# Vehicle Mechanics

Abstract Before embarking on the focus of this book it was felt necessary to provide a basic understanding of the dynamic forces experienced by any road vehicle during normal operation. This chapter introduces such forces on a vehicle when considered as a rigid body. It discusses the source of each force in some detail and how they may be applied to predict the performance of a vehicle. It extends the normal straight-line driving to include non-steady state cornering and the case of car-trailer combinations.

## Modelling Philosophy

Most of the analyses of vehicle performance rely on the idea of representing the real vehicle by mathematical equations. This process of mathematical modelling is the cornerstone of the majority of engineering analyses. The accuracy of the resulting analysis depends on how well the equations (the mathematical model) represent the real engineering system and what assumptions were necessary in deriving the equations.

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## Co-ordinate Systems

There is a standard definition embodied in an SAE standard (SAE J670 Vehicle Dynamics Terminology) for a co-ordinate system fixed in the vehicle and centred on the vehicle centre of gravity (C.G.) as shown in Fig. 1.1. Note that the rotational motions of the vehicle body—roll, pitch and yaw—are defined in the figure. The vehicle fixed co-ordinate system which, therefore, moves with the vehicle is useful for handling analyses.

## Rolling Resistance (RR)

The rolling resistance is defined as the force that must be overcome to cause the vehicle to move at constant speed over a horizontal surface, assuming no vehicle body aerodynamic forces are present. It is normally assumed that the vehicle is travelling in a straight line and that the road surface is reasonably smooth. RR is represented as a force at the road/tyre interface of each wheel.