly mobile.
I think you could build a self-propelled pavement quad that cornered like that. You'd need
motorcycle tires if the wheels leaned with the vehicle, as they would with independent suspension. If
you used beam axle suspension instead, that would call for shaft drive. You could then use quad or
car tires. To my knowledge, nobody makes quad tires for pavement, so I expect you'd want to adapt
car tires. Quad tires I've seen are not only unsuitable for pavement in terms of tread design, they are
very likely incapable of coping with the speeds and temperatures they would see on pavement, even
if you retreaded them.
The vehicle would dramatically outweigh the rider, so it would still be desirable to have a fairly wide
track and put all masses as low as possible. Even at that, I would worry about having the vehicle
"high-side" or flip toward the outside of the turn, as motorcycles sometimes do. In that case the rider
would either be thrown off, or crushed by the vehicle.
A couple of years back, Daimler-Chrysler showed a three-wheeled vehicle that leaned into the turns.
As I recall from published reports, this was accomplished via semi-active suspension on the two
front wheels. If I understand correctly, the control system was a simple hydraulic valve operated by
the steering; it leaned the way you turned the steering wheel, and the more you steered the more it
leaned. I could be wrong about that, because such a control system would pose a problem if you
needed to countersteer to correct oversteer. The vehicle would lean the wrong way, and immediately
high-side. Also, the lean angle could not be optimized for both high and low vehicle speeds at a
given steer angle. To get around these shortcomings, lean must be controlled by something other
than steering position.
The way to make the vehicle lean itself would be to control the tilt electro-hydraulically from an
acceleration sensor. Since the sensor would lean with the frame, the system could simply add tilt
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until the sensor no longer detected lateral force, or until active suspension travel was exhausted. For
smaller vehicles, especially where we are trying to minimize cost and complexity, it makes more
sense to let the operator sit astride the vehicle, and lean it with body english.
The power push you describe is a universal problem in all vehicles without differentials, except
those that only turn one way and can use tire stagger. It is also a universal problem with vehicles that
are easily capable of wheelstands, at available grip level. You have both of these problems at once.
Therefore, you have to solve both of them to obtain satisfactory performance.
Quaife makes limited-slip differentials for chain drive, which are popular for motorcycle-engined
cars. These are usually used with independent rear suspension.
Go-karts race without differentials, but only because the rules demand this. One strategy for getting
the karts to turn sharp corners on pavement is to deliberately try to make them lift the inside rear.
Since all suspension is prohibited, tuners can't achieve this with soft front wheel rates in roll, so they
do it with large scrub radii (long front spindles) and lots of caster. When you have no differential,
lifting that wheel isn't necessarily a vice. You can still put power down. It doesn't mean the vehicle is
about to bicycle, although I do think a quad on pavement would bicycle pretty easily. It's actually a
form of warning, and therefore arguably a safety feature. If neither inside wheel lifts until they both
do, you have less warning of overturning. Of course, when you get on the power hard, and all the
load is on the rear tires, the inside rear plants and you get the push. So for a quad on pavement, I
think roll-compliant rear suspension and a differential would probably be the way to go.
The tendency to wheelstand depends on the ratio of CG height to the longitudinal distance from CG
to rear axle. Suspension has little influence, except that upward or downward jacking can make the
CG rise or fall a bit under power. Having ample load on the rear wheels is basically a good thing, but
we also have to steer. Optimal balance between these two concerns can only be achieved for a fairly
narrow range of forward acceleration. A vehicle with a high CG and short wheelbase is well suited
to low-grip surfaces, but is wheelstand-limited when grip is good. When the vehicle is cornering
hard and trying to gain speed, power understeer sets in before the front wheels will actually lift. This
is a characteristic of dirt vehicles operated on pavement. Sprint cars on pavement have the same
problem as your quad. In sprint cars, it helps to lengthen the wheelbase, adding most of the length
between the engine and the rear axle. This results in less static rear percentage, in addition to a
smaller ratio of CG height to CG-to-rear-axle distance. In moderation, the added front percentage
doesn’t hurt the car, because sprint cars are so tail-heavy to begin with. To maintain static rear
percentage while suppressing wheelstanding and power understeer, we would have to lengthen the
front of the car as well.
The way to put power down best, over the widest range of grip levels, is to use generous static rear
percentage, a low CG, and a long wheelbase -- think dragster. I don't mean that a pavement quad, or
a pavement oval track or road racing car, needs a 300 inch wheelbase, but longer and lower is the
direction you need to go when adapting dirt-optimized vehicles to pavement.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
NATURAL FREQUENCIES REVISITED
My January 2002 newsletter contained an error. I stated that damping a suspension system raises its
natural frequency. Actually, damping a system reduces natural frequency. At damping coefficients
exceeding critical damping (the amount of damping that makes the system return to static position in
least possible time without overshoot, following displacement from static), the system is considered
non-oscillatory. This means its damped natural frequency is undefined: it doesn’t have one.
Usually, even relatively stiffly damped race cars are below critical damping, so they do have a
damped natural frequency. This is given by the equation
d   n
where:
n
d
c
cc = 2mn
c cc
m
1  2
-
undamped natural frequency
damped natural frequency
actual damping coefficient
critical damping coefficient
damping ratio
sprung mass
We can see that as the damping ratio approaches 1, the quantity under the radical approaches zero.
At critical damping, the quantity under the radical is zero, and so is the damped natural frequency. If
the damping ratio exceeds 1, the quantity under the radical becomes negative, and the square root of
a negative number is undefined for real numbers; hence the damped natural frequency becomes an
undefined quantity.
Stiffening the damping and stiffening the springing have qualitatively similar effects on amplitude of
suspension motion, but opposite effects on frequency. Stiffening damping or springing reduces
amplitude: the suspension moves a shorter distance in a given situation. But stiffening springing
increases frequency, whereas stiffening damping reduces frequency.
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My thanks to Professor Jorge Pinto Pereira of the Escola Superior de Tecnologia de Setubal,
Portugal for advancing my education on this.
QUADS ON PAVEMENT REVISITED
The April 2002 newsletter addressed the dynamics of quads (4-wheel ATV’s) on pavement.
Newsletter recipient Chris Petersen reports meeting a person who has raced quads on pavement, in
the American midwest (Missouri or Iowa, he thought), on road courses, with pavement tires. This
person told Chris that there is now a small local racing series for these machines.
This doesn’t sound safe to me, but it sounds like it would be entertaining to watch – in somewhat the
same way as sidehack racing, or gladiatorial combat. I’d like to hear from anybody with further
information.
SPACE FRAME OR MONOCOQUE?
For cars like a D Sports Racer (DSR), what kind of chassis stiffness would you recommend? For a
home builder of DSR cars, what type of chassis construction (spaceframe, monocoque, or a hybrid)
would be most appropriate? I am contemplating building a DSR at home – but it might be easier to
have a car builder fabricate the actual chassis and suspension components since I am lacking in the
welding department.
I haven’t been to an event where DSR cars have run for many years. I know from reading that
some of the cars have become very professional, and some builders spend quite a lot on them. I
believe it is still true that many people in this class build their cars rather than buy them,
though.
There is no such thing as too much chassis stiffness, as a general rule. You can have too much
weight. You can have too little access to the engine and other components. You can have too
little room for the driver. You can end up with these problems in the pursuit of stiffness. But
stiffness is never a disadvantage in itself.
You not only want a maximum of torsional stiffness as measured by applying a torsional load
at the coilover or rocker pickup points, you also want good local stiffness at all the suspension
and steering pickup points, and good rigidity in the suspension bits themselves.
I really have no idea what torsional stiffnesses the best DSR’s are attaining these days, but off
the top of my head I would think 5000 lb ft / deg would be a reasonable target.
Over the 40 years since the Lotus 25 demonstrated the superiority of monocoque construction
by out-performing the space-framed but otherwise identical Lotus 24, a consistent pattern has
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emerged. Monocoques beat space frames wherever they’re allowed. Space frames prevail
where the rules require them, or in some cases where the builders are wedded to tubular frames
and monocoques are informally excluded through economics and culture.
The fact that space frames are still widely used, and that some people like them well enough to
write rules requiring them, tells us that they must have some attractive features – and they do.
Advantages of tubular steel space frames include cost, repairability, improved access to
components, and availability of instruction in the skills needed for construction and repair.
There are a few places you can go to learn to work with carbon fiber or sheet aluminum
monocoque structures, but it’s much easier to find a welding class. It’s also much easier to find
a welder than than a composite technician, if you want to hire help.
My next door neighbor builds sprint car chassis. He does a lot of the hands-on work himself,
including machining and fitting parts, but he hires others to do the welds. They do the welding
in his shop, with his equipment. He maintains control of design, often without drawings of any
kind, and the welds are professional quality. He currently has one welder who works day
hours, more or less full-time, and another who fabricates for a Winston Cup team and
moonlights in the sprint car shop in the evenings.
Partly, your decision will depend on precisely what cars you have to beat, and how much you
really care about winning. I’m sure you understand that you are contemplating a hobby here,
and a learning experience, rather than a career – at least in the short term, with this project.
You can certainly have fun and gain worthwhile experience building a tube-frame car.
It’s pretty certain that monocque construction is the path to best performance from the firewall
bulkhead forward. For the rear of the structure, much will depend on your choice of
powertrain. For some time, a Kohler was the engine to have. I think I heard a few years back
that some guy in Wisconsin had built his own engine specifically for DSR and was having
success with it. That is definitely not an approach for the faint of heart or the thin of wallet.
Over the years, people have used an incredible variety of powerplants for DSR cars, including
single and multiple motorcycle and snowmobile engines, Mercury outboard engines, SAAB
two-strokes, rotaries, Fiat-Abarths, you name it.
Checking the rule book (mine is from 1999 and may not be 100% current) I see that SCCA is
still encouraging diversity. DSR has five separate displacement limits: for two-strokes,
anything-goes atmospheric four-strokes, two-valve-per-cylinder four-strokes, automotivebased four-strokes, and rotaries. There are two minimum weights – a lighter one for chain or
belt drive cars. There is no limit on tire size – only a minimum wheel diameter of 10 inches.
Obviously your first step will be to think through all these possibilities. You may find that
different options give an edge on different tracks, so your choice may vary depending on where
you plan to compete the most.
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Ordinarily, the rear portion of a monocoque sports-racing chassis consists of two box structures
running alongside the lower portions of the engine. These need to be as large in cross section
as possible, to maximize rigidity. This inevitably conflicts with access to the sides of the
engine. If you are using an automotive-based engine, mounted longitudinally, a monocoque
can work pretty well. If you are using a motorcycle engine, and you need to be able to get the
side covers off without pulling the engine, a space frame design starts to look more attractive.
So you are faced with a complex set of interdependent decisions. The decision of type of frame
structure is one of them, and they all lean on each other. You need to come up with an
integrated package that satisfies your personal design objectives and makes sense taken as a
whole. The people who wrote your rules intended to give you an interesting puzzle. Have fun
with it.
TIRE CARE
It is sometimes said that lap time is 50% tires and 50% everything else. There can be no doubt that
those four little patches of rubber are vital to control of the car. Yet it is surprising how many racers
ignore the advantages to be had from tire care.
Tires vary in their sensitivity to age and care. As a rule, real racing tires are more sensitive than
street tires. Yet all tires will benefit to some degree from proper care.
All tires contain solvents. Over time, these evaporate, and this contributes to hardening of the rubber
with age. One way to slow this process down is to store your tires in the heaviest plastic garbage
bags you can find, and tie or twist-tie the bags. Plastic bags are somewhat porous, and they tend to
get torn when used to store tires or wheel/tire assemblies, so it’s not a bad idea to double-bag.
Tread compounds also harden due to polymerization. Heat cycling speeds this process dramatically.
Effect of heat cycling is related not only to how extreme the temperatures get, but also how fast the
tire is heated and cooled. Consequently, it helps to warm tires as gently as possible when you first go
out on the track, and cool them as gently as possible at the end of a run. It helps to store tires at the
coolest and most stable temperature possible.
Contrary to popular belief, moist air does not build more pressure per degree of temperature rise than
dry air or nitrogen, provided all water is in the vapor state. Water only causes disproportionate
pressure rise if it is in the liquid state when pressure is set. That said, it is surprisingly easy to have
liquid water in a tire. Chief sources of this are mounting lubricants, condensate in air tanks and
hoses, and condensation in the tire itself if pressure is set at low temperature and the tire was inflated
in muggy weather. Inflation gas can even absorb atmospheric moisture through the tire rubber. So
there is a point of diminishing returns on keeping moisture out of tires, but it’s hard to know when
we’ve reached it. Therefore, it makes sense to err on the side of dryness. This means using either
dried air or dry nitrogen for inflation, and purging after mounting and before racing.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
OILY TIRES
I recently blew an engine and got oil all over a nearly new set of racing tires. Are they junk? Is there
a way to clean them?
It may surprise you to learn that many people put oil and related substances on tires
deliberately, to soften them. Substances used for this include automatic transmission fluid,
diesel fuel, paint thinner, and WD-40.
Does it work? The answer, in Pogo’s words, is “an unequivocable maybe”. There is no doubt
that the rubber will get softer. Whether this will actually improve grip is harder to predict.
There is a difference between soft and sticky and soft and greasy. In some cases you really do
get a grip improvement. In some cases you don’t. The only way to really know is to use a test
day to try out a particular tire/solvent combination.
When you put oil on a tire, the rubber starts absorbing the oil immediately. But it takes a while
to absorb a lot, especially deeper into the rubber. So if you get oil on a rubber item that you
don’t want to soften, you can usually avoid any major impact on longevity if you wash the item
off promptly with detergent. You can even just wipe it off thoroughly with a paper towel,
depending on the importance of the item and the situation. Wiping first, and then washing, is
the most thorough. If you’re on the road, a car wash is generally the venue of choice. Use the
foam brush, then rinse.
If, on the other hand, you’re trying to soften the tread compound of a tire, you try to maximize
absorption instead. Some people use electrically driven tire rotisseries to apply softening agents
to tires. If the softener contains volatile compounds (ones that tend to evaporate), it helps to
apply the liquid to the tread, then bag the tire for days or weeks.
Are such procedures safe? Again, maybe. Certainly many racers use tread softeners and usually
don’t cause the tires to come apart. Then again, there are no guarantees, and inevitably tire
manufacturers discourage this sort of tampering. Once a tire has failed, it is uncommon for any
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systematic investigation to be conducted to determine what may have caused the failure,
particularly in small-time racing. Even if a tire does fail structurally, and even if it can be
determined that it was softened, there is usually room for doubt as to whether the softening
really was the cause, as opposed to inflation pressure, aggressive driving, suspension settings,
or track conditions.
Finally, there is the question of legality. Rules on tire soaking, and enforcement of those rules,
vary widely. This is between the racer and the officials. All I can say is investigate before you
experiment, and proceed at your own risk. Most petrochemicals do have an odor and are
detectable with a sniffer.
One other thought, for situations where an engine lets go and oils down most of the car. Try to
think of all the other rubber items that may have gotten oiled: silicone insulation, motor
mounts, suspension bushings, vibration isolators for the radiator or electrical components .
Usually we don’t want to soften any of those pieces. Any foam rubber will tend to be
especially susceptible to damage from oil, and especially hard to rid of oil.
SOME BASIC OVAL TRACK CONCEPTS FOR ROAD RACERS
Could you please clarify what you mean by “diagonal percentage” and “stagger”?
“Diagonal percentage” and “stagger” are oval track terms. However, the concepts are useful in
road racing as well. Diagonal percentage is the combined loading of the outside front and
inside rear tires (RF and LR for left turns, or if no turn direction is stated or implied), expressed
as a percentage of the total for all four wheels. We can speak of static diagonal percentage,
which is diagonal percentage as measured on wheel scales when setting up the car. We can also
speak of dynamic or instantaneous running diagonal percentage, which is the percentage of
total wheel loading on the outside front and inside rear, at a particular instant while running.
As a general rule, more diagonal tightens the car (adds understeer).
Spring rates do not affect static diagonal, since we can set that wherever we want with any
spring combination. Springs do affect the way dynamic diagonal varies as the car runs.
Stagger is generally understood to mean the difference in tire circumference between the right
and left tires at one end of the car. A car can have tire stagger at the front and/or rear, but if not
otherwise stated, we mean the rear. Many oval track cars use locked, or spool, rear ends, so
rear stagger has a big effect on cornering balance. With significant amounts of stagger on an
axle that forces both wheels to run at identical rpm, the smaller tire drags. This tends to rotate
the car toward that side. At the front end, or at the rear when the wheels can turn at different
speeds, stagger does not cause the smaller tire to drag, but it does affect left/right brake bias,
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and also left/right propulsion force bias with an open differential. If brake or drive torques are
equal, on two unequal-size tires, the smaller tire produces a greater rearward or forward force.
Ordinarily, we think of road racing cars as symmetrical. We tend to assume that if the car has
to turn both ways, we want close to 50% diagonal, and no stagger. However, that isn’t
necessarily strictly true.
Many road courses are predominantly right-turn tracks. A few are predominantly left-turn. It is
not uncommon for the car to spend more than three times more seconds per lap cornering one
way than it spends cornering the other way. In such cases, we can often gain lap time by
optimizing the car for the dominant turn direction. We want good handling balance in both
right and left turns, but it may pay to sacrifice some speed turning one way to gain some speed
turning the other way.
This most commonly involves moving ballast to the inside for the dominant turn direction.
When we do that to a significant degree, in a nose-heavy or tail-heavy car, a funny thing
happens. 50% diagonal doesn’t give us equal left percentage at the front and rear. If we want
similar cornering balance in both right and left turns, a good starting point is to have equal left
percentages for the front and rear wheel pairs, rather than 50% diagonal. The diagonal
percentage will not be really far from 50%, but there will be some difference. For a car with
60% rear and 55% left, for instance, we have 55% left at both front and rear when the diagonal
is 51%.
Another reason to depart from 50% static diagonal in a road racing car is driveshaft torque in a
live-axle rear suspension. Driveshaft torque acts through the suspension with a live axle. With
conventional engine rotation, it rolls the car rightward, and unloads the right rear and left front
tires. To compensate for this, we may want to run less than 50% static diagonal.
Ordinarily, we do not deliberately use tire stagger in road racing, but we can if we want to. We
can also have tire stagger inadvertently. Oval track racers often use manufacturing variation in
tire diameter to tune stagger. Road racers often do not even measure tire size to see if they have
stagger. Even if your desired stagger is zero, the only way to be sure you have that is to
measure. This is particularly important if you race on bias-ply tires, which in general are more
prone to diameter variation than radials, both when new and due to change after they’ve run.
We not only need to measure our tires to avoid inadvertently having undesired stagger, we also
need to understand what stagger does to car behavior so we can recognize the clues that we
might have undesired stagger.
It is also worth noting that there is a difference between stagger as usually measured
(difference in unloaded circumference) and effective stagger, which is the difference in
effective circumference, or 2 times effective radius. Effective radius is neither unloaded radius
nor loaded radius (distance from hub center to ground, under load). It is approximately the
unloaded radius minus 1/3 of the deflection under load (difference between unloaded and
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loaded radii). One important consequence of this is that we can achieve considerable effective
stagger with radial tires through pressure variation, even though pressure changes have little
effect on unloaded circumference.
NARROWER REAR TRACK THAN FRONT
Why do rear-engine and mid-engine cars so often have narrower track widths at the rear than at the
front?
The reasons for this are more practical than theoretical. In racing, we are usually designing to
an overall width limit, rather than a track width limit. Likewise, for road use overall width is
realistically the most important constraint. If the car is tail-heavy, we will often use wider
wheels and tires at the rear than at the front. Track width is measured between the centerplanes
of the right and left tires. So it’s mathematically inevitable that we will end up with the rear
track narrower than the front if the overall width is the same front and rear, and the rear tires
are wider than the fronts.
There is also a rational case to be made for having the overall width slightly greater at the front
than at the rear, simply to place the widest portion of the car in the driver’s field of view, and
discourage the tendency to hit curbs or other obstructions with the inside rear wheel in tight
turns.
There is one more reason to make the rear track narrow, which applies more often to road cars
than race cars, but may apply to race cars as well if the car is power-limited and has full-width
bodywork. For least aerodynamic drag, it is best to have the car taper toward the rear.
Therefore, when top speed and/or fuel economy are top-priority design objectives, it is
common to see a narrower rear track than one would otherwise expect.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
BRAKING/DOWNSHIFTING TECHNIQUE
I’m track-engineer on a Porsche 996 Biturbo. When I talk with our drivers, and also drivers of other
teams and cars, and we are talking about braking, the drivers are always telling me that they brake
on the engine, by downshifting and releasing the clutch. I ask them why they are doing it that way.
They explain that they can brake harder with the engine and brakes together than with the brakes
alone.
I disagree with them on this. In my opinion, the maximum braking force of a car is determined by the
coefficient of friction between the tires and the track surface. How this force is generated doesn’t
matter. It can be generated by the brakes or the engine. But if the brakes are big enough, they can
lock all four wheels by themselves, or get the ABS working. So why lose time downshifting, when the
shortest braking distance possible can be achieved using the brakes alone?
Braking technique is controversial, among drivers, driving instructors, and engineers. There is
no single best way for all cases. However, there are factors that will logically cause us to favor
one approach or another, with a particular car, for a particular turn or situation. The tradeoffs
are fascinating, and are a good example of the complexities that make racing a thinking
person’s sport.
Factors governing braking technique, including downshifting, include:
 The adequacy of the brakes, for the actual situation. That is, are we considering only
one application, or a long race? Is fade a factor? Is pad wear a factor?
 The amount of flywheel inertia in the engine, relative to compression, friction, and
pumping work on closed throttle, and relative to the car’s ability to slow using the
brakes and aerodynamic drag. Does the engine actually try to slow the car, or drive it?
 Brake bias, relative to the optimum for the level of deceleration being attempted. Does
adding engine braking at the driven wheels improve brake bias, or impair it? Does ABS
make the issue irrelevant?
 The need to be in a particular gear when we finish braking. Also, the need to be in gear,
with revs matched to road speed, at the end of braking.
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Handling properties of the car when trailbraking. Does it like to brake and corner at the
same time, or not? There may be more than one answer to this, depending on speed
range.
Properties of the transmission. Will it tolerate being being disengaged during braking,
and simply stuffed directly into the gear needed after braking, or will this destroy the
dogs or synchros? Is the shifter H-pattern or sequential?
What is before and after the turn. Is an in-slow-out-fast line the best, or an in-fast-outslow line? Or is there no turn? Are we trying to bring the car to a halt for a pit stop, or
for some other reason?
Tactical considerations. Are we trying to pass under braking? Pass after braking? Avoid
being passed under braking? Avoid being passed on exit?
Driver preference. Race driving isn’t easy. It is difficult to use any braking technique to
the absolute limit of its potential, and this makes it difficult for a driver to change from
one technique to another as circumstances vary, or even to adapt to different cars. In
general, a less-than-optimal technique executed well will beat a theoretically better
technique executed poorly.
Until the advent of disc brakes, it was quite easy to use up any car’s brakes in almost any road
race, and often on short ovals as well. Stability in braking was uncertain, especially with the
self-energizing (leading-shoe) drum brakes used on road cars. Racing drum brakes often were
made with a minimum of self-energizing effect, or were even self-de-energizing (some or all
shoes trailing), to minimize this instability, at the expense of high pedal effort.
With drum brakes, it was therefore imperative to brake in a straight line, at least most of the
time. It was also imperative to use the engine to slow the car, just to have any brakes left at all
late in the race.
When disc brakes arrived late in the 1950’s, it became possible to use the brakes much harder,
and also to trailbrake – carry the braking process into the first part of the turn. Oval track racers
have always trailbraked, if they used the brakes at all. It is not uncommon in oval racing for a
driver not to lift until the turn-in point, and do all braking in a curved path.
Trailbraking was one of the keys to Stirling Moss’s competitive edge. It was further developed
by Mark Donohue, who often used cars with spool rear ends to allow him to brake harder while
turning, without getting oversteer. Donohue is also credited with being among the first to figure
out that it pays to leave braking until really late, apex early, do a lot of braking in a curved
path, and give up exit speed, if the turn is preceded by a straightaway and followed by another
turn.
Even with discs, it was possible to use up the brakes, especially in sports cars. It still is in many
cars, notoriously NASCAR stockers on road courses. And it was still universal to heel-and-toe
down through the gears, although some cars now had close enough ratios so that the driver
could skip-shift – go two or even three gears down at once.
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By the early 1970’s, some classes of cars – notably Formula 1 and other large formula cars –
had sprouted huge wings and fat, sticky slicks. At speeds above 100 mph, such cars with a
high-downforce setup can exceed 1.0g rearward acceleration without using the brakes at all,
mainly because they are so draggy. They also have vast amounts of downforce, and when the
driver does use the brakes, the car may decelerate at more than 4.0g!
At this point a school of thought developed which held that the brakes and the drag could
decelerate the car faster with the engine disengaged, and that the engine’s rotating inertia was
such that it was actually trying to drive the car even with the throttle closed, and was fighting
the brakes rather than assisting them. Advocates of this view held that it was best to disengage
the engine while braking, and then try to find the right rpm and gear for the turn from that state
right at the end of braking. Among the drivers using this technique was Francois Cevert. When
the driver got it right, it worked pretty well. However, there was also a greater risk of not
succeeding in snagging that gear at the last moment, in which case the driver was caught out of
gear when the car needed power, and the car might easily leave the road, or at best lose a lot of
speed.
This school of thought never gained universal acceptance. Older drivers still went down
through the gears as they had always done, although the rapidity of the cars’ braking made
skip-shifting attractive – in which case the “old” method started to resemble the “new” method,
for many turns.
Of course, this controversy was only relevant for cars that had big tires and wings, and Hpattern gearchanges. Production cars, NASCAR stockers, and production-based endurance
racing sports cars still decelerated at closer to 1.0g or 2.0g than 4.0g, and still needed to
conserve their brakes, and their gearboxes. And in the last decade or so, sequential gearchanges
have become universal in the faster classes. With a sequential transmission, skip shifting is not
possible. Computer control has made rev-matching nearly foolproof, and overrevving due to a
premature downshift is prevented as the computer will forbid the shift until the road speed is
correct. So we again see, and hear, all the cars rapidly going down through the gears as they
approach a turn. In many cars, the driver has the option of having downshifts and upshifts
occur either manually or automatically. A popular choice is to downshift manually (with the
computer still having veto power) and let the car upshift automatically.
With extremely powerful brakes, the question of whether the engine assists or fights the brakes
is mainly relevant to brake balance rather than ultimate braking power.
Regardless of how we get down to the gear we need for the turn, this much is certain: we better
catch that gear by the time we need to turn in, except maybe if the turn-in is very gentle, in
which case we may do one last shift early in our trail-braking if we feel confident with this.
Once we have initiated the turn, we will need to be very smooth with the brakes and steering,
rolling out of the brakes as we wind in more steering, keeping the car as close as possible to the
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perimeter of the traction envelope. This is hard enough without trying to shift at the same time.
As soon as we’re done braking, we need to smoothly apply power to balance the car and
accelerate out of the turn. We can’t be pausing to engage the right gear after braking. We need
to be in it already. Therefore, we have to do our downshifting before the turn, while braking,
whether it’s theoretically best for braking distances or not, simply because we can’t afford to
take a hand off the wheel, and upset the car with a shift, while we’re cornering at the limit, nor
can we afford to have the car out of gear or in too high a gear when we need power to control
it. In short, we must downshift while braking because it’s the only time we can.
All of this assumes that we are slowing for a turn, and will need an appropriate gear as soon as
we finish braking. Suppose we are braking for a pit stop, or panic-stopping to avoid a wreck or
a deer, or doing a brake test?
If we just want to get the car stopped as fast as possible, most of us will simply stand on the
brakes, modulating them if we don’t have ABS and have sufficient presence of mind, and just
try to remember to declutch soon enough to avoid killing the engine. If we’re doing a brake
test, we may be able to do comparison runs with the clutch engaged and disengaged for most of
the stop. In any case, we won’t try to downshift in any modern car.
When pitting, we will usually have a pit road speed limit. To avoid violating this limit, we will
need to be in a specific gear – usually a lower one, maybe first – and at a specific rpm.
Therefore, when entering pit road we are under much the same constraints as when entering a
turn. We need to delay braking as late as possible, we need to be at a specific speed in a
specific gear right where the speed limit starts, and we need to be at that speed, in that gear, the
instant we finish braking. Therefore, we have to downshift while braking. When we reach the
pit stall, our object is to brake as late as possible, not overshoot the pit, position the car
precisely to help the crew do the stop efficiently, and have the car ready to make a good launch
at the conclusion of the stop.
This last concern may impose varying constraints in terms of getting the car in first gear before
it comes to rest, depending on the design of the gearbox, and depending on whether we’re in
first already due to the speed limit. In most cases it will be desirable, though not absolutely
essential, to get first gear while still in motion, and declutch during the stop.
To summarize, downshifting while braking may or may not be necessary to get the car slowed
down and to allow the brakes to survive. This varies with the car, the event, even the weather.
But downshifting while braking remains necessary regardless of this in many cases, to prepare
the car for what we need it to do once we’re done braking.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
UPCOMING SEMINAR
The Racing Drivers Club in San Francisco has invited me to present a one-day seminar consisting of
a lecture on basics of vehicle dynamics, followed by a question-and-answer session. Location is the
Sheraton Hotel near the SF International Airport. Time is 8:00am on Saturday, August 10. Fee is
$250 for club members, or $300 for non-members. Since dues are only $30, I think the club stands to
recruit some members.
For more information please contact Arthur Muncheryan at rose1art@earthlink.net.
STEERING GEOMETRY VARIABLES
In response to numerous requests for information on steering geometry, I am going to attempt a
reasonably complete explanation of the various parameters and their effects.
The steering axis is a line about which the wheel steers, usually through the two ball joint centers of
rotation in an independent suspension, or the kingpin axis in a beam axle. This line can be defined by
the point where it intersects the ground and by its angular orientation. These are commonly
described in terms of the X and Y coordinates of the ground intercept, with respect to a local origin
at the contact patch center, and the transverse and longitudinal angles relative to ground plane
horizontal.
The front view distance from ground intercept to contact patch center, or local Y, is called scrub
radius, or steering offset. It would make more sense to call the top view distance from ground
intercept to contact patch center the scrub radius, but most people use the term to mean the Y or
transverse component of this. This quantity is generally considered positive when the contact patch
center is outboard of the ground intercept.
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The side view distance from ground intercept to contact patch center, or local X, is called trail, or
sometimes caster trail or mechanical trail. It is positive when the ground intercept is forward of the
contact patch center.
The front view angle of the steering axis from ground vertical is called steering axis inclination
(SAI), or sometimes kingpin inclination (KPI). It is positive when the steering axis tilts inboard at
the top, which is almost always the case.
The side view angle of the steering axis from ground vertical is called caster. It is positive when the
steering axis slopes rearward at the top.
These parameters are controlled partly by the design and adjustment of the control arms, and partly
by the design of the spindle, or spindle/upright assembly, together with the hub and wheel.
The term spindle can mean either the stub axle, or pin, that carries the bearings, or the assembly
including this pin and the upright, especially when these are one piece.
The spindle or spindle/upright determines two important parameters: spindle inclination and pin lead
or pin trail.
Spindle inclination is the front-view inclination of the steering axis, relative to pin or wheel vertical,
as opposed to ground vertical. Spindle inclination approximately equals SAI minus camber. Spindle
inclination is almost exactly identical to SAI when camber is zero. It is exactly identical when both
camber and caster are zero.
The steering axis and the wheel axis do not have to intersect, unless we want the right and left
uprights to be identical parts, with bolt-on steering arms and caliper brackets. The steering axis can
pass behind the wheel axis, as it does on a bicycle. The perpendicular distance between the two axes
is called pin lead. This is equivalent to the dimension we call fork rake on a bicycle. If the steering
axis passes in front of the wheel axis, that's pin trail. So pin trail is negative pin lead, and vice versa.
Effective pin length is the distance, along the wheel axis, in front view, from the steering axis to the
wheel centerplane. This distance depends on the wheel and hub as well as the spindle/upright.
We now have sufficient vocabulary to describe and discuss basic steering and spindle geometry. If
we can specify all the quantities above, we have enough data to construct a stick model of the basic
steering geometry.
We may want to add steering arms. For purposes of spindle/upright design, we can define the
position of the outer tie rod end with respect to the pin and the steering axis. We may define a height
from pin axis to tie rod end center of rotation. To do this in a manner appropriate for drawing the
upright, or inspecting it when removed from the car, this should be the vertical dimension in side
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view, assuming zero caster and camber -- in other words, we are projecting to the wheel plane, and
taking the steering axis in side view as our local vertical.
In such a side view, we may construct a horizontal line from tie rod end to steering axis. This is our
side view steering arm length.
We may project a top view from the side view, and locate the lateral position of the tie rod end. If we
have a longitudinal line corresponding to the side view steering arm described above, we may
construct a transverse line from it to the tie rod end, and measure that distance. This we may call
steering arm offset. It will usually be outboard for a front-steer layout, and inboard for a rear-steer
layout. I don't know what sign conventions other people use, but I generally call outboard positive
for front steer and inboard positive for rear steer. Thus positive offset is the direction that gives us
positive Ackermann.
In terms of coordinates, we are establishing a local origin where the side view steering arm meets the
steering axis. The side view steering arm length is our local X, and the steering arm offset is our
local Y.
This doesn't mean there's anything wrong with assigning global or front-suspension coordinates to
the tie rod ends when doing an overall front end layout. I'm just pointing out that at some point you
will have to deal with the spindle/upright/steering arm unit as a sub-assembly, off the car, and it
helps to be able to measure and discuss it that way too.
Now we have a fairly complete vocabulary to describe steering geometry, so we can discuss what
effects these parameters have.
Trail causes lateral forces at the contact patch to produce a torque about the steering axis. This
causes the steering to seek a gravitational/inertial center. The driver feels lateral cornering force
through the steering. He also feels the lateral force that the tires must generate to make the car run
straight on a laterally sloping, or cambered, road surface. It is worth noting that this is only one
component of the self-centering forces the driver feels. Another is the tire's own self-aligning torque,
which is present whenever the tire runs at any slip angle. This will provide some feedback of
cornering force even in the total absence of trail. This effect is sometimes described as mimicking
trail. The amount of tire self-aligning torque, divided by lateral force, is sometimes called pneumatic
trail. Note that this is a calculated value which depends on tire properties, and not an actual steering
geometry parameter.
One important distinction between the forces from trail and tire self-aligning torque is that tire selfaligning torque is not a linear function of lateral force. It builds at a decreasing rate as lateral force
increases, and at a point a bit short of maximum lateral force it actually begins to decrease. This
means that if our car has little or no trail, the steering will start to go light a bit before the point of
tire breakaway. Some argue that this is a good thing, especially for a passenger car, because it gives
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the driver a signal to ease up short of the point of actual loss of control. In a race car, this type of
steering feel requires that the driver be accustomed to driving just a controlled increment beyond the
point where the steering wheel tells him/her that the limit of adhesion has been reached. If the driver
is used to having more trail, he/she will often find this very difficult.
Trail also causes a small lateral movement of the front of the car with steer, in the direction of steer.
We might call this steer yaw. It can rationally be argued that this improves turn-in, both by yawing
the car promptly and by causing the rear wheels to develop a slip angle promptly.
Scrub radius or steering offset causes longitudinal forces at the contact patch to generate a torque
about the steering axis. If right and left scrub radii are equal and longitudinal forces at the right and
left wheels are equal, no net torque at the steering wheel results. The driver feels the difference
between the longitudinal forces at the front wheels. The driver feels one-wheel bumps, brake
pulsations, and crash impacts where one wheel hits something, in direct proportion to scrub radius.
A car with a lot of scrub radius is sensitive to wheel imbalance and tire and brake imperfections, has
a lot of "wheel fight", and has greater tendency to injure the driver's hands in one-wheel crash
impacts or curb or pothole impacts. A car with very little scrub radius is less subject to these
problems, but the steering will tend to be numb and uncommunicative.
A car with large scrub radius may steer more easily at parking speeds, depending on other
parameters, provided the brakes are not applied. This is because the wheels can roll as they steer
rather than purely scuffing. With the brakes applied and the car stationary, a car with a small scrub
radius steers more easily.
Caster causes the front wheels to lean in the direction of steer. With a given spindle/upright
geometry, more caster implies more trail.
Caster combined with trail causes steer drop or steer dive. The front of the vehicle drops as the
wheels steer away from center, if caster is equal on right and left. This tends to cause an anticentering force at the steering wheel. It is the reason why the front wheels of a dragster at rest tend to
flop to one side or the other.
Caster combined with scrub radius causes the car to drop as the wheel steers forward (toes in), and
lift as the wheel steers rearward (toes out). When this occurs on the right and left wheels as one
steers forward and the other steers rearward, the result is steer roll. The car leans away from the
direction of steer. The wheel loads also change. The car de-wedges: the inside front and outside rear
gain load; the outside front and inside rear lose load. This effect can help the car turn in slow
corners, especially with a spool or limited-slip differential. In excess, it can create low-speed
oversteer and over-sensitivity to steering angle. In general, cars running on lower-speed tracks need
more steer roll, and cars on fast ovals should have very little.
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The camber change associated with caster is favorable, particularly for road racing cars, which
usually cannot get favorable camber on both front wheels any other way. We can have too much of
this good thing, but that's extremely uncommon.
Steering axis inclination (SAI) causes both front wheels to gain positive camber as they steer away
from center.
SAI combined with scrub radius causes steer lift. The front of the vehicle rises as the wheels steer
away from center. This induces a self-centering force in the steering which seeks vehicle center
rather than inertial/gravitational center. This is particularly useful in passenger cars because it
reduces the car's tendency to follow road camber, and therefore reduces the need for the driver to pay
close attention in casual driving on roads with varying slope. The centering force also tends to
suppress steering shimmy.
In race cars, the camber change associated with SAI is unfavorable on the outside wheel. The selfcentering force increases steering effort, which is a factor for any vehicle without power steering. It
also creates what could be considered a false message to the driver about the lateral forces present at
the contact patches. There is therefore a rational case for using more caster and less SAI in a race
car.
With the packaging constraints we usually face, more SAI generally implies less scrub radius. The
main limitation will often be how far outboard we can place the lower ball joint without having it too
close to the brake disc. If the wheel has generous negative offset, we may instead be limited by the
wheel rim hitting the control arms in some combinations of suspension motion and steer. Either way,
we often cannot place the entire steering axis as far outboard as we would theoretically like to. Using
SAI allows us to at least get the ground intercept further outboard in such cases. With MacPherson
strut front ends, large amounts of SAI are necessary if we are to obtain any camber recovery in roll.
Consequently, in many cars we see SAI used for reasons not directly related to SAI's own dynamic
effects.
A full discussion of Ackermann effect (increase of toe-out with steer) is beyond our scope here, but
we can at least say that in low speed turns with the wheels steered into the turn, the car generally
needs toe-out on the front wheels. For high-speed sweepers or ovals, the front wheels generally need
toe-in instead. The key determining factor is whether the turn center -- the instantaneous center of
curvature of the car's path -- is ahead of or behind the front axle line. Other determining factors
include the tendency of the loaded wheel to want a larger slip angle than the unloaded one, and what
yaw moments we wish to create with the tire drag forces.
The attitude of the front wheels at any given instant depends on both the static toe setting and the
change in wheel-to-wheel toe with steer. This means that optimum Ackermann depends on static toe
setting.
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It should be clear, then, that there is no such thing as perfect Ackermann properties. But we can at
least say some definite things about what geometric parameters will do to Ackermann. In particular,
increasing steering arm offset increases Ackermann effect.
Ackermann for oval track cars is often asymmetrical. The side view steering arm length is less on the
left wheel than on the right. This produces more Ackermann when steering left than when steering
right.
We should mention that if we are willing to tolerate a bit of additional complexity, there are ways
around some of the tradeoffs in steering geometry. For example, it is possible to create a selfcentering force by springing the steering system. This can mimick the self-centering that we get from
SAI, without the adverse effects on camber. We can also damp the steering to reduce kick and
shimmy.
We can get small SAI and small scrub radius at the same time by using compound control arms (two
single links replacing the usual wishbone or A-frame) and dual ball joints. This gives us an
instantaneous virtual ball joint outboard of the linkage itself. We can adopt this arrangement at the
upper end of the upright, or the lower end, or both.
IMPORTANCE OF STEERING RACK PLACEMENT
I have read that one should either place the steering rack above and behind the wheel axis, or below
it and ahead of it, due to deflection steer considerations. How important is this really in race cars,
where there is no rubber in the suspension or the steering mounts?
The stiffer everything is, the less this matters. Most formula cars nowadays violate the rule you
mention; the steering is ahead of the wheel axis and above it.
Of course it is still true that all cars have some deflection steer, and we would prefer that this be
deflection understeer rather than deflection oversteer.
Actually, what determines the critical height for this is not necessarily the height of the wheel axis.
Rather, it is the point of zero lateral deflection at the upright, which varies with the combination of
loads on the wheel, the geometry of the system, and the distribution of rigidities in the components.
Another consideration is that we may prefer the tie rod on the loaded wheel to be in tension rather
than compression, on the logic that the tie rod tends to be the slenderest element in the system. This
concern argues for front steer in all cases.
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BUMP STEER AS ACKERMANN MODIFICATION
I have a Pantera that has very little bump steer in compression from static position, but has quite a
lot of toe-in in droop. It also has a fair amount of Ackermann. Could it be that this is intentional, to
provide less Ackermann in hard driving when there is more roll, yet have adequate Ackermann in
tight turns at low speed? Have you ever heard of a car being designed that way on purpose?
I haven’t ever worked with a Pantera, but I don’t really think the combination was thought out on the
logic you describe. It is quite common, though, for production cars to exhibit the type of bump steer
you describe. The cause is usually that the inboard pivot axes of the lower control arms are splayed
out toward the rear in plan view, while the inboard pivot axes of the upper arms are not so much so,
or even angle outward toward the front.
This makes for a side view virtual swing arm that shortens dramatically in droop, causing caster to
diminish at a rapidly increasing rate in droop. That unavoidably causes some toe-in in droop if the
geometry is laid out to avoid major toe change in bump.
The usual reason for designing the lower control arm this way is to get more front view control arm
length, while still making room for the engine or the footwell.
THE OLD TORQUE/HORSEPOWER CONTROVERSY
More horsepower makes a car accelerate quicker – true or false?
The above question was recently included in a quiz in a magazine, written by a reputable author who
gets this newsletter. To my surprise, he said the correct answer was “false”. He explained that,
assuming all else identical, including tire size, more acceleration implies more axle torque, not
necessarily more horsepower.
What this reasoning misses is that since power is the product of torque and rpm, more torque at the
same rpm is more power, at the axle.
Now, if we have more axle torque at a given axle rpm, what can we say about conditions at the
engine flywheel? Do we have more torque at the flywheel? Not necessarily. The author himself
points out that we could have identical torque, and more torque multiplication due to lower
(numerically higher as customarily expressed) gearing.
Okay. So if there is identical torque at the flywheel, identical speed at the axle, and shorter gearing,
what do we know about engine rpm? It must be higher, in direct proportion to the gear. Again,
power is the product of torque and rpm. Therefore, if torque is identical and rpm is greater, power is
greater, at the engine.
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If the axle has more torque at a given speed, that alone does not tell us anything about torque at the
flywheel. But we can say with certainty that both the product of engine torque and gear, and the
product of engine torque and engine rpm, are greater. This means we know that both power at the
engine and power at the axle are greater.
Looking at it another way, power is the rate of energy flow. To make the engine add kinetic energy
to the car at a greater rate, energy must flow from the engine at a greater rate.
Note that this is a somewhat different question from whether to build a “horsepower motor” or a
“torque motor”. What counts at a particular instant is horsepower at that instant, not at the peak of
the power curve. In many cases, especially when running a short oval without shifting, a car will exit
a turn at an rpm closer to its torque peak than its power peak. In such a case, making the engine
strong at the torque peak may make for better lap times – but we are still talking about a power
increase (achieved through more torque at comparable rpm – or alternatively through comparable
torque and more rpm and gear, or some combination of both approaches), even though the increase
is at a point in the rpm range that is below the engine’s power peak.
So a broad power band is worthwhile, and may be worth more than maximum peak horsepower. But
at a particular instant, at a particular speed, more axle torque definitely implies more engine
horsepower, and by itself implies nothing about engine torque.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
PANTERA FRONT END REVISITED
The person who submitted last month’s question about his Pantera’s steering geometry informs me
that the car does not have increasing anti-dive in droop, contrary to my speculation. The car has
inner control arm axes that are very close to perfectly horizontal and longitudinal, meaning it has
little or no anti-dive at any ride height.
In such a front end, the presence of substantial toe-in in droop, with minimal toe change in bump,
suggests that (assuming front steer) the rack length is a little too long for the control arm layout – at
least at the height the rack is mounted. This makes the tie rods a little too short, and produces a bump
steer curve that we could call C-shaped, as opposed to J-shaped. But we can minimize bump steer in
bump, and therefore on the loaded wheel when cornering, by raising the rack, or lowering the outer
tie rod ends, relative to the setting that would give least instantaneous rate of toe change at static
position. In other words, we can tilt the C-shaped curve. We can make the wheel toe out a little, and
then in a little, through the bump range, at the expense of having it toe in a lot in extreme droop.
This is not an ideal situation, and it is doubtful that the builder is trying to get any benefits this way.
Rather, this looks like a way to use a readily available rack that’s a little longer than ideal, without
getting roll oversteer.
HORSEPOWER AND TORQUE REVISITED
The author of the article on horsepower and torque on which I offered some comments last month
points out that he was not necessarily assuming equal road speed in the cases he was comparing. I
agree that it is possible for a car with lower horsepower to accelerate faster than one producing more
horsepower, and to correspondingly have higher axle torque, if we are supposing that the car with
less power is at a lower road speed. This is an unusual way to compare two cars, but the point does
stand.
A corollary is that a given car accelerates slower and slower the faster it goes. Most of us know this
already, but perhaps not everyone is aware that this would be true even if aerodynamic drag were
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absent or did not vary with speed. As road speed rises, a car has to use a numerically lower overall
gear ratio to get a given engine rpm, and consequently torque multiplication diminishes.
Be this as it may, at any given road speed, other things being equal, more torque at the axle still
implies more power at the engine, and does not necessarily imply more torque at the engine.
FRONT AND REAR CENTER OF GRAVITY?
I write to you in the hope that you may be able to help me with a few calculations regarding center
of gravity. The situation is that I am chasing to restore the balance of our car (Australian Sports
Sedan – 20B/RX7) once had. [The writer is referring to an early Mazda RX-7 with a later twin-rotor
engine installed.] The car’s balance was disturbed once we fitted the 20B engine, adding about 200
lbs of weight. After chasing our tails for 4 years I decided to do something about it. I collected all of
Carroll Smith’s books, and Allan Staniforth to mention another, in order to gain a better
understanding of racecar dynamics.
Of interest at this time is a chapter in Allan Staniforth’s book written by David Gould. The chapter
has some nice formulae to determine lateral weight transfer and roll resistance. However, I am stuck
at determining a few things that the formulae require.
The first problem I have is that he asks for the height of the CG of the front or rear unsprung mass
(to calculate front and rear unsprung weight transfer). The only clue given to work this out is that
the figure is usually similar to the radius of the tire. Is there another way of calculating these
figures?
The second problem is similar: the equation to determine the mean center of gravity of the sprung
mass. The author has mentioned here that to find the center of gravity at the front and rear axle lines
can be an extremely difficult process and the preferred process is deduction from the known location
of major items that comprise the sprung weight. Once again, would you know of any other
techniques that can be used to determine the height of the center of gravity at the front and rear axle
lines?
It is customary to model a car as a single sprung mass, flexibly connected to front and rear axles.
Even if the suspension is independent, we approximate the independent systems at the front or rear
to an equivalent single axle for modeling purposes. We thus have three bodies, each of which has a
center of gravity (or center of mass). We may also regard the whole vehicle as a single mass, and this
will also have a center of mass, which can be taken as a weighted average of the centers of mass of
the three masses that comprise it. All three of these masses are assemblies of components, all of
which have their own centers of mass, but we treat the car as three masses because these three are
movable with respect to each other, for chassis analysis purposes.
For most designs, it works quite well to assume that the CG heights of the front and rear unsprung
masses are at their respective hub heights, or tire loaded radii. This approximation is very accurate
for the wheels and brake rotors. Other components may be higher or lower, and you can weigh them
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and estimate their individual CG locations, then calculate a CG location for the entire unsprung
assembly, but for most cars this will come out very close to hub height.
I am amazed at the number of books that talk about front and rear sprung mass centers of gravity.
The sprung mass is a relatively rigid single assembly, and it has one center of gravity (or center of
mass), not a front and a rear one, not a string of them. The sprung mass is not two men in a horse
suit, nor is it a train of flexibly connected bodies. Like any other body, it has one and only one point
at which (or through which) a linear force can be applied from any angle without causing the mass to
rotate in any direction, and that point is the center of mass. This point lies between the axles, at a
height somewhere between 12 and 20 inches for most cars.
The best method to estimate the location of the center of gravity for the sprung mass, or the whole
car, depends on whether we are dealing with a design or an actual car. If we are trying to model a car
not yet built, we have to weigh as many purchased components as we can, estimate where their
individual centers of mass are, estimate the weight and individual centers of mass for components
we’re designing, and then take moments in three planes about a convenient origin point to calculate
the overall CG. One common choice for this origin point is a point centered between the front
contact patch centers, at ground level. Another is a point centered laterally, and midway along the
wheelbase, at ground level. Any point at all can work mathematically, but these are convenient. To
estimate the overall vehicle CG location, we include the unsprung components. To estimate the
sprung mass CG location, we omit the unsprung components.
For a car that’s an assembled vehicle, sitting in our shop, we directly measure the whole car rather
than taking it apart and weighing components. To find the lateral and longitudinal coordinates of the
overall CG, we simply scale the car as we usually would when setting up for a race, and calculate the
CG position in plan view from the left and rear percentages. If the car has, for example, 55% rear,
then the overall CG is 55% of the wheelbase aft of the front axle line. If it has 51% left, then we find
the overall CG’s lateral position as follows:
1) In a top or plan view, construct lines connecting the contact patch centers on each side of the car.
2) Construct a line perpendicular to the vehicle centerline, through a point 55% of the wheelbase aft
of the front axle.
3) Find the length of the line from step 2 between the lines from step 1.
4) Find the point on this line 51% of its length from the right end. This is the plan view location of
the overall CG.
That’s two thirds of our answer. We still need to find the height of the overall CG. This is the tricky
part. The method usually described in chassis books involves elevating one end of the car, with the
other end on scales, and noting the weight change at the scales. The distance of the CG above the
unraised axle, the one on the scales, is given by: h = [(W)(L)(L2 – x2)] / (W)(x), where:
h = CG height above the axle on the scales, at static condition
W = total vehicle weight
W = weight increase on the scales when opposite axle is raised
L = wheelbase length
x = height that axle not on scales is raised
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Units of length for h, L, and x can be inches, feet, meters, or whatever, but must all match. Likewise,
units of weight for W and W must match.
One drawback to this method is that the overall CG of many race cars is not much above the axle
lines, meaning that we are measuring a very small h. This means that accuracy becomes a problem.
The smallest shift in fluids or other masses can noticeably affect the measurement, and the car may
have a significantly different CG height if we drain all the oil and fuel than it has with a normal load
of fluids. This may require a calculated correction. The end that’s raised has to be raised a significant
distance, generally at least 3 feet, and must be supported with the wheels free-rolling on perfectly
level surfaces. This requires special stands and the means to hoist one end of the car that far. The
suspension should be immobilized at normal ride height. The car may be rather precariously
balanced when raised, and in many cars ground clearance of the front and rear overhangs will limit
how far we can lift either end, unless we support the lower end on pedestals too.
A client of mine came up with an alternative method. It likewise requires immobilizing the
suspension and draining the fuel and oil. He raises one side of the car, rather than one end. He has
made large “shoes” of angle stock that cradle the two tires that remain on the ground. He uses a
wrecking truck to lift the other side of the car. He raises it until the car balances on the edges of the
“shoes”. He leaves the hoist attached, so the car can’t fall over, and gives the car just a little slack.
He can then stand beside the car, move it gently by hand, and feel for the balance point. Once he
finds the balance point, he measures the car’s tilt.
Once that point is found, he knows that the overall CG lies in the vertical plane passing through the
“shoe” edges. This we might call the balance plane. When the car is sitting normally on its wheels,
this plane assumes an angle from vertical equal to the tilt of the car when the balance plane was
found. He knows the plan-view position of the CG from scaling the car during setup, as described
above. So the CG lies on a vertical line that appears as a point in plan view. He just finds where the
balance plane intersects that vertical line, and that’s the overall CG.
Once we have the overall CG location, we can calculate sprung mass CG if we have weights and
estimated CG heights for the unsprung masses. For cars with independent suspension all around, the
sprung mass CG will be at approximately the same lateral and longitudinal position as the overall
CG, and a little higher. For cars with live rear axles, the sprung mass CG will be a bit forward of the
overall CG, and a little higher.
If all this seems intimidating, be aware that you can do calculation exercises, and learn a lot about
vehicle dynamics, using assumed values for the CG locations. You can also determine the
longitudinal and transverse location of the overall CG by measurement, and assume only the height.
For your RX-7, assumed heights of 16 inches for the overall CG, 17.5 inches for the sprung mass
CG, and tire loaded radius for the front and rear unsprung mass CG’s are probably pretty realistic.
As a general rule, to re-balance the cornering of a car that has received a larger engine, you need to
lighten whatever you can in the front, move whatever you can to the rear, increase the share of the
roll resistance at the rear, and adjust the brake bias for more front.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
MOVE THE REAR WHEELS BACK TO IMPROVE TRACTION?
Regular readers will be aware that this newsletter is used as the basis of a column in Racecar
Engineering called “The Consultant”. In the October 2002 issue, Simon McBeath has an article
about the DJ Firehawk hillclimb car, in which he remarks: Creating that slightly longer wheelbase
was achieved by sweeping back the rear wishbones, which also had the benefit of minimising chassis
overhang, effectively shifting some weight forward and keeping the major masses well within the
wheelbase. The result is almost exactly 40:60 weight distribution front to rear. The swept-back rear
suspension has, apparently, also been found to be an aid to traction in US buggy racing. Perhaps
this is one for The Consultant’s column?
First, I agree that 40/60 weight distribution is a good general-purpose target for a car where the rear
tires can be larger than the front ones. I also agree that moving the differential forward of the axle
line a bit is advantageous in terms of yaw inertia, although there is a penalty in halfshaft joint
longevity and frictional losses.
I don’t work much with off-road cars, but I can speak to the physics of traction. In any rear-wheeldrive vehicle, more rear percentage – static or dynamic – translates to more traction, in straight-line
forward acceleration or hill climbing. From this standpoint, moving the rear wheels aft (or the front
ones) hurts traction, since it reduces both static and dynamic rear percentage. So the simple answer is
that moving the rear wheels aft for better traction is wrong. For better traction, you need to move
them forward, or move major masses back.
However, in the real world we are not always dealing with pure forward acceleration, and forward
acceleration is not always limited by the rear wheels’ capability to generate forward force.
In the real world, we not only have to put power down – we also need to steer. We also have to avoid
flipping the vehicle over backwards. These considerations may lead us not to go for maximum static
rear percentage in all cases.
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The first case I can recall of somebody moving the rear wheels back on an existing vehicle occurred
in the 1970’s when Porsche moved the rear wheels on the 911 back a couple of inches. This was not
done to improve forward traction. It was done to make the car a little less tail-heavy and thereby
reduce limit oversteer without making the rear tires drastically larger than the fronts.
It is commonplace in hillclimb and drag racing motorcycles to fit a long rear swingarm and move the
rear wheel aft as much as a foot. Why is this done? Because the vehicle is wheelstand-limited rather
than traction-limited. The center of gravity is high. The wheelbase is short. When grip is good or the
grade is steep, the rider is limited by the need to keep the bike from flipping rearward on top of him,
rather than wheelspin.
Drag cars, especially ones that are required to resemble road cars, can be wheelstand-limited up to
surprisingly high static front percentages, because of the extraordinary grip of modern drag tires.
When drag slicks were less evolved, everybody tried to move the weight back as far as possible and
raise the CG as far as possible. This is the way to go, up to the point where the front wheels come off
the ground. Once that point is reached, we are faced with a delicate balancing act: we must maximize
rear wheel loading but still be able to steer with the fronts, within the range of forward accelerations
we can anticipate. It turns out that the best design is one with a very long wheelbase, a low CG, and
ample static rear percentage – a rear-engined dragster. But a funny car, with a much shorter
wheelbase and much greater static front percentage, can turn nearly as good a time – provided that
the traction characteristics of the track and tires are what we normally expect. Pit the same cars
against each other on a slippery surface, or on street tires, and the funny car has no chance.
When we are dealing with forward acceleration while cornering, things get even more complex. The
front tires not only have to afford us some measure of directional control, they also have to provide
sufficient cornering force to keep the car from developing a power push.
For a given track and tire, limiting lateral acceleration at the front or rear of the car depends on the
relationship between the dynamic normal (vertical) force on the tires and the centrifugal force they
are required to resist, plus the fact that a tire’s ability to generate lateral force diminishes when we
ask it to generate longitudinal force at the same time.
When we have a car at its limit in lateral acceleration, and we then ask it to accelerate forward as
well, we know that the car will have to reduce its lateral acceleration and widen its arc. Whether it
gets looser or tighter depends on the balance between two conflicting effects. The first effect is
rearward load transfer. The normal force on the rear tires increases, and the normal force on the
fronts decreases, while the proportion of centrifugal force at each end of the car remains essentially
unchanged since its constituent masses do not shift significantly. This tends to tighten the car
(increase understeer). The other effect is that with rear wheel drive the rear tires must give up some
lateral force capability in order to make forward force, while the front tires are not required to do
this. This effect tends to loosen the car (increase oversteer).
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Many factors other than wheelbase and CG location influence cornering balance under power,
including differential type, toe settings, tire design and inflation, and suspension design and settings.
In oval track cars, we have additional effects from suspension asymmetries, tire stagger, and static
left percentage. But let’s consider the influence of wheelbase, CG height, and front/rear CG position,
assuming other factors are held constant.
Almost any rear-drive car will be tightened by very moderate power application, and loosened if we
apply enough power to create obvious wheelspin. In between these extremes, the car has a range of
throttle position where power tightens the car compared to steady-state, and at some point a
transition to power oversteer. If that transition to power oversteer occurs only with obvious
wheelspin, and the car just gets tighter with power up to that point, we say it has power understeer,
or a power push. If anything more than minimal power application loosens the car, we say it’s loose
on power or prone to power oversteer.
Desirable behavior lies somewhere between these extremes. For best exit speed, we would like the
car to remain reasonably balanced as power is added, and just use up more road as we add more
power. The driver may like some power oversteer so he can steer the car with the throttle, but as a
rule this will exact some penalty in exit speed.
The limiting lateral acceleration at the front or rear wheel pair depends in part on the relationship
between normal force on the wheel pair and the percentage of the car’s mass that the wheel pair must
control. Let’s look at how normal force varies at the front and rear on some hypothetical cars, at 0.5g
forward acceleration. The load transferred from the front wheel pair to the rear wheel pair due to
forward acceleration is given by: Fn = Wax hcg / Lwb where:
Fn = absolute change in front or rear wheel pair normal force due to longitudinal acceleration
W = total vehicle weight
ax = longitudinal (x axis) acceleration
hcg = height of vehicle overall center of gravity
Lwb = length of wheelbase
Working in English units, we use pounds for W, express ax in g’s, and obtain Fn in lbf. With metric
units, we would classically use the vehicle’s mass in kg for W, express ax in m/sec2, and obtain Fn
in newtons. However, since our wheel scales will probably read in kg, we may find it more
convenient to use g’s for ax and get Fn in kg.
Suppose our vehicle has a CG height equal to 1/5 the wheelbase. That’s a fairly short, high car,
perhaps a sprint car or a midget. We now have a value of 0.2 for hcg / Lwb. If ax = 0.5g, then
Fn = W(0.5)(0.2) = 0.1W.
If our car weighs 1000 lb and has 50% static rear weight, then assuming no turn banking and
neglecting aerodynamic effects, our front normal force is 500 lb in steady-state cornering. If we
accelerate forward at 0.5g, Fn = 100 lb and total dynamic normal force on the front wheel pair is
400 lb. This means that the front end has a limiting lateral acceleration a bit greater than 80% of
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what it had in steady-state cornering. I say a bit greater than 80% because a tire’s coefficient of
friction usually increases a bit as normal force diminishes.
Now let’s suppose we have the same situation, except the car has 60% static rear. Fn is still 100 lb,
so we now have front normal force going from 400 lb to 300 lb. Therefore, the front end’s limiting
lateral acceleration is now a bit greater than 75% of its steady-state capability – less than in the
previous example.
If the car has 70% static rear, front normal force goes from 300 lb to 200 lb, and front lateral
acceleration capability is a bit greater than 67% of steady-state.
If we look at these three cars at ax = 1.0g, we have front end lateral acceleration capabilities slightly
greater than 60%, 50%, and 33% of steady-state. At ax = 1.5g, the first car has front end lateral
acceleration capability that is >40% of steady-state, the second car has >25%, and the third has zero;
it’s at the point of impending wheelstand.
What happens at the rear wheels is somewhat more complex. With more static rear, the percentage
increase in normal force is less for a given ax, but the forward force required to produce that ax is
also a smaller portion of the tire’s overall vector force capability. In general, it is harder to induce
power oversteer in tail-heavy cars.
My point here is that tail-heavy cars put power down better, both in a straight line and when
cornering, but as the car becomes more tail-heavy the unloading of the front wheel pair becomes
greater percentagewise for a given ax, and the car becomes more prone to power understeer. At some
point, power understeer will limit power application on exit before wheelspin will. When we have
such a condition, the car may actually achieve better ax on exit with less static rear percentage.
It will be apparent that as hcg decreases, or Lwb increases, Fn decreases for a given ax. This means
that a lower or longer car can have more static rear percentage without encountering wheelstanding
or power push. It also means that a lower, longer, more tail-heavy car will perform more consistently
as grip varies.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
ANOTHER TIRE CARE TIP
In the past I have written in these pages about bagging tires and keeping them in cool, dry, thermally
stable places. I recently read that it’s also a good idea to keep them away from electric motors or
generators that use brush contacts, as these generate ozone. I’m not sure just how significant this is,
but it sounds logical.
PULL RODS, PUSH RODS, OR BOTH?
Do push rods or pull rods have an adverse effect on handling? If so, does each selection of rod
induce oversteer or understeer in the chassis? I know a combination of pull and push rods was used
by McLaren in the early 1990’s, taking Senna to numerous victories. Has anyone tested using a
combination of pull rods on one side of the car and push rods on the other (left and right)?
Push rod and pull rod suspensions are primarily packaging solutions. They get the shock or coilover
in out of the airstream. They also allow convenient tailoring of rising-rate effects via rod and rocker
geometry, and facilitate interconnections such as third springs and anti-roll bars.
However, it is also possible to provide most of these effects with outboard or direct-acting springs
and dampers. The Z-bar on the rear of a Formula Vee, the camber compensator on a late Porsche 356
or ’64 Corvair, the swing spring on a late Triumph Spitfire, or the coil spring above the differential
on a Mercedes swing axle all do essentially the same thing as the third spring in a modern race car
suspension.
It is a fairly common misconception that push rods or pull rods affect the dynamic load transfer
(weight transfer). Actually, all the added forces are reacted within the car, and the only thing the tires
“feel” is the wheel rate – the effective spring rate, at the wheel, in the modes of suspension
movement being encountered at a given moment.
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Another misconception is that inboard coilovers reduce unsprung weight, rather like inboard brakes.
That is also erroneous. Anything that moves when the wheel moves is unsprung weight, whether it
moves horizontally, vertically, or obliquely. So adding the rod and the rocker to the system is a
disadvantage in terms of unsprung weight, and the part of the damper and spring that move with the
rocker are still unsprung.
Ordinarily, we try to make suspension layouts on road racing cars symmetrical in their behavior, and
the easiest way to do this is to make them symmetrical in their layout. It is possible to obtain
symmetrical dynamics with push rods on one side and pull rods on the other, but that’s doing it the
hard way unless we are up against some very unusual packaging constraints. There might potentially
be a reason in an oval-track car, perhaps a supermodified. I’m seeing a lot of pavement supers,
midgets, and sprint cars these days with right side coilovers hung way out from the frame on
outrigger structures. Rockers, or rockers with push rods or pull rods, could bring these inside the
body, improve the effectiveness of a low front wing, and move the weight of the right side dampers
lower and further left.
TRAIL AND STEERING FEEL
I’m on a Formula SAE team. In your August 2002 newsletter, you mention increased steering effort
and also better ability to sense the amount of traction at the front wheels, if the steering geometry
includes more mechanical trail. You also went into the difference in feel between pneumatic and
mechanical trail near the point of breakaway. I am hearing conflicting advice from other sources on
this question. Carroll Smith told us FSAE participants that ample trail is good. On the other hand,
the first Milliken book suggests that mechanical trail masks the feel from the tire’s self-aligning
torque. We are confronted with driver complaints about steering effort, but we don’t want a numb
race car. Could you elaborate on the pros and cons of mechanical trail as it relates to steering effort
and feel?
As I mentioned briefly in August, this is to some extent a question of personal preference, and
drivers differ on whether they like the steering to lighten before true breakaway, or at the point of
true breakaway. My own preference is for the steering not to lighten unless lateral force is actually
going away.
This may be partly just my own conditioning, but I do think there is a rational or objective case for
not having the steering lighten below the actual point of traction loss. Even if the driver can get used
to the feel of the steering going light short of the limit, how is even the best driver to distinguish
between lightening due to pneumatic trail reduction and lightening due to reduced grip? To some
extent the driver can “interpret from context” but basically less force is less force, and your hands
shouldn’t be expected to know if a lightening in the steering is the tire doing its normal thing or the
tire hitting pavement with less grip. With ample trail, you don’t have to be psychic. Less steering
force means less cornering force, period.
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I haven’t seen your car, but a common problem in FSAE cars I have seen is excessive U-joint
angularity in the steering shaft. In the quest for a short turning circle via short wheelbase, many
FSAE cars position the front wheels a lot further aft than they really ought to be from a weight
distribution standpoint. This not only adds load to the front wheels, but often requires outrageous
bends in the steering shaft. If your last car had this problem, consider moving the front wheels
forward, while shortening the steering arm length to get more lock with similar rack travel. The
reduced arm will add steering effort, but for a given turning circle you approximately get the
difference in effort back again from the reduced front wheel loading, and the steering shaft can be
much straighter.
KART SCALING
As part of my Mechanical Engineering degree, I have been tasked with redesigning a kart chassis to
make it easier to manufacture. I want to understand some of the dynamics of the current kart so I can
model the new one more effectively:
a) How can I measure corner weights without resorting to expensive electronic scales?
b) How can I measure the loads the chassis is exposed to as the kart corners? I want to understand
how the chassis is stressed in the dynamic state so I could load up my model in a similar way and
alter the model to achieve the same kind of handling characteristics.
That’s some assignment. Karts have been around for over 40 years, and they were originally
conceived as a simple, low-cost, easily manufactured item. Improving manufacturability of
something like that, or simplifying it at all, is a real challenge.
There are many kinds of karts, but all of them are about as simple in terms of chassis design as a
four-wheeled vehicle can be. You can simplify some of the more elaborate ones by making them
more like the lower-class ones, but that’s obvious.
I can at least offer some help with the scaling. You can’t get away from the need to use four scales of
some sort, but you can use bathroom scales, which are nowhere near as costly as electronic racing
scales. Try to get four that read as nearly the same with you standing on them as possible, and
calibrate from there as needed.
You will find that your diagonal percentage is greatly affected by whether all the scales are in a
common plane, and whether the steering is centered. You will want to level the scales carefully and
devise a repeatable regime for positioning the steering. You will also find that tire pressures affect
wheel loads, so you need to have accurate inflation for repeatable wheel load measurements.
Most karts have adjustable front ride height. The simplest system consists of washers on the
kingpins. You will find that this allows you to obtain almost any desired diagonal percentage.
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If you are setting up for road racing, and you don’t want wedge in the chassis, you can get fairly
decent results by setting front ride heights so both front wheels come off the ground simultaneously
when you jack up or lift the front end at a central point. Again, you will find that even this crude test
is sensitive to tire pressures and steering centering. This doesn’t tell you wheel loads, of course.
With a vehicle that has suspension, it is highly desirable to have platforms that allow you to roll the
vehicle back a few feet and then forward again onto the scales, to settle the suspension. With a kart,
you don’t need to do that. You can just set the kart on the scales.
You will find that left and rear percentages do not depend much at all on steering centering and tire
pressures. You can therefore easily calculate what the wheel loads would be in an unwedged
condition (equal left percentage at both ends, equal rear percentage on both sides).
Driver weight is generally at least half of the total, so things change dramatically depending on
who’s driving.
Kart frames are deliberately made torsionally flexible, and somewhat flexible in beam as well. This
design objective is a happy mate with low cost and ease of manufacturing; the simplest perimeter
frame imaginable fills the bill. The frames receive torsional loads not only from bumps, but also
from caster jacking as the wheels steer. Spindle lengths are sometimes adjustable with shims to vary
the magnitude of this effect by changing scrub radius (steering offset). Caster jacking is used to
unload the inside rear wheel in tight turns and help the vehicle rotate in yaw without a differential.
I expect you can determine stress levels in an existing kart frame while running if you can instrument
it with strain gauges. I don’t know if your school has the necessary equipment to do this. I would
think buying it yourself would be tough if affording scales is an obstacle. Stresses in any vehicle
depend greatly on operating conditions, and this is especially true for a vehicle with no suspension
except tire and frame deflection.
