Help Identifying Source of Sliding Adhesion Coefficient Equation

[AbsoluteUnit]

Hello all,

I am a graduate student working on a thesis in tire dynamics and simulation.
I have came across the following equation for sliding adhesion coefficient for the HSRI tire model (source: Schramm et. al. Vehicle Dynamics, Modeling and Simulation, pg. 182):

Unfortunately, Schramm et. al. did not provide any guidance on what the typical values for coefficients kR and a should be, so I started attempting to track down the source of this formulation in hopes that there would be some usable values.

The closest I have come to is the following form from Dugoff, Fencher, & Segel (1969) (who are members of the HSRI, Michigan, pretty cool) that is kind of similar, but not exactly:

Note: uw is the tire longitudinal velocity.

I can definitely contend and simply use this form, however I can't help but feel curious about the origins of the 1st form above since I have combed a lot of literature on the HSRI model, but Schramm et. al. is the first instance I have seen this, and it has been bothering me ever since like an itch that I cannot scratch.

I hope someone here can finally break this curse for me, thank you kindly.

AbsUnit

 

[berkeman]

Paging @Ranger Mike @cjl @jack action

 

[Ranger Mike]

The Unified Theory of Tire and Rubber Friction by H W Kummer and W E Mayer
The Physics of the Tire Traction by D F Hays and A L Brooke (more comprehensible)

 

[AbsoluteUnit]

Hello Mike, I got side tracked by a lot and was advised to focus on other aspects of my research, but I would still like to say thank you for the recommended resources, cheers.