bubufuA command-site briefing for a hypothetical Roadster-class hop on cold-gas nitrogen thrusters. The 3D run is a browser-only sketch of the phase order. The numbers below are illustrative assumptions chosen so the hop, attitude pulses, and landing can be discussed with Newton's laws — they are not Tesla measurements.
Illustrative assumptions, not Tesla data
Mass, nozzle count, thrust, specific impulse, propellant load, and suspension rates on this page are teaching values in a plausible cold-gas band. They are not official Tesla specifications, telemetry, or flight data. The hop is an interactive Three.js sketch in this browser: pitch, roll, yaw, nozzle particles, a short lift, and a damped landing.
Phase run
The canvas loads only in this browser after the text. Use play, pause, reset, or step one phase at a time. Reduced motion keeps the run paused.
Phase order
01 / IGNITIONIgnition
Belly nozzles spool up while the car is still on the wheels. Thrust is below weight, so there is no hop yet — only exhaust and a small suspension crouch.
02 / LIFTOFFBrief liftoff
Four lift nozzles at 4800 N each give about 19200 N against 17168 N of weight (thrust-to-weight ≈ 1.12). Net upward acceleration is a short hop, not a climb to altitude.
03 / ATTITUDEAttitude control
Differential lift and the two yaw nozzles apply torque. Pitch, roll, and yaw change because angular momentum responds to that torque, not because the car is “steered” like a wheel.
04 / BOOSTRearward boost
Aft nozzles throw mass backward, so the car gains forward speed. Lift nozzles stay near weight to hold the hover while the boost runs.
05 / CUTOFFCutoff and fall
Thrust goes to zero. Horizontal speed is kept; vertical motion becomes a ballistic fall under gravity until the tyres meet the ground again.
06 / LANDINGSuspension-damped landing
The arriving downward speed is an impulse. The assumed spring (90000 N/m) and damper (7000 N·s/m) spread that impulse over the suspension travel. Damping ratio ≈ 0.28.
What the hop is teaching
Newton's lawsFirst law: no net force, no change in motion. Second: a = F_net / m. Third: the gas is thrown down or aft; the car is pushed up or forward.
A parked car stays parked until an external force appears (first law). The hop acceleration equals net force over mass (second law). Exhaust going one way means the car is pushed the other way (third law).
F = ma and thrust-to-weightT/W = T / (mg). T/W ≤ 1 cannot leave the ground. T/W just above 1 makes a hop, not a launch.
Lift-off needs upward thrust greater than weight. Here the assumed lift is 19200 N and weight is 17168 N, so T/W ≈ 1.12. Net force is only a few kilonewtons, so the hop stays low and short.
Momentum and the rocket equationΔv = ve ln(m0/mf). Cold-gas Isp ~70 s keeps ve low, so even tens of kilograms of propellant buy only a small speed change.
Cold gas leaves at ve = Isp · g0 ≈ 686 m/s. With 36 kg of assumed propellant the ideal Δv is ve · ln(m0/mf) ≈ 14.3 m/s. That budget is tiny — enough for a hop and a few attitude pulses, not for travel.
Angular momentum and torqueSame-direction corner nozzles lift. Unequal corners rotate the body. The yaw pair is a couple about the vertical axis.
A nozzle off the centre of mass produces torque τ = r × F. The body rotation rate changes as Iα = τ. Opposite nozzles make pitch or roll; the side pair makes yaw.
Landing impulse and cushioningImpulse J = ∫F dt = Δp. A longer stopping time lowers the peak force. That is what the damper is for.
Cutoff leaves a downward speed. Stopping that speed instantly would be a sharp impulse. The suspension spring stores the energy and the damper removes it over centimetres of travel, which is the cushion.
Assumed numbers
Swap this typed config later without rewriting the article shell. Every value is an assumption.
| Wet mass | 1750 kg | Chosen inside 1500–2000 kg |
|---|---|---|
| Propellant | 36 kg | Illustrative cold-gas load |
| Isp | 70 s | Typical cold-gas nitrogen band |
| Exhaust ve | 686 m/s | ve = Isp · g0 |
| Ideal Δv | 14.3 m/s | Rocket equation on the assumed load |
| Lift T/W | 1.12 | Four belly nozzles at full thrust |
| Lift thrust | 19200 N | 4 × 4800 N |
| Aft thrust | 6400 N | Rearward boost pair |
| Landing k, c | 90000 N/m, 7000 N·s/m | ζ ≈ 0.28 |
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