the bicycle story - Arvind Gupta Toys

the bicycle story - Arvind Gupta Toys
THE BICYCLE STORY
Vijay Gupta
Published by
VIGYAN PRASAR
A-50, Institutional Area, Sector-62,
Noida - 201307, U.P. , INDIA.
Telephone No: 0120-2404430,31,35,36
Fax : +91-120-2404437
While telling the fascinating story of the evolution of the bicycle from its beginning as a crude
beam on wheels to its present form of a highly efficient transportation and leisure vehicle, an
attempt is made to show how the engineering designs evolved from humble beginnings. This
process of evolution of design occurs sometimes slowly and at other times in leaps and bounds,
each stage leading to an improved product.
The book utilizes a familiar machine to introduce some essential principles of engineering
mechanisms: treadles, cranks, velocity ratio, transmission, gearing, antifriction bearings,
triangulation of structures, etc. It also attempts to give a glimpse of the science of bicycling
through a discussion of force and power, wind resistance, braking and stability. As an additional
feature, some interesting Internet sites connected with the history and science of bicycling are
listed for the enthusiasts.
The author, Vijay Gupta is Professor of Aerospace Engineering of Indian Institute of
Technology, Kanpur. He has an abiding interest in education and education technology. He has
produced numerous education videos for the UGC’s Country-wide classroom. One of his
videos, The Flying Machine, won the Best Production Award at the 6th National Video Film
Festival in 1993. He has authored a number of textbooks for engineering students and has
contributed many general articles to popularise engineering concepts.
The Glorious Machine
Movement is the essence of life. All animals move to find food, attack prey, or escape a predator. Snakes slide,
caterpillars crawl, kangaroos hop, horses trot and men walk. Of all animals, humans move the most. Most travel a few
kilometres to their workplace and back everyday, go visiting relatives to a city a few hundred kilometres away or travel
halfway across the globe to a business meeting. Some travel purely for fun or adventure.
For compulsive travellers humans are not particularly well equipped. A cheetah can out run the best of men by 10 to
1. A horse has much more endurance and consumes only about one-half the energy per kilogram of body weight. But
humans design machines which increase their physical capacity. The invention of the wheel is the single most important
milestone in the human attempt to increase locomotion. Oxen, horses and camels at first and then steam and gasoline
engines increased human movement dramatically. But the idea of using is own muscular effort in driving a wheel has
always fascinated man. It is interesting to note that the bicycle was perfected much after railway trains were in full
commercial operation and the horseless carriage was just knocking on the doors. Inventors everywhere are struggling
even today to perfect a flying machine driven by muscular effort alone —eighty-five years after the first successful
petrol-engine powered flight.
A man on a bicycle is far ahead of anybody else as tar as energy efficiency is concerned
A bicycle is the most efficient vehicle ever designed. Its cost, in terms of energy spent in carrying a comparable load
over a comparable distance, is one-tenth that of the most efficient jet aircraft and about one-twentieth of the best
automobile.
The humble bicycle has a glorious past. First conceived as a plaything of the rich, it soon evolved into an efficient and
convenient means of transport. The coming of the automobile, however, relegated it to a role of an exerciser or a sportsmachine, though in large parts of the world, notably China and Southeast Asia, it is still used as the primary means of
daily transportation. In the industrialized world it seems to have come a full circle. The bicycle is re-emerging as a vehicle
of choice for short runs in urban areas. It does not pollute the atmosphere. It is almost noiseless. It does not take up
precious parking space and wide roads. It has been estimated that for distances up to 8 km in city centres a bicycle may
be faster than a car given the time taken for taking a car out of a garage, finding parking space and walking from the car
park to the place you intend to go. And above all, a bicycle provides you valuable physical exercise while you ride to
work.
This booklet narrates the fascinating story of the bicycle and its technological evolution.
The First Steps
The first mention of a two-wheeled vehicle propelled by the rider himself occurs for a 1791 toy-like machine which
was simply a wooden beam on two wheels, one behind the other. The rider sat on the beam and drove the machine by
pushing his feet alternately against the ground, as if skating. One could not turn this machine except by lifting and
dragging the front wheel to one side. It didn’t even stay erect if both feet were off the ground.
A hobby horse was displayed for the first time in 1791 in a Parisian park as a plaything for the rich.
The first notable improvements in this clumsy machine were reported in 1817 when its front wheel was turned by
moving a handle. This machine, known by various names such as a hobby-horse, a Draisienne (after the German Baron
von Drais, who is credited with this invention) or a velocifere, soon became popular among the rich and fashionable of
the day. The steerable front wheel was an important addition, and was responsible for giving the Draisienne some
measures of stability. A man on a Draisienne could exceed the speed of runners and horse-drawn carts even for long
journeys. But the awkward posture of the rider invited ridicule and the bumpy ride on solid wheels over rough roads
resulted in many cases of hernia. This led to a setback in the development of bicycles.
A Draisiene (1817). The steerable front wheel gave it some stability. “Hobby-horses rode in their carriages
and walked in the mud at the same time”.
The Treadle and the Crank
The first true bicycle, a machine which could be ridden with both feet entirely off the ground, appeared in 1830. A
Scottish blacksmith named Kirkpatrik Macmillan employed the power of the leg muscles to turn the rear wheel directly,
instead of dragging the machine by pushing with his feet on the ground. The mechanism used two bars suspended from
the front end of the frame. The lower ends of these bars, known as treadles, carried pedals which were driven alternately by feet through short arcs. The motion of these treadles was conveyed through a pair of connecting rods to the
rear wheel where they moved two cranks. The cranks converted the push and pull motion of the rods into the rotary
motion of the rear wheel.
Macmillan’s velocipede (1839) was the first true bicycle with feet ‘out of the mud’. Not a single one of this
was sold, though many copied it.
