An Introduction to the Vehiclemetrics HVE Vehicle Database

An Introduction to the Vehiclemetrics HVE Vehicle Database
An Introduction to the Vehiclemetrics HVE Vehicle Database
Ron Jadischke, Joe McCarthy, John McCarthy and Dwayne Ellis
Vehiclemetrics/McCarthy Engineering Inc.
HVE is a vehicle dynamics and collision simulation
package that utilizes mechanical and geometric models
of vehicles to conduct an analysis. There are various
modules within the HVE simulation package that allow
the user to conduct a simulation of either vehicle
dynamics and/or a collision. HVE currently has a good
vehicle database with approximately 200 vehicles.
Time constraints limit not only the ability to create but
also the number of vehicles that can be created by
Engineering Dynamics Corporation (EDC). There are
also a number of mechanical parameters that are not
measured. These result in the simulation models either
containing some “generic data” or not utilizing some
data fields. The basis for the generic data has
previously been published (Siddall, Day, 1996). The
addition of DamageStudio into HVE has placed more
emphasis on an accurate vehicle geometric model.
Therefore, it is desirable that the number of vehicle
models in the HVE program increase, including more
modern vehicles.
Vehiclemetrics is compiling a new vehicle database for
use in HVE to increase the number of vehicles for use
in HVE drastically. The procedure currently used by
EDC for building vehicle geometry, as well as various
input mechanical parameters for the vehicles, has been
published by Garvey (2000) and Day (1995) and is also
presented annually at the HVE Forum. The goal of this
paper is not to repeat a discussion of the various input
parameters. Rather, it is to present not only an
overview of the process that Vehiclemetrics uses to
generate vehicle interior and exterior geometry but also
a mechanical property dataset for use in HVE. We
have highlighted areas where Vehiclemetrics’ method
and EDC’s method differ.
The intent of the
Vehiclemetrics vehicle database is to supply modern
vehicle mechanical datasets that are vehicle specific
and, in turn, minimize the use of generic data. At this
time, all vehicle parameters cannot be measured within
budget constraints, and notes are made regarding
planned areas of improvement and future research
The most up to date measurement equipment and
software are being utilized to acquire data for
mechanical and geometric models of vehicles. The use
of this equipment allows for efficient testing and
subsequent model creation. This paper summarizes the
procedure for the creation of geometric models and
mechanical parameters needed for building the HVE
vehicle database file.
The following general parameters are recorded through
a vehicle inspection:
Vehicle class
Body style
Similar vehicles (Sisters & Clones)
Vehicle Identification Number
Date of manufacture
Odometer reading
Driver position
Number of axles
Gross axle weight rating – front
Gross axle weight rating – rear
Gross vehicle weight rating
Fuel level
Numerous photographs are taken of the vehicle. These
photographs aid in the subsequent creation of the
vehicle geometric models. Specific photographs are
also taken of the vehicle’s rim for use as texture maps
in the HVE vehicle model.
Wheelbase and track width of the vehicle are also
measured with a 4-wheel alignment system utilizing
three imaging cameras to provide real-time 3D
measurements. The data from the 4-wheel alignment
system is used for establishing the four wheel positions
in the vehicle model.
During the processing of the laser scan data, the axis
co-ordinate system is set to the centre of gravity of the
vehicle (positive X – forward, positive Y – right side,
positive Z – downward). Once the laser scan data has
been acquired and processed, the geometric surface
topology of both the interior and exterior is created
using commercially available modeling software. All
surface topology is modeled using four-sided polygons
for better and more predictable sub-division and/or
tessellation. A semi-uniform grid spacing of the foursided polygon method is also used for more uniform
crush computations within DyMESH (Figure 1). The
polygon count targeted for the current exterior
modeling process is approximately 6000 to 7000
polygons. This is greater than the current count
typically used by EDC (approximately 4000 polygons);
however, based upon our tests, we have not
experienced a significant increase in simulation times.
As a quality check, a comparison of the modeled
geometry versus our laser scan is completed (Figure 2).
The three-dimensional vehicle geometry is acquired
using a laser scanner. Multiple scans of the vehicle are
taken to acquire the geometric data for both the interior
and exterior of the vehicle. Trunk or cargo space, the
engine compartment, suspension/brake assemblies, and
the vehicle underbody are also scanned but are not yet
utilized in current vehicle models. Based upon the
scan data, the following dimensional specifications are
Front overhang
Overall length
Overall width
Overall height
Ground clearance
Track width
Frontal area
Side area
Figure 1: Typical vehicle in the HVE Environment
Figure 2: Comparison of HVE Model to Point Cloud Data
texture mapping for the vehicle body; however, this
option could easily be implemented into vehicle
geometric models if the program is modified in the
future (Figure 3).
