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Tyres, Grip and All That...

Sorting fact from fiction in tyre physics

By Dennis Jensen

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So many tyres; so many factors to consider! Do you go wider? Do you go for a lower profile? Do you increase your wheel diameter? What pressures do you run? The whole area is quite complicated, and the result is that there is a hell of a lot of misconceptions out there. What is needed is a primer to give some fairly solid grounding in the basics, so that informed decisions can be made.

So, let's go through two of the misconceptions, and see if we can get an understanding of what actually contributes to grip - and what does not.

Myth 1: Wider tyres have a larger contact patch than narrow tyres

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What actually influences the size of the tyre's contact patch? Is it the width of the tyre, or the profile? The simple answer that it is neither of these; the size of the tyre's contact patch is related to:

  • the weight on the wheel
  • the tyre pressure.

For example, say that the weight on the tyre was 900lb, and the tyre pressure was 10 psi. That internal pressure means that each square inch of area can support 10lb, so, in this case, the contact patch will be 90 square inches. If the tyre pressure was 30 psi, the contact area would be 30 square inches, and if the pressure was 90 psi, the contact area would be 10 square inches. This has been found to be almost exactly correct for most tyres (the exceptions being so-called run-flat tyres, or tyres with extremely stiff sidewalls). For most other tyres, carcass structure will have an effect, but by far the major factor is tyre pressure.

So, as you can see, the size of the contact patch of a tyre is not related to the width of the tyre - it is, in fact, proportional to the tyre pressure. What will change with the fitting of a wider tyre is the shape of the contact patch - it will get wider, but shorter longways.

Myth 2: A larger contact patch = more grip

Okay, most people will come to the conclusion that if you have "more rubber on the road" you will have increased grip. Sorry to say this folks, but to very close to 100% accuracy, the size of the contact patch is irrelevant.

The actual grip that a tyre can generate is dictated by the coefficient of friction of the rubber compound used in the tyre. The higher the coefficient, the more grip which can be generated. The relation that is used is called Amonton's Law, and the equation is:

F=uN,

where F is the force generated, u is the coefficient of friction, and N is the weight on the surface considered (in our case, the weight on the tyre).

So, if you increase the weight on the tyre, then the frictional force will increase as well, in proportion to the increase in weight on the tyre - but the coefficient of friction will remain the same. The level of grip of the tyre (forgetting about suspension niceties - we are only discussing tyres here) is totally dictated by the coefficient of grip of the tyre and the weight acting on it - not the area of the contact between the tyre and the road.

Why Not Narrow Tyres, Then?

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So, I hear you argue, why bother with wide, low profile tyres at all? Why not simply have narrow, high profile tyres? The simple reply to that is heat (remember, we are simply talking grip here, not the niceties of handling finesse). The point is that, to get a contact patch of a certain size on the road, you need a certain portion of the tyre to be flat. Taking the contact patch to be basically rectangular (though it is actually partially oval in shape), then the area of that patch will be its length times its width. Now, for a narrow tyre, the contact patch will be quite long compared with a wide tyre.

This introduces two problems for the tyre.

First, to get that long flat section to give the required contact patch, the sidewall of the tyre needs to deform quite a lot. This deformation actually causes the bending and unbending the rubber of the sidewall as it flattens and then the tread curves again. This bending and unbending process results in a lot of heat being generated. (Think about bending and unbending a piece of wire rapidly, and how hot it gets as you do so. If you bend it less, but at the same frequency, less heat will be generated). Obviously, the more it needs to bend, the greater the amount of heat generated.

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The second relates to the length itself. There will be a greater percentage of the tyre tread in contact with the road than if the contact patch length were shorter; this reduces the amount that the tread can cool. Also, there is a greater percentage of sidewall at any given time that is actually under bending stresses, again resulting in less opportunity to cool.

