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Could you please help me understand what is the difference between rocket engines designed to work in air (first stage) and vacuum (later stages)?

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The optimal shape of the nozzle will vary just slightly due the existence of a non-zero ambient pressure. I image you have to have a pretty good design to even notice. Beyond that, I have no idea. –  dmckee Apr 14 '11 at 2:44
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@dmckee is correct. I don't know enough of the technical details to justify an answer, but in qualitative terms, the only difference between a rocket made for atmospheric use versus one made for vacuum is the nozzle shape. The optimal shape produces high exhaust velocities, and its exact form is determined in part by the ambient pressure. Of course it doesn't change very much; relative to the pressure in a rocket engine, there isn't much change between atmosphere and vacuum. –  Colin K Apr 14 '11 at 3:08
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We're physicists, we don't deal with such trivialities as mere rocket science. :-P –  David Z Apr 14 '11 at 3:33
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@David: Yeah, isn't it funny that "Rocket Science" is typically associated with physics, but real rocket science is really more of an aerospace engineering discipline, and has been since long before people started using the term "Rocket Science." –  Colin K Apr 14 '11 at 4:30
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@ColinK Yeah, "I don't understand that, must be not physics" is typical reaction of certain moderator(s). I wonder, why he did not blame chemistry to be "responsible", because those rocket drives burn fuel. –  Georg Apr 14 '11 at 9:23

2 Answers 2

up vote 4 down vote accepted

The basic design difference between atmospheric and vacuum rocket design is its nozzle. The rocket thrust equation is http://www.braeunig.us/space/sup1.htm,

$$ F = q \times V_e + (P_e - P_a) \times A_e $$

where

$$ \begin{eqnarray} F &= &\mbox{Thrust} \\ q &= &\mbox{Propellant mass flow rate} \\ V_e &= &\mbox{Velocity of exhaust gases} \\ P_e &= &\mbox{Pressure at nozzle exit} \\ P_a &= &\mbox{Ambient pressure} \\ A_e &= &\mbox{Area of nozzle exit} \\ \end{eqnarray} $$

Since $V_e$ and $P_e$ are inversely proportional, maximum thrust occurs when $P_e$ = $P_a$. Nozzle exit pressure ($P_a$) can be increased/decreased by smaller/larger exit nozzle areas ($A_e$). Unless one designs a variable exit area nozzle, a single stage rocket's fuel usage can be optimal only either on Earth or in space. Fortunately however, as Nick pointed out, there's little advantage for nozzle optimization.

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I submitted an edit to format your equations into LaTeX, I hope you don't mind (you won't be able to see the edit until a moderator accepts it). Great answer. –  Colin K Apr 14 '11 at 16:21
    
Thanks for the help, Colin. –  Michael Luciuk Apr 14 '11 at 16:53

While it does have a small affect on the way a rocket works, the pressure of the atmosphere is trivial in comparison to the inertia of the rocket fuel. The atmosphere is easily pushed out of the way in the vicinity of the rocket due to the force on the rocket fuel.

The primary force exerted on a rocket is that of the pressure that forces the fuel to move in the only direction it can, the other way.

Because the rocket has so much inertia due to its single solid mass, it's relative velocity is a fraction of the fuel's velocity, but in the end, the pressure of the ignition puts the same force on both systems.

That's why both the vacuum and the atmosphere have negligable effect on the way a rocket works.

It's all in the hips.

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""That's why both the vacuum and the atmosphere have negligable effect on the way a rocket works."" Strange, why are 1st stage motors then built different from upper stage motors? –  Georg Apr 14 '11 at 15:26
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Georg: It appears that although small, there's a little more than a negligible effect. See braeunig.us/space/sup1.htm for an example with a 1.4% effect. –  Michael Luciuk Apr 14 '11 at 17:20

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