Only a few applications require a change in thrust during flight. Equations 330, 3-24, and 3-31 show that the thrust is directly proportional to the throat area A„ the chamber pressure pu or the mass flow rate m, but it is a weak function of CF, which in turn depends on k, the altitude, a pressure ratio, and A2/At. These equations show how the thrust may be varied and imply how other performance parameters may be affected by such variation. For liquid propellant rockets the mass flow to the chamber can be decreased (by throttling valves in the propellant feed system) while the chamber geometry and the nozzle throat area are unchanged. The reduced mass flow will cause an almost linear decrease in pj and thus an almost linear decrease of F. The combustion temperature does change slightly but it does not enter into the above relations. The specific impulse would also decrease slightly. Thus, there is a small performance penalty for throttling the thrust. A two-to-one thrust decrease has been achieved with throttle valves in a liquid propellant rocket engine. Random throttling of liquid propellant engines and their design features are discussed in Chapter 8.5.
Another way of varying the thrust is to change the throat area simultaneously with throttling the flow (by inserting a moveable contoured pintle or tapered plug into the nozzle); in this case the chamber pressure px can remain reasonably constant. This throttling method has been used on liquid propellant engines (e.g., a ten-to-one thrust change on a moon landing rocket) and in a few experimental solid propellant motors.
Random thrust control requires a control system and special hardware; one example is discussed in Chapter 10.5. Random throttling of production solid propellant motors has not been achieved as yet in flight. A repeatable, programmed variation of thrust for solid propellants is possible and is discussed in Chapter 11.3. For solid propellants, a predetermined variation of mass flow rate has been achieved by clever grain geometric design, which changes the burning area at different stages during the operation. This is useful in many air-launched military rockets. Liquid propellant rockets are the most appropriate choice for randomly variable thrust rockets, as has been amply demonstrated in missions such as the lunar landings.
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