A two-dimensional yaw plane model is used in practice to analyze handling performance of two-axle passenger cars. Commonly known as the “bicycle” model because it combines all tire forces associated with a given axle to act on the centerline of the vehicle, the yaw plane model allows lateral velocity and yaw rate degrees of freedom. Two parameters are used to completely characterize the steady-state performance of the two-axle yaw plane model: wheelbase and understeer coefficient. These two parameters also help to characterize the transient behavior. The two-axle yaw plane model is developed in this work with slightly different conventions than commonly found elsewhere in the literature, and the role of the wheelbase and understeer coefficient is identified in steady-state and transient analysis. The simple yaw plane model is augmented to include lanekeeping and driver dynamics, and the effect of steering the rear axle is shown to improve low-speed maneuvering and high speed lane-keeping.
The same analysis process is repeated for a three-axle vehicle. More complicated expressions for wheelbase and understeer are found to characterize steady-state and transient handling in the same way that the simpler expressions did for the two-axle vehicle. The effect of steering the third axle is shown to improve low speed maneuverability and tire wear.
Finally, for the main result of this paper similarities in the development of the two-and-three-axle models are generalized, making use of the slight changes of convention introduced in the two-axle model. These changes of convention allow a generalized vehicle model with any arbitrary axles steering. Furthermore, generalized expressions for wheelbase and understeer are developed for a vehicle with any number of axles, any of which could be steered proportionally to the driver input. The previously developed two-and-three-axle models are special cases of this generalized model.