The treadle-driven crank is a common mechanism in many applications. The common foot-driven sewing machine
uses the same mechanism to convert the rocking motion of the foot-plate into rotary motion of the wheel. This
arrangement is also similar to the one used to convert the reciprocating motion of pistons into the rotary motion of the
crankshaft in a steam or automobile engine.
The treadles drive the connecting rods which swing the cranks through full circles, rotating the wheel. The
same motion is used in the treadles of an old-fashioned sewing machine and in the crank of a piston engine.
The velocipede, though a bicycle in the true sense of the word, was never a commercial success and not many
persons knew about its bold design. For the following forty years the design of the bicycles stagnated at least in the
method of converting the motion of feet into the rotary motion of the wheel.
Michaux’s velocipede (1863) was the first commercially successful machine. Though very expensive, it created a craze that spread over Europe and America. Due to the dare-devil riding by the rich and the bold, the
bone-shaker (as it was nicknamed because of its rough ride) soon drew enough detractors so as to be banished
from the road at many places.
The first commercially successful bicycle appeared in 1863. It had a pair of pedals connected to the front wheel and
was ridden in the same manner as the basic children’s tricycles of today. Its wooden wheels (with iron tyres) on the
cobbled roads of the day gave the rider such a rough ride that it was nick-named the bone-shaker.
However the bone-shaker was more elegant than its ancestors. It was lighter, faster and a lot more comfortable
than the hobby horse. This comfort was achieved by having the seat fixed through a leaf spring which ran from the front
handle to the rear wheel.
Velocity Ratio and the Tall Ordinary
One result of the direct cranking of the front wheel was that one cycle of the motion of the legs turned the front
wheel only once. This produced a forward motion of the bicycle through a distance equal to the circumference of that
wheel only. This was not considered enough for speed. One could of course pedal at a greater rate to move the
boneshaker faster, but there was a catch. The power output (i.e., the rate of doing work) of a person pedalling a
machine depends upon the force he applies on the crank, and on the rate of pedalling measured in the number of
revolutions per minute (or RPM for short). As the RPM increases, the power output will increase, provided the applied
force does not change. But it does. Repeated trials have shown that this force decreases as the RPM increases. When
the pedals are locked, the force applied is maximum but there is no power delivered (the RPM being zero). There is
indeed a value of RPM where the rate of doing work by pedalling is maximum. This value is between 45 and 60 RPM.
For a bone-shaker to move at speeds comparable to those of modern bicycles, one would have had to pedal at
considerably higher RPM which would not have been comfortable at all.
The principle of levers. By keeping ‘effort’
arm small one can move the ‘load’ through a
larger distance. This is inverse of the usual
situation where effort arm is made larger to
overcome a larger load by a smaller effort.
A larger wheel covers a larger distance in one revolution.
A simple way to overcome this was to use a larger front wheel. The increased circumference of a large wheel moved
the machine through a larger distance in one revolution of the directly cranked machine through a larger distance in one
revolution of the directly cranked wheel. This simple principle of increasing the distance travelled (of course, at the cost
of reducing the force) can be seen in relation to a simple lever. Consider an old-fashioned railway signal. A relatively
small motion of the cable attached to the shorter (effort) arm results in a much larger swing of the signal (which is the
“load” arm in the terminology of fevers). Note that the “load” overcome by “effort’’ is reduced in this same proportion.
The ratio of the load to effort is termed as the mechanical advantage. In a bicycle we are interested in increasing the
velocity ratio, and the decreased mechanical advantage is the price that we pay for it.
Various methods of obtaining
large rates of rotation of a driven
wheel—gears, belts and chains.
Each method has its own advantages and disadvantages.
The increased diameter of the front wheel is only one of the ways of obtaining a large velocity ratio. A simple pair of
unequally sized gears a belt over two pulleys, or a chain running between a large chain-wheel and a small sprocket (a
toothed wheel) are some other ways. In each of these cases the velocity ratio is the ratio of the sizes of the two wheels,
gears or sprockets. From the automobile practice, where gears are used almost exclusively for the purpose, the velocity
ratio is commonly referred to as the gear ratio.
Each of the above transmissions (that is, the method of transmitting power from the pedals to the wheel while
obtaining a mechanical advantage) has its own advantages and disadvantages. For example, the performance of a beltdrive, which depends upon the presence of the resistance to slipping of the belt on the pulley (i.e., of the friction),
decreases sharply when the belt becomes dirty, grimy or loose. Gears give better performance, but are more expensive.
But this is getting ahead of our story. As mentioned before, the simplest and the most obvious method of increasing
the gear ratio in a bone-shaker was increasing the size of the front wheel. And that is exactly what was done. The front
wheel started growing in size, from 36 inches to 48 inches, to 54 inches, and one even had a 64 inch (163 cm.) wheel.
The limit on this was imposed by the length of the riders’ legs. To keep the weight of the machine low, the diameter of the
rear wheel shrank, giving these bicycles their definitive shape, the penny-farthing. (The British coin farthing was four
times the size of a penny). These machines were also called the tall-ordinaries or the high-wheels.
Hazards of High-Wheeling
The tall-ordinaries were not for women, non-athletes or the weak-hearted. Getting on one was not easy with the
saddle more than a metre and a half from the ground. One gave the machine a shove, and jumped-up onto the two footbraces atop the small rear wheel, and then jumped again onto the saddle. Pedalling such a bike was difficult because the
distance between the saddle and the lowest point of the crank travel was in many cases larger than the inner length of the
leg. Fully-grown men pedalled like a little kid on a modern bicycle too tall for him—leaning heavily on the side his foot
goes down, and not being able to sit on the saddle while pedalling. Furthermore, getting off was difficult.
The high wheelers introduced the bicycles to the general public. At least a hundred mounting step thousand
of these machines were built. They ruled the roads from 1870 to 1890. This vehicle is credited to be tried first to
give the freedom of the road to an individual—even if only to the athletic, brave and male. The diameter of the
front wheel grew till it was limited by the length of the rider’s legs.
