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The aircraft piston engine approached its limits of horsepower and mechanical complexity during World War Two. The development of rocket and jet engines enabled enormous advances in aviation and aeronautics.
Rocket and jet engines were both developed with military aviation in mind (although original goals were more noble). Each engine burns fuel and oxygen and provides vastly more thrust than conventional piston engines. This is where the similarities end.
Jet engines, known as gas turbines or turbo fans, ingest atmospheric air as their source of oxygen. The benefit of not carrying a supply of oxygen is also a handicap. These engines suffer from oxygen starvation at high altitudes and reduced performance in hot weather. The fuel, normally JP-4, is really a type of kerosene that contains very little water contamination and is relatively economical.
Although very expensive, jet engines are quite simple and incredibly reliable. The spinning blades you notice on those monstrous GE and Rolls Royce engines are the first stage of the compressor. These blades ingest massive quantities of air and hurl it back into the next compressor section. Each stage being smaller, the air pressure and temperature increases dramatically. This hot air combines with fuel in the burning chamber, exits as extremely hot gas, and spins additional sets of blades on its way out. These blades turn the front compressors, perpetuating the process. Tens of thousands of pounds of thrust can be produced. Some of a jet engine's thrust is from the kinetic energy of exiting hot gasses. The turbo fans, however, produce most of the thrust.
Some military engines have an additional "afterburner" section for even more, albeit crude and expensive, thrust. Raw fuel is simply burned with the exiting hot gasses. An F-15 Eagle will gulp several gallons of fuel per second in full afterburn! An afterburner is not unlike a rocket, obtaining extra thrust purely by the kinetic energy of hot gas.
Even the best jet engine cannot produce high enough thrust to pry a spacecraft from the grip of earth's gravity. Only a rocket engine can produce millions of pounds of thrust. The unfortunate drawback is that thrust of this magnitude is partially required for the purpose of lifting its own oxygen supply. A rocket engine cannot obtain free oxygen on its way up. This eliminates the altitude restriction placed on jet engines and enables spacecraft to leave the atmosphere altogether.
All of a rockets thrust is produced by the
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