OK, so you have come up with a magic thing-a-ma-bob. It makes rockets way better, improving Isp (the amount of thrust a rocket produces per pound of propellant). But does it improve rocket performance, considering that you have to now carry a thing-a-ma-bob all the way up?

Your magic device increases the final mass, so the critical equation is:

delta-v = 9.8 * Isp1 * ln (StartMass/FinalMass)

compared to

delta-v = 9.8 * Isp2 * ln ([StartMass+ThingMass]/[FinalMass+ThingMass])

If you look at this in a spreadsheet, you find some interesting results.

For 9,000 m/s rocket aircraft, starting from a 250 Isp:

If your device increases Isp 10%, it can weigh half your vehicle's mass and still come out ahead.

If your device increases Isp 20%, it can almost double vehicle mass and still come out ahead.

If your device increases Isp 40%, it can almost triple vehicle mass and still come out ahead.

On the other hand, if you start from an Isp of 350:

If your device increases Isp 10%, it can weigh a third of your vehicle's mass and still come out ahead.

If your device increases Isp 20%, it can weigh half your vehicle's mass and still come out ahead.

If your device increases Isp 40%, it can weigh one and a half times your vehicle's mass and still come out ahead.

In other words, starting from a lower Isp makes fun optimizations like air breathing ascent/descent stages more tempting...

## Monday, May 4, 2009

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