Follow the explanation
Back to the model ↑How the parts work together
Mostly propellant
On the pad the rocket weighs 400 t. The cutaway shows where most of it is: 362 t of kerosene fuel (amber) and liquid oxygen (pale blue). Tanks, engines, skirts and the interstage make up 8 percent of each stage, 31 t in all, and the payload is a 6 t satellite under a 1 t fairing. Press Play to light the first stage.
Throw mass backward
The five engines burn kerosene with the liquid oxygen from the tanks, and their nozzles throw the exhaust backward at 3.0 km/s. The exhaust pushes back on the engines, so the rocket speeds up, and the tanks drain as it goes. In the cutaway each engine is shown in section: hot gas fills the chamber, squeezes through the narrow throat and spreads out in the bell before it leaves, and the readout counts the propellant thrown out at 3.0 km/s. Halfway through the first stage's burn, 160 t of propellant has gone, the rocket weighs 240.3 t and it has gained 1.53 km/s. The second half of the same propellant adds 3.27 km/s, more than twice as much, because the same exhaust now pushes a lighter rocket. That is the rocket equation: the gain is the exhaust speed times the natural logarithm of the mass at ignition divided by the mass now.
Drop the empty stage
The first stage burned 319 t, taking the rocket from 400 t to 80.7 t: a mass ratio of 4.96, worth 3.0 × ln 4.96 = 4.80 km/s. Its empty tanks and engines, 27.8 t, are now dead mass, so the rocket lets them go. The second stage starts at 52.9 t, pulls its engine straight out of the interstage and then lights. Had it kept the empty first stage, its 42 t of propellant would add only 2.26 km/s instead of 5.03, and the flight would end at 7.07 km/s, the same as building the whole rocket as one stage.
Compare with orbit
The second stage burns its 42 t, dropping the fairing on the way, and adds 5.03 km/s: 9.84 km/s in all. A low orbit at 200 km needs an orbital speed of about 7.8 km/s, and the climb costs more. This model allows 1.5 km/s for gravity and 0.1 km/s for drag, a stated budget of 9.4 km/s that it does not compute, so two stages reach orbit with 0.44 km/s to spare. Of the 400 t that left the pad, only 9.7 t is still flying: the satellite and the second stage's empty shell. Now try One stage, Three stages and the Structure slider: the heavier the structure, the more stages it takes, up to a limit: above 13 percent structure even three stages fall short of 9.4 km/s.
The same equation on a real rocket
Under Choose a rocket, pick Falcon 9 (SpaceX) and the equation runs on published masses. Its nine Merlin 1D engines hang under an octaweb, a plate on eight beams that carries their push, and the kerosene and liquid-oxygen tanks share one curved dome, a common bulkhead, so the cutaway shows two tanks stacked in one skin. With 22.2 t of structure and 410.9 t of propellant in the first stage, 4 t and 107.5 t in the second, and the 18.5 t that Falcon 9 lifts to low orbit when it recovers the first stage, the model gives 3.78 km/s from the first stage and 5.98 km/s from the second: 9.76 km/s, 0.36 km/s above the 9.4 km/s budget. That margin is smaller than the error in the approximate masses and specific impulses, so read it as about enough, not as a prediction. After separation the grid fins and four landing legs open; they rode folded against the body on the way up. Starship, Electron and Neutron are in the same control (in the Scale lineup you can also click a vehicle to select it), each with its own stage data and a note on how reliable it is.
Zoom out to every design
Switch on Zoom out: design chart. Instead of one rocket it plots the speed of every design: structure share along the bottom, speed up the side, one curve each for one, two and three stages, and a dashed line at the 9.4 km/s budget. Your design is the dot. Click or drag on the plot and the 3D rocket jumps to that design. At 8 percent structure the curves read 7.07, 9.84 and 10.58 km/s; at 12 percent only the three-stage curve clears the line, at 9.74 km/s. The second chart plots speed against the rocket's mass over the whole flight on a logarithmic mass axis, so each burn is a straight run, each dropped stage or fairing a step to the left, and a dot follows the flight. With a real vehicle selected, the first chart plots speed against payload instead; Falcon 9's curve crosses the budget at 115 percent of the listed payload, 21.3 t.
The main parts
- Engines
- The generic rocket's engines are all one kind: kerosene burning with liquid oxygen, exhaust thrown backward at 3.0 km/s. The first stage has five, each upper stage one, and the upper stage's engine hangs inside the interstage until the stage below is dropped. The real vehicles use their own: nine Merlin 1D and one vacuum Merlin on Falcon 9, 33 Raptor and six on Starship, nine Rutherford and one on Electron, nine Archimedes and one on Neutron. A vacuum engine has a longer bell because the exhaust can expand further where there is no air. Turbopumps are drawn only as simple blocks, and valves and wiring not at all.
- Fuel tanks
- The tank that holds the fuel: kerosene (RP-1) on the generic rocket, Falcon 9 and Electron, liquid methane on Starship and Neutron. Its wall is the rocket's outer skin, closed by a curved dome at each end. Most of these vehicles put the two tanks one above the other and share one dome between them, a common bulkhead. In the cutaway, the amber liquid falls as the stage burns.
- Oxidiser tanks
- The tank that holds liquid oxygen, which the fuel needs to burn: a rocket carries its own oxygen because there is none in space. It is the larger tank on every vehicle here. In these drawings its feed line runs down through the other tank to the engines. In the cutaway, the pale blue liquid falls as the stage burns.
