So in a sense the misconception has it exactly backwards; the pressure of the atmosphere reduces the thrust by trying to push the exhaust gases back in.
As a layperson, and defintely not a rocket-scientist, the best explanation I’ve heard for this is the office chair one, it also has the benefit of being replicable.
Sit on an office chair on wheels with a ream of paper on your knee and your feet off the floor. Throw the paper away from yourself, at speed, in one direction and you and the chair will go in the other. That is all that a rocket is doing, it is ejecting mass (the exhaust) at speed in one direction and the pointy bit travels in the other direction. The energy for that ejection comes from converting the fuel used (food for the office chair, chemical for the rocket).
Right. And you are correct in that the nozzle is controlling the rate and direction of expansion. Just like a piston in a cylinder: it contains the hot gas, which does work on the piston and then the crankshaft. The gas is doing the work of course, but it’s through the nozzle (or piston, or turbine, etc.) that the expansion is channeled into work.
You can also look at it at the microscopic level. At the top of the nozzle, there is some very hot and slowly moving gas. Individual particles are moving in all directions at high speed, but the average velocity is low. The nozzle is close to horizontal here, and when a gas particle bounces off of it, it moves mostly in the down direction.
Farther down, the gas is moving faster toward the exit. It’s also cooler. So the particles are sorta moving out and downward on average. The nozzle is at maybe a 45 degree angle here, so when a particle bounces off of it it also tends to be in the downward direction.
Near the exit of the nozzle, the particles are moving very quickly aft, and the gas is relatively cool. The walls of the nozzle are almost vertical now, and any particles hitting it are at a grazing angle, because they’re mostly moving straight down. This last impact straightens them out even further.
When a particle hits the wall of the nozzle, it pushes in a perpendicular direction to the surface. But because it’s symmetrical with the other side of the nozzle, the horizontal component cancels out, and only the vertical component is left. The vertical component is strong at the top of the nozzle and weaker at the bottom, but every little bit helps. All of it contributes to the net thrust of the nozzle (the remaining part is from the gas traveling through the throat of the combustion chamber).
Well, it pushes on its own exhaust.
A car pushes against the Earth when it accelerates. The car goes forward, and the Earth is pushed back at a tiny velocity. It takes almost no energy to accelerate the Earth this way since the velocity is so low.
An airplane pushes against the air. To keep flying, it takes an enormous amount of ambient air and pushes it downward at some velocity. This is less efficient than the car, because the mass of that air is a lot less than the Earth, and so it has to be accelerated to a higher velocity, which takes more energy. It’s still pretty good, though.
A rocket pushes against its own propellant. Since there’s so little propellant available (at most, its own mass), it has to accelerate it to as high a velocity as possible to get as much momentum transfer as it can. Which makes it extremely energy inefficient, at least at low speed; that high velocity exhaust is sapping almost the entirety of the energy when the rocket has just taken off. It gets better at high speed, though.
You always have to push against something to accelerate. The NY Times apparently didn’t realize that you can push off stuff that you carry with you, though.
Which means that nothing is doing work on the nozzle. But that doesn’t mean the nozzle isn’t doing work on anything else. The exhaust is still going from stationary to moving, as a result of a force, and so something is certainly doing work on the exhaust. What do you think it is?
Just a comment, it is not the exhaust that moves the rocket, that is the equal but opposite force, and really the rocket couldn’t care less about it, but it is pressure from the gasses that are pushing it. It some ways it’s like a balloon that is allowed to fly expelling air out the hole. The only propulsive force is the pressure imbalance due to the hole (more pressure in the forward direction then the rear). Since we have no way of creating that pressure imbalance, whcb creates a force, without the equal and opposite force of some sort, that’s where the exhaust comes in. The nozzle and the combustion chamber are the parts of the rocket that experience this force on the rocket side, the exhaust gas is what experiences the equal but opposite force.
In the end how you describe it is more a matter of where you choose to stand when doing your analysis. Invoking the gas laws and how gasses flow and behave is just a convenient way of packaging the conservation laws, especially conservation of momentum. Whether you choose to keep the conservation laws nicely bundled up inside the gas laws and talk of pressure, or let them out and look at the manner in which all the forces act and momentum transfers, you end up with exactly the same thing. All that the reaction products know is that they have suddenly got a lot more energy and they keep banging into and bouncing off things - mostly other things like themselves - very occasionally some run into things like metal walls, or colder gas molecules that aren’t reaction products. The job of the engine designer is to get as much of that banging around to result in stuff going out the back carrying as much momentum as possible. To do this he applies knowledge of useful derived laws that govern such banging around of stuff. All of these laws eventually derive from the base conservation laws. It is a matter of convenience what level you need to play.
