Not so fast........:nono:
Yes the circumference of the tyre is to all intents and purposes uncompressible. Those bl%%dy army 12x20 cross ply sidewalls are not much better. But a radial tyre sidewall is immensly flexible by comparison, and can tolerate a fair degree of torsional (rotational, radial) wind-up, as well as axial flexing (sidewalls bulging under load).
Try another one of Professor Crump's illustrations (this is highly simplified but serves the purpose here):
Both tyres here have the same cirumference. The one below demonstrates that when compressed under load the effective rolling radius R2 is reduced.
But note also that the equivalent rolling radius at the top of the tyre R3 (not you Richard) becomes greater. This is because the tread cannot be compressed, so the sidewalls flex to allow it to move away from the rim to retain its 'length'. At the top the velocity of the tread relative to the hub V2 must therefore be greater than at the bottom V1. So the tyre tread effectively plays "catch-up" as it rolls around to the road once more, where it slows down to pass between the rim and the road.
So the velocity V of each point of the outside of the tyre is constantly varying - but the average velocity must be equal to that of the tyre shown at the top unless the tyre spins on the rim.
If you don't believe this, try sticking 8 tonnes in the 4t capacity bucket of a 4wd artic loader with soft radial tyres (which were admittedly 'a bit slack' :embarrassed: ) and see how the rear tyres scrabble around trying to push the machine faster than the fronts (which were doing the gripping) will allow. Come to think of it the fronts looked just like Prof. Crump's lower tyre :wow:
In fact large earthmover tyres are a good example of how different tyre pressures - for front / rear on multi axle drive machines with differing axle loadings and no centre differential - are critical to achieving the same rolling radius, and resulting smooth non-kangaroo ride.
When matching truck tyres, the cirumference is always going to be proportional to unloaded diameter. Maybe some people measure the circumference (3.142 x dia.) as it gives a much more accurate way of matching tyres of the same diameter (and hence circumference) than by trying to accurately measure the diameter. You have to assume that two truck tyres of similar circumference / diameter and pressure will have the same rolling radius. You can't play around with truck tyre pressures to jiggle rolling radius, because truck tyres require a specific pressure to carry the load safely.