Coordinate System¶
Understanding the coordinate system is essential for interpreting simulation results and configuring your vehicle correctly. Applied Racing Dynamics follows the ISO 8855:2011 international standard for vehicle dynamics.
Why Coordinate Systems Matter¶
Every force, moment, and motion in vehicle dynamics is defined relative to a coordinate system. Understanding these conventions helps you:
- Interpret simulation results correctly
- Understand load transfer during cornering and braking
- Configure suspension geometry and tyre models
- Analyze telemetry data and compare with real-world testing
ISO 8855 Standard
We follow ISO 8855:2011, the international standard for road vehicle dynamics. This ensures consistency with professional motorsport tools and academic literature.
Vehicle Coordinate System¶
The vehicle coordinate system is a right-handed system with its origin at the vehicle's Center of Gravity (CG).
Axis Definitions¶
- x-axis (Longitudinal): Points forward in the vehicle's direction of travel
- y-axis (Lateral): Points to the left when viewed from above
- z-axis (Vertical): Points upward from the ground
Right-Handed System
If you point your right thumb in the +x direction and curl your fingers, they point from +y to +z. This is the right-hand rule.
Rotations: Roll, Pitch, and Yaw¶
Vehicle rotations are measured about the three axes using the right-hand rule.
| Rotation | Axis | Positive Direction | Negative Direction |
|---|---|---|---|
| Roll (φ) | x-axis | Right side drops, left side rises | Left side drops, right side rises |
| Pitch (θ) | y-axis | Nose drops (front dips down, braking) | Nose rises (front lifts up, acceleration) |
| Yaw (ψ) | z-axis | Nose turns left (counter-clockwise) | Nose turns right (clockwise) |
Roll Angle (φ)¶
Rotation about the x-axis (longitudinal).
- Positive roll (+φ): Right side of car drops, left side rises (rolling right in a left turn)
- Negative roll (-φ): Left side of car drops, right side rises (rolling left in a right turn)
Pitch Angle (θ)¶
Rotation about the y-axis (lateral).
- Positive pitch (+θ): Nose drops, front dips down (braking)
- Negative pitch (-θ): Nose rises, front lifts up (acceleration)
Yaw Angle (ψ)¶
Rotation about the z-axis (vertical).
- Positive yaw (+ψ): Nose turns left (counter-clockwise from above)
- Negative yaw (-ψ): Nose turns right (clockwise from above)
Steering and Sideslip Angles¶
Steering Angle (δ)¶
The steering angle follows the yaw convention:
- Positive steering (+δ): Steering wheel turned left
- Negative steering (-δ): Steering wheel turned right
Vehicle Sideslip Angle (β)¶
The sideslip angle is the angle between the vehicle's longitudinal axis and its velocity vector.
| Sideslip Angle | Direction |
|---|---|
| Positive (+β) | Velocity vector points left of vehicle heading |
| Negative (-β) | Velocity vector points right of vehicle heading |
Corner Entry
When entering a corner, the rear of the car may slide outward (oversteer), creating a sideslip angle.
Tyre Coordinate System¶
Each tyre has its own coordinate system with the origin at the contact patch center.
Tyre Axes¶
- XT (Longitudinal): Points in the direction of wheel travel
- YT (Lateral): Points left perpendicular to the wheel (right-hand rule)
- ZT (Normal): Points upward away from the road surface
Tyre Forces¶
Forces are defined as forces on the tyre by the road:
| Force | Symbol | Direction | Physical Meaning |
|---|---|---|---|
| Longitudinal | Fx | Positive = Forward (traction) | Accelerating or braking force |
| Lateral | Fy | Positive = Left (in tyre frame) | Side force for cornering |
| Normal (Vertical) | Fz | Positive = Upward | Load on the tyre (compression) |
Force Sign Conventions
- Positive Fx: Traction (accelerating)
- Negative Fx: Braking
- Positive Fy: Cornering force to the left (in tyre frame)
- Positive Fz: Tyre is loaded (compressed)
Load Transfer¶
During vehicle maneuvers, weight transfers between tyres. Understanding load transfer is critical for setup optimization.
