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Pulsejets are mostly known for propelling the V-1 flying bomb, and have some use as small remote-controlled plane engines. In either case, the pulsejets aren't particularly big, as far as jet engines go.

How big can a puslejet be realistically made? Assuming that, for some reason, there was a need to power a much bigger plane with pulsejets, at which point would it stop making sense to make the pulsejet bigger, and use multiple smaller pulsejets?

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At the point where the structural rigidity needed to overcome the vibration of a single enormous pulse train becomes so heavy that the aircraft can't fly anymore, replace the single large pulsejet with several smaller ones, whose individual pulses are smaller.

Conversely, imagine replacing a car's V8 engine with a single-cylinder engine of the same power. It would need much stronger engine mounts, flywheel, clutch, transmission, etc. (Single-cylinder car engines weren't that rare a century ago; good luck finding one today.)

But the main reason that large pulse jets are rare is their low fuel efficiency. The bigger the engine, the more that matters.

See also: What are the pros and cons of a pulsejet?

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The bigger the pulse jet, the combustion becomes lower frequency but much great power per pulse. So it generates low frequency of very loud pulses, which in turn causes low frequency of high amplitude vibrations. If you are planning to mount it on airplane, it's airframe should be very strong. And unlike continuous jet engines, pulse jet thrust to weight ratio may become constant or decrease with scale because combustion pulse rate/frequencies decrease. So it's not advantageous to use single big pulse jet. Better go with small or medium pulsejets but multiple of them.

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