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Comparing photos of combustion chamber designs from the the 1940's and 1950's to those of today, it looks to the amateur observer such as myself that the size of the chamber proper, where fuel and oxidizer are mixed and burn, as compared to the divergent sections of nozzles, has gotten very much smaller. An example is comparing the early V2 engines to those of the NASA Saturn rocket and shuttle engines. Is this true and if so, how does it reflect advances in design efficiency ?

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It's more likely that you're seeing a trend toward relatively larger nozzles, in particular on upper-stage engines.

The size of the combustion chamber is more or less fixed by the chemistry of the fuel and the thrust of the engine. None of the advances made since the 50s have significantly altered this.

The size of the nozzle relative to the combustion chamber depends on pressure; the expanding cross section of the nozzle lowers the pressure of the exhaust as it flows, and ideally you want the pressure at nozzle exit to match that of the atmosphere outside.

For a sea-level engine running at low chamber pressure, this means a relatively small nozzle. For an engine running in vacuum, you want a much larger nozzle.

Early rockets were single stage, so early engines were optimized for low altitude. Later engines also tend to run at higher pressures, which require longer nozzles to take full advantage of.

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