But while atop and coasting, with both feet off the pedals, the rider looked down from his high throne on the world
beneath him. The speed of up to twenty miles per hour was more than that of almost anything else on the road, and
people got out of his way. But the thrill of speed and the sense of superiority that a rider felt came at a high cost. With the
rider atop the big front wheel, the centre-of-gravity was too high and forward for the machine to have stability. Even
small obstructions such as a pebble on the road, or a sudden application of the brakes, sent the rider flying face down
into dirt. Even experienced riders had mishaps which were frequent enough to give them their own distinctive names of
a cropper or an imperial crowner.
The man hurtling through space perched on a high wheel felt graceful and regal, but it called for extreme
skill in 1. Starting a ride
2. Pedalling an oversized wheel and
3. Coasting downhill.
Dogs, pigs, chicken and children, bricks and
potholes in the road, all could easily cause the
infamous ‘header’. So also could a row of bricks, a
taut length of string, or a stout rod poked among
the spokes. A high wheeler seemed to bring out the
worst in people. One could also easily gat a foot or
clothing entangled in that great expanse of spoke
work that the big wheel was.
Various efforts at increasing the stability of the high wheelers didn’t result in any success. A new design was needed.
The rider had to be moved back and lower—which was not possible with the basic high-wheel design. One of the
attempts at a solution reversed the entire geometry, with the rider now sitting on the enlarged rear driving wheel. But one
couldn’t pedal the rear wheel directly, unless one sat slightly behind it on an overhang—something impossible because
of the reasons of equilibrium. The famous American Star bicycle of 1882 attempted an indirect drive through a system
of levers, drums and straps (much in the fashion of treadles). The star had some success in making bicycling safer, but for
the next few years the tricycle was the centre of attraction for the inventors and the manufacturers. The British royal
patronage also helped popularize the tricycle among fashionable women who were beginning to demand equality with
men.
Lawson’s chain-driven ‘bicyclette’ (1879) was the first to use the modem layout of a chain-driven rear wheel.
The handle bar is operated through an indirect steering because the seat is placed far in the rear.
The Safety Machine
The first machine that closely resembled the
modern bicycle hit the roads in 1879.
In these low machines, the rider sat between the
two wheels and paddled a low crank which drove
the rear wheel through a chain. A large gear ratio
was obtained by using a large chain wheel and a
small sprocket attached to the rear wheel. This did
away with the need for a large driving wheel. The
size of the wheel no longer determined the velocity
ratio, which could be varied by changing the size of
the chain wheels.
Early Rover Safely bike (1885) also had an
indirect steering. It introduced the compact diamond
frame which has been the standard till today.
The rider could reach his leg down to the ground in case he lost balance. The low and rearward centre-of-gravity
removed the tendency of the machine to come a cropper— even if it ran into a low wall and quite appropriately the
bicycle was called a ‘safety’.
The later Rover Safety (1889) completed the development of the bicycle form.
Inspite of the demonstrated safety, this bicycle met with a lot of resistance. Solid-tyred safeties vibrated more than
the corresponding high-wheelers, and pedalling so close to the unprepared ground muddied the feet. But with later
improvements and continued experience with its qualities, the ‘safety’ won almost everybody over within 10 years.
Since the front steering wheel was unaffected now by the pressures of pedalling, the strain of keeping the machine
balanced reduced drastically, so that one could even ride with both hands off the handle bar. These machines carried
more luggage, either on the handlebars or on the rear-wheel. Learning to ride one was child’s play
Moulton (1967) design is the one major change that has taken place in the last 100 years; it has 16" wheels
and a cross-frame. It is easier to handle, more comfortable to ride and fashionable as well.
There were innovations in other design features too. The tubular diamond frame appeared in 1885 and has been an
essential feature, largely unchanged till today. This reduced the weight of the bicycle significantly. Air-filled tyres, first
fitted in 1888, cushioned the rides dramatically, and by 1890 the safety bicycle had become comfortable and convenient
enough to be generally accepted as the conveyance of choice by all including those who earlier considered a bicycle
beneath them or who thought their physique to be unsuitable for the rigor of cycling. The bicycles were used by vendors
and workers and ladies for afternoon spins. The gentry used it for undertaking tours and exercise and sportsmen for
competitive racing.
The bicycle has changed little in the last 100 years. The picture of an 1885 Rover safety resembles a modern touring
bicycle. There have been some changes no doubt. We use much lighter and stronger materials now. The ball bearings
are improved. Calliper brakes are much more effective.
The Parts of a Bicycle
Wheels
It is often said that the most fruitful source of ideas for a creative engineer is the natural world around him. Evolution
has ensured the most efficient solutions to almost all problems that he is even likely to face. In the field of transport, the
greatest single invention is the wheel. A cylindrical wheel rolling on a smooth surface offers up to 100 times less resistance
to motion than an equivalent weight being dragged on the ground. Humans most probably observed things like stones
rolling down surfaces. The inspiration could also have come from logs or other cylindrical objects displaying the mechanics
of rolling friction.
A cart wheel with stout compression spokes.
We know that a steel train wheel rolling on a steel rail-road offers the minimum resistance to motion among all
moving things, less than one-thousandth of the weight on the wheel. But when this wheel rests on a soft surface, the
surface deforms forming a pit like depression. Further rolling of the wheel would now require a greater effort because
the wheel now has to climb out of the pit. Similarly, soft wheel rolling on a hard ground deforms under its load at the
point of contact. The ‘deformed’ wheel is no longer perfectly round and so it can not roll on smoothly. In either situation,
the effort required for motion is increased because of the deformation.
The wheels of hobbyhorses and bone-shakers were heavy and similar to those of carts. They had thick spokes of
wood which supported the load. The relative inflexibility of the wheels and the spoke resulted in the rider feeling every
bump or pebble on the road.
The load applied at the hub is borne in compression by the stout spokes of a cart wheel, but in tension in thin
wire spokes.
The first real advance in the design of wheels came with the Penny-Farthings.
