Roadster Physics Check

The telemetry comes from Tesla's broadcast. During the ramp and kickflip runs the broadcast shows live gauges: downforce (kg), pitch (degrees), altitude (ft) and G. We stepped through Tesla's official stream at 0.1 to 1 second intervals and wrote down every reading. They are the gold dots on the charts.

The altitude gauge lags. On both flights the G gauge spikes about a quarter of a second before the altitude trace bends, and a rear-view shot shows the car clearly airborne while the gauge still reads 0.0 ft. We shift the altitude readings 0.25 s earlier. On the slow wall ride the altitude gauge lags and drifts (it still reads 18 ft with the car parked at the bottom), so there we place the car using the pitch gauge and the ramp's shape instead. Heights on this page are of the car's floor, so a parked car reads 0 whichever way up it is; upside down at the lip that reads 67 ft against the gauge's 68.

The ramp is close to a circle. Pitch and altitude fit a loop of radius 9.5–10.6 m depending on how the gauge's lag is handled. We use 10.5 m, running from flat to 170°, which puts the lip about 21 m (69 ft) up, where the gauge settles.

The finale has no gauges. For the tower flip we measured the car's height in pixels, assuming a 2 m width for scale (Tesla hasn't published the car's dimensions). The camera cuts mid-flight, so treat that stunt's numbers as rough (about ±30%).

The air. Tank gas is modelled as real nitrogen (CoolProp equation of state) in 600 L. As it empties it expands and chills, which lowers both the pressure and the exhaust speed. Exhaust speed comes from the isentropic nozzle equation from the regulator (or tank) pressure down to the open air, scaled by an efficiency of 80% by default. That 20% covers nozzle losses plus two things the ideal equation misses: gas cooling as it drops through the regulator, and the exhaust starting to condense late in a run. With a regulator, thrust stays at full strength until the tank falls below the regulator pressure; without one, thrust falls with tank pressure. Air used is thrust divided by exhaust speed, added up over time.

The flight model. Nothing here follows the video's path. Each stunt is a program for the car's flight computer, read off the video: where to lift off, how hard to burn, how high to go, which roll to fly, and how to land. The car then flies that program as a rigid body, 240 times a second. Ten nozzles sit where they are on the car: four corner nozzles fire down to push toward the roof, four rear nozzles push the nose forward, and two front jets fire sideways to control yaw. The wheels are still spinning when the car leaves the ground, and a spinning wheel acts like a gyroscope: roll the car and it tries to swing the nose sideways. The yaw jets fire to cancel that, so a faster take-off costs a little more air. Each push makes a turning moment as well as a force, so a roll comes from one side pushing harder, and that also shoves the car. The flight computer holds the attitude it wants with those nozzles and plans its landing burn from the thrust it actually has at that moment. If the air runs out, the nozzles are too weak, the roll isn't finished in time or the car comes down on a parked car, it crashes. Change a slider and the same program may not make it.

The fans. The wall ride uses the force balance on a loop: road push = mv²/R + suction + mg·cos(pitch). The tyres must hold the car's weight along the ramp with grip μ = 1.26, the figure Tesla quoted. Fan power comes from the air leaking in under the skirts: flow ≈ 0.6 × perimeter × gap × √(2Δp/ρ), with a sealed floor of about 4 m² and an 8.5 m perimeter.

What this can't tell you. It can't show whether the footage is real, only whether the motion it shows is physically possible with the hardware Tesla described. It also can't show what the car weighs. That number moves every result, so it's the first slider.

• Tesla, "Roadster Event" livestream: gauges and on-stage figures (600 L, about 250 kg of air, 10 nozzles, over 80 kN, 2 G of suction, 1.26 G tyres, 0.81 s)
• Lars Moravy's Hagerty interview, via Tesla North: "just under 1,700 kilos" (trim not named, final numbers pending), a 200 L nitrogen tank at up to 10,000 psi plus 400 L more on the Rocket, four fans of about 20 kW, a 6–7 hour refill
• Paul Tan: the "Thruster 5,500 psi" readout in Tesla's interior photos
• CellCog: an independent estimate of exhaust speed and hover time
• Vehicle outlines traced and redrawn from Wikimedia Commons photos: Model 3 by Kazyakuruma (CC0); Cybercab by Dllu and Semi render by Jzh2074, both CC BY-SA 4.0; Cybertruck by Mpelas199 (CC0). The Roadster's shape is our own, estimated from Tesla's livestream.