Interaction of wheels and tread with carpet is a very complex subject. Coulomb friction (F=mu*N, with fixed mu) becomes a pretty poor model for the interaction when you get into macro-scale effects like roughtop digging into carpet fibers. Add in the fact that both tread and carpet are compliant (they compress under load), and I am not surprised that Cyberblue has made some "puzzling" findings.
Factors that I would expect to be involved in the final determination of maximum tractive force (traction-limited assumption):
* Tread material
* Tread pattern
* Tread wear
* Tread orientation relative to carpet grain (the carpet is not rotationally symmetric)
* Carpet wear
* Contact patch size
* Normal force (note: will not necessarily be uniform across all contact patches, such as in a drop center 6WD)
* Temperature (can affect the compliance of many types of rubber)
* The sides of the wheel (in our testing, with worn tread, the plastic sides of a Plaction wheel start making contact with the carpet)
This identifies 9 different independent variables. There might be more (or less...some of these may not turn out to be big factors). For any single team, doing a 9-dimensional study across all of these factors would be pretty daunting.
Would someone want to make a test bed to bring to Championships? Just a patch of carpet and a scale to measure pushing force (and robot weight) - along with a system to log the data - would go a long ways. Invite teams to come test their pushing capabilities, then roll up the data into a report on CD. Maybe someone could even make a trophy for the "Highest CoF in FRC 2011".
