Optimal Size of Rocket Engine Nozzle for Vacuum Performance

In summary, the optimal size of a rocket engine nozzle is determined by the ambient pressure around the nozzle, with a larger ratio being more efficient at higher altitudes. However, at very high altitudes or in vacuum, it is not possible to match ambient pressure, and a longer nozzle may be necessary. This can result in condensation or freezing of exhaust gases, which is undesirable. Despite this, a rocket can still function in vacuum, as momentum is always conserved. In the experiment using a balloon, the baffle attachment prevented any forward movement because the exhaust was redirected sideways. The concept of optimal nozzle diameter was misunderstood by the New York Times in their article apologizing to Robert Goddard for doubting his ideas about space travel.
  • #1
Jackamus
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I'm interested in how rocket engines perform in a vacuum. My first impression is that an atmosphere is needed for the action/reaction to push against in order to get forward movement.
I saw a demonstration using a long balloon attached to a long length of string stretched across a room. When the inflated balloon was released it flew along the string as was expected.
Next a paper baffle was attached to go over the end of the balloon nozzle and when released the balloon stayed where is was and the air expelled from the balloon hit the baffle and went left and right so there was no forward thrust of the balloon.

I then looked at this link on Wikipedia https://en.wikipedia.org/wiki/Rocket_engine_nozzle and found this explanation:

'The optimal size of a rocket engine nozzle is achieved when the exit pressure equals ambient (atmospheric) pressure,[why?] which decreases with increasing altitude. The reason for this is as follows: using a quasi-one-dimensional approximation of the flow, if ambient pressure is higher than the exit pressure, it decreases the net thrust produced by the rocket, which can be seen through a force-balance analysis. If ambient pressure is lower, while the force balance indicates that the thrust will increase, the isentropic Mach relations show that the area ratio of the nozzle could have been greater, which would result in a higher exit velocity of the propellant, increasing thrust. For rockets traveling from the Earth to orbit, a simple nozzle design is only optimal at one altitude, losing efficiency and wasting fuel at other altitudes.'

Followed by this:
'For nozzles that are used in vacuum or at very high altitude, it is impossible to match ambient pressure; rather, nozzles with larger area ratio are usually more efficient. However, a very long nozzle has significant mass, a drawback in and of itself. A length that optimises overall vehicle performance typically has to be found. Additionally, as the temperature of the gas in the nozzle decreases, some components of the exhaust gases (such as water vapour from the combustion process) may condense or even freeze. This is highly undesirable and needs to be avoided.'

It would seem that the nozzle diameter is dependant upon the ambient or atmospheric pressure round the nozzle. There appears to be a problem here since space travel appears to be a fact. Can anyone offer a solution?
 
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  • #2
Jackamus said:
It would seem that the nozzle diameter is dependant upon the ambient or atmospheric pressure round the nozzle.
No. You omitted a key word from the texts you quoted, optimum diameter.
A device can still function even if it is not optimal.
 
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  • #3
Jackamus said:
My first impression is that an atmosphere is needed for the action/reaction to push against in order to get forward movement.
This is not correct. A rocket does not need to "push" against anything to work, The same is true for the balloon in the example you gave, it would also work in vacuum.

Rockets "works" because momentum is always conserved. You can try this yourself by standing/sitting on something with low friction (ice skates or an office chair on a flat, even floor) and throwing something heavy, you will find that you will move in the opposite direction.
 
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  • #4
Thank you for your explanation.
Why did the balloon in the first part of the experiment move and not in the second part?
 
  • #5
Jackamus said:
Thank you for your explanation.
Why did the balloon in the first part of the experiment move and not in the second part?
Because the baffle was attached to the balloon. The exhaust pushes the balloon forwards and the baffle backwards so nothing happens overall; the exhaust is just redirected sideways. If the baffle was only weakly attached to the balloon the attachments could snap and the balloon and baffle would fly off in opposite directions.
 
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  • #7
Jackamus said:
Thank you for your explanation.
Why did the balloon in the first part of the experiment move and not in the second part?
 
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  • #8
anorlunda said:
No. You omitted a key word from the texts you quoted, optimum diameter.
A device can still function even if it is not optimal.
Optimum diameter is that diameter which offers to most efficient operation for a given ambient pressure or altitude. The article clearly states that the nozzle ratio must increase as the air pressure reduces due to altitude.
Of course a non-optimal nozzle will still function but badly as the air pressure decreases to the point where it will not function at all when there is no air pressure. So what is the optimal nozzle ratio when there is no air pressure?
 
  • #9
Jackamus said:
So what is the optimal nozzle ratio when there is no air pressure?
The point is that in atmosphere the exhaust has to push air out of its way, and it loses energy doing so. The optimal design is one that minimises the energy wasted moving air out of the way of the exhaust plume.

If there is no air then this constraint does not exist, so there is no optimisation necessary. (At least, not for this reason - doubtless the fuel combustion process will impose design constraints of its own.)
 
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  • #10
Jackamus said:
Of course a non-optimal nozzle will still function but badly as the air pressure decreases to the point where it will not function at all when there is no air pressure.
No, that doesn't follow. I expect that every nozzle would work in space. In fact I think it impossible to eject mass in a weightless vacuum without some reaction force acting on the craft. That is Newton's 3rd law.

Edit: This is the Apollo Command module. It was designed to operate only in space. You can see the nozzle.

1675276247291.png
 
  • #11
You don't seem to sure
Ibix said:
The point is that in atmosphere the exhaust has to push air out of its way, and it loses energy doing so. The optimal design is one that minimises the energy wasted moving air out of the way of the exhaust plume.

