Requirements for Describing the Mechanics of Tires Used on Single-Track Vehicles

The adequacy of Sharp's analysis to predict the dynamic behavior of single-track vehicles is reviewed. A noteworthy feature of Sharp's analysis is his inclusion of the lag between lateral force and lateral slip which is exhibited by a tire undergoing a time rate of change in lateral slip. In another study, Eaton has pointed out that every analysis of single-track vehicles published prior to 1960 failed to include external forces created by a sideslipping tire. The question is raised as to whether the nonstationary response to inclination is comparable to the nonstationary response to lateral slip or slip angle. The review of Sharp's analysis and Eaton's findings indicates that the attainment of better agreement between theory and experimentation will require that the motorcycle tire be described in greater detail, from both static and dynamic points of view. Transient measurements of lateral force resulting from inclination show that a small component of this force is in phase with inclination, whereas the remaining component lags the inclination angle. The component of force lagging the inclination angle appears to involve greater lag, i.e. larger relaxation length, than the force produced by lateral slip. The overturning moment caused by inclination also contains lagging and nonlagging components, although the lagging component is very small relative to the nonlagging component. It is concluded that lateral force and overturning moment due to inclination should be accurately described, statically and dynamically, to predict the dynamics of single-track vehicles. There is also a need to analyze the pneumatic tire with respect to lateral force and overturning moment produced by fixed and time-varying inclination.