How do I figure out how many people my domed city on a hostile planet can support?
I have a colony of humans on Mars, living in enclosed cities to maintain breathable air. (If they need to leave, they suit up.) Assuming modern-day technology, how do I figure out how many people a city of volume V can support? Or, to reverse the question, how large a domed city would I need to support a population of size P? (I assume that if we can solve one of these we can solve the other, so attack it from either end.)
The protective enclosure dates back to the founding of the colony; its purpose is to enclose breathable atmosphere so they can live on Mars. I have been assuming that a transparent dome is preferable for (a) getting sunlight and (b) combatting any feelings of confinement because they can see farther than the city borders, but I'm open to alternatives.
The people living on Mars need to be self-sufficient (no deliveries from Earth, though they could have brought whatever starting equipment they'd need). They do not necessarily all live in the same city. (How I distribute my population among cities will depend in part on the answer to this question; I'm trying to figure out what's practical.)
I assume that there would need to be ample vegetation to consume CO2 and emit oxygen -- which is fine, because those people are going to need a food source anyway. That vegetation requires space, so factor that into the calculation (or tell me why that's not an issue). I am flexible about what my people eat.
The question of how large a structure can be built, engineering-wise, is separate. Here I'm trying to get a handle on the life-support side of the problem.
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The major problem with living in a surface dome will be radiation. Mars radiation is too high for constant exposure. People will spend most of their time under radiation shelter.
A tall thin dome won't provide much radiation protection. Although one that generated a powerful magnetic field of its own would provide some. More likely the dome would begin as a cluster of small, domes covered in dirt for shielding. Later as the colony grew some of the intention domes could be linked together to provide support for larger domes, and so on. Eventually, fairly thick leaded glass could be used although this would be a very heavy and substantial structure, like a vast stack of old school CRT screens.
The dome would only be able to show light part of the year. In winter CO2 and water ice would form on it unless it was highly heated (just as they do on Earth.) Worse, the martian dust, especially in the month long stand storms, would coat it over. A big dome of glass or plastic, even grounded, would be one hell of static electricity generator.
Power would have to be nuclear. Solar would be weight/watt cost prohibitive and would suffer the same problems with dust, ice and storms that forced the Pathfinder robots to hibernate for months at a time.
Primary oxygen will come from algae tanks with food plants providing oxygen in the carbon cycle. Algae will be part of waste recycling as well.
The problem with domes is that while they are very efficient enclosures of volume, they are poor encloses of area. If you look at images of interiors of large existing domes, you see small areas with vast amounts of open air above them. On Mars all that air is generated, filtered, heated and pressurized. To make efficient use of the space, you would have to fill it with large tall buildings, and then you've lost your open spaces.
A better and bigger dome could be produced underground using a nuclear charge technique, experimented with back in the 60's. An underground nuke in relatively soft rock compresses the rock and melts it, followed by an injection of water into the center of the molten mass which expands and presses the melted material into a dense glass, then a type of cement is injected. Soviets used that to build big chambers for storing oil. After it cooled, a coating of plastic sealant makes it airtight. Radiation is minimal, actually less than surface construction on Mars, don't have to worry about heating the air, external radiation or sandstorms or efficient use of space. Plus, the materials you need to ship to mars are much lighter.
The population density of the dome is really dependent on how dense you want to pack them in. The energy production and rest of the physical plant will be outside the dome as will the agricultural. Plants don't need a vista and plants will have to grown under false light on mars anyway. As always, energy is your final limitation. With enough energy, you can do anything.
Having spent a summer knocking around in a hazmat suit directing aerial spraying, I kind of doubt people on Mars will be big fans of wide open spaces. The nicest spring day pales when view through a face plate and filtered air. A 3 billion year unchanging landscape will get old in a hurry. Most likely a deep, secure efficient underground facility with some nice projections of Earth on the walls and ceilings might go over better.
I would suggest looking at the population densities of contemporary Tokyo, one of the highest in the world, to get a feel for how many you could cram in.
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While I don't have the answers I can give you a starting point: Forget the volume, ignore what the people need to live in. It doesn't matter.
The limiting factor will be food production. If the plants are growing directly in the city the needs here are going to be substantial--remember, Mars only gets 60% of the sunlight that Earth does, you're looking at about half the growth rate you would get on Earth.
I have read that you can get by with only 10% of the light by supplying only the best frequencies but counting all conversion losses this means an area of solar collectors nearly as big as the growing area if you planted things directly. Fossil fuels are obviously out of the question and nuclear power would be quite problematic because it would be so hard to cool the reactors. (Remember, on Earth reactors are generally on rivers to get cooling water.)
Build your dome, the surface layer is pretty much all food crops, the people live underneath. You'll have enough space for the people.
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The book at hand is Red Mars. In it we find quite a lot of details of the first cities on Mars, infrastructure (including air), water supply (not recycled), radiation protection, etc.
You need to check bare necessities:
How much space does a person need? Manila has a population density of 42k people per km2 (the entire city). 1 You can make that even bigger with taller buildings up to the dome limit.
How much energy does a person need? Not really important, since you can simply put thousands of solar panels out of the dome.
How much oxygen does a person need? A person uses about 550 liters of pure oxygen per day 2 and that is around what seven or eight trees produce 3, but trees are very inefficient. What about covering every single square centimeter (including vertical sides of buildings) with grass? Problem is that, in fact, grass does not produce oxygen 4 so what we need is growing plants that store carbon. Potatoes, carrots, and soy are the best bet, storing carbon that we can eat (and release) later, and producing oxygen while growing.
How much water does a person need? Unimportant, since it can be all recycled using a short surface.
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There is no real way to give a number here as the city can support however many people you want it to support. The support infrastructure just has to scale up to the size of the population.
The most likely situation would be large hydroponics farms providing both oxygen and food. The diet would be essentially vegetarian. You may have park-style areas inside the city that would contribute some oxygen but would mostly be for recreational purposes.
The hydroponics may well have separate crops optimized (and most likely genetically modified) for food and for oxygen production, or the two purposes might be combined so long as the harvesting was staggered appropriately to keep oxygen supplies up.
A variety of plants should be used to protect the colony from anything that badly affects one species of plant from killing the whole colony.
It would be possible to do the same thing simply using greenhouses and growing plants in beds within the greenhouses as well, no hydroponics necessary. Hydroponics give more control over the process though and with something this essential to the city that is likely to be an important factor.
It's also likely that a lot of the oxygen production (and possibly some of the food production) would be done in the form of algae in transparent tubes, it allows you to present a large surface area to the light and produce oxygen that way. This technology is already being developed for producing bio-fuels as well so is likely to be well developed by the time any martian city is being constructed.
Power would come from either solar or fission (fusion in a potential future-tech scenario) and be essentially unlimited. On Mars the thin atmosphere makes solar fairly efficient even though they are far from the sun.
So in other words so "how big can it be" is: "however big you want it to be" And "how many people can I fit inside": "however crowded you want to make them"
The settlement would be placed near a source of ice and the ice heated to provide raw materials for water. That water can also be split to produce more oxygen in emergencies.
One of the major hazards though is radiation due to the thin atmosphere and lack of magnetosphere. The city would actually most likely be built underground and/or heavily shielded - or at the very least have underground shelters the inhabitants retreat to during solar storms.
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