Cold Gas Thruster to space engineering challenges

I have seen this question.

The natural extension of this question would be - could you lift a human or an equivalent payload to LEO with cold gas thruster only? For numbers, take 100 kg mass for the human, and 400 km ( ~ ISS orbit) as the height for LEO.

No one is currently doing such a thing as far as I could see.

So, if the answer to my question is negative, I'd also like to know the reason behind it, including engineering challenges and physics limitations please.

Playing with the rocket equation calculator I see that 3500 kg propellant, exiting at 3000 m/s will bring us to 1st cosmic velocity. So the challenge is now to cause the cold gas thruster to exit at that velocity. But I dont see why that should be a problem.

Any help is appreciated.

• What has your research shown is the Isp expected from a cold gas thruster? What kind of launch vehicle would result from using an engine with such an Isp? Commented Apr 11, 2022 at 1:06
• @OrganicMarble this paper says 65 s with a Moog 58X152. researchgate.net/publication/… Falcon 9 on sea level has about 300 s. So, what is the actual physical problem? Why cant we use many such thrusters like this ? space.stackexchange.com/questions/15501/…
– Sean
Commented Apr 11, 2022 at 1:26
• You must figure out how much your engines, tanks, structure, capsule for the crewperson, etc weigh. You must put all that mass into orbit, not just the 100 kg person. You must allow for ~9.5 km/s, not 6. Plug that into the calculator and see how much propellant you need with an Isp of 65. Then figure out how many cold gas engines you need to lift that mass off the launch pad. You're looking at something like this space.stackexchange.com/a/48703/6944, a million tons. Commented Apr 11, 2022 at 1:29
• Okey, so this is a poor performance of a cold gas system. So perhaps doing a lot of optimizing, even that could be done. Thank you for your comment.
– Sean
Commented Apr 11, 2022 at 1:41
• @Sean One way to think about the "cold gas" is to consider what property the gas would have such that it has an Isp of 300s. Basically the Isp increases with the gas temperature and so the usual way of achieving this condition is for the gas to be hot and for this to be created as reaction products, i.e. combustion. Commented Apr 11, 2022 at 22:08

Cold gas thrusters, per their description have some hard performance limits tied to the speed of sound for the gas that cannot be optimized while still being a cold gas engine.

Nitrogen has a speed around 300 m/s and ISP of 72 seconds, lofting a 1000kg gets maths suggesting using most of earths atmosphere as propellant, assuming a magic zero weight tank to put it all in (putting the atmosphere inside the rocket would at least reduce drag)

moving to Hydrogen with it's higher speed of sound you go from an ISP of 65 to 272 from a speed of sound of 1320 m/s. This is not terrible, and some real world rockets had this sort of performance, though the very low density of hydrogen makes storing enough of it in a small and light rocket tricky. For comparison the space shuttle RL10 has an ISP of 465 from an exhaust velocity of 4500 m/s.

Throwing some very generous numbers around, if we take the space shuttle external tank and swap the LOX volume for liquid hydrogen, we get a tank holding 140 tonnes of liquid hydrogen, with an empty mass of 26 tonnes. Dump that into a calculator with an ISP of 272 and we get a total Delta V of around 5 kilometers a second, which is a quite reasonable first stage, but this is with a payload of zero so no second stage.

We could shave some tank mass down, but we also should add mass for whatever is turning the liquid hydrogen into gas that we can use for our cold gas engine. And the easiest way to do that is burn it with oxygen, and if doing that we might as well burn more to add thermal energy... and now we have a normal hydrolox rocket not a cold gas system.

Trying to store the hydrogen as gas will end up with very heavy tanks, hence why existing rockets use cryogenic hydrogen even with the issues it brings.

There are other ways to boost performance from a 'cold gas' Nuclear thermal rockets add thermal energy to hydrogen, making them 'hot gas' rockets, and various ion and plasma engines bypass the speed of sound physics by using magnetic or electrostatics forces to accelerate the reaction mass and get four digit ISP from exhaust velocities where relativity starts to matter. Neither of these are good options for launch from earth, hence the continued use of chemical rockets.

So cold gas thrusters are pretty much the worse possible thing to do with reaction mass in a rocket, and are not going to get anything to orbit from Earth. They generally only make sense when safety or simplicity concerns mean show up for things like reaction control or manned maneuvering systems.

• Hi @GremlinWranger. Thank you. So, to continue - if we have an equipment, which can pump the gas to a "heating chamber", and instead of burning it - could supply a large amount of heat to rapidly expand it (may be using a resistive heater) - will that be able to create an expansion front with a speed faster than sound? In a 4 digit ISP? Thanks again
– Sean
Commented Apr 11, 2022 at 19:30
• @Sean That's a resistojet en.wikipedia.org/wiki/Resistojet_rocket and once again, no one would ever consider them for a booster engine. "4 digit Isp"? No possible way. Also, for the thrust levels needed for a booster, you'd need a nuclear reactor to power the resistors. Forget all this and use good old engines that burn prop. Commented Apr 11, 2022 at 20:42
• @OrganicMarble Thank you for giving me the keyword "Resistojet". That has brought me to a lot of interesting patents and experiments. I did not know that category existed. So, given that, I'd ignore the pep talk, and not forget any of this. Thanks anyways.
– Sean
Commented Apr 12, 2022 at 9:00
• @sean with your question on ISP for such thermal systems they remain constrained by the same physics as other rockets though can cheat a bit by using pure hydrogen rather than a lower performance mix, see the link on nuclear thermal rockets for the upper limits. If this is an area of interest I strongly recommend the book 'ignition' by John Clark, while old it explains the complex trade offs in rocket design very well. Commented Apr 12, 2022 at 10:50