Contact Area and its Relation to Friction?

[Qbranch]

Ok, I've searched around and have found many posts on CD dealing with this question... but no one has given a concrete answer.

As many of you know... a normal force * coefficient of friction = friction force... at least in everybody's text book.

Obviously more contact area increases traction, or else race cars would have little skinny tires, not big fat wide tires. So... where does contact area factor in to friction force? I think it might have something to do with the non-homogeneous nature of tires and carpet or tires and asphalt or whatever the contact situation may be in most real world tire/track/other land propulsion applications... but I don't have an equation to give me friction force with non-homogeneous surfaces in that case.

I'm hoping i don't have to break down and dervie a formula from empirical data, but if thats what has to happen so be it.

Does anyone have a concrete (preferrably mathematical) answer to this vexing (or first-ing ) problem?

Thanks CD'ers/FIRST'ers,

-q