Variable Center of Mass

Control Rigidbody center of mass and inertia for realistic physics behavior.

Overview

VariableCenterOfMass allows precise control over a Rigidbody's:

  • Center of Mass (CoM) - The balance point of the object
  • Inertia Tensor - Resistance to rotation around each axis
  • Mass Distribution - How mass is distributed throughout the object

Proper CoM setup is critical for realistic vehicle physics.

Why Center of Mass Matters

Center of Mass affects:

  • Stability - Lower CoM = more stable, less likely to tip
  • Handling - CoM position affects oversteer/understeer
  • Suspension - CoM determines weight distribution on wheels
  • Rotation - Determines pivot point for physics forces

Example: A car with high CoM (like an SUV) tips more in corners than one with low CoM (like a sports car).

Component Setup

Adding to GameObject

  1. Select GameObject with Rigidbody
  2. Add Component → NWH → Common → Variable Center of Mass
  3. Adjust CoM position and inertia in inspector

Inspector Fields

Center of Mass:

  • Position - XYZ offset from GameObject origin (local space)
  • Visualize - Show CoM gizmo in Scene view (yellow sphere)

Inertia:

  • Inertia Tensor - Resistance to rotation [X, Y, Z]
  • Auto-Calculate - Automatically calculate from colliders
  • Manual Inertia - Manually set inertia values

Setting Center of Mass

Visual Adjustment

With Visualize enabled:

  1. Enter Play mode or enable gizmos
  2. Yellow sphere shows CoM position
  3. Adjust Position values to move CoM
  4. Lower Y value = lower CoM = more stable

Typical Values

Cars:

Position: (0, -0.3, 0)
// Slightly below origin, centered laterally

Trucks/SUVs:

Position: (0, -0.1, 0)
// Higher CoM than cars

Race Cars:

Position: (0, -0.5, 0)
// Very low CoM for maximum stability

Bikes/Motorcycles:

Position: (0, 0.3, 0)
// Higher CoM, naturally unstable

Effects of CoM Position

Vertical (Y-axis):

  • Lower (-Y): More stable, less roll, harder to flip
  • Higher (+Y): Less stable, more roll, easier to flip

Longitudinal (Z-axis):

  • Forward (+Z): Front-heavy, understeer
  • Backward (-Z): Rear-heavy, oversteer

Lateral (X-axis):

  • Left/Right (±X): Causes vehicle to lean to one side

Setting Inertia

Inertia tensor controls rotation resistance around each axis.

Auto-Calculate

Most common approach:

VariableCenterOfMass vcm = GetComponent<VariableCenterOfMass>();
vcm.autoCalculate = true;

Unity calculates inertia from collider shapes automatically.

Manual Inertia

For precise control:

vcm.autoCalculate = false;
vcm.inertiaTensor = new Vector3(700, 1400, 400);

Typical Car Inertia (mass ~1400kg):

  • X (Roll): 400-800 - Resistance to rolling (tipping sideways)
  • Y (Yaw): 1200-1800 - Resistance to spinning (turning)
  • Z (Pitch): 400-800 - Resistance to pitching (nose up/down)

Inertia Effects

Too Low:

  • Vehicle jitters
  • Floaty, unrealistic motion
  • Over-responsive to forces

Too High:

  • Sluggish rotation
  • Vehicle feels extremely heavy
  • Unresponsive handling

Rule of Thumb: Inertia values should be roughly proportional to mass.

Usage Examples

Example 1: Standard Car

GameObject vehicle = ...; // Your vehicle
Rigidbody rb = vehicle.GetComponent<Rigidbody>();
VariableCenterOfMass vcm = vehicle.AddComponent<VariableCenterOfMass>();

// Set low CoM for stability
vcm.centerOfMassOffset = new Vector3(0, -0.3f, 0);

// Auto-calculate inertia
vcm.autoCalculate = true;

Example 2: High-Performance Race Car

// Very low CoM
vcm.centerOfMassOffset = new Vector3(0, -0.5f, 0);

// Manual inertia for precise handling
vcm.autoCalculate = false;
vcm.inertiaTensor = new Vector3(600, 1600, 500);

Example 3: Truck

// Higher CoM (less stable)
vcm.centerOfMassOffset = new Vector3(0, -0.1f, 0);

// Higher inertia (heavier vehicle)
vcm.autoCalculate = false;
vcm.inertiaTensor = new Vector3(1200, 2400, 800);

Example 4: Adjusting CoM for Balance

If vehicle pulls to one side:

