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In rockets, smaller nozzles are used at lower altitudes because atmospheric pressure would cause problems by pushing air into nozzles with higher expansion ratios.

However, it seems to me that once the vehicle reaches Mach 1, no air would be able to enter the nozzle because the vehicle is moving faster than the speed at which air would be sucked in.

If that’s true, why aren’t vacuum-variant engines flipped on as soon as the rocket is supersonic?

Thanks

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    $\begingroup$ "because the vehicle is moving faster than the speed at which air would be sucked in." Irrelevant. See space.stackexchange.com/questions/49772/… $\endgroup$ Nov 27 '21 at 22:43
  • $\begingroup$ Mach 1 would be with reference to free stream, which is air that is a bit far out from the rocket. There is some air (very close to the rocket) that is moving along with the rocket. $\endgroup$
    – AJN
    Nov 28 '21 at 0:36
  • $\begingroup$ @OrganicMarble that one engine designed for vacuum operation has engine bells that couldn't withstand external atmospheric pressure while operating doesn't mean that it's impossible to do. Reinforcing the nozzle is a much easier problem to solve than flow separation. $\endgroup$ Nov 28 '21 at 3:10
  • $\begingroup$ Apart from the issue @AJN mentioned, where would such vacuum engines be located? First stages generally need most of their base covered with engine nozzle to provide enough thrust at the start of their flight. Vacuum engines take up lots of room, plus this adds dead mass. You could just stage earlier (if you can survive it that near max-Q), but this means your booster barely gets the vehicle supersonic, and the upper stage has to do all the rest of the work. This means your upper stage has to be even bigger and more complex, and heavier in comparison to its payload. $\endgroup$ Nov 28 '21 at 3:24
  • $\begingroup$ @ChristopherJamesHuff the answer to the linked question does a good job of explaining why you don't start high expansion ratio engines at high Patm. The particular engine is also irrelevant - the answer doesn't even mention it. $\endgroup$ Nov 28 '21 at 3:56
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However, it seems to me that once the vehicle reaches Mach 1, no air would be able to enter the nozzle because the vehicle is moving faster than the speed at which air would be sucked in.

Multiple reasons.

One reason is the shock front that envelopes the launch vehicle. It's the air well removed from the vehicle that is moving at Mach 1 or higher relative to the vehicle. In the vicinity of the vehicle, the air is moving at subsonic speeds. Once a vehicle exceeds the speed of sound (with respect to air well removed from the vehicle), a shock front develops in front of and around the vehicle. Inside the shock front, the velocity of the air with respect to the vehicle remains subsonic. This invalidates the basic premise of the question.

Another reason is safety criticality. The second stage is enshrouded until first stage separation in most launch vehicles. It would be a very bad idea to have the second stage engine fire while it remains enshrouded. Doing so would mean pluming the first stage propellant tanks with hot second stage exhaust. This is a prime example of a "must-not-work" function.

Safety critical functions are categorized as "must-work" or "must-not-work", with the categorization possibly switching from one to another depending on phase of flight. For example, ignition of the second stage in a typical launch vehicle (a vehicle in which the second stage is enshrouded) transitions from a "must-not-work" function prior to first stage separation to a "must-work" function after first stage separation.

The Space Shuttle was the only vehicle I know of in which the vacuum engines could have been fired prior to stage separation. Even with the Space Shuttle, firing of the Orbital Maneuvering System engines was a "must-not-work" function below 70000 feet (21.4 km) altitude. Below that altitude there was a risk of having the nozzle collapse due to gross over-expansion of the exhaust. Multiple inhibits prevented the Shuttle OMS engines from firing below this altitude.

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Your idea that "no air would be able to enter the nozzle because the vehicle is moving faster than the speed at which air would be sucked in" is inaccurate. But the vehicle speed is irrelevant here.

The answer is pretty well-summarized in the top answer here as someone else linked, but to re-state it:

Vacuum-optimized engines are not operated in the atmosphere because of flow separation in the nozzle, which leads to large side loads (against the walls of the nozzle) and instabilities in the nozzle, likely leading to structural failure or collapse of the nozzle. Flow separation can also generate shocks inside the nozzle, which will also lead to structural failure.

Flow separation occurs when the pressure at the exit of the nozzle is significantly lower than the outside ambient pressure; exit pressure lower than ambient pressure is referred to as overexpansion. There is not an exact ratio at which flow separation occurs, but common estimates are in the range of P_exit/P_ambient = 0.2-0.4. The pressure difference at the nozzle exit leads to the lower pressure exhaust being "pinched" towards the center axis by the higher pressure ambient gas. If this force becomes too high, likely in the range of the ratios mentioned, the nozzle flow will detach from the walls of the nozzle, which is called flow separation.

To optimize the performance of a rocket nozzle, the exit pressure should be as close to the ambient pressure as possible; since vacuum engines are optimized for in-space use, the exit pressure is extremely low. The exit pressure will be controlled by the expansion ratio or area ratio of the nozzle (A_exit/A_throat); for vacuum engines, we see much larger nozzles in order to maximize the expansion ratio and minimize exit pressure.

So, to briefly answer your question:

  • Rocket velocity (or Mach #) is not the same as nozzle exit velocity
  • Flow separation ("air sucked in") is dependent on the ratio of nozzle exit pressure to ambient pressure, not on rocket or nozzle exit velocity.
  • Even at high altitudes, the vacuum nozzle would generally still be overexpanded and be at risk for flow separation.
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