Planar Dynamic Car Model

Main reference: Macro Monster's Car Physics Guide

Check out the learning journey on my blog: yuk068.github.io

Model 1-5 (Longitudinal Simulators) are in this repository: duy-phamduc68/Longitudinal-Car-Physics

Model 6 (Planar Kinematic Car Model) is in this repository: duy-phamduc68/Planar-Kinematic-Car-Model

I try to break down each model both mathematically (continuous math) and implement them in code.

This repository contains code for Model 7 of the roadmap.

Model 7: High-Speed Lateral Tire Model (2D)

Technical Breakdown

To be honest, I've tuned the default settings and reworked this model to get it to be more video-game-fun, all constants are customizable if you want to try to make it more realistic, but I've decided to not go deeper into realism for this model.

Input Guide

Click on the grid tiles to toggle their highlighted state.

Keyboard Controls

Key(s)	Action
W / Up	Throttle
Space / Down / S / LShift	Brake
A / Left	Steer left
D / Right	Steer right
J	Downshift
K	Upshift
1	Toggle auto shift
2	Zoom in
3	Zoom out
4	Toggle true form
Q	Timer cycle (idle → running → stopped → idle)
R	Reset scenario
F	Toggle fullscreen
Esc	Open/close options

Xbox Controller (XInput)

Control	Action
RT	Throttle
LT	Brake
Left Stick X	Steering
X / LB	Downshift
B / RB	Upshift
A	Toggle auto shift
D-pad Left	Timer cycle (idle → running → stopped → idle)
D-pad Right	Toggle true form
Back / Select	Reset scenario
D-pad Up	Zoom in
D-pad Down	Zoom out
RS	Toggle fullscreen
Start	Open/close options

Completed models:

• Model 1: Longitudinal Point Mass (1D)
• Model 2: Load Transfer Without Traction Limits (1D)
• Model 3: Engine Torque + Gearing without Slip (1D)
• Model 4: Wheel Rotational Dynamics (1D)
• Model 5: Slip Ratio + Traction Curve (1D)
• Model 6: Low-Speed Kinematic Turning (2D)
• Model 7: High-Speed Lateral Tire Model (2D)