After posting a reply to the Thin Man thread, I've been doing some reading on tires. There's a whole lot more there than I was expecting. This thread in particular is pretty enlightening:
http://www.eng-tips.com/viewthread.cfm? ... 250&page=1
And here's a link to the discussion of Pacejka's Magic Formula, albeit for a racing simulator and not for actual tires:
http://www.racer.nl/reference/pacejka.htm
Tire geometry is a tricky problem. Treating it as a simple friction coeff x normal force equation apparently isn't entirely accurate, even in the case of a robot (i.e. no wet roads, oily conditions, oddball camber, frame twist, etc.)
One distinction I've seen tossed around a lot is the difference between global deformation and localized deformation on a tire. It's for this reason that larger contact patches really do equate to more gripping force, but it also means more rolling resistance.
Another neat one is that for a given contact patch size, a wider tire may have an advantage over a narrower tire because of the shape of the contact patch. It's wide rather than long, so the global deformation means less rolling resistance.
Inflation pressure comes up over and over and over again. For cast urethane tires that more or less equates to the hardness of the rubber being used. Softer rubber maps to lower inflation pressures. The benefit is a larger contact patch, but in the case of a pneumatic tire it also means less lateral stability and higher sidewall wear. I'm curious if those two can be separated when casting solid tires of two different materials. It may be possible to get a larger contact patch, but not allow much in the way of lateral instability. Testing!
Anyway, lots and lots of room to play. Now I need to pick up some urethane casting supplies!
I'm going to try digesting Pacejka's formula over the next few weeks and see if I can find any way to link enough parameters back to observables to stick it in the two wheeled robot spreadsheet. At least to play with. But if it's not possible to go from a part-in-hand (like those lint rollers!) and derive enough information to be useful, it won't be a useful extension of the model Colin already has posted.
Tom