The design of their wheels was based on the principle of suspension—the load (represented by the central hub) was
carried suspended on fine wires from the top portion of the rim, rather than being supported by stout columnar spokes
on the lower portion of the rim. We all know that a slender rod can carry a much heavier load when the load is
suspended from it (so that the rod is being stretched, i.e., is in tension) than when it props up the load from below (so
that it is being compressed by the load). A slender column under compression buckles easily when loaded. This is the
principle of construction used in elegant and light rope-or wire-suspension bridges. The thin wire spokes of the new
wheels exploited this principle and represented substantial savings in weight.
The earlier tensioned-wire spokes ran
straight in to the centre of the wheel. These
spokes could take the vertical load at the hub
but couldn’t transmit the torque at the hub to
the rim. A couple of rigid bars with their own
tensioned spokes were added for the purpose.
The earliest of these wheels had radial spokes
which could be tightened to give them an initial
tension. By carefully adjusting the tensions in the
various spokes, one could make the rim concentric
with the hub so that the wheel run true, i.e., without a
wobble. But the radial hubs could not transmit the
large torques exerted by the pedals at the hub. Any
application of torque simply bent the thin spokes.
Hence two rigid bars, each with its own tensioned
spoke (see wheel of a penny-farthing), were added
to the driven wheel making it heavier.
Spokes tangent al the hub is the lightest
solution for a wheel. It is restrained in all
the six degrees of freedom.
It was not long before these torsion spokes were eliminated through the use of a very innovative way of lacing the
spokes at the hub. The spokes, instead of running in radially towards the centre, were now so placed that they were
tangential to the hub. When a torque was applied to the hub of such a wheel through its sprocket, the wire-spokes were
tensioned, driving the rim in the same direction. A series of triangles formed by the spokes and the hub ensured that all
loads were resisted by just the tensioning of spokes. This principle of triangulation of structure was later used in the
design of the diamond frame of the safety bicycle.
Two spokes and the hub form a triangle:
the strongest geometry for carrying a load.
The torques that arose during deceleration were resisted in a similar manner, every alternate spoke ran in tangentially
in the backward direction. Application of braking torque was resisted by the resulting tension in these spokes. All
modern spoke-wheels have essentially the same design.
Pneumatic Tyres
The air-filled tyres of modern bicycles were first introduced on the safety bicycle in 1888 as a means of reducing the
vibrations that a solid rubber tyre produced. The principle is simple: the bicycle now rode on a pocket of air which
cushioned the ride.
Cross-section of a rim and a
conventional wire-bead tyre. Beads are
tensioned and keep the tyre in place.
The air is contained in a thin pressurised inner tube which is protected by a thicker outer tyre. The tyre is strengthened
by many layers of reinforcing cords embedded in the rubber. It has two steel-wire beads which snap into grooves in the
wheel rim. As the inner tube expands under pressure, the tyre bead is pressed firmly in the rim grooves keeping the tyre
in place.
When a soft tyre rolls on a soft ground,
both the tyre and the ground deform. The
deformed ground sets up a reaction force
so directed that it resists the motion.
Similarly, the deformation of tyre, too, does
not permit smooth rolling.
The rolling resistance of the pneumatic tyres arises because of the flexing of the tyre under load. As a loaded tyre rolls
on ground, the different portions of the tyres are constantly flexing, dissipating energy. One obvious way to reduce the
rolling resistance is to increase the inflation pressure of the tyre. Increased pressure means that the tyre sinks less under
the load and, therefore, flexes less. Typical pressures used in modern tyres are between 2.5 to 4 atmospheres (that is,
250-400 kPa or 35-60 psi). Every bicyclist knows that a bicycle runs faster with higher tyre inflation. He also knows
that stiffer tyres absorb shocks poorly and that the ride is a lot rougher. All the pebbles and pot-holes on the road appear
to be transmitted directly to the saddle.
The construction of a tubular.
The fabric casing is the main body
of the tyre with the inner tube sewn
in. A rubber tread is glued to the
casing on the outside of the tyre.
Racing cyclists who prefer speed over comfort use higher inflation pressures than others. The sink of the tyres (and
hence their resistance to rolling also depends upon the total weight carried by the tyres which includes the weight of the
rider, the bicycle and the tyres themselves. Besides cutting down on all other weights (including their own) the racers use
specially designed tyres called the tubulars. These are made of silk or polyester fabric (impregnated with latex) and is
sewn around a light-weight inner tube. The whole assembly is then glued on to the rim. Such tubular are very light, and
high inflation pressures make them run very fast. But the decreased protection makes them much more puncture prone.
Bearings
The holes in a frame through which rotating shafts run are called bearings. In the early days of bicycles, the bearings
needed constant lubrication and cleaning to keep the friction low. An improperly lubricated bearing resulted in (a)
increased effort due to increased friction, and (b) heat built-up in the bearing itself because of the rubbing of the rotating
shaft with the walls of the hole. The increased temperature often caused local melting of the walls and resulted in
jamming-up of the wheels. Frequent cleaning of the bearings was recommended because the lubricating oil tended to
catch the grit and dust which spoiled the bearing surfaces.
Schematic of a typical ball
bearing in a bicycle. The shaft
constitutes the hardened ‘cone’ and
the frame has the ‘cup’. The balls
run between the cup and the cone.
A section of the front hub bearing.
The introduction of ball and roller-bearings is an extension of the idea of the use of the wheel itself. A hardened roller
running between two surfaces eliminates the relative sliding and reduces the resistance due to friction drastically. The
typical design of a bicycle bearing consists of a row of balls rolling between an outer cup and an inner cone. The balls,
cone and the cup, all are made of hardened steel to resist wear or deformation. The reduction in friction is so dramatic
that these bearings are also known as the anti-friction bearings. Their life is fairly long, even without frequent oiling.
Furthermore, these can be replaced easily and inexpensively, if necessary.
