![[purpleball]](http://www.chris-longhurst.com/carbibles/images/redball.gif) Fat or thin? The question of contact patches and grip.
If there's one question guaranteed to promote argument and counter argument, it's this : do wide tyres give me better grip?
Fat tyres look good. In fact they look stonkingly good. In the dry they are mercilessly full of grip. In the wet, you might want to make sure your insurance is paid up, especially if you're in a rear-wheel-drive car. Contrary to what you might think (and to what I used to think), bigger contact patch does not necessarily mean increased grip. Better yet, fatter tyres do not mean bigger contact patch. Confused? Check it out:
Pressure=weight/area.
That's about as simple a physics equation as you can get. For the general case of most car tyres travelling on a road, it works pretty well. Let me explain. Let's say you've got some regular tyres, as supplied with your car. They're inflated to 30psi and your car weighs 1500Kg. Roughly speaking, each tyre is taking about a quarter of your car's weight - in this case 375Kg. In metric, 30psi is about 2.11Kg/cm2.
By that formula, the area of your contact patch is going to be roughly 375 / 2.11 = 177.7cm2 (weight divided by pressure) Let's say your standard tyres are 185/65R14 - a good middle-ground, factory-fit tyre. That means the tread width is 18.5cm side to side. So your contact patch with all these variables is going to be about 177.7cm2 / 18.5, which is 9.8cm. Your contact patch is a rectangle 18.5cm across the width of the tyre by 9.8cm front-to-back where it sits 'flat' on the road. Still with me? Great. You've taken your car to the tyre dealer and with the help of my tyre calculator, figured out that you can get some swanky 225/50R15 tyres. You polish up the 15inch rims, get the tyres fitted and drive off. Let's look at the equation again. The weight of your car bearing down on the wheels hasn't changed. The PSI in the tyres is going to be about the same. If those two variables haven't changed, then your contact patch is still going to be the same : 177.7cm2 However you now have wider tyres - the tread width is now 22.5cm instead of 18.5cm. The same contact patch but with wider tyres means a narrower contact area front-to-back. In this example, it becomes 177.7cm2 / 22.5, which is 7.8cm.
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| Imagine driving on to a glass road and looking up underneath your tyres. This is the example contact patch (in red) for the situation I explained above. The narrower tyre has a longer, thinner contact patch. The fatter tyre has a shorter, wider contact patch, but the area is the same on both. |
And there is your 'eureka' moment. Overall, the area of your contact patch has remained more or less identical. But by putting wider tyres on, the shape of the contact patch has changed. Actually, the contact patch is really a squashed oval rather than a rectangle, but for the sake of simplicity on this site, I've illustrated it as a rectangle - it makes the concept a little easier to understand. So has the penny dropped? I'll assume it has. So now you understand that it makes no difference to the contact patch, this leads us on nicely to the sticky topic of grip.
The area of the contact patch does not affect the actual grip of the tyre (strange though it may seem) but it does allow the tyre to distribute heat across the contact patch better, making their operational range greater. The things that affect grip are the coefficient of friction and the load on the tyre. Well we know from above that the load on the tyre remains pretty much the same. Of course it varies in corners as more weight is transferred because of cornering forces, but for the sake of simplicity, load is constant. That leaves on last factor - coefficient of friction. Friction is basically dependant on the rubber compound used to make the tyre, and how that compound changes it's coefficient of friction based on heat. Generally speaking, tyre rubber gets stickier the warmer it gets. At least to operating temperature, then it starts to overheat and it can all go pear-shaped. That's why my comment right at the top about heat dispersal on larger tyres is so important. That's also why Formula-1 teams have tyre-warmers in use before the tyres actually get put on the cars. The rubber compound that's in your tyres is something you'll only be able to find out by calling a tyre dealer, or the manufacturer. But the equation you need to know is simple : softer rubber = quicker wear = shorter tyre life. Generally speaking, that's why fatter tyres are generally regarded to have more grip - they're normally made of a softer rubber compound with a higher coefficient of friction. It's nothing to do with contact patch size after all.
I can tell you're still thinking about this. And the question bubbling around your head now is this:
Why doesn't friction depend on surface area? Well, although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together. In this case, gravity is the force holding your car on the road. As I told you above, pressure = weight / area. So it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the force holding them together. If you were to increase the force as you increased the area to keep pressure the same, then increasing the area would increase the frictional force between the two surfaces.
In laymans terms : the weight of your car isn't changing - that's the force keeping your tyre pressed against the road. The contact patch area doesn't change - I've explained that above. Your tyre isn't changing it's coefficient of friction (unless something is going badly wrong). To get more grip, you need to increase the force as well as the coefficient of friction. This is exactly what you see in Formula 1. Wings on the car increase the pressure on the tyres as the car goes faster, and the rubber compound in the tyres increases it's coefficient of friction as they get hotter. That equates to massive grip in the corners and ground-hugging speed on the straights. In fact the wings on an F1 car generate so much extra downforce that it more than doubles the weight of the car. In real terms, that means if someone built a racing track upside down, you could race Formula 1 cars on it and they'd stick to the track because the downforce is greater than the weight of the car under gravity. Neat eh?
That last paragraph also explains why dynamic setup on your car is pretty important. All the theory I've gone through so far is based on a static system - the car is driving at a constant speed in a straight line. In reality of course, the contact patch is effectively spinning around your tyre at some horrendous speed. When you brake or corner, load-transfer happens and all the tyres start to behave differently to each other. This is why weight transfer makes such a difference the handling dynamics of the car. Braking for instance; weight moves forward, so load on the front tyres increases. Pressure stays the same, so by your newly-learned formula, the contact patch area must increase. Using a bastardised version of the friction theory, the same load-per-m2 of contact patch, but more contact patch = more grip. The reverse happens to the rear at the same time, creating a car which can oversteer at the drop of a hat. The Mercedes A-class had this problem when it came out. The load-transfer was all wrong, and a rapid left-right-left on the steering wheel would upset the load so much that the vehicle lost grip in the rear, went sideways, re-acquired grip and rolled over. (That's since been changed.) The Audi TT had a problem too because the load on it's rear wheels wasn't enough to prevent understeer which is why all the new models have that daft little spoiler on the back.
If your brain isn't running out of your ears already, then here's a link to a raging debate that happened in 2000 on one of the Subaru forums about this very subject. If you decide to read this, you should bear in mind that Simon de Banke, webmaster of ScoobyNet, is a highly respected expert in vehicle dynamics and handling, and is also an extremely talented rally driver. It's also worth noting that he holds the World Record for driving sideways...........
If you decide to fatten up the tyres on your car, another consideration should be clearance with bits of your car. There's no point in getting super-fat tyres if they're going to rub against the inside of your wheel arches. Also, on cars with McPherson strut front suspension, there's a very real possibility that the tyre will foul the steering linkage on the suspension. Check it first!
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wheel width, contact patch, and traction ....read - 
