So I was watching a video of a talk by Geoffrey Landis (my old mentor when I was an intern at Glenn), and he made a very interesting point.
If you’re trying to maximize energy efficiency for a rocket and you have the ability to change Isp, you should set the exhaust velocity equal to the rocket’s current velocity. Think about it for a little bit, and you’ll see that it’s true.
We make some simplifying assumptions here, such as assuming arbitrarily good mass fraction, and thrust occurring outside any gravity wells (or, equivalently, thrust that is arbitrarily higher than acceleration due to gravity at that point). But with these assumptions, this finding is true.
One thing that’s a little surprising is that you’d have PERFECT efficiency under this scenario. That means you’re wasting exactly no energy by accelerating all that propellant, which goes a little counter to the intuition. A perfectly efficient rail gun (with an arbitrarily low-mass acceleration cart) would not be any more energy efficient.
…the downside, here is that your initial exhaust velocity is zero, which implies an infinite amount of fuel. This isn’t so bad because we can just truncate the initial portion of the flight by picking a certain minimum Isp to keep mass fraction to a reasonable number. We lose some efficiency this way, but it’d small. Alternatively, you could use rail-launch for the low-speed portion of the flight and maintain arbitrarily-good efficiency. The other side of this is that it implies 700-900s Isp for the last portion of the flight if going all the way to Earth orbit. That implies use of non-chemical thermal rockets (such as NTR), but you’d be no better off energy-wise since the only practical propellant for those (while still reaching those Isps) is hydrogen, and producing hydrogen requires a lot of energy (energy which is not at all utilized in the rocket! Hydrogen is considered basically inert… you could also use helium). Besides, terrible mass fraction.
Anyway, there is also an energy-ideal exhaust velocity if you can’t adjust the Isp. I believe it’s about 5/8th the final delta-v, if I remember geoffrey’s talk. I may try to recreate this calculation.
Another point: It makes things like Aerojet’s thrust-augmented rocket look pretty interesting from an energy standpoint.
I have a bunch of thoughts related to this that I may blog later on. Here’s Landis’s talk. (He argues for NTR here. I disagree with him, but very interesting talk, and he definitely makes a convincing case that NTR is not some unobtainable technology.)
Overall, I appreciate the change in focus to energy. I think we have an (understandable) obsession with mass in the rocketry world, but that doesn’t tell the whole picture and can somewhat bias our intuition.