General Characteristics of Terminal Vehicle Speed as Function of Wheel Diameter

The dependence of terminal vehicle speed on the wheel diameter is examined. A general approach is presented, where the characteristics of a specific engine power output curve and the power generated by external dissipative forces acting on the moving vehicle are left arbitrary. One only assumes some general mathematical properties of the power curves, which are expected to hold from experience. Some general conclusions are derived. For theoretical interest it is proved that there exists (in the local sense) a unique behavior of the terminal vehicle speed as function of the wheel diameter. Also proved is that an “optimum” wheel diameter exists for which terminal velocity of a given vehicle is maximum. This diameter corresponds to the intersection of the resistance power with the wheel power at its maximum point. Based on these facts an approximate expression is obtained relating terminal velocity with the wheel diameter near the optimum point. This expression also introduces a new influential parameter which absorbs some details of the power curves of the engine and the external dissipative forces. A simplified expression for the vehicle terminal velocity is given, adequate for small values of the vehicle parameter.