The photographic documentation taken during our
initial inspection of the vehicle also allows for texture
mapping of various vehicle features and/or the entire
vehicle exterior. Currently, HVE does not accept
Figure 3: Texture Mapped Vehicle in the HVE Environment
The CGz height is then calculated using the following
Equation 3 (Milliken, 1995, p 669).
The vehicle mass data gathered during our vehicle
inspection includes:
𝐶𝐺𝑧,𝑡𝑜𝑡𝑎𝑙 =
The total mass at each wheel position.
The three-dimensional Centre of Gravity
(CG) location of the vehicle.
The unsprung mass at each wheel position.
The mass of a tire and rim.
𝐶𝐺𝑦,𝑡𝑜𝑡𝑎𝑙 =
𝑊𝑅𝑟 𝑡𝑟
�𝑡𝑓 −
+ 𝑟𝑡𝑖𝑟𝑒
[rearward of front axle] (1)
�𝑡𝑓− 𝑡𝑟 �
𝑊𝑡 ×tan 𝛼
To assess the unsprung mass at the wheel, we utilize a
quarter vehicle model (Figure 4), as summarized by
Tsymberov (1996), and a commercially available
suspension analyzer.
The total vehicle mass and CG location in the X and Y
is determined by simultaneously measuring the force
below each wheel using four wireless scales. The total
vehicle mass is the sum of the mass at the four scales.
The CGxy location is calculated by using the measured
total mass, wheelbase, and track width(s). The CGx
and CGy locations are computed as indicated in
Equations 1 and 2 (Milliken, 1995, p. 666-670) below:
𝐶𝐺𝑥,𝑡𝑜𝑡𝑎𝑙 = 𝑊𝐵 − 𝑊𝐵 ×
𝑊𝐿𝑓 �𝑡𝑓− 𝑡𝑟 �
[right of centre line] (2)
Figure 4: Quarter Vehicle Model
For this testing procedure, each individual wheel is
oscillated vertically from a frequency of 25 Hz to 0 Hz.
The wheel hop natural frequency2 is determined from
the suspension test (Milliken, 1995, p. 240), and the
total unsprung mass at each wheel is calculated by
using Equation 4. We also remove one wheel from the
vehicle and measure the mass.
The CGZ (height) is measured by raising the rear axle
of the vehicle. The front wheels are located on slip
plates to allow the vehicle to translate rearward and
eliminate the introduction of horizontal forces. The
vehicle is raised under the unsprung mass to prevent
suspension sag. 1 The inclination of the vehicle varies
depending on the wheelbase of the vehicle. The
vehicle typically undergoes a total change in
inclination of 6 to 9 degrees in this test. Reaction loads
at the loaded wheels (front), angle of the raised vehicle,
wheelbase, and tire rolling radius, along with various
other parameters, are measured/monitored throughout
the test.
𝑓ℎ𝑜𝑝 =
𝑚𝑈 =
𝑘 +𝑘
� 𝑡𝑚 𝑠
Solve for 𝑚𝑈
𝑘𝑡 + 𝑘𝑠
�2 × 𝜋 × 𝑓ℎ𝑜𝑝 �
Wheel hop is the minimum contact force between wheel and ground
during suspension test.
If excessive suspension sag occurs, the rear wheels are placed on fabricated
aluminum boxes.
The above method of calculating unsprung mass is
different from the method utilized by EDC. Currently,
EDC utilizes the following assumptions for the
calculation of unsprung mass:
The suspension parameters primarily consist of data
relating to the springs (coil, leaf, or torsional springs);
the anti-roll bar (auxiliary roll stiffness); and the shock
absorbers at each wheel. We conduct tests to:
If the wheel has independent suspension, then
the mu is assumed to be mwheel (mtire + mrim).
If the wheel location has a solid axle, then the
mu = maxle/2 + mwheel.
HVE uses the CG height of the sprung mass and the
unsprung mass from its vehicle models to perform
calculations. To approximate location of the sprung
mass and unsprung masses, we utilize the equations
presented by Milliken (1995, p. 671-673). This
methodology assumes the height of the unsprung mass
is located at the wheel centre and the lateral location of
the sprung mass is at the tire centre line. The equations
we use to calculate the CGsprungmass are appended for
reference. EDC uses these same equations.
