On Fri, 19 Aug 2005 20:27:08 -0400, Ned Simmons
wrote:



It seems to me no matter what the shape the tire is forced into, the
distance traveled will be 2*pi*r per rev, where r is the distance from
the ground to the axle. Think about it from the standpoint of torque. If
the tire is driving the auto, the torque at the axle is clearly equal to
F/r, where F is the force required to move the car. If the car travelled
more than 2*pi*r per rev you'd have the basis for a perpetual motion
machine.

r is not constant because the tire has a flat patch. C = pi *2 r
comes from integrating dC = r(theta) d(theta) thru 2 pi radians with r
constant. If r(theta) is not constant, then the formula for
circumference of a circle (C = pi *2 r or C = pi * D) is no longer
valid.

Even a properly inflated tire has a flat patch. An underinflated tire
just has a bigger flat patch. Circumference can remain unchanged, so
revs/rolled_distance also can remain unchanged.