Mathematical Modelling of Vehicle Drifting

Abstract

A mathematical model and condition for drifting of vehicles are presented in this paper. Employing the condition for possible steady-state drifting, the mathematical model of a vehicle with lateral weight lift during turning and drifting as well as adopting a combined tyre force model enables to reduce the number of equations of motion to a set of nonlinear coupled algebraic equations. The solution of the equations are the longitudinal and lateral components of the velocity vector of the vehicle at its mass centre and the vehicle’s yaw rate. The numerical values of the variables are associated with an equilibrium at which the vehicle drifts steadily. The equilibrium point should be analysed for stability by examining for any small disturbance should disappear. The procedure applied to a nominal vehicle indicates that an equilibrium point exists for every given value of the steering angle as the input. Also, it is shown that the equilibrium point is unstable. Hence, to keep the vehicle at the associated steady-state drifting, the value of the yaw rate must be kept constant.