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On a sea-Level engine, what is the average nozzle ratio? What about an upper-stage vacuum engine?

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It varies widely with the chamber pressure and other details of the engine design. Some examples of first-stage engines with their approximate nozzle ratios:

For ideal performance, the expansion should reduce the exhaust pressure to be equal to the ambient atmospheric pressure, but since first-stage engines operate over a range of altitudes, the expansion ratio must be a compromise.

Note that the SSME on the shuttle burns from liftoff all the way to orbit, so it is tuned more towards vacuum performance than the others, with a higher expansion ratio.

Some upper stage engines:

Since upper stage engines exhaust into near-vacuum, extremely high expansion ratios would be ideal for performance, but the nozzle sizes are constrained by mass and space limitations.

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  • $\begingroup$ This does answer the direct question, but I wouldn't mind seeing a brief discussion (or link to such) as to the optimum expansion vs. atmospheric density. $\endgroup$
    – Carl Witthoft
    Commented Nov 11, 2019 at 17:04
  • $\begingroup$ Added a bit of info. $\endgroup$
    – Russell Borogove
    Commented Nov 11, 2019 at 17:36

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