Friday, April 25, 2008

Green and purple people

kw: musings, photosynthesis, poverty

On a walk together recently, my wife, who had been gardening earlier in the day, remarked on how aggressive the plants were to shade one another out. This early Spring season we see new leaves frantically (on their time scale) striving for every bit of light. Our discussion led to my remembering a couple stories I've read, that included the concept of people becoming photosynthetic so as to reduce or eliminate the need to eat anything other than a few mineral nutrients.

I noted also that most plants are only about one percent efficient at turning photon energy into calories of sugar energy. So we discussed just how much food could be displaced by light, if people had chloroplasts or something similar in their skin. Here are some of the numbers:

The people at the University of Prince Edward Island have an analysis of green plant photosynthetic efficiency here. Basically, starting with a photon efficiency of just under 30%, other factors such as wavelength dependency reduce the total system efficiency to 6.6% or less. Measured productivity figures I've found range from 0.25%-1% for most trees to 3%-5% for sugar cane. I've also read somewhere that purple bacteria start with a photon efficiency more nearly 90%, so perhaps their total system efficiency ranges to 15%.

Thus the range of solar energy in to calories out ranges from 0.25% to 15%.

Next, the solar constant averages 1,366 w/sq.m above the atmosphere, but only 60% of the energy gets to the surface, or ~820 w/sq.m.

Finally, basic metabolism ranges from 1200 kcal/day for a small, elderly woman to about twice that for a large young man. Those with very strenuous physical jobs (e.g. lumberjacks) can require 4000-6000 kcal/day of food.

But lets look at 1200 and 2400. A kcal is 4184 watt-sec, or 1162 watt-hr (1.162 kwh), so those metabolic rates come to about 1.4 and 2.8 kwh per day.

Somebody who has the time might have the patience to face the Sun for 6 hours daily, striving for unobstructed solar access. Each square meter of photosynthetic surface would intercept 820x6 = 4920 watt-hr or 4.92 kwh.

We can grind all the figures together to determine, if photosynthesis could be produced at 100% efficiency, 1200 kcal/day, or 1.4 kwh/day, requires 0.285 sq.m of exposed surface, and 2400 kcal/day needs double that, 0.57 sq.m. For the various efficiencies, we get this table of the square meters of sunlight one must collect:

Efficiency1200 kcal/d2400 kcal/d
0.15 (purple)1.93.8
0.05 (cane)5.711.4
0.01 (shrub)28.557
0.0025 (tree)114228

All figures below the third line conjure visions of people with great sail-like appendages they can unfurl to the sun. Even spreading 11 square meters (the size of a barn door) per person, is a daunting prospect. A naked human of ordinary size, with a mirror behind to shine light on the otherwise shadowed side, could capture only about 1.5 square meters of sunlight.

Assuming then that a method could be devised to insert the purple bacterial photosystem into human skin cells, there would remain the need to engineer winglike extensions of the body, or be limited to gaining at most a quarter to half one's calories by spending half one's time basking above a mirror. No wonder that photosynthesis in motile creatures is limited to the protozoa!

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