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I want to put 10,000 humans in a space ship and send them into space. They don't have a set destination - they're having to flee their homeworld, and they don't know what planet will take them in, so they need to have a way to grow food in addition to having stores onboard. How big should this area be? How much space should they devote to storing nutrients for the plants? Is there a good way to recycle the nutrients?

These people have access to hydroponics and high-yield crops that will survive in space. Additionally, since their situation is desperate, they don't need to have space for luxury crops, just the necessities.

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In optimal conditions it takes about 50 square meters to grow enough food and oxygen for one person. Lets double that to be safe and to make it a round 100.

http://www.tylerdwyer.com/files/OASIS_Final_Report.pdf

Zero g may may this more interesting, you might need to spin your spaceship to allow the plants to grow properly and to keep water in the right places.

So you're going to want something like this crammed into a big cylinder.

plants

10,000 people would need 1,000,000 square meters of plants to keep them alive at a bare minimum.

Assume trays 1 meter apart, that's 1,000,000 cubic meters.

For ship size I'm going to use supertankers.

https://en.wikipedia.org/wiki/Oil_tanker

enter image description here

The the largest supertankers can carry a little over over 500,000 tonnes, assume half or more of the space is lost from having to have some space to let people get between the trays, for equipment, for spare parts so assume the equivalent very minimalist 4 but more likely 6 spinning supertankers to grow your food.

Now you're also going to want significant stores, you don't want to starve because of a few failed pipes so add another couple of the same size for warehouses of food, oxygen and water.

If this is to be very long term you're also going to need a few more supertankers that can produce all the spare parts etc.

Then you're going to need a supertanker or 2 for people to actually live in.

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    $\begingroup$ Don't forget the energy requirements for doing all that. Without a sun, how much energy do they need to bring with them just for food and living? $\endgroup$ – JDługosz Sep 16 '15 at 18:06
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    $\begingroup$ @JDługosz they've got interstellar ships so I'm going to assume a "good enough" energy source. Rustbird can decide how big his energy sources are. Compared to the energy needed to get between stars these greenhouses are going to be cheap to run. $\endgroup$ – Murphy Sep 16 '15 at 18:08
  • $\begingroup$ However many supertankers you end up needing for crew, parts, supplies, and food, you'll also need thousands of times that filled with some type of propellant if you want to get anywhere. So maybe you have a dozen supertankers of payload, and maybe 10,000 supertankers filled with propellant. Hope they can swing around a gas giant for a quick refueling before they head out... $\endgroup$ – Caleb Hines Sep 17 '15 at 6:30
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Murphy is right. It is going to be an outrageously vast space required for "green" crops. You could, however, genetically modify fungi species to produce high energy human-ingestible products such as vitamins, glucose and proteins. That would take far lesser space, would take far lesser time to ripen and would be lesser hassle to handle.

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  • $\begingroup$ What about yeasts? Don't forget the yeasts! $\endgroup$ – Joe Bloggs Sep 17 '15 at 12:22
  • $\begingroup$ I had that in mind but I thought yeast and fungi are the same thing :S $\endgroup$ – Youstay Igo Sep 17 '15 at 12:27
  • $\begingroup$ They're in the same group (eukaryotic, I think) but they're different. Same thing with molds. $\endgroup$ – Joe Bloggs Sep 17 '15 at 12:28
  • $\begingroup$ Ah. Thanks for the mention then, buddy. Any prokaryote group that could be utilised? $\endgroup$ – Youstay Igo Sep 17 '15 at 12:30
  • $\begingroup$ If we're genetically engineering I don't see a reason why not, but the eukaryotes are simpler (hence why engineered yeast is already a thing) $\endgroup$ – Joe Bloggs Sep 17 '15 at 12:33
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Why would they have to grow food? At this very moment in time, we are 3D printing food. Even NASA is looking at its viability for long term space trips. All you need is space for the materials and you can print food that will provide the nutrition they need.

Growing food on an extended space flight doesnt make a lot of sense. Just like on Earth, yield's and quality vary. A plant disease could wipe out the entire crop, and then you would have nothing. There are simply way to many things that could go wrong to make it worthwhile. Not to mention the amount of water it would take. Farming in space is not something that will likely happen.

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    $\begingroup$ 3D printing can change the appearance, but you still need a process to convert energy into a human-digestible form. Currently the most efficient known process to do that is growing plants. Of course it is possible that by the time humanity is able to build large space ships it is also able to produce all food substances efficiently by purely chemical processes. But that's orthogonal to the question of 3D printing. Just bringing enough nutrients from the home planet (as in the NASA case) is not an option for a huge space ship that won't be able to restock for an unspecified time. $\endgroup$ – celtschk Sep 20 '15 at 8:48
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    $\begingroup$ This doesn't answer the question. Assume that 3D printing of chemically produced nutrients will work. How much space do they need to do it? How big are the 3D printers? How big is the chemical plant for the creation of the nutrients from sewage? That's what an answer needs. It's a neat and off the wall suggestion but it is not an answer to this question. This is a comment masquerading as an answer. $\endgroup$ – Brythan Sep 20 '15 at 22:06
  • $\begingroup$ To address your last point, if a ship is making a long enough journey that they'll be growing crops onboard, I think its safe to assume that they'll be using a closed loop water recycling system (e.g. no blowing wastewater out of an airlock). So no water should be lost by growing plants, runoff water can be collected and recycled and the water in the actual plants will turn into human waste which can be recycled. Earth doesn't lose any water when you water a plant afterall $\endgroup$ – Austin Philp Mar 10 at 18:13

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