When I, and the motorcycle folks, derived our effective radius formula for the case with very high friction and no slip, we assumed that as you pushed down on a tire, the points on the surface of the tire would move straight down until they touched the ground (as shown in Figure 2 below), and then they would stick there, resulting in the configuration shown in my original Figure 1.
Mike has suggested that the contact patch is shorter than this. This would mean that as the tire moves down under the weight of the rider, the points of surface of the tire move in toward the center of the patch as shown by the red arrows in Figure 3.
Mike, what force is causing this to happen?