It is a long-established tradition in motorsports to do laboratory tests on frames which do not
necessarily faithfully reproduce running stresses but are easy to do. For a kart, relevant tests would
be overall torsional stiffness and maybe yield strength, with load points where the axle and spindles
attach, and beam stiffness and yield strength with load applied at the seat and support points at axle
and spindle mounts.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
ACKERMANN RECOMMENDATION
I am modifying a road racing Formula Ford for SCCA Solo 2 [American autocross]. I am
considering adding more Ackermann effect to make the car work better in tight turns. Is this a sound
idea, and if so, what do you suggest for geometry?
Without writing a really long piece on Ackermann, yes you will probably help the car. I don’t know
what geometry you have now, but as a general rule a car needs more Ackermann for events with
tight turns, e.g. autocross or hillclimbs.
There isn’t a universally agreed way to express how much Ackermann (toe-out increase with steer) a
car has. The closest thing we have is to take the plan-view (top-view) distance from from the front
axle line to the convergence point of the steering arm lines, divide the wheelbase by that number,
and express the quotient as a percentage. If the steering arms converge to a point on the rear axle
line, that’s said to be 100% Ackermann. If they converge to a point twice the wheelbase back, that’s
said to be 50%. If they converge to a point 2/3 of the wheelbase back, that’s said to be 150%. If they
are parallel, that’s zero Ackermann. If they converge to a point twice the wheelbase ahead of the
front axle, that’s said to be –50%.
Supposedly, with 100% Ackermann, the front wheels will track without scuffing in a low-speed turn,
where the turn center (center of curvature of the car’s motion path) lies on the rear axle line in plan
view. This is actually not strictly true, even for the simplest steering linkage, which would be a beam
axle system with a single, one-piece tie rod. With either a rack-and-pinion steering system or a
pitman arm, idler arm, and relay rod or center link, we can’t fully predict what the Ackermann
properties will be at all, merely by looking at the plan view geometry of the steering arms. The
whole mechanism affects toe change with steer.
Even knowing what instantaneous toe we want in a specified dynamic situation is not simple. We
don’t necessarily want equal slip angles on both front tires. For any given steer angle, the turn center
might be anywhere, depending on the situation. All the infinitely numerous possible situations will
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have different optimum toe conditions. Therefore, there is no relationship between steer and toe that
is right for all situations.
The toe we have at any particular instant results not only from Ackermann effect, but also from static
toe setting and toe change with suspension movement (roll and ride Ackermann).
Because of these complexities, there is no single obvious way to define what constitutes theoretically
correct Ackermann. It is possible to come up with a rationally defensible definition for your own
purposes, but there is no standard rule, and it is unlikely that there ever will be.
Having entered these abundant caveats, I will now make some general-purpose recommendations for
autocross and hillclimb applications:
1. In plan view, at zero steer (straight-ahead position) the steering arms should converge to a
point somewhere between the rear axle line and the midpoint of the wheelbase. In traditional
parlance, that’s somewhere between 100% and 200% Ackermann. The tighter the turns, the
higher the percentage.
2. At all steering positions, the rack or relay rod should be either slightly behind the outer tie
rod ends or even with them. This applies to both front steer and rear steer cars. With rack and
pinion steering, it means that at zero steer, the rack should be a bit behind the outer tie rod
ends on a front steer car, and about even with the outer tie rod ends on a rear steer car.
Purpose of this is to assure that tie rod angularity adds Ackermann at large steer angles,
rather than subtracting.
3. Angle between any arm and any link in the system should never be less than 30 degrees or
greater than 150 degrees. This helps to assure that the mechanism cannot snap over-center
due to deflections of the components. Alternatively, over-centering can also be prevented by
provision of stops at appropriate points in the mechanism.
TORQUE, RPM, AND POWER DISTRIBUTION IN DIFFERENTIALS
I would like some clarification on the issue of torque distribution between the front and rear axles on
4wd vehicles. I find the matter fairly easy to understand when you have wheels spinning, and a
limited-slip differential, but I find it more confusing when I read statements that a vehicle has a
permanent torque distribution of, say, 32% front and 68% rear.
To me, torque and revolutions go hand in hand: reduce rpm and you increase torque, as in a ring
and pinion. Doesn’t that mean that if you want different torque at the front and rear axles, they have
to turn at different speeds?
I know that in vehicles with viscous coupling drive to one axle, one can have a different overall drive
ratio at each end, and this is often deliberately employed just to load the system in normal driving,
and make it respond quicker to traction loss. But how does a rigid system, with a planetary
differential for example, split torque unequally?
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When we are dealing with one input torque, from one gear or shaft, and one output torque on a single
shaft or other member, the relationship you describe between torque and speed does hold. Neglecting
friction, power in equals power out. If rpm is changed, torque must change too, in inverse
proportion, for the product of the two (power) to remain constant.
However, when the output power is divided between two shafts by a differential, things change a bit.
Total power in still equals total power out (again neglecting friction), but power at each of the two
output shafts is not necessarily equal to power at the other shaft. Any non-locking differential
maintains a fixed distribution of torque between the two output shafts, while letting their relative
speeds vary freely. In a conventional differential, the torque split is 50/50. In a planetary differential
with one planetary gearset, the torque split is unequal but still fixed, while the shafts can turn at
different speeds.
Usually the differential carrier or planet carrier is driven by a gear, which receives power from
another gear driven by the input shaft. At the carrier, the simple inverse relationship between speed
and torque applies. Torque at the carrier is input torque times rpm reduction factor. The sum of the
output torques equals the carrier torque. The average of the output speeds equals the carrier speed.
Power at each individual output shaft can be any value at all. It is even possible to have negative
power (retardation) at one output shaft if that shaft is being forced to turn backward (opposite to
torque). But the sum of the two power outputs must equal the power input. (That’s the sum of their
signed values, not their absolute values.)
It is helpful to think of each spider or planet gear as being similar to a beam, with a load applied at
its midpoint, and reaction or support forces at two points equidistant from the load. The load is the
drive force applied at the spider or planet gear’s shaft. The reaction forces are the output shaft
resistances to vehicle motion, acting at the points of mesh between spider and side gears, or between
planet and sun and planet and annulus. Since the spider or planet shaft is always at the gear’s center,
the forces at the mesh points are always equal. This is true regardless of the rotational speeds of the
various elements.
In a conventional differential, the side gears are equal diameter, so the equal forces at the mesh
points act on equal moment arms, and produce equal torques. In a planetary, the annulus is larger
than the sun, so the output torque at the annulus is greater than the output torque at the sun. The ratio
of the output torques is the ratio of the pitch diameters of the annulus and sun. So the bigger the
planet gears are in comparison to the sun, the more unequal the torque split becomes. Usually, the
annulus drives the rear axle and the sun drives the front axle.
We can, in fact, regard the conventional differential as a unique version of the planetary, cleverly
reconfigured by the use of bevel gears to allow the sun and annulus to be the same size.
All of this determines the torques at the front and rear drive shafts. Usually, the main rpm reduction
and torque multiplication (after the transmission) happens at the axle, not at the transfer case. It is
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possible to use different ring and pinion ratios at the front and rear axles, and/or different tire sizes
front and rear, and further alter the drive force distribution at the tire contact patches. At the axles,
the usual rpm/torque inverse proportionality applies. To get more front torque and less rear by using
dissimilar axle ratios, the front drive shaft must turn faster than the rear. That will increase wear at
the center diff, rather like traveling a long distance with unequal size tires on an axle. Actually, the
least wear at the center diff comes with slightly less torque multiplication at the front axle than at the
rear – say a 4.10:1 ring and pinion at the front and a 4.11 at the rear. This is because even on a
straight road, the car doesn’t quite go perfectly straight, and in most turns the front wheels will track
outside the rears. Consequently, the front wheels travel a few more revolutions per mile more than
the rears, even if the effective radii of the tires are equal.
A spool or completely locked differential drives both output shafts at the same rpm, and does not
split the torque in any fixed proportion. This is opposite to an open differential, which controls
relative torque at the output shafts but not relative speed. With a spool, torque distribution depends
on relative resistance at the two output shafts. It is quite possible for one output shaft to have
negative resistance (wheel dragging and trying to drive the axle), while the other output shaft has a
torque greater than the sum of the two (wheel driving the car plus overcoming drag from the other
wheel). The former condition exists on the outside wheel, and the latter on the inside wheel, when
making a turn with a spool and no tire stagger.
A partially locking or limited-slip differential is midway between. It allows some difference in
speed, but adds torque to the slower output shaft and takes that torque from the faster output shaft.
A viscous coupling transmits torque according to the amount of slippage at the coupling. The faster
the input shaft turns relative to the output, the greater the torque at the output shaft. Unlike a gear set,
however, the relationship is usually not a simple linear function of the rpm ratio.
Note that none of these alternatives split power equally. No known passive mechanical device does
that.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
SHOCKS WANTED FOR RESEARCH
In previous newsletters, notably August 2000 and December 2001, I have discussed acceleration
sensitivity of shock absorbers. (Acceleration is the rate and direction of change in velocity.) I noted
that just looking at the difference between the extended end of the stroke and the compressed end of
the stroke in a standard sinusoidal shock dyno test will give you a crude indication of a damper’s
acceleration sensitivity. If the two ends of the stroke look substantially different, that suggests a high
degree of acceleration sensitivity.
It is reasonable to suppose that differences in acceleration sensitivity are a big part of the reason why
shocks that generate similar traces in the most common dyno test (sinusoidal motion produced by a
crank, 2” stroke, 100 rpm) can act so different on a car.
I have for some time been interested in investigating the matter more systematically. I would like to
come up with test procedures that will give us a way to measure and quantify sensitivity to
acceleration, and also investigate the importance of jerk sensitivity. (Jerk is the rate and direction of
change in acceleration.)
It now looks like I’ll get the chance. At least one, and quite possibly two, shock dyno manufacturers
are interested in working with me on this. At least one up and coming damper manufacturer has
expressed interest in building shocks for test. At least one racing team has expressed interest in
working with us. That’s enough to get started.
What I’m looking for now is additional teams actually running cars, who are interested in
collaborating on this. As things stand, teams won’t pay us, and we won’t pay them. Teams will
furnish shocks they already run, and/or experimental ones, for dyno testing, and provide us with
feedback regarding how the various shocks affect their car. We are particularly interested in
obtaining shocks that are reported to dyno similarly but act different. The team gets free shock dyno
testing and a better understanding of how shocks work. We get free shocks to test, and a better
understanding of how shocks work. At some point, perhaps I will write a feature article in Racecar
Engineering, and get some publicity for the consulting business. Teams interested in being on the
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inside of this cutting-edge effort are invited to contact me at the address, e-mail, or phone at the top
of this page.
TIRE WARMERS FOUND
Back when the forum on www.RacecarTech.com was running, somebody asked me where to get tire
warmers for their dirt Late Model. At that time, I pursued several leads, but they all ultimately came
up dry.
Finally, at the PRI show last month in Indianapolis, I found a US source. They are Chicken Hawk
Racing, at 249 Hapeman Hill Rd., Red Hook, NY 12571. Their phone is 866-HOT-TIRE (4688473). They have a website at www.chickenhawkracing.com.
For those unfamiliar with tire warmers, they are basically high-temperature electric blankets that
wrap around a tire’s tread and heat it up. Apart from the obvious advantage of giving you sticky
rubber right from the green, tire warmers also allow you to heat and cool the tires gently, and keep
them hot between runs. This reduces the effects of heat cycling, keeping the rubber soft longer.
Additionally, they allow you to set your “cold” pressure at a controlled temperature, rather than
ambient. This temperature can be high enough to assure that the tire won’t have any significant
liquid water in it. Regular readers may recall that water in a tire does not cause any unusual pressure
rise if it’s in the vapor state when you set the pressure.
Why wouldn’t you use them? First of all, many sanctioning bodies and tracks have outlawed them as
a cost-containment measure. And they aren’t cheap. Chicken Hawk sells two models, one for around
$1500 and one around $2000. That’s each, and you need at least four for a car (they make them for
motorcycles too). The less expensive model has a pre-set thermostat, ordinarily 175deg F (80deg C).
The more expensive model has an adjustable thermostat, and a digital thermometer so you can see if
the tire’s up to temperature yet.
Whether the performance gain is worth the money depends on your personal situation, but the
performance gain is real.
SPRING PLACEMENT ON TRIANGULATED 4-LINK
I have a question on rear spring placement on a stock metric 4-link suspension. I have built several
chassis and have been mounting the rear spring centerline forward 2½ inches of the centerline of the
axle. I’ve started on a new chassis and thought I would go back to mounting the spring directly on
the axle centerline. Since the housing does not rotate under power I don’t feel I’m gaining anything.
Does mounting the spring forward of centerline affect the static rear percentage or in any way
change the motion ratio of the spring?
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US oval track racers will need no introduction to this type of suspension. For readers unfamiliar with
it, this is what is sometimes called a triangulated 4-link, or Chevelle-style 4-link. It has been used on
various GM cars, including the “metric” series referred to here, and also recent Mustangs. It is
illustrated on p.648 of Milliken and on p.260 of Gillespie. It uses four angled trailing links to locate a
beam axle both longitudinally and laterally, with no Panhard bar, Watt linkage, or other purely
lateral locating device.
In most such layouts, the side-view geometry gives a substantial amount of anti-squat. The axle does
rotate with ride motion, nose-down in bump and nose-up in droop. However, the only rotational
compliance with drive torque comes from flexure of the parts, mainly the bushings. When the
questioner here says the axle does not rotate, he means that there is no highly compliant torque
absorbing device such as a torque arm or pull bar incorporating a spring.
In roll, there is little or no axle housing rotation.
The location of the springs has no effect on static rear percentage, except that the mass of the springs
is positioned slightly further forward or back. Spring location fore-and-aft does affect motion ratio a
little bit in ride. Moving the spring forward makes the spring-to-wheel motion ratio slightly less than
1:1 in ride. In roll, the motion ratio is the same as it would otherwise be, assuming the lateral spring
spacing is unchanged. Note that this motion ratio in roll is always less than 1:1 for any beam axle,
which means that any beam axle without an anti-roll bar has a substantially softer wheel rate in roll
than in ride.
So on a stock metric suspension, moving the springs forward softens the wheel rate in ride
somewhat, without softening it appreciably in roll. This makes the ride and roll wheel rates less
unequal. However, if the spring is moved forward only 2½ inches, that will have only a small effect.
Note that we are speaking here of springs (on buckets, on coilovers, or on sliders) mounting directly
to the axle, not to a link or a birdcage.
Even in cars with compliant torque arms or pull bars, mounting the springs forward of the axle does
not add a lot of rear jacking, and rear jacking only adds total rear wheel loading due to the overall
vehicle CG being slightly higher when accelerating forward. Such effects tend to be small.
Remember that jacking up both rear corners does not increase rear percentage, in and of itself.
Remember also that jacking one rear corner up more than the other also doesn’t significantly change
rear percentage, but it does change diagonal percentage.
Correspondingly, fairly significant effects in torque-compliant axles can result when the fore-and-aft
spring offset differs on the right and left, as when the left spring is ahead and the right spring is
behind. Then there can be a meaningful change in instantaneous diagonal percentage as power is
applied. This in turn will affect the car’s cornering balance under power.
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ROLL CENTER WITH A J-BAR
Many books, forum posts, and websites go into great detail on on the front roll center and only touch
on the rear. I run an IMCA modified with a j-bar [short, off-center Panhard bar, bent into a J shape
to clear the pinion snout – usually mounted to the left side of the frame and the right side of the
pinion snout, with the left pivot somewhat higher than the right]. I would like to determine where my
rear roll center is.
This is actually a fairly complex question. First let’s discuss what a roll center is, and isn’t.
A roll center isn’t a real thing. It’s a modeling construct – an invented idea that helps us think and
talk about the suspension’s behavior. It’s a way of representing the geometric roll resistance of a
front or rear wheel-pair suspension system, to simplify prediction of wheel loads when cornering. In
the simplest method of modeling wheel load changes due to lateral acceleration, the suspension is
imagined as a beam axle (which yours actually is), and the roll center describes a height at which
lateral force is transmitted between the axle and the sprung mass.
It is vital to recognize that we are not talking about a point the car actually rotates around, or a point
whose lateral location determines how vertical forces react. The roll center is best thought of as a
point in a side view of the car, that has no defined lateral location at all, or perhaps as a point in the
same longitudinal plane as the sprung mass CG. In other words, we should imagine the roll center as
the height of a pin in a vertical slot, or the height of a horizontal Panhard bar, not as a pin joint. It is a
notional device that transmits horizontal force only.
Okay, now with a Panhard bar that’s curved, offset, and inclined, how do we assign that imaginary
point to get the best wheel load prediction? There are two answers to this, depending on how much
work we want to do, and how accurate we want our model to be. In both methods, we disregard the
bend in the bar, and think of it as a straight link connecting its two pivot points.
In the simpler method, we find the point where the centerline of this imaginary straight bar intersects
the longitudinal CG plane, and take that point’s height as the roll center height. With this method, we
disregard effects due to the off-center, inclined Panhard bar jacking the rear of the car up or down.
In the more rigorous method, we take the midpoint height of the imaginary straight bar as the roll
center height. We then must also take into account the vertical forces resulting from bar inclination.
We likewise consider these as acting at the bar’s midpoint. When the left pivot is higher than the
right pivot, in a left turn the jacking force tries to raise the sprung mass. When the bar centerpoint is
left of the sprung mass CG, this effect tries to roll the car rightward, reducing effective roll resistance
at the rear. So we have a higher roll center, suggesting more roll resistance, but also a pro-roll
moment from the jacking. Net result will be similar to the load transfer predicted from the lower roll
center in the simpler method, though not exactly the same. (As described here, both methods have
some inaccuracy due to the bar being forward of the axle. Correction for this is possible, but beyond
our scope here.)
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
SHOCK RESEARCH UPDATE
Last month I announced that I am undertaking a project to explore sensitivity of suspension dampers
to acceleration, jerk, and perhaps other factors. I am still looking for shocks to test, particularly
groups of two or more shocks that produce similar results in typical crank dyno tests but act different
on-track.
I do have some preliminary feedback. One shock company tested one of their dampers at the usual
2” stroke and 100 cpm (5/3 Hz), then at 1” stroke and 200 cpm (10/3 Hz). These two tests produce
equal ranges of velocity, but at any velocity the second test produces 2 times the acceleration and 4
times the jerk (change of acceleration). In this case, the forces were identical in both tests, within the
window of accuracy attainable. This doesn’t mean the test was a failure. It means that the shock
tested is insensitive to acceleration and jerk, at least at the values tested.
I think it is quite possible that many shocks are acceleration-insensitive. My object is to devise ways
of systematically testing to find out, and also to find out whether acceleration sensitivity can be a
performance advantage if used correctly.
The shock dyno company I’m working with at this point, Performance Data Systems, also tested two
shocks that were provided to them by a different shock company, which were identical except for
gas pressure. PDS has a unique dyno design that allows unusually precise motion control, and will
follow almost any desired motion pattern, since it uses a linear motor rather than a crank. One test
this dyno can do is a step test: the shock is rapidly accelerated to one velocity, held at that velocity
for a given distance, then accelerated abruptly to a higher constant velocity, held at that velocity for a
specified distance, and so on.
The acceleration zones between one step and the next can be programmed to have defined limiting
values for acceleration and jerk. The machine can also be programmed to reach a particular peak
acceleration with either maximum jerk at the ends of the acceleration zone, or minimum jerk for a
desired mid-zone acceleration, within a specified acceleration time between velocity steps. If jerk is
set at maximum, then jerk is zero in the middle of the acceleration zone. If jerk is set at minimum,
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then peak jerk is much less, but there is still a non-zero jerk value in the middle of the acceleration
zone. This means that this test can produce points where both velocity and acceleration are the same,
but jerk is either zero or some known value. This allows isolation of jerk effects from acceleration
effects, which is not possible in sinusoidal testing. Alternatively, a shock can be tested at different
known accelerations, with identical velocities, and zero jerk. This allows isolation of acceleration
sensitivity from both velocity and jerk effects.
In the test of the similar shocks with differing gas pressures, PDS reports that varying accelerations
did not produce different forces at mid-acceleration, but varying jerk values did produce differing
forces. And the difference was greater in one shock than in the other. In other words, the shocks
appeared to be jerk-sensitive without being acceleration-sensitive, and the jerk sensitivity appeared
to vary with gas pressure.
Stock car teams are reporting that shocks with a given piston and shim package definitely feel softer
to the driver when gas pressure is reduced.
Some caveats here: I was not present at the tests I am describing. I am relying on the accounts of
others. Also, we are not looking at results of an exhaustive, systematic testing program. What we do
have is preliminary, anecdotal evidence that suggests there are effects worth measuring and
exploring through unconventional damper testing.
MORE ON REAR WHEEL PLACEMENT AND TRACTION
Simon McBeath, whose comments regarding rear wheel placement and its effects on traction
prompted my remarks in the October 2002 newsletter, writes:
I've just been catching up on some overdue reading and noticed in your October newsletter that you
picked up my suggestion for a discussion on the above. Many thanks a) for doing that and b) for
reading the feature (on the DJ Firehawk hillclimber) where the suggestion was placed!
I read what you had to say in your newletter with great interest. But is there also another mechanism
at work with swung back rear suspension? The Firehawk's designer mentioned to me something I
was very unclear about, and hence did not go into in the article, but it involved the suggestion of
gyroscopic effects aiding traction, and it was in reference to buggy racing. Have you heard of this
effect being exploited this way? I couldn't figure how that would work, to be honest.
I tried an experiment in the workshop with a hand held grinder, angled back, as it were, as if the
grinder's disc was a wheel swung back on its suspension, and as you move such a tool around up
and down you can feel gyroscopic forces, but when the tool is held still (but powered up) there are
no sensations or reactive forces.
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But when you first power the tool up there is, obviously, a reaction force. I wondered if this
instantaneous response could be usefully exploited for improved traction - to add to the weight
transfer under acceleration and make the tyre dig in harder, initially at any rate. I have a feeling as
I type this that what you might gain on one side of the car you'd lose on the other, but I can't figure it
out in the middle of a Sunday afternoon! Any thoughts would help still my curiosity and soothe my
confused brain!
What you’re feeling when you turn the grinder on is mainly the grinding wheel acting as a flywheel,
not a gyro. The body of the grinder is more analogous to an axle housing than a semi-trailing arm in
a buggy rear suspension, because drive torque reacts through the grinder body. The arm on the
buggy only reacts thrust under power. Drive torque reacts through the powertrain mounts, and does
not act through the suspension.
Wheels on a car do produce gyroscopic forces, but only when their toe or steer angle changes, or
their camber angle changes. Rotational acceleration or velocity about the wheel’s main axis (axle
axis) does not produce gyroscopic forces. When we steer the wheel to the left, it tries to lean to the
right. When we lean the wheel to the left, it tries to steer to the left. These effects are called
gyroscopic precession.
The precession force depends on the wheel’s angular velocity in the plane perpendicular to the force.
That is, when the wheel steers left, the magnitude of the rightward camber-wise or roll torque about
the wheel-longitudinal axis depends on the wheel’s velocity (not acceleration, not position) about the
vertical axis. The wheel’s rotational speed on its axle also matters. More rpm, more precession force;
wheel not rotating, no precession. Lastly, the wheel’s moment of inertia about the axle axis matters.
More flywheel effect, more precession force.
In a motorcycle or bicycle, precession forces are an important factor in vehicle behavior. We use
them to hold the vehicle upright, and to steer it. But in a tricycle or a car, we just live with these
forces; we don’t harness them. If anything, they’re a problem, because they are part of the reason for
shimmy in steering systems.
With the grinder, you are holding the device by the body, which is not quite in the same plane as the
disc. Consequently, the grinder may try to move in a complex manner when you power it up. It may
try to tilt the disc as well as rotate the body about the spindle axis. If the disc tilts, then there will be
some gyroscopic precession.
In any case, gyroscopic precession does not increase traction.
As for transient (short-lived) forces that try to lift the car momentarily increasing traction, that’s
possible. However, the brief traction improvement is followed by a corresponding unloading of the
wheel a fraction of a second later. What counts for this is the vertical acceleration (not position, not
velocity) of the sprung mass (F = ma). The sprung mass is lifted a bit, but only to a point. So its
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velocity upward increases to some value, and then decreases to zero again. That means its
acceleration is first upward, and then downward. When the sprung mass acceleration is upward,
there is a wheel load increase. When the sprung mass acceleration is downward, there is a wheel
load decrease.
It’s probably better for traction not to have such an effect. In certain instances, the driver may be
able to time the momentary traction increase to occur when it’s most needed, but in general the car is
limited by its instants of poorest traction, rather than its instants of greatest traction. Therefore, we
would like the wheel loads to vary as little as possible.
There is also another effect when the car is being carried in a lifted position: the center of gravity is
higher, and that increases rearward load transfer. So anti-squat does improve traction, but not as
much as many people imagine.
Now, if you move the rear wheels back on a buggy, what happens to the anti-squat, and other
properties? The answer depends on what type of rear suspension the car has, and exactly what you
change to move the wheels back. Traditionally, buggies have semi-trailing-arm rear suspension,
derived from the design on late VW beetles. However, this is not always the case any more.
Assuming we have semi-trailing arms, there are a number of ways the wheelbase could be
lengthened, and the various methods have different effects on the rear suspension geometry.
Probably the simplest method, on an existing car, would be to merely fit longer arms, without
modifying the frame. If we do this, we get the following effects:
1. The static rear percentage decreases. As previously noted, this hurts traction.
2. The static anti-squat diminishes, assuming the trailing arm slopes up toward the front.
3. Changes in anti-squat with suspension motion are reduced, because of the longer side-view
swing arm.
4. Changes in camber over bumps are reduced, due to the longer front-view (rear-view, endview) swing arm. Also, there is less bump steer.
5. The rear roll center is lower.
6. In all likelihood, the suspension will be softer with a given spring and shock package, due to
a decreased spring-to-wheel motion ratio.
The last five of these effects could all improve traction, especially while cornering, and on bumpy
surfaces. This might account for perceived or reported improvements. Note, however, that all of
these effects could also be achieved by moving the pickup points forward, and leaving the wheel
location unchanged. That would probably involve redesigning the frame, of course. And a better
approach yet is to forget about using semi-trailing arms altogether, and build a proper five-link, or
short-and-long-arm, suspension.
If we do that, we can have any rear geometry we want, with any wheel location, and we can have
much less variation in anti-squat than with any semi-trailing arm system. And any arguments for
moving the wheels back that might apply with semi-trailing arms become irrelevant.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
FREE SEMINAR MARCH 17
For readers in the Charlotte area, I will be presenting a one-hour talk at UNC Charlotte, in Fretwell
126, Tuesday, March 17, at 12:00 noon. The title is “Minding Your Anti: Understanding Roll
Centers, Jacking Forces, and Other Factors in Weight Transfer”. This will not be a purely standard
treatment of the subject. I will include discussion of “lateral anti” and shed important light on the
much-discussed topic of lateral roll center location and migration. This is a free presentation of the
UNCC student SAE chapter.
TIRE WARMERS LESS EXPENSIVE THAN I THOUGHT
In the January issue, I mentioned I’d found tire warmers, supplied by Chicken Hawk Racing , 866HOT-TIRE or www.chickenhawkracing.com. I said they had a standard model for around $1500 and
an adjustable one with temperature readout for around $2000. I was under the impression that those
prices were for a single warmer, but actually they’re for a set of four.
INDEPENDENT REAR SUSPENSION FOR DIRT?
Would there be any advantage to running an independent suspension on the rear of a dirt car? This
refers primarily to a modified, but would it help on a dirt Late Model, also? We were wondering if a
design similar to a Corvette would work.
There is no doubt that independent rear suspension can work very well on dirt. This is provable not
only by theory, but by example. Independent rear suspension is used with great success in off-road
buggies, rally cars, and Unlimited hill climb cars at Pikes Peak. The only place IRS isn’t used on dirt
is in oval track racing.
The biggest single reason for this is that in most classes, and in most sanctioning bodies, independent
rears are illegal, presumably for cost containment. I’m not sure about the high-dollar mods that
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D.I.R.T. runs in the northeastern US, but in IMCA, UMP, NASCAR, and WISSOTA, there are
specific rules against independent or “sports car” rear ends. They don’t even allow quick-changes.
Down here where I live, we have the Carolina Modified Tour, which runs similar cars, but with
quick-changes permitted.
For Late Models, the rules vary. I haven’t checked all the sanctioning bodies that run these cars, but
WISSOTA abolished all suspension rules in the Late Model class a few years back, after previously
prohibiting independent rears. To my knowledge, everybody still runs live axles, partly so they can
go on the road and race in other series, and partly because they are mostly car buyers, not builders,
and no Late Model builders offer independent rears.
Far as I know, all sprint car and midget sanctioning bodies, including World of Outlaws, now require
beam axle suspension front and rear.
So the first obstacle to overcome is to find a sanctioning body that will let you run IRS. You have to
think about not only what the current rules are, but also how the organization is likely to react if you
are successful with an independent rear, and everybody else faces the prospect of having their cars
obsoleted. You will have to invest a lot of time and money in building your own car and developing
it. If it’s outlawed as soon as it starts winning, you take a big loss.
You will face another problem that besets all innovative owner-builders: when you tear up
equipment, you can’t just order replacement cars or parts; you have to make them. If you have a
heavy schedule and are running for points, or you’re on tour, this is a major concern.
Twenty years ago, there were some attempts to build independently suspended sprint cars. These
efforts were mainly the work of backyard builders, who had little formal training. They attempted to
build systems that looked like what they’d seen on road racing cars of the era, with little real
understanding of what they were doing. I recall one case where the builders didn’t realize they’d still
need tire stagger, and blamed the suspension when the car went straight into the wall the first time
they ran it.
The lesson here is that a mediocre concept, executed and set up well, will beat a superior concept,
executed or set up poorly. Independent suspension has the potential to win races on dirt, but only if
it’s done right. Since you’ll be pioneering a new idea, you won’t be able to rely on conventional
wisdom; you’ll have to study sufficiently to understand the principles of the system. I will be happy
to help you as a consultant, but those actually doing the project will need considerable knowledge as
well.
Okay, assuming you aren’t daunted by the practical aspects of trying something radical, and
assuming you’ve found a class where IRS is legal, what are the pros and cons of IRS, and what sort
of design would be best?
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Independent rear suspension is good, but it is a mixed blessing in some respects. In general, overall
weight is greater for independent suspensions than for beam axles. However, unsprung weight is
much less for an independent suspension, especially if the brakes are inboard, and most Late Models
run to a minimum weight rule that requires them to add ballast. So in terms of weight, the only
drawback to IRS is that you have somewhat less ballast to move as desired. There is a big benefit in
roadholding, meaning ability to keep the tires in contact with the track, and minimize tire load
variation, on bumpy surfaces – and dirt tracks are often bumpy, though not always.
Anti-squat in independent systems is different than in live axles. In a live axle system, we can
separate rear jacking forces under power into thrust anti-squat and torque anti-squat. In a typical Late
Model, torque anti-squat is the lift we get from the torque arm, and thrust anti-squat is the lift we get
from the geometry of the linkages at the ends of the axle, which most commonly attach to birdcages
(brackets that can rotate on the axle). With independent suspension, we only have thrust anti-squat to
work with, because axle torque reacts through the differential mounts and does not act through the
suspension.
This leads some people to suppose that overall anti-squat is necessarily less with independent
suspension, and that therefore independent suspension would be at an inherent disadvantage
compared to current state-of-the-art dirt Late Model live axles. I question this myself, although I do
agree that in theory at least, a live axle can probably be made to lift more under power than an
independent system. As I have mentioned at various times in the past, the advantages of anti-squat
are often over-estimated, and it is possible to get ample lift from an independent system.
It is safe to say that the live axle has some edge in terms of anti-squat properties, particularly as
regards the potential to manage variation in anti-squat properties as grip varies. However, current
systems do not exploit the possibilities in this area as fully as they could, so this potential advantage
of the live axle is hypothetical until somebody decides to exploit it. These possibilities might be a
future newsletter topic.
Compared to current live axles, an independent system could have similar, or at least adequate, antisquat, and much better adhesion over bumps. The independent system might reasonably be expected
to compare most favorably on a bumpy track, and least favorably on a smooth and slippery one.
For Late Models, there are rules about transmissions, at least in WISSOTA. They have to be
mounted to the engine, so transaxles are out. That means the diff would be an IRS quick-change,
with either a spool or a Gleason.
You mention Corvette rear suspensions. There are two basic styles of independent suspension used
on Corvettes. The C2 and C3 used the halfshafts as upper lateral or camber-control links, a lateral
link sometimes called a strut rod below the halfshaft to complete the camber-control linkage, and a
trailing arm for toe location, longitudinal location, and brake torque reaction. A variation of this
system, with a third lateral link for improved toe control near the front of the trailing arm, was used
in second-generation Corvairs.
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The C4 and C5 Corvettes have a 5-link system. There are three transverse links to control camber
and toe, and two longitudinal links to provide longitudinal location and react brake torque. On the
C4, the halfshaft is still used as the upper camber control link. On the C5, the model currently in
production, the halfshaft is only used to transmit power, and the five links are all purely suspension
parts. Similar 5-link systems are used on the Viper and most purpose-built race cars. On some
current race cars, two pairs of links are combined into upper and lower a-arms, with a toe-control
link. The system then visually resembles a front suspension.
If I were designing an independent rear for any form of racing, including dirt oval-track, I would use
a five-link system, or the a-arm and toe-link variation of the 5-link. Using the halfshafts as camber
control links saves a little weight and cost, but it compromises geometry. Specifically, it forces you
to choose between a high roll center or meager camber recovery in roll. Also, the consequences if
you break a shaft or U-joint are particularly nasty, though of course they aren’t pleasant regardless.
One key decision is whether to use inboard or outboard rear brakes. The advantage of inboard brakes
is that you reduce unsprung mass, and thereby maximize the system’s roadholding advantage on
bumps. The advantage of outboard brakes is that you can have ample anti-squat under power,
without having excessive anti-lift under braking. A lot of anti-lift in braking tends to cause wheel
hop when used with generous rear brake bias, and many dirt drivers like to use a lot of rear brake to
get the car to turn in. Typical 4-bar Late Model rears have more than 100% anti-squat and zero or
negative anti-lift.
To get such properties with an independent system, you need geometry that makes the hub travel
rearward approximately .15” to .20” per inch of suspension compression, and makes the upright
rotate rearward approximately 0.6 to 1.0 deg per inch of suspension compression. In terms of side
view geometry, this means a side view instant center something like 80” behind the rear wheel, and
at or slightly above ground level.
That’s with outboard brakes. With inboard brakes, you’d want the hub to move rearward no more
than .10” per inch of suspension compression, unless the driver never uses a lot of rear brake.
Upright rotation doesn’t matter with inboard brakes. Probably the simplest approach would be to
make the whole upright move along a line inclined about 5 deg rearward, and not rotate at all.
In either case, I’d consider having a bit more anti-squat on the left than on the right, to make the car
gain wedge under power.
For lateral location, I’d try instant centers between 70 and 100 inches from the wheel and try to keep
the force line slopes between zero and 10 degrees, upward toward the center of the car, in all
combinations of ride and roll. This would correspond to a static roll center height of 3 inches, give or
take an inch. I would try to make the lower control arms as long as possible – all the way in to the
center of the car if possible – and have the upper arms shorter than the lowers by as much as needed
to achieve least possible force line slope changes in both ride and roll, with perhaps a bit more
emphasis on roll than ride.
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April/May/June 2003
My apologies to anybody inconvenienced by the lateness of the April and May issues,
and my thanks to those who have kept me so busy lately,
especially those who have done so on a paid basis!
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
SHOCK AND SPRING FORCES
With the increased emphasis on tuning using shocks, could you explain how the shock absorber
forces are fed through the chassis to affect the tire loads? How do these forces differ from the forces
that are transmitted through the springs and sway bars?
To discuss any subject, we need a vocabulary. So first, let’s define some terms.
Car wheels move in three dimensions, but we can simplify and think of the suspension as mainly just
letting the wheel go up and down. Viewed this way, the suspension for a particular wheel can move
in two directions: compression and extension. We also sometimes use the terms bump and droop or
rebound for these. As with any motion, the system can be said to have a position, a velocity, an
acceleration, and a jerk at any instant we may choose to look at.
Position, or displacement, is the inches (or millimeters) of compression or extension from some
designated reference or zero point. Usually, we take the static position as this zero – the position the
suspension is in when we set the car up on the scales.
Note that suspension position or displacement (for one wheel) can be expressed as a single number.
(Position or displacement of the sprung mass requires six numbers to completely express it: three for
linear position along three axes, and three for angular position about those axes. Rotation about a
longitudinal axis is roll; rotation about a transverse axis is pitch; rotation about a vertical axis is
yaw.)
The suspension’s position may be one-dimensional, but it is still a vector quantity: it has a
magnitude, and a direction – so many inches or millimeters, compression or extension.
The position or displacement can change over time. This change of position with respect to time is
called velocity. It likewise has a magnitude and a direction – so many inches or millimeters per
second, compression or extension.
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The velocity can change over time. The change of velocity with respect to time is called
acceleration. Acceleration has a magnitude and a direction – so many inches or millimeters per
second per second (in/sec2 or mm/sec2), compression or extension.
The acceleration can change over time. The change of acceleration with respect to time is called jerk.
Once again, this is a vector quantity – so many inches or millimeters per second per second per
second (in/sec3 or mm/sec3), compression or extension.
Readers who’ve had calculus will recognize that we are taking a series of derivatives here. Velocity
is the first derivative of displacement, with respect to time. Acceleration is the second derivative of
displacement and the first derivative of velocity. Jerk is the third derivative of displacement, the
second derivative of velocity, and the first derivative of acceleration. We could go on taking
derivatives indefinitely (the next one is called quirk – no, I’m not making this up), but the usefulness
of doing so is doubtful.
It definitely is useful to look at longitudinal and lateral acceleration and jerk. As we will see, the
car’s accelerations determine the suspension’s displacements, and the changes in the car’s
accelerations (its jerk values) determine the individual suspensions’ velocities. And since the
suspensions’ velocities are not constant, the suspensions likewise have non-zero acceleration and
jerk values.
Those with engineering backgrounds may feel I’m belaboring the obvious in this discussion.
However, I have recently been recruiting volunteers to collaborate in a project to test sensitivity of
dampers to suspension acceleration and jerk, and I have found that many readers and clients have not
understood what I meant by acceleration or jerk as applied to a shock or a suspension system.
We can express the direction of any of these quantities with a mathematical sign – positive or
negative. Which way should we do this? Should positive be compression or extension? It is
customary to use positive for compression displacement in data acquisition, so maybe that’s the way
to go. Calling compression positive also more or less agrees with the conventional tire axis system,
in which normal or road-vertical force is considered positive. In general, we think of increased
suspension compression displacement and increased normal force as going together, although this is
not always so. Then again, compression displacement generally implies extension force within the
suspension, so if extension is positive, then positive force in the suspension corresponds to positive
force at the tire, at least as a crude generalization.
In shock dynamometer testing, the dyno manufacturers have to establish sign conventions within
their own software. In the software for Roehrig dynos, the most popular make in the US,
compression strokes have positive force (that’s extension force, resisting the compression motion)
and negative velocity. This agrees with the extension-positive reasoning above. However, it
disagrees with the conventions generally used in data acquisition. No matter what we do, we will
either disagree with the shock testing convention or the data acquisition one, since they disagree with
each other.
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If this were not confusing enough, even these sign conventions are not universal, as we will see
shortly.
One might think we could avoid all confusion by dispensing with signs and simply stating direction
with the word “compression” or “extension”. This works fairly well when we are talking about
displacement, velocity, acceleration, and jerk direction. However, some confusion arises when we
discuss damping force. It is customary to speak of compression (or bump) damping force as the force
occurring when the shock is compressing, and extension (or rebound) damping force as the force
occurring when the shock is extending. But in fact these forces ordinarily are opposite in direction to
the shock’s velocity: compression damping force acts in the extension direction; extension damping
force acts in the compression direction. So substituting words for mathematical symbols is no refuge.
Either way, we have to keep in mind the actual physical phenomena we’re trying to describe, and
apply some common sense, to avoid confusion.
When a number or quantity has a positive or negative sign, we may speak of its absolute value. A
quantity’s absolute value is the greater of the quantity and its opposite. The absolute value of 4 is 4.
The absolute value of -4 is 4. (4 = 4; -4 = 4)
Correspondingly, when we have a unidimensional vector quantity such as suspension displacement,
velocity, acceleration, or jerk, whose direction can be expressed by a positive or negative sign, we
may speak of the quantity’s absolute value. This means the quantity’s magnitude, irrespective of
direction. So, for example, when we speak of large absolute velocities, that means large
compression or extension velocities. When we speak of large velocities, on the other hand, that
means large velocities in whatever direction we call positive.
In casual conversation, these distinctions are often disregarded, so again we face the need to apply
common sense, and understand people’s words (and also their math symbols) in context.
A familiar synonym for absolute velocity is speed.
The most common type of shock dyno plot is force (vertical axis of the graph, forces resisting
compression positive, forces resisting extension negative) versus absolute velocity (horizontal axis,
all values positive). Also available is force versus velocity. Here it is customary to show velocity as
negative in compression, and force resisting compression as positive. The trace is generally Sshaped, and lies mainly in the second and fourth quadrants. These sign conventions are opposite to
the compression-positive convention used in data acquisition, but they do show a realization that the
velocities and the most common forces should have opposite signs.
That’s with most dyno software I’ve seen. A correspondent in Australia recently sent me forceversus-velocity traces from an SPA dyno, in which the compression stroke has both velocity and
force positive, and the extension stroke has both velocity and force negative. The trace then lies
mainly in the first and third quadrants of the graph. With this choice of sign convention, velocity
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agrees with the data acquisition, but forces acting opposite to velocity are shown with the same sign
as velocity.
Note that I refer to the most common forces associated with a particular velocity direction, rather
than all the forces. A true damping force acts in opposition to motion – otherwise it wouldn’t
suppress motion. However, not all the forces our dampers generate are actually damping forces in
this sense.
If you examine shock dyno plots, you will see that sometimes shocks generate forces in the same
direction as velocity. There are at least three known phenomena at work here, and perhaps additional
ones. The first known phenomenon is gas spring effect. In gas pressure shocks, the gas compartment
acts as a rising-rate spring. The smaller the gas volume, and the higher the pressure, the greater the
gas spring rate. The gas spring force always acts in the extension direction. So when the shock is
moving very slowly in extension, it exerts a net extension force.
If we look at a force vs. absolute velocity plot of the full stroke from a crank dyno, there will be two
noses or points at zero velocity, representing the extended and compressed ends of the stroke. In a
gas-pressure shock, the compressed end of the stroke will show a higher force reading (meaning
more extension force) than the extended end. If the dyno is cycled very slowly, and the shock has
very soft low-speed valving – especially if it has bidirectional bleed – the difference between the two
noses will be almost entirely from gas spring effect.
It is customary to zero the dyno, and omit gas spring force from the force reading, at some point in
the cycle – typically the extended end of the stroke, although mid-stroke and full-compression
zeroing are also common. Even when this is done, the force reading will be higher at full
compression than at full extension. Thus, the shock will either show an extension force early in the
extension stroke, or a compression force early in the compression stroke, or both, just from gas
spring effect.
There is a second known effect that will cause the noses to spread further apart as low-speed valving
is stiffened, and as the shock is cycled at higher frequencies or longer strokes. This effect is fluid
compressibility.
Suppose we have a shock with the body sprung, mounted body-up. As the shock nears the end of the
extension stroke, the fluid below the piston is under substantially greater pressure than the fluid
above the piston. If it is not allowed to bleed off very rapidly, it will still be under pressure as the
piston comes to rest and starts to move upward. Consequently, the shock will not resist compression
until it is some distance into the compression stroke. This effect is sometimes called lag. If the fluid
were perfectly incompressible, this couldn’t happen. Pressure would equalize instantaneously as
soon as velocity reached zero. But shock fluid has substantial compressibility, despite our efforts to
reduce this.
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Thus, the fluid itself will act partially as a spring rather than a damping medium. And until there is
greater pressure above the piston than below it, there will be no flow downward through the piston,
and therefore there will be no extension force damping the compression. Indeed, as long as pressure
is greater below the piston, fluid will try to flow upward through the piston.
Lag occurs at both ends of the stroke.
Lag is somewhat distinct from acceleration sensitivity, but it does relate to accelerations, especially
when the velocity is changing sign.
A third known effect comes from the masses and inertias of the valving elements. With deflectivedisc valving, these effects are generally small. Where a valving element of considerable mass acts
against a spring, the effects can be large. Shocks made by Ricor and sold under the Edelbrock name
make deliberate use of this effect and advertise it as a selling point. These shocks use a weighted
element on top of the piston, which softens the valving when acceleration is in the extension
direction, i.e. during the more compressed half of the stroke, or the compression closing/rebound
opening (cc/ro) portion. I have also seen a patent description for a shock with a similar weighted
element under the piston, to soften the rebound closing/compression opening (rc/co) portion.
Intentional acceleration sensitivity usually reduces the forces generated by the shock – although it
could be made to increase them – when acceleration is in a particular direction, and sometimes only
when a particular combination of acceleration and velocity directions is present. Since lag is related
to valving stiffness when the velocity is changing sign, acceleration sensitivity affects lag.
Acceleration sensitivity affects force whenever relevant accelerations are present, not just near
velocity reversals. Thus, although acceleration sensitivity affects lag, it is a distinct phenomenon.
Acceleration sensitivity is not necessarily bad for car behavior, and may in fact be beneficial when
intelligently applied, but it’s a complication in terms of modeling or understanding.
So shock forces are complex. Sometimes our dampers create spring forces. Sometimes we can’t
predict their behavior just by knowing their velocity.
Spring forces can also be complex. In leaf springs especially, there is damping in the spring, mainly
from inter-leaf friction. In some large vehicles, with many leaves in the springs, this effect provides
all the damping; there are no shocks. Even coils and torsion bars have some internal hysteresis. They
will heat up as they flex, and they will come to rest after a number of oscillations, even in the
absence of external damping.
There is also friction in all the pivots in the suspension and steering, and there is friction in the
sliding contacts in the shocks.
So we get some damping forces from our springs, and from other components in the system.
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I am not trying to confuse matters here. I merely wish to point out that the remarks which follow are
based on simplifying assumptions, rather than comprehensive models of spring and shock behavior.
In understanding how shocks and springs affect wheel loads, we think of springs as being
exclusively sensitive to position or displacement. We estimate their forces on the basis of their
displacement. We think of shocks as being entirely velocity-sensitive. We assume that they always
make compression forces when they are extending, and extension forces when they are compressing.
We assume that if the shaft speed is greater, the absolute force is greater, in some predictable
relationship, though usually not a linear one.
An anti-roll bar is an interconnective spring. It generates forces based on its displacement, but its
displacement depends on the relative displacement of the two wheels it connects, rather than their
individual displacements. It generates equal and opposite forces in the two suspensions it connects.
It is useful to divide suspension forces affecting wheel loads into the forces present at static
condition (as the car stands on the scales at the conclusion of static setup) and the forces that add to
or subtract from these static forces as the car runs. At static condition, all suspension displacements
from static are zero, suspension velocities are all zero, suspension accelerations are zero, and
suspension jerks are zero. The anti-roll bar or bars may have preload or may not. In a road racing car
they usually will not.
The springs, shocks, and anti-roll bars act on the suspension in parallel. Although these elements
may act through different motion ratios, each of them can be thought of as exerting a particular force
at the wheel at any given instant, and these forces can simply be summed (with proper attention to
sign) to arrive at the resultant effect. A 400 pound extension force from the spring, with no force
from the a/r bar and the shock, is equivalent to a 600 pound extension force from the spring,
countered by a 100 pound compression force from the a/r bar and a 100 pound compression force
from the shock (all as measured at the wheel). Or, either of these is equivalent to a 200 pound
extension force from the spring, and a 200 pound extension force from the shock, and no a/r bar
present. The tire doesn’t know the difference. It only responds to the total force spreading the wheel
away from the sprung mass.
With springs and a/r bars, we have a wheel rate. That’s the rate of the spring, or the bar at the lever
arm end, times the square of the spring-to-wheel, or arm-end-to-wheel, motion ratio. The wheel rate
defines a simple relationship between force and displacement. Using the wheel rate, we can calculate
the spring and bar forces at the wheel when we know displacement at the wheel.
A shock doesn’t have a wheel rate in the sense that a spring does, because it is not a displacementsensitive device. To find shock force at the wheel, we need to know either velocity at the wheel, or
velocity at the shock. If we are working from data acquisition outputs, often the sensor will be set up
to read shock motion one-to-one, or as nearly so as practicable. If we are calculating from an
assumed or predicted suspension motion, or from photographic data, we may be working from wheel
motion. To calculate shock force at the wheel from velocity at the shock, we first estimate the force
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the shock generates at that velocity, based on dyno testing, then multiply this by the first power –
not the square – of the shock-to-wheel motion ratio. To calculate shock force at the wheel from
velocity at the wheel, we first find shock velocity by multiplying wheel velocity by the shock-towheel motion ratio, then proceed as before: estimate shock force, multiply by motion ratio. So we do
multiply by the motion ratio two times in this process, but in between, we estimate the shock force.
A complete dissertation on all possible wheel loading effects from springs and dampers is beyond
our scope here, but let’s consider a simple case: a turn on a level, smooth surface. We will assume
that the road has no small-scale or large-scale irregularities – billiard-table flat, no hills, no crests, no
dips, no banking. We will also ignore aerodynamic effects. This means that the sum of our four
wheel loads is the same as we’d see in the shop while doing our setup on the scales. It also means
that any change in the distribution of those wheel loads is entirely the result of the way the
suspension transfers weight or wheel loading in response to horizontal forces generated by the tires.
This lets us isolate these effects and look at them.
We will also assume that the suspension generates no extension or compression forces due to linkage
geometry: no anti-roll or pro-roll, no anti-dive or pro-dive, no anti-squat or pro-squat, no anti-lift or
pro-lift. This is actually impossible to achieve for all conditions of suspension motion, and it
wouldn’t be desirable, but we can imagine it, and it is not too far from the actual properties of
current four-wheel-independent chassis. This simplifying assumption lets us focus on wheel load
changes from the springs and dampers.
As when the car is on the scales, an increase in positive (meaning extension) force at one corner
of the car adds wheel loading at that corner and the diagonally opposite one, and
correspondingly reduces loading on the other two corners of the car. And a negative
(compression) force reduces loading at that corner and the diagonally opposite one, and adds
load at the other two corners. This is true regardless of whether the force is generated by the
damper, the spring, or the a/r bar. The tire doesn’t know which part does what. It only behaves
according to the resultant loading generated by the suspension elements acting together.
Unlike the static condition, front, rear, left, and right percentages do change. However, the
suspension does not control these changes in this simplified case; the wheelbase, track width, and
CG height – not the suspension – control how much load transfers at a particular longitudinal and
lateral acceleration. The springs and shocks control how the diagonal percentage varies as all this is
going on, and thereby influence the car’s cornering balance. More diagonal percentage (meaning
outside front wheel load plus inside rear, as a percentage of total) at any point in the cornering
process adds understeer, or tightens the car. Less diagonal percentage adds oversteer, or loosens the
car.
The July 2001 newsletter contained a troubleshooting chart based on five parts of a turn, with
complete explanations of what the five parts were. For the convenience of readers receiving the
newsletter by e-mail, I am sending that back issue with this one, as a reference. Readers seeing this
issue as hardcopy can order back issues from me.
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Part One, or early entry – braking increasing while turning in: This may or may not happen at all.
In oval track racing, it is very common. In road racing, braking force more commonly reaches its
maximum while the car is still running straight.
The car as a whole is accelerating rearward at an increasing rate, and accelerating laterally in the
direction of the turn at an increasing rate. Angularly, it is pitching forward and rolling out of the turn.
Its roll displacement is outward. Its pitch displacement is forward. Its roll velocity is outward. Its
pitch velocity is forward.
Therefore, the outside front suspension has a compression displacement, and a compression velocity.
The inside rear has an extension displacement, and an extension velocity. Without more information,
it is hard to say exactly what the displacements and velocities at the inside front and outside rear are,
but they are relatively small, because the effects of roll and pitch are subtractive at those corners.
Consequently, spring and damper changes at the outside front and inside rear will have the greatest
and most certain effects on the car.
Taking springs first, the important principle is that a stiffer spring creates more load change with
displacement change – not necessarily more load. So a stiffer outside front spring increases load at
that corner (negative displacement, positive load change), and at the inside rear, and correspondingly
unloads the inside front and outside rear. This adds diagonal percentage, which tightens the car, or
adds understeer.
A stiffer spring on the inside rear creates a bigger load decrease with displacement change. That
translates to less diagonal percentage, and a looser car (more oversteer or less understeer).
A stiffer front anti-roll bar creates a positive (extension) force at the outside front, and an equal and
opposite negative (compression) force at the inside front. This also creates equal and opposite load
changes at the rear – more load at the inside rear, less at the outside rear. Result: more diagonal
percentage, tighter car (more understeer). A stiffer rear bar does the opposite, and loosens the car.
As for the dampers, if we stiffen the outside front low-speed compression valving, that adds a
positive (extension) force at the outside front, adding diagonal percentage and tightening the car
(adding understeer). If we stiffen the inside rear low-speed extension valving, we are creating a
negative (compression) force at the inside rear. This reduces diagonal percentage and loosens the car.
Important things to note regarding the role of the dampers:
1) When the suspension velocity and the suspension displacement are in the same direction,
stiffening the damper and stiffening the spring have qualitatively similar effects on
oversteer/understeer balance.
2) Contrary to a very common misconception, stiffening the dampers does not slow down or
momentarily reduce the load changes at the outside front or inside rear – these load changes are
sped up, or are momentarily increased. Spring loads are momentarily decreased at the outside
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front and increased at the inside rear – in other words, spring load changes are momentarily
decreased by the shocks – but the effect on tire loads is the opposite.
3) If the low-speed valving is soft and the velocities are small, the damper forces may be relatively
insignificant.
Also, note that:
1) We are assuming that the road is smooth. As long as this is true, the shock movements will be
low-speed (less than 2 in/sec) and will be caused by sprung mass motion. When the surface is
bumpy, bumps become the main factor in shock motion and none of what we’ve been saying
about load transfer effects from the dampers applies. There still are sprung-mass-motion
components to the shock motion, superimposed on the motions from the bumps. When looking at
track data we can, at least to some degree, separate these components, but the shocks can’t do
that. They only know their actual motion at a particular instant.
2) We are assuming that the brake bias is such that the front wheels do at least half of the braking. If
the car is slowed primarily by the rear wheels, the effects of diagonal percentage may reverse.
This is due to the distribution of rearward force at the rear tires, and not to any fundamental
difference in tire properties during entry.
3) Contrary to the contentions of some writers, tire load sensitivity (the decrease in coefficient of
friction with increasing load, which is responsible for the car getting tighter with increasing
diagonal percentage) does not reverse or work backwards during entry or with cold tires.
Part two, or late entry – braking decreasing, cornering force increasing: This may be the first or
only phase of entry if the driver reaches peak braking while traveling straight. It is also possible for a
period of “semi-steady-state” braking and cornering to exist between early (increasing) and late
(decreasing) braking, particularly on ovals. More on this later.
In terms of spring and damper behavior, the difference between part one and part two is the direction
of pitch velocity. In part one, the car has a forward pitch displacement and a forward pitch velocity.
In part two, the car has a forward pitch displacement and rearward pitch velocity. We may say it’s
de-pitching; it has a forward tilt, but a decreasing one.
Roll displacement and velocity are both outward, same as in part one. However, roll displacement is
increasing at a decreasing rate, which reaches zero at the conclusion of part two. So roll velocity is
outward and decreasing, and roll acceleration is inward.
At the beginning of part two, the car has a combination of outward roll displacement and forward
pitch displacement. At the conclusion of part two, the car has near-zero pitch displacement and
increased outward roll displacement.
The biggest individual suspension displacement changes from the conclusion of part one, and the
greatest individual suspension velocities, are at the inside front and outside rear. These are the
wheels where the effects of rearward pitch velocity and outward roll velocity are additive.
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At the beginning of part two, the displacements of the inside front and outside rear will be small. At
the conclusion of part two, the inside front will have an extension displacement, and the outside rear
will have a compression displacement. The velocities, therefore, are in the extension direction at the
inside front, and in the compression direction at the outside rear.
Consequently, the low-speed extension (rebound) valving on the inside front and the low-speed
compression valving on the outside rear are in a position to influence wheel loads. Stiffening inside
front extension introduces a negative (compression ) force and increases diagonal percentage,
tightening the car (adding understeer). Stiffening outside rear compression introduces a positive
(extension) force, which decreases diagonal percentage and loosens the car (reduces understeer).
Inside front and outside rear spring rates will be of little importance at the beginning of part two, but
will be as significant as outside front and inside rear rates at the conclusion of part two. Stiffening
the inside front spring will tighten the car (add understeer), and stiffening the outside rear will loosen
the car (reduce understeer). As in part one, velocities and displacements at the most influential
wheels have the same sign, and stiffer springing and stiffer damping have qualitatively similar
effects on balance.
Part three, or mid-turn – steady-state cornering: Most turns, with most drivers, will include some
interval of approximately steady-state cornering. This means that the driver applies just enough
power to maintain or slightly increase speed, and most of the tires’ traction is used in the car-lateral
direction. The car will be traveling in a nearly constant-radius path. In a street-intersection turn on a
street circuit, this phase may be so brief as to be negligible. In a carrousel-type turn or long sweeper,
or on a high-speed oval, the car may experience approximately steady-state cornering for as long as
five seconds.
In this situation, the car has pitch and roll velocities very close to zero. Pitch displacement is also
close to zero. Roll displacement is substantial, and outward. Suspension displacements are
compression on the outside wheels, and extension on the inside wheels. Suspension velocities are
close to zero. Therefore, damper forces will likewise be close to zero.
This means that the car will be sensitive to springs and anti-roll bars, and insensitive to dampers.
Stiffening either front spring, or the front anti-roll bar, will tighten the car (add understeer).
Stiffening either rear spring, or the rear anti-roll bar, will loosen the car (add oversteer).
Remember we are assuming that the turn is completely unbanked. In banked turns, the inside
suspensions may compress. With soft springs and stiff bars, this may happen at surprisingly shallow
banking angles. In such cases, effect of outside spring and anti-roll bar changes are the same as in a
flat turn, but effects of inside spring changes reverse. A stiffer inside front spring will loosen the car
(add oversteer). A stiffer inside rear spring will tighten the car (add understeer). With a beam axle,
we may have moderate compression of the inside spring even though we have moderate extension at
the outside tire, because the spring will be inboard of the tire. In this situation, there will be a node,
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or a point where there is neither compression nor extension, somewhere between the inside tire and
the inside spring.
I am digressing from our simplified flat-turn example here to remind the reader that our example is
simple, but the real world is complex. As we proceed through our hypothetical flat turn, it is
important for the reader to pay attention to how things work and why, rather than treating these
simplified dynamics as a universally applicable troubleshooting guide.
Part four, or early exit – car-forward acceleration present and increasing, but less important than
car-lateral acceleration: The driver now begins to apply greater throttle than required to merely
sustain constant speed, and begins to release the car in terms of cornering. The car’s lateral
acceleration is diminishing, and its forward acceleration is increasing. In this phase, lateral
acceleration still dominates the car’s behavior in terms of suspension displacements. The car has an
outward roll displacement, but this is decreasing, so the car has an inward roll velocity. The car has a
rearward pitch displacement, and a rearward pitch velocity.
The effects of roll and pitch velocities are additive at the outside front and inside rear corners, so
these will be the most influential wheels in terms of damper tuning. The outside front suspension
will have a compressed displacement, but this will be diminishing, so the velocity will be in the
extension direction. The inside rear suspension will have an extended displacement, but this will
again be diminishing, so the velocity will be in the compression direction.
The effects of roll and pitch are subtractive at the inside front and outside rear. We cannot generalize
about the net velocities at these corners, except to say that they will be smaller than at the outside
front and inside rear. Therefore, the car will be relatively insensitive to damping changes at these
corners.
Note that we now have at least two corners where the displacement and the velocity are opposite in
direction. This means that stiffening the spring and stiffening the damper have opposite effects on
wheel load, diagonal percentage, and oversteer/understeer balance. Spring and anti-roll bar effects
are as in earlier parts of the turn: stiffer front tightens (adds understeer); stiffer rear loosens (adds
oversteer). As part four progresses, the outside front and inside rear suspensions approach their static
positions, and the influence of spring rates at these corners correspondingly diminishes. So,
especially toward the end of part four, the corners where the shocks matter most are the corners
where the springs matter least.
At the outside front, stiffening the low-speed extension damping adds a negative, or compressive
force. This reduces wheel loading, reduces diagonal percentage, and loosens the car (adds oversteer)
– an opposite effect from stiffening the spring or the bar, as long as the spring is compressed
compared to static. At the inside rear, stiffening the low-speed compression damping adds a positive,
or extension force. This increases wheel loading, increases diagonal percentage, and tightens the car
(adds understeer). Again, this is opposite to the effect of stiffening the spring or bar, as long as the
spring is extended compared to static.
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Note that I am contradicting the much-repeated advice to soften inside rear compression damping to
hasten loading of the inside rear and tighten exit. In fact, softening the inside rear compression
damping momentarily diminishes total extension force, and therefore momentarily diminishes inside
rear tire loading and diagonal percentage, compared to stiffer inside rear compression damping.
Part five, or late exit – combined forward and lateral acceleration as in part four, but with forward
acceleration dominant: The difference between part five and part four is the displacement direction
at the outside front and inside rear. Forward acceleration is now large enough, and lateral
acceleration is small enough, so that the outside front is extended relative to static (though less than
the inside front), and the inside rear is compressed relative to static (though less than the outside
rear). Suspension velocities are similar to part four: greatest at the outside front and inside rear;
extension on the outside front; compression on the inside rear.
So for shock tuning purposes, exit can be treated as a single phase of the cornering process, and does
not need to be broken down into two parts. However, part five is distinct from part four for spring
tuning, because the car’s response to spring changes at the outside front and inside rear reverses.
Stiffening the outside front spring loosens the car (adds oversteer), and stiffening the inside rear
tightens the car (adds understeer).
It may be worth clarifying what basis of comparison I’m using when I speak of a change tightening
or loosening the car (adding oversteer or understeer). In the above remarks, we are referring to the
car’s behavior compared to the same part of the turn, before the change in question. It is also
possible to consider how a change affects a given part of the turn relative to the previous part of the
turn, or some other part, with the same change, as opposed to the same part of the turn, before the
change. Both of these modes of comparison are useful. We do have to be mindful of which mode we
are using, however.
For example, in a flat turn, stiffening the inside rear spring loosens the car during part four of the
turn – but less than it does in part three or part two, especially toward the end of part four. So we
might reasonably say that a stiffer inside rear spring tightens the car in part four, relative to its
condition in the preceding portions of the turn. Changing the choice of baseline for a comparison
can change the outcome of the comparison.
We have given much attention to the distinctions between inside and outside wheels. It will of course
be obvious that when the car has to turn both right and left, any given wheel will be an inside wheel
in some turns and an outside wheel in others. For most road racing applications, we can condense
spring, bar, and shock tuning to a surprisingly simple set of rules:
1) To tighten the car (add understeer) overall, add spring and/or bar to the front and/or take spring
and/or bar out of the rear. To loosen the car (add oversteer), do the opposite: add spring and/or
bar to the rear, and/or take spring and/or bar out of the front.
2) To loosen the car (add oversteer) on entry and tighten it (add understeer) on exit, add rear
damping and/or take out front damping. For opposite effect, do the reverse.
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On ovals, suspension tuning in general is considerably more complex, because we can use
asymmetries of many kinds, in addition to everything we use in road racing.
One other nuance mainly relating to ovals is that there may exist what might be called semi-steadystate cornering conditions (my own terminology) between parts one and two and parts three and
four. In steady-state cornering, longitudinal acceleration is zero, or near zero. In semi-steady-state
cornering, longitudinal acceleration is substantial, but not changing.
Such a state can occur during entry if the drivers applies the brakes and then holds braking force
roughly constant for a time before releasing the brakes. Assuming the driver is using the tires’ full
capability, lateral acceleration will also be close to constant. This will place the car on a path whose
instantaneous radius is steadily decreasing, even though the car’s vector-sum acceleration is not
changing. The car will have an outward roll displacement and a forward pitch displacement. These
will be substantially constant, and therefore all suspension displacements will be nearly constant and
suspension velocities will be close to zero. That means that damping forces will be negligible, and
the car will be unresponsive to damper tuning.
Semi-steady-state cornering can also occur during exit if the driver holds forward acceleration
roughly constant with the throttle, while using the tires’ full capability. Again, neither speed nor
instantaneous path radius is constant, but vector-sum acceleration of the car is constant. And again,
the suspension velocities will be close to zero, damping forces will be negligible, and the car will not
be affected by damper tuning.
Regarding whether to add or reduce damping on compression or extension, and at high velocities or
low, some widely repeated advice would have us set compression damping to control sprung mass
motion, and set extension damping to control unsprung mass motion. In my opinion this is incorrect.
At some time it may have served as simple advice to racers faced with setting the earliest doubleadjustable shocks, but now we have revalveable and four-way adjustable shocks, and reasonably
good shock dynos. My advice nowadays is:
1) Use low-speed damping, in both extension and compression, to manage transient weight transfer
and sprung mass motion. Do not expect this to work unless the surface is smooth enough so that
sprung mass motion is the main cause of suspension movement. Use the springs and bars as your
main means of managing weight transfer.
2) Use damping properties at velocities above 2 in/sec to manage sprung and unsprung mass
behavior over road irregularities. Again, both compression and extension matter.
3) Keep compression and extension damping in reasonable proportion to each other. At most
absolute velocities, extension damping should be at least a little stiffer than compression
damping, but usually not more than twice as stiff and never more than three times as stiff unless
you are deliberately trying to make the car jack down.
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This relatively brief discussion will inevitably not have covered all possible situations, but hopefully
it has covered the main principles, and illustrated a useful way to think systematically about springs,
anti-roll bars, and shocks. Evaluate effects of a change in terms of whether it adds to or diminishes
extension force at the corner you’re changing, then imagine the car on the scales and imagine you
are adjusting the extension force the same direction with the spring seat or jacking screw, and you
can predict the change’s effect on car behavior.
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July 2003
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
RIGHT REAR SPRING STIFFEST?
I frequently watch the pre-race shows for NASCAR events and listen carefully when they are
speaking of setups. Two times now in the past year they have spoken about the stiffest spring on the
whole car being the right rear. One crew chief asked a former driver if he ever thought he would see
the day that was the case. The driver said he had won many a race with the right rear being the
softest spring, and that has been the case with my experience as well. They spoke further to say that
the trend now was for the younger former open wheel drivers to run off the right rear tire. Physics
to my knowledge haven’t changed. Are they running extremely heavy front bars and super light
springs, or what gives? I thought the jounce bumper trend had been made illegal. Are their ways of
thinking something we local drivers could apply to our cars for an outside-the-box thinking
advantage?
At the risk of disillusioning my legions of admirers, first let me confess that I do not have throngs of
Winston Cup crew chiefs and engineers climbing over each other to tell me their setups. I’ve worked
with just a few, and a few get this newsletter. However, maybe I can be of some help, and if I say
anything wrong, maybe I’ll get straightened out.
Traditionally, the most common approach to spring splits has been to run the front end right-stiff and
the rear end left-stiff. This usually makes the right front the stiffest spring and the right rear the
softest. I never really understood that approach, and I have generally advised either running rightstiff or left-stiff at both ends, except perhaps in cases where the rear end lifts under power – a
condition normally only seen in dirt cars.
Two main considerations determine whether we run the car right-stiff or left-stiff: cornering balance
when forward and rearward accelerations accompany cornering, and adapting the car to the banking
angle of the track. Taking the former of these first, when a car has different amounts of pitch
resistance on the right and left sides, and the tires are accelerating the car forward or rearward, the
diagonal percentage changes. If the car is right-stiff, that tends to make the diagonal percentage
increase in rearward acceleration (braking) and decrease in forward acceleration. That tightens entry
and loosens exit. If the car is left-stiff, that does the opposite: frees up entry, tightens exit.
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Regardless of banking angle, stiffer right springs add roll resistance. However, if the track is banked
enough so that the left springs compress (I don’t mean more than the right ones, just compress rather
than extend), we actually increase the roll resistance with softer springs, on the left side only. This
means that with soft left springs, we can make the left wheels more compliant over bumps, and
improve camber control by reducing roll, at the same time. This is in contrast to our usual dilemma
of having to stiffen up the suspension to control roll and camber change, at the expense of
roadholding.
On a short track, with tight turns, especially on dirt, it is most common to have trouble getting the car
to turn readily enough on entry, and to have trouble hooking up the rear tires on exit. If this is a
problem, that argues against right-stiff springing. But on high-speed tracks, it is common to want to
tighten entry. The driver is going in as deep as possible, and braking hard while cornering, from
speeds as high as 190 or even 200 mph. It may take as long as ten seconds to complete the turn, and
the car is following a very large-radius path. We don’t want to achieve large yaw accelerations then.
The need is for a car that doesn’t want to come around when braking and cornering at the same time.
On top of that, the front ends on stock cars generally lose anti-dive rapidly as the suspension
compresses, because the side view projected control arm is shorter for the lower control arm than for
the upper. This means that when the car is rolled to the right, anti-dive asymmetry de-wedges the car
when braking, unless the right front has a lot more anti-dive than the left front at static position.
Right-stiff springing helps compensate for this.
It is possible to tighten entry by using lots of front brake. However, if the turns require significant
braking, using lots of front brake overworks the front brakes. As the front brakes go away, the brake
bias shifts toward the rear again. Also, we really would like to set the brake bias for shortest stops,
which means we want the rears to do around 30% of the work. If we run more than 70% front brake,
we hurt the car’s ability to stop quickly for pit stops, and to brake well when avoiding accidents on
the track. Therefore, it’s best to get the desired entry balance with the suspension.
