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Steve,
As stated above, this formula is simply for the force (or work if you like) required to over come friction and move something. It has nothing to do with grip, traction, or anything else.
The example you raised of a stock car on bicycle tires is still totally valid. The proper use of it in the formula above though would be if you were behind it trying to push it from a stanstill, would it roll any easier on stock tires rather than bike tires (assuming overall mass is same and bike tires could take the load)? Of course it would be every bit as hard to push, so the force you exerted would be the same regardless of tire surface area. So F=Nu still holds. To take this to an extreme, if you could actually get the car to balance on 4 tires made of razor blade thin materials, it would still requires the same effort to push it horizontally (car doesn't get any lighter), so F=Nu still.
So why do racing cars have those big wide tires? From an online physics site I found:
Because the size of the contact area is very important in car tires as the traction is dynamic rather than static; that is, it changes as the tire rolls along. The maximum coefficient of friction can occur anywhere in the contact area, so that the greater the area, the greater the likelihood of maximum traction. Thus, under identical load and on the same dry surface, the wider tire has a greater contact area and develops higher traction, resulting in greater stopping ability.
Or another explanation of the same:
It is true that wider tires commonly have better traction. The main reason why this is so does not relate to contact patch, however, but to composition. Soft compound tires are required to be wider in order for the side-wall to support the weight of the car. softer tires have a larger coefficient of friction, therefore better traction. A narrow, soft tire would not be strong enough, nor would it last very long. Wear in a tire is related to contact patch. Harder compound tires wear much longer, and can be narrower. They do, however have a lower coefficient of friction, therefore less traction. Among tires of the same type and composition, here is no appreciable difference in 'traction' with different widths. Wider tires, assuming all other factors are equal, commonly have stiffer side-walls and experience less roll. This gives better cornering performance.
As an aside Steve, the greater surface contact s actally a detriment whent he road is wet because that changes the rolling/static friction coefficients. The same wide flat tire that helps you accelerate and corner on dry pavement is absolutely also the best hydroplanar in wet condidtions. That's why your 'normal' tires have grooves, so the rain/snow gets diverted into the grroves and allows the rest of the tire to stay in contact with the road. You always want your tires to roll as much as possible (rolling friction) as opposed to skidding (static friction.)
Did this help at all?
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