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While I get that one is a vertically launched rocket and the other is a space plane, is it even wildly possible that there could be a vertical intake version of the SABRE engine? Maybe it can be used as a strap-on booster, which is attached to a normal rocket and uses Reaction Engine's pre-cooler tech to reduce fuel requirements and therefore increase the payload. It would stay in jet/air breathing mode as usual before mach 2 or whatever speed it needs to switch to rocket mode.

Or is it infeasible to use such jet+rocket engines in a vertical rocket launch configuration?

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    $\begingroup$ Rockets grab altitude as quickly as possible. The air breathing ability is good for only a couple of minutes and adds a bunch of mass. Almost certainly a bad tradeoff. $\endgroup$ – zeta-band Mar 27 at 19:21
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Air-breathing engines are usually combined with wings or lifting bodies because they inherently have lower thrust to weight ratios...there's just no way to beat the power and thrust density of something combining liquid propellants and blasting the combustion products out a nozzle with something that has to use ambient air streaming past the vehicle at high speed as an oxidizer. Rockets are much better than jet engines at thrust and acceleration, you strap rockets to aircraft to get the aircraft off the ground faster. Strapping jet engines to a rocket isn't going to work very well.

Making it worse, rockets launching vertically leave the significant atmosphere in a couple minutes, and reach airspeeds where airbreathing is impractical even sooner. To contribute substantially, air breathing engines have to be used with a low trajectory that keeps them in the atmosphere longer, and they have to be the primary source of thrust in that period or you're just flying a rocket very inefficiently while carrying useless jet engines. Again, that means wings or lifting bodies.

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