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## Posts Tagged ‘Mach’

I was not completely happy with the last post’s vagueness so I’m adding more formal treatment here. This long post still ends up lazily speculating around the advantages and disadvantages of air breathing propulsion in the end though. ðŸ™‚

Effective or apparent exhaust velocity (ISP to some, but that is an old-fashioned troublesome term so I won’t use it) is $v_{exeff}=\frac{F}{\dot{m}_{prop}}$. That means, thrust for a certain propellant flow. Higher is better.

For rockets, the thrust $F_R=\dot{m}_{propR}v_{exR}$ but for air breathers, $F_A=\dot{m}_{totA}v_{exA}$. Air breather is denoted by A and rocket by R.

Thus, for the rocket, the effective exhaust velocity is the real exhaust velocity (it exhausts only propellant products). $v_{exeffR} = v_{exR}$.

For the air breather it’s more complicated. Only fuel is used as propellant flow but a lot more is expelled:
$v_{exeffA} = v_{exA}\frac{\dot{m}_{totA}}{\dot{m}_{propA}}$

So, what is the ratio of fuel flows for a rocket and an air breather of same thrust? The inverse ratio of effective exhaust velocity of course. How much better is an air breather in this case?

$R_{breathe}= \frac{v_{exeffA}}{v_{exeffR}} = \frac{v_{exA}}{v_{exR}}\frac{\dot{m}_{totA}}{\dot{m}_{propA}}$ – the Air Breather’s advantage.

So, the rocket might benefit from a higher real exhaust velocity but the air breather benefits from the ratio of total exhaust mass versus propellant mass.

But that’s not all.