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An overview of existing and alternative forms of vehicle understeer/oversteer expressions is presented. New forms are derived consistent with conceptual extensions to the configurations of the vehicle's steering system, the driving mode - steady-state or transient, and the responses - path curvature or yaw velocity. Derivation of all understeer expressions is presented with a consistent use of the Ackermann reference case and the related “Ackermann vehicle” construct. The vehicle is otherwise represented in a traditional manner as a bicycle model operating in the linear range consistent with small angle approximations. The vehicle's steering system is assumed to be more generally configured with four-wheel steer and active or steer-by-wire actuation at both axles. The actuation is assumed to allow the introduction of significant speed sensitivity to the effective overall steering ratios.

A theory of vehicle steering pull, created by asymmetrical tire cornering properties, is developed. It is validated with free control data obtained on the road. The effects of tire lateral force and aligning torque asymmetries on a car's straight line stability are analyzed for both fixed and free control. Equations for front axle lateral force, steering system moment, and sideslip angle are derived. They are based on tire properties and certain assumptions about the car's characteristics. This theory is validated using data obtained in open road testing. The test techniques, as well as alternate ones, are described. In addition, the relationships between actual front axle force and axle conicity force, ply steer force, and lateral force offset are analyzed. It is found that front axle conicity force correlates very strongly with a more accurate theoretical prediction. The axle force predicted by tire conicity force is somewhat low.