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🚀 Rocket Launch (Tsiolkovsky)

Launch your own rocket into orbit! See how the Tsiolkovsky rocket equation Δv = v_e · ln(m₀/m_f) determines how fast you go, and why multi-stage rockets reach orbit more efficiently than single-stage.

Aerospace Engineering & Orbital Mechanics3DEasy60 FPS💨 Air & Wind 🌍 Earth

About this simulation

This simulation builds a rocket from your chosen parameters and flies it skyward to show whether it can reach low Earth orbit. The motion is governed by the Tsiolkovsky rocket equation, Δv = v_e · ln(m₀/m_f), where the effective exhaust velocity v_e = I_sp · g₀. Because reaching orbit needs roughly 9.4 km/s of delta-v, a single stage rarely suffices; the model lets you add stages so the vehicle can shed dead structural mass and multiply its total delta-v budget.

🔬 What it shows

It computes ideal delta-v per stage with Tsiolkovsky's equation, summing across stages, then animates a 2D ascent driven by thrust, gravity and a simplified drag loss. The vertical bars track altitude and the delta-v achieved against the ~9.4 km/s needed for low Earth orbit (LEO).

🎮 How to use

Pick a preset (V-2, Saturn V, Falcon 9 or Ideal 2-Stage), or set the four sliders: specific impulse I_sp (200–460 s), fuel fraction (50–95%), number of stages (1–3) and thrust (100–8000 kN). Press Launch to fly, Pause to hold, and Reset to start over.

💡 Did you know?

Because delta-v depends on the logarithm of the mass ratio, every extra increment of speed demands disproportionately more propellant. This is why staging is essential: discarding empty tanks mid-flight resets the mass ratio and is the only practical route to orbit with chemical engines.

Frequently asked questions

What is the Tsiolkovsky rocket equation?

It states that a rocket's change in velocity, Δv, equals the effective exhaust velocity v_e multiplied by the natural logarithm of the mass ratio: Δv = v_e · ln(m₀/m_f). Here m₀ is the fully fuelled mass and m_f is the dry mass after the propellant is burned. It expresses how a rocket gains speed by throwing mass out the back.

How does the simulation decide whether I reach orbit?

It treats roughly 9.4 km/s as the ideal delta-v needed for low Earth orbit. Your total delta-v is the sum of each stage's Tsiolkovsky contribution. As the rocket burns, accumulated delta-v is compared against that target, and orbit is registered once the budget is high enough during the animated ascent.

What do the four sliders actually change?

I_sp (specific impulse) sets engine efficiency via v_e = I_sp · g₀, so higher values give more delta-v. Fuel fraction sets how much of each stage is propellant, raising the mass ratio. Stages choose how many times the vehicle sheds structure, and thrust governs acceleration and how quickly the climb unfolds.

Is the physics accurate?

The core delta-v calculation uses the real Tsiolkovsky equation with v_e = I_sp · g₀ and g₀ = 9.80665 m/s², so the numbers are sound. The flight itself is simplified: it folds gravity and atmospheric drag into a single effective loss term rather than modelling a full trajectory, so it is illustrative rather than a precise launch profile.

Why are multi-stage rockets so much better than a single stage?

Reaching orbit needs a mass ratio of about 23 for a single stage, which is hard to build because tanks and engines weigh a lot. Staging splits the journey: once a stage's fuel is spent, its empty mass is jettisoned, so the remaining vehicle has a fresh, favourable mass ratio. The total delta-v is the sum of each stage's contribution, which beats any single stage.

⚙ Under the hood

Two-stage rocket simulation with live Tsiolkovsky Δv budget. Adjust specific impulse, propellant fraction and payload mass to see how mass ratio and staging determine whether you reach Low Earth Orbit.

Canvas 2DTsiolkovskyStagingGravity Turn

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install