Plaction/Traction coefficient of friction?

[JamesCH95]

Lat/Long traction will be different, I think, for these reasons (and possibly more I haven't thought of):

The tread typically has an asymmetric tread pattern.

Latitudinal tread has an edge exposed that might dig into the carpet.

Longitudinal direction is curved with the wheel, and when pushed in that direction will compress more on the "up-hill" side of the wheel and loose traction in the "down hill" side of the wheel leading to variations in contact pressure which can lead to variations in grip.

I've attached a very quick paint sketch of this, red representing a pushing force and the green lines representing normal force on the wheel, exaggerated for effect.