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]

The 8% for sugarcane is when they're at the peak of their abilities; you'll need to average over the entire lifecycle to work out what humans can do with a plot of land, and that takes you back down to a couple of percent again.

Re: Hall and Rao's Photosynthesis, p.67 of the fifth edition shows efficiencies of up to 12% in certain wavelengths in Chlorella, but the operative word is "in certain wavelengths". Hall and Rao are all about the photosystems and the chloroplasts, but that's not a measure of the final productivity of even an ideal farm.

[(Anonymous)]

Del, Chlorella was used because it was easiest to manipulate in a spectrometer in 1960, and that 12% is an illustration of the Emerson effect at far-red wavelengths. The pages of Hall and Rao you want are page 108:

Lastly, we can discuss the quantum efficiency of CO2 fixation. Each mole quantum of red light at 680 nm contains 17.61 * 10^4 J of energy. Thus, at least three (48 * 10^4 / 17.6 * 10^4 = 2.7) mole quanta of 680 nm light will be required for one CO2 molecule to be fixed. However, experimentall, it is found that 8-10 quanta of absorbed light are required for each molecule of CO2 fixed or O2 evolved. From our knowledge of non-cyclic photosynthetic phosphorylation we deduce that there are two different light reactions required to reduce NADP with the electrons from H2O:

2NADP + 2H2O (4e- & 2 light reactions in chloroplasts) -> 2NADPH2 + O2

Thus we need at least 8 quanta (4 quanta per 4e (1 O2 molecule) * 2 light reactions) to reduce NADP and produce the necessary ATP at the time.

Nevertheless, photosynthetic CO2 fixation itself is only about 30% efficient (2.7 quanta / 8-10 quanta) as we can measure it. Taken in conjunction with an average efficiency of less than 1% for whole plants capturing and utilizing photosynthetically active sunlight (see Chapter 1), this reinforces the concept that these energy exchanges are necessary but wasteful and could be improved in artificial photosynthetic systems.

and page 4:

Energy losses:

47% loss due to solar photons outside the photosynthetically active region (400-700 nm) [the remainder is in the lower energy IR]

30% loss due to incomplete absorption or absorption by components other than the chloroplast

24% loss due to degradation of absorbed photons to excitation energy at 700 nm

68% loss due to conversion of excitation energy at 700 nm to chemical energy of D-glucose

35-45% loss due to dark and photorespiration

These are cumulative, multiplicative losses. About half is simply because the photons are not energetic enough to make the reaction go (the energy = h * frequency thing I alluded to before). After that, the coupling from the reaction center to carbon fixation. The confusion RuBisCO makes between CO2 and O2 is due to the similar charge and size of the two molecules, and is largely insuperable.

8% efficiency, incidentally, is the maximum rate for sugarcane under cultivation. For its full life-cycle, it's more like 4%.

Carlos