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Based on the motion and reaction of the cosmonauts, the 3rd stage engine cutoff (cued video) at about T+ 08:46 in this video of a Soyuz ascent causes greater negative G-forces than

  1. the 1st stage cutoff at about T+ 01:58
  2. the 2nd stage cutoff at about T+ 04:48.

During 3rd stage cutoff the cosmonauts' arms are thrown forward much more than the previous cutoffs: in the first their arms barely move, in the second just a little.

Does the 3rd stage cutoff really produce greater recoil and negative G-forces than the previous stages? Why would that be?

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Because F = ma, and m is very small at the third cutoff.

At the first cutoff, mass is the full stack minus the first stage's burned fuel. By the time of the third cutoff, the mass is enormously less: only the third stage, with only little of its fuel left.

A rough calculation says that each cutoff has about the same acceleration:

Numbers:

Stage 1 thrust 4 * 1000 + 1000 kN.
Stage 2 thrust 1000 kN.
Stage 3 thrust 300 kN.

Stage 1 mass 180 t, including 160 t fuel.
Stage 2 mass 105 t, including 95 t fuel.
Stage 3 mass 25 + 7 t, including 22 t fuel. (7 t is the Soyuz.)

At the first cutoff,
a = F/m = (5000 - 1000) kN / (20 + 105 + 25 + 7) t = 25 m/s^2.
(The -1000 kN is because stage 2 ignited at launch, and keeps firing through the first stage cutoff.)

At the second cutoff,
a = F/m = 1000 / (10 + 25 + 7) = 24.

At the third cutoff,
a = F/m = 300 / (3 + 7) = 30.

Wikipedia's numbers aren't entirely trustworthy: for example, stage 2's dry mass plus fuel is 4 t off from its gross mass. Also, this calculation assumes that all cutoffs go instantly from full throttle to zero. So something fishy's going on. But it still seems plausible that something massing 10 t can be jostled more easily than something massing 157 t.

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    $\begingroup$ This supposes they are pulling 10 g's at the end of third stage firing, which seems excessive. Third stage would begin at about 300 / 25 = 12 m/s*s, 1.2 g. Does it throttle down some? $\endgroup$
    – Bit Chaser
    Commented Oct 28, 2019 at 23:34
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    $\begingroup$ Great answer! I think there may be more mass to consider at 3rd stage cutoff, the payload, and remaining fuel. Launches don't fly until completely empty to avoid the engines blowing up and to allow a safety margin for some contingencies. $\endgroup$
    – uhoh
    Commented Oct 29, 2019 at 0:06
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    $\begingroup$ This doesn't include the payload mass -- about 7 to 7.5 tons of Soyuz and cosmonauts -- which does materially change the conclusion. According to the graph in this Quora answer (which is computed from pendulum period in cockpit video, so probably not super accurate) the first stage peak is the highest acceleration at ~4g, and the 3rd stage peak is only about 3g. $\endgroup$
    – Russell Borogove
    Commented Oct 29, 2019 at 2:00
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    $\begingroup$ It's possible that the amplitude of the astronauts' motion shows something more complex than the step height in acceleration change; the way we see them jerk around may be related more closely to jerk proper (rate of change of acceleration) or how quickly the thrust drops to zero. See How much jerk do astronauts experience? Is there a safety limit? and for good measure What were Hubble's jerk and jounce limits? Did JWST have the same? $\endgroup$
    – uhoh
    Commented Oct 29, 2019 at 5:46
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    $\begingroup$ To further that @uhoh, perhaps the stiffness of the spacecraft also plays a major role. High axial compliance from first stage to capsule vs very stiff from 3rd stage to capsule, directly contributing to that da/dt. But I don't know what the numbers are for Soyuz $\endgroup$
    – Quietghost
    Commented Oct 29, 2019 at 14:10
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Soyuz rocket have no weithtlessness during stage 1 separation, as well as during stage 2 separation. Next stage ignites before the previous separates. It's some unusual for modern rocket launchers, most of them have a staging pause before ignition.

So the weitghtlessness occurs first time in Soyuz only after third stage engine cutoff.

There was an answered question about it here, I'll find it later, it's hard from smartphone..

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  • $\begingroup$ +1 Why the downvotes? This answer is completely correct. Just watch the little German toy hanging, it doesn't stop hanging until Stage 3 shutdown, even through staging. I assume this answer will be updated with links shortly, but the video is really all the evidence that is needed to see the correctness of this answer. $\endgroup$
    – Quietghost
    Commented Oct 30, 2019 at 19:00
  • $\begingroup$ @Heopps How does the next stage ignite before the previous one separates? $\endgroup$
    – Bob516
    Commented Oct 30, 2019 at 23:43
  • $\begingroup$ @Bob516 The interstage between the 2nd and 3rd stage is metal struts rather than a solid skin, so the exhaust simply passes through. $\endgroup$
    – lirtosiast
    Commented Nov 16, 2019 at 9:30
  • $\begingroup$ @lirtosiast I knew that was part of the N1 design, never noticed it was part of the Soyuz design. $\endgroup$
    – Bob516
    Commented Nov 16, 2019 at 13:20
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Thanks to @Heopps for pointing this out initially: During stage 1 and 2 separation, the spacecraft is still accelerating. See this question.

The video actually has a great clue -- The hanging toys! At stage separation for 1st and 2nd stages, the acceleration is still forwards by a significant amount, and the toys hang taught. (In the video, the graph at stage 1 separation indicates that forward acceleration continues at ~1g.) This is not so with the third stage cutoff, and that is when the toys start floating immediately.

So the arms are essentially thrown "less forward" for the first 2 separations because there is still significant acceleration forward, and thrown all the way forward when there is no acceleration to bring them back towards the body again at stage 3 cutoff.

However, I would still agree with the other answers that the rapid change in acceleration is a major contributing factor, especially for a human muscle response.

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I'd interpret the video in a different way - what you see is not the acceleration and not the absolute change in acceleration, but the rate of change in acceleration.

That is, from the movement of the astronauts/cosmonauts/people you can't tell how much acceleration changed. If there is a change from +10g to 0g over several seconds, you won't see much movement because the change is gentle and muscles can compensate for this. If it happens within a tenth of a second, everybody would be flung around because it happens so abruptly.

What you (most likely) can tell is that the jerk (the rate of change of acceleration or it's first derivative) is larger during 3rd stage shutdown. This might be simply an effect of the rather small engine that can shut down quickly while the larger engines on the first stage go off slowly.

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