# Tyre Width vs Car Weight vs Grip Levels



## Moff (Sep 27, 2004)

An interesting topic which I cannot seem to find anything out about is an optimum tyre width for grip.

Forgetting the different type of tyre, I am talking about the downward pressure created by a tyre by the size of footprint on the road.

Eg if you fitted a 415 width tyre, then granted you have loads of tread on the road, but the weight of the car is spread over such a large area, that the down ward pressure on the road will be minimal.

Other Eg, if you fitted a 125 tyre, there would be massive amounts of downward force on the road through a small surface area, but not enough grip.

Is there a way or working out optimum tyre width or a science behind it ?

I believe BTCC run equivalent of 245 on full slicks. Based on this, a road tyre on a heavier road car, you might want a 295 for example, but no idea if BTCC tyres have to be regulation width or not ??

Discuss.........


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## Moff (Sep 27, 2004)

One of you clever chappies out there must know a starting point to this question


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## ru' (Feb 18, 2007)

Some stuff on contact patch etc.:

Browser Warning

Fact or Fiction? Tire contact patch and air pressure.

Automotive tire/wheel engineering - wider is better? or not? size of contact patch arguement

Car Bibles : The Wheel and Tyre Bible Page 2 of 2

(Google is your friend? tyre width contact patch - Google Search)


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## Moff (Sep 27, 2004)

Nice links, will cut and paste useful info as I go...

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


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## Moff (Sep 27, 2004)

*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.


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## Moff (Sep 27, 2004)

*Why Not Narrow Tyres, Then?*
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.

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.

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.

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.


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## Moff (Sep 27, 2004)

*Conclusion*
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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## Andy_P (Feb 4, 2007)

Have I read that conclusion right???
You're saying 
width
size of contact patch
and tyre pressure 
has no direct relation to grip.

That is not really a conclusion....just telling us what it isn't.
So what IS the relationship??


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## ru' (Feb 18, 2007)

Nice one. Now, would a wider tyre last longer than a narrower one???


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## TREG (May 20, 2004)

ru' said:


> Nice one. Now, would a wider tyre last longer than a narrower one???




Lol


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## Moff (Sep 27, 2004)

Wow, thats a lot of reading, my eyes are sore now....

None of them has answered my specific question about the downward forces exerted through tyre width, but I think for me the 2 most useful posts out of the million I have just read are below..


*1*

If looking in general at handling balance in the case of tyres, the cof drops off as you increase the weight on the wheel and you can tune a car's handling by adjusting the anti-roll bar.

The bigger the contact patch the more grip you can get. In a drag race, dropping the tyre pressure increases the contact patch area and increases grip.

When you look at lateral grip other factors start to matter. The tyre develops side force because of the slip angle between the tyre and the road. This slip angle means the tread is being pulled sideways by the road surface. At the front of the contact patch the deflection is relatively small. As you move back along the contact patch the deflection increases steadily. At some point, the sideways forces in the tyre exceed the friction between the tread and the road and the tread starts to slip relative to the road. When the tread is slipping like this it produces less grip on the road. As the slip angle increases the sideways deflection builds up quicker so the front of the contact patch works harder. But more and more of the back of the contact patch is sliding and losing grip. At some point you reach a maximum point where more slip angle means less side force because you are losing more grip at the rear of the contact patch that you are gaining at the front.

The longer the contact patch is, the more gradually break away occurs. If you shorten the contact patch, the break away occurs more abruptly but you get more absolute grip at the peak as there is less variation in sideways distortion between the front and back of the contact patch, more of the contact patch reaches maximum grip and starts to slide at the same point. 

When you fit wider tyres the contact patch wider and shorter for the same tyre pressure. This means you get a more abrupt breakaway but more grip right on the limit.

If this logic is correct then increasing pressure in the tyre further improves grip, since more pressure = less contact patch area = shorter contact patch = better grip?
However more rubber on the road does help grip due to the hysteresis properties of rubber. As rubber expands to fill a depression in the road, it takes some time to do so. When a tyre is sliding (and due to the slip angle, the rear most portion of the contact patch slides at even low cornering forces), this means that the upward rise of the depression to which the tyre is moving has more rubber acting on it that does the upwards rise on the other side. This allows a pressure differential in the lateral plane, providing frictional resistance over and above that offered by simple friction. As the tyre vertical load increases, the rubber is forced more fully, and more quickly into the depressions, overcoming the hysteresis and reacting on both sides of the upward rise from the depression more evenly – giving less pressure differential and less grip.
Low tyre pressure is better for grip from deformation and hysteresis.
Tuning the pressure is about balancing the contact patch length (which is better as pressure goes up), and the contact patch pressure (which is better as tyre pressure goes down). Even though the optimum grip may be achieved at low pressures higher slip (because the hysteresis element is significant),low pressure increases tyre deflection, which increases heat (less even radius over longer contact patch). It therefore appears that the best way to increase grip is a wide tyre as this gives a shorter contact patch for the same inflation pressure.