The LM ascent and descent propulsion systems and service module SPS were tested in vacuum chambers at Arnold Engineering Development Center (AEDC) near Tullahoma, TN:
History: https://media.defense.gov/2019/Jul/12/2002156636/-1/-1/1/AEDC%20SUPPORT%20TO%20APOLLO%20PROGRAM.PDF
Summary of SPS altitude testing at AEDC: [PDF] Summary of Five Years of Altitude Testing of the Apollo Service Module Engine in Altitude Test Cell (J-3) | Semantic Scholar
To answer the OP, a launch vehicle experiences two notable performance losses: air drag losses and “gravity” losses from the vertical ascent phase. Of these two gravity losses are much higher. On the shuttle drag losses were only about 1% of orbital delta V, whereas gravity losses were about 16%.
Gravity losses are one reason why all launch vehicles pitch over as soon as possible. In the earth’s atmosphere, they can’t pitch over too soon due to atmospheric dynamic pressure.
On the moon, the lack of air means drag losses are zero, but that would typically only be a few % anyway for a streamlined vehicle. However – the lack of atmosphere means the LM can pitch over dramatically, soon after lunar liftoff to reduce gravity losses.
In the Apollo 17 lunar liftoff you can see the LM ascent stage pitch forward soon after liftoff, accompanied by the callout “pitchover”: https://youtu.be/9HQfauGJaTs
Integrate f ds over a distance interval where d1=d2. You get 0. The work the nozzle does is 0. The gas has a velocity due to the pressure of the gas compared to the ambient pressure. The gas accelerates due to that pressure difference and the net force on the rocket is due to the pressure difference between the gas and the environment.
The nozzle serves to control and direct expansion but it does no work. It’s similar to an elbow in a pipe system. The water flowing past the elbow is accelerated. The elbow puts a force on the water. However the elbow does no work on the water. This is just by definition of what work is.
Is the nozzle supplying any energy to do this so-called work? No. All the energy comes from the chemical reaction of the rocket fuel and oxidizer. The gas is the source of work in a rocket. Not the nozzle.
It’s been awhile since I read this and I can’t really recall the source but wasn’t the actual performance of the Lunar Rover much better then expected attributed to the fact that the lack of air resistance had not been really factored in?
AerospaceWeb has a decent explanation of rocket exhaust overexpansion/underexpansion, including a diagram that shows what to look for on a rocket engine in flight. the diagram shows the rocket exhaust having been overexpanded inside the engine bell at low altitude (after which it gets pinched back in to a smaller diameter again), and underexpanded at high altitude (the exhaust plume swells to a much larger diameter after leaving the engine bell).
You can clearly see this on the Saturn V in this launch video. At 0:40, it’s still at low altitude; the exhaust plumes are overexpanded. It’s hard to see the atmosphere forcing the plumes to contract in again since there are five exhaust plumes in close proximity, but you can see that the exhaust definitely isn’t expanding out beyond the outer perimeter of the whole vehicle. Contrast this with the rocket exhaust at 2:00 and beyond, when the vehicle is somewhere between 50,000 and 100,000 feet; the exhaust plumes, now relatively unconstrained by the thin atmosphere, expand to a huge diameter after escaping the confines of the engine bells. That expansion is wasted energy; it could have been harnessed to propel the vehicle forward if the designers had incorporated much longer/larger engine bells, but the weight penalty of larger bells wouldn’t have been worth it.
Hadn’t heard that, but it seems unlikely. The designed top speed of the rover was only 8 MPH, at which speed aero drag (if there had been any) would have been pretty minimal compared to the rolling resistance of those tires and the drag imparted by driving around on soft powder.
This is a good point. A lunar liftoff would not only eliminate drag losses and greatly reduce gravity losses due to enabling early pitch over, it would allow a vacuum-optimized nozzle.
However even launch vehicle first stages on earth do not always (or even generally) use sea-level-optimized nozzles. This can be seen from the Saturn V flight instrumentation, available for each mission in “Saturn V Launch Vehicle Flight Evaluation Report”, e.g, Apollo 16: Saturn 5 launch vehicle flight evaluation report-AS-511 Apollo 16 mission - NASA Technical Reports Server (NTRS)
I don’t know what altitude the Saturn V F1 nozzle was optimized for but it was obviously not sea level. The actual flight instrumentation showed first stage thrust increased from 7.6 million lbf at liftoff to over 9 million lbf at stage separation altitude of 37 miles:
So the question is how much additional nozzle performance optimization was available between the F1 engine as desgined vs a pure vacuum-optimized nozzle? The relevance is on the LM ascent stage engine nozzle (which was vacuum optimized), how much performance benefit came from that vs a less-optimized (but not sea level) nozzle more typical of a terrestrial launch vehicle first stage.
