“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Sunday, March 22, 2015

Eating energy

In round numbers, there are 7 billion people eating on planet Earth each day. It's pretty clear that my diet here in Southern California is very different from that of a subsistence farmer in Namibia or a subsistence fisherman (or fisherperson) in Madagascar. It's also true that, as a fully grown adult of age 60, I probably consume more calories than my one year old grandson. But I estimate that my daily intake is on the order of 2000 kilocalories per day of food energy and I don't think that long term survival for an adult is possible on much under 1000 kilocalories per day. Of course, not all humans are adults and estimates of population in each quinennial group are available from the UN. Still, for rough estimates, 7 billion people consuming 1000 kilocalories per day will work.

Thus, in raw terms, this equates to humanity ingesting food energy at the rate of 7*10^12 kilocalories per day or about 10 "quads"/year (for some reason, lots of analysis of world primary energy is done in quads, where a quad is 10^15 or a quadrillion btu(a so-called "short scale" quadrillion)). Of course, the amount of chemical energy in our food as measured by bomb calorimetry exceeds this number since we cannot oxidize 100% of the mass that we ingest, the unburned residue leaves us in ... various ways... ahem. And we certainly don't ingest 100% of the food plants we eat. Further, many of us eat the meat of animals who have ingested the plants, or even the animals who have eaten the animals who...

But, in my simplistic model world, I'm going to estimate that 20% of the mass of a food plant is edible, that we burn 50% of it for energy, that meat represents 20% of the kilocalories consumed by humanity, and that the "hit" on losses due to an animal intermediary is the square of the losses inherent in eating plants directly. Thus, 10*0.8*P+100*0.2*P=C where P is the available kilocalories of "primary burnable energy" ("PBE")and C is kilocalories ingested as metabolizable food energy. So we have that 28 kilocalories of PBE are required for every dietary kilocalorie in this model.

So, we're now talking about 28*10 or 280 quads per year in photosynthetically created PBE. Depending on the plant species involved, the efficiency of using solar energy to convert carbon dioxide and water to biomass is in the range of 3% to 6%. I'll use 5% since it makes the arithmetic easy, and thus 5,600 quads of solar energy per year are needed to feed us. Let's move to SI units: the 5,600 quads are 5.9*10^9 terajoules and 5,600 quads/year are 187 terawatts.

This energy comes, of course, from the sun. There are approximately 14 million km^2 or 14*10^12 m^2 of arable land on our planet so, on average, each arable square meter must be responsible for converting (5.9*10^9 terajoules)/(14*10^12m^2)=422 megajoules/year or an average rate of 13.4 watts of incoming solar energy into ingested food energy.

And, as we see in the graphic at right, this is something like an order of magnitude away from the total incoming energy absorbed by the surface of the Earth. While I've looked at other articles that come to different conclusions about solar energy embodied in our food, I'd be shocked if I were off by an order of magnitude. The lesson? There's not a lot of spare capacity in our system for squandering our biota's ability to feed us.


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