Vehicle Dynamics

Intro

Turns

Turning Radius

Turning radius is the minimum circular path a vehicle can make while turning (e.g. U-turn)

Bicycle Kinematic Model

$$ R = \frac{L}{\tan(\theta)} $$

• $R$ — turning radius
• $L$ — wheelbase
• $\theta$ — steering angle

• Bigger steering angle → larger $(\tan (\theta ))$ → smaller radius

Full geometric / real wheel model

• Vehicle modeled with all four wheels and wheelbase geometry
• Turns account for:
  • Wheelbase (b)
  • Steering angles of front wheels
  • Tire width (w) (for curb-to-curb or wall-to-wall radius)
  • Right-triangle geometry for inner vs outer wheels

$$R=\frac{b}{\sin ({\theta }_{\text{front}})}+\frac{w}{2}$$

• $(b)$ — wheelbase (distance between front and rear axles)
• $({\theta }_{\text{front}})$ — steering angle of the front wheel(s)
• $(w)$ — tire width

Why Some Cars Have A Bigger Turning Radius Than Others

Corner Behavior

The behavior for a vehicle turning a corner: Brake → Ease off → Neutral → Maintain → Accelerate → Full throttle

6 Phases of a Corner

1. Braking – Slow down in a straight line
2. Trail Braking – Gradually release brake while turning
3. Transition – No brake or throttle (smooth switch)
4. Balanced Throttle – Maintain speed at apex (~10–20%)
5. Increasing Throttle – Accelerate as steering opens
6. Max Throttle – Full acceleration on exit

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