What about exit balance? On a short track, we are often fighting to get the car tight enough, to
control wheelspin. However, even on a short track it is possible to get exit too tight, and have a
power push. At high speed and with steep banking, it is harder to get wheelspin. Cup cars do have
stout motors, but they also have ample tire loading from the banking and the aero, and a lot less
torque multiplication from the gears than they would on a short track. It is therefore not uncommon
for the driver to report a “push-loose” condition. That means the car is basically tight power-on, so
the driver feeds in more power trying to get it loose, but this doesn’t happen until power is sufficient
to really cause wheelspin, whereupon the car goes wheelspin-loose. The driver then has a hard time
finding a stable point where the car has good balance. In this situation, if the car is freer power-on,
the driver can find good balance at moderate throttle.
We see an analogous situation in road racing or short-track racing in classes like Formula Ford or
pavement mini-stock, where the car has good grip and modest power. Such cars often want a freer
setup than more powerful cars would, to get proper exit balance.
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Are soft front springs and stiff anti-roll bars still favored since bump rubbers have been outlawed?
Yes. The springs can’t be as soft as when bump rubbers were legal, but it is common to run the front
end as soft in ride as is possible without the rubbers. This soft ride rate makes the front end run lower
through the turns. That adds aero downforce. This will work on a short track too, though the effect
will be less pronounced. One might think we could do the same thing by running a lower static ride
height, but stock car racing rules usually include a minimum static ground clearance.
In the August 2001 newsletter, I addressed the subject of things that make spring changes work
backwards. I introduced the term critical angle to describe the track banking angle at which the left
spring neither compresses nor extends. This angle is usually not identical for both ends of the car. At
angles steeper than critical, effects of left spring changes reverse, for the end of the car in question.
Running soft springs and a stiff bar reduces critical angle. The left spring will compress rather than
extend at surprisingly small banking angles. (Putting it another way, with the soft ride rate, the entire
front end will drop more on the banking.) That means a softer left front spring tightens the car. This
is neither a disadvantage nor an advantage, just something to be aware of when running such setups.
Regarding the suggestion that the young drivers come from open-wheel racing and therefore like to
run a stock car with the right rear tire heavily loaded, I question that.
First of all, it may be true that some drivers are getting seat time in sprints and midgets – Jeff Gordon
and Tony Stewart for example – but the most common road to Cup is through lower pavement stock
car divisions: NASCAR Weekly Racing Series, USAR Hooters Pro Cup, ARCA, ASA, Busch. It is
normal for young drivers to spend time in these series before transitioning to Cup. And not all
drivers who do well in sprints and midgets are able to run well with a stock car. Some do, some
don’t.
As you correctly note, no laws of physics have been repealed. A stock car doesn’t have 60% rear and
a huge right rear tire, or a big rear wing. If you make the right rear carry a lot of load when cornering
in a stock car, you get a loose car. Driver preferences on car balance vary, but only within a narrow
range. Nobody likes a car that’s way loose at 150+ mph. Also, the car has to be fairly neutral to
avoid having a tire wear problem.
But you can’t necessarily conclude that the right rear is more heavily loaded just because the spring
is stiffer. Other things being equal it would be, but other things don’t have to be equal. If you
combine a stiffer right rear spring with more static diagonal, a bigger front anti-roll bar, or a lower
Panhard bar, you can compensate for the effect of the spring and load the tire about like you were
loading it before.
Of these different possibilities, the one that looks most appealing to me is running more static
diagonal. If we do that, then when grip is poor and lateral acceleration is less, the springs have less
effect on wheel loading and the static loadings have more influence. That means the car loads the
right rear less, and runs tighter. When grip is good and lateral acceleration is greater, the spring
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affects wheel loadings more, so right rear loading is greater and the car runs looser. This means that
with more right rear spring and more static diagonal, the car will have less tendency to go loose on
slick, as stock cars have traditionally done. With enough rear roll resistance and static diagonal, a
stock car can even be made to go tight on slick. Between these extremes, we can find a setup whose
balance varies relatively little with changes in the condition of the track or the tires.
I have clients successfully applying this reasoning on dirt and pavement short tracks, although
generally the added rear roll resistance is achieved without a right-stiff spring split, except in cars
that lift the rear under power.
INFLUENCE OF PUSHROD ANGLE ON WHEEL RATE
I would like to know how to calculate vertical stiffness and roll stiffness taking into account the
angle of the pushrods. I have seen lots of formulas but none of them take into account the pushrods.
Also, how do I calculate the total roll of the car starting with the difference in movement between the
wheels?
Taking the second question first, take the difference between the right and left wheels, and divide by
the track width. The quotient is the tangent of the roll angle, so you find the angle that has that
tangent. As an equation:
r = tan-1[(hl-hr)/T]
where:
r = roll angle
hl = left ride height (average of front and rear)
hr = right ride height (average of front and rear)
T = track width (average of front and rear)
Now, as to the angle of the push rods, you need that if you want to calculate stresses in the pushrods.
But to calculate wheel rate in ride or roll, you just need to know the motion ratio from the spring to
the wheel. Everything in between – the pushrod, the rocker, the control arm – only matters to the
extent that it influences the motion ratio. The pushrod angle does affect the motion ratio, but it is just
one factor. For an existing car, the easiest method is to simply measure how much the spring
shortens or lengthens for an inch or centimeter of wheel motion. For a car that’s in the design
process, if you’re designing on a computer, you can move the wheel and measure the spring length
on the computer. If you’re drawing manually, you basically do the same thing by hand and estimate
the motion ratio.
Once you have the motion ratio, square it and multiply by the spring rate, and you have the wheel
rate in ride. Then do the same for the anti-roll bar, which may have a different motion ratio. Add the
rate from the anti-roll bar to the wheel rate in ride, and that’s the wheel rate in roll. Be sure that when
figuring the rate of the anti-roll bar, you calculate the pounds or Newtons per inch or millimeter per
wheel – that is, the force change per unit of opposite motion on both wheels, not just one.
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August 2003
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
LOAD TRANSFER BASICS
I am a bit confused regarding the subject of load transfer. I have always thought that the load
transfer in a curve should be maximized (if tire wear is not an issue), and that one will achieve that
by stiffening the suspension.
Now I have met people saying that load transfer should be minimized and the reason is that you want
as near the same load at all tires as possible – claiming decreasing tire friction with increasing load.
Okay, a softer suspension gives more grip, I know, but how come you run faster with a stiffer setup
(to a certain limit).
I have also met people saying the opposite is the truth. By softening the suspension, the CG moves
more towards the outer side in roll, and therefore more load will be transferred to the outer side.
Sounds reasonable, but isn’t it so that the shocks have a role here, absorbing energy?
Another point of view from a well renowned man is that you will always have a certain amount of
load transfer at a constant speed in a constant-radius turn, no matter the chassis setup – the thing is
to find the balance front to rear. Okay, I fully accept that, but what is the importance of the general
stiffness of the setup then? Why are we bothering at all about roll centers, cambers, springs, and
anti-roll bars?
Can you please enlighten me (and probably many more) what is happening when load transfers, and
what it is we want to achieve? Can you please also discuss how this applies to different types of cars
and the differences in thinking regarding suspension design and setup?
This is not exactly the first time the subject of load transfer has been addressed, even by me. In fact,
the April/May/June issue dealt with the influence of springs and dampers (shocks) on load transfer at
considerable length. So by addressing the basics of the subject now, I’m doing things backwards. But
the question above came in recently, reminding me that the whole world hasn’t been reading my
newsletter like a textbook, and the newsletter cannot have the logical progression of information
from issue to issue that a textbook has from chapter to chapter, and still respond to questions.
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So we will tackle the basics of load transfer this month. Hopefully, those readers who found the
April/May/June discussion a bit over their heads can read this, and then read April/May/June and
have it make more sense.
For simplicity, I will ignore aerodynamic factors, even though these are often highly significant.
Let’s also consider pure steady-state cornering only, for now, and assume that the turn is unbanked.
I share the preference for calling what we’re discussing load transfer rather than weight transfer.
Actually, if we are considering an unbanked, level turn, and we’re ignoring aero, then the total tire
loading really is due to gravity acting on the car’s mass, and therefore is weight. Any transfer of this
load can then legitimately be called weight transfer. However, since the terms weight and mass tend
to be confused, and used interchangeably in informal discourse, “weight transfer” suggests that the
change in tire loads is primarily due to movement of the center of gravity, or center of mass, relative
to the tire contact patches – and that is not mainly what’s going on, although it is a small factor.
What is mainly happening when load transfers is this: The tires are generating a horizontal force
(toward the center of the turn, called centripetal force) at ground level. This produces an acceleration
of the car (toward the center of the turn, called centripetal acceleration). The car resists this with an
inertia force (centrifugal force) which acts horizontally at the center of mass, in the opposite
direction to the tire force.
These two forces are equal and opposite, but their lines of action are offset. The sum of the tire
forces acts at ground level; the inertia force acts at CG height. We therefore have a couple: a torque
or rotational force due to the offset lines of action – equal to the force times the offset: the
centrifugal force times the CG height. This torque acts about an axis lengthwise to the car, so it tries
to move the car in the angular mode we call roll. It is therefore called a roll couple. It acts opposite
to the direction of the turn: in a left turn, it tries to roll the car to the right.
Short of the point of rollover or wheel lift, this couple is resisted by an antiroll couple which takes
the form of a load increase on the two outside wheels and an equal load decrease on the two inside
wheels. Essentially, the ground pushes up harder on the outside wheels, and less hard on the inside
wheels, in response to the way the tires are pushing down on it, and exerts a counter-torque on the
car that keeps it right side up. The load change on the inside or outside wheel pair, times the track
width, has to equal the centrifugal force times the CG height.
So the person who told the questioner that suspension design and setup have no effect on total
amount of load transfer is basically correct. The important factors are CG height, track width, and
the amount of centrifugal force. It is true that when the vehicle rolls, the CG moves a little bit toward
the outside wheels. Therefore, softening the suspension increases load transfer slightly, and
stiffening the suspension reduces load transfer slightly. However, for cars these effects are small. For
tall vehicles such as trucks, CG movement is somewhat more important. For trucks with cargoes that
can shift or slosh, CG movement can become highly significant.
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So the questioner’s idea that stiffening the suspension increases load transfer is incorrect – as it
relates to TOTAL load transfer. But it’s correct as it relates to the front or rear wheel pair’s share
of the total.
The anti-roll couple we mentioned is actually the sum of two anti-roll couples – one from the front
wheels, one from the rears. These two couples are not necessarily equal. The front and rear tire pairs
split the job of resisting roll according to their relative roll resistance: the stiff end sees a greater
share. In considering the roll resistance, we need to include both the springs (anti-roll bars are
interconnective springs) and the suspension geometry.
In steady-state cornering, on a smooth surface, the suspension is not in motion, so the shocks, at least
theoretically, have no effect on load transfer. For a more detailed discussion of the effects of springs
and dampers on load transfer, see the April/May/June 2003 newsletter.
Now, is lateral load transfer beneficial or harmful to cornering (centripetal) force capability? The
questioner correctly notes that the answer to this is directly dependent on how friction varies with
load.
Does friction decrease with load? No, it increases. But the coefficient of friction decreases with load.
The coefficient of friction is the ratio of friction force to normal (road vertical) force – how many
pounds of cornering force we can get from the tire, per pound of loading.
According to the classical model of Coulomb friction, which models sliding friction between hard,
dry, clean, smooth materials, the coefficient of friction is a constant for any given pair of materials.
The friction force is directly proportional to load. For many situations, the Coulomb model is fairly
accurate. However, tires and roads do not conform to this model. This should not be too shocking,
since neither the tire nor the road is smooth and hard. The road is generally hard compared to the
tire, but it isn’t generally smooth. It is gritty, like sandpaper. The tire may be smooth, but it isn’t
hard. It is soft enough to conform to the road’s gritty surface, and interlock with it. It is tough,
meaning it resists being torn apart. If it is a racing slick, it may actually be tacky, meaning it sticks to
a smooth surface even in the absence of sustained normal force.
Moreover, a tire is not a rigid structure; it is a flexible – but not totally limp – bladder, carrying an
inflation gas under pressure. This means that the macroscopic, or visible-scale, size of the contact
patch increases with load.
These factors make it very difficult to mathematically model a tire’s behavior. That hasn’t kept
people from trying, but any equation that seeks to express the relationship between tire loading and
limit cornering force will not only be complex, but must necessarily include values for the particular
tire that can only be determined by test, because whatever the relationship may be, it isn’t the same
for all tires. Therefore, it is impossible to accurately know the relationship between loading and
cornering force without testing. And any equations seeking to describe tire behavior must be
developed by fitting curves to experimental data, rather than predicting behavior from abstract
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theory. And if this weren’t enough, tire properties vary with temperature, tire age, camber, inflation
pressure, and of course the road surface – which also has properties that vary with the weather, the
age of the surface, how much rubber and oil have been deposited, and so on. To avoid the effects of
real-world road surfaces and weather, tires are now tested indoors, under fairly careful climate
control, against belts or drums rather than roads. This is a valid necessity if we want to meaningfully
test one tire against another, but it is important to remember that tire behavior in the real world is
much more variable than tire behavior in a controlled environment.
Fortunately, it is much easier to look at trends in tire behavior than to predict precise numbers. And
one trend that all tires exhibit is that the coefficient of friction decreases with load. It may decrease
rapidly, or almost imperceptibly. It may decrease very little at light loads, and more rapidly at greater
loads. But it always decreases with load. This property is termed load sensitivity of the coefficient of
friction, or just load sensitivity for short.
This means that a pair of identical tires has the greatest cornering capability when loaded equally,
and as we load the outside one more and the inside one less, we lose cornering capability. It’s not
that the outside tire loses friction force. The outside tire gains grip – but the inside one loses grip at a
greater rate, so the total decreases.
Some writers contend that there are times or conditions where load sensitivity reverses. Some say it
reverses on dirt, some say just on dry-slick dirt, some say on snow or ice, some say when the tire is
cold, some say during corner entry. I don’t believe any of these theories myself. If load sensitivity
worked backwards, the car’s responses to roll stiffness adjustments and static corner weight
adjustments would also reverse, and I have not encountered this – except in situations where there
was clearly some explanation other than reversal of load sensitivity.
Now, if load transfer in cornering does not depend significantly on overall suspension stiffness, why
does overall stiffness of our setup matter at all? It matters for other reasons than load transfer:
control of camber and aerodynamics, ability to absorb road irregularities, how high we have to set
the static ride height.
A stiff setup reduces camber changes, particularly with independent suspension. It reduces changes
in the car’s roll and pitch angles, relative to the airflow and relative to the road. It allows the car to
run with a lower static ride height, without bottoming excessively. It makes the car more responsive
to driver inputs.
A soft setup allows the wheels to follow bumps better. Loads on the tires vary less, and they spend
less time airborne. The tires often heat up more slowly, and wear less. The car and the driver don’t
get beaten up so badly by the bumps, improving endurance of both car and driver.
So overall stiffness has to be a compromise that balances these conflicting factors in a manner
appropriate to the conditions, while relative stiffness of the front and rear suspensions manages load
transfer distribution.
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September/October 2003
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
SHOCK RESEARCH UPDATE
Regular readers will recall that I am coordinating an effort to investigate sensitivity of dampers to
factors other than velocity, including acceleration and jerk. I still have a long way to go on this, and
am still seeking persons to contribute shocks for test, especially shocks that dyno similarly in
standard crank dyno testing but behave differently on the track.
I have been able to learn a little already, however, and I would like to relate these findings.
When I look at dyno output for a shock, I like to look at a force-versus-absolute-velocity trace for the
full stroke: both the rebound-closing/compression-opening (extended) end and the compressionclosing/rebound-opening (compressed) end. Such a trace will have two “noses” or points at the left
side of the graph, each having its vertex at the zero-velocity point. Another way of displaying the
information is a force-versus-velocity plot. This will generally take the form of an S-shaped loop,
which will cross the zero-velocity line at two distinct points. The force-versus-absolute-velocity
trace is just the force-versus-velocity trace, with the negative-velocity part of the trace folded over to
the positive side because the velocities are being expressed as their absolute rather than signed
values.
Almost invariably, the zero-velocity point for the cc/ro trace will be higher (indicating greater
extension force) than the rc/co trace.
When the shock is cycled very slowly, if it has any bleed or leakage at all past the piston, and
especially if we hold the shock stationary at the ends of the stroke and let the force readings stabilize,
we will get a reading of the gas spring effect. We should expect the two nose points to be separated
by this amount even in the absence of acceleration sensitivity or other effects.
The appearance of a loop-shaped force-versus-velocity trace has led some writers to call the effect
hysteresis. This may or may not be strictly correct, depending on exactly how we define the term,
and how meticulous we want to be. My Webster’s dictionary defines hysteresis as “a retardation of
the effect when the forces acting upon a body are changed (as if from viscosity or internal friction)”.
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My dictionary traces the etymology of the word to the Greek verb hysterein, meaning to be late or
fall short.
How does this relate to what dampers do, or to what we’d like them to do? I think it’s pretty safe to
say that we want a damper to generate a force opposing motion of the suspension at all times. How
big this force should be, in what circumstances, is less certain. But we can at least say that if the
damper is generating a force in the same direction as the system is moving, the damper is
exaggerating motion rather than damping it, for as long as this state of affairs prevails. A suspension
system in such a condition is sometimes said to be self-exciting, which is the opposite of damped.
I am not saying that damper opposition to motion is always optimal for roadholding – merely that
this is what damping means. And the shock, being a passive mechanical device, cannot be expected
to know when damping is desirable. All we can reasonably expect a damper to do is damp motion,
and do so in some consistent manner with respect to velocity, acceleration, and jerk of its sprung and
unsprung elements.
Note that motion, force, and force change are different from each other. Actually, viscosity does not
always retard response to a change in force as the dictionary’s language would suggest. Sometimes it
exaggerates response to a change in force – so even my dictionary doesn’t make perfect sense. For
example, suppose we have a system damped by an ideal viscous fluid (totally incompressible and
non-volatile). Suppose the system is in motion, and the force moving it is diminishing or reversing,
and the motion is slowing. The damping force will oppose the motion, and therefore hasten the
slowing – meaning the viscosity is actually hastening response to the force change, not retarding
response.
So when we discuss the meaning of “hysteresis”, we confront a situation where even those charged
with defining the term have an imperfect grasp of the phenomena the term attempts to describe. Does
hysteresis mean damping? If we’re talking about rubber, it does. Does it mean a response lag in
damping? Maybe, as some people apply it to shocks. But clearly then it does not mean damping. It
may even imply temporary absence of damping, or anti-damping – behavior more like a spring than
a damper. But would we speak of an ideal spring (no self-damping or non-linearity) as having
hysteresis? Not ordinarily.
Engineers tend to think of hysteresis as anything that produces a loop-shaped data trace when a
system is subjected to forced oscillation. But of course the meaning of this will depend on what
variables we’re plotting. The earliest shock dynos generated a force-versus-displacement plot. For a
damper that’s working reasonably well, this will always be a loop, typically shaped something like
an egg, and sometimes called an egg plot. More modern dynos, including crank dynos with
continuous computerized data acquisition, can also produce an egg plot.
Looking at such a plot, we may say we’re seeing a hysteresis loop. A shock is supposed to have
hysteresis in this sense. It won’t do its job if it doesn’t.
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An ideal spring should produce a force-versus-displacement plot that’s a straight line – or actually
two straight lines, overlaid.
A spring is not a velocity-sensitive device, but in a sinusoidal test, we have a fixed relationship
between velocity and displacement. Therefore, we know the velocity at any given displacement, and
we can create a force-versus-absolute-velocity trace or a force-versus-velocity trace based on that.
For an ideal spring, the force-versus-absolute-velocity trace will be half of a sine curve, stood on its
side, or an arcsine curve for half a period – or, more precisely, two such traces, overlaid. That trace
may be regarded as having two “noses” at the zero-velocity line or vertical axis, rather like what we
see with many shocks. The force-versus-velocity trace will be the same, only with the negativevelocity trace folded over to the left side of the vertical axis instead of overlaid on the positivevelocity trace. That gives a loop-shaped trace, resembling an ellipse, although mathematically not a
true ellipse.
So an ideal damper, with nothing in it that acts like a spring, produces a loop-shaped force-versusdisplacement trace, and produces a force-versus-velocity trace that is not a loop but rather two curves
overlaid. Its force-versus-absolute-velocity plot is likewise two traces overlaid. The force-versusvelocity and force-versus-absolute-velocity plots have only one zero-velocity point.
Conversely, an ideal spring produces no loop in its force-versus-displacement trace, but produces a
big loop in its force-versus-velocity trace, and two widely-spaced noses in its force-versus-absolutevelocity trace, which is two traces overlaid.
A device that acts as both a spring and a damper will produce loop-shaped traces for both forceversus-displacement and force-versus-velocity. Other effects may also produce a loop-shaped forceversus-velocity trace.
In an automotive suspension damper, we can get spring effects from both the gas spring and other
compliances, primarily compressibility of the fluid.
What we see when testing some – but not all – shocks is that the noses are separated by a greater
amount than gas spring effect alone can account for. We also sometimes see that the nose separation
tends to increase as the valving gets stiffer. This is particularly easy to see when dynoing certain
adjustable shocks at a series of settings: as you stiffen the damping, the noses spread further apart.
Also, in some cases, the noses spread further apart when the shock is cycled faster, with stroke
unchanged. In such a case, we are looking at an unchanged shock, but greater velocities,
accelerations, and jerks.
What my collaborators have done to date is to test single-tube, deflective-disc shocks at twice the
usual frequency and half the usual stroke (1” stroke, 3.2 Hz rather than 2” and 1.6 Hz), and also test
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them upside down. So far, these tests have not been done on shocks with other types of valving, or
on low-pressure, twin-tube gas shocks.
The results have more or less confirmed what the appearance of a deflective-disc valve suggests: this
type of valving is not highly acceleration-sensitive. The discs do have some inertia, of course, so this
was not entirely a foregone conclusion.
When a typical stock car shock, with reasonably soft valving and some bleed, is tested upside down,
the forces it generates do not change noticeably. When the shock is body-up, as it’s usually installed,
the piston and discs are subjected to accelerations. When the shock is body-down, the body moves
instead, and the piston and discs have a constant velocity of zero – therefore no acceleration or jerk.
When the shock dynos the same both ways, that implies that, at least within the range of
accelerations present in the test, the shock is not acceleration-sensitive.
Also, when typical stock car shocks are tested at half the stroke and double the frequency, that
generally does not have much effect on the forces. Compared to the standard test, this test produces
identical velocity at any given crank angle or point in the cycle, but twice the acceleration and four
times the jerk. The lack of much effect on forces in this test suggests that, at least for relatively
moderate acceleration and jerk values, the shock is a predominantly velocity-sensitive device.
The finding that many dampers are not truly acceleration-sensitive is not a setback. The important
thing is that we have a test for this, and therefore we can separate true acceleration sensitivity from
other effects that may make a damper act different at the compressed and extended end of its stroke,
and act different when cycled at differing speeds or adjustment settings. I would like to explore some
such effects here.
I am adding some six shock dyno graphs to this newsletter. Three of them are on pages 6, 7 and 8.
The other three are separate attachments. These last three are Adobe pdf files. You will need Adobe
Acrobat to open them. An Adobe Acrobat reader is available free at www.adobe.com.
The first two plots are from a mountain bike shock used on a Formula SAE car. This is a deflectivedisc shock. It has relatively little bleed, judging by the lack of a soft, progressive region at low
absolute velocities. This shock is adjustable, and the plots are for a soft setting on both compression
and extension, and a stiff setting on both compression and extension. The test is the same in both
cases: 1” stroke, 200 rpm. This shock is so small that it can’t be tested at 2” stroke and 100 rpm. It
doesn’t have 2” of stroke. Consequently, the only way to get the absolute velocity up to the 10 in/sec
customary in race car shock testing, using a crank dyno, is to turn the crank faster than customary.
The first two pdf files are from Bilstein stock car shocks, with valving codes 5030 and 7030. Plots
were furnished by Bilstein’s Mooresville, North Carolina facility. These are full-size, non-adjustable
shocks, also with deflective-disc valving. I chose these for comparison with the mountain bike shock
because they generate roughly similar forces around 4 to 5 in/sec, but they have much more piston
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area (hence lower working pressures) and more bleed, as indicated by the relatively soft and
progressive behavior at low absolute velocities.
Now consider the zero-velocity points on these four plots. The ones on the soft mountain bike and
soft stock car shock are separated by very similar amounts: about 20 lb. However, the zero-velocity
points on the stiffer stock car shock are separated by about 30 lb., while those on the stiff mountain
bike trace differ by at least 130 lb. The spread on the small shock with high working pressure and
little bleed grew much more as the damping was stiffened.
The third pdf file is from an 8060 Bilstein. It is stiffer at 4-5 in/sec than either of the two mountain
bike calibrations shown. Yet it also shows relatively little spread at the zero-velocity points. Big
piston; substantial bleed; still not much spring-like behavior.
The plot on page 8 is from a correspondent at Bilstein’s Australia headquarters. It shows a shock of
specifications unknown to me, tested two different ways with no changes to the shock. The Bilstein
8060 appears to be similar, although perhaps a bit softer at high speeds. The 8060 is considered a
stiff shock by stock car standards, so the Australian shock is definitely stiff by stock car standards.
Yet the progressive character at low speeds suggests it has similar bleed and preload to the 8060.
The plot from Australia is different from what most Americans will be used to looking at, in two
obvious ways. First, the sign conventions for the velocity are reversed. (This is because the dyno is
in the southern hemisphere and therefore upside down – no, not really; it’s because these sign
conventions are arbitrary and the choice is up to the dyno manufacturer.) Second, the units are
metric. Handy conversion factors:
1” = 25.4 mm
1 mm = approx. .04 in
100 mm/sec = approx. 4 in/sec
200 mm/sec = approx. 8 in/sec
300 mm/sec = approx. 12 in/sec
400 mm/sec = approx. 16 in/sec
500 mm/sec = approx. 20 in/sec
1 Newton = approx. .225 lbf
1 lbf = approx. 4.45 N
1000 N = approx. 225 lbf
2000 N = approx. 450 lbf
3000 N = approx. 675 lbf
4000 N = approx. 900 lbf
5000 N = approx. 1125 lbf
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I am told that the Australian shock was tested at the same stroke, at two different rpm’s. The smaller
trace appears to have been done at 30% the speed of the larger one. Applying the above conversion
factors, if the stroke was 50 mm, which is close to the 2” common in shock testing, the rpm’s would
have been about 60 and 200. So compared to the standard 2” stroke, 100 rpm test, we are looking at
a considerably lower-speed test, and one about twice as fast.
In the low-speed test, the trace shows almost no spring effect. We very nearly have two identical
traces overlaid – hardly a loop at all. The medium-speed 8060 test, shown in force-versus-velocity
format, would be only slightly more of a loop. But double that speed, with more high-speed damping
thrown in, and we see a really fat loop. This indicates that even a shock with generous piston size
and significant bleed starts to act like a spring if the speeds and forces get high enough.
Okay – what conclusions can we draw? One would be that when we set out to investigate a
particular phenomenon, we may stumble upon others we weren’t looking for. Nothing new here;
many of the greatest discoveries in science were accidentally made this way.
Another is that end-of-stroke phenomena include not only acceleration sensitivity but effects related
to entrapment and compressibility of the damping fluid – and possibly some deflections of other
components. These effects are not readily separable from acceleration sensitivity, although testing
the shock upside down can tell us quite a bit. Of course, not all shocks can be tested upside down.
Finally, it appears that it is highly desirable to be able to create tests that vary acceleration and jerk
in mid-stroke, without altering velocity. This will involve exploiting the capabilities of recently
introduced linear-motor dynos.
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CLRL
150
100
50
0
-15
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5
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Force (lbs)
-50
CLRL
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CHRH
200
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CHRH
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9
Force vs. Absolute Velocity
500
Thursday, February 21, 2002 8:07:02 AM
-400
-300
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Force vs. Absolute Velocity
500
Thursday, February 21, 2002 8:40:16 AM
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Force vs. Absolute Velocity
500
Thursday, February 21, 2002 8:42:10 AM
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Velocity (Inch/Sec)
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November 2003
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
NEW VIDEO
I am pleased to announce that I now have videos available of the presentation I gave at UNC
Charlotte this past March. The one-hour lecture is entitled “Minding Your Anti: Understanding
Factors in Load Transfer”. It deals with the origins of load transfer and presents a “force-based” or
“lateral anti” approach to the notion of roll centers. This is original and very current thinking on the
matter, and not to be found elsewhere. Videos are single VHS cassettes, and sell for US$50.00. This
price includes shipping to any destination, worldwide. North Carolina residents please add 7½ %
($3.75) sales tax.
WEIGHT DISTRIBUTION AND TIRE SIZE
At what point is it worthwhile to install wider wheels and/or tires on the back of a rear-wheel-drive
car – specifically if the car has close to 50/50 front/rear weight distribution? Directly related to this
point, I often wonder: why is it that an F1 car can brake so much more rapidly than it can
accelerate, even though the front tire contact patches are smaller?
The basic rule of thumb is that tire size should be roughly proportional to tire loading, assuming we
are talking about a car that has to corner well. So if the rear percentage is close to 50%, the tires
should be equal size, and if the weight distribution is 40/60, the rear tires should be half again as
wide as the fronts. Ordinarily, we go by tread width for this, rather than overall width at the
sidewalls. Of course, the rule is only an approximation in any case.
The rule gives us roughly optimal values for steady-state cornering. That may not be the only thing
we’re trying to get the car to do well, but it’s certainly important in most cases.
In many cases, we do not have a free choice of tires or tire sizes. Often, our task is to optimize the
car for the tires, rather than the other way around. With race cars, our tire sizes are usually limited by
the rules. For street cars and some race cars, we may be constrained by the fenders. In many
production cars, if we just put the biggest tire at each corner that will fit without hitting the fenders,
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we end up with the rears bigger than the fronts. This is partly because the rears don’t have to steer,
and partly because it is usual to allow for snow chains on the rears, with equal size tires.
Other practical constraints may intrude as well. I have an old Chevy Impala station wagon that
serves as both my transportation and my bedroom. When I first got the car, I set it up with 8” wheels
with ½” offset all around, a rear anti-roll bar, and a much stiffer front anti-roll bar than stock. The
car was fun to drive, cornered quite flat, and was well-balanced. Only trouble was that it kept
breaking front a/r bar links and other a/r bar hardware, and I couldn’t keep front wheel bearings in it
for more than 10,000 miles. I could have put a full racing front end in, but this is an old, beat-up car
that I don’t want to put huge amounts of money and time into. So I went to 7” wheels with zero
offset in front, a much softer front a/r bar from a sedan, and 8 ½” rear wheels with the same stiff rear
bar as before. The car is balanced this way too. It rolls more, but less than stock. The ultimate lateral
grip is less, but acceptable. And I don’t have to fix the front end all the time.
I help out a Formula SAE team. Sometimes they take my advice, and sometimes they don’t. They
have had a policy of doing their car in a single year, and making minimal changes from the previous
year’s car. One consequence of this is that many design elements get adopted simply as carryovers.
The team has been using wider tires in back, and the 2003 car had the same feature, despite my
urging the team to use the widest and biggest tires possible all around. The car has only 52% rear.
The rear tires have 58% of the tread width. We still managed to get balanced handling, by using
stiffer springs and anti-roll bar at the rear.
My point here is that in many cases tire sizes are chosen based on factors other than vehicle
dynamics theory – sometimes rationally, sometimes irrationally. And because cornering balance
depends on suspension as well as tires, a surprisingly wide range of tire size combinations can be
made to work acceptably on any given car.
Well, okay – but limiting ourselves to considerations of vehicle dynamics, why might we want
bigger tires on the rear, when the car is not markedly tail-heavy?
Depending on aerodynamic balance, higher speeds may argue for bigger rear tires, or alternatively
for more nose-heavy weight distribution. We know that a tire has limited capability for combined
lateral and longitudinal force. To get more longitudinal force from a tire, we sacrifice some ability to
generate lateral force. We speak of the traction circle, traction ellipse, traction perimeter, or traction
envelope, as a representation of the limiting values for the vector sum of lateral and longitudinal
force.
When somebody mentions steady-state cornering, we may think of a typical skidpad test, with
speeds somewhere in the 60 mph (100 kph) range. Throttle application to maintain this speed will
probably be fairly moderate, meaning the rear tires have a large percentage of their traction
envelope available for cornering. But we can also have steady-state cornering at, say, 150 mph (250
kph). Just to run that fast in a straight line requires a fair amount of power. Add the drag of four tires
operating near peak slip angle, and the car may need full power, or something close, just to maintain
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constant speed. And powerful cars can sometimes spin the wheels in top gear, in a straight line. So in
this situation, how much of our rear tire traction envelope do we have left for cornering? Not a lot,
unless the traction envelope was generous to start with (big tire). Or maybe quite a lot, if the car
generates sufficient rear downforce at high speed to compensate for the other effects. In a case such
as a NASCAR Cup car, both the tires and the aerodynamics (except for details) are dictated by the
rules, and we pretty much tune the suspension and the ballast placement around the tires and aero
package. The tires are required to be equal size at both ends, and for medium to high speed tracks,
the car likes around 52% front. To run more rear percentage, wider rear tires would be helpful. We
could run more rear, with equal tires, but we would be making less use of the left front tire, and midturn speeds would be lower.
We may want to run larger rear tires in search of greater forward acceleration. Any tire has an
optimum inflation pressure for making lateral force, and another, lower, optimum pressure for
longitudinal force. Consequently, if we have a car that’s balanced with equal size tires front and rear,
and then we install larger rears but run them somewhat underinflated for cornering, we still have a
balanced car, but it puts power down better.
We can take this a step further, and add roll resistance at the rear, reduce roll resistance at the front,
and further increase the tire size disparity. If we take this to an extreme, we have a car that is
optimized for drag racing, but also has acceptable cornering balance – although it isn’t really
optimized for cornering. The inside rear tire will be very lightly loaded when cornering, but with a
limited-slip diff, this may be acceptable. With a live axle rear, we improve the car’s launch at the
drag strip if we provide a very stiff wheel rate in roll at the rear and a very soft wheel rate in roll at
the front. This helps because driveshaft torque produces less change in diagonal percentage when the
car is stiff at the rear and soft at the front. We may disregard cornering completely in a car we only
race in a straight line, but even if we are concerned with balanced cornering behavior on the street, a
drag racing suspension setup will often call for larger tires in back. Note that this reasoning
regarding reduction of driveshaft torque effects does not apply with independent rear suspension,
where these effects are absent regardless.
Looking at the opposite end of the spectrum, IMCA-style modifieds, as raced in the US, may have as
much as 59% rear, or even 60% with a full fuel load, and they are required to run equal size tires
front and rear. In this case, we have a car that often runs on very slick dirt tracks, with tires that don’t
give much grip, and has lots of power. It needs the rear percentage to put power down. Even in the
turns, a large percentage of the cornering force is car-longitudinal drive force from the rear tires,
applied at an angle to the car’s direction of travel because the car is powersliding. To get decent
cornering balance in such a car, we have to make it corner on three wheels, or very nearly so. We
under-utilize the left front tire, but we accept this to get forward traction.
If we run the same car on pavement, we need to move ballast, and perhaps even the engine, forward
in the car.
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In answer to your question of why F1 cars achieve greater accelerations rearward when braking than
forward under power, even though the front tires are smaller than the rears, actually almost all
vehicles exhibit this property. The main reason is that we have brakes on all four wheels, but
propulsion on only two. A secondary reason is that drag, aerodynamic and mechanical, acts
rearward, so it assists braking but opposes propulsion. About the only way we could produce a
vehicle that accelerates faster forward than rearward would be to have no front brakes.
WIDTH VERSUS DRAG
I’m preparing an SCCA GT2 car (production car shape fiberglass body, tube frame). I have the
opportunity to increase the car’s width up to 4 inches, either by splitting the body or extending the
flares. I have always assumed that going with the widest width is best chassis-wise, to minimize load
transfer and maximize grip. However, I would think that at some point you lose more due to drag
than you gain from improved cornering. These cars don’t make much downforce, so I don’t think
there’s much gain there from building the car wider. Is there any way to calculate an ideal width?
As long as cornering is an important part of the game, the best approach will usually be to go for
greatest allowable width. This is particularly true when power is ample. Certainly, the drag does cost
you some speed on a long straight. But if you come out of the preceding turn faster, and you also
enter the following turn faster, you are faster not only through those turns, but also over the first and
last portions of the straight.
Width is a mixed blessing though, even for cornering. A narrow vehicle lets you take a better line,
especially if the turns are tight and the road is narrow. This is one of the main reasons motorcycles
are as fast as they are. Narrowness can be very important in autocross, especially for slaloms. A
narrow vehicle also can have an easier time passing other cars, which was the reason the FIA
narrowed the width limit for F1 cars a few years ago. But on most road courses, the cornering power
gained from a wide track width is worth more than the improved line and reduced drag with a narrow
track width.
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December 2003
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
RAISING MY RATES
For the first time in three years, I have decided to raise my hourly rate for consulting. The new rate
will be $50/hour, which is still reasonable compared to what other consultants have told me they ask.
Retainer rates will likewise go up proportionately. A month will be $300; a year will be $1500.
I was considering having the new rate take effect at the turn of the year, but what I’m going to do
instead is offer the old rate of $40/hour, and the corresponding $240/month or $1200/year for all
services paid for before March 1, 2004.
MORE ON RACING FRONT-DRIVE CARS, AND ON LOAD TRANSFER
Racecar Engineering based my column for the December 2003 issue on my March 2002 newsletter,
which dealt with some aspects of racing front-wheel-drive cars. Some readers have written in
response to this column, and one of the questions also relates to the basics of load transfer, the topic
of the August 2003 newsletter and November 2003 column.
I am a new (1 year) racer who bought a used VW Sirocco mini stock. We race on a slightly banked
¼ mile paved oval. The suspension is VERY stiff, and the right side springs are a higher rate than
the left. I do not know the rates, and I plan to install new springs this winter.
Two of the fastest fast guys at the track tell me they use soft suspension, and what perplexes me, their
right side springs are softer (by 100 lb.) than the left side springs. Their logic is that the inside
wheel will now carry more load as the car moves downward in the corner, therefore giving more
equal tire loading and less push on our FWD cars.
Does this make sense to you?
The reasoning doesn’t, but running softer springs on the right does, when the track is close to flat –
or at least for many cars it does.
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Having softer springs on the outside wheels does not reduce overall load transfer. If the turn is
slightly banked, and we are comparing setups with the same average spring rate, there will be
slightly more roll with a left-stiff setup than with a right-stiff one. Since roll slightly increases load
transfer, the left-stiff setup will actually have slightly more overall load transfer – but not by enough
to worry about.
On a perfectly flat turn, the car will roll about the same amount with a left-stiff setup of the same
average stiffness, but the right wheels will be better able to follow bumps – at the expense of the left
ones. Since the right tires provide more than half of the cornering force, it is worth more to have
them follow the road surface better.
There will not necessarily be less understeer (push) with a left-stiff setup, in steady-state cornering.
Now, if we were to take your car, which you say is relatively stiffly sprung overall, and we soften
just the right front spring, that will reduce understeer. If instead we soften just the right rear, that will
increase understeer. If we soften both the right front and the right rear, the effect on understeer will
depend on how much we soften each one.
If the track is banked modestly enough so that the left-side suspensions both extend in the turns, we
will also reduce understeer if we soften the left front or stiffen the left rear, and we will increase
understeer if we stiffen the left front or soften the left rear.
If the track is banked steeply enough so that the left-side suspensions compress in the turns instead
(the car still rolls rightward; the right-side suspensions compress more than the lefts), then the effects
of left-side spring changes reverse. More left front spring reduces understeer. More left rear
increases understeer. Effects of right-side spring changes do not reverse on steep bankings. They just
get bigger.
As we encounter steeper banking, it becomes easier to keep the inside rear wheel on the ground.
Recall that stiffening the rear suspension relative to the front reduces understeer, at least up to the
point where the inside rear wheel lifts. If the turns are banked, we can go much stiffer on rear roll
resistance, either with springs or anti-roll bars, before we encounter the limitation of wheel lift. This
is very important when racing front-drive cars on ovals.
One other effect of left-stiff springing is that it loosens the car when braking or decelerating, and
tightens it under power. This is true for both front-drive and rear-drive cars. So if you enter the turns
while slowing, as is usual in oval-track racing, the car will be freer (have less understeer) on entry
with a left-stiff suspension. And since a push, once initiated, tends to persist, a freer car on entry may
also be freer mid-turn.
One drawback to watch out for when pursuing this approach is that the car will be more prone to
inside front wheelspin on exit. This may or may not be a problem on your oval, with a small engine.
In road racing and autocross, or on a very small oval with tight turns, it is definitely a factor. I don’t
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know if your rules allow you to use a spool in that car, or if you are allowed to run a limited-slip. If
you are, then you definitely need to pay attention to front tire stagger. Your tire rules may or may not
allow you much choice of stagger, but the car will be sensitive to it. With a spool or limited-slip, a
larger tire on the right will help the car turn. With an open diff, you want a bigger tire on the left
instead.
Finally, be aware that the car is sensitive to static wheel loads, just like a rear-drive car. These work
about the same as they do in a rear-drive car. Less diagonal (RF + LR) percentage frees up the car,
just like stiffening the left rear spring or softening the right front.
SINGLE OR DUAL REAR BRAKES FOR FSAE?
I am a Formula SAE team member. As you know, some teams use one differential-mounted rear
brake disc and some use two discs mounted on the driveshafts or outboard on the wheels. I am
having a bit of a time rationalizing the idea of using one rear brake. I spoke to the Wollongong team
president at the ’03 Detroit event, and he explained that a single rear brake causes corner entry
understeer (bad for small-radius SAE courses!) by effectively “locking” the diff. You said basically
the same thing in the FSAE message boards. We are using the common Torsen 1 type diff. Does this
diff lock in the same way when applying a braking torque as if you were applying an acceleration
torque? Looks as if it would. I realize that a clutch diff could act differently under
brakingdepending on ramp angles.
Situation:
 Maximum torque bias ratio 80:20
 Diff mounted disc
 Car approaches corner. Brakes are applied. Enter left hand turn.
 Weight is transferred to front and to right side. Left rear wheel loses most of its normal load
and traction.
Will 80% of the braking force be sent to wheel with traction, while the wheel with low normal load
receives 20%? Does the unbalanced braking or the locked diff create the understeer, or is it both?
Now with 2 outboard mounted discs it is obvious that I will always have 50% available rear braking
force at each wheel (but different normal loads).
Is this correct? What equations can I use to calculate my braking force, or acceleration force
distribution through a locking diff?
P.S. Are you a design judge, and where can I get info on FSAE-sized cam and pawl diffs?
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Taking the last items first, a few people have talked with me about the possibility of my doing design
judging, but this has all been purely tentative. My understanding is that SAE is no longer even
paying expenses for judges, so the judges are actually taking a loss on the activity. I try to get paid if
I’m going to have to work.
The only ready-made diffs for FSAE that I know of come from either Quaife or Gleason. These are
both Torsen style. The UNC Charlotte team made their own in 2003, using Gleason gears. This was
done purely to reduce weight.
You could probably make a ZF-style clutch diff, with the ramps on the pinion shafts, but I think
you’d need to do the clutches and carrier yourself, and maybe use spider and side gears from a small
car. You could probably also make a Detroit locker style diff yourself, but you’d probably have to
make everything.
All things considered, I think it’s easier to make or find two small brakes instead.
Somebody may have some equations that describe the behavior of limited-slip diffs, but I don’t.
Even modeling the friction in these units at known speeds and forces is a bit tricky, because the
friction forces are a combination of Coulomb and viscous friction, in proportions that vary with load,
speed, temperature, and lubricant properties.
Not only that, the forces are history-sensitive! That is, to model or understand the unit’s behavior at
a specific instant, we need to not only know the speeds and input forces at that particular instant, we
need to know the events immediately preceding that instant. For example, suppose we have either a
clutch or a Torsen diff, with no preload. If there is no force on the diff, and we jack one wheel off the
ground, and apply rotation to the carrier, we just spin the airborne wheel, get no locking, and
transmit no torque to either wheel. But if the car is in motion, and the diff is transmitting torque, and
then one wheel gets airborne, there is torque on the diff, and therefore loading on the clutches or
worm gears, and therefore locking or friction in the unit, at the time the wheel goes airborne. That
means we will continue to transmit torque to the wheel that’s on the ground, as long as there is no
interruption of input torque.
Now, examining the situation you’ve posited, where we apply the brakes before a turn and continue
braking while initiating a left turn, with a single brake acting through a Torsen: First of all, yes the
diff does act the same when transmitting reverse (braking) torque. If the diff locking or transfer
torque is less than half of the brake torque, both rear wheels are retarding the car (exerting a
rearward force), but the torque on the outside wheel is half of the brake torque plus the transfer
torque, and the torque on the inside wheel is half of the brake torque minus the transfer torque. If the
transfer torque is large enough, it may exceed half of the braking torque. In that case we may have a
forward force at the inside wheel. In either case, in a left turn we have a rightward yaw moment due
to the diff locking effect, and this moment adds understeer.
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It is more common for the inside front tire to reach the limit of grip during trailbraking than for the
inside rear to do so. But if the inside rear locks, the outside rear is seeing whatever torque it took to
lock the inside rear, plus the transfer torque. In an FSAE car with a single rear brake and a Torsen,
there will be more transfer torque if there is continuous braking up to this point than if the brake is
applied with the inside rear already unloaded due to cornering.
With two rear brakes, the rearward force is equal on both rear wheels up to the point where the
inside one locks. If there is a limited-slip diff, there will be transfer torque. This may be very small,
or if there is substantial preload and engine braking, it may be considerable. Even with an open diff,
when one wheel locks, the braking forces are no longer necessarily equal on both sides of the car.
We can say with certainty that the force at the unlocked wheel is at least as great as on the locked
wheel, and possibly greater.
This also applies on the front wheels of a rear drive car, and the above remarks also apply to the
front end of a front-wheel-drive or four-wheel-drive car, and to the front end of a rear-drive car with
frictional device connecting the front wheels to prevent lockup and flat-spotting of the inside front
tire. In all of these cases, the presence of limited-slip or anti-lock transfer torque creates a yaw
moment that adds understeer.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
VIDEOS STILL AVAILABLE
I still have available videos of my lecture, “Minding Your Anti”, presented March 2003 at UNC
Charlotte. Price is $50.00, which includes shipping and handling worldwide. North Carolina
residents please add 7½ % sales tax.
RAISING MY RATES
For the first time in three years, I have decided to raise my hourly rate for consulting. The new rate
will be $50/hour, which is still reasonable compared to what other consultants have told me they ask.
Retainer rates will likewise go up proportionately. A month will be $300; a year will be $1500.
I was considering having the new rate take effect at the turn of the year, but what I’m going to do
instead is offer the old rate of $40/hour, and the corresponding $240/month or $1200/year for all
services paid for before March 1, 2004.
REVERSE ACKERMANN OR TOE-IN ON OVALS
I race stock cars and am from the old school of using about 1/8” toe-out. Recently, I’ve heard of
successful stock car racers using significant straight-ahead TOE-IN (e.g. ½” toe-in). And racers
who used to believe in running shorter steering arms on their left front spindle to get more
Ackermann are now doing the opposite to get reverse Ackermann. They are using tire steering
plates [turn plates] to adjust Ackermann and have the toe they want when the tires are steered, but
still use a very small amount of straight-ahead toe-out. It’s all related to tire slip angles, tire temps,
optimized handling, etc. I would appreciate a newsletter addressing this topic.
The December 2002 newsletter did address Ackermann a bit, more in the context of road racing. To
recap from that issue:
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There isn’t a universally agreed way to express how much Ackermann (toe-out increase with steer) a
car has. The closest thing we have is to take the plan-view (top-view) distance from from the front axle
line to the convergence point of the steering arm lines, divide the wheelbase by that number, and
express the quotient as a percentage. If the steering arms converge to a point on the rear axle line, that’s
said to be 100% Ackermann. If they converge to a point twice the wheelbase back, that’s said to be
50%. If they converge to a point 2/3 of the wheelbase back, that’s said to be 150%. If they are parallel,
that’s zero Ackermann. If they converge to a point twice the wheelbase ahead of the front axle, that’s
said to be –50%.
Supposedly, with 100% Ackermann, the front wheels will track without scuffing in a low-speed turn,
where the turn center (center of curvature of the car’s motion path) lies on the rear axle line in plan
view. This is actually not strictly true, even for the simplest steering linkage, which would be a beam
axle system with a single, one-piece tie rod. With either a rack-and-pinion steering system or a pitman
arm, idler arm, and relay rod or center link, we can’t fully predict what the Ackermann properties will
be at all, merely by looking at the plan view geometry of the steering arms. The whole mechanism
affects toe change with steer.
Even knowing what instantaneous toe we want in a specified dynamic situation is not simple. We don’t
necessarily want equal slip angles on both front tires. For any given steer angle, the turn center might be
anywhere, depending on the situation. All the infinitely numerous possible situations will
have different optimum toe conditions. Therefore, there is no relationship between steer and toe that is
right for all situations.
The toe we have at any particular instant results not only from Ackermann effect, but also from static
toe setting and toe change with suspension movement (roll and ride Ackermann).
Because of these complexities, there is no single obvious way to define what constitutes theoretically
correct Ackermann. It is possible to come up with a rationally defensible definition for your own
purposes, but there is no standard rule, and it is unlikely that there ever will be.
With oval track cars, we can have additional complexities. As the questioner notes, it is common to
use unequal-length steering arms on oval track cars, usually shorter on the left. In fact, this is the
only way to get positive Ackermann on a front-steer stock car, unless the rules allow fabricated
spindles and we accept a much larger scrub radius than we’d like. A shorter left steering arm only
gives positive Ackermann when the wheels steer left, at the expense of exaggerating negative
Ackermann when steering right. This is not an option when the turns go both ways.
The questioner referred me to a website where an expert says that tire slip angle is a property of the
tire, which should be available from the tire manufacturer. That is incorrect. Slip angle is an
operating condition of a tire at a particular instant: the angle between the wheel’s aim and its
direction of actual travel. A tire does not have a single slip angle. It has a measurable slip angle,
when tested on a machine, at a specific load (or normal force), a specific desired lateral force, a
specific camber, a specific pressure, a specific temperature, a specific rim width, and a specific wear
condition. Change any of these factors, and the slip angle changes. Change the properties of the road
or simulated road surface, and the slip angle changes.
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The body or sprung mass can also be said to have a slip angle, since it also has a definable direction
of aim and direction of travel. An aircraft or watercraft also has this type of slip angle. Slip angle as
measured by recently introduced GPS-based data acquisition systems is body slip angle. In a largeradius turn, body slip angle is very similar to rear wheel slip angle, provided there is no large amount
of roll steer, ride steer, or static steer at the rear wheels. Front wheel slip angles can be very different
from the body slip angle, since the front wheels can steer.
Defining the tire’s direction of travel can be a bit enigmatic. At first blush, we might suppose it
would simply be the same as the body’s direction of travel. For situations where we don’t need
tremendous precision, and for large-radius turns where the vehicle’s yaw velocity is small, this can
be an adequate approximation. But when the body has a yaw velocity – and it must have some in any
steady-state cornering condition – the tires will not be traveling in exactly the same direction as the
body’s origin point or CG.
As an example, suppose we are running on a quarter-mile oval where the turns are half of the lap
distance. These would be fairly tight turns by oval track standards, about 105 foot radius. Let’s
suppose for simplicity that the car’s CG, or our chosen origin point, is midway along the wheelbase
and centered side to side. If the car has a 9’ (108”) wheelbase, the wheelbase subtends or spans an
arc of about 5 degrees on a 105’ radius. If the car is driving through this turn very slowly, the tires
not sliding significantly, then the center of curvature of the car’s path will lie on the rear axle line as
seen from above. The body’s origin or center of gravity will track outside the midpoint of the rear
axle. The midpoint of the front axle will track still further out, and the front wheels will track outside
the rears. The front wheels will be steered an average of about 5 degrees to the left. The left front
will be leading the right front, and will need about ¼ degree more steer angle than the right front if
we want least scuffing, tire wear, and rolling resistance. That’s about 1/8” toe-out as measured with
typical toe plates, or 1/16” total as measured at the wheel rims using a string or laser.
If we measure the car’s body slip angle using a GPS-based data acquisition system, it will tell us the
car has a negative slip angle: it is traveling about 2.5 degrees left of the direction it’s pointing, while
making a left turn!
Now suppose the car is going faster, and the rear wheels need to run at about 2.5 degrees of slip
angle to keep the car on course at the speed it’s running. The center of curvature will now lie on a
line perpendicular to the car’s centerline, intersecting the centerline at the CG or origin. The GPS
will now tell us we have a slip angle of zero. That won’t be what the tires are feeling.
The front tires will now need only half as much toe-out as in the previous case, or about 1/8 degree,
for their slip angles to be equal. The rear tires will need about 1/8 degree toe-in for their slip angles
to be equal. At the front, the left wheel leads the right slightly. At the rear, the left trails slightly.
Okay, now let’s raise the speed again, to a point where the rear wheels have about a 5 degree slip
angle. The GPS will now tell us we have a positive slip angle: the car is travelling about 2.5 degrees
to the right of the direction it’s pointing, while making a left turn. The center of curvature now lies
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on the front axle line. Neither front tire leads the other. For the front tires to have the same slip angle,
they now need to have no toe-in or toe-out with respect to each other. At the rear, the left now trails
enough so the rear tires would need ¼ degree toe-in to have equal slip angles.
If we go still faster, the center of curvature moves ahead of the front axle line. The front wheels now
need toe-in for their slip angles to be equal.
Now suppose we try a similar comparison, except the track is 2 miles long, and the turns have a
radius of 820 feet. The same car’s wheelbase now subtends an arc of only about 0.6 degree. The
center of curvature is now on the front axle line at only 0.6 degree rear wheel slip or 0.3 degree body
slip. Any time the car is cornering hard on this turn, the center of curvature is well ahead of the front
axle line, and the front wheels will require toe-in for equal slip angles.
Do we want equal slip angles? Not necessarily.
Although we cannot describe a tire’s properties as they relate to slip angle behavior with a single
number, we certainly can meaningfully discuss them, and also generalize about them to some extent.
For a desired set of conditions, we can measure them on a tire testing machine. For a given set of
conditions, a tire will have some slip angle at which it develops maximum lateral force. If we
increase slip angle beyond this, lateral force drops off. This is what happens when a tire reaches its
limit and breaks away. For street radials at typical loads and pressures, this occurs somewhere
around 6 degrees.
In general, bias-ply tires develop peak cornering force at higher slip angles than radials. Narrow tires
develop peak cornering force at higher slip angles than wide ones. Tires at low inflation pressures
develop peak cornering force at higher slip angles than at high inflation pressures. Tires with thick or
deep tread develop peak cornering force at higher slip angles than tires with shallower treads. This is
particularly true with treaded tires, but the effect is measurable with slicks also.
As we increase normal force on a given tire, other conditions constant, the slip angle for peak lateral
force increases. For most applications, this means that in a left turn, the right front tire develops peak
lateral force at a higher slip angle than the left front. This is why we might want toe-in when
cornering, or more toe-in than required for equal slip angles.
If both front tires are operating at peak cornering force together, that should be the greatest total
cornering force available from the pair. However, we should also think about the longitudinal forces,
as these also affect the car’s balance. If both front tires are optimized for lateral force, the right one
will not only be making more lateral force than it would with more toe-out or less toe-in, it will also
be making more drag. This will tend to add understeer. So the toe for least understeer may be a little
different than the toe for greatest front lateral force.
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We also need to remember that if both tires peak together, they break away together too. So part of
the price for greatest peak lateral force is more sudden breakaway. That means that exploiting the
lateral force capability may be harder for the driver.
Looking at effects on tire temperatures, in oval track racing the right front tire can easily overheat.
The left front seldom gets hot enough to be a problem. Running less toe-out or more toe-in through
the turns doesn’t help this, it makes it worse.
Whatever slip angles we decide we want on the front tires, we can definitely say that we are going to
want less toe-out or more toe-in as the center of curvature moves forward relative to the car. In other
words, the larger the radius of curvature or the more the rear tires are sliding, the more toe-in or the
less toe-out we want.
What are the implications of this for the optimum relationship between the steering arm lengths? Do
we want more positive Ackermann, or less negative, when steering left, or when steering right? I
think the tradition of having the left steering arm shorter, if anything, is sound. When the wheels are
turned left the most, the center of curvature is furthest aft. When the car is crossed up, steered right
in a powerslide or catching a slide, the center of curvature is ahead of the car and we need toe-in.
Some experts say having toe-in or less toe-out when countersteering “pins the front end” and spins
the car. This is based on the misconception that the wheels always drag more when toed in. As we
have seen, this is not the case when the center of curvature is ahead of the car, and the left front is
trailing the right front.
So here are my recommendations:
1. Whatever your strategy, the combination of static toe and Ackermann has to give you a good
toe value for your prevailing conditions. Wrong Ackermann with a toe setting that
compensates is better than improved Ackermann with static toe that doesn’t suit.
2. For road racing or street use, where a wide variety of conditions will be encountered, a
combination of substantial positive Ackermann and moderate static toe-in is the way to go.
This is the prevailing factory approach for road cars, and also, I’m told, the approach taken
by Cornell on their winning FSAE cars.
3. For pavement oval-track applications, toe-in may make sense, if combined with positive
Ackermann when steering left, especially on high-speed tracks, provided that right front tire
temperature considerations don’t overrule the decision. Making the right steering arm shorter
than the left does not make sense, although it may work as a way to crutch static toe-out on a
high-speed track.
It is worth noting that this whole question has been subject to fads throughout the history of racing.
In road racing, the first successful rear-engined cars used negative Ackermann. This was in the late
1950’s and very early 1960’s. The designers claimed this was because the more heavily loaded
outside tire required a larger slip angle. In the early ‘70’s, a bit of static toe-out, with zero
Ackermann, was the most popular choice. By the 1990’s, it was becoming commonly recognized,
especially in CART, that high-speed ovals demanded much less Ackermann than road courses, and
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street circuits demanded the most. Far as I’ve heard, nobody has yet tried static toe-in for the highspeed ovals, but it’s possible my latest information isn’t entirely current.
MANAGING THE BEHAVIOR OF THE UNBALANCED
I recently read your article, Load Transfer Basics, in the November issue of Racecar Engineering
(Vol.13 No.11)[based on the August 2003 newsletter] and was very interested in the concepts you
discussed. I am currently an engineering student in Australia and I am doing some work experience
with a Porsche racing team out here. I would be very grateful if you would be able to help me with
several questions I have concerning load transfer and suspension set up.
Firstly I was wondering if you could recommend any text books relating to load transfer and
suspension set up so I can pursue some further research in this area.
Secondly during a race meeting held a month ago it was mentioned that the way to get faster lap
times is to "balance" the car by getting the static load on the front left suspension divided by the load
on the back right equal to the opposite diagonal. In other words getting the following ratios equal:
Front Left : Back Right = Front Right : Back Left
Our team thought that this sounded a reasonable proposition but we are unable to see exactly how
this works. It seems to me that if this theory does in fact make the car more "balanced" it assumes
that the left handed corners are similar to the right handed corners. Since this is often not the case
surely the car must be preloaded to suit the important corners on the track, in which case the broad
statement of balancing the car isnt helpful...?
I like the chapter in Milliken & Milliken’s Race Car Vehicle Dynamics by Dave Segal on the subject
(Chapter 18). The book is published by SAE, and available from their bookstore at www.sae.org. I
would also of course not pass up the opportunity to plug my own video on the subject, mentioned at
the beginning of this newsletter.
Another way of stating the relationship you were told would be to say that the rear percentage taken
diagonally is the same for both diagonal wheel pairs.
For a car with 50% left, this works. You would have a car with 50% diagonal, the same rear
percentage on both sides, and the same left percentage at both ends. Such a car should corner with
similar balance in right and left turns.
However, as you note, sometimes even in road racing we want the car heavier on the side it turns
toward the most, on a particular track. It may also happen that we get something other than 50% left
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unintentionally, due to packaging or rules constraints. We still will normally want the car to corner
similarly in both right and left turns, even though it will be faster when turning toward its heavy side.
My recommendation for this is to start with what I call an unwedged car. My definition of this is a
car with equal rear percentage on both sides, and equal left percentage at both ends. This is different
than what your instructor taught you, and also different from 50% diagonal weight.
Let’s consider an example. Suppose we have a 2000 lb. Porsche with 60% rear, and we are racing on
a road course with predominantly right turns. Suppose the car has right hand drive, and we have
enough ballast so we can get 55% right. An unwedged car, as I define it, would have 55% of 60%, or
33%, on the right rear (660 lb.); 55% of 40%, or 22%, on the right front (440 lb.); 45% of 60%, or
27%, on the left rear (540 lb.); and 45% of 40%, or 18%, on the left front (360 lb.). The car has the
same 45% left at both ends, and therefore LF/RF = LR/RR. Also, it has the same 60% rear on both
sides: LF/LR = RF/RR. This setup imposes no static torsional load on the frame.
Note that we can get either of these equations from the other by algebraic manipulation. (Starting
with the former, we multiply both sides by RF, and divide both sides by LR.) They are different
forms of the same expression. However, there is no way we can manipulate either equation to obtain
the form LF/RR = RF/LR. That is a different equation.
If we look at the ratios in your instructor’s equation, in the above example, we get: LF/RR =
18%/33% = 360/660 = .545; RF/LR = 22%/27% = 440/540 = .815. Not close at all.
Suppose we look at the above example with reference to the target more conventional wisdom would
set, namely 50% diagonal. That would mean 2(RF+LR) = RF+RR+LF+LR. Our example doesn’t fit
that rule either. Its diagonal percentage is 27% + 22% = 49%. Close, but not the same.
Diagonal weight would be 980 lb. To increase that to 1000 lb. and make the diagonal 50%, we
would have to adjust the suspension to transfer 10 lb. left-to-right at the front and transfer 10 lb.
right-to-left at the rear (assuming equal track widths, for simplicity). That would mean that the static
left percentage at the front would be 350/800 = 43.8%; left percentage at the rear would be 550/1200
= 45.8%. If the car has equal roll resistance in both directions front and rear, we can see that the
change we’ve made to the static load distribution will help the front wheels in a right turn and the
rear wheels in a left turn. We would therefore expect more understeer in left turns than in right turns,
which is probably not what we want.
Now, suppose we wanted to set this car up to your instructor’s rule. Could we even do it? Well, yes,
we could, but it would take a pretty freakish setup to do it. We’d have to have 600 lb. on the LF, 900
lb. on the RR, 200 lb. on the RF, and 300 lb. on the LR. This is obviously not what we want. Our
diagonal percentage would be 25%. Our left percentage would be 75% at the front, 33% at the rear.
Yow! The car would push like a dump truck in right turns and spin if you sneeze in left turns.
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Rather interestingly, if the car has 50% left, all three rules work. If the car has either 50% left or 50%
rear, the 50% diagonal rule works. If the car has neither 50% left nor 50% rear, my rule works, or
gets you closest.
Even with my rule, small adjustments may be needed. If there is more understeer turning right than
turning left, add load to the RF and LR. If there is more understeer turning left than turning right,
add load to the LF and RR.
INDEPENDENT OR BEAM AXLE FRONT SUSPENSION FOR PAVED OVAL?
We race primarily on quarter-mile asphalt ovals – no banking, no bumps. The car weighs 700 kilos
(1500 lb.) and runs on 10-inch Hoosier slicks front and rear. Everyone uses A-arm front suspension,
with a mandatory beam axle rear. Would there be any advantage running a beam type front end? If
the steering rack is mounted on the axle, would the driver feel roll-induced steer?
The main advantage of a beam axle front end for an oval-track application is that it reduces overall
weight, and also usually reduces the torsional stiffness needed from the frame. Even if you have a
minimum weight requirement, reducing car weight is advantageous because you have more ballast to
move as desired. This is especially beneficial if you have no limit on left percentage, or if an engine
setback limit prevents you from getting as much rear percentage as you’d like.
A beam axle also eliminates camber change due to roll, which is good. However, on an oval,
independent suspension can be set up with sufficient static camber so that you can also obtain
desired camber when cornering with an independent system.
Back when I was doing consulting for fun and experience, I worked with a west coast super
modified team. At that time, there were no rules on suspension design. Beam axles have now been
made mandatory front and rear for these cars. (Interestingly, in the US, other classes prohibit beam
axles and mandate independent front ends. There is no universal consensus as to which is better.)
Back in the ‘80’s, people ran both styles, and the usual practice was to mount the rack on the axle on
the beam axle cars. This works fine. The driver does feel a little roll steer, but it’s not bad, and it’s in
the right direction, i.e. roll understeer.
The main advantage of the independent setups in this class was that the car was more controllable at
the point of inside front wheel lift. With a beam axle, especially with a high roll center and a soft
wheel rate in roll, when the inside front wheel comes off the ground, the roll center rises as the axle
rises, causing the wheel to rise further. The wheel tends to rise a lot then, causing unfavorable
camber on the outside front, and therefore understeer. It is difficult for the driver to maintain an
attitude where the inside front tire is carried just a little way off the ground. With independent, this is
much easier. However, I believe that with a low roll center and a high wheel rate in roll, a beam axle
could deliver similar controllability. And if your cars never reach the point of carrying a wheel, the
whole issue is moot.
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March 2004
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
VIDEOS STILL AVAILABLE
I still have available videos of my lecture, “Minding Your Anti”, presented March 2003 at UNC
Charlotte. Price is $50.00, which includes shipping and handling worldwide. North Carolina
residents please add 7½ % sales tax.
RAISING MY RATES
For the first time in three years, I have decided to raise my hourly rate for consulting. The new rate
will be $50/hour, which is still reasonable compared to what other consultants have told me they ask.
Retainer rates will likewise go up proportionately. A month will be $300; a year will be $1500. New
rates take effect March 1.
DIFFERENTIATING DIFFERENTIALS
A 2200 lb., 300 bhp, rear-wheel-drive car is doing circuit racing on a short, twisty asphalt circuit
with mostly right-hand turns. It runs the same rubber on all four wheels. Which of the following
differential setups would be quickest around the track, giving good turn-in and good traction out of
the corners?
1. A spool type locked rear
2. A Positraction rear with 250 lb. preloading
3. A Detroit Locker rear
4. A Torsen rear
All of these options have their adherents. One thing that complicates the picture is that the choice
interrelates with setup and driving style.
Conventional wisdom is that spools are a bad idea for road courses. To get good steady-state
cornering with a spool, the car needs to have tire stagger, or alternatively the power available and the
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nature of the track surface have to be conducive to powersliding. Tire stagger is generally an
impossibility if the turns go both ways, although maybe if most of them go one way it is possible to
accept poor behavior in the few that go the wrong way. If, as the questioner posits, the tires are truly
identical all around, in circumference as well as all other properties, then we definitely don’t have
stagger.
Driven more or less normally, a car with a spool tends to understeer, or push. It does this much more
in tight turns than in large-radius ones. We can free it up by putting lots of roll resistance in the rear
suspension, but when it’s right in the slow turns, it’s too loose in the sweepers. One cure for this is to
have a lot of aerodynamic downforce at the rear. Whether we can get that will depend on the
bodywork rules.
There are situations where the locked-axle push is helpful. If we are trying to brake and turn at the
same time, the car tends to oversteer. This limits how hard we can brake while turning. The car also
will oversteer under power, if there is enough power applied, because the rear tires are using a lot of
their available grip to make forward force and have less grip available for making lateral force.
Again, if the car is tight to begin with, the driver can feed it more power before it goes power-loose.
This means that a spool can work on a road course if we have a driver who trail-brakes deep into the
turns, and then gets on the power hard right away. In most of the slower turns, the car never sees
steady-state cornering when driven this way. Mid-turn speed isn’t necessarily best with this
approach, but we get good entry and exit speed, and a late brake application point and an early
power application point. Consequently, elapsed time, or average speed, on any straightaways before
and after the turn improves.
Not surprisingly, the driver best known for making this work is the one who popularized trailbraking when most drivers were still completing their braking before turning: the late Mark
Donohue. Donohue could win races on a road course with a spool, even in a car with huge tires and a
massive rear wing, such as the Can-Am Porsche 917-30. Other drivers would get into cars set up to
his liking, and not be able to do anything with them.
We might reasonably suppose that a driver could simply learn this, and adapt. Actually, drivers’
abilities to do this vary considerably, and even those who can learn require practice to use a new
technique well. Then again, we may have a driver who learned to drive this way, and has to learn a
new style to do anything else. Not only do personal preferences differ on the question of trailbraking,
so do driving schools.
To perform the best, a race driver needs to be able to drive the car without thinking, and focus
his/her conscious mind on observation. This means that it’s not easy to learn and unlearn new
driving styles to adapt to different cars. For some talented individuals, it’s merely difficult. For
others, it’s impossible. And for all drivers, just having to think about technique costs speed, all by
itself. Therefore, when we set up a race car, we need to accommodate the driver, and not simply
write off to stubbornness a driving style that doesn’t suit our setup. If we have a driver who is in the
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habit of driving like Donohue, a spool may be worth considering. If not, that argues against the
spool.
The spool is simpler and lighter than any alternative. Its simplicity is a plus for both cost and
reliability, although a spool is generally harder on axles than any form of limited-slip.
For those unfamiliar with the Positraction, or Posi for short, it is a clutch pack style limited-slip,
usually with a single clutch pack establishing friction between the right side gear and the carrier. The
clutch pack is preloaded either by having a dish in one pair of discs so they act like Belleville
washers, or by having coil springs bearing on the clutch pack. Added clutch loading is applied to the
pack by the spreading force on the side gear when torque acts on the ring gear. At a given ring gear
torque, this spreading force depends on the tooth profile and the diameter of the side gears. That
makes the preload the only adjustment.
