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> A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure. A rocket engine produces thrust when its ch

> A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure. A rocket engine produces thrust when its chamber pressure exceeds ambient pressure, which is trivially true for any rocket engine. The flow coming out of the nozzle can have lower pressure at the exit plane than ambient and still make plenty of thrust. This is called "overexpanded" flow, and is the regime that produces shock diamonds in rocket and afterburning jet engine plumes at low altitudes. Reduced to quasi-1D form, thrust is given by: T = mdot*(delta V) + (p_e - p_a)*A_e Where mdot is mass flow coming from the nozzle, delta V is change of velocity of that efflux with respect to the vehicle reference frame (in a rocket, it is just exit velocity, in an airbreathing system, you have to take into account the incoming momentum), p_e is static pressure at the exit plane, p_a is ambient pressure, and A_e is the area of the exit plane. In an overexpanded scenario, p_e < p_a , but the majority of thrust is coming from the momentum change term, which is the one containing mdot. Nozzle performance is optimal when pressure at the exit plane matches the ambient pressure. This is when the exhaust velocity is maximized and the pressure thrust term vanishes. It can be shown (undergraduate aeropropulsion course homework) that you get more thrust from ideal expansion than from pressure thrust (underexpanded regime). The point you are trying to make is that an air-launched system allows the rocket to start with a higher area ratio than if it were ground-launched. In the ground-launched scenario, a large nozzle area ratio will suffer overexpansion losses and how large you can go will also be limited by structural implications from the internal nozzle separation that will occur with gross overexpansion. While this is all true, the reality is that the additional rocket performance you can get from a larger nozzle area ratio is not that compelling in light of building, operating, and maintaining an entire air-launch aircraft platform. You're better off putting that money into incrementally larger propellant tanks due to the lower mission-averaged Isp associated with the ground-launched vehicle.

Gravityloss 7y ago
I think you're arguing against something I didn't say.
- ThenAsNow 7y ago
  You said: > A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure. This is trivial at best and wrong at worst. When you say "the pressure", what do you mean? If chamber pressure, this is trivial and also not relevant to air launch vs. other modalities. If you mean pressure at the nozzle exit, the statement is false. Most of what I wrote above addressed why the latter is false.
  - Gravityloss 7y ago
    It's the nozzle, so how could it be chamber pressure? I also don't mean nozzle exit, and I didn't write such a thing. Take some small patch of the nozzle surface. If the pressure inside is bigger than outside, that area contributes to thrust. If the pressure inside is smaller than outside, then it contributes negative thrust. Curious to hear if you think that is wrong.
    - ThenAsNow 7y ago
      If you look at the quasi-1D form of the thrust equation, you'll note the two terms I mentioned. Yes, you can integrate the surface pressure times the surface normals to get the pressure contribution to thrust, which will be negative in the case of the specific regions of the nozzle that are at lower-than-ambient pressure. As long as the geometric throat of the nozzle is sonic (as it would be in any meaningful rocket engine) and you have some divergent portion after the throat, the whole nozzle will not be at negative pressure thrust. But to say "the nozzle is producing negative thrust" is fallacious because in any non-trivial case, the rate of momentum change term in the thrust equation, i.e., the first one, will be very significant, and hence the flow leaving the nozzle will be contributing to thrust regardless of if it was overexpanded within the nozzle or not. Even in the most overexpanded case, the nozzle directly contributed to accelerating the flow - how can you say the nozzle is not producing thrust? You can construct some pathological cases, like a very small thruster that is highly overexpanded to get the rate of momentum change term at or below the magnitude of the pressure contribution, but that doesn't represent a practical rocket engine (maybe more like a Reaction Control System thruster fired at ambient conditions). I suspect your notion of thrust may be based just on the pressure contribution and is missing the rate of momentum change term, which will be significantly larger than the pressure term in launch system rocket engines.

Gravityloss 7y ago

I think you're arguing against something I didn't say.

ThenAsNow 7y ago
You said: > A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure. This is trivial at best and wrong at worst. When you say "the pressure", what do you mean? If chamber pressure, this is trivial and also not relevant to air launch vs. other modalities. If you mean pressure at the nozzle exit, the statement is false. Most of what I wrote above addressed why the latter is false.
- Gravityloss 7y ago
  It's the nozzle, so how could it be chamber pressure? I also don't mean nozzle exit, and I didn't write such a thing. Take some small patch of the nozzle surface. If the pressure inside is bigger than outside, that area contributes to thrust. If the pressure inside is smaller than outside, then it contributes negative thrust. Curious to hear if you think that is wrong.
  - ThenAsNow 7y ago
    If you look at the quasi-1D form of the thrust equation, you'll note the two terms I mentioned. Yes, you can integrate the surface pressure times the surface normals to get the pressure contribution to thrust, which will be negative in the case of the specific regions of the nozzle that are at lower-than-ambient pressure. As long as the geometric throat of the nozzle is sonic (as it would be in any meaningful rocket engine) and you have some divergent portion after the throat, the whole nozzle will not be at negative pressure thrust. But to say "the nozzle is producing negative thrust" is fallacious because in any non-trivial case, the rate of momentum change term in the thrust equation, i.e., the first one, will be very significant, and hence the flow leaving the nozzle will be contributing to thrust regardless of if it was overexpanded within the nozzle or not. Even in the most overexpanded case, the nozzle directly contributed to accelerating the flow - how can you say the nozzle is not producing thrust? You can construct some pathological cases, like a very small thruster that is highly overexpanded to get the rate of momentum change term at or below the magnitude of the pressure contribution, but that doesn't represent a practical rocket engine (maybe more like a Reaction Control System thruster fired at ambient conditions). I suspect your notion of thrust may be based just on the pressure contribution and is missing the rate of momentum change term, which will be significantly larger than the pressure term in launch system rocket engines.