When an expendable booster rocket stage nears the end of its burn, does the guidance computer shut the engine(s) off at a certain velocity/altitude for the mission, or does the stage completely exhaust its propellants?
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5$\begingroup$ Solid fuel booster stages are not easy to shut off. Closing a valve is possible only with liquid fuel. Blowing a large hole into the hull using explosive charges may help but the other stages should not be damaged. $\endgroup$– UweCommented May 30, 2017 at 8:31
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First stages are generally run to depletion (though not complete depletion - I'll get to that later). First stage ascents often use a preprogrammed, open loop guidance system to get out of the atmosphere with a good chunk of downrange velocity. Because winds aloft and other factors may vary, first stage performance also varies somewhat.
Upper stage guidance is almost always closed loop, targeting a specific position and velocity combination. As a result, upper stages of boosters are shut down when that target is reached, with some amount of reserve propellants left to cover dispersions during ascent and a disposal burn.
Liquid fueled first stages are not run dry. Cutoff is triggered with some amount left in the tank. This is because the turbopumps operate at ridiculous velocities and need something to pump, at a specific inlet pressure. The heat source (gas generator, expander, or preburner) that drives the pump is downstream of the inlet in the flow path, so cutoff has to happen by cutting off the drive force to the pump before the inlet loses pressure or runs dry.
If that pressure drops below minimum specifications or if the inlet goes dry, you will get cavitation and/or overspeed conditions, both of which would result in a violent reconfiguration of the hardware.
Solid lower stages are much simpler in this regard. At some point, the thrust will tail off until the booster no longer supports its own weight. At that point, it is jettisoned.
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111$\begingroup$ is "violent reconfiguration of the hardware" same thing as "rapid unscheduled disassembly"? $\endgroup$– LopeCommented May 30, 2017 at 5:58
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5$\begingroup$ The GIF in this answer may help you understand how a SRB works $\endgroup$– le_daimCommented May 30, 2017 at 9:55
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4$\begingroup$ @mickburkejnr It did (the first stage's center engine shut down early due to excessive pogo oscillations), but IIRC only because the Instrument Unit was specifically designed such that it could handle that situation gracefully. An open-loop configuration would have caused shutdown at the preprogammed time, likely resulting in inability to attain the intended parking orbit. en.wikipedia.org/wiki/Apollo_13#Launch_and_translunar_injection but the main source cited appears to be unavailable. $\endgroup$– userCommented May 30, 2017 at 11:26
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22$\begingroup$ I joined this group just to upvote "violent reconfiguration of the hardware". $\endgroup$– JasonCommented May 31, 2017 at 1:07
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5$\begingroup$ Solid lower stages: What if individual boosters run out at different times? This could cause unscheduled direction changes. Perhaps you could address this in your answer(?). For Soyuz-ST all four are jettisoned at the same time - see e.g. 03 min 03 secs in Arianespace Flight VS17 / SES-15 (though from a different launch). $\endgroup$ Commented May 31, 2017 at 9:07