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Most rocket engines have their efficiency measured by the specific impulse of the engine, which is just how fast the exhaust of the engine is going. Is there another measure of efficiency that's thrust/mass flow? Or does ISP take that into account, I think I'm missing something.

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ISP is really just the effective exhaust velocity of the engine normalized by a gravitational constant. It does take into account thrust and mass flow and is a first-order measure of an engine's efficiency. Note that it is effective exhaust velocity and not actual exhaust velocity. For air-breathing engines, for example, effective will be significantly greater than actual.

ISP isn't the whole story though. Probably the second most important measure for an engine is thrust to weight ratio (TWR) of the engine. TWR is indirectly a measure of efficiency as it usually dictates the time you will spend fighting gravity drag or thrusting at non-optimal times -- which is inefficient.

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    $\begingroup$ Because the mass of a rocket stage is usually dominated by tankage rather than by engines, the TWR of the engine itself tends to be less important than specific impulse -- which is not to say that it's of no concern; the original Atlas launcher reached orbit on a single stage of tankage via careful management of engine mass. $\endgroup$ – Russell Borogove May 29 '17 at 1:14
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Is there another measure of efficiency that's thrust/mass flow? Or does ISP take that into account

Specific impulse (more fully, mass-specific impulse, or impulse per unit mass) is, in fact, equal to the thrust per mass flow per unit of time for a pure rocket. This is because momentum is conserved; momentum of the propellant mass ejected out the engine is exactly opposite to the momentum gained by the rocket.

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    $\begingroup$ Thank you, found an equation online after searching which was ISP = Thrust/Mdot x g0, your explanation helped me understand $\endgroup$ – Jake Blocker May 29 '17 at 2:14
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Erik gave the second "big thing" from the pair - indeed, in space $I_{sp}$ is the king, TWR being secondary, while on ascent the relation is reversed.

But these two aren't all. For electric propulsion, alpha is very important - it's a bit of counterpart to TWR but involving electric power, as opposed to raw thrust. This is important, as ion engines are quite power-hungry and still subject to tyranny of rocket equation, especially if dry mass goes considerably up. Whatever gains you get to superior specific impulse, you may lose due to need to haul heavy power sources. That's also why plain old engine mass matters in space.

There's technology readiness level. The engine may look great on paper and even work promisingly in the laboratory, so what if it's still not "space-worthy" or reliable enough? The 12,000s of specific impulse of VASIMR aren't much of help when it's simply still not ready to leave the laboratory. Reliability and safety fall close on this spectrum.

Next, we have price of the engine and the fuel, both absolute and per unit. Why do so many missions - both commercial and scientific - still fly on these nasty hypergolics, instead of the nice, lean, efficient ion engines? Because both these engines and xenon cost an arm and a leg, and hypergolics, while old, corrosive, dangerous, inefficient, are cheap. It's often more cost-efficient to pack more cheap fuel and an old, less efficient engine, than the new great thing. And solid rocket boosters are very popular for first stage despite completely lousy specific impulse, simply because they are cheap and give good thrust - you're often better off financially with a couple of big and heavy SRBs than with a better, larger liquid fuel engine.

There's social/political acceptability. Read up on NTR. An engine of 1600s of specific impulse and enough thrust to propel large manned missions to Mars was scrapped for the sole reason that people don't want nuclear reactors in space.

Availability and handling properties of fuels are quite important - SpaceX flies on kerosene strictly because liquid hydrogen is difficult to handle. All amateur rocketry flies on nitrous oxide, which, while lousy as an oxidizer, is quite safe and accessible, unlike "nastier" stuff like LOX or RFNA.

Military applications have their own requirements. Visual (including smoke) signature is a big thing. Storability of fuels over long periods. Freezing temperature, boiling temperature, outgassing / vapor pressure, stability (insensitivity to shock and similar) are important factors.

So, $I_{sp}$ is really just a tip of the iceberg...

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