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Most rockets generally throttle back when they reach max-q to prevent structural failure. This could be the only throttleback event of the launch.

But crewed rockets normally do a second throttleback when acceleration hits 3g to prevent harm to the astronauts on board. The human body doesn't like super high accelerations, and 3g seems to be a common upper limit.

My question: How much do crewed rockets throttle back when they hit that 3g limit? What does the throttle profile look like, and how do the achieve it? Does the throttle program linearly scale back from full throttle in proportion to acceleration above some threshold?

I know it can't possibly just drop suddenly from full throttle to minimum throttle because it would show as a dramatic drop in the acceleration profile, and what I've seen in STS acceleration plots is that acceleration hovers near its upper limit once it hits it. This means the throttleback needs to be smooth and gradual. It needs to be just enough to keep acceleration from going up while also keeping it from going down.

EDIT: Below is a space shuttle launch acceleration profile I found on the web. Notice that region F is at constant peak acceleration. This can only be accomplished by careful throttleback. Acceleration seems to hop up and down about some mean value, which suggests to me they used a deadband within which throttle was to stay constant, something useful if chatter is a concern---but this is guesswork.

enter image description here

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    $\begingroup$ That's not a Saturn V accel graph. It's a shuttle one. Notice the label says "STS 121" $\endgroup$ – Organic Marble Jan 12 at 23:39
  • $\begingroup$ @OrganicMarble: You're right! Thank you for correcting. I've edited the post. $\endgroup$ – user36480 Jan 12 at 23:40
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    $\begingroup$ @OrganicMarble Off the top of your head, do you know how the endgame throttledown schedule is controlled? $\endgroup$ – Russell Borogove Jan 12 at 23:42
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    $\begingroup$ Closely related: space.stackexchange.com/q/7829/195 $\endgroup$ – Russell Borogove Jan 12 at 23:44
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    $\begingroup$ Yes, but I'm looking for a reference. $\endgroup$ – Organic Marble Jan 12 at 23:46
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Shuttle:

tl;dr - Shuttle throttled down based on the sensed acceleration. The "bobbling" about the 3g limit you see is because a proportional-integral control scheme was used and because the rate of change of the throttle command was limited.

Details -

The throttling algorithm works on an integral and proportional error. This algorithm tends to drive the actual acceleration of the vehicle to the acceleration limit "on the average" since an integral error is included. ...

(I've summarized the rest)

When the current measured vehicle acceleration is greater than the pre-mission I- loaded constant (e.g. 3 g's), the throttle setting is updated, based on a function of the previous throttle setting, the current acceleration, and the desired acceleration. The desired acceleration is determined from proportional and integral errors. The desired acceleration of the vehicle can now be computed by taking the previous desired acceleration and subtracting the current (proportional) acceleration error multiplied by the proportional gain minus the accumulated (integral) acceleration error multiplied by the integral gain. This equation updates the desired throttle setting as a function of the previous throttle setting, the desired acceleration, and the current acceleration. The throttle setting is rounded off to the nearest percent.

Source: JSC-19041 Booster System Briefs paragraph 1.3.3.3 3-G Throttling

Here's a run from the Shuttle Mission Simulator showing a somewhat representative1 3-g throttle down sequence of commands. (The command at 1:21 Mission Elapsed Time is in response to a malfunction entered into the sim. This is also pretty old; at the end of the program they would only have throttled down to 67%.)