Preload is measured in lb.ft. of torque, rather than pounds – though it is common to say pounds for
short in casual conversation. The procedure is to jack up one wheel, or jack up both rears and have a
helper hold one, put the transmission in neutral, and measure the torque required to turn one wheel.
This requires an adapter to allow a torque wrench to turn the wheel. For best accuracy, it’s best to
turn both wheels at once with the torque wrench first, to measure brake and bearing drag. Then you
divide that value by two to find the drag for one wheel, and subtract that from your torque reading
when turning just one wheel.
250 lb.ft. in this test is a lot. Typical values for stock road cars are more like 50. If the car is on
racing slicks with a coefficient of friction of 1.3, and a rear wheel has a static load of 550 lb. and an
effective radius of one foot, the tire’s breakaway torque under static load is 715 lb.ft. For the inside
tire in a corner, with a substantial portion of the traction circle being used for cornering, 250 lb.ft.
could easily be enough to overpower the tire. And under power, we get more clutch pack loading. In
such a situation, a heavily preloaded Posi can act a lot like a spool.
However, when the tires can overpower the clutch pack, the Posi acts tamer than a spool. Like a
spool, but less severe. This will tend to save the axles to some extent, as well.
It might be worth mentioning the ZF style differential, which the questioner didn’t list. The ZF and
the Posi are both sometimes called Salisbury differentials, but they differ a bit. Like the Posi, the ZF
has multi-disc clutches that can be preloaded and are loaded additionally by engine torque. The
difference is that in a ZF, the clutch discs are outside the carrier, and the carrier is split into two
halves at the pinion shafts. The pinion shafts have angled flats on them that bear against mating flats
on the carrier halves. The angle of these flats can be varied, by installing different parts having
different angles. This allows us to adjust the severity of the lockup under power. There are similar
flats that spread the carrier halves under reverse torque (engine braking). The angles of the flats for
power and decel can be varied independently, allowing the unit to lock more or less strongly on
deceleration compared to acceleration.
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The Torsen, or Gleason, is also two designs that have very similar properties. Both use worm gears
in place of the spider and side gears of a conventional diff. The worm gears provide a very smooth,
yet strong lockup under load, yet turn very freely with no load, provided they are not preloaded.
Gleasons can be preloaded. One problem with preloaded Gleasons is that the preload is highly
sensitive to gear wear.
If I were to make a general-purpose recommendation for road racing, it would be the Gleason. It has
the ability to lock strongly, yet smoothly, with little or no preload. This makes it very driveable.
It does have some drawbacks. It is generally the costliest of all the types we’re considering here,
although not prohibitively so. The power and decel lockup are not separately tunable, as with the ZF.
If the unit is not preloaded, it will not prevent one wheel from spinning if that wheel is very lightly
loaded, or is airborne, or is on a very slippery surface.
The Detroit Locker is not really a differential in the sense that the Salisbury and Gleason are. That is,
it has no gears at all, and there is no way it can be set up to split torque equally between the two
output shafts, while letting their speeds vary, even at very low torques. The locker contains a center
element consisting of a dog ring driven by the carrier, like the spider gears and pinions in a Salisbury
or an open diff. This central dog ring has dogs on both sides. These mate with driven dog rings on
either side, which drive the axle shafts.
The driving dog ring can float a bit side to side. It is held centered by two conical coil springs. When
the driving dog ring is centered, it engages both driven dog rings, and we have a locked axle. If the
driving dog ring moves to one side or the other, it moves more deeply into engagement with the
driven dog ring it moves toward, and if it moves far enough it disengages from the other dog ring.
We then have drive to only one wheel.
For a wheel to disengage, it has to overrun the carrier. For this reason, the locker is sometimes called
a ratchet. This isn’t really accurate, but the unit is somewhat similar to a pair of ratchets, each
driving one wheel, in that it drives the slower wheel and lets the faster one overrun. It differs from a
pair of ratchets in that only one wheel can overrun at a time. In decel, the slower wheel sees the
engine braking. In a race car, this promotes very free turn-in. If the driver likes to finish braking and
then turn, this can work well. If the driver likes to do heavy trail-braking, it may be a disadvantage.
When the driver gets on the power, the inner wheel drives, up to the point where it spins. As soon as
the inside wheel reaches the speed of the outside wheel, the unit locks and drives both wheels. The
lockup is not smooth at all. The dogs are either engaged, or they’re not. The unit cannot slip. This
requires the driver to develop a feel for when the unit is going to lock, and anticipate the change in
car behavior at lockup. It also rewards decisive driving. That is, lockers are somewhat unpredictable
if the driver is on and off the throttle trying to balance the car. It can be hard to predict whether the
rear will be locked or unlocked when the power is reapplied after a brief lift. So the locker responds
best to a driver who gets on the power and stays on it.
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One peculiarity of the locker is that when backing up, it drives the faster wheel rather than the slower
one. This means that we don’t have drive to the wheel with traction if one wheel is off the ground or
on very slick ice. Normally, this is of no concern in road racing, but it is something to consider for
street or off-road use.
The locker develops less heat than a Salisbury or Torsen, since it has no slipping friction elements.
The rear end can still get hot, due to the friction in the ring and pinion gears. And if it gets hot, the
springs in the locker can lose their temper. This will cause erratic locker behavior. For this reason, it
is customary in racing to replace the springs frequently.
Lockers are universal in NASCAR, because the rules require them. Salisburys and Torsens are
prohibited. This rule originated with a prohibition against all limited-slips and spools. The inspection
procedure was to test the rear end by turning one wheel with the transmission in neutral, as described
above for testing a Posi. The wheel had to turn freely. Since a locker would pass this test, people
started using them, and they were such an advantage over an open diff in a stock car that they
became universal. NASCAR saw that the racing was better when the cars could put power down
with both rear wheels, so they never prohibited lockers. Now, they are specifically written into the
rules by name.
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Please note: This document has been revised to correct an error. Corrected text appears in red.
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
EFFECT OF CALIPER MOUNTING POSITION
What effect on wheel loading does the positioning of the calipers in a leading or trailing location
have – i.e. mounted at 3 and 9 o’clock positions? Does a trailing caliper add or subtract load on the
front tires? In a rear independent suspension, does a leading caliper add or subtract wheel loading,
and is it the same in a live axle situation?
The short answer is no. Caliper location has no effect whatsoever on wheel loading. Having the
caliper’s mass lower or higher does have a very minute effect, because it affects the CG location a
tiny bit, but there is no difference between a 3 o’clock mounting position and a 9 o’clock position.
However, there is an effect on bearing loads. It might seem counterintuitive that we can change the
bearing loads and not change the tire loads, but that is in fact the case. As the questioner appears to
have considered, the disc tries to carry the caliper upward if the caliper is trailing, and downward if
the caliper is leading. That reduces bearing loads if the caliper is trailing, and increases bearing loads
if the caliper is leading. However, these forces are reacted entirely within the
hub/bearing/spindle/upright/caliper/disc/hat assembly, and do not change the loads on other parts of
the car.
We can think of it like this: Gravity acts downward on the car, with additions and subtractions due to
inertia effects and aerodynamic effects. The road surface holds the car up. Or, we may say the road
holds the tire up; the tire holds the wheel up; the wheel holds the hub up; the hub holds the bearings
up; the bearings hold the spindle up; the spindle holds the upright up; the upright holds the
suspension up; the suspension holds the sprung mass up. If the caliper exerts an upward force on the
upright and a downward force on the disc, that just means the brake is helping the bearings and
spindle hold the upright up. It doesn’t change the total support force, only the load path within some
of the unsprung components.
It is worth noting that in braking there are also horizontal forces acting through the wheel bearings.
The car is trying to keep going forward at a constant speed. The road surface is exerting a rearward
force on the car, through the tires, wheels, hubs, bearings, spindles, uprights, and suspension. We can
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reduce the bearing loads due to this component if we mount the caliper below center, or increase the
bearing loads if we mount the caliper above center. In fact, the horizontal force may be greater than
the vertical force on the tire. With racing slicks on dry pavement, the horizontal force may be 1.3 or
more times as great as the vertical load on the tire. So for least bearing loads during braking, the
caliper should be somewhere in the upper rear quadrant – around 5 o’clock or 7 o’clock, depending
on which wheel we’re looking at, and from what direction.
Now, do we actually want maximum cancellation of the bearing loads by the brakes? We might
suppose so, but actually there is an argument for not having maximum cancellation. The effective
radius of the brake (roughly the radius to the middle of the pad) is often less than half of the tire
effective radius. This means that the force at the caliper is more than twice the rearward force at the
tire contact patch, and it may also exceed the vector sum of the vertical and horizontal forces at the
contact patch. Consequently, the caliper force may not only reduce the bearing loads, but reverse
them. If there is any free play in the bearings, or deflection in the components, this load reversal may
result in a vibration or a small variation in the steer angle of the wheel. So there is a case for building
the components nice and strong, and positioning the calipers so the bearing loads will not reverse.
Of course, as a practical matter, if we are using purchased calipers we need to mount them with the
bleed screws at the top, or very nearly so, just to facilitate good brake bleeding without requiring the
calipers to be dismounted. This may well outweigh any theoretical considerations. If we are
designing from a blank sheet of paper, we don’t face this constraint, but most of us, most of the time,
are designing around purchased calipers.
Another practical constraint is packaging, particularly of the steering arms and cooling ducts.
There are some ways in which we can affect wheel loads by the design of the brake system and the
suspension. I am referring here to the longitudinal “anti” or “pro” effects: anti-dive or pro-dive in the
front suspension, anti-lift or pro-lift at the rear. With independent suspension, it makes a difference
to these effects whether the brakes are inboard or outboard. With a beam axle, it makes a difference
if the calipers are mounted directly to the axle, or on birdcages or floaters that rotate on the axle and
have their own linkages.
However, with all of these, we cannot significantly alter the loading on the front or rear wheel pair,
nor on all four wheels. We can change the way the sprung mass moves in response to braking, and
this may have small effects on CG height, with corresponding small effects on overall load transfer.
But the big effects come from having geometry differences on the right and left sides of the car.
These may be present even in supposedly symmetrical road racing cars, because no car stays
symmetrical when it rolls. In oval track cars, we often design in, or adjust in, asymmetry even in the
static condition. Such asymmetry can produce significant changes in diagonal percentage when
braking, and we can use these to tune corner entry behavior.
All such effects are independent of the “clock” position of the caliper mount.
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MORE ON WEIGHT DISTRIBUTION
In the April 2004 issue of Racecar Engineering [see November 2003 newsletter], you mentioned that
a 52/48 front to rear percentage works well on medium to high speed tracks. How does it change
when you go to a short track? Is there an optimum left/right percentage and cross weight for
medium speed track with moderate banking (18 degree corners and 12 degree straights)?
Regarding rear percentage, it depends to some extent on the design of the track, but assuming that
we are required to use equal size tires front and rear, and assuming the bodywork rules permit only
very limited downforce, something close to 50/50 works well for mid-turn speed. More rear helps
braking. More rear also helps forward acceleration, provided that the car is traction-limited.
So if that short track is bowl-shaped – short straightaways and long turns, no really straight running,
small speed variations between mid-turn and end of straight – we want close to 50/50. If the track is
paperclip-shaped – tight turns, long straights, two drag races and two hairpins per lap – we want
more than 50% rear, especially if the tires are narrow and hard, and the car has lots of power.
If the track has more banking, that tends to make the car less prone to wheelspin, at least during
corner exit. That reduces the need for rear percentage greater than 50%.
Regarding left percentage, there’s no such thing as too much, at least within most rules. Ordinarily,
you are limited either by an outright limit on left percentage, or by a minimum right side weight, or
by rules on engine and frame offset. In west coast supermodifieds, these days you have a choice of
two left percentage limits. If you use the lower left percentage, they let you run a bigger wing.
Having more left percentage does change the car’s behavior, so it only makes the car faster if the
setup is suitable. It can happen that a team will reduce left percentage and find speed, but this is
because they haven’t figured out how to make the left-heavy setup work.
When the car has lots of left percentage, it tends to turn right when braking and turn left under
power. That makes it tighter on entry and looser on exit. So the key to making the car work is to
compensate for this, but not overcompensate.
Regarding diagonal percentage, there is no ideal amount just based on the track and type of car. It
interrelates with the rest of the setup. If you have more roll resistance at the rear compared to the
front, you need more diagonal, to keep the same amount of understeer. If the car goes loose on slick,
add diagonal percentage and add rear roll resistance or reduce front roll resistance. If the car goes
tight on slick, do the opposite.
SPRING SPLITS WITH BIG BARS
I just read your article in the Racecar Engineering October issue [see July 2003 newsletter], about
stock car setups where the right rear spring is the stiffest, due to the front end having soft springs
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and a stiff anti-roll bar. You say that you have some clients using this type setup without the rightstiff spring split. How are you doing that?
What effect does the left rear spring have on these setups, and does a stiffer LR tighten or loosen the
car on entry?
We are running on a D-shaped 5/8-mile track, with a maximum banking of 6 degrees, minimum of
2.8 degrees. The surface is old, worn out, and bumpy. The car is a Howe XL Late Model with
coilovers all around. It weighs 2900 pounds, 56% left side, 58% diagonal.
Spring rates: LF 200 RF 200 LR 150 RR 200
Front bar: 1.250 dia., 9.5inch arm
Track bar height: 11.5 inches
To answer the first question, of course if the RR spring is the stiffest on the car you do have a rightstiff rear spring split, but you can have the car rear-stiff in terms of roll resistance with geometry, or
a rear anti-roll bar – or with a stiff LR spring if the turns are flat enough so the LR extends in the
turns.
Those are definitely soft springs for the weight of the car, even allowing for using coilovers, which
improve the motion ratios compared to a big spring car. I can’t actually calculate the wheel rate
contribution from the front bar without knowing its length and the motion ratio from the arm end to
the wheel, but it appears pretty substantial compared to the springs. The Cup cars are using much
stiffer ones, though. Their diameters can get as large as 2 inches in some cases, and the wheel rates
in the rear are also higher than yours. They sometimes use rear anti-roll bars too.
As to what happens in your case when you stiffen the left rear spring, all I can say for sure is that
any time the LR spring is compressed relative to static position, a stiffer spring will add diagonal and
usually tighten the car. Any time the LR spring is extended relative to static, a stiffer spring will
reduce diagonal and loosen the car. These effects can sometimes reverse during early entry, if the car
is being slowed mainly by the rear wheels.
To really know what that spring is doing, you need to have data acquisition. The best way is to have
motion sensors and electronic data logging like the big boys use, but you can also improvise with
video cameras. Either mount a camera under the car aimed at the spring, or clamp a piece of welding
rod to the axle near the spring, with the rod poking up into the interior through a hole. Then mount
the camera in the interior and aim the camera at the rod.
My guess would be that the spring is extended most of the way through the turn, with the greatest
extension occurring during late entry, and the least extension during exit. Based on that assumption,
I would predict that a stiffer LR would loosen the car through most of the turn, with the greatest
effect about ¼ of the way through, and the least effect on exit. If you add more diagonal or more
front roll resistance to tighten the car back up, you may have a condition where entry is looser, midturn is similar to before, and exit is tighter. Remember, this prediction is based on a number of
assumptions, so if the driver reports different results, don’t automatically assume he’s wrong.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
MORE ON LAST MONTH’S TOPIC
Last month’s newsletter contained a minor error. To reduce the longitudinal or X-axis forces on the
wheel bearings during braking, the caliper should be below center rather than above. I am sending
out revised April issues with this issue, and the archived April issue incorporates the correction.
Thanks to Eric Zapletal in Australia for catching me on this.
Also, Ramon Mendoza at Bridgestone/Firestone pointed out that caliper location has some effect on
steering feel. Centrifugal force acting on the caliper during cornering creates a torque about the
steering axis. When the caliper is ahead of the steering axis, this adds steering effort. When the
caliper is behind, it reduces steering effort. In general, the increase is better than the decrease,
because the driver is somewhat better able to feel the lightening and heavying of the steering as the
front tires dance back and forth across the limit of adhesion. We might also conclude that having the
caliper closer to 6 o’clock or 12 o’clock might be desirable in this regard, as it would reduce the
magnitude of the effect.
THE NEW NASCAR TIRE
A number of people have written me with questions about the new NASCAR Nextel Cup tire.
NASCAR has a new tire. The common thread is a new soft sidewall. What happens to spring and
shock rates to adjust for sidewall flex?
On the NASCAR commentaries the announcers say the teams are adjusting their tire pressures by ½
to 1 pound increments. I am assuming the increase in pressure makes the tire stiffer,
hence making that corner stiffer – lowering the pressure vice versa. I would assume that these small
adjustments are from the optimum pressure required to give good tire footprints with even
temperatures. Would the same scenario apply to other radial tires, including street tires, or are the
NASCAR tires unique in their sensitivity to changes?
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Darrell Waltrip described the old tire (hard sidewall and compound) versus new tire (soft sidewall
and compound) as hard Jello versus soft Jello. Larry McReynolds said that teams were looking at
control arm angles. It would seem to me that the tire needs to be tilted out at the top (positive
camber) to compensate for the sidewall flex.
I don’t have any special information on these tires. I’m relying here on what’s publicly available.
I understand that the teams are using significantly higher pressures with the new tires. I’ve heard
figures as high as 7 psi more. I am therefore unsure whether the sidewalls really do flex that much
more, as the tires are actually run.
All tires are quite sensitive to pressure. Part of the reason small differences matter so much in racing
is that the competition and on-the-limit operating conditions make small changes in car balance more
noticeable to the driver.
A tire has an optimum pressure for greatest lateral grip and another, lower, optimum pressure for
longitudinal grip. Above or below optimum, grip diminishes. This effect is more important than the
effect that pressure has on tire loading by softening or stiffening a corner of the car.
The key to understanding tire pressure settings in stock car racing is to recognize that the tires are all
overinflated when hot, and this is unavoidable because if they are run any softer they are
unmanageable right after leaving the pits. If tire warmers were allowed, this might not be so. But
under existing rules, softer inflation improves grip once the tire is hot – not so much because it
makes the carcass a softer spring, but more because it results in hot pressure closer to optimum.
Anyway, to adjust spring rates for a more compliant tire, yes you would go stiffer. Or maybe you
wouldn’t if the rules include a minimum spring rate and a minimum ride height, and you’re trying to
get the car to run lower. But barring special considerations, you’d go stiffer.
As for camber and control arm geometry, in general more compliant tires want more aggressive
camber when cornering, and are also more tolerant of camber when running straight. On an oval
track car, that means more positive camber on the left front and more negative on the right front.
Pavement stock cars were already surprisingly aggressive in terms of “camber gain”. Front view
swing arm lengths substantially less than the track width have been the norm for years. This is much
shorter than used in any other kind of racing. I don’t know how much shorter they can go.
One point I’ve thought the NASCAR folks are missing has to do with left front suspension
geometry. On banked tracks, and even on relatively flat ones when running big bars and soft springs,
the left front suspension compresses in the turns, rather than extending as it would in pure roll. In
such a condition, a geometry that places the front view instant center near the centerline of the car
actually hurts cornering camber instead of helping it. To get the car behavior and tire temperatures
we want, we then have to run extremely aggressive static positive camber. We could actually get
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more favorable camber change in the turns with an instant center to the left of the car. That would
involve having both arms slope up toward the frame, the upper one more steeply. If that isn’t
possible with legal spindles, a long front view swing arm with an instant center far from the car
(implying control arms close to level) would give a smaller unfavorable camber change than the
short front view swing arms usually seen.
Note that this does not apply for the right front, nor does it work for road courses – which brings us
to a related question from another reader:
CONTROL ARM ANGLES IN FORMULA 1
I’ve just been watching F1 qualifying [this was written in September 2003], and I noticed that the
front upper wishbones on the Jaguar slope down from the chassis to the uprights. I had seen some
cars with them roughly level before, but the ones on the Jag had a very pronounced drop to them.
This seems to fly in the face of conventional wisdom of camber gain in bump. Is it because the tire
construction is different, or are the suspensions getting to the point where there just isn’t enough
travel to worry about camber gain? After seeing this, I looked at the other cars again. Most
wishbones were angled in the “normal” direction, with the Ferraris’ being the most pronounced. Is
Jag onto something (points don’t seem to reflect this)?
I must confess that I share the questioner’s mystification regarding the front upper control arm
angles we have been seeing on F1 cars over the last ten years or so. This season I’m noticing a
similar slope on the Williams cars. More commonly, the arms are very close to level, much more so
than they were up to around 1994.
It is true that geometry makes less difference when the suspension moves very little. I am fond of
quoting Colin Chapman’s famous aphorism: “Any suspension will work if you don’t let it.”
In spite of that, I find it hard to imagine why a designer would want camber to go toward positive as
the suspension compresses and toward negative as the suspension extends – except, as noted above,
on the left wheel in an oval track suspension, when the left suspension compresses in the turns.
Tires do have different preferences regarding camber, but none of them like to be tilted out of the
turn. They all like to be tilted in the direction of the turn at least a little, and they all like to be close
to upright when running straight. Front view swing arm length is therefore a compromise between
creating a camber change that compensates for adverse camber change due to roll in cornering (I
prefer to call it camber recovery rather than camber gain), and minimizing camber change when roll
is absent, or over bumps when cornering.
If the front view swing arm length is “negative” (instant center outside the track width, on the same
side of the car as the wheel), we get camber change greater than the roll angle in cornering, in the
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wrong direction, and also get camber change in ride. The camber change in ride can be beneficial in
certain circumstances -- specifically in braking on the front wheels, when negative static camber is
used. Of course, this approach also requires more static negative camber to get acceptable outside
wheel camber in cornering, and this produces more unfavorable camber on the inside wheel than
we’d have with more conventional geometry. Overall, I don’t see a gain.
If the control arms are close to horizontal, that makes the system insensitive to ride motion, which is
good, especially in high-downforce cars. I am still inclined to allow a bit of camber change in ride,
to reduce camber change in roll – just not a lot – and limit roll with high wheel rates in that mode.
It should be mentioned that camber characteristics also depend on the angle of the lower arms, which
are hard to see from trackside on an F1 car due to the wings. It would be possible in theory to have
the upper arms slope down toward the spindles, and still have the camber go toward negative in
compression, if the lower arms sloped the same direction but more steeply. However, this would
produce a very high roll center, and I very much doubt that the F1 teams are doing that.
ARM ANGLES IN TRIANGULATED FOUR-BAR BEAM AXLE REAR
I run a figure-8 car – we have to turn left and right. We have to run a stock four-link rear end. Ours
is out of a ’78 Impala. We have moved some of the suspension points, but my question was what
angle I should run the lower trailing arms. I’m trying to get the tops around 10 degrees.
For readers unfamiliar with this setup, this is a live axle locating linkage with four semi-trailing
links, and no purely lateral links. The upper links converge to a point above and slightly behind the
axle. The lower links converge to a point well forward of the axle, and lower. These two
convergence points define an axis about which the axle moves in roll. The roll center is considered
to be the point where this axis of rotation intersects the axle plane (vertical plane containing the axle
centerline).
There is no theoretically ideal angle for any of the links. Ordinarily the lower links slope up a bit
toward the front. In a three-link rear, this would produce roll oversteer (rear wheels point toward the
outside of the turn when the car rolls), but in this type of linkage we just get reduced roll understeer.
If we level the lower links out in side view, we actually get more roll steer.
The side-view angles of the links also affect anti-squat under power and anti-lift under braking.
Leveling out the lower links reduces both of these effects. That can help the car if wheel hop under
power or in braking is a problem.
My general-purpose recommendation is to run all the links close to factory angles, or level them out
a little. I wouldn’t make any of them steeper. I wouldn’t aim the lowers down at the front. There are
no miracles available here, but as long as you don’t make the geometry extreme in any regard, you
won’t have a disaster.
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MORE ON F1 CONTROL ARM ANGLES
Last month we discussed F1 control arm angles. This question from a reader relates to that.
Additionally, after more examination of photographs of the 2004 Williams, I need to correct a
misconception held by this reader, and, until recently, by me.
With regards to the recent discussion about the F1 control arm angles, could they be using the
“negative” swing arm to achieve a below-ground roll center? I suppose there are arguments for
both below-ground and above-ground roll centers at the front – seems to be a preferential design
variable. I notice that the Williams does not droop limit (observation during pit stops) [The
questioner means that the car does have some droop travel from static ride position, although not
necessarily to the point where the springs completely unload.], so the geometry would be susceptible
to lateral migration of the front roll center in roll, though with modern design tools this can
probably be optimized.
In the attached picture, the front legs of the wishbones are nearly parallel, but it is hard to discern
the front view swing arm geometry without knowing the attachment of the wishbones to the tub.
I am inserting the questioner’s photo on the next page. It shows the Williams front end , from the
front, with the car on stands, wheels off, and suspension at full droop. The appearance is that the
upper and lower control arms are approximately parallel in this condition, and both are lower at the
outboard end than they are where they attach to the tub.
After studying other pictures of the car, taken from other angles, I have concluded that the angle of
the upper control arms is not what you’d think from a frontal shot. Those airfoil-shaped links with
the Michelin decals on them are not the front legs of the top wishbones; they are the tie rods, or
steering links. And they are not parallel to the front legs of the wishbones, which lie immediately
behind them. At static condition, the upper and lower control arms are very close to horizontal. The
front legs of both the upper and lower wishbones are very nearly transverse, and there appears to be
little anti-dive, so the geometry of the front legs of the wishbones very closely approximates the
front-view projected geometry of the suspension.
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So, unless I’m still missing something, for small displacements from static we have geometry that
produces little camber change in ride, camber change in roll approximately equal to angular roll
displacement, and apparently a substantial amount of bump steer (!).
I hestitate to attribute a car’s racing record to any single observed design feature, because I know that
results come from the whole package. However, even with the modest amounts of suspension
movement seen in F1, significant bump steer can’t be good. If the bump steer characteristics are
what they appear, that could easily explain the team’s difficulties making the car work this year.
Looking at other aspects of the geometry, it is evident that the length of the front view projected
control arm is shorter for the lower arm than for the upper, which is unusual. I am certain that the
reason for this is aerodynamic, not mechanical. The designer has chosen to compromise suspension
geometry in pursuit of aerodynamic efficiency, particularly that of the center portion of the front
wing. The idea is to get all aerodynamic obstructions in line with the “tusks” that carry the front
wing, and have as large a clear region as possible aft of the wing’s mid-section. For an F1 car, there
is a rational case for ordering the priorities this way.
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That said, what are the mechanical effects of having the lower arms shorter than the uppers?
First off, it’s not good but it’s not a disaster. Practically every strut suspension in the world
approximates a short-and-long-arm system with a long upper arm and short lower.
We do get large changes of force line slope with suspension movement. (Force line is my term for
the line from contact patch to instant center.) The roll center, when defined in the customary way as
the front view force line intersection, can move around quite a bit.
When the force line intersection is near the ground, or when the force lines are close to horizontal,
small changes in force line slope can produce dramatic changes in the lateral whereabouts, and even
the height, of the force line intersection. This is true even when force line slope change rates are
moderate. Some people suppose that this dramatic force line intersection movement translates to
similarly dramatic changes in car behavior. However, this is not necessarily so. In real life, the
location of the force line intersection can migrate wildly, with no adverse effects, provided that no
abrupt changes in force line slope occur. This demonstrates that the practice of treating the force line
intersection as a roll center or as a “moment center”, about which we can take moments to predict
the car’s tendency to roll, is not scientifically sound.
Indeed, there are cases where there is no force line intersection (when the force lines are parallel to
each other but not horizontal), and one case where there are an infinite number of force line
intersections (force lines both horizontal).
Some may say this is heresy, but actually there is widespread recognition in the automotive
engineering community that the whole notion of roll centers needs to be re-thought.
Full discussion of the issue is impossible in a document the size of this newsletter. My video
“Minding Your Anti” ($50.00 from me, shipping included) explores it in depth. We can cover some
basics here, however.
The two front or rear wheels in an independent suspension system each generate an individual
upward or downward jacking force when lateral force acts at the contact patch. This force may act to
oppose roll, in which case the individual suspension is said to have anti-roll. Or the force may act to
exaggerate roll, in which case the individual suspension is said to have pro-roll, or negative anti-roll.
The magnitude of these jacking forces depends on two things: the slope of the individual wheel’s
force line, and the magnitude of the lateral force acting on the contact patch. This means that the
amount of overall anti-roll or pro-roll moment from a wheel pair depends not only on the control arm
geometry but also on the tire loadings, cambers, and slip angles. Change the anti-roll bar stiffness or
the springs, and you not only change the elastic, or spring-derived, component of the roll resistance,
you change the geometric component as well because you change the wheel loadings.
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The effects we are discussing here are sometimes called “lateral anti” effects, because they are
directly analogous to anti-dive, anti-squat, and anti-lift effects in side-view suspension geometry.
The location of the force line intersection doesn’t matter at all! We can define some relationships
between the force line slopes and their intersection, of course, but we cannot say, for example, that
the car necessarily has a lot of geometric anti-roll if the force line intersection is high, or a lot of
geometric pro-roll if the intersection is below ground. We also cannot necessarily say that the
suspension has little anti-roll in a banked turn if the force line intersection is toward the inside of the
turn, or a lot of anti-roll if the intersection is toward the outside of the turn.
Even the force line slopes don’t matter as regards any tendency toward roll resulting from carvertical forces.
There is a way to assign a roll center height for modeling and discussion purposes that takes account
of these realities. The video explains how to do that.
Anyway, returning to the question of what happens when we have the lower arms shorter than the
uppers, if the arms are all horizontal when roll is absent, as approximated by the Williams, then in
the unrolled condition, neither the inside nor the outside wheel has any anti-roll or pro-roll. As the
car rolls, the outside wheel acquires rapidly-increasing pro-roll (downward jacking), and the inside
wheel acquires rapidly increasing anti-roll (also downward jacking). Since the outer wheel generates
a progressively larger share of the lateral force as we corner harder, we can confidently say that the
net result is pro-roll for the wheel pair, increasing relatively rapidly with increasing roll. We may
model this, or think of it, as a roll center that is at ground level to begin with, and drops relatively
rapidly as the car rolls.
As for camber properties, in roll the outside wheel starts out with a camber recovery rate of zero
(wheel tilts out of the turn an amount equal to roll angle) and gets worse from there – in other words,
the camber recovery goes negative (wheel tilts out of the turn an amount greater than roll). On the
inside wheel, camber recovery starts at zero and improves from there. In ride, camber goes toward
positive in both bump and droop. Of course, any static or initial camber value will be superimposed
on these effects. And again, the foregoing discussion assumes an initial condition where all arms are
horizontal.
CLUTCH USE WHEN DOWNSHIFTING
In the July 2002 newsletter, we explored the question of whether to downshift while braking for a
turn. I pointed out that we really can’t do it any other time, since we need the car in the proper gear
for the turn as soon as braking ends, and we generally can’t downshift it before we get it slowed
down.
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A letter in the February 2004 Racecar Engineering notes that it is not common anymore to doubleclutch, or double-declutch as they say in England, while heel-and-toeing to match revs while
downshifting. The writer asks whether there is actually any penalty or benefit to letting the clutch
pedal up while matching revs.
Normally, the reason for doing this is to match the speed of the meshing parts inside the gearbox,
and thereby reduce wear in the box, especially to the dogs or synchros, as opposed to merely getting
a smooth-feeling shift that won’t upset the chassis or break the tires loose.
To some extent, it depends on the type of clutch and gearbox. Many multi-disc racing clutches drag a
bit even when released, and if that’s the case and the rotating parts are light, it may not matter much
if the clutch pedal is up or down while the revs are being matched.
If the gear ratios are close, the mismatch in revs without double-clutching is less than if the ratios are
widely spaced.
The situation where double-clutching is perhaps the most beneficial is with a wide-ratio
transmission, or a skip-shift (two gears at once) with a close-ratio box, and a single-plate clutch that
does not drag at all when released.
I think rev-matching is definitely beneficial with both dog and synchromesh boxes. I can’t think of
any reason it wouldn’t be desirable in terms of gearbox life.
Another option popular with some drivers, particularly with dog boxes, is to not use the clutch at all.
If done right, this can work quite well, but the consequences can be relatively severe if the driver
misses the rev match. Clutchless shifting does have the advantage of allowing left foot braking. This
permits a quicker transition from braking to power, at least in theory. It also offers an advantage in
speed of response with a laggy turbo motor. The driver can feed the engine some throttle before
getting completely off the brakes, and thereby help the turbo get spooled up.
It is also fairly common to upshift clutchless, and use the clutch, either once or double-clutching, for
downshifts only.
All these techniques have their adherents. And any one of them, done right, beats any one of them,
done wrong.
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This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
SETUP FOR LOWER GRIP
All the books talk about setting the car up in a general manner but do not mention anything about
what to do with regard to the grip level at different circuits. I run in a classic cars series where the
aerodynamic downforce is very small and we have to use the same type of tires for all of the season.
I’ve set the car up at a track where the grip level is considered to be high. The car goes well there
and the times are good, but when I’ve been to slicker tracks I don’t know what to do. Should I make
the car softer?
In general, a lower-grip surface does call for softer settings.
However, there can be exceptions. If you are restricted to a relatively hard tire, and if the tire needs
to heat up to work properly, a stiffer setup may help get the tire up to temperature. Given a free hand,
you’d go softer on both the compound and the suspension.
Many street tires, and some tires used in vintage racing, do not get stickier as they get hotter, in
which case you would generally go softer with the suspension.
Another factor that enters into this is how bumpy the surfaces are. Bumpier surfaces require softer
suspension. So if the slicker tracks are also bumpier, the decision is pretty easy. We then have two
factors that would tend to demand softer suspension settings. On the other hand, if you have a
situation where the grippy tracks have bumps and the slick ones are smooth, things are not so clearcut.
You don’t mention what kind of car you have, or what class you’re running. It would be possible,
particularly in vintage racing, to have a car that is favored by a grippy track merely because it has a
power advantage against the cars it’s classed with, and also has a handling disadvantage. In such a
case, you may just have to live with the situation.
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If you have not tried softer suspension at the slicker tracks, and you are less competitive there, I
would say trying softer settings would make sense. Keep good records, and you can always go back
to your old settings if the softer ones don’t help.
LOWERING BLOCKS ON TRUCK ARMS
What is the effect of using lowering blocks on a truck arm suspension?
First of all, there is no effect to the anti-squat or anti-lift properties, assuming that the pivots at the
front of the arms are not moved, and assuming the ride height is adjusted back to its previous setting.
In most big-spring cars, the springs act on the truck arms, near the axle. In such cases, the car will be
lowered by the lowering blocks. If there are jacking bolts at the springs, the ride height can be reset
to the previous position, assuming sufficient available adjustment.
On most stock car truck arm suspensions, the shocks and the Panhard bar attach to the truck arms. It
would be mechanically possible to build a truck arm suspension without this characteristic, however.
In some classes, coilovers are allowed on truck arms. Usually, the coilovers attach where the shocks
would attach on a big-spring car. But again, they wouldn’t have to.
If you have coilovers attached to the truck arms, the same thing happens to the ride height as if you
had big springs on the truck arms. If you have coilovers that attach to brackets on the axle tubes, ride
height adjustment won’t be affected.
With coilovers or big springs, if the shocks attach to the truck arms, lowering blocks will cause the
shocks to be extended more at a given ride height. This means the shocks have more compression
travel and less extension travel available. This may hurt, or help, or make no difference. If you use
bump rubbers on the shocks to keep other components from hitting, you may need bigger bump
rubbers.
If the Panhard bar attaches to the truck arms, the end of the bar that attaches there will be lowered.
On racing truck arm suspensions, you usually have at least a couple of inches of adjustment on this
attachment. As with ride height, if sufficient adjustment is present, the Panhard bar can be returned
to its original setting, but the overall range of possible settings moves lower.
Assuming the lowering blocks have no taper, they will change pinion angle slightly, upward. This
effect will be small, and should not affect the car’s behavior.
So is there any advantage to using lowering blocks? If you want a lower rear roll center or more
bump travel from the shocks, maybe. Otherwise, the blocks are added weight, with no benefit.
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OHLINS HIGH-FREQUENCY PISTON
Are you familiar with the Ohlins high-frequency shock piston? The claim made by Ohlins, and by
those who use them, is that they offer more grip.
Great description of the pistons’ benefits, huh?
Ohlins is not the kind of company to build such an odd piston without a reason, but I have yet to hear
a scientifically sound explanation. Any input?
Last year I attended a seminar presented by Ohlins, where they showed us these pistons. (If you get a
chance to attend an Ohlins seminar, do it – they’re good.)
This piston provides what might be called relative position (or displacement) sensitivity. This would
contrast with absolute position sensitivity, meaning sensitivity to position of the piston in the shock
body. This relative position sensitivity is sensitivity to the piston’s position relative to last velocity
reversal. The shock is softer for a few millimeters of motion after any reversal of piston motion.
This effect is more or less the opposite of “stiction”, the phenomenon where the friction is higher in
the first little bit of motion.
The shock therefore has a softer action on low-amplitude disturbances. It might be a bit more
descriptive to call it a low-amplitude piston, but high-frequency disturbances tend to also be lowamplitude. Or maybe it should be called a negative-stiction piston. That would cause some headscratching.
Here’s how it works: under, or inside the teflon piston sealing ring is an o-ring. Unlike many designs
that use the o-ring to load the sealing ring against the wall, in this design the o-ring is a loose fit in its
gland. The o-ring can float up and down, and will also let fluid pass around it.
The lands that form the top and bottom surfaces of the o-ring gland have holes drilled through them,
rather like vertical gas ports in a drag racing engine piston. When the o-ring seats against the top or
bottom land, it closes off these ports. When the ports are open, they add bleed to the shock, and
soften its action.
The o-ring is moved partly by its own inertia, but mainly by oil flow. When the piston comes to rest
after moving in one direction for a while, the o-ring will be seated and the ports will be closed. As
soon as the piston starts moving the other way, oil flow unseats the o-ring and starts driving it toward
the other land. When it gets to the other land, it seats against the holes there. When the o-ring is
floating from one land to the other, the ports are open and the shock has increased bleed.
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On a series of small-amplitude disturbances, the o-ring might be floating between lands most of the
time. The piston’s unique properties would have the greatest possible effect under these conditions.
Most race cars have considerable stiction in the suspension due to the large number of slidingcontact pivots. One reason passenger cars use rubber bushings at the pivots is that they don’t have
stiction. So this piston to some extent compensates for the stiction not only in the shock itself but in
the rest of the suspension.
WHICH SHOCK TO SOFTEN?
I have a quick question about my DIRT modified. To get off the corner harder, would you use an
easy-up (soft rebound) shock on the right front, the left front, or both?
Quick answer would be right front.
The basic rule here is that anything that adds an extension force or reduces a compression force
(extension damping force acts in the compression direction) adds load to the near tire and the
diagonally opposite one, and unloads the other two. If that adds diagonal percentage, we tighten the
car. If it reduces diagonal percentage, we loosen the car.
We are making a few assumptions here, though. We are assuming that you’re trying to tighten the
car. If you’ve already got a power push, making the car tighter won’t help you come off harder.
Instead it will make you be gentler with the throttle to keep the front end stuck.
We are also assuming that the surface is smooth enough so that sprung mass motion is the main
cause of suspension motion. This may not be the case at all, especially on dirt.
The effectiveness of using shock valving this way will also depend how much extension velocity the
right front has.
My own preference is to try to work with the springs instead, and valve the shocks for optimum
roadholding rather than trying to trick the shocks into controlling wheel load distribution.
WHY THE CHAINS, SIR?
When NASCAR teams use a chain for one of the sway bar links, are they using it as a lost motion
device, allowing wheel travel before the bar rate becomes active?
More common than a chain nowadays is an adjustable pad on the end of the sway bar, bearing on a
pad on the lower control arm. Chains are still seen sometimes in the lower divisions, where originalequipment-style bars are required. But the basic idea is the same either way: have a connection that
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transmits force in only one direction. The bar only resists rightward roll, unless it’s preloaded, in
which case it does resist leftward roll up to the point where it unloads.
The intent here is to help keep the car from going quite so loose when the driver gets the left front
wheel on the apron of the track, which is sometimes abruptly flatter than the banked turn.
Usually, the bar is run snug or slightly preloaded at static condition. That means that the bar acts just
like it normally would in a left turn. When the car is cornering, the bar has substantial load on it. The
one-way connection, be it a pad or a chain, will only go slack if the left front wheel hits the apron
hard enough to put the front suspension into a left roll condition – left front deflection greater than
right front. This leads me to question the use of these devices, especially since they make the car
loose when turning or spinning to the right, which can happen during a crash or when avoiding one.
Nevertheless, they are very popular.
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This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by email to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just email me and request to be added to the list.
ROLL CENTER MIGRATION, SOME MORE
The discussion of roll center definition in the June newsletter prompts this question from a reader:
Would you be able to discuss the effects of front lateral roll center migration for an oval track car
with a solid axle rear end (NASCAR style) – perhaps an example on a short track where there are
low speeds and aerodynamic loads, and higher amounts of vehicle roll where the left side suspension
could be travelling into rebound?
The questioner mentions that he is an engineer for a major car manufacturer, and expresses a desire
to remain anonymous, which is my usual practice in any case. Knowing that the questioner is an
engineer, I am going to assume here that the reader is conversant with the basics of roll center theory
as usually understood, and will not start at square one.
As those who read the June newsletter will know, I do not believe that the intersection of the front
view projected force lines can properly be considered the roll center, or moment center, or anything
of the kind. There are situations where you don’t get big modeling errors if you use the force line
intersection as a roll or moment center, and other cases where you get huge errors. This merely
illustrates that an incorrect analysis method can coincidentally produce correct or nearly correct
answers in certain cases, despite the incorrectness of the method itself.
I have also said that the roll center, properly assigned, should be considered a point in side view (of
the car), and its lateral position should be considered undefined. It lies in the transverse plane
containing the wheel center in all cases, or, in side view, it lies straight down or straight up from the
wheel center. So we really need only one number to define its position, namely its height. This
height is not the same as the height of the force line intersection. Rather, it is the mean height of the
two force line intercepts on a line I call the resolution line.
The resolution line is a vertical line in the front view, positioned according to distribution of lateral
force generated by the two tires. For example, if the right front tire is generating 75% of the front
lateral force, the front suspension resolution line is 75% of the track width away from that tire.
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Unfortunately, we do not know this distribution of lateral force exactly, in most cases. We have to
estimate it. That means our modeling of the suspension’s behavior is only as good as this estimate.
This is unfortunate, but ignoring the fact doesn’t make it go away. The behavior of the suspension
really does depend on the distribution of lateral force. To predict the jacking forces each of the
individual wheels generates, and thereby calculate an anti-roll or pro-roll moment, we must not only
know the suspensions’ geometry, but also the forces at the contact patches. Any analysis method that
takes this into account, even using an estimate for the lateral force distribution, is better than a
method that ignores this factor altogether.
What we’re doing here is directly analogous to modeling longitudinal anti effects – anti-dive, antisquat, anti-lift – in side view. It is widely recognized that when modeling longitudinal anti effects,
we have to know the front/rear distribution of longitudinal force, or try to estimate it with reasonable
accuracy. For example, for braking short of lockup, we use the calculated brake bias. If the front
brakes make 70% of the rearward force, we construct our resolution line 70% of the wheelbase back
from the front wheel center. We then look at where the front wheel side view force line intercepts
this resolution line. We take the height of this intercept as a percentage of sprung mass center of
gravity height, and that is our percent anti-dive. We can do the same for the rear wheel, and that’s
our percent anti-lift. When these are both 100%, the car will not pitch at all in braking, regardless of
wheel rates, nor will the whole car jack up or down.
We can likewise define a percent anti-roll for the right and left wheels in an independently
suspended front or rear pair, and we may also average these to define a percent anti-roll for the
wheel pair. The average height of the intercepts makes a good value to use for roll center height –
much better than using the force line intersection height, though in some cases the two values may
be similar. The average height of the intercepts, or roll center height, may also be described as the
sprung mass c.g. height times the percent anti-roll for the wheel pair. Also, the height of each of the
intercepts, as a percentage of sprung mass c.g. height, is that wheel’s percent anti-roll.
This definition of the roll center provides a number that can be accurately used for load transfer and
roll angle calculations, for it is a valid measure of the suspension’s geometric anti-roll properties.
Assigning a roll center location is useful not only for modeling or analysis, but also for discussion.
To use the method I’m advocating for discussion, it is useful to have default assumption for lateral
force distribution. I think assuming that the outside wheel generates 75% of the force is appropriate,
absent better information.
Note that suspensions only generate geometric anti-roll or pro-roll moments in response to carhorizontal (lateral or longitudinal) forces. Force line slopes, force line intersections, and force line
intercepts of the resolution line do not affect any tendency to roll, or resist roll, in response to carvertical forces. (Spring splits, or wheel rate splits, do affect this. So does an offset c.g., or static left
percentage other than 50%.)
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Of course, the questioner here is not asking about effects of changes to the location of the roll center
as I prefer to define it. He is asking about effects of lateral migration of the roll center as most
people conceive it, namely the intersection of the front view force lines.
And in fact we can say some things about the position of the force line intersection, and the
conclusions we can draw from it, for particular classes of situations. We can’t necessarily say the car
has more tendency to roll, other things held constant, if the intersection moves to the inside of the
turn, nor that the car has less tendency to roll if the intersection moves in the direction of roll, even
in a banked turn. However, we can make some more complex and qualified statements, for particular
sets of conditions or assumptions.
To begin with, there are certain situations where we don’t know much at all from the force line
intersection. If the force line intersection is at the contact patch center for either of the wheels, we
know that the opposite wheel’s force line is horizontal, and therefore the opposite wheel has no antiroll or pro-roll. However, the force line for the wheel on top of the intersection could be at any angle,
and therefore this suspension could have any amount of anti-roll or pro-roll. In this situation we
can’t say anything about the overall amount of anti-roll or pro-roll in the geometry from the location
of the force line intersection, nor can we infer the location of the roll center as I define it, without
additional information.
Parallel lines do not intersect. When the force lines are parallel, there is no force line intersection. In
this situation, users of force line intersection as the roll center will either say the roll center is
undefined, or that it has disappeared, or – arbitrarily – that it is on the vehicle centerline, at the
average height of the two force line intercepts of the centerline, which will be at ground level.
However, the parallel force lines could be at any angle, relative to car-horizontal. We don’t know
what that angle is; all we know is that it’s the same for both of them. We know that one wheel has
anti-roll and the other has pro-roll, but we don’t know how much. We know that the anti-roll and
pro-roll forces are equal if the tires are making equal car-lateral force, which would equate to a roll
center at ground level. But if the tire forces are unequal – and they usually will be – we cannot say
how much overall anti-roll or pro-roll the system has, and we cannot define the roll center my way,
without additional information.
There is a third unique class of situation – or, if you like, a special case of the parallel force line
situation – the one where both force lines are horizontal. In other words, the force lines are not only
parallel, but coincidental. In this case, we cannot say what the lateral location of the force line
intersection is. We may say there is an infinitely large number of them. We do know, however, that
all these points are at ground level, and we can say with certainty that the suspension has no anti-roll
or pro-roll, regardless of the magnitude of car-lateral forces at the contact patches. We can also say
that the resolution line intercepts of both force lines are at ground level, no matter where the
resolution line lies. Therefore we can define a roll center height my way, at ground level, despite the
fact that we cannot define a single force line intersection. In this case only, we can do this without
knowing, estimating, or assuming lateral force distribution.
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For all cases except the above three classes, we can calculate the slopes of the force lines from their
intersection. Knowing this, and a known, estimated, or assumed lateral force distribution, we do
know enough to assign a roll center my way, and to say something about the overall anti-roll or proroll characteristics.
We can also say which direction the force line intersection will move, for a known roll displacement,
if we know one more characteristic of the suspension: how the force line slope changes with
suspension movement.
William C. Mitchell, in his SAE paper no. 983085 entitled Asymmetric Roll Centers, introduces a
definable parameter that is useful in discussing this. He calls it the incline ratio. I find this
nomenclature to be suggestive of a different meaning, and I think Bill deserves recognition for
coming up with the idea, so I call it the Mitchell index.
By either name, we calculate this number as follows: We look at the centerline intercept of the force
line, and we note its rate of height change as the suspension moves in ride. We express the rise and
fall of the intercept as a proportion of the ride motion, and that’s the incline ratio, or Mitchell index.
If the intercept moves up and down at the same rate as the sprung mass, we have a Mitchell index of
1. If it doesn’t move at all, we have a Mitchell index of zero. If it moves up when the sprung mass
moves down, we have a negative Mitchell index. If it moves down when the sprung mass moves
down, by a lesser amount, we have a Mitchell index between 1 and 0. If it moves down when the
sprung mass moves down, by a greater amount, we have a Mitchell index greater than 1.
The case the questioner raised in the June newsletter, where a short-and-long-arm suspension has the
lower arms shorter than the uppers, illustrates a Mitchell index substantially greater than 1.
Likewise, a strut suspension has a Mitchell index greater than 1. A pure trailing arm suspension has
a Mitchell index of 0. Most short-and-long-arm layouts have Mitchell indices fairly close to 1 or a
bit greater. With unusually short upper arms, stock car front ends can have a Mitchell index a bit less
than 1. To get a Mitchell index of zero with a short-and-long-arm suspension, we need either very
long lower arms, or very short uppers. The lengths have to be in accordance with Olley’s Rule: the
lengths of the control arms have to be inversely proportional to their height above ground level,
usually as measured at the ball joints. For typical stock car lower arm and spindle (upright)
dimensions, that means upper arms somewhere around six to seven inches long, rather than the
lengths of 9 inches or more commonly seen. Not surprisingly, Mitchell indices less than zero are
uncommon.
The Mitchell index can be different for the right and left wheels, and in oval-track stock cars it
usually is, though not by much. It also varies some as the suspension moves, but it does not undergo
large, sudden changes. We also end up defining it differently if we take the centerline as being where
the frame builder marked it, or as being at the midpoint of the front track, or as being the edge view
of the longitudinal c.g. plane. These nuances aside, if we consider roll to be angular motion about the
ground intercept of whatever centerline we’ve defined, then we can say certain things about how the
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force lines and their intersection will move in particular combinations of ride and roll, based on the
Mitchell indices of the two individual wheel suspensions.
If the Mitchell index is 1, the force line slope doesn’t change in roll. If the Mitchell index is 1 for
both right and left wheels, the force line intersection doesn’t move in roll.
To take the most common category of cases first, suppose that, at static condition, the force line
intersection is above ground level and between the wheels. In this condition, if the Mitchell index is
greater than 1, the force line intersection always moves laterally opposite to the direction of roll. The
force line for the outside wheel (right wheel in a left turn) loses inclination, while the force line for
the inside wheel gains inclination. In the case the questioner cites, the intersection would move to the
right. If the Mitchell index is less than 1, the force line intersection moves toward the outside wheel
instead. The outside wheel force line gains inclination, while the inside wheel force line loses
inclination.
In general, the former case implies a decrease in overall geometric anti-roll, and the latter implies an
increase in overall geometric anti-roll, even with no change in force line intersection height, because
the outside wheel generates more lateral force. Correspondingly, the roll center, defined my way,
drops in the former case and rises in the latter case, even with no change in force line intersection
height.
Now let’s change things a little. Let’s suppose the force line intersection is between the wheels but
below ground level. This is actually not an uncommon condition in stock cars, especially drop-snout
cars on banked turns.
Now, if the Mitchell index is greater than 1, the force line intersection moves toward the outside
wheel in roll! The outside wheel is still losing anti-roll, or should we say gaining pro-roll. The inside
wheel is still gaining anti-roll, or losing pro-roll. So the change in roll resistance is still the same as
when the force line intersection was above ground, but the lateral migration of the force line
intersection is in the opposite direction – toward the outside wheel.
If the Mitchell index is less than 1, again the change in roll resistance is the same as with an aboveground intersection – it increases. And again, the lateral migration of the intersection is in the
opposite direction – toward the inside wheel.
This illustrates that we cannot infer the change in roll resistance knowing only the direction of lateral
migration of the force line intersection, even supposing that the intersection height isn’t changing.
The wildest migrations of the force line intersection occur when the force lines are close to
horizontal, and close to parallel. Small changes in force line angle will make the intersection move
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all over the place. Small ride motions can make it move from above ground and way out to the right
to below ground way off to the left. Does this mean the geometric anti-roll or pro-roll moment is
varying all over the place, or that the car’s properties in a banked turn are varying all over the place?
Not at all, because the force line slopes and individual wheel anti-roll and pro-roll are not changing
much. And, correspondingly, the height of the roll center as I define it doesn’t change much.
All of this holds true regardless of whether the turn is banked, and regardless of what kind of
suspension is at the other end of the car.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
ERRATA AND ADDENDA
Thank you to readers who have pointed out some detail discrepancies in my recent columns in
Racecar Engineering, which are drawn from this newsletter.
In the April newsletter I originally stated that for least bearing loads with an outboard brake, the
caliper should be somewhere in the upper rear quadrant of the disc. Shortly after sending out that
issue, I sent out a correction saying that should be the lower rear quadrant. This correction was
supposed to be incorporated when the material was published in the magazine, but unfortunately the
original version was what ran (July 2004 issue). So a correction is in order on this point, for those
who read me in the magazine.
In my October 2004 column, drawn from the June 2004 newsletter, there was some disagreement
between what I said about the Williams Formula 1 suspension and the second picture that ran in the
magazine, showing the suspension from above and behind. I had said the forward portion of the
upper wishbone was not aligned with the tie rod, whereas in the picture it appears to be aligned.
Some readers have understandably called this to my attention.
The picture in question was chosen by the magazine, not supplied by me. I based my comments on
other pictures, which I did not have in electronic format. If anybody is to be faulted here, I am.
Anyway, it appears there have been two versions of the suspension. In the version shown in the
magazine, the bump steer and aerodynamics appear good, but the camber control properties appear
poor. In the version I was looking at when I wrote the text, the control arm appears to have been
leveled out by moving the forward pickup point down a bit, without the steering rack being lowered
to match.
Without inside knowledge of the team’s internal affairs, I am of course speculating as best I can from
partial evidence. The best explanatory theory I can devise is this: the original version had the
wishbone and the tie rod as shown in the October column’s illustration. Perhaps the camber control
was consciously compromised to get the nose higher and aid airflow underneath it, which was also
partially the object of the tusk nose design. To get the floor of the nose up, the driver’s feet had to go
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up. That forced the steering rack, the pedals, and everything else to go up. The wishbone then had to
agree with the steering, to prevent bump steer and get good airflow over the tie rod and wishbone.
When it was found that the car lacked front grip, and other fixes didn’t cure the problem, the team
tried moving the wishbone pickups down. Moving them down a little on the existing tub was
feasible, but moving the steering rack was tougher. So as a temporary experiment and hopefully a
temporary solution, the team decided to accept some bump steer and rely on driver skill to deal with
that, and see if improved camber control would help the grip.
Raising the upper ball joints and outer tie rod ends was not an option, because the wheel rim was in
the way. Lowering the rack was not an option, because the driver’s feet (or maybe other elements of
the car) were in the way. So the team made the only modification they could, under the
circumstances.
I also noticed elsewhere in the October issue that as of the Hungarian Grand Prix the team had
abandoned the tusk nose design, although the tub has not been re-done.
I understand they are going to try an entirely new approach for 2005.
TIRE LOAD SENSITIVITY AND WEIGHT TRANSFER IN TRAILBRAKING
In the Forum (letters) column of that same October issue was a letter from a physicist, responding to
an earlier article on the theory of cornering line and trailbraking by Erik Zapletal. Erik had correctly
noted that forward load transfer (weight transfer, in customary vernacular) tends to improve the
lateral acceleration capability of the front wheels, at the expense of the rear ones. The physicist took
issue with this, and pointed out that adding weight to a wheel pair reduces lateral acceleration
capability, because due to the phenomenon we call tire load sensitivity, the coefficient of friction
diminishes as we add load. Mr. Zapletal replied that this is true, but load sensitivity is a minor effect.
(He also noted that other factors enter into this, including aerodynamics, brake bias, and camber
changes.)
Who is correct? Both are, partly. But I think I can explain the matter a little better.
By the way, Erik is a sharp guy and it was he who first pointed out my aforementioned error on
brake caliper location. Hopefully, I am returning a favor and shedding some light here, not being a
pain.
This question illustrates perfectly why I prefer to speak of load transfer rather than weight transfer.
The effects of forward load transfer under braking are quite distinct from the effect we get if we
move mass forward in the car. Moving mass forward in the car adds understeer. Forward load
transfer in braking adds oversteer. Both effects can be said to relate to tire load sensitivity.
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When we move mass forward in the car, we increase both the normal (vertical or perpendicular to
the road) force on the front tires and the centrifugal (inertial) force the tires must overcome to
produce any given lateral acceleration. Consequently, the front end’s lateral acceleration capability
depends not on whether the force capability of the tires increases, but on whether it increases at the
same rate as the normal (and centrifugal) force. The ratio of the tire’s force capability to the normal
force is the coefficient of friction. This diminishes with increasing normal force, so in any situation
where we add weight to the front end, the lateral acceleration capability diminishes.
When we brake, however, most of the load increase on the front wheels does not come from mass
moving forward on the wheelbase, although a small amount of such motion does usually occur. The
increase in front wheel loading comes primarily from the forward pitch couple which inevitably
results from the tires exerting a rearward force at ground level and the car’s inertia exerting an equal
and opposite forward force above ground level. To prevent the car from somersaulting, the front tires
exert an increased support force against the ground, and there is a corresponding decrease in support
force at the rear, creating an equal and opposite anti-pitch couple. Because the center of mass has not
moved appreciably on the wheelbase, the front wheels are not required to overcome an increased
centrifugal force per unit of centripetal acceleration in proportion to their increased normal force.
The normal force increases, while centrifugal inertia force for a given car-lateral (centripetal)
acceleration remains largely unchanged. Consequently, lateral acceleration capability for the front
wheel pair increases.
In both cases, the normal force increases and the coefficient of friction decreases. But in the former
case, the centrifugal force per unit of acceleration increases with the normal force, whereas in the
latter case it does not.
The latter case may be said to be similar to what happens when we add aerodynamic downforce. We
add significant normal force, or load, without adding significant mass.
WHY ARE WIDE TIRES BETTER?
It has been recognized for about 40 years now that wide tires provide more grip, at least when we are
not limited by aquaplaning. One might suppose that this effect would be be well understood by now,
on a theoretical level as well as a practical one. Yet the matter seems to be receiving a lot of attention
from various authors lately. This seems to be due in part to the need for mathematical tire models to
be used in computer simulation. I have encountered the question at least twice in the past month,
once in a seminar presented by Paul Haney, based on his recent book about tires, and once in Paul
Van Valkenburgh’s November Racecar Engineering column. The issue has also come up in my
work as an advisor to the UNC Charlotte Formula SAE team.
On the face of it, one might wonder why there is any controversy about this, and also why it took
people until the 1960’s to try wide tires. More tire, more rubber on the road. More rubber on the
road, more traction – right? Why wouldn’t this be obvious?
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Essentially, there are two reasons it wasn’t obvious. First, according to Coulomb’s law for dry
sliding friction, friction is independent of apparent contact area. It depends instead on the nature of
the substances in contact, the normal (perpendicular) force, and nothing else. Second, a tire’s contact
patch area theoretically doesn’t vary with its width anyway. If we widen the tread, the contact patch
just gets shorter, and the area theoretically stays the same.
Let’s consider each of these notions. Coulomb’s law applies quite accurately to hard, dry, clean,
smooth surfaces. However, a tire tread is a soft, tough, sometimes tacky substance in contact with a
hard, rough surface. When two hard, smooth surfaces are in contact, they actually touch only at a
small percentage of their apparent or macroscopic contact area. Friction depends on molecular
bonding in the small microscopic contact zones. As normal force increases, the microscopic contact
area increases approximately proportionally, and consequently friction is directly proportional to
normal force.
With rubber on pavement, however, there is not only the usual molecular bonding but also
mechanical interlock between the asperities (high points) of the pavement and the compliant rubber.
Sliding then involves a combination of shearing the rubber apart and dragging the asperities through
it as the rubber reluctantly oozes around the asperities. The interface somewhat resembles a pair of
meshing gears. With gears, when we increase the size and number of teeth in mesh, we increase the
force required to shear off the teeth. It would be reasonable to expect a similar effect with the
interlock between the tread and the pavement.
With increasing normal force, this interlock gets deeper, as the asperities are pushed further into the
rubber. However, we might reasonably expect that at least beyond a certain point, the asperities are
pushed into the rubber to pretty nearly their full depth, and further increase in normal force does not
proportionately increase the mechanical interlock. With greater macroscopic contact area, it should
take a greater normal force to reach this region of diminishing return.
A tire typically does show characteristics that would match this hypothesis. It will often have a range
of loadings where its coefficient of friction is almost constant; where friction force is almost directly
proportional to normal force. Above this range, the tire exhibits much greater load sensitivity of the
coefficient of friction. The curve of friction force as a function of normal force goes up almost as a
straight line for a ways, then begins to droop at an increasing rate.
Of course, the contact patch does not remain the same macroscopic size as load increases. It grows
as we add load. Nevertheless, this contact patch growth is evidently not enough to keep the
coefficient of friction constant.
The contact patch growth is interesting in itself, and a bit counter-intuitive. A tire can be considered
a flexible bladder, inflated to some known pressure, and supporting a load. If such a bladder is
extremely limp when uninflated, like a toy balloon, and we inflate it, place it on a smooth, flat
surface, and press down on it with a known force, the area of contact with the surface is equal to the
normal force divided by the pressure: A = Fn/P.
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If a tire approximates this behavior, then it follows that the contact patch area depends only on the
load or normal force and the inflation pressure. If we make the tire wider, then at any given load and
pressure the contact patch doesn’t get bigger, it just gets wider and shorter.
Accordingly, much discussion of the reasons a wide tire gives an advantage focuses on reasons we
might expect a wider tire to yield greater lateral force than a narrower one, assuming similar
construction and identical pressure, tread compound, and load.
One theory, advanced by the late Chuck Hallum and evidently picked up by Paul Van Valkenburgh
in his recent column, is that a tire is primarily limited by thermodynamics. It generates drag when
running at a slip angle. The drag times the speed equals a power consumption, or rate of energy flow.
This energy is converted into heat. For the system to be in equilibrium, the heat must be dissipated as
fast as it is generated. Even short of the point of true equilibrium, the tread compound needs to be
kept below a temperature where it softens to the point of being greasy rather than tacky. If the
contact patch is shorter, that means that each square inch of tread surface spends less time getting
heated and more time getting cooled.
Also, when a tire is operating near its lateral force limit, the front portion of the contact patch is
“stuck” to the road and the rear portion is a “slip zone” in which the tread moves across the
pavement in a series of slip-and-grip cycles. The slip zone grows as we approach the point of
breakaway. Beyond the point of breakaway, the entire contact patch is slip zone. The slip zone
generates less force and more heat than the adhering zone. A shorter, wider contact patch is thought
to have a larger adhering zone and a smaller slip zone at a given slip angle, and wider tires are also
known to reach peak force at smaller slip angles. Therefore, a wider tire is not only better able to
manage heat, but also generates less heat at a given lateral force.
This all makes sense, but it fails to explain why wide tires give more grip even when stone cold.
There is little doubt that they do. If you have a street car with four identical tires, and you replace the
rear tires and wheels with ones an inch wider, using the same make and model of tire, with no other
changes, the handling balance will shift markedly toward understeer. You will see this effect at all
times, from the first turn in a journey to the last. Surely this effect is not coming from heat
management.
Paul Haney explains this by the larger-adhering-zone theory described above. The tire makes more
efficient use of its contact patch, even if the contact patch isn’t larger.
As much sense as the above theories make, they ignore some real-world effects that have a bearing
on the situation.
First of all, the degree to which tires follow the A = Fn/P rule varies considerably. A very flexible
tire, at moderate load, may have a contact patch as large as 97% of theoretical. A fairly stiff tire may
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be well below 80%. We are all aware of run-flat tires currently being sold, which will hold up a
Corvette with no inflation pressure at all. As P approaches zero, Fn/P approaches infinity. If A does
not approach infinity, and the tire does not go flat, the contact patch area as a percentage of
theoretically predicted area approaches zero.
One might suppose that the effect of carcass stiffness would be significant mainly in street tires, with
run-flats being an unrepresentative extreme. Yet I have seen dramatic differences in carcass rigidity
in different makes of racing tires intended for the same application. The Formula SAE car run by the
University of North Carolina Charlotte uses 10” wheels. Hoosier and Goodyear both make 6”
nominal-width tires for the application. The stiffnesses of these tires differ dramatically. The
Hoosiers are much more flexible than the Goodyears. The Goodyears are so stiff that they will
support the front of the car (without driver), with little visible deflection, when completely deflated –
run-flat racing tires! How closely do these tires approximate A = Fn/P in this load range? Not very
closely at all.
My point here is that tire stiffness, vertically, laterally, and otherwise, is not purely a function of
inflation pressure, so it is a bit risky to try to infer contact patch size from pressure and load.
Therefore, we don’t necessarily know that two tires differing only in width do have the same contact
patch area at the same inflation pressure and load, or even that tires of the same size do.
Anyway, if it is approximately true that A = Fn/P, it follows that a wide tire will have greater vertical
stiffness, or tire spring rate, than a narrow one, at any given inflation pressure. It will also have a
smaller static deflection at a given load, which is why the contact patch is shorter. The flip side of
this is that for a given static deflection or tire spring rate, a wide tire needs a lower inflation pressure.
Consequently, if we compare wide and narrow tires at similar static deflection or tire spring rate,
rather than similar pressure, they will have similar-length contact patches and the wider one really
will have more rubber on the road, just as we would intuitively suppose from looking at them.
As we make a tire wider, not only does vertical stiffness increase for a given inflation pressure, so
does the tension in the carcass due to inflation pressure. A tire is a form of pressure vessel. We may
think of it as a roughly cylindrical tank, bent into a circle to form a donut or torus. Borrowing from
the terminology of pressure vessel design, we may speak of the “hoop stress” in the walls: the tensile
stress analogous to the load on a barrel hoop. For a given inflation pressure, the hoop stress is
directly proportional to the cross-sectional circumference, or mean cross-sectional diameter. When
the carcass is under a higher preload, the tire acts stiffer laterally. This effect can easily be seen in
bicycle tires. A fat bicycle tire will feel harder to the thumb than a skinny one, at any given pressure.
If we try to inflate a mountain bike tire to the pressure we’d use in a narrow road racing tire, the tire
will expand its bead off the rim and blow out. So when we compare narrow and wide tires at equal
inflation pressures, the wider one will be stiffer laterally as well as vertically, and it will achieve this
at no penalty in contact patch size.
Finally, there is the question of tread wear. As we have noted, if the contact patch is longer, it has a
larger slipping zone near the limit of adhesion, and it also spends a greater portion of each revolution
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in contact with the road. Not only do these factors influence how hot the tire runs, they also influence
how fast it wears. Therefore, assuming good camber control, a wide tire should last longer than a
narrow one, with similar tread compound. The astute reader will see where I’m headed with this. If
we need to run a given number of laps or miles on a set of tires, then with wider tires we can trade
away some of the inherent longevity advantage, and run a softer compound.
Okay, summing up, what does a wider tire get us?
1. It runs cooler, and/or
2. it makes more efficient use of its contact patch by having a greater percentage adhering,
and/or
3. it can run at lower inflation pressure and therefore actually have a larger contact patch,
and/or
4. it can have greater lateral stiffness at a given pressure and therefore keep its tread planted
better, and/or
5. it can use a softer, stickier, faster-wearing compound without penalty in longevity.
Note that most of these effects in turn play off against each other. We can blend and balance them,
and get a tire that is somewhat cooler-running, has a somewhat lower operating pressure and
somewhat larger contact patch, has somewhat greater lateral stiffness, and survives long enough with
a somewhat stickier compound, all at the same time. That would explain an improvement in grip,
wouldn’t it?
REAR PERCENTAGE VERSUS YAW INERTIA
Setting up race cars is invariably a compromise. Most of these are well documented, but I have
found little on the compromise between longitudinal weight distribution and polar moment of inertia.
I race a 250bhp, 900K V8 MGB which, unfortunately for a rear-wheel-drive car, has a frontal
weight bias of around 60%. The fuel tank of around 40L overhangs the rear axle, which creates a
moment around the rear axle and thus helps to remove weight from the front.
There is space in front of the rear axle to place two tanks where the batteries would have gone on
the road car. This would have the effect of reducing the polar moment of inertia while slightly
lowering the center of gravity and possibly allowing softer rear springing. It would also improve
safety (as long as it is protected from the prop shaft running between the two tanks!). However, it
would increase the front bias.
This would be quite a lot of work and expense, so I would be grateful if you could comment on the
benefits or otherwise of this approach.
From a vehicle dynamics standpoint, I would opt for more rear percentage rather than less yaw
inertia, especially in a car that is so nose-heavy now.
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Within limits, yaw inertia can be coped with by driving technique. In some situations, it can even
make the car faster. Overall, though, less yaw inertia is better, particularly when the course demands
high yaw accelerations, as when negotiating chicanes or street-circuit turns that come in quick
succession. But steady-state handling and ability to put power down are more important. A reardrive car with only 40% rear weight and a powerful engine is seriously traction-challenged,
especially when exiting turns. Any further reduction would not be good.
With more front percentage, you will actually have to stiffen the rear suspension, at least in roll, with
respect to the front. Otherwise, you will be adding understeer. The inside rear will then be extremely
light when cornering. It probably is now.
One situation where yaw inertia can make a car faster is where the car may unexpectedly encounter a
slippery spot in the middle of a turn. If the slippery patch is short enough so the front and rear of the
car hit it separately, the car will experience understeer and then oversteer in very quick succession: it
will do a wiggle. If it has little yaw inertia, it will do a big wiggle. If it is close to the limit, it may
spin. If the driver wants to allow a margin of safety to increase the chances of catching the wiggle
before it becomes a spin, for a given level of risk the driver must stay further from the limit in a car
with little yaw inertia.
