I was curious about how effective farting/urination would be as a propulsion system, but I couldn't find any data on the specific impulse of human farts/urination. Could you actually get a couple of centermeters per second of delta-v from it?
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2$\begingroup$ I'm giving you a provisional up vote for asking a question that generated a well received answer, but I hope your next one is about something more closely related to space exploration - baseball for example. $\endgroup$– uhohCommented Feb 6, 2017 at 9:45
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From the ballistics, I estimate the "exhaust velocity" of a urination stream at about 0.5-1.0 m/s2 (i.e. 0.05-0.1 sec specific impulse) though a number of factors can influence that. Assuming a liter of fluid in the bladder massing about 1kg, and a person massing 75kg "dry", we get via Tsiolkovsky a delta-v figure of $$ \sim 0.75 \, ln \, \frac {76} {75} \approx 0.01 $$ i.e. on the order of 1 cm/s.
I assure you that it's a lack of data rather than any kind of dignity that prevents me from making a similar calculation for flatulence.
answered Feb 5, 2017 at 5:13
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1$\begingroup$ When urine is expelled into a vacuum, the liquid would turn quickly into a gas which should expand in all directions (much faster than the pee was travelling away from the urinater). Surely that expanding gas hitting the torso would also provide some small amount of propulsion. But hey, talk about 'blow back'! ;) $\endgroup$ Commented Feb 5, 2017 at 6:34
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1$\begingroup$ I'm assuming the urinator is not in vacuum for safety reasons. If it's an astronaut in a space suit, the exhaust velocity will be determined by the elasticity of the collection bag and the geometry of the waste relief port. $\endgroup$ Commented Feb 5, 2017 at 15:27
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3$\begingroup$ @AndrewThompson I think you have hit upon something interesting! The question doesn't specify an ambient pressure. Water could boil at body temperature, why not keep it and try to make a rocket out of a plastic bag or... hmm I am not sure this helps much after all, but who knows. Unfortunately this question is set a pressurized space. $\endgroup$– uhohCommented Feb 6, 2017 at 9:29
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2$\begingroup$ +1 for using the correct equation for the problem! I would have just used $m_1v_1=m_2v_2$, but that only holds to first order in delta-pee. I'm not even going to try to make a pun about "natural logs". $\endgroup$– uhohCommented Feb 6, 2017 at 9:33
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A fart, or equally breathing out, would approximate a cold gas thruster, for which Isp is often taken as about 60s, i.e. Ve = 600 m/s, though this depends on a few factors. I'm presuming that the relationship to space exploration is that this is the familiar hypothetical "stranded in the middle of a large void in a space station" question.
Sums
As a very rough supporting argument with as little a reference to thermodynamics as possible: Each propellant molecule as three degrees of translational freedom, each with an energy of
(1/2) k T
Just thinking practically, it wouldn't be valid to say that all the translational energy from three dimensions, (3/2) k T, is available propusively as we don't necessarily have a good nozzle, but lets use 3/2 as an upper limit. Each molecule has a mass and a velocity that we can relate to the thermal energy through
(1/2) m Ve^2
- k, Boltzmanns constant, is 1.38 x 10^-23 J/K
- T, human core temperature is (273 + 37) deg K
- One atomic mass unit is 1.66E-27 kg
- Lets assume the composition is methane, CH4, with a molar mass of 16 AMU
Put all this together and you get 70s for (3/2) kT, or 40s for just a (1/2) kT which envelopes the 60s rule of thumb we started with. Note that this does not account for the presence of air in said space station which will affect the degree of nozzle expansion that is possible.
Practicalities
Whilst the Isp is above Russell Borogove's answer for urination we haven't yet considered the thrust level which will be rather lower so the stranded astronaut would have to do a trade-off to decide what to do, not least to think how they would maintain attitude control during the manoeuvre.
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1$\begingroup$ May I point out that cold gas thrusters typically operate at high pressure (e.g. 100 bar), which would cause a slight inconvenience for the pressure tank or, in layman terms, "the astronaut"? Exhaling into a vacuum produces 1 bar of pressure difference, but not much more. $\endgroup$– asdfexCommented Feb 6, 2017 at 20:39
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1$\begingroup$ See my point in the last paragraph about the thrust level. The thrust level will come from the diameter of the exit plane and the storage pressure allows the system to supply gas through the whole exit plane for the manoeuvre length. On the other hand the gas pressure doesn't so much affect the exhaust velocity as its temperature. $\endgroup$– PuffinCommented Feb 6, 2017 at 21:29