Robert Nichols wrote:

For each
turn of the wheel, that unchanging circumference also makes one complete
revolution. When the tire is flat its shape changes, but not that total
length. For the car to travel anything other than that fixed distance
per revolution, something other than normal contact has to happen where
the rubber meets the road. It has been suggested that a ripple forms
under the tire, which is the only way I can think of that would allow 6"
of tire circumference to travel along less than 6" of road surface.**
Absent such a ripple, the car has to travel essentially the same
distance per revolution regardless of whether the tire is inflated or
flat.

So the big question is, "Does such a ripple actually form?" On a
_really_ flat tire I strongly suspect that the answer is, "Yes," but I
have my doubts that such a ripple forms under a tire that is only
moderately underinflated.

I would argue that that question is irrelevant, and here's why: I
believe what has been proposed is a ripple that stays more or less
centered within the contact patch. If that's the case, consider the
front edge of the contact patch. This edge is always in contact with
the road (by definition), and each point on the circumference has to
pass through that edge during each revolution of the wheel.

The other possibility is one or more "permanent" indentations that
remain at fixed points on the tire (i.e., that rotate as the tire
rotates). Such indentations could result in less than 100 percent of
the circumference contacting the road each revolution, but they would
also lead to a bumpy ride, and I can't think offhand of a physical
reason why such indentations would form in a normal under-inflation
scenario.

** A slipping tire could also do that, but a slipping tire running
faster than the road surface beneath it requires a source of
energy, and that would be absent on an undriven wheel.

Yep.