Railway Wheel and Automotive Tyre

In the present paper the theories of the railway wheel and the automotive tyre are discussed. After an introduction the paper opens with a discussion of the common ground, viz. the rolling motion of deformable bodies. Then the railway wheel is discussed, and it is shown that all aspects may be calculated numerically from the material constants Poisson's ratio, Young's modulus, and the coefficient of friction, and from the geometry of wheel and rail. Next the automotive wheel is considered. Such a wheel is very anisotropic, to the extent that the theory of the lateral motion (out-of-plane dynamics) is radically different from the longitudinal, or in-plane motion. Moreover, the analysis of the automotive wheel heavily relies on experiments. In the conclusion, the theories are compared.