Chain
The design of chain also went through a process of evolution. The earliest chains were simple pin types in which the
pins rolled directly on the sprocket teeth resulting in large rates of tooth wear. The latter designs introduced rollers and
bushes so that neither the sprocket teeth, not the end plates bore and rolled on the pins directly, and thereby, increased
their life immensely. The modern bush-roller chain, designed essentially in 1880, is so efficient and reliable and it is still
used to drive the cam-shafts of automobile engines.
The bush-roller chain (1880) combines high efficiency, low weight and long life. Except for better materials
and precision of manufacturing, the chains have not changed in one hundred years since their invention.
The details of a seven-speed hub. The chain runs on one or the other of sprockets which are screwed only
to the freewheel. The internal ratcheted teeth are shown alongside. The spring-loaded pawls engage when
the free-wheel rotates in one direction, and drives the hub and the wheel. The pawls are depressed when it
rotates in the other direction, permitting slippage between free-wheel and the hub. Where are the pedals
located relative to this free-wheel—to the left or to the right?
The essentials of a free-wheel.
The ratchet like teeth engage
with spring-loaded pawls when
rotating in one-direction
Free Wheel
A free wheel is a device which connects the sprocket of the driven wheel to its hub in an ingenious manner. It engages
the wheel to the sprocket when the sprocket rotates in the forward direction, but lets the wheel roll forward freely when
the sprocket runs in the backward direction, or is not running at all. It is easy to see that such a device makes getting on
and off a moving bicycle much easier than when the sprocket and wheels are attached without a free-wheel. This
happens because without a free wheel the pedals must rotate constantly with the moving wheels. Similarly, coasting,
which is the forward motion of a bicycle due to its inertia alone without pedalling, will not be possible without a free
wheel.
Before free-wheels were introduced,
the riders sought relief from the everturning pedals through the use of foot
rests — sine qua non for all who
wished to ride with ease.
A free-wheel assembly has a number of spring-loaded blocks termed as pawls. Each pawl folds into a cavity in the
shaft when it is pressed down, but pops out when the pressure is taken off. The corresponding sprocket has a number
of ratchet-like teeth cut on the inside. When the sprocket rotates in the reverse direction, the pawls are pressed down
by the sloping sides of ratchet teeth and let the sprocket roll on the shaft. But when the sprocket rolls in the forward
direction, the pawls open out and are engaged against the straight sides of the ratchet teeth. This happens whenever the
pedalling moves the sprocket faster than the wheel, so that the muscle power is fed into the wheel, accelerating it.
The free wheel, thus, allows coasting on a bike with one’s feet on stationary pedals, or even pedalling backwards.
The introduction of free wheels made the bicycle safe to get on and off, and one could coast down a hill without having
to pedal constantly.
Brakes
There was no particular need for brakes until the time free wheels were introduced since the pedals moved with the
wheel. One could brake the bicycle simply by attempting to rotate the pedals backwards. But this required a large
amount of force, particularly if one was going fast.
This made downhill bicycling a very hazardous sport.
The earliest of the bicycle brakes consisted of just a
metal spoon which was operated by a hand lever
and was pressed against the rim of the front wheel.
It was quite effective on a solid rubber tyre, but
tended to play havoc with the air-filled ones.
The stirrup brakes, still common in Indian bicycles,
operate on the underside of the rim. The operating
mechanism of these brakes is quite unreliable. These
also need tar too frequent adjustments.
Soon after the introduction of pneumatic tyres the stirrup brake was developed. It is still used on many bicycles. It
consists of a couple of rubber pads which were pressed against the underside of the rim. The force of friction between
the pad and the rim acts on the rim to stop its rotation. This force of friction depends on the material of the pad and the
pressure with which it is pressed against the rim. A large value of this pressure is obtained by using lever mechanisms that
transmits the motion of the hand operated brake lever to the brake pads with a large value of mechanical advantage.
The stirrup brakes were soon replaced by calliper brakes in which the brake pads are pressed against the flat sides
of the rim rather than on the underside. The main advantage of the calliper brakes lies in the fact that these brakes are not
affected by the inevitable non-circularities of the rim. The stirrup brakes on the other hand lose contact with the rim at
places where the rim is out of circle.
Also, the calliper brakes are not disturbed while changing tyres whereas the stirrups need to be moved out of the
way.
Calliper brakes operate against the
sides of the rim. They are operated by the
pull of the brake wire through &n outer
casing. The outer sleeve is attached at A
and the inner cable at B.
The outer sleeve is attached to one
arm of the callipers and the inner cable
to the other. When the cable is pulled
through the sleeve (through a similar
arrangement at the brake lever end) the
two arms of the calliper brakes are
squeezed together against the sides of the
wheel rim.
Calliper brakes are operated through a flexible cable which is made up of an inner-wire running through an outersleeve. The operation of the lever puts the inner wire in tension and the outer sleeve in compression. The tension and
compression act on the two halves of the callipers closing the brake shoes against the rim.
The inner tension-cable running in an outer compression-sleeve is a most effective means of remote operation of a
number of mechanisms. The gear-change of a bicycle or a motor cycle, the operation of a clutch or an accelerator of a
motor bike is all operated by such a system. A variation of such a cable is also used for remote operation of rotating
components. A car speedometer cable is an example of such a use.
Gears
As long as the direct cranking of the front wheel was the method of
moving a bike, the only method of increasing the distance travelled per
revolution of the pedals, also known as the gear ratio, was to increase the
size of the wheels, as was done in penny-farthings. A large gear ratio meant
that the torque at the hub was much smaller than the effort torque applied
on the pedals. This was alright as far as going on a level ground was
concerned, but it made going uphill or accelerating quite difficult.
What was required was some way of changing the gear ratio at will:
low for starting or going uphill, and high for travelling on level ground. This
was not possible in a penny-farthing because the gear ratio was determined
solely by the size of the front driven-wheel.
An inner-cable-through-outer-sleeve pulls the derailleur
to a side, derailing the chain from one sprocket to another.
The spring loaded idle roller takes up the slack of the chain.
