Paper 5: Vehicle Behaviour in Combined Cornering and Braking

This paper considers first the steady-state motions of a simple two-wheeled vehicle model having non-linear sideway force relationships with respect to tyre slip angle. It is shown that any steady-state conditions may be represented and their solutions found by simple graphical means, using only the non-linear curves. The curves can be modified to take into account the influence of vehicle parameters such as compliance, roll steer, wheel camber, and load transfer.

Stability boundaries are discussed and criteria are presented showing that stability of the motion depends only on the slopes of the curves and the speed of the manoeuvre at the cornering acceleration being considered.

A more involved four-wheeled vehicle model is then considered when subjected to braking while cornering on a fixed radius path of 45·8 m on a wet Bridport macadam surface. Actual sideway force–slip angle curves for combined braking and cornering, as presented by Holmes and Stone (see reference (6))^†, are used with the equations of motion derived for the quasi-steady state conditions of decelerating while cornering. The effects of front wheel steered angle and body slip angle on the forces necessary for the manoeuvre are also considered.

An envelope of maximum cornering acceleration at various braking decelerations is presented. This shows that for those particular conditions up to about 70 per cent of maximum deceleration may be obtained before there is more than about 10 per cent loss in maximum cornering ability. Outside the envelope the vehicle fails to maintain the path. At the lower deceleration the car spins, and at higher values it continues tangentially to its original path without spinning.

It is also shown that the total sideway force–slip angle curve for a pair of front or rear wheels, when one or both wheels have a high braking force coefficient, can have a sharp peak, such that for small increase in slip angle there is a rapid fall in sideway force. It is suggested that this is why a rear wheel skid which occurs while braking and cornering is more difficult to correct than one which occurs when only cornering.