Solar Energy

 “[Nobel Laureate Wilhelm] Ostwald’s energetic imperative – Waste no energy but value it – is relevant as humankind makes the inevitable transition to a permanent economy based exclusively on solar radiation.” – Vaclav Smil

“My own preference is to fill the Mojave with solar concentrating plants, and save some of this wonderful stuff [oil] for our descendants.” Dave Rutledge

 “I’d put my money on solar energy… I hope we don’t have to wait til oil and coal run out before we tackle that.” – Thomas Edison

 When Edison and Ostwald were alive there were only 2 billion humans on the planet so capturing solar energy offered more than enough low entropy to support human society sustainably with a generous quality-of-life.  In 1972 when the world population was 3.8 billion, the authors of Limits to Growth concluded that global population and industrial activity were still below the levels that could be supported indefinitely by Earth.  Today there are 7 billion people and it is less clear that sustainability is achievable.  In the 2004 edition of Limits to Growth the authors concluded that both population and industrial activity had already grown above sustainable levels [Meadows, 2007].  Sometime in the not too distant future it may become impossible to achieve sustainability, if we do not act responsibly now.

 Fossil fuel resources are running out and we are only arguing about when.  As we will discuss in some future article, nuclear power is severely limited by the availability of uranium resources and reserves and it is a simple fact that we still have no idea how to process or store the waste nor how much whatever the solution (assuming there is one) will cost in terms of energy and money.  That leaves solar, which includes tidal, wind and biomass; and much more limited and dispersed geothermal energy. 

The radiation intensity of the sun through a plane perpendicular to the line connecting the center of the Earth to the center of the Sun measured at the top of the atmosphere is 1366 Watts per meter squared.  This is called the solar constant.  The Earth has a mean radius of 6371 kilometers.  The solar energy flux through the circular area projected by the Earth onto a planar surface is 1366 X 6,371,0002 X p = 174,000 terawatts.  

 According to the British Petroleum 2009 statistical review, humans consumed 11300 million tonnes of oil equivalent energy in the year 2008.  One tonne of oil can produce 12 million Watt-hours according to the same source.  There are 24 times 365 hours in a year.  Thus humans consumed energy at the rate of 15 terawatts in 2008.  BP excludes biomass, solar and wind but these numbers are accurate enough for our purposes. 

 Humans therefore consume energy at a rate equivalent to 0.008% of the sun’s energy flow.  We would have to intercept 6371 kilometers (km) squared times p times 0.00008 or 10,000 square km of land on Earth beneath the sun with 100% efficient solar collectors and while there is no cloud cover.  We can work out the other bits.  Solar panels are about 15% efficient and if we situate our collectors in the world’s deserts we can ignore any cloud cover.  We then have three remaining issues to consider.  The Earth is a sphere, it rotates and it has a 23.5 degree “seasonal” wobble.  Because the Earth is a sphere we only need 10,000 square km if we build our solar array at the point on the Earth surface directly below the sun.  If we are 10 degrees to the north then we only intercept cosine (10) of the total power or 98%, which is not bad.  But if we are 40 degrees to the North, we only intercept cosine (40) or 77% of the power.  Because the Earth rotates, our selected point 12 hours later will be in the dark of night.  And because the Earth wobbles once a year, the sun is directly overhead in the Sahara desert at noon in the summer but directly over Botswana during the winter. 

 To avoid cloud cover, the best places for our collectors are on the Tropic of Cancer, where the Sahara is located, or the Tropic of Capricorn, in the middle of the Australian Outback.  The cool thing to do right now would be to get a globe and play with it.  You will note that when the Earth rotates and positions the middle of the Pacific Ocean towards the Sun, there are no land masses available for our collectors.  So we would have to be able to store energy.  Concentrated solar thermal power promises to be cheaper than solar photovoltaic panels and easier to manufacture and heat is easier to store than electricity. The United States is a leader in this technology as we once were in photovoltaic technology as late as 1998 before we gave that lead up to Germany and China. 

Getting back to our 10,000 square kilometers, since collectors are 15% efficient, we need 67000 square kilometers and because our surface is not directly under the sun most of the time, we need to increase the area by another 40% or so to 90,000 and if we add a cushion for cloud cover lets round it up to 100,000.   This is a little less than the total area of Arizona. We need several such stations around the Earth to cover night and day.  Concentrated solar thermal power can work round the clock by storing heat generated during the day but it only collects the energy from solar photons during the day.

There are other things we can do though.  I have solar panels in my back yard here in Virginia.  They contribute.   Additional solar collectors can be distributed throughout the economy.  Integrating distributed and concentrated sources of energy is an important part of the Smart Grid evolution.  There are other ways to capture the sun’s energy such as wind, tidal and biomass.   Algae can be used as a solar collector [Westervel, 2010].  And finally, the biggest part of the solution to America’s energy problems, at least, is conservation.  We can simply use less. 

 Still, the big problem with this dream of sustainability is building out the necessary infrastructure.  The entire energy infrastructure we have now was build using fossil fuels when such energy sources had an energy return on energy investment ratio (EROEI) of about 100.  Because we are using all the easy stuff first, the light sweet crude and anthracite, what we have left is tar and lignite with EROEIs closer to 5 or less.  They are also dirtier in every respect.  We need to use the energy from remaining fossil fuels to construct our solar powered future.  Building more nuclear reactors has an opportunity cost since it wastes resources that could have been marshaled to build out solar plant and it has a huge liability cost since we do not know what we have to do with the waste and don’t know how much that will cost.

 Tony Noerpel


[Meadows, 2007] “Evaluating Past Forecasts”, in Sustainability or Collapse, eds. Costanza, Graumlich and Steffen, Dahlam Workshop Reports, 2007.

 [Westervel, 2010]

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