# Efficiency required of a photosynthetic system to support human level activities

Chlorophyll as we know it on earth is estimated to be between 3% and 6% efficient in converting light energy to useable biomass. This support slow growth and no movement of plants like that observed in herbivores or carnivores. Higher up the food chain, animals directly or indirectly depend on plants to convert vast quantities of solar energy into useable biomass. Given that 3% efficiency can't support human level activities, how much more efficiency do we need from photosynthesis to change humans from omnivores into photovores?

Assumptions:

• Human surface area: average 1.9m^2 for adult males. 1.6m^2 for adult females. Source.
• Want to keep humanoid shape and movements as much as possible. These photosynthesis based creature needs to be able to move comparably to a human.
• Assume a Sol light spectrum and earth atmosphere absorption spectrum.

How much more efficient would a photosynthesis process based on neo-chlorophyll need to be to support human level activities with the surface area of a human?

I'm interested in how much more efficient photosynthesis would need to be to support human level energy needs. How to achieve that increased efficiency is not expected as part of a good answer (unless you work in organic chemistry and feel frisky).

• Photosynthetic animals are generally infeasible. Mathematically, the largest a photosynthetic animal could be is 30cm in diameter and then only if its metabolism is ectothermic. What few photosynthetic animals exist on Earth all fall within this limit. – Anonymous Jul 22 '16 at 12:37

The average adult human has a surface area of 1.75 square meters. Now, obviously at least half of that is going to be pointed away from the sun at any given point in time, plus a bit for the skin on the sides of the body instead of on the front or back. I don't know precisely how much skin is actually usable, but for simplicity we'll assume that 0.75 square meters are usable at any given time.

"An average amount of sunlight received at the Earth surface per square meter is 341×0.48=163 W/sq.m, or 15 watt per square foot." This is averaged across the entire surface of the planet, including the night side, so we won't need to make any further adjustments for the fact that it's night time about half the time, and humans can't sit in the sun during the night. Note that this number ignores any energy lost traveling through the atmosphere.

A human consumes 96 Watts of power, assuming a 2000 Calorie daily diet.

So, Assuming your humans live somewhere where the nights and days are of equal length, and that they spend the entire day spread out in the sun with the maximum amount of their body exposed to sunlight without any breaks or need to move, and that it is never cloudy, the required efficiency is somewhere in the area of 96/(0.75*163) = 78.5%. This isn't really achievable, it far outstrips pretty much anything we see either in nature or the best of human design. Furthermore, all of this is assuming no energy lost to anything while it's traveling through the atmosphere, in practice a significant chunk of the energy will be bounced off of clouds and thereby lost. Humans probably can't actually be run on integrated solar power systems in their current forms.

However, there are two important and easily changed terms in the above equation. Plants can survive off of sunlight because the ratio between their surface area exposed to the sun and their energy needs is much larger than a human's. If your variant on humans are able to either dramatically increase the surface area of the skin they're exposing to the sun, or dramatically decrease their energy consumption, living off of sunlight may be feasible.

• And in fact, we DO live off sunlight, having found a way to dramatically increase our photosynthetic surface area, either by eating plants, or eating animals which have done the work of collecting plants for us. And more efficiently, since we don't have to a) lug around all that surface, and b) worry about spending enough time in the sunlight :-) Though we can't give humans all the credit, since animals (and some few parasitic plants) have been doing it since the Cambrian). – jamesqf Mar 19 '16 at 4:16
• @jamesqf True enough. – Saidoro Mar 19 '16 at 4:22
• Additionally the light that you absorb as energy, you do not absorb as heat. Ectothermic creatures will have a lot of problems with this. – Derk Jan Hulsinga May 4 '17 at 10:41
• One way to "dramatically increase the surface area of the skin they're exposing to the sun" - give these humanoids "solar wings" - lightweight organs that they can fold or extend, which collect sunlight. – G0BLiN Aug 25 '17 at 14:49

Conversion of light to chemical/electrical energy isn't really that simple. Remember, we see objects due to the light REFLECTED from it.That automatically precludes 100% efficiency.

Secondly, part of the energy generated is used to transfer nutrients internally. That is an energy cost and must be subtracted from available energy.

Thirdly, plants draw nutrients form the soil and air and energy from the sun. Your photosynthetic human would still need to eat and drink. It's far more efficient to stand in one place to actively uptake than to waste energy moving around looking for food.

Fourthly, the sunlight causes leaves to heat up. In order to cool them, plants use capillary action to draw up water from the soil, which evaporates at the leaves, both cooling them and causing more water to be drawn up. Part of this water is used to bind CO2, forming carbohydrates. You need a continuous flow of water for photosynthesis to work.

Maximum insolation is about 900 Wm^-2 at high noon on the tropics during a solstice. A human standing upright, would receive only the bit directly on top of his head. The rest of the time, sunlight would hit him at an angle, but from the side, so less energy density, but over a larger surface.

What would really make the difference is diffuse radiation, i.e., light reflected from his surroundings. In areas like deserts or icy wastes, this would exceed the beam radiation, but leaves the shortages of water and accessible nutrients respectively.

To summarise, photosynthesis only really works if you put down roots. Literally. It's why no animal is photosynthetic, even though that was a valid and explored evolutionary path by the time the first parasite came along.

Note: the math is wrong (see Saidoro’s comment) and the poster naver came back to edit. —Ed.

This article does quite a bit of legwork for us. It calculates the energy a single cubic cm receives in a 12 hours as 1.8 x 10^6 mJ

You already stated that an adult male is 1.9 cubic meters, so multiply the above by 190 cubic cm of human surface area, if we were to assume every inch of skin gets the full amount of energy (ignoring clothes or simply having your back to the sun) and we get a maximum possible energy, at 100% efficency, of 3.42 x 10^8 mj in 12 hours.

Of course that was a calculation of the energy in 12 hours. Lets be really generous and double that to calculate the energy available in a day (ignoring the whole 'night' thing entirely). The maximum possible energy we could get is 6.84 x 10 ^ 8 mj in a day.

The average human burns 1060 'calories' of energy a day I put 'calories' in quotes because what is listed as calories on the nutritional label of food is really a kilocalorie, but everyone is use to calling the calories by now that they would get confused if I started talking in terms of actual calories.

Finally, there are 4184 joules in a kilocalorie. Thus a human burns a total of 4435040 joules a day, or 4.43 x 10^6 joules or 4.43 x 10^9 mj

So we need to get 4.43 x 10^9 mJ of energy out of sunlight when at most 3.42 x 10^8 mj of energy will hit our skin. We would need an efficiency of about 1200%

Unless I've screwed up my math I don't think photosynthesis will suffice :)

• Kilocalories aren't called calories, they're called Calories. Which is admittedly a dumb bit of naming by whoever decides these things, but it is what it is. Also, both human skin surface areas and the NASA article you referenced use square meters, not cubic. Finally, we've both come up with drastically different values for the efficiency, so you should probably check my math and sources while I check yours, there shouldn't be a difference that large if we're both doing things right. – Saidoro Mar 18 '16 at 20:09
• Found it: "1.9 cubic meters, so multiply the above by 190 cubic cm". 1.9 square meters is 19000 square centimeters, not 190. Your power generation is underestimated by a factor of 100. That puts your actual required efficiency at 12%, which seems reasonable given that you made some fairly generous assumptions while I made relatively conservative ones. – Saidoro Mar 18 '16 at 20:20