Measure the wheel centre rate,
Measure the tire rate,
Measure the auxiliary roll stiffness, and
Estimate the damping rate at each wheel.
Wheel Centre Rate and Tire Rate
HVE does not use actual “spring stiffness” or geometry
to transfer the load from the contact patch to the coil
spring. Instead, it utilizes the wheel centre rate and the
tire stiffness. The “wheel centre rate” is the vertical
force per unit of vertical displacement of the wheel
relative to the chassis (Milliken, 1995, p. 581). To
obtain wheel centre rate measurements for the vehicle,
an automotive alignment lift equipped with slip plates
under the front and rear wheels is used. The vehicle is
raised above the lift by lifting under the vehicle chassis
until the suspension is fully extended and the wheels
are airborne (Figure 5a). The vehicle is then lowered
(through the rebound phase) until reaching its static
ride height (Figure 5b) and then compressed downward
(through the jounce phase) onto the lift (Figure 5c) by
pulling down on the vehicle chassis.
Commercially available equipment to undertake whole
vehicle inertial measurements are extremely costly and
currently outside the scope of our budget. Therefore,
we are utilizing the method being used by EDC to
estimate inertial properties, as described by Garvey
(2000), and through personal correspondence with
personnel of EDC. The method currently used is based
upon the National Highway Transportation Safety
Association (NHTSA) inertia database that was
previously published. 3 A curve fit of this data is
completed based upon the total vehicle mass. The
unsprung mass inertias are also currently calculated
based upon the same methods used by EDC.
Wheel inertia is a large component of the unsprung
mass inertia. A test apparatus has recently been
obtained to measure wheel (tire and rim) spin inertia,
and an additional test device is being developed to
measure wheel (tire and rim) steer inertia. We are
currently conducting research to assess alternative
methods of calculating or measuring vehicle inertia
(total vehicle and sprung mass inertia).
Figure 5a: Vehicle raised to full suspension travel
VIMPD Document, Accessed 2011.
(Figure 6).
The wheel centre rate utilized for the front
and rear wheels is an average of the left and right
Figure 5b: Vehicle at static ride height
Figure 6: Wheel Centre Rate
A similar analysis method is undertaken
approximate the static tire rate (Figure 7).
Figure 5c: Vehicle with suspension compressed
During the test, wheel movement relative to the chassis
and tire deflection are measured in conjunction with
the tire-ground contact force. The scales used to
measure tire contact force are placed on the unlocked
slip plates on the alignment lift. This allows the
suspension to move freely through its designed range
of motion. Wheel movement relative to the body is
measured with string potentiometers, and tire
deflection is measured using laser sensors.
Measurements are recorded incrementally throughout
the range of suspension travel. Wheel positions are
also measured with the 4-wheel alignment system
utilizing three imaging cameras to provide real-time
3D measurements.
Figure 7: Approximate Tire Rate
Full suspension travel distances are recorded. The
maximum rebound is assessed by measuring the travel
distance from ride height to full rebound with the
vehicle lifted off of the lift. For some vehicles,
compressing the suspension to full-jounce is not
possible. In these cases, the travel to suspension stop
is measured. If there is no stop, the coil spring
dimensions are utilized to assess additional travel that
would occur until the coil spring bottoms out.
The wheel centre rate in HVE is a linear approximation
of wheel load versus displacement of the wheel relative
to the chassis. Therefore, to assess the wheel centre
rate for the vehicle, a linear curve fit is created using
the collected data. The slope of the line represents the
vehicle’s wheel centre rate at each individual wheel
Alignment Data versus Jounce and Rebound
Jounce [cm]
During the wheel centre rate test, the wheels are
equipped with targets for use with the 4-wheel
alignment system. Changes in camber, toe, track
width, wheelbase, and other parameters are measured
through the travel of the suspension. The recorded
parameters are then used to create the following tables
for HVE:
Camber versus jounce/rebound,
Halftrack change versus jounce/rebound,
Roll steer versus jounce/rebound.
Figure 10: Toe versus Jounce/Rebound
Illustrations of an example set of data for a vehicle is in
Figures 8 to 10.
Jounce [cm]
HVE also accepts input data for anti-pitch versus
jounce/rebound. Currently, there is no test method to
assess anti-pitch versus jounce/rebound.
