Momentum Change and Thrust

One assumes a propulsion engine operated in the atmosphere, as shown in Fig. 1.3. Air enters in the front end i, passes through the combustion chamber c, and is expelled from the exit c. The heat generated by the combustion of an energetic material is transferred to the combustion chamber. The momentum balance to generate thrust F is represented by the terms  

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Ducted rockets are intermediate between solid rockets and liquid ramjets in their propulsion characteristics. The propulsive force of soHd rockets is generated by the combustion of propellants composed of oxidizer and fuel components. Thus, no additional fuels or oxidizers need to be introduced from the atmosphere into the rocket motor. The momentum change of the exhaust gas from the nozzle attached to the aft-end of the combustion chamber is converted into the thrust for propulsion. On the other hand, the propulsive force of Hquid ramjets is generated by the combustion of a liquid hydrocarbon fuel with air introduced from the atmo-sphere.Ii] jjjg incoming air is compressed by a shock wave formed at the air-intake attached to the front end of the combustor. The air taken in from the atmosphere serves only as the oxidizer for the ramjets. The thrust is created by the momentum difference between the exhaust gas from the combustor and the air taken in from the atmosphere. 

Referring to Fig. 1.3, the momentum entering the air-intake is given by rhj> and that exiting from the nozzle is given by (m -i- m v. The thmst created by the momentum change is fundamentally represented by Eq. (1.62). When the air-intake and the nozzle attached to the ducted rocket are designed to obtain maximum thrust efficiency, the pressures at the front end of the air-intake and at the aft end of the nozzle become Pa = Pi = Pr> and then Eq. (1.62) is represented by... 

By accelerating the gaseous combustion products through the exhaust nozzle, a thrust is imparted to the nozzle and motor case. This thrust is determined by the time rate-of-change of the total momentum of the bounded fluid, as indicated by the expression... 

Rocketry. Rockets are key to space study. Rockets are entirely self-contained and do not need to take in air to operate. They may be either liquid or solid fueled. Rockets operate on the principle of conservation of momentum. High-speed gases exiting the rocket carry momentum, so the rocket must have momentum in the other direction to conserve momentum. The rate of change of momentum is force and is the thrust of the rocket. 

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