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A cluster of say 8 F-15 or SR-71 engines in my mind could make a viable first stage for a small rocket. Second they can land the stage back to the ground and if my guess is right they could go to up 50,000 to 70,000 feet and a respectable Mach 2 on the conservative side. This could provide a good point for a second stage fire in a low dynamic pressure zone using a vacuum only rocket engine. Unlike SpaceX, turn around time to use again would be one day or sooner.

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    $\begingroup$ A Pratt & Whitney F100-PW-220 turbofan engine has a thrust of 64.9 kN and 105.7 kN with afterburner. A Merlin 1D rocket engine has a sea-level thrust of 850 kN. A Falcon 9 uses 9 Merlin 1D engines. Do you really want a cluster of 118 or 73 turbofan engines? $\endgroup$
    – Uwe
    May 23 at 20:42
  • $\begingroup$ I did say small rocket $\endgroup$ May 23 at 21:57
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    $\begingroup$ Well, you did not say a tiny rocket. The concept of first stages with rocket engines did work very well for more than 70 years now. Tiny, small, medium and huge size first stages were build successfully using different engine sizes. $\endgroup$
    – Uwe
    May 23 at 22:06

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70,000 ft (~21 km) and Mach 2 (~700 m/s) is a pitiful booster stage.

Consider the energy state (mass specific kinetic + potential energy of the rocket) during launch, this is a metric for measuring how well the booster performs. Here is one for a simulated launch vehicle (close-ish to an expendable Falcon 9) showing the booster stage at stage separation, and your proposed alternative:

energy state diagram MJ

(Personal work)

The black lines show equal energy contours ($\frac{MJ}{kg}$). The airbreathing first stage is only able to deliver the second stage with ~20x less energy than a traditional booster stage. Therefore your upper stage has a lot more work to do, good luck!

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    $\begingroup$ That plot nicely illustrates the misconceptions behind proposals for balloon launch, air launch, etc. Everyday activities rarely involve velocities greater than even 100 m/s. People unaccustomed to thinking about orbital dynamics seem to expect those lines to be mostly horizontal, when in fact they almost immediately become mostly vertical. Air-breathing engines are limited to a tiny area in the lower left corner, covering at most 2 or 3 of the ~20 contour lines. A suborbital hop to 100 km crosses barely more than 3 of them. And that's just a minimal, temporary <200 km orbit. $\endgroup$ May 23 at 19:00
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    $\begingroup$ The plot is incredible! I never saw such a brilliant illustration showing the huge difference between the air breathing stage 1 and a conventional stage 1 with rocket engines using a liquid oxidizer. $\endgroup$
    – Uwe
    May 23 at 20:17
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    $\begingroup$ @user3660060 the problem isn't getting a vehicle to space with an air breathing engine, it's economically delivering payload to orbit. The GTX would have used air breathing as an act of desperation, accepted wisdom at the time being that SSTO was the only path for reuse, and SSTOs needing every last scrap of performance just to work. But a first stage is actually the easiest part of the launcher to recover and reuse, and staging gives you mass ratios that make an upper stage far easier to reuse than a SSTO, with more payload to orbit, all without wings and complex air-breathing engines. $\endgroup$ May 24 at 0:34
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    $\begingroup$ Just noticed that this was supposed to be a Dragon: it's more consistent with the just-launched Starliner OFT-2, on an Atlas V. A Dragon would stage quite a bit sooner, around 2 km/s, at around 70 km altitude. Falcon 9 stages relatively early compared to more traditional rockets, which both allows the first stage to be recovered more easily and allows the upper stage to take more advantage of a dense propellant and common engine, with large propellant tanks and a high mass ratio to compensate for its relatively low specific impulse. $\endgroup$ May 24 at 0:48
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    $\begingroup$ Compared to everything else in a launch, fuel is basically free. A Falcon 9 burns about $200k worth of propellants per mission, far less than the cost of even a single jet engine, let alone refurbishment. A design that has higher on-paper efficiency but more complexity is going to lead to higher lifecycle costs (testing, manufacture, refurbishment for reusables, etc.) that obliterate any gains from lower fuel cost. $\endgroup$
    – Cadence
    May 24 at 8:51

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