Typical sprocket and chain wheel sizes (in number of teeth) in a ID-speed bike. The various combinations
give gear ratios from a low of 34" (travel on ground in one rotation ot a 27" wheel) to a high of 100". Low gears
are useful for uphill climb or acceleration. High gears are used for cruising or downhill runs.
The chain-driven safety bicycle, however, permitted quick change of gear ratios. Various mechanisms have been
suggested for changing gears, but the one that is increasingly used these days consists of a number of sprocket wheels
of different diameters at the rear wheel. When the chain runs on a larger diameter sprocket, the gear ratio is lower than
when it runs on a smaller diameter sprocket. The slack of the chain resulting because of the change in the diameter of the
sprocket is taken up by a spring-loaded pulley mechanism known as a derailleur. As the gear-change lever is shifted it
actuates a cable. The cable pulls the derailleur mechanism to one side, making the chain ‘derail’ from one sprocket to
another. This arrangement is fairly light and efficient, but requires careful adjustments. The hub in a derailleur may have
three or five sprockets, giving three or five ‘gear ratios’ or speeds. The ten-speed bikes have a similar mechanism at the
hub and, in addition, two sizes of chain-wheels at the pedals. The combination of a two-speed chain wheel and a fivespeed hub gives the 10-speed bicycle commonly used by sportsmen.
Dudley-Pederson first appeared in
1907. It had the lightest frame ever,
because of the full triangulation.
Hammock seat was a particularly
appreciated feature. These are being
reissued by a Danish firm.
Frames
The frames of bicycles have shown much development over the
years. The modern tubular diamond frame is quite far removed from
the crude wooden planks of the original hobby horse. A modern
frame is strong and yet light. This economy of design is obtained by
exploiting the fact that a structural member is weakest when it
supports a load which tends to bend it. If this member is propped
up from below, the load is carried in compression, and much more
load can be carried. A still better arrangement is the one when the
member is strengthened by a cable which takes the load in tension.
Thus, the lightest structure results when its components support loads
in tension or in compression, but not in bending. Such a structure
consists of a series of triangles. Tower cranes, roof trusses and steel
bridges all use this triangulated construction. The diamond frame
of a modern safety bicycle is also triangulated to a large extent. The
ultimate in frame triangulation is seen in a 1907 Dwaley-Pederson.
It was so light that the total frame weighed only 6.4 kgs.
Moulton bicycle has a cross
frame which is simpler but not as
strong as a triangulated frame. The
convenience of an open frame is a
trade-off for higher weight.
The top member resists load by
bending. The bending is reduced in the
other arrangement, resulting in much
more efficient structures.
The classical diamond frame is well triangulated and
quite efficient. This has been the standard frame for the
last 100 years, except for the famous Moulton frame,
which is net as strong, but gives other advantages.
Diamond frames were introduced in 1887, and since then almost all bicycles have had such frames. A notable
exception is the Moulton bicycle introduced in 1964 which uses an X-frame construction. This frame is definitely heavier
than a diamond construction but other advantages, such as the fact that it is suitable for skirt-wearing women as well,
make this acceptable.
Another weight saving device is the use of hollow tubes as main-frame members. A bamboo exhibits the excellent
properties of the hollow circular tubes. It takes up to twice as much load as any wooden beam of equal weight.
The Science of Bicycle
Force and Power
The first consideration in the design of any vehicle is the calculation of force and power. Whenever a body moves or
rolls over a surface some forces come into play which tend to oppose the motion. We, therefore, need to apply a force
to overcome these resisting forces. Acceleration of a body needs an additional force. Larger the weight of a body or
larger its acceleration, larger is the force required. Therefore, racing bicyclists who need to accelerate fast, attempt three
things:
· keep the resistance low,
· keep the weight small,
· apply as large a force as possible.
Effect of duration on the pedalling power
output. The graph shows that the power output
level in short bursts could be up to six times
that in long runs. Comfortable level for routine
bicycling is taken at 60 W.
Similarly, going uphill requires a larger force because the weight of the body has to be hauled up the hill. We have
learnt that a large force is applied by changing to a low gear. That is one reason why we start in a low gear, and shift up
when we have built up speed and do not need to accelerate further. Similarly, going uphill requires low gears.
Power refers to the rate of energy consumption in motion. It depends upon the force of resistance and the speed of
motion. Larger the force or the speed more is the requirement of power. In pedalling a bicycle, the power for motion
comes from the human engine through its muscles. Muscles are like fuel cells, converting the chemical energy in food into
mechanical energy at the crank. The speed of the bicycle is limited to a large extent by the capacity of power delivery by
the muscles.
The maximum power is obtained at
an optimum pedalling RPM which
decreases with the duration of
pedalling. A rate of 50 RPM is
recommended for ‘healthy males’ for
routine bicycling. Racers are known to
go up to 150 RPM in very short bursts
(up to 5 seconds).
The functioning of our bodies is quite complex. One can obtain really high bursts of power if one goes only for a short
duration. But the level of power output sustained over a long time is much lower than this. Thus, the speed on shorter runs
is far larger than the speed during long endurance runs. Chart below shows the rapid decline of the power output with
duration. A comfortable level of power output on a sustained basis for an ‘average’ bicyclist is usually taken as 50 W.
Power Audit
Let us account for the power spent in bicycling. When a bicyclist starts from rest, the power that he spends goes into
overcoming the various frictional resistances and in providing the kinetic energy increase associated with his acceleration.
When he pedals uphill, a part of the power is also spent in increasing his potential energy because of his increased altitude.
Let us first consider a level steady run at constant speed. All the power delivered by the rider now goes to overcome
the various resistances. The most significant loss occurs in the tyre rolling resistance. Typical resistance force is about 4
Newton, which at a speed of 18 km/h (or 5 m/sec) consumes 20 W. This power increases proportionately with speed,
that is, when the speed is doubled, the power is doubled too.
