Alternative, renewable, and sustainable energy is on my mind a lot these days. An awful lot. While I was at the Materials Research Society‘s Fall Conference in late November, I was fortunate enough to hear Dr. Stephen Chu‘s plenary address on renewable energy and climate change. One of the things that struck me about his lecture was his utterly upbeat attitude towards the problem and his optimism that we would be past this latest energy crisis and into an era of sustainable energy.

As energy goes, there are only a few ultimate sources. You can harness energy from solar radiation, from decaying isotopes, from the residual heat of the earth, and from gravity via the tides. Obviously, fossil fuels and biomass energy sources are merely ways of capturing and storing solar energy. Many of the proponents of solar power, whether that is photovoltaic or solar thermal power, claim that solar will ultimately be the most efficient and cheapest source of power to harness. I’m inclined to believe this assertion personally, although I do know that there are many interesting geothermal and tidal power projects under development.

As I have been doing my own study and research into this area, I thought about the limits of the problem. At our current state of technology, or really at any given state of technology, there is a finite amount of energy that can be harnessed. But even if you assume there is an evolutionary growth in efficiency of capture, there has to be some limit, some budget that you cannot exceed without a true step-change in the technology available for energy capture and storage.

So where is the limit here? For solar energy, there is clearly a finite amount of solar radiation available to the planet. Earth subtends a vanishingly small solid angle in the solar system; we cannot capture even the barest fraction of the Sun’s output. The assertions I allude to above can essentially be rephrased as “the Sun sends enough energy to Earth to provide our civilization with enough power to grow for the indefinite future.” I want to test that assertion and find out what the limit is.

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Rather than computing the Sun’s energy flux from first principles, which I vaguely recall having to do while studying for my Ph.D. qualifying exam, I resorted to the Intergovernmental Panel on Climate Change’s Working Group I report, which gives the average solar flux as 342 W/m^2. (There’s a great chart on page 4 of the linked pdf showing what happens to that 342 W/m^2.) Assuming 5.1 x 10^8 km^2 as a rough estimate of the Earth’s surface area, this gives an total annual insolation of about 5500 zettajoules (5500 x 10^ 21 joules.)

Remember that number. That’s an important number because it represents the total solar energy budget available to the planet. Within some margin of error, that’s it for solar power.

Now, how much energy does the planet use? Ignoring the solar energy utilized by the Earth’s biosphere and considering only the energy use by the human race, we find that number in a table published by the Energy Information Administration: 488.3 exajoules (488.3 x 10^18 joules) in 2006. The site also has historical information going back to 1980. From that data and the projected growth over the next 10 years, I estimated an average annual growth rate of 1.75%. This seems pretty low to me, but I’ll stick with it for this calculation, since undoubtedly we’ll get better at using energy efficiently. At 1.75%, the amount of energy the planet uses will double every 40 years.

Let’s make some further assumptions, even though they won’t really significantly affect the outcome. Let’s assume that the limit to the efficiency of capture we can reach is 95%. That leaves us 5125 zettajoules. Let’s also assume that the biosphere requires 10% of the solar flux. I have no idea if this is correct or not – the number I typically see for photosynthesis is 5%, so I’m adding a safety factor. This leaves us at 4675 zettajoules.

Now, do the division. 4675 * 10^21/488.3 * 10^18 = 9574. log2(9574) = 13.2. Therefore, there are 13.2 doublings before our energy usage outstrips the solar budget. 13.2 * 40 = 528 years.

This is a pretty hack calculation, to be sure, but the implication should not be ignored because I waved my hands in a few places. In less time than it took us to get from the Renaissance to the modern age, we will outgrow the solar energy budget. This is truly not a lot of time in a historical perspective.

What I believe this implies is that we need to be thinking about the next half-millenium right now as we work to solve the current energy crisis. There are ways to increase this budget. Geothermal and tidal power are two of them. Orbital solar power stations are another. These are within reach given our current technology. There may be other ways to capture energy that we’ll discover over the next century.

But in order to do that, we have to not treat our energy technologies as “good enough.” That sort of thinking after the Arab Oil Embargo and the energy crisis of the 1970’s has put us in a state right now where we’re really still only ramping up the development of non-fossil fuel technology. If we recognize that cheap, clean energy may not only be the solution to world climate change and pollution, but also to world poverty (I state this without proof, but there is some evidence to support the assertion), then it should be obvious that thinking beyond the next 20 years is necessary.