Rocket Staging Simulator

Build a one, two, or three stage rocket. Set the dry mass, propellant, specific impulse, and thrust-to-weight ratio for each stage and watch the Tsiolkovsky equation produce a total delta-v, a vertical-ascent trajectory, and a mission capability readout.

kg

Stage 1 (booster)

kg
kg
s

Stage 2 (upper)

kg
kg
s

Altitude vs time (vertical ascent, no drag)

020040060080010000.01000.02000.03000.04000.05000.0Time (s)Altitude (km)apogee 2291.8 km
Stage 1 burn
Stage 2 burn
Coast

Per-stage results

Stagem initial (kg)m final (kg)Mass ratioΔv (m/s)Burn (s)
1557,700146,7003.803,694148.4
2124,50017,0007.326,797200.3
Total Δv
10,492 m/s
Total burn time
348.8 s
Liftoff mass
557.7 t
Payload fraction
2.33 %

Mission capability

Reach low Earth orbit (LEO)10,492 / 9,400 m/s
Translunar injection (TLI)10,492 / 13,100 m/s
Earth escape velocity10,492 / 16,700 m/s

Reaches low Earth orbit.

Mass breakdown

S1 prop: 73.7%S1 dry: 4.0%S2 prop: 19.3%S2 dry: 0.7%Payload: 2.3%557.7 t

Solid blocks are propellant. Striped blocks are dry mass. The payload sits at the top.

Tsiolkovsky rocket equation

The total Δv of a multi-stage rocket is the sum of each stage's Δv. Staging works because shedding empty tanks lifts the mass ratio of the next burn. This simulator uses a vertical-launch model with constant gravity (9.81 m/s²) and no atmospheric drag, so the numbers represent ideal Δv. Real rockets lose roughly 1.5 to 2 km/s to gravity and drag during ascent.

Reference Guide

Tsiolkovsky rocket equation

Δv=Ispg0ln ⁣(m0mf)\Delta v = I_{sp} \cdot g_0 \cdot \ln\!\left(\dfrac{m_0}{m_f}\right)
  • Δv. Velocity change a stage can deliver, in m/s.
  • Isp. Specific impulse in seconds. Higher Isp means more delta-v per kg of propellant.
  • g₀. Standard gravity, 9.81 m/s².
  • m₀ and mf. Stage mass at ignition and burnout. Their ratio is the mass ratio.

Total mission delta-v is the sum of each stage's delta-v. That is why staging multiplies the achievable delta-v.

Why staging helps

Single-stage rockets must lift their empty tanks all the way to orbital velocity. The dry mass becomes a tax on every additional kg of propellant.

Staging drops empty tanks. The next stage starts with a smaller final mass, so its mass ratio (m₀ / mf) jumps. Since delta-v scales with the natural log of the mass ratio, even modest jumps add hundreds of m/s.

Try this. Set Falcon 9 to 1 stage by combining the propellants and dry masses. Notice the total delta-v drops below LEO.

Δv targets for common destinations

Destination Δv from Earth surface Notes
Suborbital~3,000 m/sUp and down only
Low Earth orbit (LEO)~9,400 m/sIncludes gravity and drag losses
Geostationary transfer (GTO)~11,800 m/sUsually with a kick stage
Translunar injection (TLI)~13,100 m/sApollo Saturn V flew this
Earth escape~16,700 m/sHeliocentric trajectories

Real rockets pay an extra 1.5 to 2 km/s for gravity and atmospheric drag during ascent. The simulator shows ideal delta-v, so figures are optimistic.

Specific impulse by propellant

Propellant class Isp (vacuum) Example
Solid (APCP)220 to 270 sShuttle SRB, Castor
Kerosene + LOX280 to 340 sFalcon 9 Merlin, Saturn V F-1
Methane + LOX320 to 370 sRaptor, BE-4
Hydrogen + LOX420 to 460 sRS-25, J-2, RL10
Ion (electric)3,000 to 10,000 sDawn NSTAR, NEXT

Higher Isp means each kg of propellant produces more delta-v. Hydrogen's high Isp comes with low density, which forces bigger tanks. That trade-off is why most launchers use kerosene first stages and hydrogen upper stages.

Reading the trajectory plot

  • Solid colored lines. Each stage's powered burn. The slope is the climb rate.
  • Dashed line. Coast phase after the last stage burns out.
  • Stage markers. Dots mark ignition, separation, and apogee.
  • Apogee. Highest altitude reached during the simulated vertical climb.
  • Burn time. Stage propellant divided by the mass flow rate from thrust and Isp.
  • No drag. The model ignores atmosphere and Earth rotation, so apogee figures are upper bounds.

Try these experiments

1. Trade Isp for mass

Cut Falcon 9 second stage Isp by 50 s. Compare the loss in total delta-v against doubling the propellant.

2. Add a third stage

Take the Space Shuttle preset and split it into 2 or 3 stages with the same total mass. Watch the payload fraction climb.

3. Tyranny of the equation

Increase payload by 20 percent on Saturn V. Notice how much more total propellant is needed to keep delta-v above TLI.