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Air-augmented rockets have not historically been very successful. In most cases, adding a shroud around the outside of an existing rocket was a large weight cost in exchange for only a modest increase in thrust specific fuel consumption. Because they weren't optimized for using the air as reaction mass, most of the added thrust was the result of secondary combustion between the fuel-rich rocket exhaust and the atmospheric air, making them essentially very inefficient ramjets.

If, however, an air-augmented rocket engine were designed in an inside-out configuration with a central bypass rather than an external bypass, you'd could end up with a simpler, lower-drag design which could be scaled up and would likely be pretty high in efficiency.

central bypass air-augmented rocket

Such a design could allow a really, really high bypass ratio, causing thrust specific fuel consumption to drop ridiculously low. The combination of really high thrust and really high specific impulse is pretty nice. How high of a bypass ratio would be possible before diminishing returns made the added drag too high?

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  • $\begingroup$ Are you familiar with a Scramjet? en.wikipedia.org/wiki/Scramjet#Basic_principles This seems similar in nature. $\endgroup$
    – PearsonArtPhoto ♦
    Jan 28, 2016 at 1:04
  • $\begingroup$ Yeah, I'm quite familiar with a scramjet. This is a similar concept, but very different in execution. Ramjets and scramjets use atmospheric oxygen as the oxidizer for their fuel, eliminating the need to carry oxidizer. An air-augmented rocket, on the other hand, uses atmospheric air only as a source of additional reaction mass, allowing it to operate at a wider range of velocities and air densities. Air-augmented rockets have better T/W ratios than ramjets with comparable Isp. $\endgroup$
    – sevenperforce
    Jan 28, 2016 at 14:58

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For an upper bound, the exhaust velocity of of the rocket sets an absolute limit. If you are flying faster than that, the intake air is actually slowed down when added to the mix, because the rocket exhaust is moving so slowly. For the most efficient propellant combination in use, LOX/LH2, the exhaust velocity is about $4,500 m/s$, and for hydrocarbons, about $3,500 m/s$. That places the limit approximately in the same range as scramjets.

However, even if the extra air is increasing the ISP, it steals energy from the propellant, reducing the exhaust velocity. (when using air-breathing engines, ISP and exhaust velocity is not equivalent) The limit is then also dependent on the ratio of rocket propellant and intake air flow.

Furthermore, for the extra efficiency to matter, the throughput of intake air has to stay high for quite some time, necessary meaning that the rocket has to fly for a long time experiencing high drag.

At high velocities, minimizing the drag of the intakes is important, calling for a straight-through design. At that point you can ask yourself the qustion: What is preventing the rocket exhaust from escaping in that direction as well? If the rockets are firing in the wrong direction, you are having a bad problem, and you will not go to space today.

In short, the limit is at most $4,500 m/s$, and certainly quite a bit less.

As a rule of thumb for an acceptable bypass ratio, you can assume that the exhaust velocity is divided by the square root of the airflow to total flow ratio.

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  • $\begingroup$ Perfect. This is exactly the analysis I was looking for. I knew there was a limiting factor in there somewhere, and you got it exactly right. $\endgroup$
    – sevenperforce
    Jan 28, 2016 at 20:49

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