Use of numerical optimisation to determine on-limit handling behaviour of race cars.

The aim of this research is to use numerical optimisation to investigate the on-limit behaviour of an open wheel downforce type race car using the best compromise of modelling accuracy and computational effort. The current state of lap simulation methods are identified, and the GG speed diagram is described. The use of constrained optimisation, which is a form of optimal control, is used to develop the methods described in this thesis. A seven degree of freedom vehicle model validated by other researchers is used for method validation purposes, and is extended, where possible, to make the modelling of vehicle components more physically significant, without adversely affecting the computational time. This research suggests a quasi steady state approach that produces a GG speed diagram and circuit simulation tool that is capable of optimising vehicle parameters and subsystems in addition to the prevailing control vector of steer and throttle response. The use of numerical optimisation to optimise the rear differential hydraulic pressure and the roll stiffness distribution to maximise vehicle performance is demonstrated. The optimisation of the rear differential hydraulic pressure showed a very small improvement in vehicle performance in combined high speed braking and cornering, but highlighted the ability of the differential to affect the cornering behaviour of the vehicle. The optimisation of the roll stiffness distribution research showed that a significant improvement in the lateral acceleration capability of the vehicle could be achieved at all vehicle speeds between 20 and 80m/s, especially in combined braking and cornering. In addition, a parameter sensitivity study around a realistic Formula One vehicle setup was conducted, looking at the sensitivity of vehicle mass, yaw inertia, tyres, centre of gravity location and engine torque to vehicle performance. An investigation into the importance of the path finding calculation is also reported.