Air resistance, tyres and friction
Dragsters use a combination of large wide tyres or the rear and small narrow
tyres on the front this combination is used for the following reasons:
The front wheels:
The front wheels are very narrow. This is so a minimum of air resistance or drag
affects the dragster with lower drag better acceleration an in turn a better top
speed can be achieved all leading to a better pass (race time).
Now lets try to understand the concept of air resistance and drag. A basic
example is placing your hand out the window with your palm facing forwards as
you are driving your car along at about sixty kilometres per hour. You will feel
a strong force of the wind (air resistance) pushing back at your hand. Now turn
your hand side or so that your little finger is facing the front and your thumb
is facing the rear at the same speed. The force of air resistance exerted on
your hand is greatly reduced. This force is similar as to that exerted on the
front wheels of the dragster.
Now dragsters reach speeds of up to five hundred kilometres per hour, imagine
the force needed to hold your hand against the wind if your palm was facing the
front. It would be much easier to hold your hand side on. The same as it would
be much easier for the dragsters engine to push the narrow front wheels compared
to large ones.
Air resistance is a form of friction (namely fluid friction) a friction from the
air, as we know friction is defined as a force that opposes movement.
The formula used to determine aerodynamic drag is as follows:
Drag = 0.5 * rho * Cd * v2 * S
Aerodynamic drag is a function of the following:
rho is the air density, which we cannot change.
v2 is velocity squared which is endeavoured to be maximized for the best time
and/or pass.
S is the frontal or cross sectional area which we want to minimize. I.e. less
frontal area means that a less significant amount of air resistance impedes the
top speed and acceleration.
Cd is the coefficient of drag, which we want to minimize.
So the two things with which can be worked with or changed, the frontal area and
coefficient of drag, both of which need to be to minimized for the best results.
Having very narrow front wheels minimizes the frontal area. This is the main
reason why narrow front wheels are used.
If the smaller the wheel the lower the drag, why not have the wheels narrow and
very short as well? You ask. Well the reason is that if the wheels were very
small they would drop into all the bumps and cause a loss of speed not to
mention control. As the wheels would bounce into the depression and then launch
up into the air as they come out of the bump. This is extremely dangerous in
that the driver can no longer steer the vehicle that is travelling at near five
hundred kilometres per hour, the car can also get air flowing underneath the
car, with the effect of air resistance the car will lift up of the ground and
flip through the air.
Also the rotational force is much harder on the bearings causing more wear and
friction meaning slower times.
Large wheels are used because they will skim over the bumps and keep the car
moving along a flat plane. They also exert less force on the bearings meaning
less friction and better times.
Now if drag cars use narrow front wheels so they can get less air resistance and
a better top speed why don’t all racing vehicles run narrow front wheels? The
answer is friction. The front wheels of drag cars do not have high cornering or
driving force travelling trough them. I.e. they are only there to hold the front
of the car up and allow it to roll along the road. In conventional racecars high
forces are exerted on the tyre in the horizontal plane meaning that they need to
have a good tread area so that they grip the road well and hold the car on the
track so it does not slide off into the dirt.
A consequence of this is that narrower wheels mean less mass or weight which in
turn means less force is required to move the wheel which means more force can
go into propelling the car forwards.
The rear wheels:
The rear wheels on a dragster are used in an entirely different matter. The rear
wheels on a dragster are very wide and very tall when compared to the front
wheels. This greatly increases the air resistance, which we saw in the front
wheels impedes the performance of the dragster. However this increase in air
resistance is greatly outweighed by the gains due to friction. The rear wheels
have a large tread width and circumference, which means they have a very large
‘footprint’ in comparison to the front wheels. A footprint it tyre
terminology is basically the amount of the tyre that comes in contact with the
road at one time. In terms of the rear wheels the larger the rear wheels the
better. This is because huge amounts of force are put through the rear wheels by
the engine to drive the car forwards at the maximum possible acceleration.
Stress= Force
Surface Area
Where:
Stress, is the amount of force that can be put through the wheel without
breaking the friction force
Force is the energy that is put onto the tyre by inertia.
Surface area is the footprint of the tyre.
