Paper 3: An Analysis of the Dynamics of Automobiles during Simultaneous Cornering and Ride Motions

Abstract
A mathematical model of an automobile is described, which permits the study of simultaneous cornering and ride motions on irregular terrain. A major departure from previous analytical treatments of vehicles is abandonment of the concept of a vehicle-fixed ‘hinge’ to approximate the changing virtual axis about which roll takes place. Eleven degrees of freedom and all major non-linearities are included in the equations of motion, which are programmed for time-history solutions on a digital computer. Empirical relationships used to generate tyre forces over extreme ranges of operating conditions are presented in detail. To ease the task of interpretation of the extensive output information, a computer-graphics display technique has been developed to produce detailed perspective drawings of the vehicle and terrain at selected intervals of time during a simulated manoeuvre. Comparisons are presented of analytically predicted vehicle responses and test results. Future applications of the described mathematical model, in research related to highway safety, are briefly discussed.

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