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What exactly is collected

Rocket landing simulator: grid fins, thrusters and the control allocation

An interactive landing lab. A 1200 kg rocket descends from 120 m over 30 seconds while you hit it with wind gusts from four sides, and four grid fins and eight RCS thrusters fight to recover the vertical. Next to the 3D scene the fin rotation matrices, the torque allocation and the state of every thruster update frame by frame — free, in the browser, nothing to install.

What the model computes

Six degrees of freedom integrated at 1/120 s, with a quaternion carrying the orientation. The nominal descent is h(t) = 120 (1 − t/30)². The engine is rigid and its axis passes through the centre of mass, so thrust controls vertical motion only — tilting the vehicle produces no steering moment by itself. Everything that rights the rocket has to come from the fins and the thrusters.

How the vehicle is steered

Each grid fin produces a side force F = q S CLα δ, and the moment about the centre of mass is r × F. A PD controller asks for a torque; the pseudo-inverse of the allocation matrix turns that one request into four fin deflections, limited to ±30° and 90°/s. Eight thrusters in four pairs add a fixed 220 N per active nozzle, modulated in 50 ms pulses. This is the part worth watching: one desired torque, several actuators, and a matrix deciding who does what.

What counts as a landing

A soft landing needs tilt under 8°, vertical speed under 2 m/s and horizontal speed under 3 m/s at touchdown. Miss any of the three and the run is scored as a hard landing. Because the wind is yours to choose, the interesting question is not whether it lands but how much disturbance the allocation can absorb before the fins saturate.

What it deliberately is not

An educational model. No CFD, no stall, no fuel slosh and no changing mass; it does not hold horizontal position and does not promise to return to the centre of the pad. The numbers are chosen to make the control problem legible, not to reproduce any particular launch vehicle.

More from DaisyMath: the robot kinematics simulator — six axes and the transformation matrices behind them — and DaisyMath, the times-tables game for iOS and Android that pays for both.