Hey, wait!! You guys started the discussion without me!!
And if you haven't freaked out by the volume of information Ernie posted, allow me to add:
Barry's Tire Tech
If you read everything on the web site - and not just that page, - you'll find the Ernie and I disagree about calculating the size of the contact patch, and the role air plays in holding up the vehicle, and a few other things that aren't important to the discusssion at hand, so I won't debate those issues here.
But for those who don't want to wade through all that information:
1) Rolling Resistance in tires is mostly caused by Hysteresis - the internal energy consumption of the tire. You could look at this is as internal friction generating heat.
2) Most of the rolling resistance is caused by 3 things: The material properties the tire is made out of, the amount of movement that those materials experience, and the amount of material there is.
3) Most of the energy loss occurs in the tread area, and because most of the tread area is tread rubber, it becomes the most important item in a tire's rolling resistance.
4) The amount of movement that causes this energy loss is mostly controlled by inflation pressure - very little is controlled by the stiffness of the sidewall by itself.
5) Tread rubber chemistry results in a 3 way technology triangle: Treadwear / Traction / Rolling Resistance. Put another wasy: To improve one, you have to sacrifice on of the others (or both).
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OK, that's enough for now. Carry on.