A rocket nozzle works perfectly at exactly one altitude and nowhere else
The bell at the bottom of a rocket engine is not decoration. Roughly half the thrust comes from exhaust pressing against its inner walls. But the ideal bell shape depends on outside air pressure, which falls steadily during climb, so every fixed nozzle is a compromise tuned for a single design altitude.
Unlike a jet engine, a rocket carries its own oxidiser, which is why it works in a vacuum. Burning propellant at pressures of roughly 10 to 300 bar produces hot gas that squeezes through a narrow throat, reaches the speed of sound, then keeps accelerating as the passage widens. This is the de Laval nozzle, and its exhaust commonly leaves at up to ten times the speed of sound in sea-level air. With no atmospheric nitrogen to dilute the flame, the chamber runs hotter than any ordinary jet, and heat pours into its walls.
The trouble is matching pressures. For best results, exhaust should leave the nozzle at the same pressure as the surrounding air. Too low, and the outside air effectively pushes back, sometimes creating the glowing shock diamonds visible behind launches; too high, and usable energy escapes unused. Near the ground most nozzles are over-expanded, and during startup almost all of them briefly suffer a shock wave inside the bell. If the flow peels away from the wall unevenly, it can shove the engine sideways and upset steering.
Engineers have tried to cheat the problem with plug nozzles, stepped nozzles, expanding bells and the aerospike, designs that adapt as the air thins. In vacuum a different limit takes over: a longer bell adds weight faster than performance, and exhaust expanding too far can chill until some of its chemicals freeze into snow inside the jet, making it unstable.
Rockets are the most powerful jet engines yet the least thrifty with propellant. Designers improve efficiency by running as hot as possible and choosing light, hydrogen-rich exhaust made of simple molecules. Propellants range from solids and liquids to hybrids and monopropellants such as hydrazine, which a catalyst breaks down.
Source: Rocket engine
