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I am given a scenario where I need to create a program to give the initial launch mass of a spacecraft that can vary between 4 and 20 stages.

I am given that the "specific impulse for all stages is 180s".

Since it is specific impulse, this value should be multiplied by the number of stages present. For example, if I had 5 stages, the specific impulse would be 900s. And if I had 10 stages, the specific impulse will be 1800s.

Is my logic correct? I think this makes sense considering each stage will have their own effect (i.e. impulse) on the spacecraft itself, and they will add on to each other as stages are utilized.

The other way I could go about this is treating the specific impulse as always 180s, regardless of how many stages are present. So for 5 stages it will be 180s, and for 10 stages it will be 180s.

Any help is appreciated, thanks.

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    $\begingroup$ "Since it is specific impulse, this value should be multiplied by the number of stages present." From where did you get this idea? $\endgroup$ – Organic Marble Oct 29 '19 at 14:06
  • $\begingroup$ I was under the impression that each stage will have its own effect on the rocket itself, and since we're given specific impulse, and not total impulse, I assumed this is how the calculations should be done. Is this not correct? $\endgroup$ – Scotch Jones Oct 29 '19 at 14:15
  • $\begingroup$ This is just an ideal scenario, but I believe a real rocket would have different engines with different propellants, ultimately giving each with a different specific impulse. So if you're trying to get the total impulse that will act on the spacecraft for a number of stages, you'd have to add them all up. $\endgroup$ – Scotch Jones Oct 29 '19 at 14:19
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Specific impulse is a measure of the fuel efficiency of a rocket engine. It’s established by the design of the engine, not by the size of the rocket. Specific impulse of multiple stages is definitely never added together.

For a very rough analogy, imagine a car that gets 30 miles to a gallon of gas. Ten of them driving in a convoy do not achieve 300 miles to the gallon.

For your problem, deal with each stage separately with a specific impulse of 180 seconds.

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    $\begingroup$ Thanks you so much. I wasn't too confident on my original approach and trying to research it through online sources and books left me more confused. Your analogy makes sense though and it is quite clear. Thanks. $\endgroup$ – Scotch Jones Oct 29 '19 at 14:44
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Supplemental answer: Here are the relevant equations and discussion from Sutton, 4th edition.

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