[AR] Re: airbreathing engines (was Re: Re: to the stars, soon)

  • From: Henry Spencer <hspencer@xxxxxxxxxxxxx>
  • To: arocket@xxxxxxxxxxxxx
  • Date: Tue, 5 Apr 2016 00:04:43 -0400 (EDT)

On Tue, 5 Apr 2016, Ian Woollard wrote:

> The cost is carrying the extra mass of the LOX.

Partly, but if the issue was just carrying oxidiser you'd only lose 2/3 of the Isp. Going to a rocket the Isp drops by a whole order of magnitude...

No, that's not a fundamental law; it depends on what kind of jet engine you're using as your base, and what speed it's operating at. Subsonic turbofans can have very impressive Isp, yes. Supersonic ones, less so. Up in ramjet territory, typical airbreathers don't have much more than that 2/3 advantage. Scramjets don't do even that well.

The advantage is energy; throwing reaction mass at a speed comparable to
flight speed is much more efficient than the fixed speed rockets give you,
unless the flight speed is comparable to rocket exhaust's speed.

Unfortunately for the relevance of that theory, the extra advantage of airbreathing is lost long before then -- ramjet speeds are still far below the exhaust velocity of a decent rocket engine.

A *rocket* engine is most energy efficient with an exhaust velocity matched to its flight speed, yes. (This is, however, of no practical importance, since energy efficiency is not the dominant design issue for most types of rocket.) But jets are different. Adding momentum to air that is already flowing past you at high speed is very costly in energy. Having *ambient* nitrogen to use as reaction mass is useful at low speed, but becomes much less so as speed builds up. A quick bit of algebra suggests that airbreathing Isp should be roughly inversely proportional to flight speed, and indeed if you plot Isp vs. speed for a wide range of real airbreathers, and draw a curve through the best-Isp peaks, the curve is pretty much a simple 1/x shape.

Henry

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