On a sea-Level engine, what is the average nozzle ratio? What about an upper-stage vacuum engine?
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:
- Merlin 1D Vacuum (Falcon 9) 165:1
- J-2 (Saturn V) 27:1
- RL10 (Atlas V, Delta IV) 84:1 or 130:1 depending on model
- HM7B (Ariane) 83:1
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.