Slide exhaust velocity, propellant fraction, and stage count to launch a 3D rocket and read its live delta-v gauge against the delta-v low Earth orbit actually needs - the same rocket equation Konstantin Tsiolkovsky published in 1903.
The gauge bar beside the rocket fills toward the white marker at the 9.4 km/s low Earth orbit target - green once the current settings clear it, red or amber while they fall short. Ignite plays a launch: a rocket that clears the target keeps climbing, one that falls short stalls partway up and settles back to the pad.
Tsiolkovsky Rocket Equation 3D Explorer
Slide exhaust velocity and propellant fraction, pick 1 to 3 stages, and press Ignite on the Tsiolkovsky Rocket Equation 3D Explorer to see whether your rocket's live delta-v clears the 9.4 km/s low Earth orbit target or falls short.
Drag to orbit the launch pad, scroll or pinch to zoom, and watch the gauge bar beside the rocket fill toward the target marker as you move the sliders. The facts panel updates the mass ratio and the exact delta-v figure on every change.
Try the three presets to feel the two levers side by side: a single stage that falls short of orbit, the same hardware split into stages, and the maximum exhaust velocity a hydrogen/oxygen engine can reach.
- Exhaust velocity slider from 2.0 to 4.4 km/s, the real span from kerosene/oxygen to hydrogen/oxygen engines
- Propellant mass fraction slider from 50% to 97% of each stage's own mass
- 1, 2, or 3 stage buttons that multiply the delta-v the same hardware can reach
- Ignite button plays a launch animation - clears the target and the rocket keeps climbing, falls short and it stalls and settles back
- Delta-v gauge bar with a fixed marker at the 9.4 km/s low Earth orbit target
- Facts panel with the live mass ratio, delta-v total, and published reference figures
- Runs fully in the browser with the vendored three.js engine - no account, no upload
Students use it to see why a single-stage rocket with a realistic propellant fraction cannot reach orbit no matter how the fraction is pushed toward the limit, teachers use the stage buttons to show why staging is the standard fix, and curious readers just want to watch the number cross 9.4 km/s.
| Figure | Value | Source |
|---|---|---|
| Rocket equation, published 1903 | delta-v = v_e · ln(m0/mf) | Konstantin Tsiolkovsky |
| Delta-v needed to reach low Earth orbit | about 9.4 km/s, including gravity and drag losses | Standard launch-vehicle reference figure |
| Hydrogen/oxygen exhaust velocity | about 4.4 km/s (specific impulse about 450 s) | Chemical-propulsion reference figures |
| Saturn V liftoff mass to low Earth orbit payload | about 2,970 t liftoff for about 140 t delivered | NASA |
| Share of Saturn V liftoff mass that was propellant and stages | about 95% | NASA |
Everything renders on your device with WebGL. The 3D engine loads once (about 0.7 MB) and is cached; no scene data is sent to a server.
The scene is an educational approximation of the rocket equation and a launch, not a trajectory simulator. It assumes every stage shares the same exhaust velocity and propellant fraction, and the rocket's on-screen rise is an illustration of the delta-v gauge, not a modeled ascent path with steering, drag, or gravity turns.
For a step-by-step walkthrough, read the Tsiolkovsky Rocket Equation 3D Explorer step-by-step guide. The Space 3D collection also includes an Escape Velocity 3D Explorer for the energy target a launch is aimed past and a Hohmann Transfer 3D Explorer for the path a spacecraft flies once it is already in orbit.
Frequently Asked Questions
What does Tsiolkovsky Rocket Equation 3D Explorer show?
A 3D rocket whose live delta-v, computed from your exhaust velocity, propellant fraction, and stage sliders with the real Tsiolkovsky rocket equation, is measured against the 9.4 km/s a rocket needs to reach low Earth orbit.
Why can a single stage fall short of orbit?
Delta-v grows only with the logarithm of the mass ratio, so pushing the propellant fraction toward its practical limit adds far less delta-v than it looks like it should. A realistic single stage with a sensible propellant fraction and a chemical exhaust velocity often lands below the 9.4 km/s target.
How does staging help?
Splitting the same hardware into more stages lets each stage drop its own spent structure before the next one burns, so the total delta-v climbs well beyond what a single stage with the same propellant fraction could reach - the Add a stage preset shows the jump directly.
What does the exhaust velocity slider represent?
The real span used by chemical rocket engines: from around 2.0-3.0 km/s for kerosene/oxygen engines up to about 4.4 km/s for hydrogen/oxygen engines, the highest common chemical-propellant exhaust velocity.
Is the on-screen launch a real trajectory?
No. The rocket's rise is an illustration of whether the computed delta-v clears the target, not a modeled ascent with steering, drag, or gravity turns. The delta-v number itself is genuinely computed live from the rocket equation and your slider settings.
How is this different from Escape Velocity 3D Explorer?
Escape Velocity 3D Explorer compares speed thresholds a spacecraft already has. Tsiolkovsky Rocket Equation 3D Explorer is upstream of that question - it is the propellant mathematics of whether a rocket can build up enough delta-v to afford the trip in the first place.