For this reason, in the days of high-speed open-road racing, many engineers regarded yaw inertia as
desirable, and this was thought to be one of the advantages of a front-engined car with a transaxle,
and a problem for the rear-mid-engine layout.
Even back then, everybody recognized that weight distribution change with fuel burn-off was not
good. The Lancia-Ferrari of the mid-1950’s, with its pontoon fuel tanks between the front and rear
wheel on each side, appears designed to get much of the fuel amidships longitudinally, while
preserving high yaw inertia. As Ferrari developed the car after taking it over from Lancia, they
moved the side tanks inside the body, reducing yaw inertia, and this is generally thought to have
improved the handling.
It is worth noting that the Lancia-Ferrari predated foam-baffled fuel containers. Even with some
sheet metal baffles, there must have been considerable fuel slosh in those tanks, and that can’t have
been good for controllability.
As regards crash safety and fire risk with the fuel inside the wheelbase versus outside, there are pros
and cons both ways. If the fuel is within the wheelbase, it is less likely to spill when the rear takes a
hit. On the other hand, if it does spill, it is more likely to spill into the driver’s compartment. And it
can still spill, as recently demonstrated in Dale Earnhardt Jr.’s crash in the Corvette at Sebring.
At the recent SAE Motorsports Conference in Dearborn, Michigan, I had the opportunity to ask a
very distinguished panel of safety experts about the safety aspects of fuel location. Gary Nelson of
NASCAR said that they strongly considered having the fuel ahead of the axle in the new NASCAR
chassis they are developing, but decided against it. The reason, he said, was that the greatest risk of
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fuel fires occurs in refueling during pit stops. The present rear location was considered preferable
from that standpoint. This may be less of a factor where the races are short and there are no fuel
stops.
ROLL SPRINGING PRELOAD IN MONOSHOCK SETUPS
I race a 1998 Dallara F398 F3 car in an amateur series in the UK. The car is fitted with a
monoshock front suspension with Belleville washer stacks to control lateral movement of the rocker.
I have attached a couple of photos and a copy of the setup page from the Dallara build manual.
[To keep file size manageable for e-mailing, I am including only one photo in the newsletter. As it
appears here, it’s on its side. Rear of the car is to the left, left side of the car is up. The assembly
shown is located on top of the footwell area of the monocoque tub.]
My questions concern spring preload. I have read many books and can find little information on the
subject.
Question 1: The front spring is preloaded so that in a static condition there is sufficient load to
support the weight of the car, i.e. there is no front droop travel. Can you explain to me the effect of
increasing the amount of preload compared to, say, fitting a stiffer spring with less preload? Does
this cause the car to behave differently in low-speed corners when there is little downforce,
compared to high-speed corners?
Since the coilover only acts in ride, its action only affects the wheel rate in ride, and has no effect on
the wheel rate in roll. It does affect ride height, and that has effects on both downforce (higher ride
height makes less downforce, as a rule) and geometric roll resistance (roll center height – higher
front ride height means more front roll resistance, as a rule, because the roll center usually rises and
falls with the sprung mass).
With a setup as the questioner describes, with preload just equal to static load, if there is no
downforce, the wheel pair cannot extend synchronously (in ride) past static position, but one wheel
of the pair can if the other moves into compression a similar amount. If there is slight downforce, as
at low speed, there can be a little ride movement in the extension direction. When there is a lot of
downforce, the suspension can move quite a bit in ride extension before it reaches static position and
tops out.
What happens if we preload the suspension more in ride? Assuming non-spring components to be
rigid, we then get no ride motion at all in either direction, until force in the compression direction
(from aero, road irregularities, or rearward acceleration, or any combination of these) overcomes the
preload.
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If, on the other hand, we add spring rate and not preload, we get less ride motion in compression for
a given load increase, but we always get some.
So a stiffer spring begins to move with any load increase. A softer spring, with more preload, doesn’t
yield at all until the preload is overcome, but then moves more per unit of load increase.
Well, do we want the suspension to move more or not? It’s a tradeoff. If the suspension moves more,
wheel loads change less, but camber, suspension geometry, and aerodynamic properties change
more. If we cinch down the suspension so it can’t move, then we keep camber and geometry from
changing, but wheel loads will vary greatly over irregularities, and the wheels may even become
airborne. We get good aerodynamic consistency, up to the point where the wheels come off the
ground. Beyond that point, ride height and pitch angle can change very rapidly.
Suppose we have to keep the car at a certain height at a certain peak speed, with a certain aero
package. Suppose we have a choice of a soft ride spring, heavily preloaded, or a stiff ride spring, set
to zero droop but with no other preload, or the stiffer spring allowed to move in droop.
What would give better behavior in low-speed corners? If there are bumps to contend with, the stiff
spring not preloaded will be best, because it will alow the wheels to follow the bumps best. The stiff
spring set for zero droop will be next best. The soft spring heavily preloaded will be worst, because
it will essentially be locked solid in both directions.
If, on the other hand, the track is very smooth, the heavily preloaded ride spring may actually confer
a slight advantage, because it will control camber a little better due to the lack of ride motion.
These are the same basic advantages and disadvantages we see with soft and stiff setups generally.
Question 2: Roll control of the front suspension is achieved by using Belleville washer stacks, which
can be configured to various spring rates. The build manual recommends minimum and maximum
amounts of preload that should be applied to each stack configuration. I understand that if the
preload is lost on one of the stacks during roll, then the total stack stiffness suddenly halves, which is
why there is a minimum preload. I guess that the maximum value is ther to ensure that stacks do not
go solid. Apart from the above, am I right in thinking that changing the Belleville preload will have
no effect on the car?
Assuming the washers themselves are fairly linear, as suggested by the listing of a single rate for
each stack configuration, there should be no change in handling properties or rates with variations in
preload, provided nothing unloads or goes solid.
You might be able to test the washers to see how linear they really are.
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It will be apparent that you could create stacks that are non-linear if you wanted to. To do that, you
would have to have some of the washers doubled, tripled, or quadrupled, and others not. None of the
factory stacks include anything like that.
I wouldn’t really suggest trying deliberately non-linear stacks, but if you did, that would create a
situation where the system would become more sensitive to preload. If you had enough preload to
compress the softer portions of the stacks to solid when the rocker is centered, you could create a
stepped falling rate. If you had the softer portions not compressed to solid with the rocker centered,
you could get a stepped rising rate instead.
I imagine you don’t race on ovals, but this could get interesting when using asymmetical setups with
diagonal percentages other than 50%.
WHY SO FEW REAR MONOSHOCK SETUPS?
With monoshocks appearing on more designs at the front, is there any reason, other than packaging,
that they are never used on the rear of a car?
The Dallara system above is typical in that the roll mode is undamped. I do think it is possible to
incorporate a damper in such a mechanism, but it would involve making your own, and the relatively
small travel might be a disadvantage.
The Dallara information sheet has a partial sectional view of the rocker mechanism, showing
something that looks like a needle valve, which conceivably might be part of a damping mechanism,
but the questioner informs me that it’s part of a position sensor, and there is no roll damping.
With a conventional two-coilover suspension, we get damping in both ride and roll.
If a car has no roll damping at either end, it will oscillate in roll and possibly in warp (opposite roll at
the front and rear). Really, we’d like to have roll damped at both ends, and have at least the lowspeed roll damping adjustable.
But if we are going to damp only one end of the car in roll, it should be the rear. Here’s why: rear
roll damping creates an anti-roll moment at the rear when roll velocity is outward, early in the turn.
It creates an anti-de-roll (in other words, pro-roll) moment late in the turn when the car’s roll
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velocity is inward. That loosens the car (adds oversteer) during entry, and tightens it (adds
understeer) during exit. This tends to compensate for the tendency of yaw inertia to create understeer
during entry and oversteer during exit.
Actually, we don’t always want this, or if we do, we can have too much of a good thing. Driving
style, brake bias, driver preference, and other factors enter into this, so really we’d like adjustable
roll damping at both ends of the car. But it’s better to have the roll damping loosening entry and
tightening exit than vice versa, for the majority of setups, drivers, and situations.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
ROLL CENTER BELOW GROUND
Your October column [based on the June 2004 newsletter] addressed a reader’s question about the
possibility of a roll center being deliberately placed below ground level. I’ve thought quite a bit
about what I call “anti-jacking”, and I’ve seen no real references to below-ground roll centers. If
we put the roll center below ground, wouldn’t this tend to put more force on the inside wheels than
the outside wheels? Because of the non-linearity of the coefficient of friction, wouldn’t this give,
effectively, more total friction, and therefore more centripetal acceleration?
Taking the last question first, if we assume that the inside and outside tires are symmetrical and
identical, and are running at identical absolute camber, with the same camber direction relative to the
turn (e.g. x degrees positive on the inside wheel and x degrees negative on the outside wheel), and
assuming the car has 50% left weight at static, then we’d ideally like no load transfer inward or
outward. If the outside tire has more favorable camber than the inside one (common in road racing),
or the outside tire is larger (common in oval track racing, rules permitting), then we’d ideally like a
bit more than 50% of the load on the outside tire.
As a practical matter, however, we always get more load transfer than we’d like, and we’re always
trying to reduce it. We don’t really want more than half of the load on the inside wheels, but we’re
always trying to move the situation in the direction of more load to the inside.
The total load transfer for both wheel pairs, at a given lateral acceleration, depends only on the
center of gravity height and the track width. The only way to get zero load transfer at both ends of
the car would be to have the c.g. at ground level. The only way to get load transfer inward at both
ends of the car would be to have the c.g. below ground level. This is of course impossible for a car as
we would normally conceive it, running on a flat road. It would only be possible if the car could
hang in a trench between two tracks, or if the wheels ran on elevated rails.
About all we can do with roll center height (or, more properly understood, with geometric antiroll/pro-roll), springs, and anti-roll bars is to control what share of the inevitable load transfer is
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borne by the front wheel pair compared to the rear. We also can control the amount of roll, which
has a small effect on total load transfer because the c.g. moves outward slightly as the car rolls.
We normally think of the sprung mass as a rigid body, supported on two roll-compliant support
systems (the front and rear suspensions and wheel pairs). The two roll-compliant systems resist the
rigid body’s roll moment in parallel with each other. Each suspension system absorbs a portion of
the roll moment proportional to its overall roll resistance.
That overall roll resistance has three components: geometric (from the suspension linkages), elastic
(from the springs and anti-roll bars), and frictional (from the dampers and the mechanical or
Coulomb friction in the system).
There is another component of load transfer as well: the unsprung mass component. This is
commonly thought of as acting only through the tires, and not through the suspension. It would
therefore be unaffected by suspension geometry. Actually, this is not strictly true with independent
suspension, although it is correct for beam axles. A reader recently sent me some very insightful
information about this, which we will take up in a future issue. The unsprung masses in an
independent system do usually create some moments on the sprung mass, through the suspension
linkage, which are resisted by the springs and anti-roll bars and are affected by both elastic
coefficients and linkage geometry. We will ignore these effects for now, in the interest of simplicity.
If the roll center for the front or rear wheel pair – understood in the usual way, as the intersection of
the front view force lines – is below ground level and between the wheels, that implies geometric
pro-roll on both wheels. The outside wheel’s linkage generates a downward jacking force in that
wheel’s suspension, and the inside wheel’s linkage generates an upward jacking force. The resulting
couple acts to roll the sprung mass outward, exaggerating roll. Considered in isolation, this does add
load to the inside wheels, and remove load from the outside wheels.
However, if this moment were not resisted somehow, the sprung mass would accelerate outward in
roll and wouldn’t stop: the car would turn over. So it falls to the springs, anti-roll bars, and any
frictional forces to resist the overturning moment, unassisted by any anti-roll forces from the linkage
geometry. Additionally, the springs, anti-roll bars, and frictional effects must resist the pro-roll
moment created by the linkages.
Therefore, if we have pro-roll geometry at both ends of the car (roll axis below ground), the elastic
component of the roll resistance just gets very large, and there is still a net anti-roll moment from the
suspension as a whole. Since the suspension is supported only by the tires, any moment generated in
the suspension reacts through the contact patches and creates a load change there. That means there
is net outward load transfer, even if the geometric moments are the “wrong” way.
Actually, it is theoretically possible to get inward load transfer, with a c.g. above ground level, at one
end of the car only. I doubt that there is any real-world situation where we’d want such a setup, but it
is an interesting hypothetical curiosity. If we used geometric pro-roll, combined with a wheel rate in
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roll of zero or nearly zero, at one end of the car only, we could achieve inward load transfer at that
“soft” end. To get sufficient ride stiffness, we’d have to use a springing system that acted only in
ride, such as the Z-bar at the rear of a Formula Vee or the third spring on a modern high-downforce
car.
The other end of the car would then have to resist not only the overturning moment of the entire car,
but also the pro-roll moment from the suspension at the “soft” end of the car. We would then get
outward load transfer at the “stiff” end greater than the total outward load transfer for the car, and a
small inward load transfer at the “soft” end, equal to the difference.
This would work up to the point where the “stiff” end lifted a wheel. The car would then
immediately flop over onto the bump stops at the “soft” end. The “soft” end would then no longer be
soft, and we would start getting outward load transfer at both ends of the car.
As for net downward jacking, in most cases if the front view force line intersection is below ground
and between the wheels, we will get some net downward jacking. However, it is possible we could
get net upward jacking if the inside wheel has a substantially steeper force line slope than the outside
wheel. That might create an upward force from the inside wheel’s linkage greater than the downward
force from the outside wheel’s linkage, despite the smaller contact patch force at the inside wheel.
This would imply a force line intersection off-center toward the inside wheel, though still within the
track width. That is not necessarily an unrealistic case. We could easily encounter it in a lowered
production car strut suspension, in a rolled condition. This is an interesting case, because it illustrates
that there are situations where the car does not roll about the force line intersection, or even do
anything close to that. If it did, it would have to move downward rather than upward with roll – and
if the upward jacking on the inside wheel exceeds the downward jacking on the outside wheel, the
car clearly doesn’t do that at all.
ROLL MOMENTS FROM LONGITUDINAL ANTI
Some people tell me that anti-dive and anti-squat act to stiffen the suspension when forward or
rearward forces are present at the wheels. Does that mean these effects add roll resistance? How
does this really work?
Anti-dive at the front wheels does impose a bit of a roadholding penalty, because it requires the
contact patch to move forward as the suspension compresses, at least if we imagine the imagine the
wheel as locked. Or, we might view this effect as requiring an increase in wheel rotational speed
with respect to the caliper, as the suspension yields to a bump. The effect varies somewhat with the
abruptness and height of the bump, the outside diameter of the tire, whether the hub moves forward
in compression or not, and how hard we’re braking. However, anti-dive, even in an amount that
completely eliminates dive (100% anti-dive), does not completely lock up the suspension as some
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authors have suggested. It merely acts counter to our desire to have the wheel move backward
relative to the car, as well as upward, when the wheel hits a bump.
At the rear of the car, things are a bit different. Anti-lift in braking and anti-squat in forward
acceleration cause the contact patch to move rearward in compression rather than forward, while of
course the bumps still come at the wheel from the front. So rear longitudinal anti actually improves
the system’s ability to yield to a bump.
Jacking forces, whether lateral or longitudinal, do not in themselves add to wheel rate or subtract
from it, provided that the jacking forces do not change with wheel movement. The jacking force
simply acts in parallel with the wheel rate or elastic forces, which are displacement-dependent. That
doesn’t mean the jacking forces can’t create roll moments or affect wheel loads. They definitely can.
While anti effects do not necessarily vary as the suspension moves, it is very common for both
longitudinal and lateral anti effects to vary with suspension displacement. Most often, both lateral
and longitudinal anti diminish as the suspension compresses, and increase as the suspension extends.
This is not so in all cases, however. A counter-example would be the trailing arm front suspension
on a VW beetle. The arms are equal-length and parallel to each other, and at static condition they
slope down a bit toward the rear. As the suspension compresses, the arms quickly reach horizontal,
then begin to slope upward to the rear. The suspension goes from decreasing pro-dive to increasing
anti-dive. The direction of change is consistently toward anti-dive as compression increases.
A NASCAR front end is an extreme case of the opposite, and more common, tendency. It changes
rapidly toward pro-dive with compression, because the lower control arm is a semi-leading arm
(pivot axis angled dramatically outward at the rear in plan view) while the upper control arm is
almost a purely transverse arm (pivot axis close to longitudinal in plan view).
If the slope of the suspension’s longitudinal force line varies with suspension displacement, then
assuming a constant longitudinal force at the contact patch, the jacking effect can act in a manner
analogous to a spring force: it may increase or decrease according to displacement. It won’t
necessarily increase with compression, however. If it does increase with compression, as in the case
of the VW, it can loosely be thought of as adding wheel rate. If it decreases with compression, as
with the NASCAR suspension, it can be similarly thought of as subtracting wheel rate.
On the face of it, we might suppose that if the front wheels have the same amount of anti-dive – that
is, the same longitudinal force line slope – then their longitudinal-force-induced jacking forces will
lift both the right front and the left front corners of the car with the same force, and this will not
create any roll moment, although it will create a pitch moment. Therefore the anti will neither wedge
nor de-wedge the car.
This is true, but we must remember that the longitudinal forces at the two contact patches may not be
equal. In fact, if we are cornering, they are unlikely to be equal.
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The longitudinal forces at the front contact patches actually come from two sources. One is braking,
which may or may not be present. The other is the induced drag that a tire produces when running at
a slip angle, which is present any time we’re cornering. That induced drag varies with the amount of
load on the tire, and it is also affected to some degree by camber and toe. Generally, though, it is safe
to say that the induced tire drag is greater on the outside wheel. Therefore, the jacking force on the
outside wheel will be greater for a given force line slope than on the inside wheel. That will tend to
wedge the car (add diagonal percentage, i.e. outside front tire load plus inside rear, as a percentage of
the whole), and tighten it (add understeer).
Braking forces, on the other hand, tend to be more nearly equal. Theoretically, if we are short of the
point of lockup, with no front tire stagger, and the brakes are as identical as we can make them, the
braking forces will be identical at the two front wheels. Actually, with no tire stagger, the outside tire
will act slightly smaller if we are braking while cornering, because it will deflect more vertically and
therefore have a reduced loaded radius. Reducing the loaded radius reduces the effective radius
(increasing the revs/mile), though not by the full amount of the deflection change. This effect will
make the braking force slightly larger on the outside wheel.
If we are braking and cornering at the same time, we will have both a drag component and a braking
component. If we are braking hard and cornering gently, the rearward forces at the front contact
patches may be fairly equal, especially if the car has some toe-out. If we are braking gently and
cornering hard, the rearward force may be substantially greater on the outside wheel, especially if
there is some toe-in.
When we are off the brakes entirely, and cornering hard, we can say fairly confidently that the
rearward force will be greater on the outside front.
Can we say, then, that adding anti-dive makes the car tighter? Well, we almost can. If we add antidive only on the outside wheel (right front, for oval track), that will tighten the car. It will do this
even when we’re not braking. If we add anti-dive evenly on both front wheels, that may also tighten
the car, due to the greater rearward force on the more heavily loaded tire. Any such effect will tend
to be more pronounced in hard cornering than in hard braking.
However, if we increase anti-dive only on the inside wheel (left front, for oval track), that will loosen
the car (add oversteer) instead. This effect will be present whether we are braking or just cornering.
So this would be a situation where we’d be increasing overall anti-dive yet adding oversteer.
One might suppose that adding anti-dive on just the inside or outside wheel is impossible for road
racing, but as we have noted, suspension layouts vary as regards how anti-dive changes with
suspension movement, and such effects can be used to control the left/right balance of anti-dive
when the car is in a rolled condition, even when the car has to turn both ways. Such effects are often
hard to manipulate on an existing car, but they deserve consideration in the design phase.
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All of the above is based on the principle that adding diagonal percentage tightens the car and
reducing diagonal percentage loosens it. When applying these principles, it is also important to bear
aerodynamics in mind. More anti-dive will cause the front of the car to ride slightly higher through
the turns, particularly with soft front springs. If static ride height or valance height are not adjusted
for this, the greater ride height when cornering may add understeer purely by reducing front
downforce.
Now, what about anti-lift and anti-squat at the rear? As at the front, the jacking forces will depend on
both the force line slopes and the magnitude of the forces at the contact patches. And, as at the front,
any roll moments created will depend on the difference in jacking forces at the right and left sides.
Two things are different at the rear: we can have forces forward or rearward (this whole discussion
assumes rear wheel drive), and we have various kinds of differentials (or lack of) that can influence
the relative magnitude of the longitudinal forces, and in some cases even their relative direction.
Like the front tires, the rears generate drag when running at a slip angle. However, it is unusual for
that to be the only longitudinal force. The rear tires are almost always either propelling the car or
retarding it. Even in roughly constant-speed cornering, the rear tires are making enough forward
force to overcome the front tire drag and the aerodynamic drag.
The rearward forces at the rear contact patches when braking or trailing the throttle will tend to be
fairly equal if we have an open differential. If we have a spool or a limited-slip, however, any
rearward force will be greater on the faster (usually the outside) wheel. When under power, again the
forces will be fairly equal with an open diff, but any locking effect will result in more force at the
slower (usually the inside) wheel. At least, that holds true up to the point of inside wheelspin. Then
the outside wheel may make more forward force than the inside.
All of this makes it fairly complex to predict the distribution of longitudinal force at the rear.
However, we can say this much: in braking, more anti-lift or less pro-lift on the inside rear loosens
the car (adds oversteer); more anti-lift or less pro-lift on the outside rear tightens the car (adds
understeer). Under power, more anti-squat or less pro-squat on the inside rear tightens the car (adds
understeer); more anti-squat or less pro-squat on the outside rear loosens the car (adds oversteer).
Effect of more anti-lift or anti-squat geometry added evenly on both sides depends on the
distribution of longitudinal force between the two rear contact patches.
Distribution of longitudinal force also affects handling balance because it creates yaw moments. In
general, we can state that more longitudinal anti of any type intensifies these effects. For example,
more induced drag at the outside front creates a yaw moment promoting understeer. If there is more
anti-dive, there is also an increase in diagonal percentage, which intensifies the tightening. If there is
more forward force at the inside rear, that creates an understeer-adding yaw moment. If there is
ample anti-squat, again we get an increase in diagonal percentage, intensifying the effect. More
rearward force at the inside rear creates a yaw moment that adds oversteer. More anti-lift there
reduces diagonal percentage, again intensifying the effect. So we may say that, in general, increased
longitudinal anti geometry makes a car more sensitive to its tires’ load and force distribution.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
IDEAL SPINDLE OR STEERING GEOMETRY
I have a fairly simple question for you, but I don’t know how simple the answer will be. In any
literature I read, we are always dealing with things like kingpin inclination (KPI) and scrub
radius. Usually these cannot be eliminated in a sedan with big tires, and we are told in the
books to “not have too much”. But if I have more design freedom, and it is possible to get zero
scrub, and zero or very close on kingpin inclination, would this be a favorable setup? I know
that scrub + caster can give weight jacking, and that KPI gives a self-centering effect, but
otherwise both of them seem like something I want to get rid of. So to sum up, is it a good idea
to completely eliminate scrub, or KPI (or any other variables) entirely if the design allows?
To help readers who are less conversant with steering geometry, I am inserting some comments
of mine from the August 2002 newsletter, which explain various steering geometry parameters
and their effects:
The steering axis is a line about which the wheel steers, usually through the two ball joint centers of rotation
in an independent suspension, or the kingpin axis in a beam axle. This line can be defined by the point where
it intersects the ground and by its angular orientation. These are commonly described in terms of the X and Y
coordinates of the ground intercept, with respect to a local origin at the contact patch center, and the
transverse and longitudinal angles relative to ground plane horizontal.
The front view distance from ground intercept to contact patch center, or local Y, is called scrub radius, or
steering offset. It would make more sense to call the top view distance from ground intercept to contact patch
center the scrub radius, but most people use the term to mean the Y or transverse component of this. This
quantity is generally considered positive when the contact patch center is outboard of the ground intercept.
The side view distance from ground intercept to contact patch center, or local X, is called trail, or sometimes
caster trail or mechanical trail. It is positive when the ground intercept is forward of the contact patch center.
The front view angle of the steering axis from ground vertical is called steering axis inclination (SAI), or
sometimes kingpin inclination (KPI). It is positive when the steering axis tilts inboard at the top, which is
almost always the case.
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The side view angle of the steering axis from ground vertical is called caster. It is positive when the steering
axis slopes rearward at the top.
These parameters are controlled partly by the design and adjustment of the control arms, and partly by the
design of the spindle, or spindle/upright assembly, together with the hub and wheel.
The term spindle can mean either the stub axle, or pin, that carries the bearings, or the assembly including this
pin and the upright, especially when these are one piece.
The spindle or spindle/upright determines two important parameters: spindle inclination and pin lead or pin
trail.
Spindle inclination is the front-view inclination of the steering axis, relative to pin or wheel vertical, as
opposed to ground vertical. Spindle inclination approximately equals SAI minus camber. Spindle inclination
is almost exactly identical to SAI when camber is zero. It is exactly identical when both camber and caster are
zero.
The steering axis and the wheel axis do not have to intersect, unless we want the right and left uprights to be
identical parts, with bolt-on steering arms and caliper brackets. The steering axis can pass behind the wheel
axis, as it does on a bicycle. The perpendicular distance between the two axes is called pin lead. This is
equivalent to the dimension we call fork rake on a bicycle. If the steering axis passes in front of the wheel
axis, that's pin trail. So pin trail is negative pin lead, and vice versa.
Effective pin length is the distance, along the wheel axis, in front view, from the steering axis to the wheel
centerplane. This distance depends on the wheel and hub as well as the spindle/upright.
We now have sufficient vocabulary to describe and discuss basic steering and spindle geometry. If we can
specify all the quantities above, we have enough data to construct a stick model of the basic steering
geometry.
We may want to add steering arms. For purposes of spindle/upright design, we can define the position of the
outer tie rod end with respect to the pin and the steering axis. We may define a height from pin axis to tie rod
end center of rotation. To do this in a manner appropriate for drawing the upright, or inspecting it when
removed from the car, this should be the vertical dimension in side view, assuming zero caster and camber -in other words, we are projecting to the wheel plane, and taking the steering axis in side view as our local
vertical.
In such a side view, we may construct a horizontal line from tie rod end to steering axis. This is our side view
steering arm length.
We may project a top view from the side view, and locate the lateral position of the tie rod end. If we have a
longitudinal line corresponding to the side view steering arm described above, we may construct a transverse
line from it to the tie rod end, and measure that distance. This we may call steering arm offset. It will usually
be outboard for a front-steer layout, and inboard for a rear-steer layout. I don't know what sign conventions
other people use, but I generally call outboard positive for front steer and inboard positive for rear steer. Thus
positive offset is the direction that gives us positive Ackermann.
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In terms of coordinates, we are establishing a local origin where the side view steering arm meets the steering
axis. The side view steering arm length is our local X, and the steering arm offset is our local Y.
This doesn't mean there's anything wrong with assigning global or front-suspension coordinates to the tie rod
ends when doing an overall front end layout. I'm just pointing out that at some point you will have to deal
with the spindle/upright/steering arm unit as a sub-assembly, off the car, and it helps to be able to measure
and discuss it that way too.
Now we have a fairly complete vocabulary to describe steering geometry, so we can discuss what effects
these parameters have.
Trail causes lateral forces at the contact patch to produce a torque about the steering axis. This causes the
steering to seek a gravitational/inertial center. The driver feels lateral cornering force through the steering. He
also feels the lateral force that the tires must generate to make the car run straight on a laterally sloping, or
cambered, road surface. It is worth noting that this is only one component of the self-centering forces the
driver feels. Another is the tire's own self-aligning torque, which is present whenever the tire runs at any slip
angle. This will provide some feedback of cornering force even in the total absence of trail. This effect is
sometimes described as mimicking trail. The amount of tire self-aligning torque, divided by lateral force, is
sometimes called pneumatic trail. Note that this is a calculated value which depends on tire properties, and
not an actual steering geometry parameter.
One important distinction between the forces from trail and tire self-aligning torque is that tire self-aligning
torque is not a linear function of lateral force. It builds at a decreasing rate as lateral force increases, and at a
point a bit short of maximum lateral force it actually begins to decrease. This means that if our car has little or
no trail, the steering will start to go light a bit before the point of tire breakaway. Some argue that this is a
good thing, especially for a passenger car, because it gives the driver a signal to ease up short of the point of
actual loss of control. In a race car, this type of steering feel requires that the driver be accustomed to driving
just a controlled increment beyond the point where the steering wheel tells him/her that the limit of adhesion
has been reached. If the driver is used to having more trail, he/she will often find this very difficult.
Trail also causes a small lateral movement of the front of the car with steer, in the direction of steer. We might
call this steer yaw. It can rationally be argued that this improves turn-in, both by yawing the car promptly and
by causing the rear wheels to develop a slip angle promptly.
Scrub radius or steering offset causes longitudinal forces at the contact patch to generate a torque about the
steering axis. If right and left scrub radii are equal and longitudinal forces at the right and left wheels are
equal, no net torque at the steering wheel results. The driver feels the difference between the longitudinal
forces at the front wheels. The driver feels one-wheel bumps, brake pulsations, and crash impacts where one
wheel hits something, in direct proportion to scrub radius.
A car with a lot of scrub radius is sensitive to wheel imbalance and tire and brake imperfections, has a lot of
"wheel fight", and has greater tendency to injure the driver's hands in one-wheel crash impacts or curb or
pothole impacts. A car with very little scrub radius is less subject to these problems, but the steering will tend
to be numb and uncommunicative.
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A car with large scrub radius may steer more easily at parking speeds, depending on other parameters,
provided the brakes are not applied. This is because the wheels can roll as they steer rather than purely
scuffing. With the brakes applied and the car stationary, a car with a small scrub radius steers more easily.
Caster causes the front wheels to lean in the direction of steer. With a given spindle/upright geometry, more
caster implies more trail.
Caster combined with trail causes steer drop or steer dive. The front of the vehicle drops as the wheels steer
away from center, if caster is equal on right and left. This tends to cause an anti-centering force at the steering
wheel. It is the reason why the front wheels of a dragster at rest tend to flop to one side or the other.
Caster combined with scrub radius causes the car to drop as the wheel steers forward (toes in), and lift as the
wheel steers rearward (toes out). When this occurs on the right and left wheels as one steers forward and the
other steers rearward, the result is steer roll. The car leans away from the direction of steer. The wheel loads
also change. The car de-wedges: the inside front and outside rear gain load; the outside front and inside rear
lose load. This effect can help the car turn in slow corners, especially with a spool or limited-slip differential.
In excess, it can create low-speed oversteer and over-sensitivity to steering angle. In general, cars running on
lower-speed tracks need more steer roll, and cars on fast ovals should have very little.
The camber change associated with caster is favorable, particularly for road racing cars, which usually cannot
get favorable camber on both front wheels any other way. We can have too much of this good thing, but that's
extremely uncommon.
Steering axis inclination (SAI) causes both front wheels to gain positive camber as they steer away from
center.
SAI combined with scrub radius causes steer lift. The front of the vehicle rises as the wheels steer away from
center. This induces a self-centering force in the steering which seeks vehicle center rather than
inertial/gravitational center. This is particularly useful in passenger cars because it reduces the car's tendency
to follow road camber, and therefore reduces the need for the driver to pay close attention in casual driving on
roads with varying slope. The centering force also tends to suppress steering shimmy.
In race cars, the camber change associated with SAI is unfavorable on the outside wheel. The self-centering
force increases steering effort, which is a factor for any vehicle without power steering. It
also creates what could be considered a false message to the driver about the lateral forces present at the
contact patches. There is therefore a rational case for using more caster and less SAI in a race car.
With the packaging constraints we usually face, more SAI generally implies less scrub radius. The main
limitation will often be how far outboard we can place the lower ball joint without having it too close to the
brake disc. If the wheel has generous negative offset, we may instead be limited by the wheel rim hitting the
control arms in some combinations of suspension motion and steer. Either way, we often cannot place the
entire steering axis as far outboard as we would theoretically like to. Using SAI allows us to at least get the
ground intercept further outboard in such cases. With MacPherson strut front ends, large amounts of SAI are
necessary if we are to obtain any camber recovery in roll.
Consequently, in many cars we see SAI used for reasons not directly related to SAI's own dynamic effects.
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A full discussion of Ackermann effect (increase of toe-out with steer) is beyond our scope here, but we can
at least say that in low speed turns with the wheels steered into the turn, the car generally needs toe-out on the
front wheels. For high-speed sweepers or ovals, the front wheels generally need toe-in instead. The key
determining factor is whether the turn center -- the instantaneous center of curvature of the car's path -- is
ahead of or behind the front axle line. Other determining factors include the tendency of the loaded wheel to
want a larger slip angle than the unloaded one, and what yaw moments we wish to create with the tire drag
forces.
The attitude of the front wheels at any given instant depends on both the static toe setting and the change in
wheel-to-wheel toe with steer. This means that optimum Ackermann depends on static toe setting.
It should be clear, then, that there is no such thing as perfect Ackermann properties. But we can at least say
some definite things about what geometric parameters will do to Ackermann. In particular, increasing steering
arm offset increases Ackermann effect.
Ackermann for oval track cars is often asymmetrical. The side view steering arm length is less on the left
wheel than on the right. This produces more Ackermann when steering left than when steering right.
We should mention that if we are willing to tolerate a bit of additional complexity, there are ways around
some of the tradeoffs in steering geometry. For example, it is possible to create a self-centering force by
springing the steering system. This can mimick the self-centering that we get from SAI, without the adverse
effects on camber. We can also damp the steering to reduce kick and shimmy.
We can get small SAI and small scrub radius at the same time by using compound control arms (two single
links replacing the usual wishbone or A-frame) and dual ball joints. This gives us an instantaneous virtual ball
joint outboard of the linkage itself. We can adopt this arrangement at the upper end of the upright, or the
lower end, or both.
When using dual ball joints, it is important not to splay the two links too widely. Otherwise it may
be possible for the linkage to snap over center if it has to take an impact near full lock. As a rule of
thumb, it is probably advisable to have the front link around 25 degrees forward from transverse and
the rear link around 25 degrees back.
Ackermann also gets interesting when using dual ball joints. As we steer, the steering axis moves
rearward with respect to the ball joints and tie rods on the outside wheel and forward with respect to
the ball joints and tie rod on the inside wheel. This means we lose Ackermann as we steer if the
steering linkage is behind the wheel axis (rear steer layout), or we gain Ackermann as we steer if we
have a front steer layout. Conversely, it is difficult to get the outer tie rod ends far enough outboard
to have positive Ackermann at small steer angles with front steer. With rear steer, it is easy to get the
tie rod ends inboard far enough to have initial positive Ackermann, but it is hard to avoid having too
much initial positive Ackermann. It becomes very important to evaluate the steering geometry
through the full range of steering motion. In many cases, we find that outer tie rod end packaging
limits our steering axis location, rather than ball joint and control arm packaging.
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I might also mention that we can get small SAI and small scrub radius together by using an actual
kingpin, as on a beam axle, and bushings rather than ball joints at the top and bottom of the upright.
The kingpin can then be placed much further into the wheel and brake than would otherwise be
possible. This was actually the most popular way to build independent front ends up until the mid to
late 1950’s.
Okay, returning to the current question, is it desirable to completely eliminate SAI/KPI, and/or scrub
radius/steering offset? As the comments above indicate, these questions relate heavily to steering feel
and the answers are therefore to some extent a matter of personal preference.
The nature of the track influences the decisions too. There is a stronger case for minimal SAI and
scrub radius on a high-speed oval than on a street circuit. There may also be a stronger case for
minimal SAI and scrub radius for off-road racing than for pavement competition.
The high-speed oval requires steadiness and freedom from vibration at high speeds. We don’t want
the car’s properties or wheel loads changing much with steering wheel movement. We want stability
and predictability more than responsiveness or communicativeness. The driver will tend to drive
more in “open-loop” mode, steadily holding a smooth line, by eye, through the wide turns rather than
responding reflexively to constantly changing information received through the steering wheel.
He/she will still need to feel whether the front wheels have grip, and may still want the steering to
seek center, but the need to sense the road wheels’ exact position is much diminished.
On a street circuit or tight road course, the driver will tend to operate more “closed-loop”, relying on
input from the steering wheel to tell him/her where the wheels are on the road. The driver senses this
by seeing the bumps in the road at a distance as they approach, and then feeling through the steering
what the wheels actually run over. This is true even in a car where the driver can see every bit of the
front wheels, because at speed the driver has to be looking ahead at where he/she wants to go, and
not down at the wheels. Speed on a tight course depends heavily on using all the road, and that
depends on being able to position the car precisely.
Road courses also tend to be bumpier and contain more varied surfaces than high-speed ovals.
Consequently, the driver relies on the steering for information about the ever-changing grip level.
This really is more a matter of trail than scrub radius, but in braking in conditions where there is
more grip on one side of the car than the other, scrub radius may make it easier to detect lockup on
the slicker side. On the downside, when the steering pulls toward the side with more traction, the
driver needs to resist the pull, and maybe even steer against it a little, to keep the car pointed straight.
For this reason, Volkswagen used to advertise the negative scrub radius on their cars as an aid to
stability in braking.
If the car has really stiff suspension, as with current high-downforce cars, the driver will have little
problem sensing which wheel hits a bump, even if he/she can’t feel it through the steering wheel. On
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the other hand, a car with soft suspension has greater need for communicative steering, because it
doesn’t transmit so much information by other paths.
If we are running off-road, precise vehicle placement may be somewhat less critical, although there
are situations where it is important. The wheels will be hitting big bumps all the time, and it becomes
important to avoid beating up the driver. If the vehicle has a beam axle in front, steering oscillations
and kick from lateral movement at the contact patches on one-wheel bumps are particularly
troublesome. Consequently, there is a case for a small scrub radius for off-road use.
There are a lot of vehicles out there that successfully use zero scrub radius with zero SAI. Most of
them have only one front wheel, but they work fine. The faster ones do often use steering dampers. I
am referring of course to motorcycles. It should be equally possible to have similar geometry on two
front wheels, all packaging considerations permitting.
Is that the best solution? As previously noted, it depends on what you want, or what the driver wants,
in terms of steering feel. If you want light steering and minimal feedback of bumps, wheel vibration,
and brake pulsation, try zero scrub radius and zero SAI. If you want a “natural” feel of which wheel
is hitting a bump, you probably want some positive scrub radius. If you are trying to unload the
inside rear wheel in tight turns, you want a lot of scrub radius.
It is possible to have a large scrub radius with little or no SAI. This combination is prone to
oscillation, particularly at low speeds, and particularly with large caster settings. However, in a race
car, it may make sense to either live with that, or damp and/or spring the steering to control it, rules
permitting.
It is also possible to have large SAI with small scrub radius, or even negative scrub radius. Indeed,
ample SAI is generally the easiest way to get a small scrub radius. There is a case for this sort of
geometry in street cars, especially with front wheel drive and strut suspension, or with a beam axle
front end. It is not a good idea for a situation where we are designing for racing, with rear wheel
drive and generous design freedom.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
FINER POINTS OF ANTI-ROLL BARS ON STOCK CARS
I race primarily on two ovals, one a 1/3 mile with 7 degree banking and short straights, and one a
5/8 mile with 15 degree banking and long straights. I am not clear on some of the finer points of
setup and adjustment of front anti-roll bars for a specific track, especially for a car running at two
tracks such as these.
Most cars in my area run a solid link to the anti-roll bar on the right, and a slider link on the left,
where the left front A frame in droop would cause tension on the link, but the left front in bump
would remove any tension. I have run many cars with this setup, and a few with solid links on both
sides. I don’t really understand why there would be a preference for one over the other, or in what
situation the solid links on both sides would be preferred over the slider setup.
I have found from home-made data acquisition that once a car is up to speed on the 1/3 mile oval,
the left side never returns to ride height, as the car always has considerable g’s throughout the lap.
Many competitors run play in their anti-roll bars, as much as ¼ to 5/8”. While it is easier to
duplicate a setting if there is a specific gap to measure rather than a preload when making lastminute changes in tire size or wedge adjustments, it seems to me it might be better if there is less
spring in the front of the car and less or zero gap in the bar.
For most bar play settings, the gap is gone as soon as the car comes up to speed, and the gap
doesn’t return until the cool-down lap at the 1/3 mile oval. Running play in the bar at a track with
long straights, where the chassis returns to zero roll angle on the straights, seems like it would
create a variable roll rate at the front, as the initial roll resistance would be only on the RF spring.
Then the anti-roll bar and the resistance from the extension of the LF spring would kick in, greatly
increasing the front roll resistance.
The car running the 7 degree banked turn would be in true roll, with the right frame rail down and
the left rail up, while at the 15 degree track, the right rail would be down, but the left rail would be
at approximately static ride height in the turn. It would seem that the bar would be half as stiff
dynamically for the same right side travel at this track.
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Another concern I have is that I’m not always sure in which situation it would be best to change the
bar rate as opposed to the front spring rate. I realize the bar controls only roll, but in many
situations where a rate change is desired, I have a hard time deciding which would be best, bar or
spring.
Concerning small adjustments in bar play made at the track, consider a situation where a car
running at the 1/3 mile, 7 degree track has a bar rated at 800 lbs. per inch of movement at the right
front, at the location where the bar link is mounted, and ½” of static play. Suppose an adjustment is
made to the bar reducing play to 3/8”, or 1/8” less than before. This would presumably increase
roll resistance by 100 lbs. For a particular right front travel, but would not increase the roll rate.
How would this compare to changing to a bar that rates at 900 lb/in, with the original ½” play
retained?
It has long been common on oval track stock cars to use some type of “soft link” on the front antiroll bar. These may take the form of a slider, a chain, or a pad on the anti-roll bar arm that bears
against a pad on the lower control arm. The last of these is the form commonly seen in the upper
divisions of stock car racing. Chains and sliders are common in “street stock” type cars, where the
suspension components actually come from production passenger cars.
All these variations do the same thing: they create a connection that transmits force in only one
direction. The anti-roll bar resists rightward roll only. The bar may be preloaded, in which case it
will resist leftward roll up to the point where the preload is relieved. (Some sanctioning bodies
prohibit preloading the bar. The reason for this is a mystery to me.)
The reason the soft link is there at all is to make the front suspension more compliant when the
driver gets the left front wheel on the flat apron of a banked track. In this situation, the car tends to
go loose (develop oversteer) and spin. This is partly because of the leftward yaw moment created
when the left front encounters increased resistance, and partly because the car de-wedges (load
increases on the left front and right rear, and decreases on the right front and left rear). If the
suspension is more compliant, both effects are reduced, especially the de-wedging.
However, even in this situation the front suspension only acts softer beyond the point where the left
front suspension compresses enough to put slack in the bar. If the bar has no play and no preload,
the front suspension must go into leftward roll (left front compressed more than right front) before
the soft link has any effect. And the soft link will make the car looser if the driver needs to turn right
to avoid a wreck. So the soft link is a mixed blessing.
Wheel rates and arm end rates of anti-roll bars are a confusing subject for many. The main cause of
this confusion is that there is no agreed convention as to what an inch of arm end or wheel motion
means. Does it mean an inch of motion at just one wheel? An inch of motion in opposite directions
at both wheels? An inch of difference between the two wheels?
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I find it convenient to express the rates of all springing devices, including interconnective ones such
as anti-roll bars, in terms of pounds per inch per wheel. This agrees with the way we always express
the rate of non-interconnective springing devices, i.e. the main springs or ride springs. We then have
numbers that easily tell us what change of anti-roll bar rate equates to what change of spring rate.
However, it has become customary to rate anti-roll bars by testing them in devices originally
intended for testing non-interconnective torsion bars. The bar is placed in a fixture that holds one
end of the bar stationary, and the arm on the other end of the bar is moved one inch. The force
required to do this is measured, and that is taken as the bar’s rate in pounds per inch.
This isn’t wrong. But it can create confusion when we try to translate it into pounds per inch per
wheel, because what we have from the test is pounds per inch per wheel pair. An inch of roll per
wheel pair is only half an inch of oppositional motion per wheel. Therefore the number from the
testing machine is only half the bar’s equivalency to wheel springs, if the bar and the springs acted at
equal motion ratios.
On the other hand, it is common for anti-roll bar manufacturers to express the rate of their bars the
way I like to see it, as pounds per inch per arm end, not pounds per inch per arm end pair. This
sometimes leads to acrimonious exchanges between bar manufacturers and customers who test a bar
they just bought and find that it “rates” at only half the advertised value.
Often, we encounter situations where we do not have “pure” roll motion. Pure roll, for a front or
rear wheel pair, would mean equal amounts of suspension motion at each wheel, in opposite
directions. Pure ride would mean equal amounts of motion at each wheel, in the same direction.
Ride and roll are the two modes of motion for a front or rear wheel pair. Any possible motion of that
wheel pair can be resolved into some amount of ride and some amount of roll.
Applying this to the questioner’s example of a situation where a car in a banked left turn rolls purely
by compressing the right front suspension, and the left front neither compresses nor extends, that is a
condition of equal ride and roll. If the right front compresses an inch and the left front doesn’t
move, we have half an inch per wheel of rightward roll, plus half an inch per wheel of compressive
ride. On the left wheel, the effects are subtractive and exactly cancel. On the right wheel, the effects
are additive, and we have twice the half-inch per mode, or one inch of compression.
If we compare this to a pure roll situation (zero ride motion) which creates an inch of compression at
the right front, yes, the bar creates twice as much force. But the bar’s rate is the same. The
difference is that there is twice as much roll. If the roll were equal to the previous example, the right
front compression would be only half an inch, the difference between right front and left front would
still be an inch, and the force generated by the bar would be the same as in the first example.
Once we learn to separate the ride and roll components of the motion, and remember that the bar acts
only in response to the roll component, things get much simpler.
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Regarding how much of the front wheel rate in roll should come from the springs and how much
from the bar, it mainly comes down to how much we want the front of the car to drop in the turns
due to the banking. This in turn relates to both suspension geometry and aerodynamics.
It is normal in all stock car racing classes to have a minimum static ground clearance requirement.
The car has to pass over a barrier of a certain height to get through tech inspection. Yet we would
like the valance to run just off the track, and have as much forward rake in the car as possible,
through the turns. This gets us the greatest aerodynamic downforce available, within the bodywork
and ground clearance rules.
Additionally, with passenger car front suspension, we usually have insufficient camber recovery in
roll for racing. The control arms are close to parallel at static, causing the wheel to change camber
very little in ride, but a lot in roll. This is good for tire wear in gentle driving, but not good for hard
cornering. In some cases, the rules will allow us to use extended upper ball joints to improve the
geometry for racing. Sometimes this may be enough, but in most cases the geometry will benefit if
we run the car lower. To do this, within the ride height rule, we need to soften the springs and
stiffen the bar.
In the upper divisions of stock car racing, we can get as much camber recovery as we want, so only
the aerodynamic factor argues for soft front springs. In general, with soft front springs and a big bar,
we’ll want the front view instant centers a bit higher and further from the wheels at static than we’d
want with stiffer springs and a softer bar.
In either case, a flatter track calls for more of a soft-spring/big-bar approach than a steeply-banked
track.
Regarding rate of a bar with slack in it: the bar has a rate of zero until the slack takes up. Then it has
the same rate it would have without slack.
We can speak of the bar’s rate as an instantaneous value, at any given point in roll travel, or we may
speak of its average rate, over a specified interval of travel. When there is slack in the system for a
portion of the interval, but not at the end of the interval, the bar has the same instantaneous rate at
the end of the interval whether there is slack or not, but it has less average rate over the interval if
there is slack.
Relating this to the questioner’s example comparing an 800 lb/in rate with 3/8” of slack (let’s call
this Case A) to a 900 lb/in rate with ½” of slack (Case B), we may say that these two systems have
the same instantaneous rate (namely zero) at any displacement less than 3/8”; the same average rate
(450 lb/in) over the displacement interval 0” to 1”; the same force (zero) over the displacement
interval 0” to 3/8”; and the same force (450 lb.) at 1” displacement.
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Case A has less rate than Case B when the slack is absent; more force at displacements between 3/8”
and 1”; and less force at displacements greater than 1”. At ½” displacement, Case A generates 100
lb. more force than Case B. From there, the forces converge to a point of equality at 1”, then diverge
again, with Case B making more force, beyond 1” displacement. At 1½” displacement, Case B
generates 100 lb. more than Case A.
In terms of car behavior, if all other setup parameters are equal we would expect Case A to have
more understeer (or less oversteer) from 3/8” displacement to slightly less than 1” displacement;
both setups to have similar understeer around 1” displacement; and Case B to have more understeer
at greater displacements. We would expect Case A to have a lesser tendency to get looser (or a
greater tendency to get tighter) as grip diminishes.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
TOO MUCH LEFT PERCENTAGE?
My question is regarding left side weight percentage on oval track cars, specifically dirt Late
Models. I have heard it generally stated that more left side is better in all situations, and I see a lot
of paved track classes have limits on left side percentage. I understand the concept of load transfer
and equal tire loading in steady state cornering.
My question is about the point of diminishing returns. My understanding would be that as grip
decreases or banking increases, left side weight should be reduced to keep the left side tires from
being more heavily loaded than the right sides. Is this a correct assumption, or have I missed
something?
In theory, yes it is possible to have too much left percentage, and to have the left tires more heavily
loaded than the right tires even at the limit of adhesion in steady-state cornering. In almost all cases,
however, practical constraints or rules will stop us short of that point.
We can also have too much left percentage for the tire package short of that point, if the left side
tires are smaller than the rights, or if the lefts are inflated to a much lower pressure than the rights.
Or, we might conceivably want more than 50% left dynamically, if the left tires are about as big as
the rights, and we have a rule requiring a hard tread compound on one or both of the rights but not on
the lefts.
Let’s consider a simple, if not very typical, case. Suppose we have a car with a one foot c.g. height,
a six foot track width, and identical right and left tires. Suppose that the overall coefficient of
friction is 1.00. That would be about what we’d get from sticky street-legal radials. For this car to
have 50% left dynamically at the 1.00g lateral acceleration that those tires will theoretically sustain,
it would need 66.7% left statically. That’s a wider, lower car than most, on tires with less grip than
racing slicks.
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If the same car is fitted with racing slicks that have a coefficient of friction of 1.30, the static left
percentage needed to have 50% left dynamically increases to 71.7%.
If the car has a wing that acts equally on the right and left tires, lateral acceleration increases and the
desired static left percentage goes up still more.
What happens if we put the car on a banking? It’s a bit surprising. If the coefficient of friction
stayed the same, the ratio of car-horizontal (y-axis, per SAE conventions) force to car-vertical (zaxis) force would be unchanged, although all forces would increase. This assumes the car is at the
limit of adhesion both with and without the banking, not at an identical y-axis acceleration or an
identical earth-horizontal acceleration.
However, due to the same tire load sensitivity that makes us want equal loading, on the banking the
coefficient of friction will diminish, so the questioner’s intuition is correct after all, and the optimum
static left percentage will decrease.
In an earlier newsletter dealing with this question, I noted that if we do get to the point where left
percentage is excessive for conditions, wedge or diagonal percentage adjustments will work
backwards, and so will roll resistance adjustments. After that, a reader wrote in and said he had
encountered this, with a go-kart on a very steeply banked dirt track.
Upon further discussion, it came to light that the kart had a much smaller tire on the left rear than on
the right rear. This not only affected the optimum load distribution for the rear wheel pair, it also
meant the kart had a lot of tire stagger. More load on the left rear increased the stagger-induced yaw
moment on the kart, also causing more diagonal percentage to loosen the vehicle (add oversteer),
contrary to what one might expect. This effect can easily occur in any car with a locked or partially
locking rear end. This in turn affects our ability to infer whether left percentage is excessive, purely
by noting how the car responds to adjustments.
I have also noted in earlier discussions that large left percentage makes a car tend to turn right under
braking and turn left under power. This tightens the car (adds understeer) during entry and loosens it
(adds oversteer) during exit. There are ways to counter this tendency with suspension design and
tuning, but sometimes these are not legal, or the team doesn’t understand them. In such cases, the
car may well turn faster laps with less than optimal left percentage, even though it is slower in
steady-state cornering.
These complexities can muddy the waters when tuning an actual car, but it is still fundamentally true
that more left percentage is almost always better, provided we are able to work with the full package
of consequences.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
DYNAMICS OF THREE-WHEELERS
If you were building a three-wheeled vehicle, would you put some roll in the two-wheeled end, or
not?
I am assuming that the questioner is asking whether there should be some roll compliance at the
wide end, or whether the suspension should be essentially rigid in roll.
This is a reasonable question because, at least at low speed, a three-wheeler doesn’t need suspension
to keep all its wheels on the ground. Because any three points invariably lie in a common plane, a
tricycle can trundle over very uneven ground at low speed with very little load change at the wheels,
and without picking up a wheel, even if the entire chassis is rigid.
This fact led many of the earliest designers of motor vehicles to adopt tricycle layouts. Among these
vehicles was the very first self-propelled off-rail vehicle, the Cugnot steam tractor of the 1760’s (or
1771, if we go by the still-existing second model). Carl Benz’s first gasoline buggy, in 1885, was
also three-wheeled.
The trike layout was not universal, however, even in the early days. Benz’s gasoline buggy was
preceded by two models of internal-combustion, gasoline-fueled (or more accurately, benzenefueled) cars built by Siegfried Marcus in 1865 and 1874. I don’t know what the first of these looked
like, but the second model, of which three were built, had four wheels. In 1879, George Selden
applied for a US patent on the automobile. The model he submitted to the patent office had four
wheels. It also had unitized body/frame construction and front wheel drive!
By the time automobiles became common, a wagon-style four-wheel layout had become the norm.
This is not surprising, because this layout provides the best resistance to roll and pitch available
within an envelope defined by a maximum length and width. Despite this, the tricycle layout has
refused to die out completely.
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The primary reason people have kept building trikes is economic. In most of the world, trikes are
licensed and taxed as motorcycles rather than cars. Where cars are heavily taxed, this gives the trike
a substantial price advantage. A secondary reason is that a trike can be made very light. Due to the
aforementioned fact that a trike’s tire contact patches always lie in a common plane, the vehicle’s
frame does not see the torsional loadings that a four-wheeler’s does. Consequently, it can be built
considerably lighter.
The tricycle layout brings problems, however. The main problem is poorer resistance to rollover. A
trike can tip over by rolling about a line connecting the contact patches of the outer tire at the wide
end and the single tire at the narrow end. For a given wheelbase and track, the vehicle’s center of
mass will unavoidably be closer to this line in plan view than it would be to a line connecting the
front and rear outer-tire contact patches on a four-wheeler. Strictly speaking, the tipping motion we
refer to here is not pure roll, but a combination of roll and pitch. Still, regardless of what we call the
motion, the vehicle is limited by the easiest way it can tip.
The key to minimizing this problem is to put the c.g. toward the wide end as far as we can. If the
single wheel is at the front, we need a rear-engine layout, similar to the VW-engined tricycles that
are still fairly common in the US. If the single wheel is in the rear, we need a front engine, as in a
Morgan trike. It is important to assure that the operator does not place any heavy cargo toward the
narrow end.
It is best to drive the two wheels at the wide end, rather than the single wheel at the narrow end. Not
only does this provide much better traction, but it further concentrates the masses at the wide end.
One problem we encounter when the c.g. is toward one end of the vehicle is that in hard longitudinal
acceleration, the single wheel may lift, or become so lightly loaded as to impair directional stability.
In a front-engine trike, the rear wheel will tend to lift in braking. In a rear-engine trike, the vehicle
will tend to wheelstand under power. We can minimize this problem, and improve rollover stability,
by making the wheelbase long, and by getting the c.g. as low as we can.
When choosing between the rear-engined and front-engined approaches, there is a safety advantage
to the front-engine, front-drive layout. It has its best rollover resistance when decelerating, whereas
the rear-engine, rear-drive layout is most likely to flip when the driver tries to lose speed upon
entering a turn too fast. The front-engine, front-drive layout also provides much better crosswind
stability.
Returning to the original question, what sort of characteristics should the suspension have at the
wide end? First of all, it should not have large jacking forces. Either it should be an independent
layout with a low roll center, or it should be a beam axle layout.
Particularly with an independent suspension, the wheel rate in roll needs to be substantial, but it
should not approach infinity. If there is too much wheel rate in roll, the vehicle will se large roll
accelerations, and large wheel load changes, when traversing one-wheel bumps at speed.
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Barring a great increase in the popularity of trikes, we are unlikely to see a class for them in racing,
except vintage racing where one does see Morgans and their contemporaries. We do, however, have
racing for sidecar rigs. These are normally constrained by the rules to have two wheels in line, with
the rear one driven, and a third wheel to one side. This is not the way to design a three-wheeler if we
have a free hand, but it retains the connection to a roadgoing motorcycle with sidecar, and it
provides thrilling, if dangerous, racing.
To optimize the sidecar layout, the wheels should again be spread as far in all directions as the rules
will allow. The heavy side should, if possible, be toward the predominant turn direction. The c.g.
should be away from the two-wheeled side, and fairly close to the single wheel in the fore-and-aft
direction.
Even when all of this is carefully attended to, there will be no substitute for a good “monkey” or
passenger, and the best possible helmet and leathers.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
LOAD TRANSFER QUESTION
For argument’s sake, let’s assume the following:
1) Total rear roll resistance is 600 lb/inch of rear suspension travel.
2) The static weight on each rear tire is 400 lb.
3) The car’s rear suspension compresses 1 inch when cornering at the limit. Thus there is 600 lb of
load transfer onto the outside rear tire.
This car starts to corner and 400 lb of load is transferred from the inside rear tire to the outside rear
tire. This leaves zero load on the inside rear tire. The car continues to speed up in the turn,
reaching the limit of adhesion, and now there is 600 lb of load on the outside rear tire. Where does
this additional 200 lb of load come from? Does it all come off the inside front tire? If you have rear
anti-roll bar, it can actually push the inside tire up into the tire well. I guess this would be a
negative load on the inside rear tire?
If I understand the question correctly, you are supposing that the outside rear suspension compresses
one inch from static, implying that the tire gains 600 lb of transferred load, which would make its
load 1000 lb.
If we are assuming that the car is in steady-state cornering, on a flat, smooth, unbanked turn, with no
geometric anti-roll or pro-roll, and no aerodynamic downforce, you are describing an impossible
case. Unless something adds load to the rear wheel pair beyond the static value, the outside wheel
cannot have more load than the total for the wheel pair.
There can be no such thing as a negative tire load, unless the tire can somehow pull upward on the
road surface. Short of creating a tread compound that is sticky beyond our usual conception, or
nailing the tire to the road (either of which would make it very difficult for the car to attain enough
speed to corner hard), that just can’t happen.
It is also impossible for load to transfer from the front wheels to the rear wheels when the car is only
accelerating laterally.
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What will happen if the rear suspension reaches 100% load transfer, and then further lateral
acceleration is applied to the car, is that the inside rear wheel will lift off the ground. The car will
continue to roll, but without any further motion of the rear suspension. That implies that the rear
ride height, measured from middle of the frame to ground, will increase as the wheel lifts.
The anti-roll bar will push the inside tire up into the wheel well only in the sense that it may prevent
the inside suspension from reaching full droop – not in the sense of compressing the inside
suspension beyond static position. The suspension’s ride displacement from static will be zero. Its
roll displacement will be two-thirds of an inch per wheel. The inside wheel will be off the ground,
yet the suspension will be extended only 2/3” beyond static. The outside wheel will be compressed
2/3” from static. The average displacement of the two wheels, from static, will be zero.
We may say that in this situation, the rear suspension is saturated in terms of load transfer: it has
absorbed all the load transfer that it can. Any further load transfer must be absorbed by the front
suspension alone. This implies that the inside front wheel will lose load, but that load will not go to
the outside rear; it will go to the outside front. The total load on the front wheels, and the total load
on the rear wheels, cannot change.
Remember, though, that we made a number of simplifying assumptions here: purely lateral
acceleration; no bumps; no banking; no geometric anti-roll or pro-roll; no aerodynamic downforce.
In the real world, any combination of these might be present, meaning that we could very well have
data acquisition traces showing an inch of compression from static on the outside rear.
To know how much added load we would need to get that added 1/3” of ride compression, we would
need to know the rear suspension’s wheel rate in ride as well as in roll. The required extra load
wouldn’t necessarily be 200 pounds. If the wheel rate in ride were 300 lb/in, we’d have that
condition. (100 lb/wheel divided by 300 lb/in = 1/3 in/wheel)
If the only factor compressing the rear suspension is banking of the turn, and if the tires are racing
slicks with a coefficient of friction around 1.30, we’d need about a 25 degree banking to generate
200 lb of extra load. A banking around 35 degrees would do this without the tires generating any
cornering force.
If the turn is flat, and the only factor compressing the rear suspension is aerodynamic downforce,
we’d need 200 lb of that at the rear axle if the wheel rate in ride is 300 lb/in. If the wheel rate in ride
is less, these values decrease. If the wheel rate in ride is greater, the values increase.
The suspension geometry can generate a downward jacking force. This would be most likely in a
lowered strut-style suspension, when most or all of the load is on the outside tire. In most cases, this
will not be enough to compress the suspension a third of an inch unless the ride rate is very soft, but
the effect could add to other effects to produce that much compression.
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Forward acceleration will usually compress the rear suspension. In a front wheel drive car, it always
will. We think of steady-state cornering as purely lateral acceleration, but actually there will be a
car-longitudinal (x-axis) component, even at constant speed, because of the car’s attitude angle or
drift angle.
Since any or all of these effects can be present, it is entirely possible for the rear suspension to be
compressed more than we would calculate for pure cornering on a flat surface. But something has to
add ride compression for the condition described here to occur.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
OPTIMIZING ENGINE-OVER-DRIVE-WHEELS LAYOUTS
My question concerns taking a front-wheel-drive car and giving it the response of a rearwheel-drive car.
It seems that for large sedans the trend in the market today is to build rear-wheel-drive
platforms. The ideal seems to be to emulate the handling characteristics of the BMW and
Mercedes RWD sedans. This is becoming a big deal as first Chrysler, and now Hyundai and
the Chinese (new Cherry V8 of 4.8 liters), are heading down the RWD path.
Recently GM put the Pontiac GXP into production with a 327 cid V8 driving the front wheels.
It can cut a 13.8-second ¼ mile and it’s an automatic. It’s faster than a standard Mustang! I
discovered that the GXP was ready to produce ten years ago but GM couldn’t afford to tool
special parts for it then! Nor could they justify retooling the platform of the time in order to
move the suspension hard points to more favorable locations. The recent new model
introduction allowed the V8 option as they completely revised the platform for all model
variants (Chev, Pontiac, Buick) and all engine options. It’s an excellent car by all accounts
(available only as a wrong-side-of-the-road model, so they can’t export it – tsk tsk).
[Questioner is in Australia.]
GM makes the point that front wheel drive is better in winter when traction is poor, for
example in snow. Large parts of America (and many other countries) have difficult winters
with snow and ice, so that’s a valid argument.
This got me thinking about chassis response. I have a question about handling. Would it be
possible to make a front-wheel-drive car behave like a RWD car (or feel like it had similar
response) by applying some active rear wheel steer? I don’t mean like Honda’s mechanical
system (where rear steer was a fixed function of front wheel steer regardless of speed, weight
transfer, yaw rate, available traction, or chassis balance), but active. It wouldn’t have to be
much, perhaps just a degree or maybe even two at appropriate moments. What do you think?
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This question implicitly raises a larger question: how can we get the most from an engine-overdrive-wheels two-wheel-drive car? To answer this, we need to look at the advantages and
disadvantages of the whole engine-over-drive-wheels idea.
But first, to answer the question, yes it certainly is possible to use active rear wheel steering to
point the rear wheels out of the turn in response to inputs from a steering position sensor, a
throttle position sensor, a yaw acceleration sensor, wheel speed sensors, and any other inputs
we can get a control computer to read and process. This would provide a yaw increase, or car
rotation, in response to throttle application, as when throttle steering a rear-drive car. Getting
exact reproduction of rear-drive behavior would probably be impossible, but getting the car to
point the tail out when the driver applies power would be possible.
One reason that it would not be possible to duplicate rear-drive behavior is that we would have
different behavior at the front wheels. At best, we’d be simulating the behavior of a throttlesteerable all-wheel-drive car, rather than a rear-wheel-drive car.
Another problem is that steering the rear wheels is not the same as powering them. Powering
the rear wheels does not simply produce a slip angle increase; the effects are somewhat more
complex. Light application of power actually plants the rear end, with front drive or rear drive.
With rear drive, as throttle application increases, sooner or later we reach a crossover point, at
which the use of the rear tires’ friction envelope for propulsion starts to erode their lateral force
capability faster than the normal force increase increases the lateral force capability. Then the
tail starts to point out. With modest static rear percentage, this crossover point occurs
relatively early. In tail-heavy rear-drive cars, there is a substantial range of throttle application
in which power actually makes the tail stick rather than slide.
So the question arises: what sort of rear-drive response would we be trying to mimick? Reardrive cars aren’t all alike in their response to power application.
Regarding the Pontiac referred to: actually, the current Grand Prix GXP is the second V8,
FWD car to bear the GXP designation. The 2004-2005 Pontiac Bonneville GXP has an engine
closely related to the Cadillac Northstar V8, which has been used in FWD layouts branded as
Cadillacs for many years now. This is a 4,565cc (279 cubic inch) engine with 4 cams and 4
valves per cylinder.
The current platform, using the 327 cid LS4 engine, is shared with the Chevrolet Impala and
Monte Carlo. It is the first use of a pushrod “small block” family engine in a transverse frontdrive layout.
This is little remembered now, but GM’s first FWD cars were big V8-engined designs. The
first was the Olds Toronado, in 1966. That was a really big, heavy car. As I recall, it weighed
close to 5,000 pounds. A Cadillac variant followed, which had engines as large as 500 cubic
inches. These cars had longitudinal or “north-south” engine mounting.
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So putting large amounts of power through the front wheels can definitely be done. Power
steering becomes a necessity, but power steering has become so commonplace, even on light
cars with rear wheel drive, that we are generally not accepting an increase in cost or
complexity if we include it.
With a transverse V8, the engine compartment packaging really gets tight. This makes it hard
to find room for controls on either side of the car, to provide both left and right-hand-drive
versions. It also becomes hard to find room for large-section structural rails beside the engine.
The rails have to be narrowed to make room for the wheels to steer, and then the only way to
make them adequately stiff is to make the walls thick, which adds weight. GM is using strut
suspension, which helps some as the loads from the top of the struts can be fed into the cowl
area. However, with struts and wide tires, the steering geometry doesn’t work out very
favorably. We have to accept either a large steering axis inclination, or a large scrub radius, or
both.
Looking at the mechanics of putting ample power to the pavement, a FWD car doesn’t look
that much worse on dry pavement and street tires than a RWD, front-engined car. In fact, if
both cars are relatively nose-heavy, the front-drive car may be better. For example, suppose
both cars have a center of gravity 18 inches above the ground, and a wheelbase of 108 inches.
At .50g forward acceleration, 1/12 of the car’s weight, or about 8%, will transfer from the front
to the rear.
If the front-drive car has 60% static front weight, it ends up with about 52% on the drive
wheels. If the rear-drive car has 56% static front weight, it also ends up with about 52% on the
drive wheels.
If the front-drive car has 62% static front weight and the rear-drive car has 58%, the front-drive
car has 54% on the drive wheels at .50g, and the rear-drive one has 50%. That means the
front-drive car will actually put power down better, assuming the coefficient of friction is such
that the .50g figure is realistic. With 50% of the weight on the drive wheels dynamically, that
would be a coefficient of friction around 1.00.
If we put slicks on the cars, things change. Assuming wheelspin still sets the limit, rear drive
starts to look better, because more weight transfers rearward as the forward acceleration
increases.
Conversely, if the surface is so slippery that it’s a challenge to get the car moving at all, the
front-drive car is clearly better. If the road slopes uphill, the front-drive car loses some of its
advantage, but will generally still have an edge.
Note that we are comparing a fairly typical front-drive car to a decidedly nose-heavy rear-drive
car. The more static rear percentage we have for the rear-drive car, the better rear drive looks.
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Readers who like Porsches and Corvairs will be quick to point out that there is no law of nature
that says an engine-over-drive-wheels car has to be front-engined. Assuming we are ruling out
all-wheel-drive for reasons of cost, complexity, and weight, we really should be considering
three layouts: front engine/front drive; front engine/rear drive; and rear engine/rear drive.
From the standpoint of propulsion, the rear-engine configuration has clear advantages over the
other two layouts. The drive wheels can have 60% or more of the static weight, and this
percentage increases when accelerating forward or climbing hills. Under hard braking, the
front and rear brakes share the workload. In straight-line limit braking, the front wheels will
do around 60% of the work, as opposed to 70% for a front-engined car with 50% or a bit less
static rear weight, or 75-80% for a typical front-drive car.
The rear-engine layout can also be throttle-steered without any added contrivances. It can
often do without power steering if desired. There is lots of room for the controls, making left
and right-hand-drive versions relatively simple to accommodate.
The biggest problem with the two engine-over-drive-wheels layouts is the difficulty of
achieving balanced cornering with four equal sized tires. This was more of a problem when
tires were less reliable than they are now. Until recently, it was fairly important to have a
single spare tire that would fit any corner of the car. Now, most cars have compact spares that
are only suitable for limp-home use and don’t match any of the regular tires anyway.
With four equal-size tires, we can build a FWD car that understeers, or a front-engine RWD
car with balanced handling, or a rear-engined car that oversteers. The first two options are
clearly preferable from a safety standpoint.
However, if we are willing to entertain the use of bigger tires at the heavy end of the car, some
interesting possibilities open up. If we are careful with the body shape so that we maximize
aerodynamic stability, and if we use a longish wheelbase, we can have a rear-engined sedan
that will out-handle any front-engined design, and outperform it in the snow. This approach
would be well suited to a transverse V8 powertrain. The problem of finding room for
structural rails would be greatly eased since the wheels wouldn’t have to steer. The car would
be, just barely, mid-engined.
There would be some drawbacks. There could be two trunks, as in some mid-engined sports
cars, but fold-down rear seats with a pass-through from the rear trunk would not be an option.