Fair question. Several plots of interest here. Check out the third plot, halfway down the page, which shows altitude versus time after launch. During first stage, due to acceleration, it’s spending more time between 0-18.5 miles than between 18.5-37 miles, so you’d think they would want to optimize it for some altitude below 18.5 miles. But I think if we replace altitude with ambient pressure, we’d see that ambient pressure decreases very rapidly. At 20,000 feet for example, ambient pressure is already less than half that of sea level; the pressure at 35,000 feet is about 1/4 that of sea level. This means that first stage spends much more of its time at an ambient pressure closer to zero than to 14.7 psi. So you could optimize the engine for, say, 35,000 feet and it would only be significantly suboptimal for the first ~1/4 of its burn, and pretty darn good for the rest of it.
The thing is, even vacuum-optimized rocket nozzles don’t extract that maximum possible thrust from the exhaust plume. At some point the benefit of greater thrust is offset by the penalty of carrying all that extra engine bell around. just eyeballing rockets that are vacuum-optimized, it doesn’t look like they add much more bell length/diameter beyond what is seen on rockets that have to deliver decent sea-level performance. Here for example is the lunar lander ascent engine; its aspect ratio doesn’t seem far different from the Saturn’s F-1 engine.
I think that to have optimized the F-1 engine for operation in vacuum, they would have added a bit more bell length/diameter, but not much.
Can you elaborate on the “can damage the nozzle” detail?
As a quick note, atmospheric pressure drop as follows
p=p[sub]o[/sub]e[sup]-k*h[/sup] where k is a constant and h is the height from sea level. Basically at 5km, pressure is ~50% of sealevel and by 10km it’s only 20%
Just to expand on that a little. k is a constant (called “scale height”) for each planet - it depends on the composition of the atmosphere, the temperature and the gravity of the planet. For Earth, scale height is about 8 km (depending on the temperature), while on Mars it’s about 11 km.
SpaceX uses a significantly larger 2-piece (extendable) nozzle on the vacuum version of the Merlin engine, as seen/discussed here.
Same for the Blue Origin BE-3, though it’s difficult to compare the two pictures because of the difference in configuration.
The solid rocket boosters for the space shuttle had a two stage bell to deal with the changing air pressure. A longer and wider bell would descend down over the short narrow one used at take off. The boosters weren’t going to ascend into vacuum but it still made a big difference in efficiency. Any SSTO rocket will have to deal with that somehow, though I think sea level takeoff SSTO makes little sense anyway.
NASA literature mentions “asymmetrical, oscillating forces” which can damage the engine mountings. Maybe there could be additional undesirable effects due to cavitation or analogous phenomena? Wouldn’t want the nice rocket engine to explode…
I’m sure the engines are launched at sea level at least slightly overexpanded, though, as long as it is not too extreme. Engineers can also modify the nozzle with altitude-compensating features like annular/plug/spike nozzles.
As noted above, this regime is called overexpanded. The nozzle is trying to expand the flow to a lower pressure than ambient.
The problem comes from flow detachment: where does the exhaust separate from the nozzle? Normally speaking, this happens right at the bottom edge of the nozzle.
If the flow is slightly overexpanded, the separation still takes place on this ring shape. You’ll see the sides of the exhaust push in a bit, smoothly flowing in from the rim. In fact this is desirable, because once the rocket travels to a higher altitude, the flow will become optimally expanded and gain efficiency from that.
When the flow becomes highly overexpanded, though, the exhaust detaches from the nozzle rim, and instead detaches further up the inside of the nozzle. But because it’s a smooth surface, and because the flow itself contains irregularities, it doesn’t stay in a perfect circle, and instead moves around depending on the various random forces.
So for one, you get constantly changing forces on the inside of the nozzle. Worse, you might set up a resonance–something that causes the nozzle to bend in one direction, and then another. If this amplifies, it’ll rip apart the nozzle. Nozzle walls are thin and don’t have a lot of stiffness.
There are some solutions to the problem. One way is to have a kind of step partway up the inner surface. At high ambient pressure, the flow sticks to the upper edge; as the pressure goes down it attaches to the lower edge. But it’s not a great solution since it causes friction and a hotspot.
Other designs, like aerospike engines, avoid the problem completely, but have their own issues.
Because the Space Shuttle main engines had to work from sea level to vacuum, they had to deal with an even larger range of pressures than most engines. Its nozzles have quite a high expansion ratio for sea level, which makes them significantly overexpanded. They dealt with that by tweaking the shape of the nozzle slightly and just mechanically strengthening the nozzle to cope with the extra forces.
are you asking if the atmosphere is used in the combustion of the rocket fuel? If so, the answer is no.