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= ěN
Where:
Fr= Friction force which we want to maximize
ě= 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= ěN
Where:
Fr= Friction force which we want to maximize
ě= 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.