Originally Posted by genericbikedude
I dunno--but you'd have to calculte the surface area beneath your tires, as well as the force required to lift your rims out of the gook if they are buried (the weight of the material above your tires).
The rolling resistance function (whatever that may be) given the area beneath your tires + the force required to "un-bury" your tires as you go. Since we are dealing with tubular sections of circular bodies, there are going to be lots of sines and cosines and sh*t. Who needs that? Just go and ride your bike and eat total in the morning.
You can figure out rolling resistance through sand and dirt the same way as on normal roads. You figure out momentum first, MV at the time you first hit the sand/dirt (coasting). Then time how long it takes to stop the bike and measure how far you went. With those three pieces of data, you can come up with rolling resistance of the surface.