How big should a terrarium be to be self-sustained?

Problem 1: Food

This is the major contributing factor to the size of the biosphere. Humans need to consume around 2,250 calories per day (averaged between men and women) to sustain themselves, and more if they are doing physical work. 2,250 cal = 10,460 joules (or 10.46kJ), but that's not very useful. More useful: 100g of potato (in any form) = 77cal. One medium potato (defined by Google via USDA as 213g) contains 163 calories. If you live off potatoes alone, you'll need:

$$ 2,250 \div 163 = 13.80 \approx 14\text{ potatoes/day} $$ $$ = 14 \times 365 = 5110 \text{ potatoes/year} $$

That's quite a lot of potatoes. As you can see here, potatoes can be planted March-May and harvested Jun-Oct. You could always plant several crops to be harvested at different times.

The same website as linked above says potatoes should be planted around 30cm apart. Assuming you follow this guide, then you'll need:

$$ 5110 \times 30 = 153300\text{cm} = 1533.00\text{m} $$

for all your potatoes in one row. However, you could plant in multiple rows to save space:

$$ 1533 \div 50 = 30.66 \text{m length} $$ $$ 50 \times 0.3\text{m} = 15\text{m width} $$ $$ 30.66 \times 15 = 459.9\text{m}^{2} $$

So, to survive on potatoes for one year, you will need 460 square metres of space in the biosphere. However, take into account that

• You won't want to survive on potatoes for a year, so you need more land for other foods;
• If you do just stick with potatoes, you can't plant them in the same place in consecutive years, so double the land required (920 square metres)
• Potatoes may not be the best plant. That said, at some quick calculations, carrots would require around 140 square metres less land for the same crop. However, carrots have less calorific content per unit (41 per medium carrot), so you would need more. Growing wheat, while more space efficient, requires work after it's harvested an other ingredients to bring it to an edible state.

Problem 2: Oxygen

I see two options. You can either filter outside air or grow lots of plants.
Filter outside air
If you're assuming today's tech, you need some costly and space-inefficient filtering units. If you have advanced tech, then the walls of your biosphere can be filters, but I'll stick to today's tech. This site has a very good explanation of the oxygen requirements of an average human. To summarise:

8.3ft² of air per adult for 5 hours (with an 8ft ceiling)

However, this is a bare minimum. If the size is much less, you won't last 5 hours. The FEMA recommendation is 10ft² per adult for 5 hours. Given that air is 21% oxygen, this comes to $8.3 \times 0.21 = 1.74$ square feet for 5 hours. Using more appropriate numbers, this is $1.74 \times 8 = 13.92$ cubic feet for 5 hours, and $13.92 \div 5 = 2.78$ cubic feet per hour. That sounds like a fairly reasonable number: what output would you need?

$$ (2.78 \div 21) \times 100 = 13.23 $$

This line shows that 2.78 cubic feet per hour of oxygen equates to 13.23 cubic feet per hour of normal air.

$$ (13.23 \div 60) \div 60 = 0.003675 $$

This is the amount of air that your concentrator needs to take in per second to keep you alive. That's a perfectly good number: given that many home fans can move around 2 cubic feet of air per second, a commercial fan in a concentrator will have no trouble. A unit capable of doing this takes up less than 1 square metre.

Grow lots of plants
According to NASA, the average human needs 0.84kg of oxygen each day to survive. This can be produced by any size plants, but the space requirement changes depending. For example, a mature broadleaf tree such as an oak produces 10-15kg of oxygen per day, plenty to support a human. However, it can easily take up 20 square metres of space and can reach up to 30m high. Smaller plants may be easier: since they produce less oxygen, you can use a more exact number to produce closer to the right amount of oxygen per day, saving space. However, keep in mind that an exercising human uses much more oxygen - up to 7kg per day.

The really easy way is to just pull in air from outside. However, this may not be possible, so your best bet is probably the filter, as it takes up the least space.

posted almost 10 years ago

ArtOfCode‭ staff

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