Mehcanisms of Tire grip.
Friction
Mechanical Keying
Adhesion
As they are madr from deformable rubber, tires dont exactly follow basic friction theory. So to just say that F=mu*r is strictly wrong. Although it basically does floow this during the elastic range.
Tires only give grip when they are at the correct temperature. this is the most important thing you can remember about tires .
Now on to business.
Tires are the most important part of the suspension, either they are designed to fit it, or the suspension is designed around the tire.
People who say wider tires make more grip because ;''there is more rubber on the road' are wrong. They are both wrong that it makes mroe grip and that there is more rubber on the road.
When you make a tire wider, you alter the contact patch to be wider , but it reduces in length. So depending on sidewall stiffness, a wider tire can actually give less rubber on the road.
The main reason for tires being the size they are is actually heat management. Wider, low sidewall tires will cool better than narrow tall tires. If you can;'t get a tire up to temperatie it will give no grip, if you get it too high you will cook the rubber and ruin the set of tires.
Back to contact patch, you can safely assume that contact patch stays roughly the same area with wide or narrow tires (as long as the load stsys the same). Narroe will have longer contact patches and wide tires will have shorter.
The reason why F1 tires are wide is primarily so that they dont cook (remember they arent just wide, they are fairly high sidewalled), but they ten dto have wider contact patches because they will give better grip going round corners.
A wide tire will generate more lateral force per slip angle making cornering better. F1 cars DO NOT have wide tires for linear acceleration.
Conversely (Mike im goin to have to disagree with you here) drag racers acutally use the tires not becuase of the width, but the tallness. As we know a wider contact patch gives better cornering performance, a narrow but long contact patch is what you want for linear acceleration.
so strangely, drag racers will actually be better with narrow tires. So why do they use wide tires? (remember the most important gip aspect of tires) Temperature! They want as longer contact patch as they can get, but need the width for cooling. (eith 4000+ horsepower you do kind of build temp rather well)
But if you look at the contact patch shape between say, an F1 car or drag racer. (both are considered to use wide tires). The F1 patch will be wider and shorter for good cornering, the drag patch will be longer and narrower (relatively) for good linear acceleration.
So to sum up: Wider tires are not always better. They dont always give better traction. It depends on the car, the situation, the conditions.
Eg. Rally cars use wider tires when on tarmac rallys, and use (surprisingly) very thin tires on ice rallys.
F1 cars used to use narrow tires until aero began to be used in the 60's.
Drag racers acutally want tall tires, width is there to stop the tire being destroyed.
Reference
https://www.physicsforums.com/threads/w ... te.330790/