Re: If friction is independent of surface area, wide tires should not matter?

The idea that friction forces do not vary with surface area dates back to 
1699, from Amontons.  He stated that friction force is independent of the 
apparent area of contact.  For hard materials, this is nearly correct.  
The true area of contact varies with the applied load.  The apparent area 
does not.  If you can imagine the contact zone from a microscopic 
viewpoint, only a tiny portion of the apparent area actually touches.  
This tiny area is the true area of contact.  But this applies to hard 
materials.  It does not apply to elastomers, such as rubber.

Tire tread rubber compounds vary greatly from one application to another.  
Race car tire tread compounds can be very soft, viscoelastic materials, 
while heavy truck tread rubber can be quite hard.  In general, soft rubber 
materials have greater friction.  With drag racing 'slicks,' the tire 
tread material literally sticks to the pavement--and the rubber is sheared 
from the tire.  Clearly, the greater the apparent contact area, the 
greater this shear force.  Cleanliness is important to getting the 
surfaces to 'stick.'  This is one reason why drag racers have a 'burn-out' 
before each race (another is to raise the tire tread surface temperature).

However, there is another reason for wide tire treads on some road and 
track racing cars.  They need tread volume to provide enough wear life.  
Tires wear rapidly under racing conditions.  Some long races wear out 
several sets of tires.  

There are trade-offs with traction and tread life.  That is why heavy 
truck tire tread compounds do not have as much friction as those used on 
passenger cars.  However, truck tire tread compounds provide longer wear 
life and less heat build-up.  Like many things in this world, tire tread 
choices involve compromises. 

You seem to have some interest in racing car tires.  These URL's will 
provide more information.
 http://members.home.
net/rck/phor/02-Tires-Stuck.html 
http://www.
turnfast.com/tech_handling/handling_traction.lasso