However tuning the handling balance using tyre pressures, appears to be a combination of trying to match front and rear slip angles, ultimate grip at the limit, and effect of heat which may effect inflation pressure and tyre compound?



*2*

I think it important to separate the effects of ride & handeling into at least 2 different areas.
One is for vehicles with completely adjustable suspension such as race cars. For production based, even with some mods to suspension there are some other items at work which can make what is theoretically good for a race car not good for the car without completely adjustable suspension.

In general:
Contact area is primarily load/inflation pressure BUT the sidewall stiffness of the tire does carry a portion of the load and that portion can also vary with inflation pressure so there is no one simple answer which is what I think many seem to want or expect. As UBERBEN pointed out tires have a load sensitivity curve and this curve is based on a combination of construction, aspect ratio and sidewall curvature both as molded and as mounted on a rim and the curve is not linear so again there is no simple answer.
It is entirely possible to have tire "A" provide better "grip" up to a certain point of speed around a curve but tire "B" to be better at the upper ranges of cornering. You also have to decide if it is better to have a flatter response curve with a more predictable response or one with higher max grip but only over a very narrow cornering angle that can break away with little warning at it's max level.

If you have a very wide tire it becomes more important to have the suspension ensure there are minimal camber changes or you will loose the possible advantage of the wider tire.

The first post starts out stating the two different opinions and then asks which is correct. In my experience neither is completely correct and neither is completely wrong. This is because you haven't stated the boundary conditions.

EVELROD in an early made statements about his comparison of a "radial" from one mfg vs a "bias" from another. It appears he based his opinion of a faulty assumption that a tire marked "radial" had a 0° body ply angle.
Using the angle convention of 0° running from bead to bead. I have seen tires marked "radial" having 0°, 5° and 37°. I have not looked at bias lately but know than many have body angles at 45° to 60°. 

The various arguments also have ignored the other variables such as tire weight and rotational inertia.

Tread width is also a variable that few seem to take into consideration. You can have 2 tires, both marked 225/50R16 but one can have a static contact width 8 to 20 mm wider than the other. Which is "wider".

There is no simple answer to tire design be it for ride, handling, noise, fuel economy etc, etc.

37 yrs Tire Eng. Designed basic rain Firestone for CART. SCCA & IMSA Pro & Am. Set lap records at 6 different road courses in '89-91.


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## NISFAN (Oct 11, 2003)

Nice one Moff :thumbsup:

Optimum tyre size is a complicated science.


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## ru' (Feb 18, 2007)

Don't forget looks too, lol

Looks(win) = Width(mm) - Stretch(%)


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## Moff (Sep 27, 2004)

ru' said:


> Don't forget looks too, lol
> 
> Looks(win) = Width(mm) - Stretch(%)


Not to forget a negative offset


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## rasonline (Mar 24, 2005)

Brian Beckman's Physics of Racing Series

read part 19

the rest of the links are pretty useful too


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## Moff (Sep 27, 2004)

wow, thats in depth !!!!


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## mattysupra (Oct 31, 2008)

thats lot is all over my head! So have we managed to work out what the best width of tyre is for a skyline? 

Surely there must be a table somewhere that tells you weight per axle to tyre width?


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## Cris (Sep 17, 2007)

mattysupra said:


> thats lot is all over my head! So have we managed to work out what the best width of tyre is for a skyline?
> 
> Surely there must be a table somewhere that tells you weight per axle to tyre width?


Not really that easy. Suspension plays a big part in how the tyre reacts to the road. Likewise tyres themselves have a large amount of variance. One companies 255 will be a different width to another. Finally sidewall construction and rims width plays part too.


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## Moff (Sep 27, 2004)

From my personal point of view. I am going to stick with Front 235 and Rear 255 and play with tyre pressure for now.


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