lecture_32 - 16.512 Rocket Propulsion Prof Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 32: Orbital Mechanics: Review, Staging Mission Planning, Staging The remaining lectures are devoted to Mission Planning and Vehicle Design, which in reality occurs even before the rocket engines are fully specified (although iterations continuously proceed throughout the process, and engine characteristics do affect the mission plan). Very roughly, the iteration steps in planning a launch mission are: (a) Estimate the required TOTAL V using impulsive thrusting formulae, plus add- ons for gravity losses, drag losses, turning losses, etc. (b) Distribute this optimally among vehicle stages (since all orbit launches so far require multiple stages in order to avoid carrying empty tankage in the later stages). TOT V (c) Using the mass fractions from (b), perform more detailed flight simulations and refine the partial and total V for the mission. During stage (b), the total V is assumed to be unchanged when the mass distribution for the stages is varied. This is not strictly true, because often the mission optimization leads to changes in the altitude and velocity at which the various firings are executed and, as we will see, this may alter the various ’s. V This is the role of stage (c) above. Another point to be made is that “stages” and “firings” may not map one-to- one. A given stage may be turned off, allowed to coast, and then re-ignited. Or the firing of two consecutive stages may occur with no interruption (or minimal interruption), so that both can be idealized as occurring in the same place. As long as the ’s are still regarded as insensitive to mission profile details (as per the comment above), these distinctions do not impact the stage mass calculations, but they can be of great practical importance nonetheless. V Impulsive Thrusting-Gravity Losses . Because of the large accelerations imparted by rocket engines, their firings are usually short, from under one minute to about 10 minutes. In fact, there is a performance incentive in minimizing the firing time, as long as the accelerations remain below structural or other limits. This can be most easily seen in the context of a vertical ascent against gravity. The vehicle’s equation of motion is then (ignoring drag) =− dv mF m g dt ( 1 ) and dm Fm c c dt == ( 2 ) 16.512, Rocket Propulsion Lecture 32 Prof. Manuel Martinez-Sanchez Page 1 of 16
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dv d ln m c g dt dt =− ( 3 ) and integrating, 0 0 m VVV c l n g t m ∆= − = ( 4 ) The “ideal”, or gravity-free velocity increment is the familiar 0 ideal m Vc l n m ∆= (5) But the presence of gravity reduces the velocity increment by Gravity V gt (6) which can be made insignificant if t is short, but can be very important otherwise. In the limit when the thrust is barely enough to cancel weight, the vehicle just hovers indefinitely with no velocity gain.
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lecture_32 - 16.512 Rocket Propulsion Prof Manuel...

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