Tyre and Vehicle Dynamics

The operational properties of the road vehicle are the result of the dynamic interaction of the various components of the vehicle structure possibly including modern control elements. A major role is played by the pneumatic tyre. “The complexity of the structure and behaviour of the tyre are such that no complete and satisfactory theory has yet been propounded. The characteristics of the tyre still presents a challenge to the natural philosopher to devise a theory which shall coordinate the vast mass of empirical data and give some guidance to the manufacturer and user. This is an inviting field for the application of mathematics to the physical world”. In this way, Temple formulated his view on the situation almost 50 years ago (Endeavor, October 1956). Since that time, in numerous institutes and laboratories, the work of the early investigators has been continued. Considerable progress in the development of the theory of tyre mechanics has been made during the past decades. This has led to better understanding of tyre behaviour and in its role as a vehicle component. Thanks to new and more refined experimental techniques and to the introduction of the electronic computer, the goal of formulating and using more realistic mathematical models of the tyre in a wide range of operational conditions has been achieved. From the point of view of the vehicle dynamicist, the mechanical behaviour of the tyre needs to be investigated systematically in terms of its reaction to various inputs associated with wheel motions and road conditions. It is convenient to distinguish between symmetric and anti-symmetric (in-plane and out-of-plane) modes of operation. In the first type of mode, the tyre supports the load and cushions the vehicle against road irregularities while longitudinal driving or braking forces are transmitted from the road to the wheel. In the second mode of operation, the tyre generates lateral, cornering or camber, forces to provide the necessary directional contr