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Then do you know what the competing advantage of a small number of large engine is? The robustness of many small engines seems so useful to me. Cost?



It is also economy of scale when manufacturing. You need smaller tooling to make smaller engines, and because nobody makes rocket engines in quantities that would load the production line 24x7, almost only additional expense is raw materials which is negligibly small.

Also, gas dynamics in a smaller engine is simpler and easier to simulate.

And yes, it gives a lot of redundancy, if the only engine of the stage fails you are toast, if 1 out of 9 fails it's almost okay, as the most recent F-9 flight shown.


I would naively guess fuel-weight ratio.

Having multiple engines means having multiple small containers that each take up metal, manufacturing, etc. All of which is dead weight as far as lift goes. By contrast a large engine is by proportion more fuel, which means you can get more stuff to orbit.


Increasing the number of engines can also decrease the reliability, for example if one of the engines explodes or catches on fire. The Falcon 9 has an armored tub around each engine to hopefully reduce the risk of a single engine problem becoming catastrophic.


I think you end up having less total engine weight that way.


Apart from the redundancy issue, size matters. The area/volume ratio of the combustion chamber necessarily goes down with size, which changes the flow dynamics. While a lower A/V ratio would seem to make the cooling problem easier to solve, I also remember people talking about the difficulty of getting stable combustion in the F-1 engines because they were so large.


SAFETY!

If you go with a small number of rockets, it's unlikely you can sustain one (let alone) multiple engine failures. With several rockets arranged in a distributed geometrical fashion, you can significantly raise the probability of proper vehicle function even with several failures (as mentioned before, with the Falcon 9).


Redundancy is a funny issue, though. Replacing one engine with multiple engines means you can survive one failure, but you then have a multiple of the things that can fail.


The other downside to many small engines is vibration and warding off thrust oscillation.


From my amateur reading, I can say that a large number of engines leads to more failure modes due to interactions and complications, especially regarding vibration.




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