Auxiliary Roll Stiffness
Rebound [cm]
The auxiliary roll stiffness is assessed by placing the
vehicle on the alignment lift with a scale under each
wheel. The longitudinal centre of gravity is calculated,
and this location is marked on the vehicle. A hydraulic
jack is placed under the vehicle at the longitudinal
location of the centre of gravity on the passenger side
rocker panel. The jack is raised, inducing a roll to the
vehicle body. All of the wheels on the vehicle are free
to translate laterally on the slip plates as the vehicle is
lifted. Geometric measurements regarding body roll,
suspension travel, and load transfer are recorded.
Measurements are obtained at multiple angles of body
roll. The vehicle is then restored to its original
position, the front and rear (if equipped) anti-roll bar(s)
are disconnected at both ends, and the test is repeated.
The auxiliary roll stiffness is assessed by calculating
the difference between both tests.
Figure 8: Camber versus Jounce/Rebound
Jounce [cm]
Rebound [cm]
Rebound [cm]
The front and rear measured roll stiffnesses for a
vehicle are illustrated in Figure 11. The front auxiliary
roll stiffness utilized in our mechanical model is the
average value obtained from our front tests while the
rear auxiliary roll stiffness is the average value
obtained from our rear tests.
Figure 9: Half Track Change versus Jounce/Rebound
then the system is “critically” damped. If a system is
critically damped, there is no oscillation in the vehicle
body after being subjected to a force input. If a system
has a damping ratio greater than 1, the system returns
smoothly but slowly to its initial condition.
Tsymberov (1996) reports that typical damping ratios
of passenger cars are 0.2 to 0.4.
There are two methods currently available to assess the
damping ratio or damping rate at each wheel.
Use the phase angle and adhesion data from
the suspension tester (damping ratio is
II Solve the system of differential equations for
quarter vehicle model.
Figure 11: Auxiliary Roll Stiffness
The method we utilize is different from the current
method used by EDC. The auxiliary roll stiffness
values obtained in the above-described technique are
also compared to the values obtained by analyzing the
geometric installation ratio of the anti-roll bar and the
anti-roll bar physical measurements, as currently used
by EDC. An alternative comparative method is also
outlined by Milliken (1995, p. 592).
In each of these methods, we assume there is no
damping in the tire.
We have not yet determined which of the above
methods we will utilize for our database; however, the
data required for both methods are recorded and the
critical damping rate is also calculated.
Damping Rate
The above methods of assessing damping rate are
different from the current method utilized by EDC.
EDC assumes C = Ccr. Currently, vehicles in the
Vehiclemetrics database incorporate the same
assumption as EDC; however, these values will be
updated in a future release.
To assess the damping rate at the wheel, we utilize a
quarter vehicle model and the apparatus as summarized
by Tsymberov (1996). For this testing procedure, each
individual wheel is oscillated vertically from a
frequency of 25 Hz to 0 Hz. The oscillation frequency
and the load between the vehicle tire and suspension
tester is measured. Body-to-wheel and wheel-toground displacements are recorded using string
potentiometers and laser sensors previously used
during the ride rate test. Accelerometers are also
placed on the sprung and unsprung masses at each
wheel position.
The displacement data and
accelerometer data are recorded at 1000 Hz.
The vehicle is positioned on an automotive lift with
rotating slip plates positioned underneath the front
wheels. The steering assembly is rotated lock-to-lock
while measuring steering wheel angle (rotation) and
the independent front wheel (steer) angles. HVE
allows for the input of a single steering gear ratio
(steering wheel rotation/tire rotation) (deg/deg). The
collected data is plotted and a linear curve fit is
applied. A sample graph of the steering ratio test is
illustrated in Figure 12.
The input necessary for HVE is the damping rate (C).
The damping ratio (ξ) is defined as the amount of
damping in a system (C) divided by the critical
damping rate (Ccr). The critical damping rate is a
function of the spring stiffness and tire stiffness at the
wheel as well as the mass at that wheel.
If the damping ratio is less than 1, there is some
“overshoot” in the system. If the damping ratio = 1,
p = ptable, if ptable ≤ pproportioning
p = pproportion + η(ptable – pproportion), for ptable > pproportion
ptable = Ftable x R [kPa]
p = Brake system pressure at wheel [kPa]
Ftable = User input from “At pedal” table [N]
R = Brake pedal ratio [kPa/N]
pproportion = System pressure when proportion begins [kPa]
η = Proportioning ratio
The method we utilize to measure wheel brake force
versus brake pedal force is a roller brake tester.4 The
vehicle is driven onto a set of rollers where each axle is
tested in sequence. Electric motors drive individual
rollers for each wheel at 5 km/h. While the brake
pedal is applied, pedal force versus brake force at each
wheel is recorded until lock-up is achieved on a
friction surface with μ = 0.9. The brake force at each
wheel is measured independently. This test procedure
is repeated for each axle. Individual wheel drag values
are also measured with the vehicle in Neutral.
