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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 wron

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 didn't talk about the whole nozzle. The first line of my post: "A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure" With the word "part" I meant "patch of the nozzle surface". Then you went on to talk how I'm wrong and talked about the chamber and the nozzle exit area etc. All irrelevant. I guess it was a misunderstanding but it felt quite uncharitable.
    - ThenAsNow 7y ago
      > I didn't talk about the whole nozzle. The first line of my post: > "A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure" > Then you went on to talk how I'm wrong and talked about the chamber and the nozzle exit area etc. All irrelevant. Your statement is just plain incorrect (or being charitable, misleading) as written. When the velocity of the exhaust flow is > 0, even if the pressure in some section of the nozzle is below ambient, the nozzle (including the section below ambient pressure) is accelerating the flow, so every element of the nozzle's net contribution to thrust is always > 0. At the end, I think you are talking about overexpansion losses, but short of pathological cases, in a rocket engine the overexpansion losses will not outweigh the rate of momentum change term. Edit: To add further, the overexpanded nozzle is producing less thrust than the ideally expanded nozzle. But the overexpanded section is still producing positive thrust, it's just less than what you would have if the nozzle had ended earlier. It's not like that section has reversed sign in terms of thrust production.
      - Gravityloss 7y ago
        Unfortunately, you're contradicting yourself. Every element of the nozzle in an overxepanded case can not contribute to thrust. Let's break it down, it will be interesting to see which part do you disagree with? 1. Optimum expansion ratio has exhaust at ambient pressure. (we agree on this) 2. Adding more nozzle, going to overexpansion, reduces total thrust. We can call the expanded part of the nozzle the "nozzle extension". If this wasn't true, then part 1 wouldn't be true (optimum). (we agree on this) 3. The pressure in the nozzle extension, as experienced by the inside nozzle wall, is lesser than ambient. (my claim, that you disagree with) 4. Sampling some area of the nozzle extension, it constitutes negative thrust. (my claim, you also disagree with this) 5. If the overexpanded nozzle extension contributed positive thrust (like you claim), one could just keep on adding more nozzle and get more and more thrust. (Until flow separation.) 6. In vacuum one can add a lot of nozzle (because ambient pressure is zero) to get more and more thrust for the same fuel amount - until one hits mass or size constraints, or condensation or chemical effects too? It doesn't really matter if the exhaust is accelerated by the nozzle extension or not. If the sum of total pressure points inwards, then when integrating over the nozzle extension area, force points downwards. This is because the momentum given by the exhaust is not the only force acting on the nozzle. Most likely the gas is just too rarefied so the total pressure it exerts is less than ambient. Even if it gets accelerated (momentum, yay), it's not enough to overcome the pressure on the other side of the nozzle wall. I'm interested in hearing why I would be wrong.

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 didn't talk about the whole nozzle. The first line of my post: "A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure" With the word "part" I meant "patch of the nozzle surface". Then you went on to talk how I'm wrong and talked about the chamber and the nozzle exit area etc. All irrelevant. I guess it was a misunderstanding but it felt quite uncharitable.
  - ThenAsNow 7y ago
    > I didn't talk about the whole nozzle. The first line of my post: > "A rocket engine nozzle produces thrust only for the part where the pressure is greater than atmospheric pressure" > Then you went on to talk how I'm wrong and talked about the chamber and the nozzle exit area etc. All irrelevant. Your statement is just plain incorrect (or being charitable, misleading) as written. When the velocity of the exhaust flow is > 0, even if the pressure in some section of the nozzle is below ambient, the nozzle (including the section below ambient pressure) is accelerating the flow, so every element of the nozzle's net contribution to thrust is always > 0. At the end, I think you are talking about overexpansion losses, but short of pathological cases, in a rocket engine the overexpansion losses will not outweigh the rate of momentum change term. Edit: To add further, the overexpanded nozzle is producing less thrust than the ideally expanded nozzle. But the overexpanded section is still producing positive thrust, it's just less than what you would have if the nozzle had ended earlier. It's not like that section has reversed sign in terms of thrust production.
    - Gravityloss 7y ago
      Unfortunately, you're contradicting yourself. Every element of the nozzle in an overxepanded case can not contribute to thrust. Let's break it down, it will be interesting to see which part do you disagree with? 1. Optimum expansion ratio has exhaust at ambient pressure. (we agree on this) 2. Adding more nozzle, going to overexpansion, reduces total thrust. We can call the expanded part of the nozzle the "nozzle extension". If this wasn't true, then part 1 wouldn't be true (optimum). (we agree on this) 3. The pressure in the nozzle extension, as experienced by the inside nozzle wall, is lesser than ambient. (my claim, that you disagree with) 4. Sampling some area of the nozzle extension, it constitutes negative thrust. (my claim, you also disagree with this) 5. If the overexpanded nozzle extension contributed positive thrust (like you claim), one could just keep on adding more nozzle and get more and more thrust. (Until flow separation.) 6. In vacuum one can add a lot of nozzle (because ambient pressure is zero) to get more and more thrust for the same fuel amount - until one hits mass or size constraints, or condensation or chemical effects too? It doesn't really matter if the exhaust is accelerated by the nozzle extension or not. If the sum of total pressure points inwards, then when integrating over the nozzle extension area, force points downwards. This is because the momentum given by the exhaust is not the only force acting on the nozzle. Most likely the gas is just too rarefied so the total pressure it exerts is less than ambient. Even if it gets accelerated (momentum, yay), it's not enough to overcome the pressure on the other side of the nozzle wall. I'm interested in hearing why I would be wrong.