The rear seat passengers would be subjected to more engine noise. Building a station wagon
version would be problematic. Still, such a car could probably find an enthusiastic following
among buyers who need to carry multiple passengers, yet give priority to performance.
Alternatively, we can also have a FWD car with little understeer. To make the most of this
approach, we would want to have the engine well forward for at least 65% static front weight,
bigger tires in front than in back, and the rear wheels way at the back of the car, as in a Citroen
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DS21. This requires the designer and the buyer to cast aside accustomed notions of how a car
should look, but it offers the promise of better handling and traction than existing two-wheeldrive cars, with a large, quiet, unobstructed passenger and luggage space in the rear.
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This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
BIG TIRES ON THE FRONT
Last issue, I mentioned that there is a performance gain to be had in a front-wheel-drive car by
making the car markedly nose-heavy and using larger tires in front than in back. This was in a rather
lengthy response to a reader’s question partly relating to the Pontiac Grand Prix GXP. I have
recently noticed in magazine reports about this car that GM is in fact using larger tires on the front of
the V8 versions of this car: 255 section on the front, 225 on the rear.
TIRES IN THE SNOW
I have heard two schools of thought on tire pressure for winter driving. This applies to driving on
snow-covered roads. The first is that tires should be kept at the upper end of the manufacturer’s
specifications to help in cutting through the snow. The thinking is that the contact patch is smaller,
hence more weight per square inch, as well as less sidewall deflection – which may decrease the
potential for hydroplaning on the snow. The other is that running the pressure at the lower end
allows for better bite for the tread in the snow, and more stability. What do you think?
I’m with the low-pressure school.
It’s said that one measurement is worth a thousand expert opinions. Really, you’d think this might
be measurable. Surely somebody has tried measuring, say, how steep a hill a vehicle can climb, at
various tire pressures. I would be willing to defer to any actual measurement that contradicts my
expert opinion.
That said, I offer my expert opinion, and that expert opinion is based on a lot of time spent in
Wisconsin, where there are long, snowy winters.
First, tire pressure effects in snow are surprisingly subtle compared to other variables, and effects
due to other variables are surprisingly large. That explains why there is controversy about inflation
pressures, even though people have been driving cars through more than a hundred winters now.
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One reason tire testing was moved indoors, with rollers or belts substituting for pavement, is that
even on hard, dry pavement, weather, surface contamination, pavement temperature, pavement age,
and other factors make enough difference that small variations in tire performance are hard to
measure repeatably.
When we’re dealing with snow, we have similar variability, exaggerated at least tenfold. Snow and
ice come in dozens of different varieties and depths, and all of these have properties that are highly
temperature-sensitive. Compared to snow, pavement is simple and consistent.
The explanation I have heard from sources that advocate high tire pressures is that the tire needs to
penetrate the snow and get to the pavement, where it can find traction. But clearly, in most snow
conditions that never happens, at any inflation pressure. If it did, we’d see bare pavement where the
tire passed.
Instead, we see compacted snow, with an imprint of the tire tread. Or at least we see that if the tire is
rolling, and not spinning or sliding – and if we are dealing with snow that has not already been
compacted. We also usually see a small area alongside the track where the snow appears slightly
raised, apparently having been pushed out of the way, perhaps just by the sidewall. This is not a lot
of snow, however. Most of the snow stays put horizontally, and gets compacted vertically.
The tire evidently gets traction by packing the snow into a relatively solid form, and simultaneously
interlocking with it. To break traction, the compacted snow projections residing in the tread grooves
must be sheared off, and the layer of snow lying under the tread blocks must also fail in some
manner.
The failure of the snow in the grooves is easily visualized as simple breakage. The failure of the
snow under the tread blocks is a bit harder to visualize. It appears that the snow under the tread
blocks contributes more to traction than one would imagine, because the tire’s grip is greatly
improved by siping the tread blocks. It also helps to roughen the surface of the tread blocks.
I do not claim to perfectly understand the mechanics of structural failure of snow in a tire contact
patch, but I do know that it is normally a combination of breakage and melting. Ice (and snow is ice
crystals) can be melted by mechanical pressure – or, stating it a bit differently, the melting point of
ice is lowered by mechanical stress, either compressive stress or shear stress. Anyplace that the
snow or ice liquefies, its mechanical strength disappears, and it turns into a lubricant. The closer the
ice or snow is to its melting point, the less mechanical stress is required to turn it to liquid.
So, when we compact snow, we make it stronger, but only up to the point where we start to get
localized melting. The unit loading required to reach this point depends on how cold the snow or ice
is. Moreover, short of the point where we encounter melting by compression alone, we see an
increased likelihood of melting by the combination of compression and shear. In other words, as
unit loading increases, we gain hardness but lose melt resistance. The hardness gain is fairly
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independent of temperature. The melt resistance loss is heavily affected by temperature, or at least
its importance is.
From this, we might logically expect that the ideal contact patch size would be smaller in really cold
weather than when we’re near thaw temperature.
I suspect that this is academic, however. I think the optimum contact patch size is far bigger than we
can ever get with a tire. Consider the transportation devices that people have devised specifically for
snow: snow cats, snowmobiles, snowshoes, cross-country skis. All of these operate by compacting
the snow minimally, over a large area, and then trying to get maximum purchase on that large
interface. For best performance on snow, or any other soft surface, we really want a belt or track,
not a tire.
It would seem to follow that the more we can get a tire to act like a track, the better it should work.
That would suggest a radial tire, at low pressure.
Note that it does not necessarily follow that we want a wide tire. It is generally agreed that for most
winter conditions, a tire should be narrow. I think, based on the reasoning above, there will be
winter conditions where a wide tire may be preferable. These may include bare ice and hard-packed
snow, probably even shallow soft snow. But in snow of significant depth, narrow tires are better.
The reason for this doesn’t have to do with an increase in traction when the tire is narrow, as such.
Rather, it has to do with the force required to move the tires, which is less when the tires are narrow.
As the tire rolls forward, it is resisted by the snow in front of it. To advance, the tire must, in effect,
climb a ramp of snow. The ramp of snow is not strong enough to support the tire, and it is
continually collapsing under the weight of the car. The amount of collapse is fairly similar
regardless of the width of the tire; for any practical tire size, we will compact the snow to a pretty
solid state, no matter what. Yet the snow has substantial resistance to this compaction, and this
translates to a resistance to the wheel’s forward motion. The taller and wider the mass of snow we
must compact, the greater the resistance to motion. The height of the snow we must compact
depends on the snow’s depth. The width we must compact depends on the width of the tire.
It would also seem that a narrow tire should provide more directional control, since it is better
shaped to act like a blade or rudder.
From this reasoning, we might expect that the ideal tire for deep snow would resemble a bicycle tire.
Such a tire would be easy to push along, and should have good directional stability.
However, it doesn’t quite work that way with really narrow tires, as anybody who has tried riding a
bicycle in deep snow will attest. The problem is that the ramp of compacted snow that the tire rides
on is so narrow that the tire is forever sliding off the side of it into the soft snow alongside. As soon
as the tire moves forward again, another narrow compacted ramp is formed beneath it, and again it
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slides off one side or the other – no predicting which side. The result is that the tire absolutely will
not run straight.
So there is such a thing as too narrow. The tire needs to be wide enough to sit on top of the
compacted ramp it is making for itself. A square-shouldered profile, or one with concave shoulders
that compact a sort of retaining berm along the side of the main compacted ramp, also can be
expected to help.
Returning to the question of inflation pressure, this also affects resistance to forward motion. And
even this relationship is not as straightforward as one might think. Based on our experience with
tires on pavement, on a smooth, hard surface, the higher the inflation pressure, the easier the tire
rolls, at least within practical limits.
But on a rough surface, a softer pressure can actually roll more easily. For this to be so, the surface
must have roughness as opposed to waviness: the ups and downs must come fairly close together.
The tire rolls easier because it can yield to the bumps rather than having to climb over them. This
was realized very early in the history of the pneumatic tire. John Dunlop immediately noticed that
his new pneumatic tire would roll further across his bumpy back yard than a solid tire.
This has relevance to driving in snow because often the situation that gets us stuck is one where one
or more wheels are in a fairly modest-sized depression, and we have to move the tire over the lip of
the depression with the meager traction available. In at least some such situations, soft inflation will
make getting over that lip easier.
It will be apparent that I am writing here from a mixture of practical experience and inference. I
invite readers with further experience, or contradictory experience, to comment.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
ROLL AXIS INCLINATION
What is the influence of a roll axis inclination biased to the front suspension – meaning a front roll
center always closer to the ground than the rear? At least in passenger cars, the roll axis is always
inclined to the front except in some special cases, for example the BMW Series 1 which is reported
by BMW to have the roll axis parallel to the ground.
I supposed I had an explanation, but after reading Race Car Vehicle Dynamics by Milliken my
potential explanation has flown away. My explanation was based on the idea that the more the roll
axis is inclined toward the front, the more load transfer there will be at the front axle, and the more
understeer the vehicle will have.
But I have put into an Excel spreadsheet the formulation from Milliken and I find to my surprise that
the higher the front roll center, the greater the load transfer at that end – which works against my
intuition.
Can you explain this?
Short answer: higher roll center at the front implies more geometric roll resistance at the front, hence
more load transfer at the front, other things being equal. So the typical nose-down roll axis
inclination does not increase front load transfer.
There are cars that have a nose-up roll axis. They are all rear-engined. Probably the most extreme
example is the Hillman Imp, which had a front roll center near hub height and a rear roll center near
ground level.
Like many things, the subject of roll resistance and load transfer is fairly simple once you understand
it, but will drive you crazy until you get to that point.
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When discussing this subject, I am always quick to plug my video, Minding Your Anti, which covers
the subject at length. It costs US$50.00, shipping included, payable by check or money order to me
at 155 Wankel Dr., Kannapolis, NC 28083-8200, USA.
In steady-state cornering (constant speed, on a constant radius), on an unbanked road surface, the
total load transfer from the inside wheels to the outside wheels depends entirely on the height of the
whole vehicle’s center of mass (center of gravity, or c.g.) and the track width at the c.g.
Suspension design and tuning have almost no effect on the magnitude of the total load transfer.
What we mainly do with suspension design and tuning is control the distribution of that total,
between the front and rear wheel pairs.
We customarily consider the car to be a rigid object, supported by a single compliant structure at
each end. The sprung structure is the rigid object; the front and rear suspension systems are the
compliant structures.
As an analogy, imagine that you and a friend are carrying a sailboard, as used for windsurfing, along
the beach. Each of you is carrying one end of the sailboard. The sail is up, and there is a breeze
blowing. The force of the wind on the sail tries to overturn the sailboard.
The overturning force depends entirely on the design of the sailboard and the amount of wind. The
total counterforce that you and your friend together need to exert to balance this does not depend on
you and your friend. However, the amount of counterforce that you individually need to exert
depends on the amount exerted by your friend, and the amount of counterforce he has to exert
depends on you.
You and your friend are like the front and rear suspension systems. The sailboard is like the sprung
mass.
There are portions of the load transfer that come from the unsprung components, and there are
portions that come from the dampers if the car is rolling upon corner entry or de-rolling on exit.
However, for simplicity in answering the present question let’s look just at the components of the
load transfer that come from the inertia force (centrifugal force) of the sprung mass acting through
the suspension, in steady-state cornering. There are only two such components: elastic load transfer
and geometric load transfer. Elastic load transfer comes from elastic roll resistance: the roll
resistance supplied by the springs and anti-roll bars. Geometric load transfer comes from the
properties of the structural components attaching the wheels to the sprung mass, which can be
arranged to generate forces opposing roll, or geometric roll resistance.
With independent suspension, these two components influence each other more than is commonly
recognized. The load distribution on an independently suspended wheel pair affects how much
geometric roll resistance the wheel pair has, for any given suspension geometry. To illustrate with
an extreme case, if the inside wheel is off the ground, the geometry of its suspension linkage is
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irrelevant and only the geometry of the outside wheel has any effect on the car. My video deals with
these effects in detail. For simplicity, I will ignore them here, but I do want note in passing that they
exist.
When we speak of roll center height, we are speaking of an imaginary point whose height represents
the amount of geometric roll resistance for the front or rear wheel pair. If this point is assigned
properly, we can closely approximate the geometric load transfer at one end of the car as: roll center
height times sprung mass centrifugal force at that end of the car, divided by track width at that end of
the car.
When the suspension is symmetrical, the point you generally see in the chassis books – the force line
intersection – is a good approximation. When the suspension is not symmetrical, using the force line
intersection as the roll center can lead to major mis-predictions of car behavior. Sometimes the force
lines may be parallel, in which case there is no intersection.
We may define a line connecting the front and rear roll centers, called the roll axis. The car doesn’t
really roll about this line, but as a crude approximation we can reasonably think of it as doing so.
If we raise the roll axis at both ends, the geometric roll resistance is greater at both ends. If we raise
one end of the roll axis and lower the other, leaving its height at the c.g. unchanged, the total
geometric roll resistance is unchanged, but we increase the geometric roll resistance at one end and
lower it at the other. The elastic elements – the springs and anti-roll bars – are not affected by this.
So the end where we lowered the roll center has less geometric load transfer and the same elastic
load transfer as before – hence less load transfer overall. This will make that tire pair grip better,
because they will be sharing the work more equally. At the opposite end, the elastic component will
likewise be unchanged, but the geometric component will be increased – hence more load transfer
overall.
Okay, so if we want understeer for most drivers, why have a nose-down roll axis? There are a
number of explanations.
The most obvious explanation is that when the car has independent suspension in front and a beam
axle in back, we don’t have much choice. Independent suspensions with roll centers much above
four inches generally jack excessively. Front suspensions with high roll centers generate lateral
contact patch motion over bumps, which creates kick at the steering wheel. It is possible to build a
beam axle suspension with a roll center below any component of the suspension, but the linkage
required is somewhat complex. Consequently, beam axles on cars with enough ground clearance to
be practical on the street generally have roll centers at least six inches high, and usually at least ten
inches. Of course, with independent rear suspension, the roll center is usually much lower, but most
often still a bit above the front one.
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The next most obvious reason is that passenger cars are generally too nose-heavy to have balanced
handling, and the front suspension doesn’t control camber when cornering nearly as well as the rear
suspension. Consequently, we need to kill understeer, not increase it.
A somewhat less obvious reason has to do with driver-perceived car behavior in abrupt transient
maneuvers, such as the lane-change test commonly used in passenger car testing. With a nose-down
roll axis, there is a small yaw component with roll. The nose points out of the turn slightly, relative
to the four contact patches. This makes the car feel steady to the driver, rather than twitchy.
Another reason sometimes cited is that when a car is abruptly steered into a turn, the geometric
component of the load transfer is the first to act on the car. If this component is greater at the rear,
we will momentarily have less understeer and the car will turn in more responsively. Note that this
explanation is somewhat at odds with the one immediately preceding it.
There are somewhat logical variations on both of these two explanations. We could say that if the
main mass of the car is yawing out of the turn relative to the four contact patches, that steers the
contact patches into the turn, or steers the rear wheels out of the turn, momentarily adding oversteer!
Some people also believe that tire load sensitivity momentarily works backwards until the tires start
heating. I personally don’t believe this, but if so it means that if there is initially more rear load
transfer, that adds understeer rather than oversteer, and makes the car feel stable.
Isn’t this fun? If it weren’t for vehicle dynamics, I’d have to do something sane for a living.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
DIFF DIFFERENCES
Which differential would be best for road racing, in my 300hp Porsche? The question arises because
a supplier suggests that a plate-type limited-slip is better suited to road racing than a worm gear
style torque bias diff. I have used both and found Iliked the torque bias diff. I thought it was a better
design, from what I read. The supplier states that the lsd will be better in corner entry and exit.
What is your opinion?
Clearly, both worm gear and clutch pack differentials have their adherents, and both are used
successfully in racing. You say you have experience with both types, and have already formed a
preference. The most obvious answer would be that you’ve already answered your own question,
and don’t need advice.
However, the situation is actually a bit murkier, because the behavior of both types of differential
can vary according to design and tuning details. Both types are similar in that they generate a
locking torque in response to the total torque being transmitted. In both types, the locking torque
depends on pressure angles. In a ZF-style clutch pack design, the angles are those of the ramps on
the spider shaft and the housing halves. In a worm gear design, it’s primarily the helix angle on the
gear teeth, and secondarily the pressure angle of the tooth profile. Lubricant choice also influences
behavior.
Consequently, all clutch pack diffs don’t act alike and neither do all worm gear diffs. A lot depends
on how a specific example is tuned.
That said, the clutch pack design probably offers a greater range of tuning options, and probably
greater wear resistance. With the worm gear designs, we are trying to make gear teeth act as a
friction device. Clutch discs are designed to be a friction device; gear teeth can be made to act as a
friction device, but they are less comfortable in that role.
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This affects the ability of the differential to maintain consistent properties over time, and its
longevity.
The pressure angles determine how rapidly locking torque builds as transmitted torque increases.
The preload in the diff determines how much locking torque there is when no torque is being
transmitted. A clutch pack is easily preloaded, and it maintains its preload relatively well, especially
if the preload is applied by springs or some other compliant system such as dished clutch plates.
Worm gears can also be preloaded, but because they are not very compliant, the preload rapidly goes
away as the teeth wear.
One limitation in worm gears is that the pressure angle is generally the same for forward torque and
rearward torque (as when engine braking, or when transmitting brake torque from a single rear
brake, as seen in FSAE cars). In a clutch pack diff, we can use different ramp angles for power and
decel.
Another peculiarity of worm gear designs is that because power and decel apply force to opposite
sides of the gear teeth, preload doesn’t have identical effects in both directions. If we preload the
gears in the direction they’re loaded under power, what happens under decel is that we have
diminishing friction with increasing reverse torque, until the preload is overcome, at which point
locking torque is zero. As reverse torque increases beyond that point, locking torque builds again.
With a clutch pack, preload has similar effect in both drive and decel modes.
This does mean that we can make a worm gear diff act different in drive and decel, but not in a
manner that’s independent of preload.
One interesting, though uncommon, trick we can use in a worm gear diff is to use plain thrust
washers to absorb the thrust of the worm gears in one direction, and needle thrust bearings to absorb
the forces in the other direction. This can afford us some limited measure of difference in friction
depending on torque direction. Last year’s North Carolina State University FSAE car had a diff like
this.
It will be clear, however, that using these tricks is not nearly as straightforward as varying the ramp
angles in a clutch pack diff.
Finally, neither option is ideal, because neither is speed-sensitive. Both clutch pack and worm gear
diffs rely on Coulomb friction, which is largely dependent on normal force and not speed. We
would rather have the locking torque vary with the speed difference between the wheels, either
entirely or at least in part. This argues for either a pure viscous limited-slip, or a design that uses a
pump, driven by relative ouput shaft rotation, to load a clutch pack, or a design that combines
viscous effects with a clutch pack.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
SPRINGS, BARS, AND LOAD TRANSFER
I've been reading around and am having a hard time comprehending a spring's effects on load
"change" and how they effect understeer/oversteer balance as stated in your April/May/June 2003
newsletter.
What I know (or think I know):
Longitudinal Load Transfer = acceleration x [(weight x cg height)/wheelbase]
Lateral Load Transfer = (Lateral Acceleration x weight x cg) / Track width
So, by looking at the equation, spring rates are not part of the formula, therefore they play no role in
the amount of load transfer. However, I do know that sway bars DO affect load transfer by
unloading the inside wheel and loading the outside wheel. In Carroll Smith's "Tune to Win," he
states:
"The greater the resistance of the springs, the less roll will result - but there will be no significant
effect on the amount of lateral load transfer because the roll couple has not been changed and there
is no physical connection between the springs on opposite sides of the car. The same cannot be said
of the resistance of the anti-roll bars. In this case, because the bar is a direct physical connection
between the outside wheel and inside wheel, increasing stiffness of the anti-roll bar will both
decrease roll angle and increase lateral load transfer."
By looking at the above information, we would assume springs are merely there to control body roll
which affects camber, toe, etc.
And from your article, I gather that the amount of load transfer between the two front wheels vs the
two rear wheels indicates how much oversteer/understeer a car will have. However, the above
equations show that spring rates don't affect load transfer.
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What I don't understand:
I realize that using higher spring rates in rear vs. spring rates in front will cause a car to oversteer given a simplified car with equal motion ratios front/rear and without using sway bars. In the real
world, it proves true. However, I'm having a hard time comprehending how spring rates can affect
the balance of the car when they play no role in load transfer? What do you mean when you say
stiffer springs cause more "load change"?
The questioner is quite right that springs do affect car balance, and that this could not be so if they
had no effect on load transfer.
With all due respect for Carroll Smith’s memory and legacy, significant portions of the passage the
questioner cites here are simply incorrect. Springs and anti-roll bars both affect load transfer – or
more properly, load transfer distribution – in cornering or lateral acceleration, and they do so in
essentially the same way. Indeed, anti-roll bars are springs, and the ride springs are connected sideto-side, by the car’s frame.
The only difference between an anti-roll bar and a ride spring is that anti-roll bars act only in roll and
warp, whereas ride springs act in all four modes of suspension movement: roll, pitch, heave, and
warp. In the modes in which it is active, the bar is just another spring.
The equations cited are for total load transfer, in lateral or longitudinal acceleration. Taken as such,
they are correct. The springs and the bars do not affect these total quantities, or at least not very
much. However, the springs and bars affect the apportionment of that total, between the front and
rear wheel pairs in lateral acceleration, or between the right and left wheel pairs in longitudinal
acceleration.
Let’s consider lateral acceleration first. The roll-resisting moments produced by the springs and bars
are called the elastic component of roll resistance, and they produce the elastic component of load
transfer at the tires. There is also a geometric component, at each end of the car, which comes from
the forces in the (comparatively) rigid suspension components. These two components make up the
total roll resistance for the front or rear suspension.
For purely lateral acceleration, in steady-state cornering, assuming equal track width at both ends,
the total sprung mass load transfer at the front or rear is the total sprung mass load transfer for the
whole car, times the percentage of the total roll resistance at that end. For example, if the front
suspension’s combined elastic and geometric roll resistance is twice as great as the rear suspension’s
combined elastic and geometric roll resistance, the front end then has 2/3 of the total roll resistance,
and it will see 2/3 of the total sprung mass load transfer.
Increasing the front roll resistance or decreasing the rear will increase front sprung mass load
transfer, and decrease the rear. Increasing front and rear roll resistance together, maintaining 2/3 of
the total at the front, will result in no significant change in the wheel loads. It doesn’t matter
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whether we change roll center heights (the measure of geometric roll resistance), springs, bars, or all
three, as long as the totals front and rear are in the same ratio as before we made our changes.
In longitudinal acceleration, the same principles apply, except that the effects of the bars are
negligible since we are dealing with pitch rather than roll, and we are concerned with the relative
pitch resistances of the right and left wheel pairs, rather than the relative roll resistances of the front
and rear wheel pairs.
In either case, the elastic component of the wheel pair load changes depends on the rate of both
springs in the pair, and increasing the rate of either spring in the pair increases the average or total
for the pair.
So, for the rear suspension in roll for example, stiffening either the inside or the outside spring adds
roll resistance. On the outside wheel, a stiffer spring increases the rate of force increase with
respect to suspension compression: more pounds of load change per inch of suspension movement.
On the inside wheel, a stiffer spring increases the rate of force decrease with respect to suspension
extension: again, more pounds of load change per inch of suspension movement.
Either way, we have more pounds-feet of roll-resisting moment per degree of sprung mass roll.
So in any situation that decreases the load on a spring, a stiffer spring gives less load on the wheel at
a given suspension movement: more load change, implying less load, compared to same
displacement with a softer spring.
More knowledgeable readers will note that this discussion is simplified somewhat compared to real
life. Springs can somewhat affect total load transfer, chiefly because they can create ride height
changes with roll and pitch. For example, if we put stiff springs in the rear and soft springs in the
front, and the car has little anti-squat, then under forward acceleration the rear suspension will
compress little and the front suspension will extend much. The car will therefore be sitting higher
off the ground, c.g. height will be greater, and therefore rearward load transfer will be greater.
Thus, it is not strictly correct to say that springs do not affect overall total load transfer. However,
for all but extreme cases, we can treat such effects as negligible.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
REAR PERCENTAGE OR POLAR MOMENT?
I am wondering about the relative merits of Front / Rear Weight Distribution versus Polar Moment of Inertia. I
road-race a Mustang in a class that allows extensive engine and suspension modifications to late-model muscle
cars, but the rules are strict enough to prevent extensive body, floorpan, and frame modifications. As a result of
the rules, and the large V8s, the cars are inherently heavy in the front end – usually to the tune of 51-55%,
depending on platform, fuel load, etc. So when deciding on the placement of heavy components (such as batteries,
fuel cells, ballast, etc.) I’m wondering what the ideal position is. Obviously lower is always better, but how far
back is ideal? You could place the masses as far back as possible to improve F/R balance, but at the expense of
Polar Moment. You could put the mass in the center of the car, minimizing polar moment but failing to take
advantage of an opportunity to improve the car’s balance. Or you could put it somewhere in between.
Instinctively, my engineering training tells me that the two things have different functions. F/R distribution should
make the car generally behave in a more balanced fashion, and certainly more weight on the back tires will help
corner exit traction – which is a key in this type of car. Keeping polar moment low should help keep the car
rotationally responsive, and more willing to respond to corrections if the tail steps out.
Several years ago I ran a simple analysis, and found that the average cornering speed of the car seemed to be a
determining factor between these two trade-offs. This was not an in-depth analysis. Basically I broke cornering
down into the energy it took to rotate the car (start it rotating and stop it rotating) and the energy it took to
redirect the velocity vector, and compared the two. It seemed to me that the faster the mid-corner speed, the more
the velocity vector change became the dominant force requirement, and therefore we might assume the F/R
balance would be more important. My analysis said that, in the kind of racing I do, F/R distribution would be far
more important, but I’m surprised at the number of competitors, in amateur and pro competition, who seem to
disagree. Of course, my analysis was simplified to a great extent, with numerous assumptions being made that
are not necessarily always valid.
So I ask – how far back should I place that ballast, or those movable components? On an average road course,
where mid-corner speeds probably average from 40mph to about 100mph or so, which would you deem more
important? Would you place that ballast in the back bumper, or under the floorpan or inside the inside frame
rail?
And as a secondary question – what would you consider the ideal weight distribution for a car of this type.
Obviously, if I can achieve whatever I decide is “ideal”, then I want to work to reduce polar moment, but what is
that “ideal” number – in your estimation of this type of race car? I’ve heard arguments for 50/50 and arguments
for as much as about 58% rear weight. I tend to think the answer is closer to 55%, but I’m very curious as to
your input on this matter as well.
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Taking the last part first, the ideal rear percentage, or the desirable range, depends on your tire rules
and the nature of the course. To a lesser extent, it is also influenced by the level of available grip,
and by aerodynamics.
Suppose we have no tire rules, ample power, lots of freedom with our wings and other aero devices,
and a track with serious straights and tight turns. Suppose also that the rules require rear wheel
drive. In such a case, we might want as much as 65% rear, or even a bit more, and rear tires about
twice the size of the fronts. We would want more than 2/3 of the downforce at the rear. We would
want ample area in rear wing sideplates and/or tail fins, for yaw stability.
The reasoning here is that the car will spend a lot of its time accelerating longitudinally: accelerating
forward out of the turns and down the straights, and accelerating rearward (braking) at the end of the
straights. Propulsion comes only from the rear wheels, so we want as much of our weight on the rear
as possible to maximize forward acceleration. Braking is shared by all four wheels, and if the car
has ample braking capability, the fronts will do more than half of the braking even if they only carry
a third of the car's weight at rest. This is due to the large amount of dynamic load transfer forward
during hard braking. So for both forward and rearward acceleration, we want as much rear
percentage as possible, at least within practical limits for a road racing car.
This would be so even if we are constrained to equal size tires front and rear. If our event is, say, a
zero to 100 to zero competition (accelerate from a standstill to 100mph, then brake to a standstill, all
in a straight line), we'd want to build the car so it just barely picks the front wheels off the ground at
launch, or almost does so. Note that the rear percentage needed for this varies dramatically
depending on the wheelbase, the c.g. height, and the amount of grip available. With a productionbased car – relatively short wheelbase and high c.g. – and good drag slicks, the ideal rear percentage
may be less than 50%. The grip of modern drag tires is so good that a 50/50 car can actually be
limited by wheelstand rather than wheelspin. With a high c.g. and a short wheelbase, the ideal rear
percentage varies dramatically with the grip level.
If we have more chassis design freedom, we'd rather have a dragster than a pro stock: long
wheelbase, low c.g., lots of static rear percentage. With such a layout, rearward load transfer is less,
and consequently dynamic rear percentage varies less with grip level. A single layout and setup will
therefore be more nearly optimal over a wider range of conditions. With street tires or road racing
tires, the ideal rear percentage will be considerably over 50%. As long as the car doesn't have to
turn, we'd want to build it like a dragster, even if the front and rear tires have to be the same size.
Of course, the questioner here doesn't have such design freedom, nor is he running on a track with no
turns. I'm just examining extreme cases, to illustrate some points.
The opposite extreme case would be a skidpad competition: the car just has to corner at the highest
possible constant speed. Accelerations now are almost purely lateral. We might suppose that the
ideal design here would have equal-size front and rear tires, and 50% static rear weight. That is
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indeed close to correct, although if we can use unequal tire sizes, we can get as good cornering from
a tail-heavy car as from a 50/50 one. If there are no limits on tire size, two practical considerations
will limit us: camber control and steering geometry. We can control camber about equally well at
both ends of the car, but there is a case for using smaller tires on the front from the standpoint of
steering dynamics. If we do that, we want the car tail-heavy, roughly in proportion to tire size.
Oddly enough, the radius of the skidpad affects the optimum rear percentage. This is a bit counterintuitive, but it's true. Really small skidpads (or really tight turns) call for a more tail-heavy car than
the tire sizes would suggest, and really big skidpads (or really big turns) call for a more nose-heavy
car. The reasons for this are of different natures for the two cases.
On a really small skidpad, such as the 50-foot diameter one used in Formula SAE competition, the
front wheels track noticeably outside the rears, even when the tires are sliding. Consequently, the
drag forces of the front tires, especially the heavily loaded outside front, act at a larger radius than
the radius the c.g. is following, and the propulsion forces from the rear tires act at a smaller radius
than the c.g. is following. This creates a yaw moment out of the turn, and tightens the car (adds
understeer). Additionally, in some cases there may be effects from a limited-slip differential or a
locked rear that create understeer in small-radius turns.
When the turn radius is really large, the car will need to transmit substantial amounts of power
through the rear tires just to maintain constant speed. On really fast turns, the car may actually be
near full power, and not gaining any speed at all. The rear tires are transmitting hundreds of
horsepower, just to overcome aerodynamic drag and the induced drag from the front tires as they run
at a slip angle.
This means that the rear tires are using a substantial portion of their performance envelope, or
traction circle, to propel the car, so they have less of their capability available to generate lateral
force. The car is consequently subject to power oversteer. The best way to counter this is to have a
disproportionate amount of aerodynamic downforce at the rear of the car. However, in many classes,
including stock cars running on high-speed ovals, the rules may not allow the aerodynamic devices
needed to achieve this. It then becomes desirable to make the car a bit nose-heavy to add understeer
and counter the power oversteer.
I am not trying to confuse the issue. I am merely pointing out that, as the questioner has already
come to appreciate, we cannot state categorically that a particular rear percentage is ideal. It depends
on other factors.
That said, the questioner appears to be correct that in his class, more rear percentage is better, within
the limits imposed by the rules, without going above minimum legal weight. And there is indeed a
tradeoff in such a situation between getting good rear percentage and reducing yaw inertia (polar
moment of inertia in yaw, commonly "polar moment" for short). I agree with the questioner's
tentative conclusion that it is better to go after rear percentage and forget yaw inertia, for road course
applications.
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It is interesting to consider what it might take to make us go the other way, and put the ballast closer
to the middle. I think we might do that if we were autocrossing, particularly if a large part of the
course was made up of a long, constant-speed slalom, and if the course had no significant straights,
so that the car was continually cornering and continually changing direction, and never had to spend
a lot of time accelerating longitudinally – in other words, if there was a lot of yaw acceleration and
relatively little longitudinal acceleration.
But no road course is like that. Almost all of them have serious straightaways, and few really abrupt
transitions. A car with large yaw inertia will tend to understeer into the slower turns and oversteer
coming out, but to some extent the driver can overcome the entry understeer with trailbraking, and
the exit oversteer by using an "out fast" line and judicious throttle management.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
EFFECTS OF SPRING RATES AND DAMPER SETTINGS DURING CORNERING
I would be interested to hear your comments about the effects of relative spring rates (front/rear)
and damper settings on steady-state cornering characteristics. I do not race, but I am interested in
the effects of suspension settings on the relative under/over-steer characteristics.
I presume that (all other things being equal) any increase in spring rate at the front will increase the
apparent roll stiffness and therefore make the car trend towards an increase in understeer (which I
presume is the same as an increase in static directional stability) – and an increase in the rear will
cause the reverse. And an increase in damper rate at one end would seem to have a similar dynamic
effect during turn-in, while the load transfer is actually taking place.
I own a Morgan – which as you are aware does not have any anti-roll bars – and I am about to
change the front springs to a higher rate (140 lb/in vs. 105 lb/in) and I presume that this is going to
cause some change in behavior. It would be interesting to know what order of magnitude of change
I could expect, though, and whether it would be worth experimenting with the (adjustable) damper
rates to try to modify turn-in behavior.
If I had more extensive experience with Morgans, perhaps I could predict the change with more
confidence. As things stand, I can say that you have correctly understood the effect that spring rates
have on steady-state handling balance in most cases: stiffen one end, and you get more load transfer
at that end and less at the other, so you reduce grip at the end you stiffened and add grip at the other
end.
However, in certain cases we can add roll resistance at the front and reduce understeer! This is most
often seen in cars with beam axles in back, and independent suspension with poor camber recovery
in roll in front – most commonly small rear-drive sedans that roll a lot and have lowered
MacPherson strut suspension in front. What's going on in these cases is that although the front tires
are less equally loaded, the reduction in roll improves their camber so much that the camber
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improvement more than makes up for the more unequal loading. At the rear, the beam axle gives
100% camber recovery at any roll angle, so rear camber is unaffected.
The Morgan is a similar case in some respects. It rolls a lot less than a tall, narrow sedan, but it has
no camber recovery in roll at all with that sliding-pillar front suspension. The front wheels lean the
same amount as the body. So when you add roll resistance at the front, you are hurting the load
distribution at the front but helping the camber. At the rear, you are helping the load distribution and
leaving the camber largely unchanged.
Also complicating prediction in the case of the Morgan is that the frame is unusually flexible in
torsion. That mutes the effect of relative roll stiffness changes.
Actually, all cars with independent suspension in front and beam axles in back have poor camber
recovery in front compared to the rear, so they all are subject to the same conflicting effects when we
add front roll stiffness. Interestingly, when we change rear roll resistance the effects on front load
distribution and front camber are additive rather than subtractive, and we can predict the effect on
car behavior with much better certainty. Reducing rear roll stiffness will hurt both camber and load
distribution at the front, while helping load distribution and not affecting camber at the rear. We
know that will add understeer. Conversely, adding rear roll stiffness will help both camber and load
distribution at the front, while hurting load distribution and not affecting camber at the rear. We
know that will add oversteer.
As to the effect of shocks, yes stiffening the fronts will add understeer during entry and stiffening the
rears will add oversteer, provided that the road surface is smooth. This effect requires that the car
have a roll velocity outward, and that this be the main source of suspension movement. When the
car is cornering steady-state on a smooth surface, the roll velocity should be zero, the suspension
should have displacement from static but not velocity, and shocks shouldn't matter. During exit, the
car has a roll velocity inward (it's de-rolling). In this situation, the effect of the shocks reverses.
Stiffening the fronts adds oversteer; stiffening the rears adds understeer.
So to add understeer or oversteer overall, we use the relative stiffness of the front and rear springs
(and/or bars, if present). To change entry and exit properties in opposite directions, we use the
relative stiffness of the front and rear shocks (remember, only on smooth surfaces).
I sometimes refer to damper forces as creating frictional anti-roll or pro-roll (anti-de-roll). Even
forces generated purely by a liquid may be termed a form of friction if they act in opposition to
motion. Speaking of friction, I believe I have observed a phenomenon watching Morgans run that
may be of interest here. I think that these cars can easily experience excessive friction in the sliding
pillar mechanism when subjected to the forces modern racing tires can generate. This causes
understeer until the driver finally gets the car rotating, gets on the power, and starts unwinding the
steering. Then the car snaps into oversteer as the front end suddenly frees up and can roll. I
therefore always tell people running these cars to keep the pillars in good condition and well lubed.
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Readers may be a bit baffled by the questioner's reference to "static directional stability". After all,
aren't a car's static properties the ones it has when it's motionless? And any car is directionally stable
when it's sitting still, right?
The questioner is in fact using terminology that is familiar to engineers. It has been traditional to
analogize a car's directional stability to a statically stable stationary object, i.e. one which rights itself
when disturbed a moderate amount by an outside influence or force, rather than tipping over. A
directionally stable car tends to "right itself" similarly in yaw. If the car is disturbed in yaw while
running straight, say by one wheel hitting a piece of debris, it will then travel down the road in a
yawed condition, with all tires running at a slip angle. The car's inertia then has a car-lateral
component, as in cornering. If the car understeers in gentle cornering, it is said to have greater
cornering stiffness at the rear than at the front. If that is the case, it will also tend to straighten itself
out when disturbed; it will tend to rotate in the direction of its own inertia rather than the other way,
absent any steering input from the driver.
Usually, discussion related to this ignores aerodynamic factors in directional stability, but actually
the analogy applies, and its relation to under/over-steer applies, when aerodynamic yaw moments
and downforce/lift are present.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
BEAM AXLE PROS AND CONS
You mentioned in your latest newsletter [June 2006 issue] that a beam axle recovers camber in
roll (pretty much all of it) but that the usual case for an independent front end is that camber is
not recovered in roll at all. So, why not put a beam axle at the front of the Morgan? I know
that there is a possibility of tramp and shimmy but surely these can be avoided with
appropriate engineering. Most trucks have beam axle front ends as did the Indy roadsters.
There do not appear to be shimmy and tramp troubles with those vehicles.
A while back a friend (ex-chief of Ford New Product Development) of mine told me about a '48
Zephyr he had. This had a beam axle front end. He reckoned there was no shimmy trouble at
all. This was due to the transverse leaf spring system which put the attachment points of the
spring well outboard. The GM cars of the time had longitudinal leaf springs which were
located some distance inboard, in order to provide reasonable lock for the front wheels. They
had terrible problems with shimmy and tramp. He surmises that, due to the advantageous
outboard positioning of the spring attachment to the axle, in the Ford the spring had better
control of the axle. Hence no shimmy or tramp.
He also thinks that the geometry of the shackles had a beneficial effect during cornering as
well. When the car negotiated a corner on the tension side the shackle would rotate to form a
straight line with the spring while on the compression side the shackle would move more
upright. How this worked probably needs some further consideration and thought...
I've searched the literature for any information or papers about the Ford transverse leaf spring
front beam axle but without luck. There is plenty about the GM or conventional longitudinal
leaf spring and all its woes.
Surely people must have been aware that the transverse spring with its outboard mounting on
the axle was far less susceptible to the troubles that plagued the conventional system. The fact
that Indy roadsters employed a torsion bar system with outboard pickup points for the lever
arms suggests it was known that outboard actuation had a beneficial effect controlling the axle
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to prevent shimmy and tramp etc. I have not been able to locate anything that records or
documents this knowledge in the literature though.
Are you aware of anything written up about this? Is there any technical information with a
mathematical or even a descriptive treatment of the outboard or transverse spring front beam
axle?
I understand from the Milliken book about Olley that front IRS was used to replace the front
beam primarily for the purpose of eliminating steering kick, shimmy and tramp. It's likely
Ford followed suit for marketing and competitive reasons but they didn't need to as their axle
was already under good control. So, it may well be that a modern road car (sedan) could
benefit from the fitting of a front beam axle since that suspension would keep more tyre on
road in most situations. Since the COG tends to be relatively high for such road cars
(compared to a race car) and since it is usually not possible to arrange for enough anti-roll
stiffness (without wrecking the ride and mechanical grip) surely there is a case for the reintroduction of the front beam.
Have you any comments on front beam axles for race cars as well as the potential for
application to modern road cars?
I doubt that the earlier questioner is up for the kind of major surgery and engineering involved
in converting an existing car to a different style of suspension. Street rodders do this, of
course, but usually only in the course of a comprehensive frame-off rebuild involving many
other modifications.
Regardless, it is definitely interesting to explore the pros, cons, and possibilities of beam axles,
and to try to understand what is involved in optimizing them.
I have never driven one of the early GM cars with the beam axle front end, but I have driven a
few cars and more trucks with beam axle front ends, and although at times you can feel the
axle gallumphing around down there, shimmy and tramp are not common problems. This is
true even with parallel leaf springs.
Many trucks nowadays have power steering, which tends to damp out vibrations, but I drove
one Class 8 (big) truck a few times that had no power steering, parallel leaf springs, and, I'm
pretty sure, no damping aside from inter-leaf friction in the springs. The steering was really
heavy, but it didn't shake. It gave you a workout, but it didn't beat you up.
I Googled <"wheel tramp" or "shimmy"> just to see what would come up. Four pages into the
search, I had seen a lot of mention of wheel imbalances and worn parts as causes, but
absolutely no mention of beam axles as a cause, nor of greater susceptibility in beam axles.
There was plenty of mention of independently-suspended cars having shakes in the front
wheels.
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It may be useful to briefly discuss exactly what we mean by the terms tramp and shimmy.
Tramp means a linear up-and-down oscillation of the wheel: basically, the wheel hopping up
and down. Shimmy means an angular oscillation of the wheel about the vertical axis (in the
yaw or toe direction) and/or the horizontal axis (in the roll or camber direction).
I have read in chassis books explanations of a theory of a combined tramp and shimmy effect
in beam axles which relates to gyroscopic precession on a one-wheel bump causing the wheels
to want to steer in the direction that the axle tilts, while tire scrub is trying to steer them the
opposite way, and somehow all of this gets into a self-exciting feedback loop and the steering
shakes like crazy. Oddly, in all the beam axle vehicles I've driven, I've never seen this happen.
I have also read that steering shake didn't become a problem until people started putting front
brakes on cars. This apparently caused problems for two reasons. One was that the torque
from the front brakes would cause wrap-up of the parallel leaf springs. This would cause the
caster to diminish under braking, or even go negative, and this would cause a loss of selfcentering in the steering, reducing forces that try to hold the wheels straight or even creating
forces that try to pull the wheels away from straight. Additionally, the axle could oscillate
rotationally on the springs (springs cyclically wrapping and unwrapping). With a longitudinal
drag link, this could also cause the wheels to steer back and forth as the axle rotated, creating
all sorts of playful behavior. Height of the drag link, relative to the axle's center of rotation,
would have a big influence on this.
Speaking of drag links, in the old days most of them on parallel-spring front ends didn't move
in arcs that agreed very well with the motion of the axle, at least for large motions. The springs
generally had single pivots in front and shackles in back, so the axle roughly moved in an arc
about a point in front of the axle, while the drag link pivoted about a point behind the axle.
Modern parallel-spring suspensions on trucks often have the steering box ahead of the axle,
and the motions of the drag link and axle agree much better.
The Ford layout of the early '30's was better than the conventional layout of the time in this
regard, and would have had less bump steer. Actually, there were two Ford steering layouts.
Later models had transverse drag links. The Zephyr would have been one of those.
The Fords also reacted brake torque through radius rods rather than leaf springs. Although the
radius rods were fairly thin in section, they were a lot more rigid than a leaf spring.
The other thing that changed when front brakes were added was that the unsprung mass natural
frequency in roll greatly decreased. We are considering the frequency at which the axle
assembly will oscillate resonantly, in a mode where one wheel moves up as the other moves
down – that is, a two-wheel, 180-degree out-of-phase tramp. Other things being equal, this
frequency goes down dramatically as we add mass at the outboard ends of the axle. As the
frequency goes down, there is increased likelihood that road irregularities will excite the
system at or near its natural frequency and cause a resonant oscillation.
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Because of this, early front brakes were often smaller than the rears, to keep them lighter, and
also to reduce the torque the front springs would have to react. However, it became apparent
that for shortest braking distances, the front brakes should be not only as powerful as the rears,
but at least twice as powerful. So the front brakes grew, and with them the antics of the front
axles.
The questioner brings up the attendant issue of what is sometimes called spring base: how far
outboard on the axle the springs act. If the springs act further out, the wheel rate in roll
increases, and so does the natural frequency in roll, for both the sprung and unsprung masses.
Assuming no anti-roll bar, the wheel rate in roll, and the angular anti-roll rate, increase with the
square of spring base. The sprung and unsprung mass natural frequencies in roll increase with
the square root of the wheel rate in roll, or the angular anti-roll rate. So the natural frequencies
in the roll mode are directly proportional to the spring base.
It is also possible to raise the wheel rate in roll by adding an anti-roll bar. This can help a car
with the springs set close together. I don't know when the first anti-roll bar was used or
patented, but their widespread adoption coincided with the widespread adoption of independent
suspension, and people didn't start using them on beam axles until later.
Incidentally, I have read one or two authors who say that anti-roll bars are unsuitable for beam
axles. That is not so. Anti-roll bars may be less necessary with beam axles than with
independent suspension because of the usually ample geometric anti-roll of a beam axle, but
they do exactly the same thing in a beam axle suspension as they do in an independent
suspension, and can be very useful.
Not only does it matter how far apart the springs are, but also how far apart the shocks are.
Most dampers in 1930 were lever-action designs. Many were still friction shocks. Some were
relatively crude hydraulics. In the Fords, the shocks were mounted with the levers extending
transversely, outboard from the frame, so that they acted further out on the axle than in most of
the parallel-spring designs. In a traditional parallel-spring design, the shock levers extend
longitudinally, parallel to the springs and frame rails, and the shocks act on the axle near the
spring mounting points. This results in a system that is not only comparatively lightly sprung
in roll, but also lightly damped.
This is particularly true with dampers like the early hydraulic shocks, which were more or less
fixed-orifice dampers and therefore steeply progressive. To prevent excessive harshness at
high velocities, they had to be very soft at low velocities. This resulted in wallowy vehicles,
and poor wheel control over low-amplitude disturbances. And with the shocks mounted well
inboard, even a fairly large disturbance at the wheel looks small to the shock.
Consequently, if you were a passenger car manufacturer around 1930, seeking shorter stopping
distances with large front brakes, and seeking less impact harshness by replacing friction
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shocks with the early hydraulics, you would end up producing front suspensions that were
prone to 180-degree out-of-phase tramp. If this weren't bad enough, any attempt to improve
ride by using softer springs would worsen every problem we've discussed so far.
Another factor in this would have been the roads of the day. In 1930, most roads in the US
were still dirt or gravel. Until the discovery and development of the oil fields in Texas in the
1920's, asphalt was expensive. Even after it became cheaper, it took time to lay the acres of
pavement we drive on today.
Dirt and gravel roads are prone to washboarding: they develop regular ripples that coincide
with the unsprung mass natural frequencies of the vehicles that run on them. Nowadays, we
mostly see in-phase ripples that excite rear axles in the ride mode. However, in an era where
front axles were prone to excitation in the roll mode, we would have had out-of-phase ripples
developing that would create resonant oscillation in that mode. I wasn't around then, but this
would seem a logical expectation.
This would at least partially explain why we aren't seeing today the tramp and shimmy
problems in beam axles that Olley and his associates faced.
One of the big reasons Ford abandoned beam axles was packaging. If we want to build the car
low, and if we want to place any portion of the engine in the plane of the front wheel axis, we
have a problem finding room for a beam axle under the engine. Since the axle has to move up
and down, it needs more space than the frame crossmember we have under the engine in an
independent suspension layout. If Ford had retained the beam axle, the '49 Ford would have
had to be a much taller car, or a considerably longer one.
Packaging remains a dominant issue in passenger car suspension design. If a suspension will
give at least decent dynamic properties, and it saves room, it is attractive for a passenger
vehicle. This is a big factor in the continuing popularity of strut suspension. Any rival concept
must be competitive in terms of space-saving, even if it offers superior dynamics.
For race cars, I think beam axles offer interesting possibilities. The UNC Charlotte team,
which I have been advising, has considered beam axles in the past, and is taking a fresh look at
them for 2007. In many classes of racing, the choice of beam axle or independent is made for
us by the rules. Even where the rules do not explicitly dictate the choice, packaging
considerations may virtually dictate independent suspension at one end of the car. In that case,
we may want independent suspension at the other end, merely to maintain similar properties at
both ends of the car.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
PANHARD BAR LONGITUDINAL LOCATION
What is the effect of locating the Panhard bar in a live axle rear suspension a) behind the rear axle,
or b) just ahead of the rear axle, or c) even further forward in the car? For example, the Frankie
Grill All-American Race Car chassis is now attaching the Panhard bar to the right-side rear door
post. From there the bar runs across the car and about eight inches rearward, and attaches to a
bracket extending about eleven inches forward from the left axle tube. These cars appear to be
dominating at the current time.
These cars are a variety of Super Late Model, running on paved ovals in the northeastern US.
Longitudinal axle location is by a form of 3-link system, with dual, compliant upper links. One
upper link reacts tension forces occurring under power. The other reacts compression loads
occurring in braking, including engine braking. The two links generally have different angles. They
both have rubber or urethane biscuits in them that can be varied to change the rigidity of the link.
The rules prohibit compliant lower trailing arms, which are commonly used at the right rear where
legal.
The effect of locating the Panhard bar forward or back with respect to the axle depends on the layout
of the rest of the rear suspension system. In some cases there is little or no effect; in other cases
there can be a significant effect.
To understand this better, it is helpful to introduce the concept of the rear axle axis of rotation in roll.
This is sometimes called the axle's roll axis. There is nothing wrong with calling it that, provided
one understands that it is not the same as the the car's roll axis, the line connecting the front and rear
roll centers.
The axle roll axis is a notional line about which the axle moves in the roll mode of suspension
movement. The point where this line intercepts the rear axle plane – the vertical plane containing the
rear wheel axis – is considered the rear roll center.
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The axle roll axis is usually constructed as a line connecting two points: the instant center of the
links or arms that locate the outer ends of the axle, and a point taken as representing the height and
longitudinal location of the Panhard bar or equivalent lateral locating device.
In some cases, the assignment of these points can be rather tricky, and may call for some
approximation. For example, it is quite possible that there may not really be an intersection point of
the lower trailing arms in a three-link system. The link centerlines may converge a bit toward the
front of the car, and may have an intersection in plan view, but they may pass over and under each
other at that location, rather than truly intersecting. Or they may be parallel in plan view and
therefore have no intersection, even if they lie in the same plane.
In the former case, it is reasonable to take as an assumed front point for the axle roll axis a point
midway between the two link centerlines, where they pass over and under each other. In the latter
case, in side view the axle roll axis is parallel to the trailing arm centerlines, or an average of their
inclinations if they are not parallel in side view.
In the former case, we need a second point to determine our axle roll axis. In the second case, we
know the inclination of our line, but not its height, so we need a point to establish that.
In both cases, we take for this a point representing the height of the Panhard bar or equivalent lateral
locating device. In a passenger car, with a Panhard bar, the usual practice is to assume that the car
has close to 50% left weight, and take the point where the Panhard bar centerline intercepts the
vehicle center plane. If the Panhard bar is centered in the car, this will also be the midpoint of the
Panhard bar.
Things get a bit more complex when the c.g., or the Panhard bar, or both, are offset significantly to
the right or left. Here, we have a choice of two methods. We can take the point where the Panhard
bar centerline intercepts the sprung mass c.g. plane (the longitudinal, vertical plane containing the
sprung mass c.g.). Alternatively, we can take the Panhard bar midpoint.
When the Panhard bar is significantly off center, and significantly inclined, as in many dirt chassis
these days, the heights of the c.g. plane intercept and the bar midpoint can differ by as much as two
or three inches. Which method is more correct? They are both reasonably correct, provided we
apply them properly. If we use the c.g. plane intercept, we do not make an additional correction for
the vertical component, or jacking force, resulting from the Panhard bar inclination, when modeling
roll behavior and wheel loads when cornering. If we use the bar midpoint, we have to include the
jacking force in our calculations. The former method is simpler, and yields a good enough
approximation for most purposes; the latter is more rigorous and accurate, but more complex.
In any case, by some rationally defensible method we choose an effective acting height for our
lateral locating mechanism. We now still have to assign it a longitudinal position. If we have a
Panhard bar that runs straight across the car in plan view, this is presents no difficulty. On the other
hand, if the bar has significant plan view angularity, we have a bit of a puzzle. I think the right
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approach for assigning the x-axis, or longitudinal, coordinate is to use the x coordinate of the bar
midpoint in all cases.
We now have vertical and longitudinal coordinates for a point that is a reasonable approximation of a
lateral force coupling point between the sprung mass and the rear axle assembly. We can now draw
our rear axle roll axis, or axis of rotation in roll, in side view. If we have an exact or approximated
instant center for the longitudinal locating links, we draw our line from that point through the lateral
force coupling point. If instead we know the inclination of our axis of rotation, we draw a line at that
angle, passing through the lateral force coupling point.
Once we do that, we can see where this axis of rotation intercepts the axle plane, and we can take
that as our rear roll center when modeling roll and wheel loads in cornering.
Now, returning to the original question, what happens to the roll center when the lateral force
coupling point moves forward or back? It depends on the rear axle roll axis inclination angle.
If the axle roll axis slopes down toward the front, then moving the lateral force coupling point
forward while keeping it at constant height raises the rear roll center. If the axle roll axis slopes up
toward the front, the effect reverses: moving the lateral force coupling point forward while keeping it
at constant height lowers the roll center. If the axle roll axis is horizontal, then we get no change in
rear roll center height from moving the lateral force coupling point forward or back.
There are other effects as well, when we move the Panhard bar forward or back. If the axle rotates
under power or braking, as it does when the upper link is compliant, the end of the Panhard bar that
attaches to the axle rises or falls as the axle rotates. That means the roll center rises or falls with
power or braking. The further the Panhard bar is from the axle centerline, the more it rises or falls,
and the more the roll center rises or falls.
When the Panhard bar is far ahead of the axle, as the questioner describes, the roll center rises under
power and drops under braking. That makes the car tighter (adds understeer) on entry and loosens
the car (adds oversteer) on exit. I don't see how that would make a car faster, but it would make it
different. There are other ways of controlling the car's balance during entry and exit, so with the
right combination overall, such a car could win races.
One advantage of having the Panhard bar really far forward, if you’re going to have it ahead of the
axle at all, is that it's easier to keep the Panhard bar out of the way of the driveshaft, without putting
a bend in the bar. There are other packaging implications as well. It becomes harder to find room
for the oil tank and the battery behind the driver. Overall, I would have to judge this idea a mixed
blessing, and ascribe any success to users having the overall combination dialed in.
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PANHARD BAR JACKING FORCES
How do jacking forces (anti-roll, anti-dive, anti-lift, anti-squat) affect transient wheel loading during
corner entry/exit? I realize that total lateral load transfer is purely a function of of c.g. height, track
width, and lateral acceleration (neglecting the load transferred due to c.g. movement); however, I
also feel that magnitude of the jacking forces should have some bearing on how the loads are
transferred during the non-steady-state stages of the corner.
Taking a NASCAR rear axle, for example, we can de-rake the track bar (increase the left side track
bar height, decrease the right side track bar height) such that the rear roll center height, as it is
traditionally understood, remains unchanged. This causes the rear axle jacking force to increase,
which will cause the rear spoiler to rise during cornering, and until the spring forces have changed
enough to balance the jacking force, keep the left rear tire more heavily loaded – thus keeping the
diagonal percentage higher during early corner entry. Is my thought process correct? Can we make
similar conclusions regarding the front suspension jacking forces?
Jacking forces are the source of geometric roll and pitch resistance. They are present whenever the
tires are generating horizontal forces (lateral or longitudinal) at the contact patches, and they
influence wheel loads whenever they are present. Therefore, they influence both transient and
steady-state car behavior.
The reason you will sometimes hear that jacking forces have disproportionate influence in transient
handling is that when we have an abrupt control input (usually steering or brakes, or both), the forces
at the contact patches build up more rapidly than the roll and pitch displacements of the sprung mass.
Consequently, for a brief time the elastic components of roll and pitch resistance are smaller than in
steady-state longitudinal and/or lateral acceleration, and the geometric components accordingly
assume greater importance.
I am reluctant to believe that this effect significantly influences entry or exit behavior in oval track
racing. The steering and braking are too gentle and prolonged. The dominant factor in oval track
turn entry is the combination of fairly steady braking and turning together, over a period of roughly
one to four seconds. The duration of this phase of the cornering process, the severity of braking, and
the abruptness of brake and steering application and release all vary with the track, the setup, and the
driver's style. However, we can say with certainty that the large radius of the turns inevitably
precludes really abrupt control inputs, compared to what we see in other realms of motorsport,
unless we are dealing with an unusually small oval.
On the other hand, I am willing to believe that lag in pitch and roll displacement is significant in a
passenger car test track j-turn or lane-change test, in a chicane or street intersection turn in road
racing, or in the sort of tight turns we encounter in American autocross.
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In a NASCAR oval track chassis, a Panhard bar that slopes down from its attachment on the left axle
tube to its frame attachment on the right does create a force trying to lift the rear of the car. This
force is present through the entire turn, not just during entry. This force does not just load the left
rear tire. It does pull down on the axle on the left, but it also lifts up on the frame on the right. Its
effect is most commonly modeled as a force spreading the axle and frame apart, acting at the
midpoint of the bar's span, approximately in the middle of the car.
If the car has little or no rear spring split, a force in the middle of the car, lifting the frame away from
the axle, gets the rear spoiler up in the air but does not significantly change wheel loads, except by
aerodynamic effects. However, current NASCAR setups use considerably stiffer springs at the right
rear than at the left rear, so there is some increase in left rear load, and diagonal percentage, because
of that. If the car has a left-stiff rear spring combination, the effect reverses, and the jacking force
actually increases right rear tire loading and reduces diagonal percentage.
Again, these effects persist through the entire turn, and only go away when the rear tires cease
making lateral force.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: markortiz@vnet.net. Readers are invited to subscribe to this newsletter by e-mail. Just
e-mail me and request to be added to the list.
ROLL CENTER IN TRAILING ARM FRONT SUSPENSION
How does one determine the roll center of a trailing arm front suspension as in the VW beam front
end? I have a Formula V with link pin trailing arms front suspension with 2 degree negative camber
offset bushings. How can the roll center be raised or lowered in this type of front end? I'm thinking
it is similar to a straight axle, because the intersection of the lines drawn through the two trailing
arms is at infinity. Please correct me if my premise is wrong.
The short answer to the first part is that the roll center is at ground level, and you cannot adjust it or
move it. As to the second point, the suspension behaves like a beam axle in ride, but it is very
different in roll. A beam axle has a roll center well above ground level.
That's the short answer, and for practical purposes it's fairly close to correct. However, while both of
the above statements are close to correct, they aren't quite perfectly accurate. A beam axle
suspension can theoretically have a roll center at or even below ground level, but the linkage
required to do this is unusual, and I have never seen an actual beam axle suspension with a roll
center that low. And when the VW trailing arm suspension is in a rolled condition, the roll center,
properly assigned, isn't exactly at ground level. That is, in the real world, the suspension actually
generates a small geometric anti-roll moment when cornering. When the car has two or three
degrees of roll, the anti-roll moment from the front suspension is sufficient to produce a significant
modeling error if we imagine the roll center to be at ground level.
In any independent suspension, the front (or rear) view force line is an instantaneous perpendicular
to the path that the contact patch center travels as the suspension moves. In the VW front
suspension, the contact patch always moves straight up and down in front view, relative to the
sprung mass. This is also true of many (though not all) beam axle suspensions, in ride, but not in
roll. That makes the VW front suspension similar to a beam axle in ride, but not in roll.
When the contact patch moves straight up and down in front view, relative to the sprung mass, the
force line, being perpendicular to the line of travel, is always horizontal relative to the sprung mass.
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We can also view the trailing arm suspension in terms of short-and-long-arm (SLA) suspension
principles. Looking at it this way, the front view projected control arms are: parallel to each other;
horizontal relative to the sprung mass; and infinitely long. There is no instant center, or we might
say that the front view virtual swing arm is infinitely long. The force line, which would normally
run through the contact patch center and the instant center, becomes parallel to the front view
projected control arms, and therefore horizontal – again, relative to the sprung mass. It remains
horizontal at all ride heights.
The two front view force lines for the two wheels lie right on top of each other: they coincide. They
can thus be said to have an infinite number of intersections, or to have no single definable
intersection. If we try to define the roll center as the force line intersection, and if we believe that the
lateral position of that intersection is significant, this is a very problematic case. The traditional
expedient is to make a special rule for this case and say the roll center is on the centerline – but that's
obviously arbitrary.
If that weren't enough, suppose we consider that nothing in the real world is made to zero tolerance,
so there is a good chance that a real VW's force lines won't be exactly horizontal or parallel. That
means they probably do have an intersection, somewhere – and it could be miles from the car, and
way above or below the ground. Horrors! The car's behavior is completely unpredictable!
But it's not, of course, and VW front ends are no less tolerant of minor production and setup
variations than any others. We merely have a case here that shows up the analytical deficiencies of
taking the force line intersection as the roll center. If, instead, we look at the system in terms of
individual wheel anti-roll geometry, and assign a roll center – a notional coupling point between
suspension system and sprung structure, for lateral forces only – things start to make sense.
The height of each force line's vehicle longitudinal centerplane intercept remains at ground level for
any pure ride displacement. The suspension thus has what I call a Mitchell index (and Bill Mitchell
calls an incline ratio) of zero, throughout its travel. This means that the suspension's anti-roll
geometry does not change in ride, but it changes in roll. In roll, the outside or loaded wheel gains
anti-roll, and the inside wheel loses anti-roll.
In the pure trailing arm suspension, the anti-roll is zero on both wheels in the unrolled condition. So
as the car rolls, the outside wheel assumes some positive anti-roll, and the inside wheel assumes
some negative anti-roll, or pro-roll. The force lines remain parallel to each other (disregarding realworld variabilities), but they are no longer parallel to the ground. They both are horizontal relative
to the sprung mass, but the sprung mass is leaning with respect to the ground, and therefore the force
lines also both lean with respect to the ground, a similar amount. With respect to the ground, the
outside wheel's force line slopes up toward the vehicle centerline, and the inside wheel's force line
slopes down toward the vehicle centerline.
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Okay, the inside wheel has pro-roll, the outside wheel has anti-roll, the force lines have the same
absolute angle relative to the ground, and they intercept the vehicle centerplane equal distances
above and below ground – so can't we just average the height of those centerplane intercepts and say
the roll center is still at ground level and there is no net anti-roll or pro-roll?
No. The reason we can't do that is that although the force line angles are equal, the forces at the
contact patches, that are acting along those force lines, are not equal in magnitude. In most cases,
the more heavily loaded tire is making more lateral force than the unloaded one, so the vertical
component of the resultant along the force line is correspondingly greater, if the force line angles are
equal. We have more cornering force on the outside wheel than the inside wheel, and therefore
greater anti-roll force than pro-roll. Net effect: net anti-roll; roll center height above ground.
How far above ground? It depends on two things: the amount of roll, and the amount of front load
transfer.
My video, "Minding Your Anti", provides an illustrated explanation of how to assign a roll center
height for known force lines and a known or assumed tire-pair lateral force distribution. I like to
think I can paint pictures in a reader's mind with words, but explaining this method without
illustrations is beyond my powers. Bill Mitchell's method for finding the force-based roll center
agrees pretty well with mine.
Anyway, let's take one case as an example: a VW front end with a 52-inch track, rolled 3 degrees,
with the inside front wheel at the point of impending lift – all load on the outside tire. Using my
method, the roll center height is 2.72 inches. That's significantly different from ground level.
Returning to the original question, you can't adjust the roll center, but it does vary somewhat
depending on how much of your total load transfer occurs at the front end and how much the car
rolls.
Just as an aside, toward the very end of the era of trailing-arm front suspensions, Porsche
experimented with inclined upper-arm pivot axes, to get more anti-roll and camber recovery. That's
a story for another time, and not applicable to Formula V, but it is interesting to note that there are
ways to make a trailing-arm front end that does not have quite the properties we usually think of.
Also speaking of Porsche – but now referring to Dr. Ferdinand Porsche himself, rather than the
modern company – I often wonder what he thought he was getting in terms of roll center with that
suspension. It may be that he thought the roll center was at the height of the springs, as with a beam
axle. His choice would have made more sense on that basis.
One other note: although a VW front end does generate some anti-roll in real-world cornering
conditions, most of the front roll resistance in a Formula V is elastic. The rear roll resistance,
assuming we have one of the so-called "zero roll" suspensions, is entirely geometric, if we disregard
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frictional and unsprung components. The car thus provides an interesting case demonstrating the
difference between elastic and geometric roll resistance, and also demonstrating that roll resistance is
roll resistance, and you can get roll resistance in different ways, but the tires don't know how you did
it. They respond to the amount of load they're carrying, but they can't tell where it came from.
MORE ON ROLL AXIS AND RELATED ANALYTICAL CONCEPTS
In your article in RCE April '06 [drawn from the February '06 newsletter] you state that "So the end
where we lowered the roll centre has less geometric load transfer and the same elastic load transfer
as before - hence less load transfer overall."
This I do not understand: assuming the CG remains in place, lowering the RC means that the
distance between RC and CG increases, and the roll moment will increase. Lowering the RC will
decrease the geometric load transfer indeed, but it will increase the roll-moment and hence increase
the elastic load transfer in my opinion. In the end the total load transfer remains the same, but the
way it is divided in elastic- and geometric load transfer differs.
Do you agree, or where am I wrong?
This is the passage in question, from the earlier newsletter:
If we raise one end of the roll axis and lower the other, leaving its height at the c.g. unchanged,
the total geometric roll resistance is unchanged, but we increase the geometric roll resistance at
one end and lower it at the other. The elastic elements – the springs and anti-roll bars – are
not affected by this.
So the end where we lowered the roll center has less geometric load transfer and the same
elastic load transfer as before – hence less load transfer overall. This will make that tire pair
grip better, because they will be sharing the work more equally. At the opposite end, the
elastic component will likewise be unchanged, but the geometric component will be increased –
hence more load transfer overall.
The context of my statement is important. I am referring to a case where we lower one roll center
and raise the other, so that the roll axis height at the c.g. remains similar. In that case, the total
geometric and elastic weight transfers remain the same, and so does the roll angle. The elastic
weight transfer at each end of the car remains unchanged. The geometric weight transfer decreases
at the end where we lower the roll center; increases at the end where we raise the roll center; and
remains unchanged in total. Therefore, the total weight transfer for the end where we lower the roll
center decreases; the total weight transfer for the end where we raise the roll center increases; and
the total weight transfer for the whole car is unchanged.
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Remember, the sprung structure is one essentially rigid mass. It has one c.g., and it is the moment
arm of this single c.g. about the roll axis that determines the overall elastic weight transfer. Treating
the car as if it had a swivel in the middle will lead you to all sorts of erroneous conclusions.
Addition:
In the same article in RCE you gave a number of reasons why many cars have a nose down roll axis.
Another reason I once heard was: to avoid torsion in the chassis you want the same roll moment in
both the front axle and rear axle. As the weights front and rear differ, the distance from CG to RC
have to differ to get the same roll-moment front and rear.
Torsion costs energy, and since there is only one source of energy - the engine - chassis torsion costs
power and consequently speed. So to save speed you want as little torsion as possible in the chassis,
and a (more or less) similar torsion-moment in the front and rear will help.
Do you agree with this vision?
No, I disagree. That is, I agree that similar roll resistance front and rear reduces torsional loading on
the frame, or at least tends to in hard cornering, but I disagree that this is necessarily what it takes to
make the car go fast. In certain cases it coincidentally is. In other cases, such a roll resistance
distribution is disastrous.
Again, the sprung mass does not have a front and a rear piece that can act independently. The car is
not a tractor and trailer, a locomotive and tender, or two men in a horse suit. The sprung structure is
made up of many pieces, all of them having weight and inertia. Each of the components has its own
center of mass, and they attach to the frame in various places. All of them apply inertia loads to the
frame as the car undergoes accelerations. These loads stress the frame in all sorts of ways, including
torsionally. No part of the sprung mass is truly rigid, nor is any other object, but we customarily
ignore the deflections within the sprung mass for simplicity. We generally get away with this,
because the sprung mass is relatively rigid, compared to the suspension and tires, in most cases. To
the extent that the sprung structure is rigid, it is properly treated as one mass, with one center of
gravity – most definitely not two independent masses with two centers of gravity.
If the car has 50/50 front/rear weight distribution and identical tires front and rear, and if the car has
good aerodynamic balance, and speed is moderate, meaning the rear tires are not using most of their
traction to propel the car, then equal overall roll resistance front and rear will get us close to a
balance that will please most drivers. If the situation is identical except the car has 55% rear, and we
make the roll resistances equal, we will have godawful oversteer. If we make the front and rear roll
resistances proportional to the front and rear weight percentages, i.e. 45/55 front/rear, we will have
even worse oversteer. Now, if we make the roll resistance inversely proportional to the weight
distribution – 55/45 – we'll be closer to right, but there is no guarantee that that will be enough front
roll resistance. Probably it will not be.
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If we now put smaller tires on the front or larger ones on the back, things change again. Now, the
car will not need as much front roll stiffness compared to rear as with equal tires.
If the car is at Daytona or Talladega, running near its top speed, with full power going to the rear
tires just to maintain speed, it will need more front roll resistance than it would at lower speeds.
If the car is running American autocross, and the turns are tight, the front wheels will track
significantly outside the rears even when the tires are sliding, and the car will need more rear roll
stiffness to prevent understeer. In really tight turns, as in Formula SAE/Formula Student, the
magnitude of this effect is quite startling.