Drivetrain inertia can also be measured.
Figure 12: Steering Ratio
The Ackermann angle and error are also measured, and
the number of turns the steering wheel turns lock-tolock is also recorded.
The recommended method of applying braking to a
vehicle when using SIMON is to calculate the brake
torque at each wheel in response to a force being
applied at the pedal. If other methods (i.e., Wheel
Brake Force and Percent Available Friction) are used,
the wheel spin degree of freedom and the simulation of
ABS and ESS are not possible (EDC, 2005).
This method of measuring brake force allows us to
bypass the calculation of brake line pressures. To
apply our data to the brake torque calculations used in
SIMON, we utilize our previously-measured tire
rolling radius and assume the brake pedal ratio (R) = 1.
Therefore, instead of utilizing brake line pressures, the
pedal force is used for subsequent calculations. This
results in the brake torque ratio (Tratio) having the units
of brake torque [N.m] produced per unit of pedal force
This Tratio is the value utilized for the
Vehiclemetrics database. As a result, the brake torque
calculation remains the same:
The equations utilized by HVE for the brake torque
versus pedal force method are summarized below. The
purpose of these various brake system parameters is to
calculate the brake torque created at each wheel for a
given pedal force input.
Tb = Tratio x (p - po)
Tb = Tratio x (F – Fo)
Tb = Attempted brake torque at wheel [N.m]
Tratio = Brake Torque Ratio (attempted brake torque per unit
F = Pedal force
Fo = Pushout pedal force
of line pressure) [N.m/kPa]
p = Current application pressure at wheel cylinder [kPa]
po = Pushout pressure [kPa]
A sample analysis of our brake tester data is illustrated
in Figure 13. This Figure illustrates Tratio for front and
rear wheel locations. It also illustrates the “Fproportion”
To model the effects of brake proportioning, the
proportioning pressure is identified and the pressure at
the wheel cylinder(s) is calculated by the following:
Roller brake tester BDE2304 K, Snap-on Equipment Testing Division,
and the “proportioning ratio (η)” for the rear brake
system for use in HVE.
The bottom stiffness of the vehicles will be assigned
the current stiffness values assigned to vehicles built
by EDC. Methods to calculate top stiffness values are
being researched.
The vehicle aerodynamic drag calculation employed in
HVE is dependent upon the Aerodynamic drag
constant (Ca), projected surface area (Ap), air density
(ρ), and aerodynamic drag coefficient (Cd).
𝐶𝑎 = 𝐶𝑑 ρ𝐴𝑝
For the Vehiclemetrics database, frontal, rear, and side
areas are calculated using the laser scan data. If a
published frontal Cd can be obtained, then it is
incorporated into the vehicle model. If published data
cannot be located, then the values reported by Garvey
are used (passenger cars = .35, vans = .45, SUVs = .4,
pickups = .45). An estimate of the frontal aerodynamic
drag coefficient is planned using a road test conducted
similar to SAE J1263.
Figure 13: Sample Brake Torque Ratio Analysis
As described, since pedal force versus wheel force is
measured, the methodology used to calculate braking
parameters is somewhat different from what is
currently utilized for building vehicles by EDC.
Each of the Vehiclemetrics vehicles will come
equipped with tires from the HVE Generic Tire
Database. There are a number of vehicle parameters
which are currently within the HVE vehicles with a
“default” type parameter. These parameters, as well as
their value, are listed below:
The current method of deriving input parameters for
wide-open throttle (WOT) and closed throttle
horsepower and torque curves into the vehicle is
analogous to the method utilized by HVE (Garvey,
2000). Future measurement of the WOT is planned
through road testing; however, it has not yet been
Vehicle torsional stiffness
Drivetrain Inertia
Suspension coulomb friction
Suspension null band
Roll centre height
Suspension linear, cubic stop rates, and
energy ratio
vii) Steering stop stiffness and damping
viii) Steering column stiffness, friction, inertia
ix) Steering linkage play, mass, damping, and
friction lag
Differential and transmission ratios are obtained
through manufacturers’ specifications.
