Last year we did a similar test with neoprene pad material (available from spi). Our test was slightly different in that we had two wheels surfaced with this material and also a large plate surfaced with the same stuff. We were using about 70 lb. of dead weight and some FIRST carpet. Our test indicated that the double wheel (still at 70 lb. of normal force) slightly outperformed the single wheel and the sheet underperformed both. We also tested all three of these at different weights, but I won't bore you with the details.
My conclusion was that there is an optimum amount of surface area for a corresponding weight for these two materials. Too much surface area and the tread floats on top of the carpet fiber. Too little and you don't have as much fiber engagement. It also seemed to me that the coefficient of friction verses contact area (at a fixed normal force) curve has a pretty flat top. Here's my ASCII drawing of what I think it looks like based on my somewhat limited experiments where mu is the coefficient of friction and SA is surface area (again for a constand normal force):
Code:
mu
| ________
| / \_____
| /
|/_____________ SA