A new formulation of the understeer coefficient to relate yaw torque and vehicle handling

The handling behaviour of vehicles is an important property for its relation to performance and safety. In 1970s, Pacejka did the groundwork for an objective analysis introducing the handling diagram and the understeer coefficient. In more recent years, the understeer concept is still mentioned but the handling is actively managed by direct yaw control (DYC). In this paper an accurate analysis of the vehicle handling is carried out, considering also the effect of drive forces. This analysis brings to a new formulation of the understeer coefficient, which is almost equivalent to the classical one, but it can be obtained by quasi-steady-state manoeuvres. In addition, it relates the vehicle yaw torque to the understeer coefficient, filling up the gap between the classical handling approach and DYC. A multibody model of a Formula SAE car is then used to perform quasi-steady-state simulations in order to verify the effectiveness of the new formulation. Some vehicle set-ups and wheel drive arrangements are simulated and the results are discussed. In particular, the handling behaviours of the rear wheel drive (RWD) and the front wheel drive (FWD) architectures are compared, finding an apparently surprising result: for the analysed vehicle the FWD is less understeering than for RWD. The relation between the yaw torque and the understeer coefficient allows to understand this behaviour and opens-up the possibility for different yaw control strategies.