Actually, that's a lot bigger than what I was expecting. After calculating it myself I got the following: t = 80 days (flight duration) n = 1.5 gallon/(person * day) (water requirement per person per day) ~= 5.7 litres / (person * day) Radius calculated from: That would place the diameter 4.4 meters or about 14'4" if I didn't just make a fool of myself by messing up the unit conversion. (EDIT: Turns out that I did, at least in a way. I wrote my radius approximation in feet and inches instead of diameter. It was originally 7'8") However, in a bit of a dick move, I have to say that a sphere of a diameter of 11 meters (just to be clear, I know that's a double of radius and used 5.5 meters for calculation) should contain roughly 700 m³ (or 700000 litres or about 185000 gallons)… so at the very worst both of us made some mistake. ;)That was a lot smaller than I was expecting.
P = 100 person (crew) V = P * t * n = 12000 gallons ~= 45600 litres = 45.6 m³ V = (4 * pi * r³) / 3 <=> r = cbrt((3 * V) / (4 * pi)) ; cbrt standing for cubic root r = cbrt((3 * 45.6) / (4 * 3.14)) = cbrt(136.8/12.56) = cbrt(10.89) ~= 2.2 meters
100 people times 2 gallons of H2O a day times 80 days is 16,000 gallons. A gallon is 8.36 pounds. Giving a total mass of 133,760 pounds, which I convert as 16,000gal to 60567 litres. This would be 60.6 cubic Meters. And fuck the Imperial System. I'm being rushed right now, but for some reason we are doing the same math and getting different numbers. Either way, this volume is way less than I expected it to be.
I went with the lazy solution and asked the Holy Wolfram Alpha to bestow the solution upon us ;). My solution is closer… for a given definition of a gallon. ;) Either way, I agree with this: It's not as unbearable amount as intuition suggest. I've posted that mainly because something felt fishy, but that's not the reason to split hairs. Amen! I'm less tense about solving and explaining some completely unintuitive special relativity problem than when I'm being asked to convert some ounces per cubic foot to metric myself.And fuck the Imperial System.
I've been enjoying this conversation a lot but waiting for someone to point out that the water can be recovered and recycled. This is already common practice, though I couldn't find a number for recovery rate on the ISS. I did see a NASA project that aims to improve the rate to 94%.
I'm assuming that they will be using water not only for keeping the people alive but also radiation shielding. And aquaculture. And fuel. etc. This is worse case scenario. Still, I anticipated the needed water being much, much more than I mathed out.
Great point. But wouldn't it pose a power concern as the distance increases? The intensity of light decreases with respect to the distance (r) as 1/r². Let's go with the 'easy numbers' approach. Solar panel the size of 1 m² gives output of 500 W (give or take, in the end it's the ratio of solar panel area that I'm concerned about), Earth is 1 AU from the Sun, Mars is about 1.5 AU from the Sun. Formula in plain words: Power * Area of solar panel / distance ² That would mean that the power output on Mars would be about 500 * 1 / (3/2)² ~= 220 W I know that it's not unfeasible to simply stack a lot more solar panels onto the ship. But the above relationship shows that to produce same 500 W we had at around Earth's distance, on Mars we would need 2.25 m² of solar panels. Although having said that, I am aware of making a silent assumption that all of the power would be provided via solar panels. I have no idea how viable would be some form of thermal generator that uses radioisotopes (as in most satellites)… or maybe I should stop thinking in such limited terms and look for ways to put a full nuclear reactor on the ship. :D
Solar at Mars is not that big of a deal. You need bigger panels, but with the massive increases in efficiency you get each machine generation (roughly 18 months). This great write up on the ISS wings says that the ISS uses an acre of panels to generate 90Kw of power. These panels are using cutting edge engineering from the early 2000's and are not as efficient as the new stuff that they are using on, for example, Juno. the Juno panels would generate 14Kw if at earth, say 1/2 that at Mars. The thing holding you back more than anything really is the battery. Batteries are big bulky, chemical soups that are not growing in efficiency nearly as fast as the Solar stuff. As as your spacecraft will go through eclipses in orbit around a body, you need batteries to store charge. This is one reason they don't want to use solar panels on the lunar surface; they get 14 straight days of night, so you need to double power and have a massive energy sink to store the excess.
Thanks for explanation! :D I got too focused with intensity and forgot about power storage. If you would not mind, I have another question that hit me while I was reading some more on ISS. Among them was a series of articles like Staying Cool on the ISS that talks about thermal control. Apparently ISS uses ammonia to 'vent' the excess heat by forcing it to radiate IR outside of the station. It's completely understandable to have such system, not only because of their power consumption, population and amount of active machinery. Even more importantly, ammonia is pretty much unparalleled as far as heat transfer goes (at least in the concerned range of temperature). But wouldn't ammonia cause a hazard in the long run? I could not find anything more serious than this false alarm about ammonia leak, but to my understanding the more people and space are involved the higher are the chances of something going wrong. It's harder to contain, able to linger undetected before concentration gets close to hazardous levels, and isn't all that easy to filter out from the air (although not impossible, as detailed in patent of continuous electrochemical scrubber… but that requires a similarly dangerous H3PO4 chemicals so we have a Catch 22 ;)). So, after all this long-winded rambling: are the hazards linked to ammonia simply something that astronauts must accept and deal with (and I'm getting waaaay too concerned about minutia) or does it pose some real problem to long-term manned missions?
They use anhydrous ammonia. Translation- no water in it. We used the same stuff on the processing ships I worked on. Ammonia is well understood, has been used for over 100 years, is cheap, is anti-bacterial, anti-fungal and (important for space flight) light weight. Yes, it is toxic to humans. But the good thing about ammonia is that it does not need crazy insanely tolerant seals like some other gasses do. Ammonia also works well in titanium and steel piping. Ammonia leaks can be cleaned up with normal air scrubbing and water vapor (the ammonia will react with the water and remove itself from the air). Carbon Dioxide coolants are more likely to stick around, are harder to get rid of when they leak and react with steel and rubber/silicon seals. Infographic In the radiators, the ammonia goes through a phase change from gas to liquid. This results in an energy transfer. As the radiators are exposed to very cold temperatures, the heat in the ammonia moves to the colder piping, which brings the temp below the critical temp needed to reliquify the gas again initiating the phase change. This waste heat is then radiated out into space. The ammonia itself is not vented. You can also run the ammonia lines on the outside of the astronaut's pressure vessel so that when you do get leaks they do not poison the crew cabin. The thing that makes ammonia a good coolant is that it absorbs a tremendous amount of energy, boils at -30C at sea level, does not vapor lock like water based solution are prone to do, and if you vent it in space, and it gets on a space suit, you sit in the sun and the ammonia will sublimate and the UV light will knock off the Hydrogen atoms and create N2 instead. The short answer is that there may be other solutions to gaseous evaporation cooling loops in space, but they all have bigger issues than ammonia.