A 2.4-tonne two-seater hovers, flips and launches on ten jets of compressed air. Every 25 ms the controller asks for a force and a moment, a constrained solver decides how hard each nozzle pushes, and on/off valves turn that into pulses. The maths is on screen while it flies: the 6 × 10 effectiveness matrix, the allocation and the valve timing of every nozzle. Free, in the browser, nothing to install.

What the model computes

A rigid body in six degrees of freedom, integrated every 0.25 ms with a quaternion for the attitude, four wheels on springs (on the runway and up a 27 m curved ramp, held on by a downforce fan), drag and an air tank. Each cold-gas nozzle gives T = C_F A_t p_c at 40 bar (specific impulse about 63 s). Four rear nozzles push 20 kN each, four lift nozzles under the corners 12 kN, two side nozzles 6 kN.

Which nozzle fires

The ten thrusts and the wrench are linked by τ = B u: six equations, ten unknowns. The pseudo-inverse answer often asks a nozzle for negative thrust, which no nozzle can give. The car instead solves a bounded weighted least-squares problem with an active-set method: attitude first, then lift, then horizontal force, using the least air.

From thrust to valve timing

The valves only open or close. Thrust becomes a duty cycle D = u / T_avail, and the valve stays open for t_on = D · 25 ms. The shortest pulse is 3 ms; below that a sigma-delta carry saves the impulse for the next period. The oscilloscope under the view shows every pulse.

What it deliberately is not

An educational model. The 80 kN of the rear nozzles and the 0.81 s to 60 mph are the figures quoted for the real car; everything else (mass, nozzle positions, tank, valves) is an estimate. The simulator gets 0.82 s. With a real 250-litre tank it can hover for only about 5 seconds.

Chase camera

Valve timing

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Flying car simulator: ten air thrusters, control allocation and PWM

What the model computes

Which nozzle fires

From thrust to valve timing

What it deliberately is not