Design Implications of a General Theory of Automobile Stability and Control

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Abstract
The lateral-directional motions of an automobile are studied by means of equations of motion derived for a vehicle assumed to have yawing and side-slip degrees of freedom only, and travelling at a constant forward speed. The equations are presented in terms of the automobile stability derivatives. The stability-derivative concept has its counterpart in aeroplane stability and control research. The automobile transient and steady-state motions following the application of steering control or externally applied side forces and yawing moments are determined from the equations of motion. The responses are discussed with emphasis placed upon their principal characteristics and the identification of the significant vehicle parameters that determine them. Approximate solutions for the steady-state response are also presented. The transient response characteristics are studied, first in terms of ‘single-degree-of-freedom’ approximations, and then in terms of the ‘two-degree-of-freedom’ representation. The transient motion is discussed in terms of the characteristics of a second-order dynamic system, and relations for natural frequency, damping ratio, and response time are derived. Conditions for system stability and oscillatory or non-oscillatory motion are also determined. The results of a series of sample calculations based on the equations of motion are in an appendix. These show the general character and magnitude of the responses of a representative passenger sedan and a high-performance sports car. The general characteristics of the transient and steady-state responses are summarized in chart form, and the influences of static margin, speed, and tyre and vehicle parameters are pointed out. A brief discussion of the desirability of certain response characteristics is presented as a generalized design objective.

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