You’d be adding pressure to the space (I guess the systems could balance it). IMO, it would be easier to use a small, powerful ducted fan and a bunch of lithium batteries.
Not much pressure. Jetpack output would be water vapor and hot air which would minimally affect the environment. I think you’re right about fans and batteries - you don’t need more than a tiny fraction of the power that you need to fly on earth - in fact, you’d want a safety system on the jetpack that limits your top speed with respect to the walls of the station. But yeah, station water heat exchanger coils would counteract this, the excess humidity would condense on the coils and they would also remove the waste heat from the jetpack.
Out of all the things that are nigh impossible to do in space, building a station big enough you need a jetpack actually seems relatively easy and practical. It would just be a gigantic kevlar balloon, similar to the stations that Bigelow aerospace has in orbit today, just scaled up.
With patience you can locomote by blowing. The air is stationary when you inhale it, and you impart a velocity when you blow it out. Conservation of momentum demands that you end up with the same m* delta(v) product as the air you blew out. (well, with v oppositely directed) With m and v of the air very modest, and M of your body being pretty large, you won’t accelerate very fast.
It is slightly more efficient if you are able to turn your head the opposite way when inhaling, but it still works if you don’t. It is the velocity you impart to the exhaust that produces the bulk of the thrust, not so much the movement of mass from in front to behind.
There is a type of toy boat called a “pop-pop boat” or “toc-toc boat” that exploits this effect in water.
For all of that, if you don’t align your thrust vector through your center of mass, you’ll get off-center thrust, wasting a lot of your delta-v by inducing angular acceleration (rotation) instead of linear acceleration.
Your mouth is pretty close to one end of your overall mass distribution, so that’s a pretty long moment to consider. I suppose exhale straight up (look “overhead” before blowing)?
ETA: If you induce too much rotation, you’ll probably have the opportunity to add different reaction mass to your acceleration attempts.
The average human male has a 5 liter lung capacaty and can exhale at a maximum pressure of 2.1 psig for about two seconds. Air is 1.19 g/L, giving a mass flow rate of about q = 3 g/s. Assume an effective velocity of approximately 0.5 m/s. Ignoring the expansion term in the Tsiolkovsky rocket equation, the force developed is around 0.0015 N and the total impulse from a single breath is 0.003 N-s. The resulting change in velocity is a miniscule ~4.3 x 10-6 m/s. (Note that I’ve used dry air in the calculation; exhaled air will be at saturation and will actually be less dense. There is also no way you’ll exhale the entire volume of the lung at peak pressure; average pressure of exhalation is 0.3 to 0.5 psi.) Even if you ignore the velocity loss from breathing in (adding back the 6 g of air per breath) and form drag from displacing the air in front of you, trying to jet yourself around by breathing air isn’t going to make an ant’s piss worth of difference.
You aren’t just pushing yourself; you are pushing the mass of air forward of your motion, and by aeroelastic coupling, pulling on all the air surrounding you creating losses through viscous drag. Trying to breathe your way around is only going to leave you out of breath. However, taking off your shoe and flinging it at a bulkhead in such a way as to make it riccochet straight back at you will result in significant momentum transfer, both by throwing the shoe and catching it upon return. While you are sitting there huffing and puffing, a decent softball pitcher is going to be making weigh like Diego Maradona through through the West German World Cup team, if you’ll excuse my mixing of sport metaphors.
Stranger