Suppose, for the sake of argument, you had an astronaut wearing a spacesuit. The suit is pressurized with pure oxygen to 5.8 psi at 25 degrees Celsius.
The astronaut’s spacecraft is on a ballistic trajectory that will intersect with the planet he launched from unless he successfully rendezvous with the mother-ship, which has powerful nuclear engines that can circularize it’s orbit before it touches the atmosphere.
He only has one chance at the rendezvous, and equipment failure means he’s a few m/s short. The mothership cannot flip to decelerate because this would put the astronaut too close to the nuclear engine’s reaction chamber, and give him a dose of radiation hundreds of times lethal levels.
So he gets the idea of puncturing a hole in his own spacesuit. He has 2.5 liters of gas at 42 mega-pascals, and the suit + astronaut mass 178 kg.
How many m/s dV could he possibly get? What would be more realistic numbers, given the hole he punctures would not be very ideal? Could he possibly control his own flight, or would he be more likely to misalign the thrust axis with his center of mass and end up just spinning?
You just have a crude hole in the suit, so you don’t gain anything from the nozzle expansion the way you would on a normal cold gas thruster. I’ll instead use the “gas flow through an orifice” calculation.
Three are various ways of calculating what we want, but I’ll use this online calculator as a start. I’m going to assume a 15 mm diameter hole.
Plugging in the numbers, I get 0.011 Nm[sup]3[/sup]/s. Note the “N” there: it means “normal”, and that the gas flow is normalized to be at standard temperature/pressure.
The tank contains just about 1 m[sup]3[/sup] of O[sub]2[/sub] at STP, and therefore we get 91 s of thrust.
So now the only question is how much thrust the hole is producing. We have the area of the hole, so we just need the pressure. A gas experiences a pressure drop as it flows through a constriction, but to be honest, I’m not sure how to calculate that. An upper bound is easy, though–it’s just the source pressure.
The opening is 0.000707 m[sup]2[/sup] and the pressure 40000 Pa, so the thrust is 28.3 N. The acceleration is therefore 0.159 m/s[sup]2[/sup], and total delta-V 14.5 m/s.
That’s pretty reasonable. It’s an upper bound, I think, but even if we use the average pressure across the orifice (i.e., halfway between 5.8 psi and vacuum), we still get over 7 m/s. Enough to make a difference in our situation.
I do think he would just spin, though… a ripped hole isn’t going to be conducive to nice axially-aligned flow.
Yeah. That’s what I think as well. You need computer-assisted control if you want controlled maneuvers in space. As I understand it, this was true from the very dawn of the space age.
I wouldn’t go that far. In this particular case it would be nearly impossible, but I don’t think that’s true in general.
Take a look at the Lunar Escape System (LESS). These were lightweight systems designed to get the astronauts back in case the LEM malfunctioned. Never used, but seriously studied.
The various LESS designs had no guidance computer, not even a mechanical one. Some designs worked solely by shifting the center of gravity via the astronaut leaning one way or another. With practice, they probably would have worked.
But this is still a carefully engineered system, with an engine that reliably fires in one direction, a symmetrical layout, and a relatively high moment of inertia. It’s a much different situation than punching a hole in your suit.
At least until enough oxygen escapes that you pass out. In a sudden decompression, you’ll only have maybe 5 to 10 seconds of useful consciousness. Since this isn’t a sudden decompression you’ll have a lot longer than that as the suit slowly empties, but once the amount of oxygen remaining in the suit gets low enough you’re going to pass out, probably before the suit completely empties. Your last few moments of thrust might be rather random as a result.
Better hope that someone on the ship can scoop you up and bring you in quickly, too. You won’t be opening the airlock on your own.
If the hole is small enough, the life support system could keep up with the leak and maintain enough O2 pressure to keep you conscious until the oxygen tanks are empty.
The propellant rate, given the density of oxygen, is 0.0157 kg/s. And the thrust (with the 28.3 N number) if 2.88 kgf. This comes to an Isp of 183 seconds.
That’s way too high! There’s zero chance that it would be that high. Even half that much is 91 s, and according to Wikipedia a real cold-gas thruster can only hope to achieve ~68 seconds.
The difference, I suspect, is due to temperature. I assumed 25 C as per your spec, but in reality–unless the tank has a heater–the temperatures will quickly drop to much below that. Although the suit will obviously have a heater, I doubt it could keep up with the gas expansion over a 90 second span.
If you could use a smaller hole, and thrust over a longer period of time, then effectively you have a crude resistojet–the suit is heating the gas to a more useful temperature, and in return you get a higher Isp. If you don’t do that, then not only do your thrust levels suck, but you freeze the suit’s occupant.
Yep. I’m a little tired atm, but if you know how to calculate the joules of energy for the resistojet, we can then figure out how much energy is available in the suit’s lithium ion battery pack. I would venture a guess that there isn’t nearly enough energy by a long shot. You would probably be much better off having a compressed hydrogen or methane tank on the space suit and using a fuel cell. (for a Mars surface suit, you would recover the water from the fuel cell exhaust and vent the CO2, making it a renewable energy source. Methane is a better choice than hydrogen when volume matters, and hydrogen is a better choice if you don’t care about tank volume). Come to think of it, I think the batteries are the limiting factor on current spacesuits - a longer duration power source , using liquid oxygen storage for the O2 reservoir, and making the CO2 scrubbing system able to regenerate it’s metal absorption bed would probably extend suit life by a factor of 5 to 10. (50 to 100 hours)
