Paper 1: Skidding of Vehicles Due to Locked Wheels

Abstract

The present paper combines older work by the first author with more recent research by the second author. A basic simplifying assumption of the entire investigation is that the height of the centre of gravity of the vehicle above the road surface has been neglected, such that the vertical wheel reactions remain constant.

In the earlier analysis it was also assumed that the drift angle of rolling wheels under lateral forces may be neglected, and the possibility of lateral skidding of rolling wheels was also ignored. The equations of motion may then be reduced to a comparatively simple non-linear second-order system of ordinary differential equations. The equations may be given a non-dimensional form in several ways, and two such methods are employed to reveal some characteristic properties of the skidding phenomenon.

The more recent analysis has been refined considerably by proper allowance for the drift angle of rolling wheels under the action of lateral forces, for the possibility of sideways skidding of rolling wheels, and for braking action on the rolling wheels. The equations of motion then reduce to a third-order system which may be solved in closed form in the linear case of small deviations from a rectilinear motion. It appears that the drift angle of rolling wheels under the action of lateral forces leads to a small increase of the critical speed and to a significant reduction of the danger when the critical speed is exceeded. The non-linear equations for larger deviations from a rectilinear motion cannot so easily be discussed qualitatively, but detailed results have been obtained by means of a digital computer.