Tyre forces vs speed

[riff_raff]

This is the first time I have heard Hooke's Law mentioned in connection with a viscoelastic material

Isn't it one of the first simple things you come to when exploring deformation properties of viscoelastic materials?

I believe Hooke's law only applies to materials with linear-elastic properties. Elastomer compounds like tire rubber have elastic properties that vary with stress, so Hooke's Law does not apply.

As for tire heating, doesn't most of this heat come from hysteresis loss in the tire body, rather than friction at the contact?

[munks]

At very low sliding velocity the temperature increase is negligible because of heat diffusion, but already for velocities of order 10−2 m s−1 the local heating may be very important, and I have shown that in a typical case the temperature increase results in a decrease in rubber friction with increasing sliding velocity for v > 0.01 m s−1.

This is one of the effects I was suggesting earlier. For given conditions of slip angle and camber, the contact patch and its distribution of static and sliding areas may be very similar at different speeds, but the sliding area is heating up much more quickly at high speed, and this will affect that area's grip immediately. And sustaining those conditions will result in more heat build-up overall, so the static area will eventually be affected as well.

[fastback33]

This is the first time I have heard Hooke's Law mentioned in connection with a viscoelastic material

Isn't it one of the first simple things you come to when exploring deformation properties of viscoelastic materials?

I believe Hooke's law only applies to materials with linear-elastic properties. Elastomer compounds like tire rubber have elastic properties that vary with stress, so Hooke's Law does not apply.

As for tire heating, doesn't most of this heat come from hysteresis loss in the tire body, rather than friction at the contact?

What JT was saying is irrellevent to linear elastic and viscoelastic materials. Put simply, he was trying to illustrate the difference between laboratory testing using some kind of curve fit and using a theoretical equation to determine the given outputs. The actual materials/situations were not important.