Model Aircraft Lift, Drag, and Stall in Matter.js

This article explains how to simulate realistic 2D fixed-wing aerodynamics—specifically lift, drag, and aerodynamic stall—within the Matter.js physics engine. Because Matter.js is a rigid-body physics engine that does not model fluid dynamics natively, these aerodynamic forces must be calculated manually each simulation tick and applied to the aircraft body using vector math, angle of attack calculations, and aerodynamic coefficient curves.

1. Understanding the Core Aerodynamic Principles

To simulate a fixed-wing aircraft in a 2D environment, you must calculate forces relative to the aircraft's motion through the air:

2. Formulating the Lift and Drag Coefficients

Aerodynamic forces are defined by the formulas:

\[F_L = \frac{1}{2} \rho v^2 S C_L\] \[F_D = \frac{1}{2} \rho v^2 S C_D\]

Where \(\rho\) is air density, \(v\) is velocity magnitude, \(S\) is wing surface area, and \(C_L\) / \(C_D\) are the dimensionless lift and drag coefficients.

In code, you can simplify the constants \(\frac{1}{2} \rho S\) into a single tuning scale factor and model \(C_L\) and \(C_D\) as functions of the angle of attack (\(\alpha\)):

3. Implementation in Matter.js

Hook into the beforeUpdate event of the Matter.js engine to compute and apply these forces before the physics solver updates positions.

const { Engine, Events, Vector, Body } = Matter;

// Configuration constants
const AIR_DENSITY = 0.0015;
const WING_AREA = 10;
const CRITICAL_AOA = 15 * (Math.PI / 180); // 15 degrees in radians
const BASE_DRAG = 0.05;

Events.on(engine, 'beforeUpdate', () => {
    const velocity = aircraft.velocity;
    const speed = Vector.magnitude(velocity);

    // Skip calculations if the body is nearly stationary
    if (speed < 0.1) return;

    // 1. Calculate the velocity angle and relative wind
    const velocityAngle = Math.atan2(velocity.y, velocity.x);
    
    // 2. Calculate Angle of Attack (AoA) normalized to [-PI, PI]
    let aoa = aircraft.angle - velocityAngle;
    aoa = Math.atan2(Math.sin(aoa), Math.cos(aoa));

    // 3. Compute Lift and Drag Coefficients with Stall
    let cl = 0;
    let cd = BASE_DRAG;

    if (Math.abs(aoa) < CRITICAL_AOA) {
        // Normal linear flight regime
        cl = aoa * 4.0; 
        cd += Math.pow(aoa, 2) * 1.5;
    } else {
        // Post-stall regime
        const stallSign = Math.sign(aoa);
        const stallFactor = Math.cos((Math.abs(aoa) - CRITICAL_AOA) * 2);
        
        // Lift collapses past the critical angle
        cl = stallSign * Math.max(0, stallFactor) * (CRITICAL_AOA * 4.0);
        
        // Drag spikes drastically during stall
        cd += 0.8 * Math.sin(Math.abs(aoa));
    }

    // 4. Calculate Dynamic Force Magnitudes
    const dynamicPressure = 0.5 * AIR_DENSITY * (speed * speed) * WING_AREA;
    const liftMagnitude = dynamicPressure * cl;
    const dragMagnitude = dynamicPressure * cd;

    // 5. Derive Force Vectors
    // Drag acts opposite to velocity
    const dragVector = Vector.mult(Vector.normalise(velocity), -dragMagnitude);

    // Lift acts perpendicular to velocity (-90 degrees relative to velocity vector)
    const liftDirection = {
        x: -Math.sin(velocityAngle),
        y: Math.cos(velocityAngle)
    };
    const liftVector = Vector.mult(liftDirection, liftMagnitude);

    // 6. Combine and Apply Forces to the Aircraft
    const totalAerodynamicForce = Vector.add(liftVector, dragVector);
    Body.applyForce(aircraft, aircraft.position, totalAerodynamicForce);
});

4. Advanced Considerations