If there is no air then this constraint does not exist, so there is no optimisation necessary. (At least, not for this reason - doubtless the fuel combustion process will impose design constraints of its own.)
That contradicts the article which states that the nozzle ratio increases with altitude. At what point in the upper atmosphere does the nozzle ratio cease from being important to being unimportant?
anorlunda said:
No, that doesn't follow. I expect that every nozzle would work in space. In fact I think it impossible to eject mass in a weightless vacuum without some reaction force acting on the craft. That is Newton's 3rd law.

Edit: This is the Apollo Command module. It was designed to operate only in space. You can see the nozzle.

View attachment 321552
You don't seem to sure as you only 'expect' every nozzle to work in space rather than 'does work in space'.
With the greatest respect showing the Apollo module is not proof if you are a skeptic since there are many examples of false and inaccurate information regarding space travel.
 
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  • #12
Jackamus said:
Of course a non-optimal nozzle will still function but badly as the air pressure decreases to the point where it will not function at all when there is no air pressure.
You are confusing efficiency with thrust. You can have a decreasing efficiency but increasing thrust, because efficiency is relative to what you could theoretically achieve at the given ambient pressure.

Jackamus said:
So what is the optimal nozzle ratio when there is no air pressure?
As large as possible. But there is decreasing return from making it larger, and very strict weight constraints.
 
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  • #13
Are you saying that as the efficiency decreases the thrust increases? So in a vacuum where efficiency is zero thrust is infinite?

But if the nozzle can't be made sufficiently large enough then how are you to reach high enough to achieve activity in a vacuum?
 
  • #14
Jackamus said:
Are you saying that as the efficiency decreases the thrust increases?
This is possible.

Jackamus said:
So in a vacuum where efficiency is zero thrust is infinite?
This doesn't follow.

Jackamus said:
But if the nozzle can't be made sufficiently large enough
You are confusing sufficient with optimal again.
 
  • #15
BTW I watched a NASA video where a presenter used a balloon to show what happens when the air is released using Newton's action and reaction caused by an inbalance . Surely when you release the air from a balloon the pressure inside the balloon is always equal on its internal surface as it reduces and therefore no action and reaction.
 
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  • #16
Jackamus said:
is not proof if you are a skeptic
Nothing is proof if you cannot do math or even think quantitatively, and just try to build arguments by misrepresenting qualitative descriptions.
 
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  • #17
A.T. said:
This is possible.This doesn't follow.It can be made "made sufficiently large enough".
None of these are answers but just, with respect, gainsaying! It is not sufficient to just contradict without saying why?
 
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  • #18
Jackamus said:
None of these are answers
See my edit: You are confusing sufficient with optimal again.
 
  • #19
A.T. said:
Nothing is proof if you cannot do math or even think quantitatively, and just try to build arguments by misrepresenting qualitative descriptions.
Again with respect this is 'scientism arm waving". It sounds impressive but doesn't really have any substance.
 
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  • #20
Jackamus said:
Again with respect this is 'scientism arm waving". It sounds impressive but doesn't really have any substance.
Conservation of Momentum has no scientific substance?
 
  • #21
A.T. said:
See my edit: You are confusing sufficient with optimal again.
I do realise the difference and I'm not confused. Either way there is a practical limit brought about by natural physics.
 
  • #22
Jackamus said:
I do realise the difference
Then you are deliberately conflating them to make flawed arguments.
 
  • #23
berkeman said:
Conservation of Momentum has no scientific substance?
I didn't realise that is what you were implying. But I 'believe' that there is a problem linking this with activity in a vacuum. This is just a fanciful thought but do you think that Newton had any concept of the vacuum of space and how his laws might work in them? Is it possible that gravity can affect the conservation laws?

I'm still trying to imagine what would happen if I were floating in space and threw a medicine ball! Something tells me that I wouldn't be throwing it but pushing it and it would only travel as far as my outstretched arm. If I pushed it hard it would still only go as far as my outstretched arm but quickly whereas if I pushed it softy the same would happen only slowly. I would not be able to push the ball further away than my arm's length. I may be wrong.
 
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  • #24
A.T. said:
Then you are deliberately conflating them to make flawed arguments.
You ignored the second part of my statement about the 'practical limit' being a real factor to be considered.
 
  • #25
Jackamus said:
You ignored the second part of my statement about the 'practical limit' being a real factor to be considered.
Repeatedly confusing sufficient with optimal doesn't become correct, just because you make some vague statement. That is "arm waving".
 
  • #26
Jackamus said:
I'm still trying to imagine what would happen if I were floating in space and threw a medicine ball! Something tells me that I wouldn't be throwing it but pushing it and it would only travel as far as my outstretched arm. If I pushed it hard it would still only go as far as my outstretched arm but quickly whereas if I pushed it softy the same would happen only slowly. I would not be able to push the ball further away than my arm's length. I may be wrong.
Yes you are wrong, and bordering on trolling. Thread is closed for a bit for Moderation...

berkeman said:
Conservation of Momentum has no scientific substance?
 
Last edited:
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  • #27
Jackamus said:
You don't seem to [sic] sure as you only 'expect' every nozzle to work in space rather than 'does work in space'.
With the greatest respect showing the Apollo module is not proof if you are a skeptic since there are many examples of false and inaccurate information regarding space travel.
This post in this thread has earned you a pretty stern infraction, and your trolling in this thread is not appreciated. The thread will remain closed.

We do not tolerate Wile E. Coyote physics at PF. Have a nice day.
 
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