Theory for Large Spin Slips

Book chapter, 2022

Large camber angles excite a two-dimensional velocity field inside the contact patch. This phenomenon causes the camber and turn spin slips to induce different effects on both the transient and steady-state tyre behaviours. As a consequence, the total spin slip is not sufficient alone to describe the tyre characteristics, and the two contributions must be regarded separately. The present analysis addresses the general problem under the assumption of a rigid carcass. First, it is shown how to solve the governing PDEs of the brush model in vanishing sliding conditions. Closed-form solutions for the bristle deflection are then derived explicitly for rectangular and elliptical contact geometries. The analysis is extended qualitatively to the situation of limited friction available inside the contact patch.