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When I read about engines like the RD-170 they might have a single turbopump feeding multiple combustion chambers, and each combustion chamber has its own nozzle. Is there, or would it be reasonable to have, an engine with multiple combustion chambers feeding into one big nozzle? Or a combustion chamber with two nozzles, for instance to allow for roll control?

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    $\begingroup$ Yes, most cable guided anti tank missiles and K-5 AA missile. And the secondary engine on RPG-7 as well IIRC. $\endgroup$ – user3528438 Jan 23 at 13:14
  • $\begingroup$ I've always wondered this myself I'd love to know what the answer is $\endgroup$ – Reuben Farley-Hall Jan 23 at 15:43
  • $\begingroup$ @user3528438 Huh. I didn't imagine in-line combustion chambers or that application, but those are rockets, and I guess it fits. $\endgroup$ – Greg Jan 23 at 15:53
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    $\begingroup$ Launch abort towers, the "tractor" kind, like on Apollo. One solid rocket motor, four nozzles. That one didn't occur to me when I asked the question. $\endgroup$ – Greg Jan 23 at 16:17
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    $\begingroup$ @Greg: Feel free to self answer. $\endgroup$ – Joshua Jan 24 at 4:19
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Partial answer:

This engine from the 1970s vintage Viking Lander is a liquid engine featuring one combustion chamber and many nozzles. (you can ignore the red arrow, it's from another question).

enter image description here

The reason for this design was to prevent exhaust plume erosion of the Martian surface below the lander, to prevent degradation of the science results.

Source Viking Lander descent engine design feature (has more pictures)

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    $\begingroup$ This is an example for one combustion chamber and many nozzles, but I think there is no example for multiple combustion chambers and a single nozzle. $\endgroup$ – Uwe Jan 23 at 21:31
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    $\begingroup$ @Uwe how about staged combustion engines like the SSME? Two preburners and a main combustion chamber, but just one nozzle. Didn't think that is what the OP was really looking for though. $\endgroup$ – Organic Marble Jan 23 at 21:54
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    $\begingroup$ There is no direct connection of the two preburners to the nozzle, the combustion chamber is necessary to join an oxygen rich gas stream to another fuel rich stream. Oxygen and fuel should react before the nozzle, not after it. I can't imagine an efficient engine without a combustion chamber, only the preburners and the nozzzle. $\endgroup$ – Uwe Jan 24 at 0:38
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Reaction Engines' Advanced Nozzle shares the nozzle for the air breathing chamber(s) as the oxygen chamber's nozzle extension, tested in their Stoic and Strident engines.

Aerospike engines designs typically have multiple combustion chambers sharing a plug nozzle, to allow differential throttling to replace gimballing.

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I would note that the RD-170 and RD-180 designs, while they appear to have two nozzles and two combustion chambers in the assembly, are said to perform as one because there is a pipe from one chamber to the next. I was fascinated to learn that Soviet engineers found they could stabilize the pressure among two or more chambers by doing this. This is the technique, IIRC, that was used in the Soviet N-1 moon rocket's first and perhaps second stages. The number of exit bells disguises the fact that it really behaves as if it has fewer combustion chambers. This is why the RD-170 and RD-180 designs always look like the end user is buying pairs of engines when it's really a single dual chamber, shared pressure engine (my wording). Russian engineers were reluctant to share much more than this when they sold the surplus engines to the US. These engines originally were oxygen-rich pre-burner designs, which US engineers believed impossible to make stable and reliable. These were believed by the US to be the only production oxygen-rich engines in the world. US engines were always fuel-rich in the pre-burners (mostly to keep from eating up the metal). (Might be some more info in the Wikipedia article by now. If someone knows more, please correct/update me.)

Naturally, gimbaling gets a little more complicated but if the engine only needs to swing along an axis parallel to the line between the two combustion chambers and the engines are ganged in a circle, then steering is accomplished by swinging opposite engines in a single direction as needed.

It also occurs to me that linking smaller chambers together this way might be the way they overcame the need for bigger engines without bigger chambers. The Von Braun team nearly failed with the F-1 engine until someone suggested "fences" along the injector plate to help stabilize combustion. These can be seen in photos of the injectors and the do not exist, IIRC, on smaller engines. Clever trick.

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