In the region where the available power
is more than the power loss, the difference
goes to increase the kinetic energy of the
bicycle and the rider. The maximum speed
is reached when the total power losses
consume all the available power.
The energy losses in the various ball bearings are very small and are estimated at less than 1 W. The transmission
chain with all its rubbing amongst various links and between links and the sprockets consumes more power—up to 3 W.
The total so far accounts for only 24 W or about one-half of the input power. Where does the rest go? Let us find out.
Wind Resistance
All bodies when moving through air experience a resisting force termed as drag. One feels this force when walking
against the wind. For speeds commonly encountered in bicycling, this resistance force varies as the square of the speed.
Thus, as the speed is increased by a factor of 2, the drag force increases by a factor of 4, and the power consumed
(which is the four times the speed) by a factor of 8. This is really a steep increase, and does, in effect, determine the
maximum speed for a given effort.
Drag force varies as square of the speed.
A survey of literature shows that a person riding an ordinary bike in the usual upright position experiences a drag
which is given by the following approximate formula
Drag force ( in Newton ) = 0.015 x (speed) x (speed),
and the power consumed in given by
Drag power (in Watt) = 0.004 x (speed) x (speed) x (speed),
where speed in measured in kilometers per hour.
Reducing frontal area by
crouching is one way to reduce
the drag and increase speeds.
Thus the power required to overcome the drag, which is only 0.5 W at 5 km/h, blows up to 4 W at 10 km/h, and up
to 13.5 at 15 km/h. At 18 km/h the drag losses are 23.3 W, almost equal to all other losses put together.
It should be noted that the above formulae are valid for
pedalling through still air only. The drag is determined by the
speed of the body relative to the air, so that with a head wind
of 5 km/h, one would encounter the same losses at a speed
which is 5 km/h less than the speed in still air. It should be clear
by now that the maximum speed is essentially limited by the air
drag. One must strive to reduce the drag as much as possible
in order to increase the speed. Our experience with designs of
high speed cars and aeroplanes has shown that the drag force
depends on the ‘frontal’ area of the body and on the contours
of the body (besides the all important speed, of course). Thus,
a racing bicyclist crouches on dropped handlebar to reduce
the counter wind flow. A bicyclist lying prone would offer still
less area and some modern bicycles have been designed to
exploit this. Further reduction in the frontal area can be achieved
by changing into tight fitting clothes as the racers do.
Drag is reduced by streamlining the
body shape, as for an aerofoil, a dolphin
and a high performance car.
The aerofoil shape and the cylindrical wire
of one-tenth frontal area have the same drag.
A fairing on the handle bar results in partial
streamlining. Lowered draw can increase the
maximum speeds by as much as 10 percent.
The contours of the body are an important determinant of the drag. Notice the smooth shapes of the racing cars in
contrast to the lines of the earlier touring cars. Notice also the tear-drop profile of a dolphin which has been copied by
the designers of aeroplanes. Such ‘streamlined’ shapes and reduce drag. If a long tapering tail is attached to a sphere,
one can reduce the drag power requirements by a factor of hundred.
An aerodynamically shaped shell around the bicycle can reduce the drag drastically.
The recumbent position of the rider reduces the frontal area, lowering the draw further.
How can this information be used in the design of a bicycle? Not easily. The human profile is far from streamlined.
But if we enclose the bike and rider in a tear- drop shell we can take advantage of the reduced drag. Some attempts
have been made recently (with the rider in the recumbent position to reduce to frontal area) with great success as far as
the maximum attainable speeds are concerned. But the handling qualities of such vehicles to date make them fit for little
else but breaking speed and endurance records on tracks.
Relative magnitude of drag for various bicycle shapes and riding positions.
The numbers represent the approximate maximum speeds attained by non-athletic
males in continuous rides. The increase in speeds is largely due to reduced drag.
Pedalling Uphill
When a rider pedals uphill, he raises his bicycle and his own weight and therefore has to apply a larger force at the
hub than when he is only overcoming the resistance. This makes going uphill very difficult, unless the rider has a geared
bike and can change down to a lower gear ratio giving him a larger mechanical advantage (though a reduced velocity
ratio). Thus he goes slower but easier.
In the energy audit, we now have an additional term. The rider’s potential energy increases as he goes up, and this
energy must also be supplied by the muscles. This reduces the power available for overcoming the resistance, and he
may not be able to go as fast as on the level ground.
While going uphill, the pedalling force
must overcome the drag, the Motional force,
as well as a component of the weight.
The fact that air-drag consumes a fair amount of power, and depends upon the relative speed of the body with
respect to air, leads to an interesting situation. Under certain conditions, it might be easier to climb a hill than go down it.
This happens when we have a wind uphill. This may assist the climb to such an extent that saving in drag power may
offset the increased cost to potential energy increases. On the other hand, increased power consumption to overcome
the drag in a head-on wind may be more than the recovery of potential energy in a down-hill run.
Braking
A bicycle is braked by jamming pads of friction material (usually rubber) against the inside or the sides of the rim.
This restrains the wheel from turning, and consequently the tyre drags on the ground instead of rolling on it. It was seen
before that the friction during sliding could be up to 100 times that in rolling and this force between the ground and the
sliding wheel is what slows down and finally brings the bicycle to rest.
The frictional force at the road tends to ‘swing’
the bicycle pivoting about point (2). Front wheel
brakes should be applied with caution.
One has to be careful while applying the brakes. If the full braking force is applied and both wheels are locked, the
large friction force at the ground can produce a torque which can swing the bicycle with the rider over the front wheel.
It is recommended not to apply the front wheel brakes fully before the bicycle has slowed down appreciably, except
during an emergency.
The total braking distance
in wet conditions is much
larger than in dry. Extreme
caution is called for in riding
when it rains.
The bicycle brakes are very unreliable in wet weather. When the brake pads are wet, the coefficient of friction
between the pads and the rim decreases drastically and it becomes difficult to bring a wet bicycle to stop in a hurry.
