This document proposes a 3D car driving simulation implemented in C++ using various libraries. It will use realistic rigid body physics with features like tire modeling, suspension, gearing and longitudinal/lateral forces. The simulation will start with basic car physics and progressively incorporate more advanced models. It provides details on reference materials, the project plan and potential extensions if time allows.

1. Rigid Body Car Driving Simulation
Cooper Findley
Charles 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. Proof of Concept

4. 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

5. 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)
● Lateral slip angle, longitudinal slip ratio
● Gear Box Model
● Gear ratios, differential ratio
● Automatic shifter logic

6. Pacejka Tire Model
Lateral Longitudinal

7. Torque Curves (V8 Engine)
First gear g1 2.66
Second gear g2 1.78 y = c + b*x + b*x^2
Third gear g3 1.30 TMax = 528.7 + 0.152*R − 0.0000217*R^2
Fourth gear g4 1.0
Fifth gear g5 0.74
Sixth (!) gear g6 0.50
Reverse gR 2.90
Differential ratio xd 3.42

8. Automatic Gear Box Shift Map

9. Project Plan
1. Implement a rigid body dynamics simulation engine
2. Begin implementing basic car physics (longitudinal forces
and engine torque/RPM coupling based on slip ratio)
3. Work on latitudinal forces (cornering, sliding, etc. based on
slip angle)
4. Research and implement the Pacejka tire model as opposed
to simple slip curves
5. Work on suspension/weight distribution by modeling mass-
spring-dashpot system for each tire
6. Work on advanced wheel-body joint constraints using
Jacobian (as seen in ODE)
7. Work on 3D rendering (car model, terrain, speedometer, rear
view mirror)
8. Add support for various input devices (joysticks, steering
wheels, floor pedals, force feedback)
9. Tweak stability and find suitable values for simulation
constant parameters based on a particular car (Corvette C5?)
10. Improve general accuracy of the simulation

10. Time-Permitting
● 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