When the L.E.M.'s upper half blew its load of rocket fuel and took off from the surface of the Moon during Apollo 11, et al, it was firing in a zero-air/ zero-oxygen environment.
Now, I know it was also lower G, and that may have helped to answer my question:
Lacking air, does one need substantially more fuel to take off from a given mass ( planet ) than one needs if there’s an Earth- like mixture of gasses in the air?
Or said another way, does X - thousand gallons of rocket fuel ( whatever it may be made up of ) have the same propulsive force on the surface of the Earth per gallon as it will on the surface of Mars?
Yep, air does provide a lot of drag, especially when you go fast. In fact, the drag increases with the cube of your velocity, so it takes quite a bit of fuel to maintain speed when trying to achieve orbital velocity. However, the atmosphere also gets less dense as you go up, so drag will eventually start to decrease. The point where these two curves meet is when the rocket will experience the maximum dynamic pressure on the craft. After that, it’s usually relatively smooth sailing.
IIRC rockets are more efficient in a vacuum than in air. Something about the maximum efficiency of the exhaust. I’m sure I got some info about this on the Dope, but search isn’t getting it for me.
This is correct. An engine designed for vacuum use is more efficient than one in an atmosphere.
Rockets convert temperature and pressure into momentum by expanding their exhaust. It’s just like any other heat engine in that respect: you start with a hot, compressed bit of gas, and let it expand, doing work in the process. For a rocket engine, the nozzle is what does the expansion.
But you can only expand the gas to ambient pressure. Beyond that, and you get no benefit, and in fact can damage the nozzle.
In a vacuum, you can expand as much as you want. You put a big nozzle that expands the exhaust as close to zero pressure as you can get away with, and this extra expansion corresponds to more work done and more efficiency.
If you look at a Falcon 9 rocket, for example, the upper stage has just one engine while the lower stage has 9. The engines are virtually identical, except that the nozzle on the upper stage fills up the entire diameter of the rocket (the lower ones are smaller, since they pack 9 of them in the same diameter). That’s because the upper stage operates in a vacuum and gets a significant benefit from the giant nozzle.
Rockets contain all of the oxydizer needed within internal tanks. No outside air is used for combustion. So an Earth like mixture of gasses in the air does not help in this regard.
Also, rocket nozzel shape plays a big role in it’s fuel efficiency and the thrust produced, so each rocket engine is designed differently depending on the environment it is designed for. And all else being equal (even ignoring drag) rocket engines designed for space will always be more efficient than those designed to operate in an atmosphere.
So when something takes off from the moon, it has a more efficient engine and it has no atmospheric drag to make it work harder. So it requires much less fuel.
The Wikipedia page says that the drag (force) increases as the square of the velocity, but the power needed to overcome the drag increases as the cube.
Power is just force times velocity. So, the force is proportional to v squared, and power has an extra v term to make it cubed.
The energy required to go a given distance goes up with the square, since the extra v term gets cancelled out by the fact that it takes less time to get there at a higher velocity. But if you’re looking at fuel burn rate, that’s energy per unit time and thus power is the right metric.
More heuristically: when traveling through air, you’re basically pushing yourself through blocks of air at some velocity. Each block of air has a kinetic energy proportional to v squared, and pushing each one aside is also proportional to v squared. But at high speed you’re also encountering more blocks of air per second, so you end up with a v cubed term. Or, if you’re talking a fixed distance, there is also a fixed number of blocks of air along that distance, so it’s v squared.
Drag is a force. Work is force times distance. Divide both sides of that by time gives: power= drag times velocity. If drag increases with velocity squared then power increase with velocity cubed.
E.g., a Rocketdyne F-1 (chosen for no special reason) has a specific impulse of 263 seconds at sea level, but 304 s in vacuum, so there you go. It also produces more thrust in vacuum.
A first-gen Vulcan rocket produced 431 s in vacuum, compared to 326 s at sea level. Point is, atmospheric pressure reduces the effective exhaust velocity even though it’s the same engine (carrying its own liquid oxygen of course).
A bit of a nitpick the nozzle isn’t doing work to expand the gas. The gas expands due to its higher pressure relative to the environment. The nozzle can control the rate and direction of expansion so that there isn’t mass and therefore momentum being wasted going to the side of the rocket.
The gas absolutely is doing work on the nozzle. It’s not completely wrong to say that the nozzle is there to keep gas from squirting out the sides, but that’s just a kind of hand-waving explanation of it.
A perfect nozzle would take the hot, compressed, stationary gas inside the combustion chamber, and convert it to a stream of gas at ambient pressure and temperature, moving in a straight line opposite the direction of movement.
In a vacuum, you can expand more. The gas expands and cools further than it would in an atmosphere. The work is being one on the part of the nozzle beyond that where the gas was at one atmosphere. Ignoring engineering concerns like cooling, an atmospheric engine is the same as a vacuum engine with the bottom part of the nozzle snipped off.
I said the nozzle doesn’t do work on the gas though. Take a test nozzle fixed in place. Is it moving when the rocket is tested? No. It’s stationary. The force on the surface of the nozzle times the displacement of the nozzle is 0. Therefore the nozzle isn’t doing work by definition.
Ok, I read your post more carefully. You were saying nozzle did the expansion not the work…
There seems to me a question in the OP that hasn’t been answered. Does the exhaust push against the atmosphere to propel the rocket? Given that I went to school 40 years ago, this might be wrong, but as I understand it, no, the atmosphere has no effect on the rocket’s acceleration. In air, or in an airless world, the effect is the same. With the caveats given above which I never knew before. You learn so much around here!
Yup. Vacuum for rocket engine testing isn’t exactly easy, and uses a large steam ejector to keep the vacuum. Tests for the LM engines was done at White Sands.
A rocket does not need to push against anything, but for maximum thrust you do need to design your nozzle to expand the exhaust to atmospheric pressure and not any more or less. Also the exhaust velocity will be lower in atmosphere.
In order to fire a live rocket engine in a vacuum chamber you have to be able to remove all the rocket exhaust as fast as it is produced while maintaining the vacuum. Our B1 test site at the Plum Brook Station in Sandusky, Ohio had the capability of firing large engines at high altitudes but not a vacuum. Looking through the site history I don’t see any mention of testing the LEM.
Later we built another high altitude chamber at the Rocket Engine Test Facility (the B Stand) at Glenn Research Center. I was an operator of that facility and it could achieve a fairly good vacuum but only had the capability to test up to 1000 lbs thrust.
That is exactly the misconception in the famous NY Times editorial from 1920 saying Robert Goddard was nuts. Which they retracted July 20, 1969. First article I found.
So whoever taught you 40 years ago must have learned the misconception a bunch of years before that.