Fr= ìN
Where:
Fr= Friction force which we want to maximize
ì= the coefficient of friction is defined as the ratio of tangential force to
normal load during a sliding process.
N= normal force. i.e. the force that is acting between the road and tyre
(gravitational and reaction forces).
The amount of force generated on the wheel by the engine is in the vicinity of
1000 horsepower or nearly 800 kilowatts. Now if the rear wheels were very narrow
the amount of force generated could only be applied at a lower rate, because the
less stress and coefficient of friction created this means that the wheels would
spin on the road more easily, causing the dragster to have poor acceleration and
a low top speed meaning a slow time. So the dragsters run a very wide tyre with
a large footprint so that a maximum of force can be applied in a minimum amount
of time so as not to spin the wheels but obtain maximum acceleration and drive
from the line obtaining the best top speed possible and acquiring the fastest
time.
The force placed though the rear tyres of a dragster under acceleration relates
to Newton’s third law of motion, in that every force has an equal and opposite
reaction. In the case of the dragster the wheel of the dragster pushes backwards
on the earth. Since it is improbable for the dragster to rotate the earth, the
dragster is propelled forwards by the earth pushing forwards on the wheel
opposing its force. The force exerted onto the earth is such however that the
tar on the road will stretch and move to the rear of the dragster with the force
of the wheel driving forwards.
So how do we obtain the greatest amount of traction (friction) from the rear
tyres, as this allows us to put more force onto the tyre and get a better
acceleration? The first method is to run very wide and tall tyres to get a
larger footprint, as explained previously, however the governing bodies limit
the size of the tires to be used. So they run smooth tyres called “slicks”
these tyres have the greatest surface area because they have a flat surface and
in turn have the greatest amount of stress and coefficient of friction.. So if
we have got the widest and tallest slick tyres possible how can we gain extra
traction? The first step is to run very low tyre pressure, around six or sever
psi (pounds per square inch) This causes the tyre to squat down and squish onto
the road creating a even larger footprint. The next method is to make the rubber
sticky so that it will grip the road like ’glue’ and prevent the wheels
spinning across the road, which reduces acceleration. So how do we get the
rubber really sticky? Well two methods are used a chemical change and a physical
change are used. Firstly the chemical change is preformed. A Hydrocarbon,
solvent Xylene is ‘painted’ onto the tread (road touching part of the tyre).
This softens the bonds between the rubber and makes it very sticky. The next
step is the physical change, which is preformed just before that start of the
pass. Where the car does a large “burn out” which involves putting a large
amount of force through the rear wheels to an extent where they spin across the
road at high velocity due to the friction force being overcome.
This causes the rubber to become extremely hot and sticky due to friction and
elastic deformation of the rubber bonds. When in this sticky state the wheels
can withstand a maximum amount of force without spinning the wheels due to and
increased coefficient of friction, gaining a up most level of acceleration in
turn obtaining a high top speed and attaining a fast time.
It is somewhat ironic that the narrow front wheels have been used to reduce
friction and the wide rear wheels have been used to obtain the greatest amount
of friction. Albeit different types of friction in the front wheels fluid
friction from the air is trying to be minimized. In the rear wheels kinetic
friction is trying to be maximised so that newtons third law is proven in that
the wheel pushing back on the earth will have a reaction of the earth pushing
back on the wheel.
Racing cars use either slicks or wet weather racing tyres. The properties and
differences between each are as follows:
Slick tyres:
In racing slick tyres are used in dry conditions. This is because a slick tyre
offers the largest ‘footprint’. The footprint of a tyre is defined as the
surface area of a tyre that comes in contact with the road surface at any one
time.
Fr= ìN
Where:
Fr= Friction force which we want to maximize
ì= the coefficient of friction is defined as the ratio of tangential force to
normal load during a sliding process.