- Propellant
- The liquid fuel (amber) and oxidiser (pale blue) together. At liftoff, with the default 8 percent structure, they are 90 percent of the generic rocket's mass; on Falcon 9, with an 18.5 t payload, about 92 percent. Burning them and throwing the exhaust out of the engines is what speeds the rocket up, so the rocket gets lighter as it goes. The levels drawn are the share of each tank left, not a flow calculation.
- Feed duct and thrust plate
- The feed lines carry the propellants down to the engines, and the thrust structure carries the engines' push into the skirt and tanks. On the generic rocket that is a coaxial duct and a plate. On Falcon 9 it is the octaweb, eight radial beams under a top plate, with the liquid oxygen line running down the middle of the kerosene tank. Real rockets route their lines in many ways, and these layouts are simplified.
- Skirts and intertanks
- Short cylinders that join the tanks into one stage: the aft skirt round the thrust structure, an intertank between two separate tanks where there is one, and the forward skirt at the top. Together with the tank walls, engines and interstage they are the stage's dead mass.
- Interstage
- The cylinder that carries the stage above and shelters its engine. It stays with the lower stage and falls away with it. The upper stage pulls its engine straight out of it before the dropped stage starts to tumble. On Starship the interstage is built into the booster and the ship lights its engines before it separates.
- Payload fairing
- Two shell halves that cover the payload while the rocket climbs through the air. They are dropped once the air is thin; here the generic rocket drops them after 90 percent of its propellant has burned, a chosen stand-in, and Falcon 9 and Electron drop theirs early in the second stage's burn. Their mass is dead mass too. Neutron's two halves are part of the first stage: they hinge open to let the second stage out and close again. Starship has no fairing, its payload rides in the ship.
- Payload and adapter
- A generic satellite on a cone-shaped adapter, which sits on a deck across the top of the last stage (6 tonnes on the generic rocket, scaled by the payload control). The model stops at the last stage's burnout and does not separate it.
- Grid fins and flaps
- Lattice fins on Falcon 9's interstage and Super Heavy, and the four flaps on the Starship ship, that steer a returning stage through the air. They are folded away on the way up and swing out once the stage is dropped. They carry no weight in the climb but the model counts them in the stage's dead mass.
- Landing legs
- Four folding legs on Falcon 9 and on Neutron that let the first stage land upright on a pad or a ship. They are stowed against the body during the climb and swing out after the stage is dropped. Reuse is why the model does not spend all the ideal speed on orbit: a landing needs propellant held back.
Questions worth exploring
How can a rocket push itself forward in space?
It does not push against air. Its engines burn fuel with an oxidiser it carries on board, and a nozzle accelerates the hot exhaust backward; by Newton's third law the exhaust pushes the rocket forward. Because the oxidiser travels with it, a rocket works in a vacuum, where jet engines and propellers, which need the air, cannot.
NASA Glenn Research Center, Rocket Thrust (Beginner's Guide to Aeronautics)
What is the rocket equation?
Δv = ve ln(m_start/m_end). With no gravity or drag, the speed a rocket gains in a burn is its exhaust speed times the natural logarithm of its mass at the start divided by its mass at the end. With a 3.0 km/s exhaust speed, burning from 400 t down to 80.7 t, a mass ratio of 4.96, adds 4.80 km/s. The second half of that propellant adds more than the first, because it pushes a lighter rocket.
NASA Glenn Research Center, Ideal Rocket Equation (Beginner's Guide to Aeronautics)Martinez-Sanchez, M., 16.512 Rocket Propulsion, Lecture 32: Orbital Mechanics Review, Staging, MIT OpenCourseWare, 2005
Why do rockets drop their stages?
Orbital speed at about 200 km is 7.8 km/s, and the climb loses roughly 1.5 to 2 km/s more to gravity and drag, so launchers budget about 9.3 to 10 km/s. A single stage would carry all its tank and engine mass to the end of its burn. Real stages put about 4 to 18 percent of their loaded mass into structure, and in this model, with 3.0 km/s engines and a 6 t payload, one stage falls short of orbit at every share in that range; it would need its structure under about 3 percent. Dropping each empty stage leaves a lighter rocket for the next burn, which is why launchers have two or more stages.
Leishman, J. G., Introduction to Aerospace Flight Vehicles, chapter 59: Rockets & Launch Vehicles, Embry-Riddle Aeronautical University (open textbook)Martinez-Sanchez, M., 16.512 Rocket Propulsion, Lecture 32: Orbital Mechanics Review, Staging, MIT OpenCourseWare, 2005Vogt, G., ed. Storm, R., Rocket Activity: Balloon Staging, NASA Glenn Research CenterDelta-v budget, Wikipedia (secondary source for the 9.3 to 10 km/s range to low orbit)
Does the rocket equation work on real rockets like Falcon 9?
Yes, as an ideal estimate. With published stage masses and specific impulses, the equation gives about 3.78 km/s for Falcon 9's first stage and 5.98 km/s for its second, 9.76 km/s in all, against the 9.4 km/s budget for a low orbit. That margin is smaller than the error in the approximate public masses, and a real launch also loses speed to gravity and drag and holds propellant back to land the first stage, so treat the result as a check on scale, not a prediction.
NASA Glenn Research Center, Ideal Rocket Equation (Beginner's Guide to Aeronautics)Falcon 9 Full Thrust, Wikipedia (stage masses, engines and thrust; secondary source)