Lateral Load Transfer (Cornering)¶
When cornering, the vehicle's mass shifts to the outside tyres.
| Maneuver | Lateral Acceleration | Weight Shift | Inside Tyres | Outside Tyres |
|---|---|---|---|---|
| Left Turn | Positive (+ay) | Right | Left: Decrease | Right: Increase |
| Right Turn | Negative (-ay) | Left | Right: Decrease | Left: Increase |
Longitudinal Load Transfer¶
Weight transfers between front and rear axles during acceleration and braking.
| Maneuver | Longitudinal Acceleration | Weight Shift | Front Tyres | Rear Tyres |
|---|---|---|---|---|
| Braking | Negative (-ax) | Forward | Increase | Decrease |
| Acceleration | Positive (+ax) | Rearward | Decrease | Increase |
Setup Implications
- Stiffer springs on the outside of a turn reduce lateral load transfer
- Anti-roll bars control lateral load transfer distribution front-to-rear
- Ride height and anti-dive/anti-squat geometry affect longitudinal load transfer
Road Geometry¶
The road surface can have banking (camber) and slope (gradient).
Banking Angle (αB)¶
Banking is rotation about the x-axis (road's longitudinal direction).
- Positive banking: Road slopes up to the right
- Negative banking: Road slopes up to the left
Oval Racing
Banked oval tracks have positive banking in left-hand corners to help keep the car loaded on the track.
Slope Angle (αS)¶
Slope is rotation about the y-axis (road's lateral direction).
- Positive slope: Road slopes upward ahead (climbing)
- Negative slope: Road slopes downward ahead (descending)
Track Curvature¶
Curvature (C) is the reciprocal of the corner radius: C = 1/R
- Positive curvature (+C): Path curves to the left (counter-clockwise)
- Negative curvature (-C): Path curves to the right (clockwise)
In simulation results:
- High curvature = tight corner (small radius)
- Low curvature = gentle corner (large radius)
- Zero curvature = straight section
Practical Applications¶
Interpreting Simulation Results¶
When viewing results in Trace View:
- Positive Fy: Tyre is generating cornering force to the left (in its own frame)
- High Fz: Tyre is heavily loaded (outside of corner or under braking)
- Positive yaw rate: Car is rotating left (counter-clockwise)
- Positive lateral acceleration: Car is cornering left
Setup Configuration¶
When configuring your vehicle in Suspension or Chassis:
- Understand that spring positions and orientations follow the vehicle coordinate system
- Anti-roll bar stiffness affects lateral load transfer distribution
- Ride height changes affect CG height and load transfer magnitude
Telemetry Comparison¶
When comparing with real-world telemetry:
- Ensure your telemetry data uses the same coordinate system conventions
- Most professional systems follow ISO 8855, but some may use different conventions
- Check the sign of lateral acceleration and yaw rate in particular
Summary¶
| Quantity | Positive Direction | Negative Direction |
|---|---|---|
| Longitudinal (x) | Forward | Backward |
| Lateral (y) | Left | Right |
| Vertical (z) | Up | Down |
| Roll (φ) | Right side drops | Left side drops |
| Pitch (θ) | Nose drops (braking) | Nose rises (acceleration) |
| Yaw (ψ) | Nose turns left | Nose turns right |
| Steering (δ) | Left turn | Right turn |
| Curvature (C) | Left turn | Right turn |
Consistency Across Platform
All simulations, results, and visualizations use this coordinate system consistently. Once you understand these conventions, interpreting any result becomes straightforward.
Next Steps¶
- Review Component Hierarchy to understand vehicle structure
- Configure your Suspension with proper geometry
- Analyze results in Trace View using coordinate system knowledge
- Compare setups in Vehicle Compare
Understanding the coordinate system is fundamental to vehicle dynamics. These conventions ensure consistency across all simulations and allow accurate comparison with real-world testing.