N= normal force. i.e. the force that is acting between the road and tyre
(gravitational and reaction forces). This only changed by the inertial force
pushing onto the outside tyres. (more detail later)
In the case of tyres the larger the footprint the greater the surface area and
the greater the grip (coefficient of friction between the road and tyre) thus
the faster we can go around corners. Now the first way to get a large footprint
is to run a slick tyre as previously mentioned. Also low tyre pressures below 20
psi (pounds per square inch) can be run to squat the tyre down onto the road and
form a larger footprint. However with lower tyre pressures there is less force
holding the tyre in shape. When under extreme force in the horizontal plane
(such as in cornering) the rubber will elastically deform and cause heat to be
generated.
This heat is advantageous in that it causes a physical change in the rubber and
it becomes soft and sticky. This translates into better grip. Though this only
occurs to a certain extent. Once the tyre reachers a very high temperature (well
over the peak operating temperature of one hundred degrees centigrade) the tyre
‘overheats’ this is when resins that help to bond the rubber become
liquefied and the centrifugal force of the tyre rotating at high velocity forces
the resins to come to the tread or surface of the tyre. These resins then act as
a lubricant between the tyre tread and the road. This causes a loss in the
coefficient of friction and consequently a loss of control and time.
Stress= Force
Surface Area
Where:
Stress, is the amount of force that can be put through the wheel without
breaking the friction force
Force is the energy that is put onto the tyre by inertia.
Surface area is the footprint of the tyre.
If the tyre is over inflated it will form a peak in the centre of its
circumference meaning a smaller footprint and lower stress.
The tyre will be stiffer in construction and will not elastically deform as much
thus not generating as much heat. However the tyre will only roll around this
narrow circumference. This causes an excess of force exerted on a small area of
the tread, this area will become very hot due to the friction on this area. The
resins then will act as a lubricant as explained previously and reduce the
coefficient of friction. This localised heat will cause an even greater peak in
the tyre as air expands under heat causing more pressure and more over inflation
of the tyre. This can be over come by running nitrogen gas in the tyre as
nitrogen expands less than air under heat. This means that the stress will
suffer less from a rise in temperature.
The next method is to keep the entire tyre on the road surface at one time,
increasing the stress and in turn the friction. When under cornering the inertia
of the vehicle is that it will want to continue to move in the straight line
that it was previously travelling in (Newtons 1st law: A body stationary or
moving with constant velocity will continue to do so unless acted on by a
force). So the force of the inertia will attempt to slide the tyre across the
road surface to continue moving along the straight path. However the friction of
the tyre is such that it will resist this force. This will transfer the force
onto the outside tyres, increasing the normal force and hence generation more
friction in those tyres. If the force of the inertia is so great it will form a
resultant force that will rotate around the outside wheels. This means that the
vehicle will attempt roll over around the tyre. The tyre will then be lifted up
off the road causing a reduction in the surface area or footprint; this can
result in two outcomes.
Table depiction the forces acting on the vehicle under cornering.
Outcome 1: the tyre will have less friction force and thus will lose traction on
the road and slide allowing the inertia to continue its movement but at a
lowered rate.
Outcome 2: if the friction generated by the tyre is so great that the inertia
force will continue to rotate the vehicle around the tyre until the inertia
force is lowered by a change in direction or until the vehicle literally rolls
past a vertical axis on rolls over and finishes on its side or upside down.
This problem is overcome by softening of the chassis. This allows the chassis to
flex or elastically deform giving a defection angle to the axle this will keep
the outmost tyre in full contact will the road surface whilst remaining
relatively horizontally aligned or flat on the road.
The next method is to run negative camber. Camber is the angle of the wheel
relative to a perpendicular of the ground.
When travelling in a straight line this means only a small portion of the tyres
tread will come in contact with the road, this does not play an important role
as little if any horizontal force is acting on the tyre when travelling in a
straight line. None the less the benefits of negative camber do not come into
play until cornering occurs. As we saw previously the inertia will attempt to
roll the vehicle around the outside tyre.
When negative camber is used the vehicle will roll up onto the tyre giving full
tread contact with the road meaning more traction which in turn means the turn
can be taken at a higher speed. The slight disadvantage of running negative
camber is that the inside tyre will barely have any tread touching the road
surface. This does not play an important role as the inertia places most of the
load onto the outside tyres.
Wet tyres:
Are the same as slick tyres with two exceptions:
1) They have grooves in the tread.
