Car Physics for Games (2003)

Summary

Car Physics for Games by Marco Monster Level: Advanced Abstract: An introduction to car physics modelling for games. version 1.9 November, 2003 Introduction This tutorial is about simulating cars in games, in other words vehicle physics. One of the key points in simplifying vehicle physics is to handle the longtitudinal and lateral forces separately. Longtitudinal forces operate in the direction of the car body (or in the exact opposite direction). These are wheel force, braking force, rolling resistance and drag (= airresistance). Together these forces control the acceleration or deceleration of the car and therefore the speed of the car. Lateral forces allow the car to turn. These forces are caused by sideways friction on the wheels. We'll also have a look at the angular moment of the car and the torque caused by lateral forces. Notation and conventions Vectors are shown in bold, we'll be using 2d vectors. So the notation a = -b would translate to the following code snippet: a.x = -b.x a.y = -b.y Throughout this tutorial I'll be assuming that the rear wheels provide all the drive (for four wheel drives apply the neccesary adaptations). I'll be mainly using S.I. units (meters, kilograms, Newtons, etc.), but I've included a handy conversion table at the end for those readers more familiar with imperial measures (pounds, feet, miles, etc.) Straight line physics First let's consider a car driving in a straight line. Which forces are at play here? First of all there's what the tractive force, i.e. the force delivered by the engine via the rear wheels. The engine turns the wheels forward (actually it applies a torque on the wheel), the wheels push backwards on the road surface and, in reaction, the road surface pushes back in a forward direction. For now, we'll just say that the tractive force is equivalent in magnitude to the variable Engineforce, which is controlled directly by the user. Ftraction = u * Engineforce, where u is a unit vector in the direction of the car...