What is the difference between ideal delta-v and achieved delta-v?

Ideal delta-v comes straight from the Tsiolkovsky rocket equation applied to each stage's mass ratio, the delta-v you'd get in a vacuum with no gravity to fight. Achieved delta-v is what the physics integrator actually delivers once gravity and aerodynamic drag are subtracted in real time.

Home▸Aerospace Engineering & Orbital Mechanics▸2D Rocket Launch — Tsiolkovsky Δv & Staging

2D Rocket Launch — Tsiolkovsky Δv & Staging

Q: How does staging get computed here?

Each stage carries its own propellant and dry structural mass. As soon as a stage's propellant reaches zero, its dry mass is jettisoned from the vehicle's total mass and the next stage ignites.

Q: Can a rocket actually reach orbit going straight up?

No, a real orbital insertion needs most of its delta-v sideways to achieve orbital velocity, not vertical altitude. This simulator simplifies to a one-dimensional vertical climb so the mass, thrust and staging physics stay clear, using the commonly cited 9.4 km/s delta-v figure as a stand-in target for orbit-capable rather than a literal vertical trajectory to orbit.

A 2D side-view multi-stage rocket ascent driven by real numerical integration: mass depletion from thrust and specific impulse, altitude-varying gravity and air density, drag, and staging — with a live Tsiolkovsky Δv budget and altitude/velocity graph.

Aerospace Engineering & Orbital Mechanics2DEasy60 FPS📱 Mobile-adapted🔥 Fire ⇄ 3D version

A side-view multi-stage rocket ascent that is genuinely computed, not animated: real mass depletion from thrust and specific impulse, altitude-varying gravity and atmospheric drag, and real staging that jettisons dead structural mass mid-flight. A live Tsiolkovsky delta-v budget tracks the ideal speed each stage should deliver against what the numerical integrator actually achieves once gravity and drag losses are subtracted, alongside a live altitude/velocity trace of the whole climb.

About this simulation

This is a real numerical rocket-ascent integrator, not a scripted animation. Every frame, it computes thrust, current vehicle mass, altitude-varying gravity and atmospheric drag, then integrates F = ma forward in small substeps — the same way an actual trajectory solver would, just simplified to one dimension (straight up). The multi-stage Tsiolkovsky delta-v budget it displays is calculated properly, including every stage still stacked above the one currently burning.

🔬 What it shows

Real mass depletion (ṁ = thrust / (I_sp·g₀)), real staging (dead structural mass is jettisoned the instant a stage's tank empties), gravity that weakens with altitude, and drag from an exponential atmosphere. A live graph traces altitude and velocity as the flight unfolds.

🎮 How to use

Pick a preset or set your own vehicle: specific impulse, stage wet mass, propellant fraction, thrust per stage, number of stages and payload mass. Press Launch, then Pause/Resume; Reset restarts with the current design.

💡 Did you know?

The "achieved Δv" readout is smaller than the "ideal Δv" from the Tsiolkovsky equation for every real flight — the gap is exactly the gravity and drag loss accumulated while the engines were firing, typically 1–2 km/s for a real orbital launch.

Frequently asked questions

How is this different from a normal rocket-launch animation?

Nothing here is precomputed or interpolated. Each simulated frame recalculates the vehicle's current mass from how much propellant has actually burned, then integrates Newton's second law with real gravity and drag terms to get the next velocity and altitude. The flight path is a genuine output of that integration.

What is the difference between "ideal Δv" and "achieved Δv"?

Ideal Δv comes straight from the Tsiolkovsky rocket equation applied to each stage's mass ratio — it is the delta-v you'd get in a vacuum with no gravity to fight. Achieved Δv is what the physics integrator actually delivers once gravity (pulling down the whole burn) and aerodynamic drag are subtracted in real time.

How does staging get computed here?

Each stage carries its own propellant and dry (structural) mass. As soon as a stage's propellant reaches zero, its dry mass is jettisoned from the vehicle's total mass and the next stage ignites — visible on screen as the rocket getting visually shorter and a piece of debris falling away.

Why does gravity change with altitude?

Newton's law of gravitation falls off with the square of distance from Earth's center: g(h) = g₀·(R⊕/(R⊕+h))². At a few hundred kilometres up this is a small but real effect, included here so the physics stays consistent rather than assuming a constant g all the way to orbit.

Can a rocket actually reach orbit going straight up?

No — a real orbital insertion needs most of its delta-v sideways to achieve orbital velocity, not vertical altitude. This simulator simplifies to a 1D vertical climb so the mass, thrust and staging physics stay clear and controllable; it uses the commonly cited ~9.4 km/s delta-v figure as a stand-in target for "orbit-capable," not a literal vertical trajectory to orbit.

⚙ Under the hood

rockettsiolkovskydelta-vstagingthrustorbital mechanics2D

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install