« on: 15/08/2017 19:09:04 »
For a man, NHS recommended energy-intake is 2500 kCal per day. That's ~3650MJoules per year.
Total solar energy in London over a year is ~1000kW per square meter.
=> 3650 square meters of green skin required*. ( In ball-park figures, about 1/3 of a ball-park ).
I thought I'd build on the "ball-park" answer from @RD
I think the accepted value for solar intensity is actually about 1kW per square metre. (From wiipedia: " the direct sunlight at Earth's surface when the Sun is at the zenith is about 1050 W/m2").
If we optimistically assume the sun shines for about 10 hours a day at this rate, that's 10h/d * 3600 s/h * 1000 W/s = about 35MJ/d * 365 d/yr = 13GJ/yr.
From wikipedia, on photosynthetic efficiency, "the theoretical maximum efficiency of solar energy conversion is approximately 11%". So the useful energy in our sunlight to a photosynthesising plant is 13GJ * 11/100 = about 1GJ per year per square metre of collecting surface.
2500kCal is about 10MJ (megajoule), so 365 days/yr * 10MJ/day = about 4GJ/yr.
Energy required / energy available = 4GJ/yr / 1GJ/yr = 4 fold under-supply.
Surface area of a human is about 2 square metres.
Therefore we would need at least 4 x 2 = 8 times the surface area of skin we do currently, and live somewhere with 10h/day of constant strong sunlight, to soak up enough energy to survive on photosynthesis.
Have I got that right?
I think that is a pretty good analysis. Good of you to include the theoretical efficiency of photosynthesis.
As I recall a human runs at about 100 watts steady state, with a high performance athlete able to deliver about four hundred watts for a limited time; maybe say an hour. Banking energy as fat ought to be in the system so a steady state figure should be OK, though the efficiencies matter tremendously and have to be multiplied.
I've done some photovoltaic design, and know that the 1000 watts per square meter figure is regarded as accurate as direct sun on a perpendicular plate; on a clear day. We then reuse this figure based on statistical sun hours in a given region. An old data set produced in the 1980's point to my location having about 4 sun hours per day averaged annually, but much shorter in the winter; down to around two sun hours per day as I recall.
The 11% efficiency shows that the 1000 watt figure happens to diminish to close to the 100 watt figure, so instantaneously a human could be solar powered at one hundred watts with just one square meter of green skin pointed straight at the sun. I won't do out the steady state figures, and would have to consider the efficiency of fat storage much like a battery backed system has to sacrifice about 15% to battery inefficiency. I wouldn't be surprised if we wound up at around ten square meters of green skin. But hey, that is way better than the acreage of space each human is consuming in food now. We've got to get this green skin thing going. Live for the sun. Stop the killing of our fellow sun worshipers.
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