My point is this: overall roll resistance should not necessarily be equal at both ends, nor should it be
proportional to weight distribution. In fact, given equal tires front and rear, roll resistance generally
needs to vary inversely with weight distribution: the light end needs more, not less. Even this is a
highly non-linear relationship, and only applies if we are comparing otherwise similar cars and
conditions. Across a broad range of tire, track, speed, and aerodynamic conditions, required roll
resistance distribution has no simple relationship to weight distribution at all!
Now as to the idea that loading the frame in torsion due to unequal front and rear roll resistance
absorbs energy and slows the car down, that's mostly nonsense. Yes, the frame does absorb a small
amount of energy as it twists and then straightens out again, but the amount is negligible compared
to tire and aerodynamic drag.
The frame also twists a bit as we go over bumps, both while cornering and while running straight.
However, since the frame is essentially undamped, most of the energy we put in when we deflect it
is returned as soon as the load is removed and the frame springs back. Movement of the suspension,
on the other hand, does absorb energy, because the dampers oppose both a deflection and the
recovery afterwards. We do save energy by softening the damping, but that doesn't necessarily
improve handling, and of course controlling the car takes priority over this relatively small energy
saving in most applications.
It is also true that at least in some cases we can make the car lighter if we can reduce torsional
loadings, and that can raise cornering speed and also save energy. However, usually we are not at
liberty to make this a dominant design priority. In passenger cars, there is a case for a live rear axle
with a high rear roll center instead of an independent rear with more elastic roll resistance, from the
standpoint of weight reduction. With ample elastic roll resistance at both ends, the car needs more
torsional rigidity to avoid shakes and creaks over bumps, and this is one reason why cars with
independent rear suspension tend to weigh more than cars with beam axle rear suspension.
Really, though, that is an argument for high roll axes rather than sloping ones, and for suspension
with a soft wheel rate in warp, rather than an argument for equal overall roll resistance front and rear
or for roll resistance proportional to weight distribution.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
TWIST BEAMS AND JOINTED DE DION TUBES
Continuing on the topic of beam axles, there was an interesting de Dion axle design produced by the
Rover Car Company. It appears it was originally invented by Stewert Tresilian for Armstrong
Siddeley. The design featured a pair of fixed length half-shafts taking drive from the differential to
the hubs. The half-shafts located the hubs transversely and were responsible for a small amount of
track width change as they moved through their fixed radius arcs.
The hubs were joined by a beam axle that passed to the rear of the differential, behind the rear
wheel axis. The beam axle was split into two portions in such a way that each portion could rotate
relative to each other. A joint between the two portions could accommodate this and was also able
to accommodate some plunge (transverse movement) so that the beam axle did not fight the halfshafts. There were trailing arms from the car body to the hubs.
Where is the roll centre? It appears that the roll centre is located at the centre of the differential
although it can move about a little. Is this correct? If so, I think this position is somewhat higher
than ideal.
Loading the differential with lateral forces is not necessarily ideal either (although many
manufacturers have successfully accomplished it). The approach requires large stiff bearings in the
differential housing and the method of locating the differential to the vehicle body becomes an
interesting design issue (usually needing a sub-frame). All told this is an expensive solution.
Despite the roll centre being non-ideal (a bit of a pain to locate on a drawing board for some wheel
articulations and difficult to place in the most advantageous location) there is an interesting and
desirable effect with this suspension system. In roll it appears that the wheels do not lose camber as
the vehicle body rolls outward. They do not adopt disadvantageous camber angles but relative to
the vehicle body they gain camber with roll so that they stay perpendicular to the road surface. This
seems to be because the split beam axle can twist at the sliding joint.
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Even a normal beam axle allows the wheels to tilt outwards with roll. There is a contribution from
tyre deflection and axle roll (tyres and axle are a spring mass system and there is deflection). With
the Rover this can be allowed for and tuned out I think. It seems this is due to the beam axle passing
behind the rear wheel axis. Am I correct?
What is the relationship between the trailing arm length, wheel camber in roll and beam axle
longitudinal position?
How can I lower the roll centre with this suspension? It would be better to have some freedom
about where the roll centre can be located. What is wanted is a way to take the lateral loading
through a link or linkage instead of the half-shafts and differential unit. If this could be done,
then the issues pertaining to mounting and locating the differential with precision would be
eliminated. Also there wouldn't be such a need for such large bearings etc. in the differential
housing.
Do you have any comments on this?
In related investigation I've looked at the torsion beam or twist beam axle used at the rear of many
fwd cars. At first they seem to be a bit of a cheap mess but there is more to it than that rather
cursory view. They are a clever and subtle design when considered in depth. And there are plenty
of new applications yet to be addressed. For example, the torsion beam lends itself to being used as
a variant of the de Dion system and being employed at the rear of a rwd car. As far as I know this
has not been done. Are you aware of any?
There are many fwd cars with the torsion beam axle but in every case the beam axle is placed ahead
of the rear wheel axis line. This means the wheels will roll outwards from a turn in the same sense
as the vehicle body does. So they lose camber with body roll. Surely it would be beneficial to place
the torsion beam well behind the wheel axis? If this were accomplished wouldn't it achieve the same
effect as the Rover two piece axle? That is, matters could be arranged so the wheels remained
perpendicular to the road regardless of body roll.
Certainly it is true with both beam axles and independent suspension that there is roll due to tire
deflection, and that the camber recovery with this component is zero. This also happens with no
suspension, as on a go-kart. The magnitude of the effect varies with tire selection and pressure.
Consequently, we cannot predict it just by knowing the suspension geometry. Merely to keep the
complexity of the discussion manageable, I generally discuss camber recovery as if the tires were
rigid. That way, we can discuss properties of the linkage in isolation.
But of course, ignoring tire deflection doesn't make it any less real. Not only would we like to be
able to compensate for camber change due to tire deflection, we would like to tilt the wheels into the
turn slightly with roll, because they make greatest cornering force that way.
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There is no free lunch here, however. There is no way for a passive suspension system to distinguish
between suspension roll (oppositional motion within a front or rear wheel pair) due to sprung mass
roll, and suspension roll due to road irregularities. Reducing camber change in the former case
inescapably increases it in the latter case. With independent suspension, to obtain better camber
recovery in sprung mass roll, we must accept more camber change both in ride and in suspension roll
motion resulting from road irregularities. With a beam axle or de Dion system, we do not have the
penalty in ride, but we still have it in roll. That is, to get more than 100% camber recovery in roll,
we must increase the already considerable camber change over one-wheel bumps. That is what the
Tresilian design does.
The twist beams used in front-drive cars typically play the tradeoff the other way, and accept poorer
camber properties in sprung mass roll in exchange for better camber properties over bumps. Also,
when the twist beam is further forward, the suspension's properties change less when the inside rear
wheel lifts off the ground, as it commonly does in front-drive cars during limit cornering.
The idea of allowing the de Dion tube to twist in roll is not unique to the Tresilian design. The
Mercedes-Benz W125 also had a de Dion tube that could twist freely, with the twist joint behind the
differential, and simple trailing arms running forward from the hubs. The Mercedes design differed
from the Rover in that the de Dion tube was not allowed to telescope. The halfshafts accommodated
plunge instead. Lateral location was provided by a roller on the de Dion tube, running in a vertical
slot cast and machined into the rear of the differential housing. Since this was a race car, and noise
isolation was not a concern, the diff was mounted solidly to the frame. Lateral force was reacted
through the differential housing, but not through the differential bearings.
We should note that thrust loads due to cornering force always have to be reacted through a bearing,
one way or another. If we do not put the load through the diff bearings, the wheel bearings have to
absorb it instead, and the wheel bearings are unsprung. Therefore, there may be a rational case for
making the diff bearings a bit heavier if that allows us to reduce weight at the outboard ends of the
de Dion tube.
Now, where is the roll center in a twist beam system? It is not at the height of whatever provides
lateral location, except in the case where the twist beam is exactly in the axle plane (the vertical,
transverse plane containing the wheel axis).
To locate the roll center on a drawing board, here's what we do: in a side view of the system, draw a
vertical line from the center of the trailing arm pivot down to the ground. Insert or establish a point
where this line meets the ground. We're going to call this point A.
Draw another vertical line from the wheel center to the ground, and also upward a ways from the
wheel center. This represents the axle plane, in edge view.
Draw a third vertical line through the twist axis of the beam or deDion tube. This represents the
twist axis plane (the vertical, transverse plane containing the twist axis), in edge view.
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Now find the lateral force coupling point between the twist beam assembly and the sprung structure.
Note that this is usually not the roll center, but it is a definable point. In a VW Rabbit/Golf rear
suspension, it is the trailing arm pivot. In the Rover system, it is the diff axis, or more precisely the
inboard U-joint center. In the Mercedes W125 system, it is the center of the roller. Draw a
horizontal line from this coupling point to the axle plane. Insert a point at that intercept. We're
going to call this point B.
Draw a line passing through points A and B, long enough so that it passes through the twist axis
plane. Find the intersection of this line and the twist axis plane, and insert or define a point there.
We're going to call this point C.
The height of point C is the roll center height. In the Mercedes or the Rover system, point C will be
above point B. In the VW system, point C will be below point B.
The roll center is a modeling abstraction. It is the effective force coupling point for lateral forces
passing between the two-wheel suspension system and the sprung structure. It is always considered
to be in the axle plane. So, to complete our work on the drawing board, we construct a horizontal
line from point C to the axle plane, and that intercept is our roll center.
If we want to be really rigorous, in a rolled condition the Rover design has slightly different anti-roll
properties for the inside and outside wheels, and overall anti-roll depends on tire lateral force
distribution, as with independent suspension. For most practical purposes, though, I think we can
safely ignore this.
It would be possible to put the twist beam or de Dion tube ahead of the diff in a front-engine, reardrive car, but there are some packaging issues. The beam or tube has to have enough room to go up
and down without hitting the drive shaft.
It is also possible to have a lower roll center than in the Mercedes or Rover designs, while still
having the tube or beam behind the diff, and still having greater than 100% camber recovery for the
suspension component in cornering roll. All that is needed is a lower point B. This can be obtained
with any of the known lateral locating devices. The roll center will still be somewhat above point B,
assuming point B is above ground level. With a Mumford linkage, point B could be below any point
on the linkage, and the roll center could then be as low as you'd probably want it.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
STIFF REBOUND DAMPING
I am working for a dirt late model stock car in the midwest. Recently I have been listening to some
pretty good racers outside our area and they started "tieing down" their front end and right rear
with excessive rebound. They are talking in the range of 200 - 300 pounds at 6 in/sec (depending on
track condition and spring rate in that corner). One of the drivers I talked to said it gives the car a
very comfortable, predictable feel. I was always taught that excessive rebound can take grip out of
the tire. I know many NASCAR teams are now coil binding and tieing down their front end, mainly I
think for aero advantage. Is there a better path to follow to get the front end down besides excessive
rebound or is the advantage of this worth the loss in grip through excessive damping? I can see
there is a trade off dilemma here. I would also like to here your opinion on linear vs. digressive
shock valving; I listened to both sides of this and I tend to think digressive seems to make more
sense.
We could say that most of the time, any damping at all takes grip out of the tire, and so does any
spring rate greater than zero. That is, ideally we'd like the tire to go over bumps with no change in
load whatsoever. This is not possible in the real world, for a variety of reasons, but the basic idea is
that we'd like the suspension to be as compliant as possible, from the standpoint of keeping the tires
in best contact with the road.
On the other hand, from the standpoint of aerodynamic control and camber control, we want a gokart: no compliance at all.
All suspension settings are compromises between these considerations.
Additionally, in some racing classes, people do funny things to work the rules. In stock car racing,
including all NASCAR classes, there is a ground clearance rule. We want the car to have enough
static ride height to pass tech, and still go through the turns with the front valance barely clear of the
ground. Once the valance is down there, we'd like it to go up and down as little as possible, so it can
stay as close to the road as possible without scraping. That means we want the front suspension to
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compress easily, especially when cornering, and then go solid when it reaches the desired ride
height. This is terrible for riding bumps, but if the track is smooth and air speed is high, it works.
Now, does this work when air speed is lower, and the track is rough? Probably not. Of course, this
depends on just how much slower and rougher the conditions are. Dirt Late Models do go fast
enough to generate serious aero forces. However, even with the setups we have come to think of as
conventional for these cars, the lower edges of the body, along the right side and the right front,
commonly dig into the track on bumps and are designed as sacrificial parts: we expect them to get
torn up. We make them out of tough plastic, and make them easy to replace.
I question whether it makes any sense to try to get the car to ride lower when it's already tearing up
bodywork against the track.
For stock car shocks, 200 pounds at 6 in/sec in extension is not really extreme. 300 is definitely
stiff. Whether either of these implies a hold-down valving depends on the corresponding value in
compression. The relationship between anti-extension (extension or rebound damping) force and
anti-compression (compression or bump damping) force, at a given absolute velocity (e.g. 6 in/sec)
is often described as the control ratio at that velocity. Conventionally, the anti-extension or rebound
damping force is taken as the numerator. A control ratio of 1 is a true 50/50 shock. 1.5 is a popular
control ratio for most purposes. Anything over 3.0 is considered a definite hold-down valving.
Anything less than 1.0 is an easy-up or hold-up valving.
Extension damping unloads the tire whenever the suspension has an extension velocity. It is widely
recognized that this reduces grip on the downhill side of a convex bump. It is less widely recognized
that compression damping also does this. This is so because when the suspension resists
compression more forcibly, the sprung mass acquires a greater upward velocity on the uphill side of
the bump. When the wheel passes over the crest of the bump, the sprung mass is still moving
upward, and accelerating downward. The downward acceleration effectively reduces the weight of
the sprung mass, giving the spring less to react against as it tries to push the wheel down. The
upward displacement of the sprung mass translates to less force at the spring, also reducing the force
pushing the wheel down.
A high control ratio does tend to improve ride quality. Or, more properly, soft compression damping
improves ride quality more than soft extension damping does. Soft compression damping also tends
to extend the life of the suspension components, and indeed many other components. Theoretically,
this might let us build things lighter.
For readers less familiar with shock terminology, "digressive" valving properly means that the force
increases with absolute velocity at a decreasing rate. Stated another way, the force vs. velocity curve
is concave toward the velocity axis of the graph (conventionally the horizontal or x axis): in a
conventional plot, the compression traces are concave down and the extension traces are concave up.
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Some shocks sold as "digressive" actually are only digressive in the upper velocity ranges. In
Bilsteins, "digressive" valvings are ones using the "digressive" piston design. The main feature of
this design is that it accommodates discs with notches at their periphery, which create bleeds. The
bleeds affect the entire curve, but most of all they affect the very lowest velocities. At these low
velocities, they actually give the curve a progressive characteristic: concave away from the velocity
axis. The force vs. absolute velocity curve has a pointy "nose" on it. The damping is soft at very
low velocities. The greater the bleed area, and the greater the preload on the stack, the further up the
velocity range this region of progressive damping extends.
Conversely, in Bilsteins at least, the valvings with "linear" pistons are either near-linear or digressive
throughout the velocity range. So the terminology can be confusing.
Anyway, is soft damping at very low velocities desirable? It depends to some extent on the driver,
and to some extent on how much sliding or mechanical friction there is in the suspension.
Mechanical friction, also called Coulomb friction, adds Coulomb damping to the system: damping
that is largely independent of velocity, and therefore highly digressive at low velocities. Having the
hydraulic damping progressive at low velocities tends to compensate for this. Racing suspensions,
with lots of fresh, tight rod ends and spherical bearings, have considerable Coulomb damping. Struts
have considerable friction as well. Rubber bushings have little or no Coulomb damping.
And is true digressiveness at higher velocities desirable? Most experience suggests so. We can say
for sure that mid-to-high-velocity digressiveness allows a more controlled feel with less harshness
when hitting curbs or big bumps.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
COIL-BINDING SETUPS IN STOCK CARS – FRIEND OR FOE?
In reading the November newsletter, a couple of thoughts came to mind. My application is pavement
late model racing (ASA, CRA, etc.).
1) To remedy coil binding, what about using torsion bars instead of coil springs? What I am
thinking of is mounting the bars parallel to the front-to-rear vehicle centerline, connecting to the
lower control arms (Chrysler-style). This would get some weight lower in the vehicle as well.
Rules permitting, certainly you can use longitudinal torsion bars. However, the coil binding
currently found in upper-division NASCAR racing is not an unintended problem; it's a deliberate
strategy, aimed at working the ride height and spring rules, and better controlling the car's
aerodynamics. The idea is to have the car pass ride height inspection, yet come down as readily as
possible to a ride height where the valance just clears the track surface, and then go solid, so the
valance stays at that height and doesn't rub or lift. This is awful for riding bumps, but if the track is
smooth you can accept that in return for good control of the aerodynamics.
Perhaps a better compromise is to have the suspension go very stiff, rather than solid. This used to
be achieved by using bump rubbers instead of having the springs hit coil bind. But NASCAR
outlawed the bump rubbers. At about the same time, they instituted a minimum spring rate of 400
lb/in.
To make the spring coil bind, you either shorten its length or increase the wire diameter and number
of coils, leaving the length the same. To make the spring operate in coil bind as much of the time as
possible, you minimize the spring-to-wheel motion ratio, and create as much downward jacking with
the suspension geometry as you can.
One insider I talked to recently tells me that crew chiefs are now using so much pro-roll on the right
front that the cars are now sitting considerably higher at static than necessary to pass ride height
inspection. Apparently, some people believe that if you have more "drop" to coil bind, that
somehow adds load to the tires.
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It doesn't.
It occurred to me that maybe having the nose of the car ride higher down the straights might reduce
drag, perhaps due to the roof masking the rear spoiler more. I asked Gary Eaker at AeroDyn about
that possibility. He says no, having the nose higher is bad in terms of both drag and lift. The
increased air under the car adds more drag than you save by masking the rear spoiler.
FALLING-FORCE SHOCKS
[Continued from previous question]
2) For shock damping on bumpy tracks, it seems that if damping forces at high shaft speeds could be
significantly reduced, grip could be enhanced. I don't mean simply digressive valving, but
significantly dropping damping force, say above shaft speeds of maybe 5in/sec. I don't know if this
is even possible?
What you are describing is a shock with a negative damping coefficient over part of the velocity
range.
I'm not sure it's impossible, but it's tricky to create such an effect in a package that would look like
the shocks we use today. It is possible to create a falling-rate leaf spring or Belleville washer (and a
shim in a damper is essentially a round leaf spring, or diaphragm spring), but usually we can't
actually obtain a negative rate, or a force that decreases with increasing displacement. There is one
exception to this, which I will discuss below.
Although it is normally not possible to create a negative-rate or falling-force spring, it is possible to
create a springing device where the force diminishes or even reverses as displacement increases, by
combining a spring with other mechanical elements. One example would be the over-center spring
found in some clutch linkages. These are coil springs arranged so that after about half pedal travel,
the spring tries to pull the pedal to the floor, rather than pull it up. These forces act in parallel with
the springs in the clutch, which resist pedal force at a steadily increasing rate with respect to pedal
displacement. The net result is a falling-rate resistance at the pedal, but not necessarily a fallingforce resistance. However, if the over-center spring is strong enough, it is possible to create a
falling-force characteristic. On some cars, the over-center spring tension can be adjusted to create
the desired pedal feel.
To produce the over-center action, the coil spring needs to have a lever or rocker to act on. I can't
think of a way to incorporate that into a shock.
Ordinarily, the over-center spring is used to make a Borg & Beck clutch feel similar to a diaphragm
clutch. The spring in a diaphragm clutch is an interesting case. It can actually have a falling-force
characteristic – not over its entire deflection range, but over a portion of it. I have not actually tested
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clutch diaphragms, but I have an old textbook that shows a force-vs.-displacement curve for a typical
clutch diaphragm (Herbert Ellinger, Automechanics, Prentice-Hall, 1972, p. 329). The curve is Sshaped. It starts out fairly linear, then becomes concave-down, and continues to bend downward
until the slope becomes negative. Then it becomes concave-up, and continues to bend upward so
that the slope becomes positive again. The force never becomes negative, but the rate does, over an
interval.
A clutch diaphragm is somewhat like an ordinary Belleville washer, but with some differences. It
has substantially more dish, and it has radial slits running from its inner diameter out more than half
way to its rim. In other words, rather than being a dished continuous disc, it is a ring with fingers
extending inward. Additionally, a clutch diaphragm has a perimeter outboard of the ring it bears
against, that moves oppositely to the motion at the inner ends of the fingers. This feature takes the
place of the release levers in other clutch designs, and retracts the pressure plate.
It would be possible to make a diaphragm spring like that, minus the reverse-motion portion of the
rim, and use it as part of the stack in a deflective-disc shock. It would then be possible to have at
least a portion of the valve stack have a falling-force characteristic. That would still not necessarily
create a damping force that falls as absolute velocity rises. The stack force does not directly
determine the piston force. Rather, it determines the flow characteristics of the orifices in the piston
which the shims mask. The piston force then depends on the resistance to oil flow through these
partially masked orifices.
A falling-force stack could, however, produce a more highly digressive shock than a stack with a
modest rate and high preload, which is the usual approach. It might even be possible to have a true
falling-force or negative-damping-coefficient shock, but a falling-force stack would not necessarily
produce this.
It would be possible to mount the shock so that its force would diminish with increasing
displacement, but that is not the same thing as having the force diminish as velocity increases.
It would be possible to deliberately make the shock acceleration-sensitive. (Velocity is the rate and
direction of displacement change; acceleration is the rate and direction of velocity change.)
Edelbrock has been selling acceleration-sensitive shocks for some years now. Acceleration-sensitive
shocks generally use a weight of some kind, working against a spring. The weight can either open
an orifice or move a needle to change the area of an orifice, or it can vary the effective preload on a
stack.
Finally, there is one type of shock that produces a negative damping coefficient over a small portion
of its velocity range, and a damping coefficient of zero over most of its velocity range. Furthermore,
it is easy to make the damping force adjustable, while retaining the zero coefficient for all
adjustment settings. What kind of advanced design might that be? Surprise: a friction shock! A
friction shock makes the same force regardless of velocity, except when it's just starting to move.
Then it has a "stiction" zone, where the friction force is greater than the force we get once it's
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moving. As the stiction goes away, the velocity is increasing; the damping force is decreasing; the
damping coefficient is negative.
Nobody uses friction shocks anymore, but all suspensions have some sliding contacts in them.
These generate what we call Coulomb damping: friction that is independent of velocity, except for
the stiction effect.
Some cars still use leaf springs. Leaf springs have a lot more Coulomb friction than coils do,
because of inter-leaf friction. In the days when hydraulic shocks were primitive, this was actually an
advantage, and potentially it still could be today, on dirt. Much of this depends on rules, but in some
dirt classes, leaf springs are actually faster than coils. Unfortunately, they are also a pain to run,
because to get the soft rates needed for dirt, the leaf springs have relatively few leaves, and stresses
are high. Consequently, the springs fatigue and lose ride height rapidly, and you have to replace
them all the time.
The normal assumption is that friction is bad, so it's smart to minimize the number of leaves. But if
Coulomb friction is actually okay, because it gives us damping that's stiff at low velocities yet no
stiffer at high velocities, maybe there's a future in leaf springs for dirt that use a larger number of
thinner leaves than those we see today. That would increase inter-leaf friction, and also increase
weight, but result in lower stresses, longer life, and better ride height retention.
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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
TALL VS. SHORT SIDEWALLS
I am a Racecar Engineering subscriber and have enjoyed your later articles regarding tyre width
and grip.
I seem to recall another one regarding wheel and tyre profile effects as well, but can't find it. Was it
written by you? Do you remember in which issue it was published?
Basically, there have been some discussions about why the current trend to big wheels/small tyre
profiles and why some racecars like F1 don't use a small-profile tyre. One of the opinions is that F1
is limited to 13" wheels (to limit brake size), but if it wasn't, bigger wheels would be of benefit.
Personally I think the bigger wheels/smaller profiles are (beyond a certain point) just a styling and
marketing exercise.
Any insight on this point?
I think I can recall having discussions about this, but I don't think I've addressed the subject in the
newsletter or column before. Perhaps I have done so on a forum at some time, or in private
correspondence. Checking my newsletter back issues list, I don't see any such article listed – only
the one on why wide tires are better than narrow ones.
Are big wheels with low-profile tires just a styling fad or marketing gimmick? In some market
sectors they have become that, but this is a styling fad with some basis in engineering.
Actually, the trend to very low tire aspect ratios began in racing. Low-profile tires are still used in
racing, where they are allowed: Trans-Am cars, touring sedans and other production-based road
racing cars, autocross cars, sports racing cars. Tall sidewalls are only seen where the rules limit
wheel diameter, and on the driven wheels in drag racing.
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Thirty-five years ago, there were no street tires below a 60% aspect ratio. If you wanted the lowprofile look that the racing cars had, you had to buy racing tires. People sometimes ran racing tires
on the street, although of course that was illegal. But that was the only way to get racy-looking tires
with stiff sidewalls and sticky tread rubber. Car shows were full of display-only vehicles with race
tires. The reason we now see low profiles on the street, and tall profiles in F1, is that street tire
technology has belatedly caught up with discoveries originally made in racing, while racing rules
have restricted F1 cars, and some other classes as well, to anachronistic wheel sizes.
Is this a bad thing? Not necessarily, although it is a bit odd. If you are running a racing series, it
makes economic sense to restrict any technological progress that would require competitors to
replace equipment or require manufacturers to retool. If you are trying to keep speeds down and
keep fields full, why would you permit anything that raises both speeds and costs? As long as the
cars go fast enough and make enough noise to put on a good show, that's enough, isn't it?
Certainly it is if you are openly promoting budget racing, with technologically restricted cars. But if
you are billing your series as the premier class in motorsports; if you are charging an arm and a leg
for tickets; if everybody knows the expense to compete is ridiculous but this is part of the draw –
then it becomes harder to defend draconian restrictions on tires and wheels. And if you are still
trying to justify the show as an exercise in "improving the breed", that really does get rather
awkward. Wide, low-profile tires are the main street-applicable technological advancement that
racing can claim to have originated during the last forty years.
Are they really an advancement? The questioner appears to have some doubt.
I say yes, they are an advancement, although they are something of a mixed blessing and have
become a customizing fad.
Making the sidewall shorter and the wheel diameter bigger has two, or perhaps three, advantages.
First, it makes the sidewall stiffer. Second, it makes room for bigger brakes. And, if we don't use all
the extra room for bigger brakes, we can get more air through the wheel. If we shape the fenders
properly, that lets us extract more air from under the car through the wheel wells. This not only
helps brake cooling, but also aids lift reduction/downforce creation. This assumes, of course, that
the car has fenders.
Are stiffer sidewalls always better? I think we can say that for racing and for high performance
applications, we want as much lateral stiffness as we can get. There is some penalty in directional
stability, because the car will have more tendency to "tramline", or follow edges in the road surface
that nearly parallel the vehicle's direction of travel. But a performance-oriented driver will generally
put up with this to get more responsiveness and greater cornering power. Greater lateral stiffness
helps keep the tread flat to the road and prevent the tire from rolling under and concentrating load on
the outside shoulder of the tread.
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Greater vertical stiffness is more of a mixed blessing, and a more complex issue. The tire is to some
extent a secondary suspension system, acting in series with the main suspension system. In stiffly
sprung winged formula and sports racing cars, tire compliance may be as much as half of the total:
the suspension may be as stiff as the tire sidewalls.
Considered as a suspension system, a set of tires is very good in some respects, and horrible in
others. For unsprung weight, it's unbeatable. The only unsprung components are the contact patch
and some material near it. It has no camber change in ride. On the other hand, it has no camber
recovery in roll, and it is seriously underdamped.
We might be tempted to decide that we could accept a very high vertical stiffness from the tire, i.e. a
very high tire spring rate, and get our compliance from the suspension proper, where we can get
camber recovery in roll and control the damping properties.
However, there is one other factor: the tire's vertical spring rate is inextricably related to the contact
patch size, and the contact patch size is related to the amount of grip we have. As the tire spring rate
approaches infinity, the contact patch length and area approach zero. If the spring rate were truly
infinitely large, the contact patch would be a line of zero width front to back, and the contact area
would be zero.
The original objective of radial tires was to have greater vertical compliance and a longer contact
patch, while still keeping the contact patch flat to the road in cornering.
Theoretical considerations aside, for most purposes practical considerations limit our sidewall
height. We have to have enough distance between the rim and the ground so that we don't damage
the rim on pavement slab edges and potholes. One of the features that has made today's short
sidewalls possible has been the development of sidewall designs with a meaty region near the rim
flange that protects the rim aginst both curb scuffs and pothole damage. This is combined with a
flexible zone closer to the tread shoulder that provides vertical compliance, albeit over a smaller
range than with traditional construction.
It is important to note that sidewall height is not the sole determinant of sidewall properties. It is
quite possible to put a big, strong bead stiffener in a tall sidewall, and make it act like a short
sidewall. It will weigh a bit more, and the brake size will suffer, but the car will corner about the
same as would with a short sidewall. I am told that most "radial" racing tires are not actually radials
at all anyway. The main plies are actually not as close to 90 degrees as physically possible. They
are more like 70 or 80 degrees – closer to radial than a true bias-ply or the bias-belted street tires we
saw in the '70's, but not truly radial. In other words, relatively stiff construction is still favored
where cornering performance is paramount, and therefore the trend toward short sidewalls for
performance tires is fundamentally sound.
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BRAKING DISTANCE, BRAKE TORQUE, AND TIRE TRACTION
I recently saw a quote by John Barnard about the early days of carbon fiber, where he said that Niki
Lauda was braking for a certain corner at 100m but when carbon brakes were tried he could brake
from 60m.
I have always been under the impression that if the brakes on a car were powerful enough to lock up
the wheels, then the shortest braking distance would be dictated by the load on the tires and the
coefficient of friction between the tires on the road. Given the same tires and road surface, how can
one type of brake stop a car faster than another one?
Perhaps John Barnard reads Racecar Engineering, and perhaps he will see this when it appears in my
column, and perhaps he will favor us with his own explanation. Absent this, I will speculate as best I
can.
In theory at least, braking is primarily limited by tire traction, provided the brakes can lock the
wheels. The brakes can only stop the tires. The tires then have to stop the car. However, real world
braking at the end of a straightaway is constrained by some additional factors besides sheer braking
power.
First of all, the driver is not locking the wheels. The driver must avoid locking the wheels, in order to
maintain directional control and not flat-spot the tires. That means it is crucial that the brakes exert a
predictable and consistent torque, and that the front-rear balance be appropriate.
It is important for the brakes to come up to desired torque promptly: they must have good initial
"bite". They must apply equally on both sides of the car throughout the braking event, so that no
large yaw moments result. Any problems in these areas will require the driver to brake earlier to
compensate.
Brake release is more important than many people realize. If the brakes continue to drag after the
pedal is released, not only does that heat the brakes unnecessarily, it saps cornering power from the
tires. That lowers cornering speed, again requiring earlier braking.
Finally, brakes relate to driving technique, particularly as regards the ability to trail brake. It is
commonly believed that trail braking was adopted primarily because certain drivers, such as Mark
Donohue, recognized that it could improve lap time by allowing braking to be delayed. This is true,
but it is also true that trail braking as we know it was not possible until the advent of brakes with
good directional stability and consistency, and controllable release properties. In the days of drum
brakes, drivers had to do their braking in a straight line because brakes were not controllable enough
to allow the driver to turn and brake at the same time, or to controllably reduce braking while
feeding in steering.
Any combination of these factors could allow one set of brakes to outperform another approaching a
particular turn, even if both designs can lock the wheels.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
MODERN DRIVESHAFT JOINTS VS. RUBBER DOUGHNUTS
I am running a Historic Formula 2 March 712 in Europe. I am working hard to improve the
handling. To make the car lighter, first I removed the heavy doughnut with heavy strong driveshafts
and I saved a total of 7 Kg after the modification to modern CV joints. Can I expect a improvement
on handling? I think the rubber doughnuts are likely working as a spring and are not so nice to
drive on corner entry and exit and I am losing power on acceleration (and the polar moment is much
higher; that means the acceleration is different.) Can you give me more information about that?
Handling should be helped a little. The difference may be too small to feel or even measure, but
anything that reduces weight should help handling, once the car is optimized for the new weight and
weight distribution. In this case, roughly 50% of the mass in question is unsprung, and that
improves the payoff, at least when there are any bumps.
Rubber doughnut joints are compliant in torsion, and this can create surging: an oscillatory
longitudinal acceleration of the car, caused by the joints wrapping up and unwrapping. Any jerky
application, release, or reversal of torque can provoke this. This is not strictly a handling issue –
more of a driveability issue. However, we do partly control the behavior of the chassis with the
application of torque to the wheels, and anything that reduces our control of torque to the wheels
inevitably hurts our ability to control the car.
As for the addition to the wheel rate from the doughnuts, no doubt there is some. However, we need
wheel rate; we aren't necessarily seeking to minimize it. We can compensate for any contribution
from the joints by running slightly softer springs.
We do want to know wheel rate as accurately as we can, and the addition from the joints complicates
this a bit. If we are really fastidious, we can measure the joints' contribution fairly accurately by
putting the car on the scales, removing the springs, jacking the sprung mass up and down, and noting
changes in the scale readings. Probably the doughnuts have a somewhat different rate when
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everything is in motion, but measuring their rate statically should be at least as valid as measuring a
tire's rate statically. Of course, all this is moot if the rubber doughnuts aren't there anymore.
Regarding improved acceleration due to reduction of moment of inertia, that's also good, but I expect
the effect here will also be small. It will be nowhere near as big as a similar moment reduction at the
flywheel or clutch, because the drive shafts turn much slower. If the engine turns, say, four times as
fast as the shafts, then any given saving at the flywheel is worth sixteen times as much as the same
reduction at the shafts. The engine has to accelerate the flywheel four times as fast as the shafts, and
any given inertia torque at the shafts looks only one-fourth as great to the engine because it is
reduced through the gears. Still, even if the effect is small, it is surely helpful.
ZERO-DROOP SETUPS
[Continued from previous question]
The next question I have is about suspension droop travel limit fwd and aft. I have seen that modern
single seaters have no droop at all. Now I am not sure about a historic racecar like my March
F2 (year 1971).
The shock stroke (fwd and aft) during hard driving is about 20mm. I know aft shocks should have
more travel than fwd shocks but how much?
Corner exit on acceleration the car is pitching fwd up and with no droop can help to get more
weight on the car fwd because the unsprung weight will help to hold the nose down. Until now I
made the shock adjustment with more rebound but I think that's the wrong way to fix the problem.
The only reason it makes any sense to not let the suspension move freely in droop is to control
ground-clearance-sensitive aerodynamic elements. From every other perspective, making the
suspension top out prematurely is a bad thing.
For best mechanical grip, we want the suspension to extend freely until the springs reach zero load,
and then stop. If the suspension extends further, so that the springs hang loose, that doesn't hurt grip
but it can cause the springs to beat up the shocks, or the spring retainers or adjusting collars, or other
pieces, if it happens very often.
If the suspension tops out before the springs unload, that abruptly unloads the tires, but it also keeps
the ground clearance from growing, at least as long as we don't pull the wheels off the ground.
That's bad for mechanical grip, but it's good for aerodynamics if we've got a floor, a valance, a
splitter, or a wing that has to be near the ground to work well.
From what I can tell by pictures on-line, the March 712 has a fairly broad chisel-shaped nose, with
two small nose wings on the sides of the chisel. The radiator is in the nose, fed by an intake below
the leading edge of the chisel, and exhausting through an outlet on the top of the chisel. The little
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wings are up fairly high compared to later cars. It doesn't look like the car would be highly sensitive
to ground clearance at the front. The car pre-dates tunnels and diffusers; the floor isn't designed to
make downforce. It has a rear wing, but this would not be highly sensitive to ride height either. So I
don't think the car would realize the same advantages as a more modern car from zero-droop
suspension.
There is no hard and fast rule for the relationship between front and rear shock travel, as shown by
travel indicators on the shock shafts. In tail-heavy, rear-engined cars, it is common for the front
suspension to have a higher natural frequency and smaller static deflection than the rear. That is, the
front suspension is stiffer in ride than the rear, relative to its sprung mass. This normally results in
more suspension travel at the rear than at the front. Also, it is normal to have more aerodynamic
downforce at the rear than at the front. This will result in the shock travel indicators showing more
travel at the rear than at the front, if the motion ratios are similar. Looking at photos, it appears that
the motion ratios at the front and rear of the March 712 are fairly similar. So if the travels are
similar, it may be that the rear springs are a bit stiff relative to the front – but not necessarily.
Keeping the front end from lifting under power will only add a little bit of load to the front tires –
and concomitantly reduce rear tire loading a little. The amount of rearward load transfer, for a given
forward acceleration, depends entirely on the height of the center of gravity and the wheelbase. How
much the nose lifts wouldn't matter at all, except that more nose lift does result in a slightly higher
c.g. If the front of the car seems to lift excessively under power, stiffer front springs will reduce
that. You may want to combine the stiffer springs with more rear anti-roll bar or less front anti-roll
bar.
Some readers may find it surprising that the front end lifts less with stiffer springs, but that is indeed
the case. A stiffer spring doesn't mean more upward force. It means less travel for a given load
change – hence less extension travel for a given load decrease.
Ordinarily, we don't want to keep load on the front tires under power; we want load to transfer to the
rear so we can put power to the ground. This is true unless the car understeers excessively on corner
exit. This is not uncommon in rear-engined cars, but a more common complaint in racing generally
is that the car spins the wheels and/or oversteers on exit. A car that is too tight (understeers too
much) power-on is a problem that racers in many classes would kill to have. If the back tires stick
too well, just feed them more power, goes the reasoning.
This doesn't always work, however. There may be no more power available; the driver may have the
throttle wide open already. This is often encountered in Formula Fords. Or the understeer may
simply increase until power breaks the rear tires loose completely, whereupon the rear end suddenly
snaps out.
The March appears to have very short control arms, especially the uppers. That means that either the
camber recovery goes away markedly as the suspension extends, or the roll center rises as the
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suspension extends, or both. Having that happen at the front would worsen a power push, and stiffer
front springs would reduce the lift. Restricting droop travel would keep the nose down too, but the
effect would be abrupt, and the roll resistance would abruptly increase, worsening the push. More
spring and less bar keeps the front end down more, without that problem.
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March 2007
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
DIAMOND LAYOUT
Attached are illustrations of a proposed car for F-1 racing, suggested during the early 1990s. [For
newsletter recipients, one of these illustrations is included as a separate attachment.] The car has a
single steered but unpowered front wheel. A pair of wheels is located further aft located on an axle
passing close to the COG or possibly ahead of it. These wheels are non-steered but are powered.
Finally there is a powered and steered single wheel right aft. The car is a diamond in plan view. I
understand the idea was to provide a chassis with better aerodynamic downforce and less drag than
a conventional layout. In addition the car featured better traction by being able to drive three wheel
drive (the rear three). Only the front wheel was not powered. This nicely got around the rules
banning four-wheel drive in F-1!
How would such a car handle? Assuming the front wheel and the rear wheel accomplish the
steering task (that is the non-paired wheels steer whereas the “axle” pair remain fixed with respect
to steering) what would happen as the car reached maximum slip angle and the driver decided to
increase the radius of cornering path (that is, reduce lateral acceleration)? In this case he’d be
adding to the rear wheel slip angle while simultaneously reducing the front wheel slip angle. What
would occur if the rear wheel lost static traction because of this? Would the effect of the single rear
wheel losing grip dominate? Would the increase in slip angle at the rear tend to over steer the car
putting it into a slide or a spin? Or would the combination of the three other wheels prevent
oversteer and slides?
An alternative arrangement would be to keep the single rear wheel fixed while steering the other
three. There would need to be some sort of linkage to do this- a sort of modified Ackerman geometry
needing to be implemented. Would this be a better arrangement? The designer must have thought
about this possibility and thought not. It would be interesting to understand why.
An interesting feature is that it would seem that only a single differential unit would need to be used
since the distance of the path traversed by the rear wheel is exactly equal to the mean of the wheel
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paths of the middle wheels. The rear wheel could be driven from a shaft taken from the crown
wheel.
Comments?
The first attempt at a diamond layout that I ever saw was a model that somebody submitted to the
Fisher Body Craftsman's Guild styling competition back in the 1960's. To my knowledge, nobody
has ever tried to actually build a race car this way.
I love this kind of outside-the-box thinking. To give a brief answer first, I think the diamond layout
holds more promise for straight-line cars such as dragsters or speed record cars than for road racing
cars. There is, at least potentially, an aerodynamic benefit. There is also, unfortunately, a handling
penalty.
There would be an advantage in forward traction with three wheels driven. Whether this would
actually be allowed would depend on the exact wording of the rules, and their interpretation by the
officials. Even if three-wheel drive were ruled legal, the rules could be changed to prohibit it if the
FIA saw fit. Any dramatic innovation that obsoletes existing cars in any class faces the same
problem. Even if it is clearly legal when introduced, it can still be prohibited by a subsequent rule
change if those in charge deem this desirable.
Whether the diamond layout stands to win road races or not, it is fascinating to consider what its
pros and cons are, and what would be involved in optimizing it.
Perhaps the most obvious problem with the diamond layout is that roll is only resisted by a single
wheel pair, at least up to the point where one wheel lifts. In low-speed turns, with minimal
aerodynamic downforce, and with racing tires, the inside middle wheel will lift before the tires will
slide, just as we know one wheel would lift in a conventional layout, with all the roll resistance at
one end. Beyond that point, the vehicle is a tricycle, or maybe a sidehack, and any further
overturning moment is resisted by the front and rear wheels and the outside middle wheel, acting on
half the track width. The vehicle is unlikely to flip, as long as it doesn't snag an edge while sliding,
but it is not making very good use of its tires. If we are driving the middle wheels, the diff had better
be able to lock with one wheel in the air.
In a road car, we would have much less grip, although we'd also have a higher c.g. Maybe a road car
could be made to keep the inside middle wheel on the ground at the limit of adhesion. Even then,
however, the middle suspension would need to be very stiff in roll to keep the roll angle within
reason.
In a conventional layout, we can control the car's oversteer/understeer balance by juggling the
relative roll resistance for the front and rear wheel pairs. With the diamond layout, we can no longer
do that.
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Another problem is that we cannot achieve camber recovery in roll on the front and rear wheels.
Short of the point of inside middle wheel lift, we have no suspension displacement to work with on
the front and rear wheels. After the point of inside middle wheel lift, the front and rear wheel
suspensions extend whether the car is rolling to the right or the left. So we really have no choice but
to make the front and rear wheels move without camber change in ride and lean with the sprung
mass in roll – and, as we have noted, the sprung mass is apt to lean considerably.
As with three-wheeled vehicles, the worst case for overturning is a combination of longitudinal and
lateral acceleration. If we compare conventional and diamond layouts, with identical wheelbase and
track dimensions, with the diamond layout the center of mass is much closer in plan view to the
nearest line connecting two contact patches. That means that the diamond layout will bicycle more
easily in some combination of lateral and longitudinal acceleration than the conventional layout will
in its worst case, which normally is pure lateral acceleration.
Short of the point of bicycling, a layout with poorer overturning resistance will experience greater
load transfer. It will load its tires less equally, and will consequently use them less effectively.
One might argue that a fairer basis of comparison would be a case where the diamond layout has
similar worst-case overturning resistance to the conventional layout. That would imply a longer
wheelbase and wider track for the diamond layout. Ordinarily, our vehicles are constrained by the
width of the lanes on our roads, and the length and width of our parking spaces. The envelopes thus
defined are rectangular rather than diamond-shaped, and therefore a conventional rectangular vehicle
fills them more effectively, with its wheels spread further from its center of mass, than a diamondshaped vehicle. So a diamond-layout car needs to take up more room on the road, if it is to have
comparable overturning resistance and comparable load transfer.
In racing, we usually have an overall width limit, an overall length limit, and sometimes a minimum
and/or maximum for wheelbase and/or track. We also have some advantage from a narrow car, in
the line we can use, especially through doglegs and slaloms or esses. All these factors favor the
conventional layout over the diamond.
For the diamond layout, many of the steering, differential, and suspension design considerations are
common to more conventional three-axle vehicles, and in some instances even two-axle vehicles.
Even when the two rear axles are quite close to each other, as in heavy trucks, in tight turns at low
speeds there is a significant difference in the speed of the rearmost axle and the middle one. Heavy
trucks consequently have three differentials, two of them housed in the forward drive axle. Many
trucks have a driver-controlled lock for the center diff. There is a noticeable increase in tire scuffing
in low-speed maneuvers with the center diff locked. I am not sure a second diff would be necessary
in a diamond-layout race car, but the mean speed of the middle wheels would not be identical to the
speed of the rear wheel in all situations.
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As for steering, in multi-axle vehicles it is most common to steer the front axles and not the rear
ones. This gives the most predictable high-speed behavior, at the expense of turning circle. A
neighbor down the road from me operates a fleet of concrete pumping trucks. The largest of these
are non-articulated trucks with seven axles. The front three steer. The linkage is designed so the
front axle steers the most, the second axle less, and the third axle still less. The rearmost axle is a
non-driven tag axle that is lifted off the ground in low-speed maneuvering.
Looking at the drawings by Mr. Scalabroni, it doesn't look like the front wheel could steer very
much without hitting the leading arm that locates it. A different design could be used, of course, but
as drawn, the car would need to have the rear wheel steer just to get around the tighter turns. If the
rear wheel is driven by a longitudinal shaft, there will be problems making it steer much either.
Making a single front wheel steer a reasonable number of degrees presents some packaging
challenges. There has to be some fairly bulky structure either alongside the wheel or above it. We
can't have the steering axis behind the wheel; we would have negative trail.
Older readers will recall the four-wheel-steer cars sold by Honda and Mitsubishi during the 1980's.
These were originally designed to cope with cramped roads and parking areas in Japan. The rear
wheels steered out of the turn, adding yaw moment, in some situations, and steered into the turn,
reducing yaw moment, in other situations. The Honda system was purely mechanical. It was
ingeniously arranged to make the rear wheels steer into the turn at small handwheel (steering wheel)
displacements, and steer out of the turn at large handwheel displacements. The Mitsubishi system,
called HICAS, was electronic and computer-controlled. It steered the rear wheels out of the turn at
low vehicle speeds and into the turn at high vehicle speeds. That is really what we want. The Honda
system was intended to approximate this with a simpler, passive system, the thinking being that large
handwheel inputs mainly occur at low speeds. In both of these systems, the rear wheels steered
much less than the fronts.
There was a four-wheeled truck made in the 1930's that steered the front and rear wheels equally and
oppositely. The idea there was to allow full-time four wheel drive with no center differential, and
have a good turning circle without excessive U-joint angle at the outboard end of the axle.
Apparently, high-speed operation was not contemplated.
In the Scalabroni, would there be a possibility of the rear tire going to a slip angle past peak lateral
force when catching an oversteer slide? I think so. In fact, this is fairly common with unsteered rear
wheels. It is also common for a driver to push the front wheels past optimum slip in an
understeering car, and actually have the front end unexpectedly grab, or bite better, as the steering is
unwound on exit. Stock car drivers sometimes call this a "push loose" condition. So, yes, it could
happen, but the problem is not unique to the Scalabroni design.
The reader will note that we have so far assumed purely passive suspension. Current F1 rules do
require this. However, active suspension could very significantly enhance the properties of the
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diamond layout. I doubt if it would equal a conventional layout even then, but again the possibilities
are interesting to contemplate.
One possibility with active suspension would be to make the car lean into the turns, essentially
making it a large motorcycle with training wheels. Very good computer control would be needed,
along with a lot of travel for the middle wheel suspensions. Why not just have a two-wheeler
instead? Well, the diamond-layout car could be larger, and would be less prone to falling over to the
inside when traction is suddenly lost, and less prone to high-siding when traction is suddenly
regained. A disadvantage versus a two-wheeler would be that the operator would not have the
advantage of being able to straighten out the turns as much as with a single-track vehicle; the line
could not be as good, due to the width of the vehicle.
It appears that the designer of the Scalabroni was thinking more of aerodynamics than mechanical
dynamics. I think that is where the concept's advantages lie, and therefore I think there are some
really interesting possibilities for diamond-layout speed record cars. By putting the middle wheels
about a third of the way back, it would be possible to have a nice teardrop shape in plan view. Large
amounts of steering lock would not be needed. Probably steering just the front wheel would be fine.
All four wheels could be driven. If the rules required, the front and rear wheels could be slightly
offset, rather than directly in line.
In any case, it is heartening to see this kind of original thinking.
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Revised 4/5/07
This document has been revised to correct an error
it contained as originally published.
Reproduction for free use permitted and encouraged.
Reproduction for sale subject to restrictions. Please inquire for details.
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
ROLL STEER AND ANTI-SQUAT/ANTI-LIFT IN STRUT SUSPENSION
As a reader of Racecar Engineering, I would like to know your opinion about a concern I have at the
moment. I hope you will consider it and will be able to include it in a future issue of RE, because I
think it is quite interesting.
I am studying the suspensions of my rally car at the moment. Our rally car is a WRC car that we use
for both gravel and tarmac events. There are some small differences between tarmac and garvel
spec suspensions but the main layout is the same. It is a 4WD, with an active hydraulic center
differential and a 50/50 torque split, most of the time.
I have a lot of toe variations during full travel at the rear suspension (pseudo MacPherson type, see
attached file). [Newsletter subscribers will receive the questioner's illustration as a separate
attachment.] In order to solve the problem, I have been testing (real tests and computer
simulations) various configurations, with varying mounting point positions.
The results give me the same direction. The toe variations during travel decrease when points B and
G are at the same height (vertical axis). We have always used our car with setups where B was
around 5 to 10 mm lower than G. Knowing the results from my tests, I would logically change this
setup to a line BG nearly horizontal.
However, some people are saying that it will greatly alter the anti-lift/anti-squat feature of the
rear suspension. I have the feeling that it's not a problem but I am unsure about that. The problem is
that I don't really know how to simply calculate the "anti" amounts of a MacPherson suspension in
general and I can't find anything in many books. Could you give me some indications about this?
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Readers are referred to the questioner's illustration. We are discussing the rear suspension, which is
shown in the right half of the illustration. The suspension has a telescoping strut located by a single
pivot at its top end, and by three links at its bottom end. Links CB and FG run transversely and
provide lateral location, controlling camber and toe. Link AM runs longitudinally and provides
longitudinal location and reacts brake torque. Link FG is partly hidden by the anti-roll bar. Point C
is hidden behind a donut-shaped object whose function is not obvious to me. Point B is adjustable
for height.
Any rear suspension that has a strut of this type, with the lower end of the strut located by some
system of arms or links, is sometimes called a MacPherson strut suspension, or sometimes a
Chapman strut suspension. MacPherson was an engineer for Ford in England, and he is credited
with inventing this type of suspension. However, he and Ford only applied it to the front end of the
car. Lotus founder Colin Chapman was the first to apply it at the rear, although arguably his idea is
a fairly obvious application of MacPherson's concept. So there is a rational case for either name
when referring to a rear suspension, and I consider them legitimate synonyms. (I would not,
however, consider it correct to call a strut-type front suspension a front Chapman strut.)
To understand the behavior of this suspension, and indeed any suspension, we need to define two
more points: the wheel center and the contact patch center or load centroid. These points are not in
the illustration, but they are easily described verbally. The wheel center is the intersection of the
wheel centerplane (the plane midway between the rim flanges) and the wheel's axis of rotation. I
will call this point J. For the contact patch centroid, I like to use a point directly below point J, even
when the wheel has some camber. Let's call this point K. Let's also suppose that the wheel has no
toe-in or toe-out at the condition we're evaluating. The plane containing points J and K, and exactly
longitudinal to the car, forms a good effective wheel plane to which we can project the suspension's
side-view geometry. Being a vertical, longitudinal plane, it is in true shape in a side view of the car.
All of these points have three coordinates in the car's axis system: x (longitudinal, per SAE
convention), y (transverse), and z (vertical).
The distance from point K up to point J is the tire's loaded radius rL.
All we really need to know about any suspension's geometry to determine the suspension's "anti"
properties is the motion path of point K. More precisely, we need to know the instantaneous sideview and end-view (front- or rear-view) slope of that motion path at the suspension position we're
evaluating, i.e. the instantaneous rate of change of the point's x or y coordinate with respect to rate of
change in the z coordinate – in calculus notation, dxK/dzK for anti-squat and anti-lift, and dyK/dzK for
anti-roll.
With good enough modeling software, it may be possible to simply move the suspension a very
small increment each side of the position being evaluated, and get a ΔxK/ΔzK that very closely
approximates a true dxK/dzK.
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Note that there are two assumptions we can make when doing this: we can assume that the wheel is
free-rolling, meaning that K always stays directly below J, and the motion path of K is J's motion
path transposed to the ground; or we can assume that the wheel is locked to the upright, meaning that
any change in the side view angle of the upright as the suspension moves creates a difference
between the motion path shapes for J and K. With independent rear suspension and outboard brakes,
we use the former method for anti-squat (under power), and the latter method for anti-lift (under
braking).
We need to know three more things to get a percent anti-squat or anti-lift value: we need to know the
percentage Pr of total x-axis force at the contact patch (or rear contact patch pair, if we are assuming
the suspension is symmetrical and we are seeking a percent anti for the rear wheel pair); we need to
have a sprung mass center of gravity height H (some estimating is normally required to arrive at a
reasonable number); and we need to know the car's wheelbase L.
Then, for anti-squat, percent anti-squat = (dxK/dzK)PrL/H. For the situation where all four wheels
are driven and the torque split is 50/50 front/rear, percent anti-squat = (dxK/dzK).50L/H. Remember
that for independent suspension the value for dxK/dzK is taken assuming the wheel to be free-rolling,
so that dxK/dzK = dxJ/dzJ.
For anti-lift, we need to know the percentage of brake retardation force, at the ground, that the rear
wheels provide. We use this for Pr . We use the dxK/dzK value for the condition where the wheel is
assumed to be locked to the upright. That is, dxK/dzK = dxJ/dzJ only if the upright does not rotate at
all in side view as the suspension moves.
Many of us do not have computerized animation of our suspension layouts. We are used to finding
the side view instant center, on the drawing board or the CAD tube, and constructing a side-view
force line from the instant center to the contact patch center or the wheel center. To do the job this
way with a strut suspension, we need to find the virtual upper and lower control arm planes, and find
their intersections with the wheel plane. The intersection of two planes is a line, so we are talking
about two lines, lying in the wheel plane. These lines are our side-view projected control arms.
Their intersection is our side-view instant center.
A strut-type suspension has a virtual upper control arm plane, which contains the strut's top pivot
point (point E, in the questioner's suspension), and is perpendicular to the strut tube axis.
This is not necessarily the same as the effective steering axis. When the strut has a single ball joint
at its lower end, the effective steering axis is a line through the ball joint pivot point and the upper
pivot point.
What to use for a lower control arm plane is more of a conundrum. I think I would start by finding
the points where lines BC and FG intercept the axle plane: the transverse, vertical plane containing
the wheel centers. Let's call these intercepts S and T. A line connecting these, line ST, would be the
end-view projected lower control arm.
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Once we have line ST, we can establish a plane parallel to that line, and containing line AM. Once
we have that, we can find the intersection of that plane with the wheel plane, and use the line so
defined as our side-view projected lower control arm.
I am suggesting using side-view and end-view projected control arms that do not actually lie in a
common plane. However, all things considered, I think this is preferable to any possible
alternatives. The suspension, so modeled, is probably not exactly equivalent to reality, but it is a
reasonable approximation.
Once we have the upper and lower side-view projected control arms, we can find their intersection,
which is our side-view instant center. We then draw in the force line for braking, from the contact
patch center to the side-view instant center. We locate a point at the sprung mass center of gravity at
height H. We draw a vertical line in our side view at a distance Pr/L forward of the rear wheel
center. I call this the resolution line for braking.
The force line will intercept the resolution line at some height h1. The percent anti-lift = h1/H. Note
that if the force line intercepts the resolution line below ground, h1 becomes negative, and we have
negative anti-lift, also called pro-lift. If h1 > H, we have more than 100% anti-lift, meaning the rear
suspension will compress in braking. As we add more rear brake, we get more rear anti-lift (or more
pro-lift, if the geometry provides pro-lift), without changing anything else.
For the anti-squat, the side-view projected control arms and instant center are the same as for antilift, but the resolution line and force line are different. The force line is different because with
independent suspension, drive torque does not act through the suspension linkage. The resolution
line is different because the rear wheels do not generate the same percentage of the longitudinal
force under power that they do in braking.
There are two variations on the basic technique. Done correctly, they both give the same answer.
The variation I prefer involves constructing a force line that originates from the contact patch center
(point K), and using the same equation or rule for calculating the percent anti that we use when the
suspension linkage reacts the torque, as with a live axle under power, or with outboard brakes in
braking. The other variation involves constructing a force line that originates at the wheel center
(point J), and using a slightly different equation or rule.
In the first method, we construct a line from the wheel center J to the side-view instant center. Then
we construct a parallel line to that one, originating at the contact patch center K. This is the force
line when the car is under power. We construct the vertical resolution line .50L forward of points J
and K for the questioner's example, or at the front axle for a purely rear-drive car. The force line
intercepts the resolution line at a height h2. The percent anti-squat = h2/H.
In the second method, we do the same thing, except we omit the second line, and just use the line
from point J to the instant center as the force line. The force line then intercepts the resolution line
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at a height h3, and h3 = h2 + rL. The percent anti-squat = (h3 – rL)/H. That is, of course, the same as
h2/H.
Adherents of the second method sometimes insist that this is the right way because the force acts on
the car at hub height, and that any force line must pass through the instant center. I say the first
method makes more sense because any force exerted on the car by the road must act where the road
touches the car, and the wheel is part of the car, not a separate entity that acts on the car. The
difference between independent and live axle suspension, or inboard and outboard brakes, is not
where the force acts on the car, but how the torque is reacted within the car – i.e. through the
suspension linkage or not. I also think it makes sense to construct force lines so that a common rule
applies once the force line is constructed, rather than having two different rules. However, I don't
think the whole debate is of much consequence, since both methods give identical answers. The
difference really has more to do with visualization and semantics than actual natural laws. It is,
however, important to understand both methods, so that one doesn't apply the rule or equation from
one method when using the other.
The questioner wants to know what effect bump steer adjustment will have on the anti properties. It
is customary to model our antis on the assumption that there is no bump steer, and treat bump steer
as a separate issue, a steering geometry issue rather than a suspension geometry issue. However, if
we really want to be rigorous, in fact there is some effect, but it is small, unless there are really large
amounts of bump steer, in which case the car will be so undriveable that optimizing the antis will not
be our main concern. Unless bump steer causes the wheel to steer about an axis precisely in the
wheel plane, there will be a small component in the side-view motion paths of points J and K
resulting from the bump steer.
If the questioner's suspension is configured for minimum bump steer, point B will lie in plane CFG.
If B lies below plane CFG, the wheel will toe in as the suspension compresses, and the car will have
roll understeer. If B is above plane CFG, the opposite will occur, and the car will have roll
oversteer. Assuming that the wheel centerplane is outboard of the effective strut axis, roll understeer
will increase anti-squat and anti-lift slightly, and roll oversteer will decrease anti-lift and anti-squat.
Note that this is opposite to the effect we would predict if we supposed that the suspension's sideview properties depended on the side view inclination of line BG, as some older suspension texts
would suggest. Raising point B decreases the anti-squat and anti-lift. This example demonstrates
the importance of looking at what happens at the wheel plane, rather than looking at the side-view
inclination of the inner pivot axes of the control arms.
One final, somewhat self-serving note: when discussing suspension antis, I generally try to get in a
plug for my video "Minding Your Anti", which includes more discussion of the topic, with more
pictures. They are available in US standard VHS cassette only, for US$50.00, payable by check or
money order to Mark Ortiz, 155 Wankel Dr., Kannapolis, NC 28083-8200, USA. Price includes
shipping and handling, worldwide.
5
E
Rear
A
C
B
Front
E
F
C
F
A
G
B
M
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May 2007
Reproduction for free use permitted and encouraged.
Reproduction for sale subject to restrictions. Please inquire for details.
WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
ROLL AXIS FOR LIVE-REAR-AXLE ROAD/HILLCLIMB CAR
I've been reading your column in Racecar Engineering for several years now and I'm gradually
increasing my knowledge of the dynamics of a suspension system, slowly but surely.
One thing I haven't been able to find much about anywhere is front roll centre height on a car with
live axle rear suspension and independent front. The car in question uses a panhard rod and 4
parallel leading links to locate the axle. With the current wheel / tyre combination the centre of the
diff /roll centre height is approx. 11.9 inches. The front suspension is double wishbone, and I have
complete freedom to do whatever I want with the front geometry.
Most things I been told, or read, suggest that the front roll centre should be close to the ground, but
surely on a car with a live axle rear this will cause a steep inclination of the roll axis.
The weight of the car is around 2100lbs, distributed approx. 49/51% F/R, car is front engined.
Can you offer any advice as to a suitable starting point from which to base my design?
The car is to be used for hillclimb and sprints, but will still be a road legal car so ground clearance
is an issue (otherwise I'd be using a Woblink at the rear).
It is true that the roll axis will be steeply inclined if the front roll center is low and the rear roll center
is high, and this is indeed the norm in cars with independent front suspension and beam axle rear
suspension. It is usual to make up for the low front roll center by adding front roll resistance with an
anti-roll bar.
In a car with close to equal front and rear weight distribution, and equal tires sizes front and rear, we
will need close to equal total lateral load transfer front and rear. That implies somewhat less total
roll resistance in the rear suspension than the front, because at the rear there is a substantial portion
of the load transfer that does not act through the suspension. I am referring to the unsprung
component of the load transfer, the portion that comes from the mass of the axle exerting a
centrifugal inertia force at a height above the ground. There is also an unsprung load transfer at the
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front, but it is much smaller because there is much less unsprung mass, and even the unsprung mass
that is there partially acts as sprung mass for purposes of lateral load transfer, because it moves
laterally with the sprung mass in roll.
In addition to the unsprung load transfer, there are three other components to load transfer: elastic,
geometric, and frictional. All of these result from the action of the suspension, and may be said to
act through the suspension.
The elastic component comes from the anti-roll moment generated by the springs and anti-roll bars.
The geometric component comes from the anti-roll moment generated by the rigid members of the
suspension: the links, uprights, and axles. The frictional component comes from all the frictional
forces in the suspension system. Frictional forces include the mostly unintentional ones in the
springs and pivots, and the mostly intentional ones in the dampers.
Cars with independent front suspension and beam axle rear suspension generally have small
geometric components and large elastic components in the front load transfer, and large geometric
components and small elastic components in the rear load transfer.
Independent suspensions cannot work well when they have large amounts of geometric roll
resistance (i.e. a high roll center or large amounts of lateral anti). If we build an independent
suspension that way, it will jack up when cornering. The reason for this is that geometric roll
resistance in independent suspension consists of linkage forces that try to extend the suspension of
the outside wheel (net upward jacking force at the outside wheel) and compress the suspension of the
inside wheel (net downward jacking force at the inside wheel). The outside wheel carries the greater
load, so the outside tire has more grip and generates greater lateral force. When the lateral force is
greater, the jacking force is greater. Thus, the upward jacking force generally will exceed the
downward jacking force, and the net jacking force for the wheel pair will be upward.
To avoid this, the roll center of an independent suspension system must be low. There is no hard
limit, but as a general rule anything above four inches is too high, and two or three is more prudent,
because the anti-roll generally increases as the suspension extends, and we know that the car will
sometimes be going over crests.
We also need to design our suspension so that we do not get any large camber changes. With
independent suspension, we cannot reduce camber change in roll without increasing it in ride, so the
best we can do is avoid any huge amount of change in either ride or roll.
To get good camber properties and an appropriate amount of geometric anti-roll in a front
suspension for a car with a beam axle rear end, I generally recommend a front view instant center
between 55 and 85 inches from the wheel horizontally, and between five and ten percent of that
distance above the ground. Make the control arms as long as possible, consistent with packaging
and bump steer constraints, with the front view projected upper control arm around 2/3 the length of
the lower one.
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At the rear, there is no need to have the Panhard bar at axle height. If we are dealing with an
existing rear suspension, and we don't want to change it, we can make the car work reasonably well
with any Panhard bar height by choosing appropriate spring and anti-roll bar rates.
However, there is a case for having the Panhard bar as low as ground clearance and mounting
constraints will permit, particularly for a road car or a road racing car, and accepting the need to
increase the elastic roll resistance accordingly. The primary reason this strategy works is that it
reduces torque roll and torque wedge: body roll and wheel load change due to driveshaft torque
reacting through the suspension. With a live axle, driveshaft torque rolls the sprung mass to the
right, unloads the right rear and left front tires, and correspondingly adds load to the left rear and
right front tires. In oval track terminology, driveshaft torque adds wedge to to the chassis. In my
application of the terminology, it wedges the car for left turns, and de-wedges it for right turns. That
makes the car looser (adds oversteer) exiting right turns, and tightens the car (adds understeer)
exiting left turns. It also makes the right rear tire spin prematurely under power if the differential
does not lock, or makes the car try to turn right if the diff is locked.
If we add elastic roll resistance at both ends of the car, we reduce torque roll but not torque wedge.
If we increase the rear elastic roll resistance, leaving the front end unchanged, we reduce both torque
roll and torque wedge. However, we can only do this if we reduce the rear geometric roll resistance.
For this reason, the fastest live-axle road racing cars place the rear roll center as low as packaging
constraints allow, and use rear anti-roll bars.
To some extent, we can compensate for torque wedge. We can set the car up with less than 50%
static diagonal (RF+LR) percentage, use somewhat stiffer springs on the right side than on the left,
and use a bit more anti-dive in the right front suspension than at the left front. If we apply these
crutches in a suitable combination, we can get reasonably good behavior in right and left turns, and
under power and braking. However, we can get away with applying these crutches in smaller
measure, or get better car behavior without them, if there is less torque wedge to begin with.
The questioner mentions the WOB link (from Watt-Olley-Bastow) suspension. This refers to a
mechanism that approximates straight-line motion for small displacements. It consists of a rocker
and two links, like a Watt linkage. It differs from a Watt linkage in having the pivot on the rocker
outside the attachment points for the links, rather than between them, with both links extending in
the same direction away from the rocker, rather than opposite directions. It can produce
approximately straight-line motion at the pivot if the links have unequal length, in the correct
proportion to each other. It provides a way to get a low roll center when the only frame members we
have available to anchor to run above the axle. It has the disadvantage that the link loads tend to be
very high. We are still unable to get a roll center lower than the lowest part of the mechanism.
With a Mumford linkage, it is possible to get a roll center somewhat below the lowest part of the
mechanism. In fact, it is possible to get a roll center dramatically lower, except that then the roll
center then moves up and down a great deal as the suspension moves. A Mumford linkage has two
rockers and three links.
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It is possible to make a Watt linkage approximate the behavior of a Mumford linkage. We can put
the rocker under the differential, lying flat, and at an angle when seen from above. We run the links
upward toward the frame from the rocker. The roll center is approximately at the height where the
two link centerlines intersect in front or rear view. Careful detail design is necessary to avoid
running the rod ends on the links out of travel.
ROLL AXIS OF THE AXLE
I have read about how to find a rear axle's axis of rotation in roll. On a triangulated four-link
system, for example, you find the intersection of the lower link centerlines (usually ahead of the axle
and above the links), then find the intersection of the upper link centerlines (usually behind the axle
and above the lower link intersection), and then connect those two points with a line. The axle
moves about this line in roll. The point where this line intercepts the rear axle plane is the rear roll
center.
It would seem obvious that the inclination of this line must determine the rear axle's roll steer
properties also. If the axis slopes down toward the front, that would seem to imply roll understeer.
Yet when I apply the suspension geometry program on my computer to such a layout, it tells me the
system has roll oversteer. Am I crazy? Can the computer be wrong?
Note that the axis the questioner is referring to here is different from the roll axis of the car as a
whole, which was the subject of the previous discussion. This is the axis about which the axle
rotates with respect to the sprung mass.
Yes, the computer can be wrong, and I have seen similarly anomalous outputs from suspension
geometry programs regarding bump steer and roll steer properties in independent systems.
For example, consider the case of a front independent suspension with the steering rack ahead of the
axle line. If you raise the rack, leaving all else unchanged, you know that the wheels will toe out
more, or toe in less, in bump as a result of this change. It always works this way, for intuitively
obvious reasons. Yet I have had the same computer program the questioner says he's using tell me
the opposite. I am leaving the name of the program out of the discussion, as the person who sells it
is a friend of mine. But I will definitely say that having a computer is no substitute for
understanding things with your own brain, and that computer outputs definitely can be wrong. (The
computer can also be right when you think it's wrong. The computer is not infallible, nor are the
people who write the programs, nor are you, nor am I. We all do the best we can.)
Returning to the triangulated four-bar, yes it generally does have roll understeer, despite the up-atthe-front slope of the lower control arms in side view. The unloaded or inside wheel moves
rearward in roll, and the outside or loaded wheel moves forward. This is due to the arms' in-at-thefront angularity in plan view, combined with the lateral motion at their rear ends in roll, which
results from their being well below the roll center.
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If the lower arms were parallel with the vehicle centerline in plan view, and sloped up at the front in
side view, then the system would have roll oversteer. It would also have a rear axle roll axis sloping
upward toward the front, not downward. The axis would pass through the upper arm intersection, as
before, and it would be parallel to the lower arms in side view, since they are parallel to each other,
meaning they have no intersection, or, to be slightly incorrect, an intersection at an infinite distance.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
ANOTHER TRIANGULATED FOUR-LINK AXLE
I am using a very light (aluminum) rear beam axle on a front wheel drive autocross car. I have read
your discusssion of live rear axle location by Watts, Mumford and others but I am using a four link
location system without a Panhard or Watts type system. I have the two lower links wide based at
the front and meeting at the middle of the axle. They are about 3" off the ground and basically
horizontal, thus lateral location of the axle is about 3 inches off the ground. My question is where is
the roll center? I once thought it had to be at the level of the lower links, but perhaps not.
