The Energy Crisis, with bunnies! A quick look at the pending energy crisis

by Andrew

2006-06-25 11:01:20

Excluding geothermal and nuclear, all the energy we have comes from or came from the sun. As our reserves of coal, oil and natural gas are used up all we'll have left is the energy currently reaching us from the sun. But is it enough?

First we need to know the total amount of energy reaching the earth. We get this total by simply multiplying the solar constant, 1367 watts/meter², times the cross sectional area of the earth, 1.27*10¹⁴ meters²
1367(w/m²)*1.27*10¹⁴ m² = 1.74*10¹⁷ watts
or joules of energy every second. Multiply that out for a whole year"s worth of seconds
1.74*10¹⁷ W*60*60*24*365.24 = 5.5*10²⁴ joules a year.
Now the earth's albedo, or reflectiveness means 30%[1] of that total is immediately reflected back into space leaving us with around (5.5*10²⁴)*.7 = 3.84*10²⁴ joules a year.

Now that we know what we have to work with, what are we using right now? The total energy consumption for the earth in 1998 was 4*10²⁰ joules[2] or about a hundredth of a percent of our solar energy. On the surface this sounds like good news, but how much of the energy reaching us can we actually use?

About 60% of that sunlight hits the ocean powering algae, evaporating water and basically keeping us alive[3]. Of the remaining 40% let's assume we can directly convert 10% of this solar energy into human usable power [4].
(4*10²⁰ J)/(3.84*10²⁴ J*.4*.1) = 0.26%
i.e. about 0.26% of all land on the earth's surface, take into account inefficiencies of storage and transport and let's say we're up to 1% of the earth's surface used for energy production. To give some perspective of size that's about 1.5 million square kilometers (about 600 thousand square miles) which is about the size of the entire interior of Saudia Arabia (except for Mecca and Medina of course).

Now that was at the 1998 level of energy consumption, the US Energy Information Administration predicts world energy consumption will rise to 7.6*10^20 joules by 2030[5], so now we've completely filled the world's 14^th largest country with solar generators. Getting back to the 1998 numbers for a sec, if we brought every human on earth up to the USA's level of per capita consumption we'd be at 2.2*10^21 or about 5.5 times higher. At that level of consumption we'd need an area the size of Australia, just for power production. It's obvious that at that level of consumption there is no reasonable way we could collect enough sunlight to keep up with demand.

To be fair I'm using some pretty loose numbers here, but the basic idea is clear, we're quickly out growing a sustainable level of power consumption. This is kind of like living off of your trust fund until one day you go to get your dog a diamond necklace and find out your account is empty and you've never had a real job before. The sollution is either to find another source of energy, cut back or let nature take it's course and wait for the crash when the oil runs out. Of course fusion or something else may step in to save the day, the consequences of that though will have to wait for another day and more bunnies.(written on June 25th, 2006)

footnotes 1. Due to changing surface temperatures and humans changing the surface of the planet the albedo is actually getting smaller (less light reflected). You can read more about it on Nasa's website. I use the albedo to calculate a convenient approximation of the solar energy that reaches the surface, but as with everything on this page it's far more complicated than I could ever hope to cover in a reasonable amount of space or number of rabbits.
2. Number's taken from the US Geologic Survey's website. I chose 1998 it was the most recent year for which I found a good breakdown of energy consumption and production.
3. Only about 29% or the earth is covered by land (according to the US Carbon Dioxide Information Analysis Center which was a very useful site), but it's disproportionately distributed around the equator where most of the solar energy falls. If you do a projection from the sun's point of view a bit less than 40% of the surface solar energy strikes land.
4. This is actually a wildly optimistic number. The peak efficiency of industrial solar cells, our most direct means of converting solar energy, is around 15-20%. Getting even 50% of peak sustained in a production environment would be an engineer's dream. Indirect means of collecting this energy, such as growing then burning biomass, or focusing light to boil water, are even less efficient.
5. Taken from the US Energy Information Administration.