Efficient food production

[james_davis_nicoll]

I was noodling around on soc.history.what-if and made a calculation I'd never bothered with before: if a human needs enough food to produce N Watts, how many square meters are required to intercept that much sunlight? OF course I was too lazy to actually look up insolation for various latitudes but the BOTEC I committed seemed to show that it should be a few square meters.

Even Fairbanks, Alaska, gets from 90 to 350 watts/m^2. Say your mark 1 human needs at least 100 watts worth of food to keep functioning [1]: They'd need about one square meter dedicated to collecting solar powers, asssuming no losses. The entire population of North America should require a few hundred to a thousand square kilometers of converters to power themselves. Even a factor of ten losses should mean that we'd need about 300 square kilometers to feed all of Canada, assuming the lowest insolation in Alaska is what we have to work with, and about 3000 square kilometers to feed all of the USA. That's a square less than 20 kilometers on an edge for Canada and a bit over 50 kilometers on an edge for the USA. Feeding the entire planet should require about 60,000 square kilometers or a square about 250 km on an edge (or less, if we pick someplace sunnier than Fairbanks to grow food).

Clearly modern methods of coverting solar (and fossil) energy into human energy are criminally inefficient.


1: Googling says "at least 2500 kilocalories" per day so call it 4000 to be safe. That works out to about 50 watts, which I will double just because.

Comments

[del-c.livejournal.com]

I did make a mistake, but in the other direction: by averaging over thirteen months instead of twelve, I cheated the poles of 10 watts per m². The maths is horrifyingly hairy everywhere else^*, but it's relatively easy to show that at the pole itself, the value is

1,370W m^-2 ÷ pi × sin(23°) = 170W m^-2

*_{I don't know enough about elliptical functions to average over a year except by brute force, or even to know if it can be done analytically at all}