Mark: The geometric derivation is indicated in my paper 3 - The section headed "the Deformed trye effective rolling radius" starting at foot of page 5. I may have to explain it a bit more if it is not clear.
I am just working on a spreadsheet model which will enable me to plot the strain as function of longitudinal position along the contact patch. I shall then be able to model the effects of having a length at the ends of the patch where I can assume slip is occurring, and see its effect on the calibration constant. I have a hunch that it will turn out that with a 10 cm contact patch, I just need to have a region about 1 cm or so the ends where slip occurs, and have the length of this slipping region vary on different surfaces to account for my experimental measurements of pneumatic tyres. I have some mistakes in the geometry at present.
Jay: I agree there are many variations in the surface finish of asphalt and of concrete. From Pete's result I am predicting that his concrete will be rougher than the asphalt