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What expansion ratio is the best for mars surface level engines?

For launches from Earth, first stage nozzles are much shorter than second stage nozzles because of Earth's high sea-level pressure. For more on that see Wikipedia's Rocket engine nozzle; Atmospheric use.

There are several futuristic proposals to launch from Mars, presumably tourists and professional astronauts on their return flight home, and the first of presumably many robotic sample return missions from Mars is expected in a few years. More on that at What kind of rocket will ESA(?) launch from Mars? Who will build it?

Since Mars has an atmosphere and so is not analogous to launching from the Moon, but it's low pressure so ot analogous to launching from Earth, I'd like to ask What expansion ratio is the best for mars surface level engines?

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    $\begingroup$ I think your question was closed because it is very ambiguous: There is no current Mars sea level. There is only a Mars surface level. You could ask about the expansion ratio for that level, or about a hypothetical past/future Mars sea level. Note that an atmosphere allowing a liquid water sea level to exist would need a higher atmospheric pressure, so the optimum expansion ratio for that surface level would be different from the current, dry one. Consider editing your question in that direction, and the question should reopen. $\endgroup$
    – AtmosphericPrisonEscape
    May 27, 2021 at 18:22
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    $\begingroup$ When in doubt, 42 $\endgroup$
    – uhoh
    May 27, 2021 at 23:43
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    $\begingroup$ @AtmosphericPrisonEscape changed it thank you for the comment $\endgroup$
    – Achillebckr
    Jun 1, 2021 at 13:11
  • $\begingroup$ A vacuum rated engine would probably be able to manage liftoff at <0.01bar. A bigger problem might be the size of the engine nozzles and the proximity to the surface. $\endgroup$
    – Slarty
    Jun 1, 2021 at 13:14
  • $\begingroup$ +1 for a good question! I see your edit, but I've further edited your question to better address the concerns raised in comments and the close votes, and now voted to reopen. $\endgroup$
    – uhoh
    Jun 2, 2021 at 3:27

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Just build for the structural needs of your Mars vehicle, the atmosphere there is thin enough that none of the standard Vacuum nozzles will be overexpanded, and for a rocket operating at the surface, the mechanical size limits will be much more stringent.

If anyone want to provide a more comprehensive answer, please do so. The true answer is a ridiculously complex balance of air pressure, speed of sound in that air, nozzle material + geometry, chamber pressure, exhaust velocity+chemical composition+temperature, proximity to the ground, relative velocity to the surrounding air, etc, etc, etc.

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