Surface Topography and the Mechanics of Asperity Contact

The deformation of an individual asperity is assumed to be governed by the Hertzian relations  

To make Eqns 12-19 through 12-22 useful for the treatment of profilometric data we introduce the standardized separation h. = c/cr, where a is the standard deviation of the height distribution, and we write N = y/A where y is the surface density of the asperities and A is the nominal macroscopic contact area. Then 

The standardized height distribution 4 (i) is the height distribution scaled to make its standard deviation unity. All this is conventional statistics. 

The next part of the problem is to find explicit expressions for the functions If the distribution of peak heights is exponential, 

From these solutions they computed the functional dependence of the dimensionless separation / j on the average loading pressure P over the 

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