2) They are made of a softer compound rubber.
In racing wet weather tyres are used, as their namesakes suggests, in wet
weather conditions. This is because they offer the best grip in wet conditions.
Yet they also may be used in snowy or icy conditions!
Why do wet weathers work best in wet conditions?
Well let’s start with why slicks are not used in wet weather. Slick tyres are
not used in wet weather conditions because as water forms on the road surface
the surface tension is such that the tyre will be unable to break this force and
will ride up on top of the water causing a loss in the coefficient of friction
to a point where nearly no friction is present. The water will act as a
lubricant between the road and the tyre. This is called Aquaplaning. When
aquaplaning occurs an instant loss of friction between the tyre and the road
occurs. This loss of traction can occur at any speed, as low as 2 kilometres per
hour or it can occur at over five hundred kilometres per hour. This loss of
traction means loss of control, and the inertial forces on a vehicle at five
hundred kilometres per hour with no friction from the tyres opposing it can
means catastrophic problem the inertia will drive the vehicle out of control and
straight ahead off the track trying to continue on its original path as in
newtons first law. Once aquaplaning occurs it is nearly impossible to reverse or
correct even in the most capable, talented and experienced hands as there is not
much a driver can do to regain the frictional forces.
Wet weathers tyres are used because the grooves in the tyre allow water to be
pumped out from under the tyre at over 300 litres of water per minute, enough to
literally dry the road. This enables the rubber to gain some if very reduced
contact with the road and hence gain some coefficient of friction..
When the rubber comes in contact with the road it generates friction. This
friction as in slick tyres generates grip. Now how do we generate enough heat to
make the wet tyres hot and sticky, if there isn’t enough surface friction?
The answer is in elastic deformation. When the wet tyre has force exerted on it
under cornering the ‘rubber blocks’ formed by the grooves in the tyre grip
on the road and the vehicle stretches over the top of them. Then when a loss of
friction occurs the block will move back into its original position and
condition this contraction forms heat. This elastic deformation happens at
hundreds of times per second. This generates enough heat to enable the tyre to
become hot and sticky generating a greater coefficient of friction. A by-product
of this heat is that it helps to evaporate the water and dry the road. It is not
uncommon for wet weather tyres to be steaming or totally dry after a race or
session.
A softer rubber compound is easier to elastically deform and therefore will
generate more heat more quickly meaning more grip. A downside to this is that
they will wear much faster then harder compound tyres, as it is easier for the
road to shear off rubber particles. This may cause a problem with wet weather
tyres if the road dries to much as they will deteriorate extremely quickly and
get extremely hot enough to bring out the resins as in the slick tyres. In the
wet however due to the cooling effect of the water this does not occur and a
very soft compound is used to gain optimum heat and coefficient of friction.
This is why during a drying race it is very common to see driver’s
deliberately driving over the wet part of the track. This is to literally cool
down their tyres.
If wet weather tyres were to be used in the dry the rubber blocks would shear
away very quickly as they would ‘bite’ (grip) the road and deteriorate as
they are very soft compound. Also wet weather tyres have a smaller footprint
than slick tyres. This means that they will generate less coefficient of
friction and less stress and grip as they do not have the same amount of surface
area in contact with the road and will slide a lot easier.
With wet weather tyres there are two main theories on tyre pressures:
The first and more commonly used theory is that using high tyre pressures will
cause the tyre to expand and inturn will open up the grooves allowing more water
to be pumped out and dry the road even more. Meaning better contact which means
greater coefficient of friction, which creates more heat and grip.
The second theory is that running lower tyre pressures softens up the
construction of the tyre and allows the rubber blocks to be elastically deformed
to a greater extent and generate more heat and thus more coefficient of
friction.
In Slick and wet tyres the objective is to gain the greatest amount of friction.
Since we cannot change the normal force this is done by inertia, we try to
obtain the greatest coefficient of friction. Slicks in dry conditions do this by
having the greatest footprint and stress area, wets weathers do this in wet
conditions by clearing the lubricating water off the road to gain some contact
with the ground so that some coefficient of friction is obtained.
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