dear colleagues
I recommend reading this recent paper
Chadha, V., Randolph, A. B., Reifler, K., Jacobs, T. D., & Beschorner, K. E. (2025). Validation of a Multiscale Hysteresis Mechanics Model in Predicting Oily Shoe-Floor Friction Across Surfaces With Varying Finishes. Journal of Tribology, 147(9).
where it is shown that while one can make many efforts to find a very elegant and accurate theory mathematically (like Persson's theory), the real friction problem even for viscoelastic materials where we expect only dry friction effects has many uncertainties which result in possibly very large errors in COF as the paper shows (up to 1050% if you use too large upper wavevector). In early papers, Persson seemed to suggest a truncation in terms of rms slope, hoping that 1.3 was the "magic" good choice slope, very optimistically, and never really showing where this number comes from, but this paper clarifies that there is very large uncertainty. So while we have made a lot of progress in understanding roughness mathematically, friction problem is another subject entirely!
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