Lap time simulation with transient vehicle and tyre dynamics

A numerical method is presented for the time optimal control of the race car. The method is then used to perform the role of the driver in numerical simulations of manoeuvres at the limit of race car performance. The method does not attempt to model the driver but rather replaces the driver with methods normally associated with numerical optimal control. The use of constraints on the method is then considered to represent the performance limits of the human driver. The method simultaneously finds the optimal driven line and the driver control inputs (steer, throttle and brake) to drive this line in minimum time. The method is in principle capable of operation with arbitrarily complex vehicle models as it requires only limited access to the vehicle model state vector. It also requires solution of the differential equation representing the vehicle model in only the forward time direction and is hence capable of simulating the full vehicle transient response. The impact of various vehicle parameters on minimum manoeuvre time, driven line and vehicle stability is shown for a number of representative manoeuvres using a quasi-steady state vehicle model. A similar process is then carried out to analyse the effect of suspension springs and dampers using a fully dynamic sprung vehicle model. The presented transient time optimal control method is then compared with results obtained from a traditional quasi-steady state manoeuvre time simulation method. A thermodynamic tyre model is developed and the time optimal control algorithm is used to evaluate dynamic tyre temperature effects on lap time and vehicle stability.