1. Rigid Body Car Driving
Simulation
Cooper Findley
Chuck Moyes
Mark Wang

2. Overall Idea

Implement OpenGL 3D car driving simulation in
C++

Libraries used: SDL, GLEW, SOLID, SDL_ttf,
SDL_image, SDL_mixer, Armadillo

Emphasis: Realistic Physics

3. Rigid Body Dynamics Simulation

Erleben “Velocity-Based Shock Propagation for Multibody Dynamics
Animation”

CS 5643: Physically Based Animation for Computer Graphics

Euler numerical integration

Collision detection, response, tangential Coulomb friction, resting
contact

Projected Relaxed Gauss-Seidel solver

ODE's “Hinge-2” Joint Constraint

Other Possibilities:
Impulse, Penalty methods
for contact

4th Order RK integrator,

Time-Corrected Verlet method

4. Car Physics Model

Short, et al. “Simulation of Vehicle Longitudinal Dynamics”

Beckman “Physics of Racing Series”

Monster “Car Physics for Games”

Longitudinal Forces

Engine Force (torque curve as function of RPM)

Resistance Forces: Fluid dynamic air drag (proportional v²),
Rolling resistance (C_rr), Brake Forces

Lateral Forces

Pacejka tire model (continued)

Slip angle, slip ratio

Gear Box Model

Gear ratios, differential ratio

Automatic shifter logic

5. Pacejka Tire Model
Lateral Longitudinal

6. Torque Curves (V8 Engine)
First gear g1 2.66
Second gear g2 1.78 Torque Model
Third gear g3 1.30 y = c + b*x + b*x^2
Fourth gear g4 1.0 TMax = 528.7 + 0.152*R − 0.0000217R^2
Fifth gear g5 0.74
Sixth (!) gear g6 0.50 Brake Model
Reverse gR 2.90 T_brake = p*K*min(1, omega/alpha)
Differential ratio xd 3.42

7. Automatic Gear Box Shift Map

8. Time-Permitting

Work on suspension/weight distribution by modeling
mass-spring-dashpot system for each tire

Work on advanced wheel-body joint constraints using
Jacobian (as seen in ODE)

A height-map terrain engine using the ROAM level of
detail algorithm for driving over bumpy terrain

The use of a special input device such as a Logitech
steering wheel controller with force feedback

A more advanced force-based model of the car
physics as discussed in Beckman’s articles

A full-fledged racing game using the simulation engine