Elements of Spacecraft Design

4.2: Theoretical Rocket Performance

4.2 Theoretical Rocket Performance

A rocket generates thrust by accelerating a high-pressure gas to supersonic velocities in a converging-diverging nozzle. In most cases the high-pressure gas is generated by high-temperature combustion of propellants. As shown in Fig. 4.1, a rocket, of any type, consists of a combustion chamber, throat, and nozzle.


Figure 4.1: Rocket nozzle.

In a bipropellant rocket engine the gases are generated by the rapid combustion of a liquid oxidizer and liquid fuel in the combustion chamber, for example, liquid hydrogen, and liquid oxygen. In a monopropellant system only one propellant is used. High-pressure, high-temperature gases are generated by decomposition of a single propellant. Hydrazine is the most common monopropellant. In a solid system a solid fuel and oxidizer are mechanically mixed and cast as a solid-propellant grain. The grain occupies most of the volume of the combustion chamber. In a cold-gas system there is no combustion involved. A gas, like helium, is stored at high pressure and injected into the chamber without combustion.

4.2.1 Thrust

Rocket thrust is generated by momentum exchange between the exhaust and the vehicle and by the pressure imbalance at the nozzle exit. The thrust caused by momentum exchange can be derived from Newton's second law:



where F m is the thrust generated as a result of momentum exchange, N, (lb); a the acceleration, m/s 2 (ft/s 2); the mass flow rate of propellants flowing into the chamber or mass of the exhaust gas, kg/s (lbm/s); V e

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