Originally Posted by Doge

Our math agrees. Except the time to drop is half the time it is in contact. I have under .005 sec in your parameters for full drop.
Parameters we don't agree on. 20mph vs 30mph is simple enough. 3 in long contact patch?
I was using 100PSI with 100lbs on the tire for a 1"sq contact patch. Using that if it were 3" long it would be .1 wide to get that 1"sq area ~30:1, so I don't like your contact shape, but that also means more drop, more tire deformation, just over more time.

I just tried measuring this with both brakes on and my own puddle of water on the garage floor and the foot print was way bigger than the contact patch - in width. A assume that capillary action of the water made this not work. I don't have an ink pad, but I assume that would be better. But to be correct the patch should have an area that lines up with the PSI I think. MEaning a 100PSI with 100lbs should get a 1sq in patch.

I'll agree the real patch is more elliptical than my near circle. My .6 and your 3, my 30mph and your 20mph - and the halving of the time explains the difference in the time.

Of course the more you pump the tire, the smaller that patch gets and the less it deflects, even though doing it more quickly. I was trying to be simple using a 1sq area patch.

Here is the net:
I am saying a tire that takes 20W to roll (as tested) will not obey Hooke's law (non-linear elasticity) the same as one that takes 10W to roll when the time for deformation takes milliseconds.

I think you are disagreeing with that.