So, how much extra bending do you really get, and how much is potential tread cooling reduced? Let's take a theoretical example, and take a 155-width tyre compared with a 225 tyre of the same circumference. Agreed, this is an extreme example, but it will suit our point very well. Assume that the wheel/tyre-unloaded circumference is 60cm. Assume the tyre pressure is 30 psi, and that the weight on the wheel is 600lb, giving an area of 20 square inches (or 129 square cm). Assuming that the contact patch is rectangular, with the wider (225) tyre, the patch will be 5.73cm long, and with the 155 tyre, the patch will be 8.32cm long. Now, the circumference of the wheel-tyre combination is 188cm, so the 225 is heating for 3% of its cycle, and cooling 97%, whereas the 155 is heating for 4.5% of the cycle and cooling for 95.5%. So, you can see that the narrower tyre is generating heat 50% longer than the 225, and is not spending so much of its cycle cooling.

Now, as far as heating of the tyre is concerned, simple geometry shows us that the 155 tyre bends by 0.29cm, and the 225 bends by 0.14cm. Now, assuming that the heating of the tyre is roughly proportional to the deformation, let's find out the results of all of this. We will multiply the deformation by the percentage of time the tyre sidewall is under stress, and divide this number by the percentage of time that the tyre is being cooled. Multiplying the resulting numbers by 100, we get a figure of 1.37 for the 155 tyre, and 0.43 for the 225. Dividing the 155 tyre's number by that of the 225, we find that the heat generation of the 155 is 3.2 times that of the 225! This is quite an amazing result, given that the 225 is only 45% wider than the 155.

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As a result on this increased generation of heat, and the reduced capacity for self cooling, the tyres need to be made of a harder rubber compound that is more able to resist heat. This harder compound will, of necessity, have a reduced coefficient of friction, particularly when cold. The tyres that are wider can have a softer compound with better frictional properties. Due to the reduced bending stresses, and greater cooling opportunities, the tyre will tend to stay within a narrow temperature range quite consistently, giving greater cold grip, while managing to have a reduced propensity for overheating. Obviously, this makes for a better performance tyre.

On the issue of wheel size (the diameter, not the width), it is therefore clear that increasing the wheel/tyre diameter combination is beneficial. The reason for this is that the tyre will not have to deform so much to get the required contact patch length, and the percentage of the tyre tread in contact with the road will be less than for a smaller diameter combination.

So, what about tyre pressure? Obviously, tyre pressure plays a very important part, but there are clearly limits on both sides of the tyre pressure equation. At the higher end, there is the maximum tyre pressure that can be sustained before there is damage to the carcass. At the low end, you don't want the sidewall almost collapsing, generating massive heat, and have the tyre slipping on the rim. So, you can play around with tyre pressures to optimise your set-up, but there are limitations.

A simple way to find out approximately what pressure is optimal for your combination is to draw a chalkline across the width of the tyre, drive for a bit, and look at the wear pattern of the chalkmark. Wearing more quickly in the centre indicates pressure that is too high, and wear on the edges indicates too low a pressure.

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One issue to consider is that, for wet weather driving, despite what you may have heard, it is better to increase your tyre pressure, not reduce it. The reason is that there is a relationship between tyre pressure and the speed at which there is the onset of aquaplaning. In the Imperial system, the equation is 9 times the square root of the tyre pressure. So, if your tyres are at 25 psi, if you drive into a puddle that is deeper than your tread depth, you will aquaplane at 45 mph (72 km/h), whereas if your tyre pressure was 36psi, you would aquaplane at 54 mph (87 km/h). The advantages are obvious.

As far as tyre profile is concerned, the main benefit is one of handling - the lower sidewalls give reduced sidewall deformation under lateral loading, which results in improved steering response and a more stable contact patch.

Conclusion

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Summarizing, what factors are important in terms of tyre grip? Tyre width has no direct relation to the amount of grip generated; it is a secondary factor, and the width basically relates to cooling potential and so the tyre compound that can be used. The size of the contact patch has no bearing on the amount of grip generated at all, apart from the extreme of where the compound is getting so hot that it no longer acts as a solid (and therefore doesn't follow Amonton's Law). The tyre pressure has no direct bearing on the level of grip (apart from aquaplaning), but it does have a bearing on the heating and cooling characteristics of the tyre. Having a lower tyre profile gives improved handling through reduced sidewall stress and improved contact patch shape stability.

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