The crush stiffness values are currently calculated
using available published crash tests for frontal, side,
and rear coefficients. When more than one vehicle
crash test is available, an average value for the stiffness
coefficients is presented. If a crash test for a specific
vehicle cannot be located, then generic values reported
by Siddall (1996) are assigned according to the proper
vehicle class.
Currently the Vehiclemetrics vehicle database will
come equipped with the parameters as assumed by
EDC. There are already plans to measure some of
these parameters.
A method has been developed and a new database is
being compiled to provide HVE users an updated
vehicle database. The methods utilized allow a vehicle
to be tested in less than a day, and the final vehicle
model can be completed in less than one week. The
database is inclusive of both interior and exterior
geometry as well as mechanical datasets. The model
geometry is based upon laser scan data and is modeled
using a variety of software applications. The increase
in number of new geometry files complements the
recent release of DamageStudio for use in EDSMAC4
and SIMON. The majority of the mechanical dataset
will be vehicle specific. Research to obtain additional
vehicle specific data is ongoing. The current number
of vehicles in the database is approximately 75 and
growing steadily. It is estimated that 100 to 150 new
vehicles will be released on an annual basis. Ongoing
support of and creation of this database is planned and
the vehicle database will be available to HVE users in
the near future (planned April 2012).
Day, T., “An Overview of the HVE Vehicle Model,”
SAE Paper No. 950308, 1995.
Garvey, J.T., “Building Vehicles for HVE,” HVE
White Paper No. WP 2000-6, 2000.
Milliken, W.F. and Milliken, D. L., “Race Car Vehicle
Dynamics,” Society of Automotive Engineers, 1995.
SAE J1263 – “Road Load Measurement and
Techniques,” SAE, 1996.
Siddall, D.E., Day, T., “Updating the Vehicle Class
Categories,” SAE Paper No. 960897, 1996.
“SIMON Simulation Model,” Engineering Dynamics
Corporation, 2005, p. 4-24 to 4-25.
Tsymberov, A., “An Improved Non-Intrusive
Automotive Suspension Testing Apparatus With Means
to Determine the Condition of the Dampers,” SAE
Paper No. 960735, 1996.
Ron Jadischke
rjad[email protected]
Vehicle Year & Model Interchange List (Sisters &
Clones List), provided by Gregory C. Anderson, of
Scalia Safety Engineering, and distributed by Neptune
Engineering Inc.
Calculation of the CGsprung Location
𝐶𝐺𝑥,𝑠𝑝𝑟𝑢𝑛𝑔 = 𝑊𝐵 −
𝐶𝐺𝑦,𝑠𝑝𝑟𝑢𝑛𝑔 =
𝑊𝑇 ×𝑙𝑟 −𝑊𝑓𝑈 ×𝑊𝐵
[rearward of front axle]
𝑊𝐿𝑓 �𝑡𝑓− 𝑡𝑟 �
�𝑡𝑓− 𝑡𝑟 �
𝑊𝑅𝑟 𝑡𝑟
𝑊𝑅𝑟,𝑈 𝑡𝑟
�𝑡𝑓 −
𝑊𝐿𝑓,𝑈 �𝑡𝑓− 𝑡𝑟 �
�𝑡𝑓− 𝑡𝑟 �
� −
� − [right of centre line]
�𝑡𝑓 −
𝐶𝐺𝑧,𝑠𝑝𝑟𝑢𝑛𝑔 =
𝐶𝐺𝑧 −
𝑅𝑟𝑓 −
𝐶𝐺𝑥,𝑡𝑜𝑡𝑎𝑙 :
Total vehicle centre of gravity in the x-axis
𝐶𝐺𝑧,𝑡𝑜𝑡𝑎𝑙 :
Total vehicle centre of gravity in the z-axis
𝐶𝐺𝑦,𝑡𝑜𝑡𝑎𝑙 :
Total vehicle centre of gravity in the y-axis
Wf :
Total weight on the front axle
Wr :
Total weight on the rear axle
Total weight on the right front wheel
Total weight on the left front wheel
Total weight on the right rear wheel
Change in total weight of the front axle
Front track width
tr :
Rear track width
Tire rolling radius
Inclination angle of the chassis during the centre of gravity test
𝑚𝑈 :
Unsprung mass
Tire rate
Wheel centre rate
Wheel hop natural frequency
Damping rate
Critical damping rate
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