// Vehicle pulls left, shift CoM right
vcm.centerOfMassOffset = new Vector3(0.05f, -0.3f, 0);

// Front-heavy (understeer), shift back
vcm.centerOfMassOffset = new Vector3(0, -0.3f, -0.1f);

Runtime Adjustment

CoM can be changed at runtime for dynamic effects:

Load-Based CoM

Simulate cargo weight:

public class CargoSystem : MonoBehaviour
{
    public VariableCenterOfMass vcm;
    private Vector3 baseCoM = new Vector3(0, -0.3f, 0);

    public void AddCargo(float cargoMass, Vector3 cargoPosition)
    {
        Rigidbody rb = GetComponent<Rigidbody>();

        // Shift CoM toward cargo position
        Vector3 shiftedCoM = Vector3.Lerp(
            baseCoM,
            cargoPosition,
            cargoMass / rb.mass
        );

        vcm.centerOfMassOffset = shiftedCoM;
    }
}

Fuel-Based CoM

Simulate fuel consumption:

void UpdateCoMForFuel(float fuelPercentage)
{
    // Fuel tank at rear
    Vector3 fuelTankPosition = new Vector3(0, -0.2f, -1.5f);

    // Shift CoM based on fuel level
    vcm.centerOfMassOffset = Vector3.Lerp(
        baseCoMEmpty,  // Empty tank
        baseCoMFull,   // Full tank
        fuelPercentage
    );
}

Debugging CoM Issues

Visualizing CoM

Enable visualization:

vcm.visualize = true;

Yellow sphere shows current CoM in Scene view.

Common Problems

Vehicle tips over easily:

  • CoM too high → Lower Y value
  • Inertia too low → Increase roll inertia (X-axis)

Vehicle feels floaty:

  • Inertia too low → Increase all values proportionally

Vehicle too stable (unrealistic):

  • CoM too low → Raise Y value slightly
  • Inertia too high → Decrease values

Vehicle spins uncontrollably:

  • Yaw inertia too low → Increase Y-axis inertia

Vehicle doesn't respond to inputs:

  • Inertia too high → Decrease values
  • CoM position incorrect → Adjust X/Z offsets

Testing CoM

Test procedure:

  1. Static Test: Vehicle should sit level on flat ground
  2. Cornering Test: Observe roll amount in turns
  3. Jump Test: Vehicle should pitch/roll realistically in air
  4. Collision Test: Vehicle should react naturally to impacts

Integration with NWH Assets

NWH Vehicle Physics 2

VariableCenterOfMass is used automatically:

  • VehicleController creates it if not present
  • CoM auto-calculated from collider
  • Can be manually adjusted for tuning

Wheel Controller 3D

Recommended for standalone WC3D setups:

// Add to vehicle using WheelController
VariableCenterOfMass vcm = vehicle.AddComponent<VariableCenterOfMass>();
vcm.centerOfMassOffset = new Vector3(0, -0.3f, 0);

Dynamic Water Physics 2

Used for boats/ships:

// Boat CoM typically at water line
vcm.centerOfMassOffset = new Vector3(0, 0, 0);

Aerodynamics

Used for aircraft:

// Aircraft CoM critical for stability
vcm.centerOfMassOffset = new Vector3(0, 0, 0);
// Often at or slightly ahead of wing center

Best Practices

  1. Start with Auto-Calculate: Let Unity calculate inertia, then fine-tune manually if needed
  2. Test in Play Mode: CoM effects are only visible during physics simulation
  3. Lower is Usually Better: For ground vehicles, lower CoM improves stability
  4. Match Real World: Research real vehicle CoM positions for realism
  5. Use Visualization: Always visualize CoM when tuning
  6. Document Values: Note final CoM/inertia values in comments

Advanced: Physics Behind CoM

Moment of Inertia Formula

For a point mass rotating around an axis:

I = m * r²

Where:
I = moment of inertia
m = mass
r = distance from rotation axis

For complex shapes, Unity calculates from colliders.

Torque and Angular Acceleration

Torque = I * α

Where:
α = angular acceleration (how fast rotation changes)

Higher inertia = more torque needed = slower rotation.

Parallel Axis Theorem

Moving CoM changes inertia:

I_new = I_cm + m * d²

Where:
I_cm = inertia about center of mass
d = distance CoM shifted

This is why changing CoM position affects rotation behavior.

API Reference

For detailed API documentation, see the API reference in the navigation menu for: