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All rocket engines produce a total thrust force which is the sum of a momentum thrust resulting from the acceleration of the exhaust gas and a pressure thrust arising from the difference in pressure between the exhaust gas at the nozzle exit and the surrounding air. The total thrust is the maximum for a given rocket engine when the pressure thrust is zero that is when the exhaust pressure is the same as the ambient pressure. For other than these conditions, the nozzle overexpands or undeerexpands the gas stream with resulting loss in efficiency. Because a ballistic missiles rises through the atmosphere during the period of propulsion, the ambient pressure varies. Ideal expansion conditions cannot be realized, and the design of the rocket engine has to be optimized to allow for the effects of incorrect expansion during part of the propulsion period.
A rocket engine thus consists of a combustion chamber in which the propellants are burned to produce a high-temperature gas, and an exhaust nozzle through which the gas is expanded and accelerated. The convergent-divergent form of the nozzle, needed to give a supersonic exhaust, produces subsonic flow up to the narrowest section, known as the throat, and supersonic flow beyond that section.
The jet velocity of a rocket engine is the velocity at which the gases are discharged from the nozzle. The momentum thrust is proportional to this jet velocity and the mass flawing from the nozzle. The jet velocity proportional to the temperature of the gas inside the combustion chamber and inversely proportional to the mean molecular weight of the products of combustion. Propellants rich in hydrogen and other light elements are thus advantageous because they lead to allow mean molecular weight of the exhaust gas.
The jet velocity is also dependent upon the ratio of the specific heats of the gas and the thermodynamic efficiency of the process of expansion through the exhaust nozzle. The effective exhaust velocity takes the pressure thrust into account is calculated from the total thrust and the mass flow.
The mass flow rate from a nozzle is proportional to the combustion and the nozzle throat area.
The thrust developed by a rocket engine is calculated in terms of the chamber pressure, the nozzle throat area, and a term known as the thrust coefficient. This latter is a function of the nozzle expansion ratio, the specific heat ratio for the exhaust gases, and the external pressure.
The characteristic velocity is proportional to the chamber pressure, the nozzle throat area, and inversely proportional to the mass flow through the nozzle. It is a measure of propellant performance. For example, the characteristic velocity is the combustion chamber pressure required to give unit mass flow for unit nozzle throat area for the propellant used.
The specific impulse of a rocket engine is the thrust per unit weight flow rate.
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