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How do I find out the ambient pressure for designing a vaccum rocket engine? I am using the propellant combustion charts from the braeunig website. But I cannot figure out the ambient pressure for the 200-500 km LEO OR SSO. Since the pressure in space is never completely zero I will need a value for the ambient pressure for moving on with the design. Please help. Thanks.

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Since the pressure in space is never completely zero i will need a value for the ambient pressure for moving on with the design.

Looks like you only consider the Isp to get the area, and your model always gives bigger Isp with bigger area. As soon as you're interested in something else - mass of the nozzle, for example - or the model of the nozzle is different - for example, too cold a gas can condense and then it stops adding to the thrust - you can find your optimum.

In practice, gas does condense in vacuum nozzles, there are some pictures of that with, IIRC, Arian vacuum stage. Added thrust is smaller and smaller for each extra unit of nozzle exit area, while mass of the nozzle is bigger and bigger for the same unit of area, so if you consider full Tsiolkovsky equation there will be some optimal area.

Look at pictures of vacuum nozzles to get an idea. Everybody has his own limitations - staging issues (avoid collision with previous stage), or rocket length (will need a longer interstage), or material of the nozzle (light carbon composites can allow wider and longer nozzles), or mechanical side forces for thrust vectoring (you'll have to consider nozzle inertia when swiveling the chamber) or manufacturing capabilities etc. so numbers can differ.

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