* Every block is treated as one unit of wing area that sees the airflow at its own position, including the part * caused by the ship's rotation. Lift is {@code K * pressure * airspeed² * CL(angle of attack)}: slow, heavy or * high-g flight needs a higher angle of attack for the same lift until a surface reaches its critical angle and * stalls. Stalls are per surface, soft (lift fades over a few degrees into flat-plate behaviour) and sticky (a * stalled surface only recovers a few degrees below its critical angle). Rotational damping is not added * separately, it comes from the surfaces' changing angle of attack while rotating, so it vanishes for stalled * surfaces and thrust vectoring can hold the nose past the stall. *
* K is chosen so that a level wing at the configured design speed makes exactly Warium's lift. */ final class ImprovedAero { // Lift slope of a finite wing per radian, about 80% of thin airfoil theory's 2 pi private static final double LIFT_SLOPE = 2.0 * Math.PI * 0.8; private static final double INDUCED_DRAG = 0.05; // Fully separated flow behaves like a flat plate private static final double SEPARATED_LIFT = 1.1; private static final double SEPARATED_DRAG = 1.8; private static final double STALL_BLEND = Math.toRadians(2.0); private static final double STALL_HYSTERESIS = Math.toRadians(3.0); private static final double MAX_DEFLECTION = Math.toRadians(20.0); // Share of the deflection that acts as angle of attack, gives Warium's control authority at the design speed private static final double FLAP_EFFECTIVENESS = 0.75; // Angle of attack of a level cambered wing, where K is calibrated private static final double REFERENCE_ANGLE = Math.toRadians(4.0); private ImprovedAero() { } /** Lift constant K for the given design speed. */ static double liftConstant(double designSpeed) { return 160.0 / (designSpeed * LIFT_SLOPE * REFERENCE_ANGLE); } /** * Adds the surface's forces to out. * * @param v ship velocity, ship axes * @param w ship angular velocity, ship axes * @param r block center relative to the center of mass, ship axes * @param input control input of the surface, -1 to 1 * @param stalled whether the surface was stalled in the previous substep * @return whether the surface is stalled now */ static boolean evaluate(AeroSurface s, double[] v, double[] w, double[] r, double input, double weight, double liftConstant, double stallAngleScale, boolean stalled, Wrench out) { // Airflow at the block: ship velocity plus w x r double vx = v[0] + w[1] * r[2] - w[2] * r[1]; double vy = v[1] + w[2] * r[0] - w[0] * r[2]; double vz = v[2] + w[0] * r[1] - w[1] * r[0]; double localSpeed = Math.sqrt(vx * vx + vy * vy + vz * vz); double p = s.pressure() * weight; double m = s.speedMultiplier(); double fd = s.fluidFactor(); if (s.type() == SurfaceType.AIR_BRAKE) { double ds = -(s.facingX() * vx + s.facingZ() * vz); double brake = -Math.abs(ds * 100.0 * s.brakeInput() * p * fd); out.addForce(r, vx * brake, vy * brake, vz * brake); return false; } // Warium's own per-block drag double parasitic = -localSpeed * s.type().parasiticDrag * p / m; out.addForce(r, vx * parasitic, vy * parasitic, vz * parasitic); // Chord c along the facing, normal n up for horizontal surfaces and to the side for vertical ones double cx = s.facingX(); double cz = s.facingZ(); double nx = s.type().vertical ? s.rightX() : 0.0; double ny = s.type().vertical ? 0.0 : 1.0; double nz = s.type().vertical ? s.rightZ() : 0.0; double u = vx * cx + vz * cz; double vn = vx * nx + vy * ny + vz * nz; double planeSpeedSq = u * u + vn * vn; if (planeSpeedSq < 1.0E-4) { return stalled; } double planeSpeed = Math.sqrt(planeSpeedSq); // Moving down through the air (vn < 0) means air hits the underside: positive angle of attack. // Surfaces work the same with air coming from either end of the chord, like in Warium double alpha = Math.atan2(-vn, Math.abs(u)); alpha += Math.toRadians(s.type().camber); if (s.type().controllable) { // Same sign convention as Warium: positive input pushes along n while moving against the facing alpha += FLAP_EFFECTIVENESS * MAX_DEFLECTION * input * (u <= 0.0 ? 1.0 : -1.0); } alpha = Math.max(-Math.PI / 2.0, Math.min(Math.PI / 2.0, alpha)); double critical = Math.toRadians(s.slab() ? SurfaceType.SLAB_STALL_ANGLE : s.type().stallAngle) * stallAngleScale; double absAlpha = Math.abs(alpha); // Flips only where both blends agree, so the hysteresis never makes the force jump if (!stalled && absAlpha > critical + STALL_BLEND) { stalled = true; } else if (stalled && absAlpha < critical - STALL_HYSTERESIS - STALL_BLEND) { stalled = false; } double center = stalled ? critical - STALL_HYSTERESIS : critical; double attached = 1.0 - smoothstep(center - STALL_BLEND, center + STALL_BLEND, absAlpha); double attachedLift = LIFT_SLOPE * alpha; double lift = attached * attachedLift + (1.0 - attached) * SEPARATED_LIFT * Math.sin(2.0 * alpha); double drag = attached * INDUCED_DRAG * attachedLift * attachedLift + (1.0 - attached) * SEPARATED_DRAG * Math.sin(alpha) * Math.sin(alpha); double q = liftConstant * p * fd * planeSpeedSq; // Lift is perpendicular to the airflow in the chord/normal plane, on the side of n double side = u < 0.0 ? -1.0 : 1.0; double lx = (Math.abs(u) * nx - side * vn * cx) / planeSpeed; double ly = Math.abs(u) * ny / planeSpeed; double lz = (Math.abs(u) * nz - side * vn * cz) / planeSpeed; // Drag opposes the airflow in that plane double dx = -(u * cx + vn * nx) / planeSpeed; double dy = -(vn * ny) / planeSpeed; double dz = -(u * cz + vn * nz) / planeSpeed; double liftForce = q * lift; double dragForce = q * drag / m; out.addForce(r, lx * liftForce + dx * dragForce, ly * liftForce + dy * dragForce, lz * liftForce + dz * dragForce); return stalled; } private static double smoothstep(double edge0, double edge1, double x) { double t = Math.max(0.0, Math.min(1.0, (x - edge0) / (edge1 - edge0))); return t * t * (3.0 - 2.0 * t); } }