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Stage 1 of Falcon 9 uses its gimballed engines during launch to control roll, pitch, and yaw.

Only the eight peripheral engines can be used for roll control since the center engine couldn't possibly exert a significant counter torque about the rocket's length axis.

But eight engines seems overkill for roll control... Do they all participate in roll control or is it just a subset of the eight that do?

It seems four engines would suffice, or maybe even just two (in pairs of diametrically opposed engines).

Sources would be appreciated, but if you don't have them handy, a comment pointing me in the right direction would still do.

Would be curious also if all engines participate in pitch and yaw control, or if again only some of them do. Thanks!!!

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    $\begingroup$ I think it has to be at least an opposing pair at the minimum; tilting a single engine only would also produce some unwanted pitch/yaw. My hunch is though that they just request some roll from the monster computer and it feeds it in with all of the other parameters (unbalanced thrusts, errors in flight path, errors in attitude) and commands to all engines reflect the best pointing for all 9 engines to accomplish all corrections at the same time. At least that's how I'd do it. $\endgroup$ – uhoh Dec 27 '20 at 9:04
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    $\begingroup$ This is yet another of many questions asked here regarding specific details of how SpaceX does things that most likely cannot be answered authoritatively. SpaceX regards many of those specific details to be trade secrets, and SpaceX zealously protects its trade secrets. $\endgroup$ – David Hammen Dec 27 '20 at 12:45
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    $\begingroup$ The system needs to allow for engine failures, so picking two would be a bad idea. $\endgroup$ – Organic Marble Dec 27 '20 at 15:33
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    $\begingroup$ I suspect @uhoh did not mean pick a fixed pair with "pick two". If only two are needed to satisfy requirements, "pick two that are available" is a good start for an algorithm. "Pick two that are available and are unlikely to be needed for pitch/yaw control in the next N control loop cycles" is even better. $\endgroup$ – David Hammen Dec 28 '20 at 14:24
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    $\begingroup$ @OrganicMarble Questions in most elements of the StackExchange, including this one, are supposed to be able to have definitive answers. One reason to close a question is that it is opinion-based: "This question is likely to be answered with opinions rather than facts and citations. It should be updated so it will lead to fact-based answers." $\endgroup$ – David Hammen Dec 28 '20 at 15:05
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As Jörg W Mittag says, we don't know. But since they can gimbal all of the engines, I'd be surprised if they didn't.

Gimbaling all of the engines a little, as opposed to gimbaling just a few of them a lot, has (at least) the following advantages:

  • It generally maximizes the clearance between adjacent engine bells, since you're turning all the engines by the same amount in approximately the same direction. Especially for roll control, if you only gimbaled some of the outer engines, the bells on the ones you did gimbal would get pushed closer to the bells of adjacent non-gimbaling engines.

  • It minimizes cosine losses: when you tilt an engine with $F$ Newtons of thrust by an angle $\alpha$, your forward thrust drops to $F \cos(\alpha)$ Newtons, but you gain $F \sin(\alpha)$ Newtons of lateral thrust in exchange. For small angles, $\sin(\alpha) \approx \alpha$ (in radians), while $\cos(\alpha) \approx 1 - \frac12 \alpha^2$. Thus, to obtain some desired amount of total lateral thrust, it's better to tilt more engines by a smaller amount, since the lateral thrust from each engine scales linearly with the gimbal angle, but the loss of forward thrust scales quadratically.

    (Of course, what you really want is some desired amount of lateral torque, and for that, engine placement matters too. In general, if you have engines at different distances from the desired rotation axis, as in the old Falcon 9 v1.0 engine configuration, you'll want to gimbal the outer ones more since they provide more torque per thrust. But with the "Octaweb" arrangement used by SpaceX since Falcon 9 v1.1, all of the outer engines are at the same distance from the roll axis. And for pitch and yaw, all the engines are approximately the same distance from the axis anyway, being all located at the tail end of the rocket.)

  • By keeping adjacent engines pointing in approximately the same direction, it also keeps the plumes of those engines from impinging on each other. Honestly I have no idea if this matters in practice, but such impingement might potentially have some negative effect on the vessel's aerodynamics and/or heat management by creating unwanted turbulence and/or pressure variations in the combined plume of the engines.

In general, the only reason why you might not want to use all your engines for attitude control is if you can't, e.g. because you prefer to save on mass and/or cost by making only some of your engines able to gimbal at all, or by restricting them to only gimbal along one axis. But AFAIK all the Merlin engines on Falcon 9 have full two-axis gimbal control, so they can all be used for all attitude maneuvers (except, obviously, that the center engine cannot exert any roll torque), so there's no really reason why they wouldn't use them all.

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  • $\begingroup$ An example for your last point would be Starship which has three sea-level Raptors with TVC mounts and three vacuum Raptors with fixed mounts. So, even in vacuum, they have to use the sea-level Raptors for attitude control. $\endgroup$ – Jörg W Mittag Dec 27 '20 at 23:55
  • $\begingroup$ For roll, perhaps "all eight outer engines" instead of "all engines"? $\endgroup$ – uhoh Dec 28 '20 at 1:34
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    $\begingroup$ I think the first point is the deciding one: there just isn't much room for the outer engines to gimbal without gimbaling the neighboring engines out of the way. They actually have "bumpers" to keep the bells from damaging each other when they do make contact. $\endgroup$ – Christopher James Huff Dec 28 '20 at 3:45
  • $\begingroup$ The Saturn 1B 1st stage had some fixed and some gimbaling. 4 of each. en.m.wikipedia.org/wiki/Saturn_IB $\endgroup$ – Organic Marble Dec 28 '20 at 3:51
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    $\begingroup$ @DavidHammen: I don't know why it's been so highly upvoted (given that, as you note, it is indeed speculative), but if you have any specific suggestions on how to make it less wrong (or less speculative), I'd be happy to accept your feedback. (I'm not sure if a significantly less speculative answer is possible without access to SpaceX inside information, though.) $\endgroup$ – Ilmari Karonen Dec 28 '20 at 15:31
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We don't know.

What we do know is that the Falcon 9 has engine-out capability which means you cannot pick a fixed setup beforehand, you have to be able to adapt to the loss of any one of the 9 engines.

Other than that, everything is possible.

We also know that SpaceX is constantly improving and changing, so what is true today is not necessarily true tomorrow and was not necessarily true yesterday. It is very well possible that the answer is "all of the above, at some point in time, in some version of the flight software".

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  • $\begingroup$ I'm sorry, but to say that anything is possible and that things will inevitably change is to say nothing at all. Of course anything is possible. But not all things are. Falcon 9 could have any number of engines, but we know it has ten, nine in S1 and one in S2. This would be a meaningful answer to that question if this info is known. If it isn't known, then so be it---lets avoid stating the obvious and instead leave it to others who may know to answer it if they feel inclined. No one doubts that "anything is possible" and that "things inevitably change" so you can leave that out. $\endgroup$ – user36480 Dec 28 '20 at 18:55

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