Rocket engines: air & vacuum

Question

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

Answer 1

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.

Answer 2

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.