Some internal hub brakes have been developed which protect the brakes from water, but they are either too expensive
or heavy to for common use.
Stability
For a kid and an adult alike, there is no experience more thrilling than ‘hands-off bicycling. Even with hands on, it
seems miraculous that a vehicle with only two wheels can stay upright over rough roads.
If the bicycle leans to the left,
the rider leans further to the left;
the wheel turns to the left and
the bicycle uprights. A rider
learns to do this automatically.
Any rider knows that a bicycle is balanced by steering into a fall just like a juggler balances a broom on his finger. If
a bicycle begins to fall to the left, the front wheel is turned to the left, and this makes the bicycle upright again. But one
has to do it consciously only when one is learning to ride. As the rider gains confidence, he relaxes, and the bicycle
seems to do the correction by itself—as it indeed docs when one rides with both hands-off the handle bar. How does a
bicycle straighten itself when it begins to fall?
Front fork geometry. The variables
that affect the stability of the bicycle.
It is a complex question, made more difficult because of the complex geometry of the steering head. It has been
shown that a bicycle rights itself because of the complex interplay of the inclination of the steering tube (termed as the
steering head angle), the bent of the front fork (resulting as the steering head angle), and the lean of the bicycle frame
from the vertical. For certain combinations of head angles and fork offset the steering automatically turns into the lean.
The reason for this automatic turning is that under these conditions the net frame height decreases as the steering turns
into the lean and as we know the natural tendency of a body is to keep the height of its centre of gravity at the minimum.
A bicycle should be stable but not too stable.
Most practical bikes have parameters that are
in the cross-hatched region. The head angle is
restricted by the clearance between wheel and
the pedals and the ease ot handling the bar
steering.
This property of a bicycle to stay erect while running is termed as stability. We can increase the stability of a bicycle
by increasing the head angle or by decreasing the offset—even making it negative. But stability is not all. One could
make a bicycle so stable that it becomes hard to steer into a curve of one’s choice. Such a bicycle would naturally follow
the contours of the road rather than go where one wants it to go. It is for this reason that there is only a small range of
practically useful head angles (between 72°-74° and of fork offset (between 6 to 8 percent of the wheel diameter).
Lesser offset would mean a more stable bicycle, but one which would require larger forces to steer.
Bicycle—a Machine Tailored to the Human Body
Due to the use of ingenious mechanisms and devices and the principles of physics, the bicycle has evolved into its
present shape. But a bicycle is more than the sum of its component parts. The high efficiency of a bicycle is only partly
due to its low weight, the reduced friction because of the ball bearings and bush-roller chains minimum rolling resistance
due to pneumatic tyres. The main reason for its high efficiency is the way the machine is fitted to the human body.
Unlike a man walking or running, a cyclist’s legs do not support his weight. The important leg muscles are now
concerned only with motion and not with keeping the torso upright. Peddling uses his thigh muscles which are the most
powerful ones in his body. During walking, the whole body oscillates in a vertical plane which dissipates work. But
during bicycling the torso is stationary, the feet go in smooth circular motion and only the thighs are bobbing up and
down. The geometry of the frame is such that the legs bear directly on to the pedals utilizing the applied muscular force
to the maximum. The handle-bar and the saddle are so located (or can be so adjusted) that the arms are nearly straight,
supporting the body somewhat but without undue strain. The racing posture is a little less comfortable but a racer is a
different breed altogether—preferring performance to comfort.
Some Interesting Websites
www.exploratorium.edu/cycling
A good resource on various aspects of bicycling. This site also contains exceptionally good introduction to the
science and arts of many sports. Highly recommended.
www.science.uva.nl/research/amstel/bicycle
Scientific and cultural aspects of the bicycle. An important learning resource.
www.pedalinghistory.com
A very good resource for various aspects of bicycling, as sport and as a movement.
www.bicyclepaintings.com
A collection of fine oil paintings of historical bicycles.
www.state.il.us/kids/isp/bikes/default.htm
Preparing to ride? Tips and rules.
www.ctuc.asn.au/bicycles
Site of the Canberra Bicycle Museum and Resource Centre.
www.cycling.org/lists/hardcore-bicycle-science
A good description of bicycle science
www.ibike.org/historymuseum.htm
Website of the International bicycle fund
www.bicyclemuseum.com
Home page of the Bicycle Museum of America
Time Line in the History of Bicycle
1791
1817
1839
1863
1865
1869
1870
1872
1888
1889
1896
1899
1903
1965
1972
1980
1985
The first reported plank-with-two wheel on which the rider sat and propelled by thrusting feet on
ground.
Baron von Drais makes the front wheel steerable. Hobbyhorse is invented. Huge success as a novelty.
Kirkpatric MacMillan of Scotland attaches treadle and cranks to the rear wheels to “invent’ the first
two-wheeled vehicle. Not well received at all. MacMillan is credited now to be the inventor of the
bicycle.
Pedals are added to the front wheel. The Bone-shaker is launched. Riding velocipedes soon becomes a
fad.
Radial (and torsion) spokes are introduced making bicycles lighter.
Solid rubber tires are introduced in place of iron tires. The term “bicycle’ is first used.
Tangential spokes are used replacing radial and torsion spokes. No major change since then.
Tall-ordinary or the Penny-Far thing makes appearance in England.
JK Starley invents the Rover safety bicycle.
Pneumatic tires are first used. The development of the basic bicycle is complete.
Coaster brakes invented.
Mile-a-minute barrier broken. Murphy completes a mile in 57,75 second.
Bicycle mechanics Orville and Wilbur Wright Invent’ the aeroplane.
Conservation movement and physical fitness buffs recognize the importance of bicycle and a bicycle
boom begins.
For the first time ever, bicycles outsell cars in United States of America.
Disc wheels introduced in competition bicycles to reduce the aerodynamics drags due to individual
spokes.
Bicycle speed exceeds 150 miles per hour. John Howard sets the speed record at 152.28 mph.
END
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