enter image description here

1I don't have any hardcopies from nominal runs :(

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    $\begingroup$ Thank you!!! This is just perfect. Exactly what I needed. Thank you thank you :) $\endgroup$ – user36480 Jan 13 at 0:22
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    $\begingroup$ It looks like the throttle-downs from 103% to 72% are occurring at about 2 second intervals and larger-than-1% steps -- was the "over 3g check" made at that rate? Any idea why it took 20 seconds to step from 72% to 71% when the steps before and after that are so much shorter? $\endgroup$ – Russell Borogove Jan 13 at 0:28
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    $\begingroup$ @RussellBorogove from the little info I still have about this run, it looks like the right engine was stuck at 104% due to the failures that were inserted at MET 1:21. Those failures allowed the R SSME to accept the 74% command at MET 7:44 and throttle down so it took a bit longer for the g's to build back up to 3. That throttledown from 104% to 74% would have taken a bit of time so the other 2 engines throttled to 72% while it was doing it, then they all sat there while the g's built up, then the C and L started throttling down again. $\endgroup$ – Organic Marble Jan 13 at 0:34
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    $\begingroup$ @RussellBorogove just another day in the SMS. $\endgroup$ – Organic Marble Jan 13 at 0:38
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    $\begingroup$ Wait, yes it is, @RussellBorogove: P. 43 of your PDF file! OrganicMarble's exact quote is right in section 1.3.3.3 "3-g Throttling"! Ohhhhhhhh this is so perfect. Thank you thank you :) :) :) $\endgroup$ – user36480 Jan 13 at 1:25
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The engines of the Saturn V were not individually throttlable. Instead, in the first two stages, the center engine of the five-engine cluster was shut off entirely -- for the first stage, this is done for acceleration limiting at about 4g, and for the second stage it was done to reduce "pogo oscillation", a resonance between the engine and the rest of the stage structure that caused a number of problems on that launcher. There's another thrust stepdown on the second stage caused by changing the fuel/oxidizer mixture ratio, but this was done to trade off thrust for specific impulse rather than to limit acceleration. These abrupt changes show as big discontinuities in the acceleration plot.

For Mercury-Atlas and Gemini-Titan flights, the crews just suffered through 7g-8g peaks.

For STS, the main engines were able to throttle more or less continuously between about 65% and 104%. After the SRB burnout and separation, the acceleration on the main engines was slightly less than 1g, increasing as propellant was burned, and the throttle-back held it to about 3g. As Organic Marble's excellent answer details, a proportional-integral controller program throttled the engine down in response to sensed acceleration with 1% throttle control granularity.

I think the Soyuz launcher doesn't throttle, but as it's effectively a three-stage launcher, the acceleration on any one stage doesn't get particularly severe for long. The booster-stage peak is about 4g and the others are much lower.

Falcon 9 has continuously throttlable engines; I'm not sure if they also shut down a couple of them for acceleration limiting for crewed launches -- I believe they try to keep acceleration limited to 6g for uncrewed flights, but that's a little on the rough side for humans.

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Supplementary answer only as this is a simulation based on data, not actual data.

I went to flightclub.io and selected a simulation of the SpaceX Crew-1 mission. This is not real data it's an example of a simulation that likely fits various public data including videos of the launch.

There are many more plots and tools there, and you can try adjusting parameters and rerunning the simulation.

The simulation shows throttling twice for the first stage; around Max-Q (from about 95% to 75% between 45 and 75 seconds) and again as the propellant runs out, the mass decreases so much that full throttle exceeds 3.3 g.

But there's no throttling shown for the second stage, where a peak acceleration of perhaps 4.5 g is seen in this simulation.

flightclub.io simulation of SPaceX Crew-1 mission flightclub.io simulation of SPaceX Crew-1 mission

flightclub.io simulation of SPaceX Crew-1 mission flightclub.io simulation of SPaceX Crew-1 mission

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    $\begingroup$ Ah, there it is, the second throttleback. I hadn't actually seen any reference to it on the Falcon 9, though I knew they must do it on crewed flights. It seems they assumed a simple step down to low throttle and held it there up to a few seconds before separation? Definitely good to know this gives reasonable numbers in case @OrganicMarble's space shuttle PI control approach becomes too much for me. Thanks! $\endgroup$ – user36480 Jan 13 at 0:26
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    $\begingroup$ @Alex in an offline test driver for the propulsion simulation I was working on, we just averaged the X-axis acceleration over a one second interval (our sim ran at 25 Hz) and throttled down 1% when the average exceeded 3 g's. That gave a surprisingly close approximation of the real throttle profile. $\endgroup$ – Organic Marble Jan 13 at 1:44
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    $\begingroup$ Oh? That's good to know! Thanks @OrganicMarble. So on first hitting 3g, you would throttle down to 0.99, causing the acceleration to drop slightly below 3g, then wait for it to rise back up to 3g (which would happen as fuel mass drops and also as pitch angle drops), then throttle down again to 0.98, and so on? $\endgroup$ – user36480 Jan 13 at 1:51
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    $\begingroup$ @Alex that's it. (103 not 99 since the nominal was 104 but you have the idea). $\endgroup$ – Organic Marble Jan 13 at 1:53
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    $\begingroup$ That seems to be a better approximation than to assume a sudden drop throttle as they do at flightclub.io: your acceleration would then hold closer to constant at 3g. Thanks for sharing :) $\endgroup$ – user36480 Jan 13 at 1:58

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