Hi Ben.
A while ago I tested a few (Firestone/Champ) tyres. They were wheel-mounted, with the wheel attached to a dummy spindle & installed in a "dyno" frame attached to one of our wheel platforms. Hence non-rotating. I slipped in some tests explicitly to explore how stiffness varied with mean load & frequency. A composite plot from those tests is shown
here.
All inputs were sinusoidal. The same tyre was used throughout, & the tyre temperature & pressure were measured to be constant.
The cyan diamonds (Run 331) were obtained from a slowly varying input, taking 20 seconds to complete a cycle. The rising rate is clear, and the regression stiffness was 345 N/mm.
The triangles (Runs 326, 329 & 332) were obtained using a lower amplitude, 5 Hz input with different mean loads. Regression stiffnesses ranged from 334 to 408 N/mm.
Arguably, the three 5 Hz runs could be considered to be three steady state load conditions with added dither. With that assumption, the "steady state" rate was represented by the three mean values (yellow circles), which gave a rate of 289 N/mm.
The Big Question is: what is the stiffness of this tyre?
My answer would probably be 395 N/mm, because I am interested in the way it supports the suspension dynamically, but I suspect the manufacturer (if pushed for a single number) would quote 289 N/mm for a mean load of 2,500 N.