In a recent lecture,I learnt that the friction coefficient "mu" between the tire and road surface is determined experimentally by using a graph. i.e a graph between the longitudinal tire force and the longitudinal slip. Well,how did engineers emperically arrive at such a graph in the first place? I know that longitudinal slip is a function of the vehicle velocity and wheel longitudinal velocity.I guess it is easy to estimate. But,how could the longitudinal tire force be estimated? The lecture slides say that this could be made possible "... by measuring the tire profile deformation,from which the information of the potential transferred forces are determined." The connection on the relations is not quite clear. Any ideas and experiences would be appreciated.