How a Rocket Engine Makes Thrust

A rocket engine has no moving parts where the thrust is made. There is a chamber, open at one end, and a bell. Everything else on the engine, the pumps, the pipes, the valves, the gimbal, exists to keep that chamber full of burning gas at a pressure of a hundred atmospheres and to point it. Throttle the engine up and down and watch what the plume does:

At full throttle the flame is a steady column with bright knots in it. Throttled down, the column shortens and the knots crowd together. Both come from one number, the pressure in the chamber, and this page is about where that number comes from and what it does.

Pressure is molecules hitting a wall#

Gas pushes on a wall because its molecules hit it. Each hit is tiny; there are a great many. Here are a few hundred molecules in a cylinder under a piston, moving at random speeds. Every hit on the piston is counted, and the pressure on the readout is computed from those hits, not drawn in. Push the piston down and watch it climb:

Halving the volume doubles the rate of hits, so the pressure doubles: that is the ideal gas law, p = NkT/V, seen from the molecules' side. Heating the gas makes the molecules faster, and each hit harder, which is the other way to raise pressure. A rocket engine does both at once. It burns kerosene and liquid oxygen into gas at about 3,500 K, and keeps feeding more in, so the chamber runs at 70 to 250 atmospheres [1]. Those molecules hit every wall of the chamber equally. The thrust comes from the wall that isn't there.

The chamber and the throat#

Cut the chamber open and look at its shape. The top is closed by the injector; the bottom narrows to a throat, then opens again into the bell. Gas pushing on the top plate has nothing to cancel it at the throat, so the chamber is pushed upward. The bell adds more: as the gas expands down the bell, it pushes outward on the flaring wall, and the forward part of that push is thrust too. Widen the bell and see how much wall the gas gets to push on:

The throat is where the gas reaches the speed of sound, and nothing downstream can change the flow through it. That is why the throat area and the chamber pressure between them fix the engine's mass flow, and why an engine at a given throttle behaves the same whatever the bell is doing. The bell's job is to turn pressure into speed: by the exit the gas is moving at about 3 km/s and its pressure has fallen a hundredfold [1]. The bell's shape is not arbitrary. It follows the contour Rao worked out in 1958 to get the most thrust from a given length [2].

Reading the plume#

The pressure of the gas leaving the bell should match the air outside. On a sea-level engine it never quite does, and the plume shows it. Leaving at lower pressure than the air, the jet is squeezed inward, overshoots, expands, and overshoots again: the bright knots are shock diamonds. Try the fuels, and drag the exit pressure through 1:

Throttling down lowers the chamber pressure and with it the exit pressure, so a throttled engine runs more over-expanded and its diamonds bunch up. That is what you saw in the first figure. Climb to altitude and the air thins instead, the exit pressure is now too high, and the plume balloons outward, which is why the same engine looks different in launch footage a minute after liftoff.

Feeding the fire#

The chamber runs at a hundred atmospheres, and the propellant has to get in. Nothing flows into a higher pressure, so the engine carries two pumps that raise the kerosene and the oxygen above chamber pressure. Both impellers sit on one shaft with a turbine, and the turbine is spun by burning a few percent of the propellant in a small gas generator [3]. Pull the pump apart:

A real turbopump turns at tens of thousands of revolutions per minute and moves a bathtub of propellant every second, with liquid oxygen at −183 °C on one end of the shaft and 900 K turbine gas on the other. The bearing housing between them keeps those two worlds apart. Here are both pumps in place on the engine, their housings cut open so you can see the rotors turn. Swing the gimbal and the whole engine, pumps and all, tilts on its two actuators:

How much thrust#

Put the pieces together. The chamber pressure and the throat area set the mass flow; the bell sets the exit speed and the exit pressure; the air outside takes its share. The graph below plots thrust against altitude for a 110 mm throat at 97 atmospheres, for three bells. Slide the altitude and compare the sea-level bell to the two wider ones:

At the pad the 16× bell wins because its exit pressure is closest to the air's. By 10 km the order has reversed, and in vacuum the widest bell wins by a large margin: it has simply let the gas push on more wall. That is why a first stage and an upper stage can share a chamber and differ only in their bells.

What it is made of#

Most of an engine's mass is in parts this page hasn't mentioned: the dome that spreads liquid oxygen over the injector, the 84 cooling tubes that make up the bell's wall and carry cold kerosene before it burns, the valves, the ducts that dump the turbine exhaust, the frame that passes the thrust to the rocket. Take it apart and point at anything:

None of it makes thrust. All of it exists so that one open-ended chamber can hold a hundred atmospheres of burning gas, second after second, and so that the push on its missing wall points where the rocket needs to go.

References#

1. G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 9th ed. (Wiley, 2017).
2. G. V. R. Rao, “Exhaust nozzle contour for optimum thrust”, Jet Propulsion 28 (1958), 377–382.
3. D. K. Huzel and D. H. Huang, Modern Engineering for Design of Liquid-Propellant Rocket Engines (AIAA, 1992).