The upper links go straight back about 9 inches above the lower links and have provision to move
the forward attachment points up and down to induce a bit of rear wheel steer in cornering (not
currently doing this).
In this case, the rear axle roll axis, or rear axle axis of rotation in roll, is a line passing through the
lower link centerline intersection, and parallel to the upper links. The roll center is the axle plane
intercept of this line, as with any rear axle roll axis. If the lower links met at the exact center of the
axle, the upper link angle would not change the roll center at all. If their attachment points to the
axle are very close, so that their intersection is a short distance behind the axle, then upper link angle
affects the roll center, but only a little. As the lower link centerline intersection gets further behind
the axle, the upper link angle has more influence on the roll center height.
In all cases, if all the links are horizontal, the roll center is indeed at the height of the lower links,
and the rear axle axis of rotation in roll is horizontal. True to this model, there is no roll steer. If we
raise the front of the upper links, the rear axle axis of rotation slopes upward toward the front. Again
true to this model, we have roll oversteer.
Anti-squat (in forward acceleration) is zero in all cases, because the rear wheels are not driven and
can make no forward force. Anti-lift in braking is affected by the side-view link angles, however. If
the lower links are horizontal and the upper links slope upward at the front, the rear suspension has
pro-lift in braking. This is not necessarily a serious problem, but we can have some anti-lift, and still
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have any desired roll steer and geometric anti-roll (roll center height), if we make the lower links
slope upward toward the front.
LARGE VS. SMALL TIRE AND WHEEL DIAMETER
I thoroughly enjoyed your article "Tall vs Short sidewalls" in the April 2007 issue of Racecar
Engineering magazine. In that article you discussed about the benefits of short sidewall tyres fitted
on larger diameter rims. So, you explained how beneficial (or not) would be a different
configuration of two wheels with exactly the same overall diameter. I would like here to enter
another parameter to the discussion. What about two wheels with exactly the same tire sidewall
characteristics but with different overall diameter? For example, let's say we have a 15" overall
diameter (not rim diameter) wheel (rim + tire) and a 17" overall diameter wheel. And now let's
assume that the sidewall characteristics of the two tires are exactly the same. Also the widths of the
two tires are the same.
Which one do you think will be more beneficial to overall handling? It is quite sure that we will have
two footprints of different shape (I am not sure if they will have a different area though).
I think that with the low wheel we will have a more round footprint shape, while with the tall wheel
the print will be more long and narrow. Do you think this will have any effect to the centroid of the
lateral force with consequences to pneumatic trail and aligning torque? What do you think?
15" and 17" are pretty small for tire outside diameters, but the question is really the same regardless
of what hypothetical sizes we might posit.
As with tire width, we need to define our basis for comparison, and this is not as straightforward as
one might suppose. Do we hold inflation pressure constant? Static deflection or tire vertical spring
rate? Do we assume identical tread compound? Do we compare fully optimized cases, which
probably implies different inflation pressures, static deflections, and tread compounds? One can
make a rational case for any of these approaches. In an actual design or modification situation,
availability of tires and compounds may constrain us. Since we are examining the principles here,
we will look at the question from a variety of angles.
What happens if we hold tire pressure constant? In theory, the contact patch should stay the same
area at a given load as the tire diameter increases, just as it should with increasing tire width.
However, with a wider tire, the contact patch gets wider and shorter. With a larger diameter, the
contact patch stays the same length and width. In both cases, the tire's static deflection decreases,
and its vertical spring rate increases, as we add size. In both cases, tensile loads in the carcass
increase. A tire is approximately round in section, so when its sectional circumference increases, the
hoop stresses acting transversely and radially increase. That increases cord tension when tire width
increases. A tire is also round in side view, so it also has hoop stresses acting circumferentially in
side view. As we increase pressure, we can measure the increase in diameter and circumference.
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This comes from the circumferential strain that goes with the circumferential stress. Tire unloaded
circumference is a measurement we commonly take, especially in oval track racing, to control tire
stagger. Road racers often ignore this measurement, but they shouldn't. You don't necessarily want
stagger on a road course, but you don't want to have it unintentionally. It is a bit harder to compare
tires of different dimensions at the same pressure, but we know that a larger-diameter tire has more
surface area for its pressure to act upon, and it therefore has to have greater cord tension at a given
pressure.
This means that the larger-diameter tire acts stiffer, at a given pressure, just like a wider tire does.
Therefore, we will probably end up running lower pressure in the larger-diameter tire. Then the
contact patch will get longer.
What happens if we set the tire pressure such that the larger tire and the smaller one both have the
same static deflection – say, ½"? Taking the questioner's 17" and 15" unloaded diameters as our
basis, for a 17" diameter a ½" static deflection theoretically gives us a contact patch 5.74" long. For
a 15" diameter, ½" static deflection theoretically equates to a 5.38" contact patch length. That's a
contact patch length ratio of 1.067, compared to a diameter ratio of 1.133. The contact patch length
does not quite go up proportionally to the diameter; it goes up by roughly half the percentage. ½" is
a fairly large deflection for a tire that small. The contact patch length in both cases is more than 1/3
of the tire diameter.
It turns out that for all reasonable diameters and static deflections, the amount of non-linearity does
not change much. If we doubled both the diameters, and calculated theoretical contact patch length
at ½" deflection, we still get a contact patch length ratio of 1.065 – not much change from 1.067.
Cut the deflection to ¼", and the length ratio becomes 1.064 – still about the same.
My conclusion is that within the range of diameters and static deflections we are likely to consider
for a particular car, contact patch length for a given static deflection has a surprisingly linear
relationship to outside tire diameter: the contact patch length ratio stays at about .94 times the tire
diameter ratio. The percentile increment of contact patch length gain remains roughly half of the
percentile increase in diameter.
Using the simplifying assumption that, for constant contact patch width, contact patch length is
simply inversely proportional to inflation pressure, the 17" tire should need only 1/1.067 times as
much pressure and should have about 1.067 times the contact patch area, for the same static
deflection and vertical spring rate. At this somewhat lower pressure, it will have around 1.062 times
the side-view circumferential hoop stress and around 1/1.067 times the sectional circumferential
hoop stress – meaning that overall cord tension and tire rigidity should be similar despite the reduced
pressure.
More contact patch, similar rigidity; that looks good. Of course, there is a weight penalty, just as
there is if we widen the tire. But overall, the bargain looks surprisingly similar.
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One might think there would be a disproportionate penalty in rotational inertia, since the mass of a
larger-diameter tire not only is greater, but also acts on a larger radius of gyration. However, a
larger-diameter tire also turns at a lower rotational speed for a given road speed, and rotationally
accelerates at a lower rate for a given longitudinal acceleration. The linear speed at the tread of any
tire has to be approximately equal to the road speed of the car. Correspondingly, the linear
acceleration of the tread has to be approximately equal to the linear acceleration of the car. So the
rotational inertia penalty is roughly proportional to the weight gain, but not significantly greater.
There is a further weight penalty in the wheel. This is somewhat variable depending on wheel
design, but in most cases it's safe to say that we add more weight to the wheel center and rim by
increasing the wheel diameter than we add to the rim by increasing the width.
As a broad generalization, it is probably true that we can increase the contact patch area more
weight-efficiently by adding width than by adding diameter. However, the difference is not
dramatic, and there are advantages to using diameter. One big advantage is that when we add
contact patch area by adding diameter, the tire does not become more camber-sensitive, as it does
when we add width. There is generally an an advantage in resistance to aquaplaning when we go tall
instead of wide, and better performance in snow.
Depending on how we play other tradeoffs, with a taller tire we may very well be able to run a softer
and/or hotter-running tread compound.
As for self-aligning torque and pneumatic trail, if the contact patch is longer, those will increase.
The centroid of lateral force should move rearward in the contact patch, at least for moderate slip
angles. It should also move forward more as the tire approaches the limit of adhesion, increasing
self-aligning torque falloff as the limit of adhesion draws near. Whether that improves steering feel
or not is a matter of driver preference and the design of the rest of the car.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
MORE THOUGHTS ON ZERO-DROOP SETUPS, AND RELATED OVAL TRACK
SPRING SPLIT ISSUES
In the February 2007 newsletter, I responded to a question regarding zero-droop setups. These are
setups where the suspension is not allowed to have any droop travel from static position. I said that
these were bad for everything except controlling ground clearance in order to have consistent
aerodynamic ground effects. As a result of further reflection, and conversation with a number of
people, I have concluded that there is another benefit.
That benefit is that when the car is in a rolled condition, the inside wheel pair has greater pitch
resistance than the outside wheel pair. This has effects similar to left-stiff spring splits on an ovaltrack car. The car de-wedges when accelerating rearward while also accelerating laterally, and it
gains wedge when accelerating forward while also accelerating laterally. That helps the car get itself
rotating in yaw on entry, provided the driver is decelerating or braking while entering, and helps it
put power down on exit.
This would apply to a car with zero-droop setup at both front and rear. If only the front is zerodroop, effects would be confined to corner exit.
This benefit does come at a price in the wheels' ability to follow bumps, but if the surface is smooth
enough, it may be worth it.
A similar effect, but more subdued, can be had by making the wheel rate increase in droop, either
using rocker geometry or using snubbers. Note that this does not mean that the spring load or force
increases in droop; it means that the force decreases at a greater rate with respect to droop
displacement, as droop displacement increases.
A third way of creating a rising rate in droop is used on dirt Late Models, and could also be applied
to road racing cars, although I have yet to hear of it being tried for road racing. This third way is to
have two springs stacked on top of each other on a coilover, separated by a slider. The slider is
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arranged to top out against an adjustable collar on the coilover threads, at some point as the
suspension extends. This adjustable collar has a smooth sleeve above the shoulder that the slider
seats against. This provides a smooth surface for the slider to ride on, and protects the threads.
These devices are usually used on the left front in oval racing.
The rate increase occurs in a single step. It would be possible to create two smaller steps by using
two sliders and three springs, but I have never seen this.
Elsewhere in oval racing, one still often encounters the erroneous belief that the way to tighten the
car (add understeer/reduce oversteer) on exit is to use a right-stiff front spring split. This belief
stems from misunderstanding of the relationship between spring rate and spring force, in a situation
that causes an extension displacement of the spring.
To understand this sometimes confusing concept, imagine a car on the drag strip, with the
suspension on the left front wheel locked solid (spring rate effectively nearly infinitely large). When
the car launches, the locked suspension will be unable to extend, and it will be quite easy to lift that
wheel off the ground, while the right wheel, whose suspension can extend, will stay on the ground.
All load remaining on the front wheels will be on the right front, and the car will have more than
50% of its weight on the right front and left rear.
The more we increase the spring rate, the more closely the suspension approximates a locked
condition. The greater the spring rate, the more the load increases with compression, and the more
the load decreases with extension. Consequently, a stiffer inside front spring increases load on the
outside front and inside rear tires, and tightens the car (adds understeer) on corner exit.
HIGH OR LOW PANHARD BAR?
Can you discuss the advantages and disadvantages for various heights of Panhard bar? For
example, on my stock car, I could run the Panhard bar as high as 12½", or I could run it as low as
10¾". In either case, I could get the car balanced by changing the combinations of springs,
crossweight, etc.
In many cases, there is an additional variable: rear anti-roll bar stiffness. In many stock car classes,
rear anti-roll bars are now prohibited, but they are still used in the top NASCAR divisions, and in
many stock-car-related road racing classes. So we have at least four variables that play off against
each other: Panhard bar height, springs, diagonal percentage, and anti-roll bar if allowed.
To start off, let's take a simple case: we are considering whether to use a high Panhard bar on an
oval, or stiff rear springs. The high Panhard bar with softer springs will ride two-wheel bumps
better. It may or may not ride one-wheel bumps better. That depends on how flexible the tire
sidewalls are. The higher Panhard bar creates more lateral tire scrub on one-wheel bumps. If the
tires have a lot of lateral flexibility, (e.g. dirt tires with tall sidewalls, running low pressures) that
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may not matter a great deal. If the tires are stiff laterally (e.g. low-profile road racing slicks, as on a
Trans Am car), it matters more.
On the other hand, if we are seeking rear downforce, we may opt for stiffer springs, and accordingly
a lower Panhard bar. The stiffer springs will keep the rear end of the car higher, resisting the
influences of banked turns and aerodynamic downforce. The higher dynamic rear ride height will let
air out from under the car better, and get the spoiler and rear deck up into the airstream more.
The higher rear ride height will also add some drag. If we're running Daytona or Talladega, that may
matter more than downforce, and we may want the rear to squash down as much as possible. In that
case, we want softer springs, and a concomitantly higher Panhard bar.
Another difference relates to torque wedge: the tendency of driveshaft torque to load the right front
and left rear tires under power. A higher Panhard bar, with softer rear springs, gives us more torque
wedge. A lower Panhard bar, with stiffer springs and/or anti-roll bar, reduces the effect.
In general, torque wedge is our friend in a left turn, and hurts us in a right turn. Therefore, for road
course work, we want to minimize the effect. Especially with low-profile tires that have stiff
sidewalls, we will want a really low rear roll center, and plenty of rear anti-roll bar.
As for diagonal percentage (right or outside front plus left or inside rear tire load, as a percentage of
the four-wheel total), for oval track applications this plays off against both geometric roll resistance
(Panhard bar height) and elastic roll resistance (springs and anti-roll bars). We can run more
diagonal percentage, and balance this with increased rear roll resistance (or decreased front roll
resistance) from geometric or elastic sources, or we may run less diagonal percentage, and
correspondingly less rear roll resistance relative to front roll resistance.
The key to finding a good combination here is getting the car consistent as track conditions vary. A
setup with relatively little diagonal percentage tends to go loose on slick surfaces and get tighter as
grip improves. This is the most common pattern. A car with high diagonal percentage may go tight
on slick instead. In my experience, it takes considerably more than 50% diagonal to get a stock car
to do this. Somewhere between these extremes is a combination that changes its handling balance
relatively little as grip levels vary.
Additionally, a car with ample static diagonal percentage and relatively great rear roll resistance
tends to be tighter on both entry and exit, and freer in the middle of the turn, than one with a
combination using less static diagonal.
The reason for both of these effects is that static diagonal is a starting point for load transfer and
does not change with lateral acceleration, while roll resistance balance affects the way dynamic
diagonal percentage varies with lateral acceleration. A setup with ample static diagonal and ample
rear roll resistance has relatively great dynamic diagonal when cornering force is moderate (low
grip; entry and exit) and relatively little dynamic diagonal when cornering force is great (high grip;
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mid-turn), compared to a setup with less static diagonal and a less rear-stiff roll resistance
distribution.
It will be apparent that this is a complex game, and there is no one-size-fits-all solution, especially
with the wide variations in driver preference. But when we understand how the variables interact,
we improve our ability to tailor the setup to the driver and the track, and to keep the car more
consistent as conditions change.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
IS IT BAD TO LIFT A WHEEL?
After watching the new NASCAR Car Of Tomorrow (COT) run on some short tracks and then at the
Sonoma road race it certainly appears that the NASCAR teams have some real development to do.
The Sonoma road race certainly illustrated what I would consider a real problem with the COT and
that is the very radical lifting of the inside front wheel during heavy cornering.
The three wheeling was not incurred by going over curbs, it was the classic three wheeling very
similar to a dirt car with lots of cross weight and plenty of traction and torque. The lifting of the
inside wheel was especially evident in the 8-9 turn complex where the car was carrying good speed
and especially coming out of turn nine, which is a flat sweeping left hander, many cars would carry
the inside front, left wheel, to the point that they had to brake for turn 10. Some cars would carry
the wheel 4-6 inches off the ground. Of course once they braked for 10 the left wheel, which is now
going to be the outside wheel in 10, would regain contact with the track and of course it is not
turning so there would be a pretty good "unsettling" of the car before it was set into turn 10. I think
that the drivers are using third gear for this series of turns so there is pretty good torque available
as they exit turn 9. Having run sports cars at Sonoma back in the '80s, I remember that we did not
do anything related to side to side weight distribution and we ran our cars with pretty much 50/50
side to side weight. Although Sonoma is a clockwise track and is predominantly right hand turns we
found that trying to bias weight to the right side of the car would adversely affect the car in the left
corners and we ran the "carousel" at that time which was a very long, high speed, down hill
sweeping left turn onto a good straight so the right side weight was not the thing to have in this
corner. NASCAR does not run the carousel so it is highly possible that right hand weight would be a
advantage in the track configuration that NASCAR runs. I am not sure if it is legal to run lots of
inside weight on the COT.
At the short tracks that they have been running these cars on, you can also see the cars lift the inside
front wheel as the power is rolled on exiting a turn, which I am sure is very much assisted by cross
weight jacking trying to keep the inside rear planted for a good drive off the corner, but at Sonoma
the cars could and would carry the inside wheel in both right and left hand corners.
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I have always believed that poor chassis stiffness in torsion is a major contributor to "three
wheeling" and looking at the COT chassis it certainly doesn't appear to be well braced for torsional
loads. What are your thoughts on the COT as to its attribute of going onto three wheels while
corning. Causes, and possible fixes???
It is not necessarily bad for a car to lift the inside undriven wheel.
Ideally, we would like to use all four tires equally at all times. This would involve not only having
all four wheels driven, but also having the c.g. at ground level. That's impossible, of course.
With only two wheels driven, and the inevitability of lateral load transfer, we have to make some
compromises. The nature of these compromises varies depending on the rules, the track, and our
overall design and setup strategy.
If the rules impose the same tire size limit on all four wheels, cornering speed is moderate, and
aerodynamic lift or downforce is negligible, we get best steady-state cornering with around 50%
static rear weight, and similar overall roll resistance at both ends of the car. In this situation, we
should not lift a wheel. To win a moderate-speed skidpad competition, we might want such a setup.
However, a road race is not a skidpad test. On most road courses, most of the turns are of modest
duration, and are separated by significant straightaways. In this situation, when cars are nearly equal
in power, the race is won on the straights, but the straights are won in the turns. That is, it becomes
very important to have good turn entry and exit speed, and late braking points. The brakes also have
to last through the race, which is a big factor in Cup cars on a road course. To make the car brake as
well as possible, and put power down as well as possible, we need as much static rear percentage as
possible. This costs us some steady-state lateral acceleration, but it gains us longitudinal
acceleration, both forward and rearward. It also saves the front brakes, which are normally the ones
that give out first, because optimum rearward acceleration will be achieved with less front brake bias
than we would otherwise use.
To make a tail-heavy car corner neutrally with equal-size tires at both ends, the front end has to
absorb the greater part of the lateral load transfer. When such a car is accelerating hard both
laterally and forward, it my very well lift the inside front wheel. This does not necessarily mean the
setup is bad. It means that some lateral acceleration has been sacrificed to increase forward
acceleration.
The COT has front and rear clips that are designed to be more deformable in a crash than was the
case in the old cars. That probably does cost some torsional rigidity as well. However, if anything,
low torsional rigidity makes a car less prone to wheel lifting, at least for a given suspension setup.
This is largely academic, because with a less rigid frame we will normally run more front roll
resistance; we will have to, to get the same wheel loads. If we are comparing flexible versus stiff
frames, with equal dynamic wheel loads, there will be little or no difference in tendency to lift a
wheel.
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One thing that does affect the tendency to lift a wheel is the c.g. height, and here there is a
substantial difference between the old car and the COT. I hear that the COT has a center of gravity
fully two inches higher than the old car. I have a hard time understanding where that much
difference could come from, but certainly the roof is higher by that much, and I understand the frame
rails are at least somewhat higher.
Once the front end reaches 100% lateral load transfer, any further increase in roll moment can only
be reacted at the rear. Consequently, the car has much less angular roll resistance beyond the point
of wheel lift, and any further increase in lateral acceleration produces a relatively large increase in
roll angle, with a correspondingly greater amount of daylight visible under the inside front tire. It
often becomes quite difficult to carry the wheel just a little.
I understand that at Sonoma, a car spends about three times as many seconds accelerating rightward
as it does accelerating leftward. That would mean a right-heavy weight bias would be advantageous.
However, I doubt that it's legal.
It's not easy for people not on a team to get NASCAR rule books. They are normally only sent out
to people getting a NASCAR license, and the rules are subject to revision and interpretation in midseason. I do know a person who works on a Busch team that started out as a Cup team, and he has
the Cup rules as they existed at the beginning of the season. At that time, there was a minimum left
side weight for the old cars on clockwise road courses, but none for the COT's. As of the start of the
season, the old cars had the same minimum weight for the left side on road courses as for the right
side on ovals: 1625 lb., without driver, out of a minimum total of 3400, without driver. COT's have
to have 1650 right side out of 3400, and there is no rule specified for road courses.
Evidently, the plan at that point was to have the old cars run the road races, and that got changed.
With 200 lb. of driver weight, distributed 50 lb. right/150 left, an old car would have 49.3% left for a
road course. If the COT is required to have 1650 left for a road course, it would be exactly 50% left
with driver, based on the same assumption for driver weight. Actually, the driver sits slightly closer
to center in the COT, but there wouldn't be any possibility to make the car markedly right-heavy.
One thing that would make the car carry the inside front wheel more readily, and higher, in left turns
is torque wedge: the effect of driveshaft torque on the chassis. This tries to roll the car to the right,
unload the left front and right rear, and load the right front and left rear.
HOLLOW VS. SOLID ANTI-ROLL BARS
I have a question about sway bars. I’m looking to upgrade the OEM bar set on my 2001 Pontiac
Trans Am, and with all the different manufacturers out there that produce many different
diameters/grades, there also is the issue of a solid vs. hollow sway bar. Do you have any
recommendations on this? I'm sure weight is definitely a reason for hollow but my question is, is the
performance of a hollow bar close to that of a solid one?
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For the same outside diameter, a hollow bar is softer than a solid one. A hollow bar can provide the
same stiffness as a solid one, with less weight, but the outside diameter has to be bigger.
Other things being equal, a hollow bar has higher stresses than a solid bar. If the bar is short, or the
arms are short, in some cases the bar needs to be solid to avoid stress levels that would cause the bar
to take a permanent set or fatigue prematurely. Short of this point, there is some reduction of
longevity with a hollow bar. The bars on a Trans Am go all the way across the car, and have long
arms, so hollow bars should work fine.
To give you some idea of what diameter you'd need with a hollow bar to equal a solid bar, if you had
a factory rear bar 5/8" in diameter, a ¾" O.D., .060" wall hollow bar would be about the same
stiffness. A ¾" O.D., .090" wall bar would be about 30% stiffer.
If you have a 1 1/8" solid front bar, then a 1 ¼" O.D., .156" wall hollow bar, or a 1 5/16" O.D., .120"
wall hollow bar, would be about the same stiffness. A 1 3/8" O.D., .120" wall bar would be about
20% stiffer.
If you buy bars by an advertised rate in lb/in at the arm end, be aware that there are two ways of
expressing this rate, and not all manufacturers use the same convention. The more common method
is to rate the bar like a ride torsion bar. That is, one end is moved a known linear amount and the
force per inch is computed. This gives you rate in pounds per inch per end pair: the force when each
end moves half an inch, meaning there's an inch difference between the two ends. Some
manufacturers prefer to double this figure to get the cataloged value. This method gives you the rate
in pounds per inch per end: the force when each end moves an inch, meaning there is 2" difference.
This method has the advantage of being easier to equate to a change in ride spring rate. Neither
method is more correct than the other, but you do need to know which method a manufacturer uses,
if you want to make comparisons based on rate.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
DROOP-LIMITED REAR SUSPENSION
I have a question for you, and it's related to something I recently discovered on my race car, and
something that you've been talking about a lot lately - droop limiting.
My car is a Mustang with a strut front, 3-link in the rear, 3100#, 400+rwhp, 275 DOT race radials
all around, etc.
In a search for lots of bump travel I made some changes to the upper (chassis side) shock mounts in
the rear. When my shocks arrived, I never noticed that they were shorter than I thought, and I ended
up with a car that has less than 1" of droop travel in the rear. For reference, the car is relatively
softly sprung (400# wheel rate in front, 300# wheel rate in the rear) and uses lots of travel with a
relatively high CG (about 17" or so).
I was wondering how you thought this lack of droop travel might affect handling? Under braking?
Into and through a corner?
I can say this with certainty: when the inside rear suspension tops out, the rear roll resistance
increases dramatically, and that makes the car looser (produces oversteer). I cannot say with any
certainty when this is happening with a particular car. Data acquisition is very useful for
determining this. (The questioner here is an engineer with a NASCAR team, but the question
concerns his own personal race car. Presumably he will not be allowed to borrow team data
acquisition gear for his own races. He didn't mention whether he has his own.)
If the 3-link rear is set up for moderate anti-squat and anti-lift, and the springing is fairly soft, it is
highly probable that the car tops out the inside rear shock when trail-braking. I would also expect
that the shock would top out in steady-state cornering.
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It is possible to have so much anti-squat in a beam axle rear suspension that the suspension tops out
under power, even when the car is running straight. It is not uncommon to see this in dirt cars, even
with as much as four inches of droop travel. I do not recommend this, but I see it when I go to races.
It is also possible to have so much anti-lift that the rear suspension compresses rather than extending
in braking.
With a simple three-link rear, ample anti-squat implies fairly ample anti-lift. This does not mean
that the car necessarily compresses the rear suspension in braking if it extends it under power. The
percent anti-lift in braking will generally be considerably less than the percent anti-squat under
power, because the rear tires have to provide all of the propulsion force, but only about a quarter of
the retarding force. If the questioner's Mustang were set up to actually lift the rear under power, the
rear suspension would very probably still extend under braking. It would be possible to have a
situation where the only time the rear suspension wasn't topped out would be when there was little
forward, rearward, or lateral acceleration.
This is probably academic, because in general road racing cars are not set up with extremely severe
anti-squat.
With the more complex suspensions sometimes used in dirt cars, it is possible to have a lot of antisquat and also have severe pro-lift in braking. I really do see dirt modifieds and Late Models that
appear to lift the left rear to the droop limit most of the way around the track. The left rear only
comes down momentarily when the driver is transitioning from power to braking at the end of the
straights.
SATCHELL LINK REAR SUSPENSION
How do you calculate the roll center for a Satchell link rear end?
For readers unfamiliar with the Satchell link suspension, it is a form of triangulated four-bar linkage
for a beam axle. This family of systems use diagonal semi-trailing links to provide lateral location
of the axle, rather than purely lateral links such as a Panhard bar.
The most common version of triangulated four-bar, sometimes called the Chevelle style, has two
upper links that are angled around 45 degrees in plan (top) view, and two lower links that are closer
to parallel in plan view. The upper links are further apart at the front than at the back. Their
centerlines converge at a point above and behind the axle center section. The lower links converge
to a point well ahead of the axle. The two convergence points, or instant centers, define an
instantaneous axis of rotation, about which the axle moves in roll. The roll center height is the
height at which this axle roll axis intercepts the axle plane: the vertical, transverse plane containing
the axle centerline.
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Note that this is not the midpoint height of the axle roll axis, or the point midway between the instant
centers, which at least one author has suggested should be taken as the roll center. Indeed, as we
will discuss, there are cases where no such midpoint can be defined.
It is also fairly common to see this system used upside down. When a low roll center is desired, it is
possible to have the lower links converge toward the axle center section rather than the upper links.
The Satchell link system is basically a Chevelle system, turned upside down and back-front, or
turned upside down by rotating it about a transverse axis rather than a longitudinal one. That is, it
has lower links that attach to the axle near its outboard ends and come close together near their front
ends. The upper links also attach near the outboard ends of the axle, and are either parallel or close
to parallel in plan view.
Finding the roll center is the same as with other triangulated four-bar systems. Find the instant
centers for the lower and upper link pairs, define a line connecting these, and find the height at
which this line intercepts the axle plane.
There are cases where the link centerlines will have no intersection. Even if they do at static
position, they won't in a rolled condition. Generally, the link centerlines will pass over and under
each other when the suspension has some roll displacement. In such cases, the best approximation is
to find where the lines cross in plan view, and then find a point midway between them in height. In
other words, find where the lines have the same x (longitudinal) and y (transverse) coordinates, and
average their z (vertical) coordinates for those points.
It is also possible for one pair of the links to be parallel in plan view. They then will not cross at all
in plan view. The axle roll axis then passes through the instant center of the non-parallel links
(lowers in a Satchell link), and has a side view inclination parallel to the side view inclination of the
links that are parallel in plan view (uppers in a Satchell link). If those links do not have the same
inclination, we take an average of the two. Note that in this case we have only one link instant
center to work with, and it becomes impossible to define a midpoint between two instant centers.
If both upper links in a Satchell system are horizontal and parallel, the roll center is at the same
height as the lower link instant center. However, if the uppers are not horizontal and parallel, the
roll center height is different from the lower link instant center. As the car moves in ride, the roll
center stays about the same height from the ground if the upper and lower links have similar side
view projected length. This is important, because the front roll center in most independent front
ends moves up and down with the sprung mass, though not necessarily the same amount as the
sprung mass. If we supposed that the roll center is at the lower link instant center in the Satchell
system, that might lead us to suppose that we'd have better compatibility with an independent front
suspension than we have with more conventional triangulated four-bar systems. Unfortunately, that
turns out not to be so. However, the system is no worse than conventional triangulated four-bar
designs in this regard.
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We also do not escape the interrelatedness of roll steer, anti-squat, and geometric anti-roll, as some
have suggested. But again, this aspect is no better or worse than in other triangulated four-bar
systems.
Advantages and disadvantages of the Satchell system mainly come down to packaging and load
paths, both in the axle and in the frame. Whether we gain or lose in those regards will depend on the
particular installation.
A WORD FROM THE INVENTOR
After I originally mailed this newsletter, I received a note from Terry Satchell, who originated the
suspension bearing his name. He contributes some interesting background on the history of the
design and his views regarding its advantages. He writes:
…I had done a Lotus Super 7 type rear for a Trans Am car where the lower A-arm has a pivot under
the axle with two upper longitudinal arms. After running it for a year we kind of got the impression
that the rear roll center was too low, it being at the pivot of the A-arm to axle joint. Since I had
designed four bar link rear axle suspensions for General Motors for several years, I knew how to
analyze them and create what I wanted. I wanted a geometry with a roll center basically midway
between the bottom of the axle housing and drive axle centerline. By reversing the lower arms to
converge to the center ahead of the axle I was able to achieve a good geometry. It worked well on
the track, and in fact one of the neat parameters was that the anti-squat increased on the inboard
wheel with roll giving a tightening effect on power that helps corner exit.
I did a version of this geometry for Herb Adams who did all of Walker Evans truck suspensions and
they were very happy with it. They in particular liked the anti-squat difference across the back with
roll on throttle for their Stadium racing trucks.
Since then I have done several versions for various disciplines and now there is a company in
Pennsylvania that provides aftermarket conversions for Mustangs, Camaros and Firebirds to get rid
of the leaf spring suspension and use this four bar link with coilovers.
I have also had success with several of the "Locost" builders using it. [The Locost is a kit car
similar to a Lotus 7.] One in particular used it to control his deDion beam.
Just thought you might like to know a little more of the story.
By the way, I never intended to put my name to this version of a four link. Herb Adams named it in
one of his books and that is how it got started being call the Satchell Link.
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I'd like to thank Terry for his contribution, and also mention that he was the person who taught me
the right way to determine the front-view and side-view projected control arm geometry in
independent suspensions.
I concur about the roll center height, and the desirability of having more anti-squat on the inside rear
wheel than on the outside rear.
In fact, this latter property is a characteristic of most trailing arm rear suspensions, including
independent ones that use trailing arms. Strictly speaking, in the case of independent systems, we
usually have less pro-squat on the inside wheel with roll, and more pro-squat on the outside wheel,
rather than anti-squat as such. However, the effect on roll and on wheel loads is similar: the
difference in longitudinal "anti" produces an outward roll moment, or pro-roll moment, in the rear
suspension that adds wedge to the car – adds load to the inside rear and outside front wheels.
It is a bit risky to generalize about this subject purely on the basis of general suspension type.
Exceptions can be found to most such generalizations, and the dynamics of any actual car will
depend on the specific design of that car.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
WHAT EXACTLY ARE SHAKER RIGS FOR?
Over the past few years I have seen and heard about all of the developments with 4-post, 5-post, and
7-post shaker rigs. However, it seems that most articles focus on the technology employed by the
latest and greatest rig rather than what type of results the rig is going to yield. My question is this,
when teams test on a shaker rig, what exactly are they going to get in return in terms of results (i.e.
lateral and longitudinal G forces or something else)? Also, maybe even a better question, what is it
they are testing for (i.e. is there a way these rigs measure “grip” in particular) and what type of
testing regiment is going to be employed? For instance if you are a team that is on a limited budget
and can only afford to put your car on the rig once per year, do you put the car through a generic
set of accelerations and simulated corners or do you try and tune for something more specific or
maybe even a particular track? And lastly, at the end of the day how do you know what was the
better setup (if there isn’t a way to measure “grip” specifically)?
Shaker rigs are an example of street driving improving the breed for racing. They originated in
passenger car development, and were later applied to race cars. The original objective was to
explore the car's response to excitation at the wheels, in a more controlled and observable situation
than could be achieved on a test track. Improving handling wasn't the main goal. Engineers were
more concerned with isolating frequency-sensitive effects that would impact durability and noise,
vibration, and harshness (NVH). Does a portion of the roof or the floor pan resonate at a certain
frequency? Are there brackets or ducts that buzz or might break? Does anything rattle? At what
speeds and frequencies do the wheels "dance", and does this agree with calculated natural
frequencies?
Early shaker rigs had posts only under the wheels, and the sprung mass was allowed to do whatever
it wanted to do in response to excitation at the contact patch. It soon became apparent that it would
be more desirable to allow the contact patches to float both laterally and longitudinally, so that the
track and wheelbase could vary with suspension movement, without having tire scrub fight the
movements. A fifth post attached to the sprung mass allowed the car to be anchored horizontally
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while all four contact patches could float. The car still needed either an anti-rotation feature in the
fifth post, or some other mechanism, to constrain the car in yaw.
This was good for replicating highway driving, but it was impossible to explore suspension behavior
in conditions of sprung mass displacement caused by aerodynamic loads, banked turns, or pitch and
roll due to longitudinal and lateral acceleration. To reproduce these displacements, three posts were
attached to the sprung mass. Conveniently, three posts also constrain the car in yaw, without any
additional devices. With this addition, it is possible to reproduce any combination of suspension
displacements that the data acquisition system may have recorded on-track, or that an engineer might
imagine.
Importantly, this does not mean that the rig reproduces all the forces acting on the suspension. The
posts only move vertically. The rig cannot apply or reproduce any horizontal forces. It also cannot
measure any horizontal forces. Therefore, we cannot measure grip at all. We also cannot reproduce
loads and frictional influences in the suspension that result from horizontal forces at the contact
patches. We do not even know vertical wheel loads with any accuracy, because horizontal forces at
the contact patches affect these.
This last phenomenon is particularly significant in stock car rear suspensions, and in any suspension
with large geometric "anti" effects. (Stock car rear suspensions, and most beam axle suspensions,
have ample geometric anti-roll.) With formula cars, where there is modest anti-roll and anti-pitch,
the wheel load values on the 7-post are closer to reality, but still not highly accurate.
I am referring here to individual wheel loads. On the rig, we do get reasonably accurate total loads
for all four wheels, and for the left, right, front, and rear wheel pairs. It's the loads for individual
wheels and for diagonally opposite pairs that are inaccurate.
Even though we do not read accurate individual wheel loads on the shaker rig, we can get a
reasonable comparative evaluation of how much these loads vary dynamically in the excitation
conditions that we test. What we are after is minimum load variation. We cannot measure grip
itself, but we do know that variation of normal load is bad for grip, and minimizing such variation
will improve grip.
This is true for two reasons. First, if the tires unload for any significant length of time, the car is
limited by whatever grip the tires have at that load. If the grip limit at that load is exceeded, the car
will break traction, and once traction is broken it is hard to regain. A slide, once initiated, tends to
persist.
Second, even if we are dealing with load variations over small time spans, so that vehicle inertia
masks the intervals of low load and grip, we do not fully recover during the highly loaded periods
what we lose in the minimally loaded periods. Why? It's our old friend, load sensitivity of the
coefficient of friction. Adding 100 pounds of load doesn't help as much as losing 100 pounds of
load hurts.
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So we try different combinations of shock valving and springing, and we try to minimize load
variation at the wheels.
I was asked recently how you valve shocks based on suspension displacement traces provided by
data acquisition. I had to reply that I don't know of any way to do that, and I don't know anybody
who claims to be able to do that. However, with the use of a 7-post rig, we do at least have a means
to make gains by trial and error.
There is another kind of test rig that does let us look at the effects of horizontal forces at the contact
patches. It's called a kinematics and compliance tester, or K&C rig. Until recently, only passenger
car manufacturers had these, and nobody was offering testing by the day or hour to racers. There is
now a K&C facility available to the motorsports community, just up the road from me in Salisbury,
NC. It's called Morse Measurements. The people who run this facility are friends of mine, so I'll
give them a plug. They are at www.morsemeasurements.com or 704-638-6515.
What the K&C rig does is grab hold of the frame of the car, and then apply horizontal loads at the
tire contact patches. The sprung mass can be kept from moving, and the changes in wheel loads
measured that way. Alternatively, the sprung mass motion can be controlled to keep the total normal
force at the contact patches constant and we can measure the displacements and load changes that
result. Roll and pitch moments are applied to the frame, based on an input sprung mass c.g. height.
Individual wheel horizontal forces are applied based on estimates, which in turn are based on tested
or estimated tire properties and calculated wheel loads.
We then see from the test results whether our estimated wheel loads approximate those produced in
the test, and we may want to adjust our contact patch forces and do another iteration on the rig.
There are other tests on the K&C rig as well, including simply cycling the car slowly in heave
through its suspension travel and measuring the camber changes, contact patch scrubs, and wheel
loads, with the contact patches allowed to float horizontally so that all horizontal forces at the
contact patches are eliminated. This test can be done on either a K&C rig or a 7-post, so it can be
used to compare the agreement of the two types of rig.
What the K&C rig does not do is move the chassis fast. The 7-post can load and move the chassis at
racing speed, but only up and down. The K&C can load and move the chassis in all directions, but
only slowly. At this writing, there is no test rig that moves and loads and measures a car in all
directions at once, at realistic on-track speeds. And even the low-speed testing done on the K&C rig
uses estimated or assumed grip levels at the contact patches.
We do have a test that does measure grip: the skid pad. It measures average grip over a lap, by stop
watch, or over smaller intervals, using accelerometers or other sensors. Of course, we have
difficulty observing the car during testing, because the car is in motion rather than on a test rig. And
the grip measured is only on a particular surface, on a particular radius.
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We thus have three useful methods of testing, all of which provide useful comparative
measurements, but none of which allows us to fully replicate track events in a controlled
environment. I could even say we have four methods, if we include wind tunnels, or a much larger
number if we include component testing devices such as tire testing machines, shock dynos, and
engine dynos. But so far we have no device that really puts the car through its paces in a manner
that replicates in full what happens on the track, on a stationary platform where we can safely watch
and measure it. The best we can do is look through a number of windows, each of which affords a
view from a different angle, and use our mind to try to put these glimpses of reality together.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
ON THE MARCH AGAIN
A few months ago I was asking you two questions, and you have been very helpful! New question:
with my Formula 2 March 712 at Dijon (France) I have on 2 corners at the beginning and end of
main straight in 3rd gear. In these turns I have UNDERSTEER and I feel I have to try first with
stronger aft spring or with stronger aft ARB, not only to worsen the grip in the rear but also to
improve the grip in the front.
I am also considering wedge adjustment. Is it also useable on road circuit like we have in Europe or
just for ovals? How about if I put more corner weight on the LH aft and or RH fwd wheel – or is this
a bad compromise?
Before I get into answering the main question here, I thought I'd pass along some information
submitted by reader Robert Koch.
You were helping a person who drives a March 712. In 1972 und 1973 I worked on such a car in
Switzerland. This car was very softly sprung. It had a very soft chassis which meant that increasing
the anti-roll bar or the springs the chassis just flexed. Now the reason why I am writing you: the
March 712 racecar had two weak points. One of them was the inserts in the back wall of the
monocoque where you fasten the tubular frame with the engine and the transmission. They are not
such that they live a long time. One has to replace them quite often. The problem is, you do not see
that they are loose! Point 2 is: the upper squared-tube where the differential and/or the gearbox is
mounted cracks on the underside, close to the two points where the springs are mounted. This is also
something you do not see just like that.
It is important to make sure you eliminate any problems like these, rather than tune around them. I
would also make sure the rear wheel pair is not aimed to the left or the right. Both rear wheels
should generally have the same toe-in relative to the vehicle centerline. Also, make sure that both
rear tires are the same size. Measure their circumference with a tape measure.
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Looking at a track map of Dijon (see http://en.wikipedia.org/wiki/Image:Circuit_Dijon-Prenois.png),
I see that the first of these turns, called Courbe de Pouas, or Turn 8, is the largest-radius one on the
track, and therefore probably the fastest. The one at the end of the straight, Double-droite de
Villerois, or Turn 1, is a slower one, but not really slow. Both appear to be double-apex turns. Turn
1, as its name suggests, is really a double-right, with two fairly small-radius segments joined by a
markedly larger-radius segment. Turn 8 has a short, somewhat tight-radius segment at its entry,
followed by a large constant radius over most of its length. The circuit is run clockwise, so most of
the turns are right-handers. There are only two left-handers of any significant duration.
The main straight, called Ligne Droite de la Fouine, connecting turns 8 and 1, is long. From the
map, its length must be well over half a mile – perhaps a kilometer, perhaps three quarters of a mile.
The back section of the circuit is almost all turns. There are four straightaways, but none of them is
anywhere near the length of the front straight. So the questioner is correct that speed in these two
turns, especially exit speed from turn 8, is important to lap time.
For a course like this, I don't generally advise a wedged setup, at least not as a starting point. I do
advise a right-heavy setup, for cars that have ballast, which the questioner's car probably does not.
Cars with flexible frames or sprung structures do respond to suspension adjustment. They just
respond less to a given adjustment than cars with good torsional stiffness. You need more change in
the springs and bars to get a given change in dynamic diagonal percentage or in cornering balance.
You need to put more turns into the spring seats to get a given change in static diagonal percentage.
When attacking a handling problem that occurs only in certain turns, I always advise looking for
characteristics in those turns that are not shared with the turns where the problem doesn't show up.
If the problem shows up in fast turns but not slow ones, that points to a problem with aerodynamic
balance. If the car has understeer only at high speeds, that is best cured by adding front downforce,
or reducing rear downforce. In some cases the rules will prevent us from making the changes
required to achieve this, but it is the best approach when we can do it.
If the car has understeer only in right turns, and the car is to all appearances symmetrical, that points
to an alignment problem, or something loose or flexing that only affects turns in one direction. A car
designed for road racing shouldn't act different in right and left turns, if the wheel alignment is
symmetrical, the right and left springs are identical, the right and left tire sizes are the same, and
there are no other asymmetries. If it does act different in right and left turns, we can crutch that by
running more or less than 50% static diagonal, but chances are that we are tuning around some other
problem that we have yet to discover.
I do recommend running some negative wedge (usually meaning less than 50% on the right front and
left rear) on live-axle road racing cars, especially for courses with lots of right turns. This
compensates for the effect of driveshaft torque on wheel loads. However, this would not apply to a
rear-engined formula car with independent rear suspension.
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RADIAL TIRE CAMBER
I have just started racing an MG Midget. The weight is about 50/50 front/rear and at present it runs
8in crossply slicks all round. Front is basically double wishbone and the rear is a live axle with
Panhard rod.
I have considered running radial tyres but have been told that I would need a lot more negative
camber (at present about -1 deg).
As far as I can tell most modern (up to F1) cars seem to run quite a lot of negative on the front but
little if any on the rear.
So, do radial slicks need more negative camber than crossplies, and if so, why? If it is needed on the
front why not the rear (though difficult with a live axle!)? With a live rear axle and a lot of negative
on the front, wouldn't the rear be relatively lacking in grip?
It is not necessarily true that radials always want more negative camber than bias-plies, but it is valid
as a generalization. Many racing radials are not truly radials, because the sidewall plies do cross
each other, although not at as great an angle as in true bias-plies.
It is very common to see more than a degree of static negative camber on independent systems of all
kinds, on bias-plies or radials.
Why do radials tend to want more camber? Mainly, I think because the sidewalls are more flexible.
This makes them tolerate more camber, and want more.
If the tires want more negative camber, and you can only get this on the front, will the car tend more
toward oversteer? Maybe. Remember, your independent front suspension allows the front camber
to change with roll, while the rear beam axle produces no camber change with roll (except a bit due
to tire deflection). Most independent suspensions provide some camber recovery in roll, but
generally not 100%, because this would create excessive camber change in ride. You may currently
have a degree of negative at the front statically, but that would mean you barely are keeping the
outside tire upright, if that, once the car has reached full roll in a turn.
In any case, if you find you have more front grip compared to rear grip with any new tire or front
camber setting, but the new tire or setting gives better overall grip, stay with the new tire or setting
and work with the roll resistance distribution to get the balance back. If the car oversteers, the
proper fix is to add more roll resistance at the front, or take some away at the rear, using springs and
anti-roll bars.
Why do you see so much negative camber at the front on F1 cars, and so little on the rear, even
though the car has independent suspension at both ends? I don't know. I can say with certainty that
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this helps propulsion and hurts braking. It may be that the engineers have decided that forward
acceleration out of the turns is worth more than rearward acceleration at the ends of the straights.
Rules permitting, I would be tempted to ask the tire supplier for bigger front tires, and run them at
less camber, or add more camber at the rear.
A RADICAL RADIAL NOTION
Instead of relying on low profile tyres with short sidewalls for handling response, why not utilize
high profile types (for good surface following capability) and employ internal bracing to resist
lateral loads introduced by cornering? One scheme would be to have tension cables or “strings”
running from the bead to the intersection of the tread and sidewall on the opposite side of the tyre.
That is, tension members would be diagonally disposed relative to tread plane. The system would
look analogous to a wire wheel but be inside the tyre itself. Such a tyre would have a high sidewall
for good ride and terrain following capability but would also be stiff laterally. Would this work?
I do think this would increase lateral stiffness, and maybe increase response, while maintaining
vertical softness. My worry would be that the tire would act more like a bias-ply with respect to the
tendency to lift or unload the inside portion of the contact patch. In a conventional radial, the tread
can move laterally relatively freely, yet stay planted relatively flat while doing so. I would think the
cables or strings would tend to lift the inside shoulder instead.
Another concern might be damage to the cables when mounting the tire. Two-piece rims might be
necessary to overcome that.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
INS AND OUTS OF TOE AND ACKERMANN
Your comments regarding Ackermann, or anti-Ackermann, or perhaps why bother with Ackermann,
would be appreciated. It occurs to me that the more heavily loaded outside front tire must operate
at a larger slip angle than is possible for the opposite unloaded front while cornering. The result is
that the lightly loaded tire is pulled sliding across the pavement not doing much work. I assume it is
reasonable to distinguish between the slip angle of a tire which is being deflected by cornering
forces and one which is sliding. Would it be more efficient to use front roll stiffness to completely
unload the inside front during hard cornering? Does Ackermann aid turn in? Would antiAckermann provide an advantage? Is it possible that toe out in combination with anti-Ackermann
might be effective? Is the turning angle of the front wheels in most hard cornering racing situations
so small that Ackermann is not a factor? What are your thoughts?
For the benefit of newbies, Ackermann effect is a property of steering geometry that causes the front
wheels to toe out as steering angle increases. If the front wheels toe in as steering angle increases,
that is called negative Ackermann or anti-Ackermann. If the toe angle does not vary with steering
input, that is zero Ackermann, or parallel steer.
Ackermann effect must not be considered in isolation. The tires do not know what kind of
Ackermann properties the steering system has. They only know how much they are toed in or out, at
a particular instant. How much the wheels are toed in or out at a particular instant depends on a
combination of Ackermann effect and static toe setting.
Additionally, there can be toe changes due to bump steer or compliance steer. For simplicity, we
will disregard these effects here.
The static setting provides a starting point when the steering is centered, and Ackermann effect adds
toe-out from there, in a fixed relationship to handwheel (steering wheel) angle.
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Trouble is, the optimal toe angle in terms of tire performance is not a constant, nor does it have a
fixed relationship to handwheel input. Unless we are prepared to engineer some sort of elaborately
programmed steer-by-wire system that controls the right and left front wheels independently, we
cannot obtain optimal geometry for all possible situations. We are stuck with striking a compromise
for a particular set of conditions.
The nature of that compromise depends in part on how much extra slip angle we wish to give the
outside front wheel. One can reasonably argue that the more heavily loaded wheel reaches peak
cornering force at a greater slip angle than a more lightly loaded one, so the front tires achieve the
greatest peak cornering force when the outside tire has a greater slip angle than the inner one.
The questioner asks whether there is a difference between slip angle of a tire that is sliding and slip
angle of a tire that is not sliding. More precisely, we might talk about a tire that is only partially
sliding, in the rear portion of the contact patch, and one where sliding is occurring in the entire
contact patch. There is no difference in the definition of slip angle; it is simply the angular
difference between the tire's instantaneous direction of travel and its instantaneous direction of aim:
the difference between its bearing and its heading. However, there is a difference in the effect of
adding slip angle in the two cases. If the tire is below the slip angle where its lateral force peaks,
adding slip angle adds lateral force and also adds drag. If the tire is above the slip angle where its
lateral force peaks, adding slip angle does not add cornering force and indeed probably reduces it.
However, up to slip angles associated with total loss of control, drag continues to increase as we add
slip angle.
One thing that makes all this a bit complex is that when a tire is near its peak cornering force, lateral
force greatly exceeds drag force, yet moderate slip angle changes have a fairly small effect on lateral
force, but a relatively large effect on drag force. This makes it difficult to evaluate the effects of toe
changes on cornering capability, purely by observing changes in car balance or amount of
understeer.
Drag forces at the tires do not turn the car in the sense of accelerating it laterally, or centripetally
(toward the center of the turn), but they do tend to steer the car: accelerate it in yaw, or rotate it.
This means that it is possible to have a case where we are adding moderate amounts of cornering
force at the front by increasing outside tire slip angle, yet the steering trace and the driver feedback
may show increased understeer, and the car may be slower! In such a case, we can, at least in
theory, dial a bit of oversteer in by juggling tire load distribution, and then we may have a slightly
faster car than we started with. The only way to know is to try this rather than immediately backing
up on the toe or Ackermann change.
We have so far been assuming that what we're after is the highest peak cornering force. We get that
if both tires are at their optimum slip angle for lateral force at the same time. However, one could
also make a case for having the tires not peak together, to make breakaway gentler and make the car
more driver-friendly. This is somewhat analogous to the question of whether to tune the engine's
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exhaust and induction systems for the same rpm, to get the highest peak power, or tune them for
different speeds, to spread the power band.
Is this complicated enough yet? We're just getting started.
Suppose we have sufficient information to decide what slip angles we want on the two front tires, or
what difference we want in their slip angles. Does that allow us to say what our toe-out or toe-in
should be at a particular instant? Nope. Without knowing the geometry of the car and the turn, and
without knowing what the rear wheels are doing, we can't even get close.
For simplicity, let's suppose we don't want any difference in the inside and outside tires' slip angles.
Let's take a look at what it would take to get that, in various situations.
Some readers will be familiar with the concept of a turn center. This is the point about which the
car's center of mass or c.g. (sometimes approximated as the midpoint of the car's centerline in plan
view) is instantaneously revolving, as it negotiates the turn. If the car has a constant attitude angle –
that is, if it is drifting or sliding a steady amount – all points on the car are moving about the turn
center.
At any given instant, the car has an instantaneous direction of travel, which is always a tangent to its
path of motion. If the car is traveling in a curved path, that path has an instantaneous radius r. This
radius is equal to square of the car's instantaneous speed along its instantaneous direction of travel,
divided by its centripetal acceleration: r = v2/a. In a totally unbanked turn, with the tires sliding only
a little, these two quantities are approximately equal to the car's speed as read by a speedometer or
wheel speed sensor, and the car's lateral acceleration as measured by an on-board accelerometer. (If
the turn is banked, or the car is sliding dramatically, these approximations become much poorer.)
If, in plan or top view, we construct at the c.g. a perpendicular to the car's instantaneous direction of
travel, and define a point on that line a distance r from the car's center of mass in the direction of the
turn, that point is the turn center.
In the car's frame of reference, the turn center can be anywhere from the rear axle line to well ahead
of the front axle line. (It could even be behind the rear axle line, if the rear wheels have a negative
slip angle. This could occur when negotiating a banked turn at low speed. Normally we can ignore
this case when studying behavior at racing speeds.)
The simplest situation is a small-radius turn, taken so gently that tire slip angles are negligible. In
this case, the turn center is on, or very nearly on, the rear axle line in plan view. For zero slip angle
at both front wheels, the front wheel axes should ideally meet in plan view at the turn center. That
implies that the front wheels will have substantial toe-out.
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The larger the turn radius, and the larger the rear wheel slip angle, the further forward the turn center
moves. At some point, the turn center will lie on the front axle line in plan view. In this situation,
we have equal slip angles on the two front wheels when the toe-out is zero.
In high-speed, large-radius turns, the turn center is usually ahead of the front axle line. We now
have a condition where the front wheels need to be toed in for the slip angles to be equal.
As a broad generalization, the front wheels are steered more in small-radius turns than in large ones,
and the turn center is further rearward in the car's frame of reference. This argues for having at least
some Ackermann in the geometry, but it is harder to come up with a general rule to calculate exactly
how much.
In high-speed turns, steering inputs are generally very small, and consequently Ackermann effect has
far less influence than static toe setting. Ackermann has greatest influence in autocross and hillclimb
cars.
Does Ackermann aid turn-in? Basically, yes, and so does static toe-out, at least up to a point. Really
excessive toe-out, whether from static setting or Ackermann, will hurt front grip and the effect will
reverse, but within a sane range, turn-in will at least feel quicker with some toe-out. This is partly
due to the early yaw moment from inside front tire drag as the handwheel is first turned.
Does using anti-Ackermann along with static toe-out make sense? It's certainly done successfully,
on winged single-seaters on high-speed ovals. Logically, however, it makes more sense to use static
toe-in with positive Ackermann. This is conventional practice in passenger cars.
What about completely unloading the inside front wheel using front roll resistance? Well, it does
make Ackermann academic, at least during the time that the wheel actually is airborne, and it
eliminates any concerns about tire drag due to the front tires fighting each other. Unfortunately, in
many cases using that much front roll resistance will create excessive understeer.
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WELCOME
Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers.
This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights
into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr.,
Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by
e-mail to: mortiz49@earthlink.net. Readers are invited to subscribe to this newsletter by e-mail.
Just e-mail me and request to be added to the list.
MORE EXOTIC VEHICLE LAYOUT IDEAS
Thanks for an interesting commentary on the diamond car recently. That certainly has had me
thinking. Below are some topics I've been pondering.
Another unusual race car
Following up on the diamond shaped car, I came across another unusual car. This one is a special
based on a Mazda Familia hatchback. The original car had four-wheel drive and was powered by a
transverse mounted engine and gearbox assembly. The engine was a turbo four (of 1.8 litres I think)
with a five speed manual box. The box drove all four wheels via a “central differential”. The car
was modified by moving the original engine/gearbox and front wheels rearwards. Another
engine/gearbox (this time an automatic gearbox) assembly was mounted ahead of it. This powered
an extra pair of road wheels up front. The car became a six wheeler with all wheels driven! The
front four were steered. The car is reported to need more development work but has been successful
on dirt and hill climbs, outperforming V-8 competitors on occasion! It is a good handler and fast
with plenty of traction.
I’d be most interested in reading your analysis of this type of vehicle.
A second type of six-wheel car I’ve thought about is one with only the front four wheels driven. In
this case the plan would be to use a pair of front wheel drive engine/gearbox/suspension/road wheel
assemblies mounted at the front of the car. The two power trains would operate independently of
each other. All four front wheels would be steered. It may be necessary to use a balance beam
linkage in the steering to ensure that the front wheels on each side of the car developed similar
lateral forces whilst cornering. The final pair of wheels at the rear of the car would be un-powered
and non-steering, as is normal for front wheel drive vehicles.
I am aware of various attempts to use independent power-trains in four wheel vehicles. Famous
examples include the Twinnie Minnie, which had an engine at each end. VW tried this for the Pikes
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Peak hill climb, as did Monster Tajima in his Suzuki at the same venue. There are some interesting
handling issues to be tamed with this type of system (where there are no links between the two
power-trains). VW used traction control and an early form of throttle by wire. In the end Monster
added a shaft linking his two engines via a computer controlled electro-magnetic clutch. The
Twinnie and various replicas of it have encountered some handling problems, which appear to be
solvable, or at least made controllable by careful engine tuning and modification to engine response
and power delivery characteristics. Still there are questions about the ultimate handling behaviour
on the limit with this type of set up.
In the case of the six wheeler with only the front four wheels driven it may be that these problems are
not present since the driving wheels are close to each other and not at opposite ends of the car.
What is your analysis of these set-ups?
In most classes of racing nowadays, we don't have the option of more than four wheels, or more than
one engine. For the most part, the rules prohibit such things. Nonetheless, there are scattered
venues where one can at least run such vehicles for fun, and it is fascinating to consider the
possibilities.
One fundamental argument against using a larger number of anything is that, as a rule, two little
ones weigh more, cost more, and take up more room than one big one. This applies to engines,
cylinders in the engine(s), and wheels. That doesn't mean that adding a component is always a bad
idea, but there has to be a compelling functional advantage in adding anything to the car, to override
this disadvantage.
Multiple engines are usually used for one of two reasons: either the engine in question is small, and
using two of them is an economically appealing way to build an all-wheel-drive special, with muchneeded additional power, or the vehicle is really large, as with land speed record cars, and highoutput engines of sufficient size are either unavailable or unaffordable.
Until recently, controlling two unconnected engines driving the front and rear wheels was a real
problem. Perhaps with the advent of by-wire controls, this can be overcome, and potentially even
turned into an advantage. The question is, who is going to invest the money to do this, when the car
is ineligible for any big-money racing class? Not only do we need to appropriately control the
power and rpm of the two engines, we also have to make the two clutches take up in sync with a
single pedal or other control, and make both transmissions shift in sync from a single lever or other
control.
If we are talking about two identical engines, with unconnected two-wheel-drive transaxles, driving
the front and rear wheel pairs, we have a 50/50 torque split front to rear, and no connection between
the front and rear wheels. This means that unless the car is severely nose-heavy, the front wheels
will tend to spin prematurely in hard forward acceleration. Either the driver will have to lift to
control front wheelspin, or, if we have traction control, the power of the front engine will have to be
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suppressed, meaning we are not making full use of that engine. If we do make the car sufficiently
nose-heavy so both engines can deliver full power, that will compromise cornering and braking.
Linking the two transaxles with a driveshaft and some form of clutch allows some transfer of power
from the front to the rear, but requires the front and rear wheels to be constrained to the same rpm at
the traction limit, which compromises handling – unless we use different final drive ratios at the two
ends, which would bring a whole set of new problems, chiefly in transmission control and rev limits.
Adding such a mechanism to two existing two-wheel-drive transaxles also involves a lot of expense
and special parts, which erodes the original economic appeal of using two cheaply available
economy car powertrains.
All things considered, if we are designing from a blank sheet of paper (or screen), it is probably
more appealing to have one large engine, with one transmission, and, if we want to drive all the
wheels, to control torque distribution with the differentials and clutches or other locking devices in
the drivetrain. Fundamentally, we have fewer parts, no synchronization issues, less metal, and an
easier time getting the torque distribution we want.
It is desirable not only to have the power, or at least a preponderance of it, go to one end of the car, it
is desirable that this be the rear end. One advantage of rear wheel drive in terms of car control is that
it affords us some measure of independent steering control at both ends of the car. This allows us to
create yaw accelerations, and control the car's attitude, with the rear wheels, even when the front
wheels are at the limit of adhesion. With front wheel drive, we have two ways of controlling the
front end, but nothing except perhaps the brakes to control the rear. If we wish to drive all the
wheels, it is desirable, at least in a high-speed road or road racing car, to make the car throttle-steer
somewhat like a rear-drive car.
If we are designing a front-engine car with all wheels driven, and we want to have a back seat and a
reasonable overall length, we will have somewhere between 50 and 56 percent of the weight on the
front wheels. To make the car throttle-steer controllably, we want at least 60% of the torque to go to
the rear wheels. If we are designing a pure performance car, it is better to choose a rear-mid-engine
layout, which will typically give us around 60% static rear weight. If nothing else, this layout gives
us better braking and less yaw inertia than a typical front-engine layout. We then want somewhere
in the range of 75 to 90 percent of the propulsion to come from the rear wheels.
There is a definite advantage in driving the front wheels, even if they receive a small percentage of
the power. It may not be obvious, but we always have to drive the front wheels, particularly while
cornering. When the front tires are running at an appreciable slip angle, they are generating
significant drag, which must be overcome. This uses power, which must be supplied somehow. In a
pure rear-drive car, the power to drive the front wheels is delivered from the rear wheels via the road
surface. That means that this portion of the car's power passes through the contact patches, and uses
up a portion of the tires' friction circle or performance envelope. If we power the front wheels, even
moderately, by some other means, we have more grip available for cornering. This explains why
cars with all wheel drive perform as well as they do, even in pure cornering, despite their inherent
weight penalty.
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The basic front/rear torque split is generally established by a planetary center differential. The
planet carrier is driven in some manner from the transmission output shaft. The ring gear or annulus
drives the rear diff. The sun gear drives the front diff. The torque ratio is the same as the pitch
diameter ratio of the sun and annulus. If the planet gears are the same diameter as the sun, the
diameter ratio is 3:1. The torque split is then 25/75. To get a 20/80 split, the planets need to be 1.5
times the diameter of the sun. Planets twice the size of the sun yield a 5:1 annulus to sun ratio, or a
16.7/83.3 split. To get a 10/90 split, the planets need to be 4.5 times the diameter of the sun. To get
a 40/60 split, the planets need to be ¼ the size of the sun. It will be apparent that there will be
practical limitations precluding extremely unequal torque splits, or ones between 40/60 and 50/50.
(Actually, splits between 40/60 and 50/50 are possible, if we are willing to machine a conventionalstyle bevel gear differential with unequal-size side gears, cut with different bevel angles, and the
pinion gears cocked at an angle. Opposing pinion gears have to be on independent shafts, rather
than a common shaft running through the carrier.)
Usual practice is to design a drivetrain so that the front and rear pinion gears and propshafts run at
equal speeds when there is no wheelspin and the car is running in a straight line. This minimizes
wear on the center diff. However, it is possible to design the center diff to withstand having its gears
in relative motion most of the time, and have the propshafts run at different speeds.
Running the propshafts at differing speeds has two effects: first, the split in propulsion forces
changes, because we are using different ring and pinion ratios at the front and rear, and the torque
multiplication at these gear sets is correspondingly unequal. The end with the faster-spinning prop
shaft gets more power, for any given torque split at the center diff. Second, the car's response to
center diff locking devices changes. It is possible to have the rear wheels slipping or overrunning
the front wheels by a predetermined percentage when the center diff locks, rather than running at the
same speed. This allows us to tune the car's throttle-steering characteristics. Ordinarily, we would
arrange for the front propshaft to overrun the rear most of the time, and lock the center diff when the
propshaft speeds equalize, or when the rear one overruns the front by some amount.
With electronic control of the lockup, we really don't need to juggle the front and rear final drive
ratios. We can pretty much get whatever torque distribution and rear overrun we want, just with the
center diff and the lockup strategy. However, there is some effect on car behavior when the center
diff is completely or largely locked, even if the lockup is electronically controlled. With simpler,
passive, mechanical lockup devices, juggling the front and rear final drive ratios offers some
interesting possibilities.
For example, it would be possible to set up the ratios so that the front propshaft overruns the rear by
30%, and add a roller clutch that locks the front propshaft to either the planet carrier or the annulus
whenever either of these tries to overrun the sun gear, but freewheels the rest of the time. That
would allow the driver to spin the rear wheels enough to throttle-steer, but prevent runaway rear
wheelspin. Front to rear propulsion force ratio short of lockup would be sun/annulus ratio, times the
ratio of front final drive ratio to rear final drive ratio, times the ratio of rear tire effective radius to
front tire effective radius.
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Another possibility is to drive the front wheels hydrostatically or electrically, rather than
mechanically. This could be a way of powering the front wheels very modestly, with far less
hardware and more attractive packaging. One way would be to use a small gear pump, perhaps one
stage from a dry sump pump, as a motor on each front wheel. These might be driven by a similar
pump at the transmission, and the circuit might include a cooler for the fluid. It might also include a
relief valve that would limit pressure to the motors.
It would only be possible to transmit small amounts of power this way, but we could eliminate or
reduce the power otherwise transmitted through the contact patches to overcome the drag of the front
tires when operating at a slip angle. If we can do that, we get the main cornering advantage of
mechanical all-wheel drive, with a smaller weight penalty.
Hydrostatic motors and pumps are available in a wide range of sizes. However, power losses in
hydrostatic drive systems are high, so transmitting large amounts of power hydrostatically is not an
attractive proposition for a high-speed vehicle.
Electric drive, as used in locomotives, offers some of the same possibilities as hydrostatic drive,
although it cannot be made a part of a transmission cooling circuit. Also, electric motors are more
delicate than a gear motor, so mounting them outboard is probably not a good idea. Electric drive
does lend itself nicely to computer control of torque distribution.
Mounting both motors and brakes inboard offers some interesting advantages. Inboard brakes do
add weight and cost, and they occupy space. So does the ducting required to cool them. However,
inboard brakes do offer advantages not commonly recognized. Everybody knows they save
unsprung weight. But additionally, they make it easier to get balanced airflow to both faces of the
rotor, reducing the rotor's tendency to dish as it heats up. Potentially, they allow a larger rotor
diameter, at least in some cases. This is particularly true in low-built race cars, where the floor
hangs below the wheel rims. Finally, they allow relatively unobstructed airflow through the wheel.
In a full-bodied car, this greatly increases the effectiveness of the wheel openings as ducts for
extracting under-car air.
Inboard front brakes do require beefy halfshafts. The torque transmitted can easily be as great as
that transmitted by the rear wheels under power, even in a tail-heavy car, and the consequences of
shaft or joint breakage are really nasty.
Either electric or hydrostatic drive to the front wheels offers the possibility of integrating the front
drive system with an energy recovery system.
So much for the pros, cons, and nuances of driving more than two wheels. What about having more
than four wheels on the vehicle?
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In the case of tires, more rubber generally gives us more grip, at a penalty in speed on long
straightaways, for reasons I have discussed in previous writings. We are limited, however, by our
ability to keep a wide tire upright enough to use the full width of the tread. As the tire becomes
really huge, suspension packaging can become problematic. So can steering geometry, in the case of
a front wheel. Frontal area of the tire increases in direct proportion to width, or height, with a
corresponding aerodynamic drag penalty. If there is standing or streaming water on the road surface,
a wide tire is more prone to aquaplaning. If we are going to have to deal with snow, a wide tire is a
disadvantage because of the greater force required to move it through the snow.
So there are reasons to consider having two small tires in line with each other, instead of one big
one, or perhaps two big ones in line with each other to provide twice as much tire, or some
compromise in between.
Two strategies immediately present themselves: double the number of wheels, and use eight, or
make the car heavy at one end, and use four at the heavy end and two at the light end.
Those who have studied Formula 1 history will recall the Tyrrell P34 6-wheeler of 1976, which had
the extra wheels at the light end. The idea there was to use much smaller front tires than usual, and
reduce aerodynamic drag. This required special tires. Conventional, large tires were used at the
rear. The reasoning was that the airflow was so disrupted by the time it reached the rear wheels that
small tires there would not return as much benefit. Also, it is easier to add more non-driven wheels
than to create the hardware to have more driven ones. The Tyrrell actually won The Swedish Grand
Prix that year. In fact, the team got a 1-2 finish.
Because rear grip was essentially the same as a conventional car, there was no benefit in exploiting
the potentially greater front grip from the four front tires. F1 cars of the time already cornered with
the inside front very lightly loaded, so there was little room for adding more front roll resistance to
use enhanced front grip to help the rear end stick. Consequently, the advantage of the design was
mainly aerodynamic, and this came at a penalty in weight.
Shortly following the Tyrrell effort, March built a 6-wheeler the more obvious way: four rears, all
driven. The transaxle was an adapted Hewland, with no center differential. The car was tested but
never raced. March was in financial straits at the time, and development was lacking. In 1979, a
retired March F1 car with the 6-wheel setup achieved considerable success in British hillclimbing.
There was also a similar car built by Williams in 1982, which likewise was never raced. After this,
the FIA banned all four-wheel-drive systems from F1.
It would be possible to have four rear wheels and only drive two. The car wouldn't throttle-steer as
one might hope, and propulsive traction would be poor, but it might be possible to get good lateral
acceleration numbers that way, and perhaps better braking than with four wheels.
6
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The idea of using four front wheels, and driving the frontmost pair from a separate engine, with a
automatic transmission, is interesting. One drawback would be that the torque distribution would
vary in a largely uncontrolled manner, because the torque multiplication at the automatic would not
have a constant relationship to the torque multiplication in the manual transmission. The two
transmissions would have differing ratios and wouldn't shift at the same time.
The questioner asks about steering four front wheels, and wonders about using some form of balance
bar. I don't think a balance bar is appropriate for the steering. All four wheels need to have a fixed
relationship to handwheel position. I think Tyrrell got it about right. As I recall, they steered the
frontmost pair of wheels from a rack and pinion in the usual manner, and ran a drag link back from
each of these to the wheel behind it. It would be normal practice to make the second wheel pair steer
a bit less than the first. This could be considered a form of Ackermann effect. For conventional, or
positive, Ackermann effect with four front wheels (i.e. to optimize for a turn center behind the front
wheels), the second pair of wheels should steer less tha