On the Other Hand…

After criticizing Fred Clark, I want to point out the intriguing part of his post, which is a link to a ScienceBlogs post by Ethan Siegel, a theoretical astrophysicist. Siegel argues that with a solar panel array of just 125 square miles–35 miles on a side–in the Arizona desert, we could satisfy the energy needs of the whole United States.

Make a solar array about that size — 35 miles by 35 miles — and you can power the entire United States. Period. Day or night, winter or summer, rain or shine. No emissions, no pollution, no risk of radiation, no dependence on oil, coal, gas, no damage to the environment.

That’s a very intriguing thought. I just don’t have the time to dig into it very deeply right now, but if he’s right about the energy output, it would seem like an idea worth investigating. We certainly have space and enough to spare in Nevada (the area’s much smaller than many of our military ranges out there), and Nevadans would, I think, be much more welcoming to that kind of investment than they were to the now-canceled (at least for the time being) nuclear waste repository.

Of course Siegel assumes too much, and gets a bit silly.

if we invested in it and made it happen — I think it would fix a huge number of our domestic problems: the economic ones, the employment ones, the manufacturing ones, etc.

Sigh. Of course energy costs are an important input for the economy, but cheap energy doesn’t by itself suddenly solve all problems. And as I keep repeating, American manufacturing was at record levels of output just prior to the recession. Why, oh, why don’t people as smart as astrophysicists put their smarts to actual use before saying things like this?

But that (mostly) aside, here are the questions the idea raises for me.

  1. What would the cost of such a project be? How would it compare to continued investment in other energy sources? Would it actually provide cheaper energy (as Siegel seems to assume), and how long would the payoff period be?
  2. Could this be done via the private sector? Fred Clark seems to assume that it could only be done as part of a large scale government project. Is he right about that, or could it be done via a consortium of energy companies?
  3. Would we actually want a single such array, or would we want multiple ones with multiple owners to provide competition? I suspect some would see it as properly done in one array and operated by the government, to avoid the evils of a corporate monopoly, but obviously I would be quite as dubious about government management of it.
  4. If we did a single big array, what would be our backup source of energy, in case of accidents (whether terrorist, operator-caused, meteorite, whatever)? Putting all our eggs in one basket is, obviously, a risky choice. (But note that Siegel is just talking about total area needed to provide enough energy–he’s not necessarily saying we should bet everything on one single solar farm.)

Important questions, of course, but all merely technical questions, I think. That is, each can be potentially be satisfactorily answered. I’m somewhat skeptical, just because we too often hear people say “X is simple and can solve all our problems,” but I’m also intrigued, because I think a theoretical physicist just might know what he’s talking about in terms of energy output, even if he knows squat about economics. And I’m all for a dependable and non-polluting source of energy, if one is available.*

*OK, obviously it wouldn’t be truly non-polluting. There would be pollution involved in the production of everything needed for creating such a solar array, meaning that from a life-cycle analysis even relative clean solar energy is not truly non-polluting. But I am assuming, hopefully correctly, that such pollution would be no greater per unit of energy produced, than what results from the production of other energy sources.

About J@m3z Aitch

J@m3z Aitch is a two-bit college professor who'd rather be canoeing.
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12 Responses to On the Other Hand…

  1. lukas says:

    Even in the Arizona desert, the sun doesn’t shine at night, so you’ll need huge energy storage facilities to provide for the nation’s night time needs (and the occasional cloud cover). So add that to the already huge expense of paving 35 x 35 = 1225 square miles (you missed a 2 there) with not-exactly-cheap PV cells.

    Theoretical physicists have great solutions to all kinds of problems, but when it comes to the practicality of it all, I’d trust an engineer over a dozen of bright theoretical physicists.

  2. D. C. Sessions says:

    One reason you don’t want a single array is that it’s subject to single point of failure. Another is distribution: getting the power out of that single source location is costly and inefficient.

    As for the “would it really produce that much power?” question, yes. Give Ethan that, please: 35 miles square is a bit over 3×109 square meters, which receive about 1 KW/m2 solar input peak. Divide by pi for diurnal variation, tims cos(33 degrees) for latitude, about 20% efficiency, and you get just about 2*1011 watts average. 200 gigawatts. Not bad.

    Cost, though, is an issue. Photoelectric solar costs upwards of $5/watt, so we’re talking about roughly a trillion dollars. Thermal solar is about the same, with different scaling at the low end, but does have the charming property of storing output for base load (and it’s more efficient on clear days.) Note that hydroelectric pumpback is already used in the West for load leveling.

    On the other hand, nuclear is about as expensive per watt as wind but has a few other externalities that many advocates (I’m a cautious one) gloss over. Solar costs more than either now, but if we were to start putting anything like as much subsidy into it as we have into fossil fuels (Iraq, anyone?) we’d get some economies of scale and progress in technology that can reasonably be expected to bring the cost down.

    As for public vs. private, well, right now it’s a matter of private sustainable power vs. subsidized fossil fuels and nuclear — which already have the incumbency advantage. Most of the alt-energy advocates I know would be content (if not happy) to just have a level playing field. Some bootstrap funding from the Feds comparable to what nuclear received wouldn’t be amiss, though.

  3. D. C. Sessions says:

    Crap. Superscript tags got filtered out — and no preview.

  4. AMW says:

    How easy/cheap is it to shut solar off when you don’t need the juice? Demand for electricity changes throughout the day: as people regularly engage in more energy-intensive activities at certain times. Nuclear could conceivably provide all the energy we need pretty cheaply, except you don’t just turn off a nuclear plant. You need to have enough demand at the base load so that all the plans can stay on (though not necessarily operate at maximum capacity).

    Regarding Siegel’s economic overreach, note that energy makes up only 7% of GDP. Even if we could get free energy the costs of doing business would stay pretty close to the same. Don’t get me wrong, cheap energy is great. But it’s no panacea for economic growth.

    Thoughts on your questions:

    1. What would the cost of such a project be? Depends on who’s in charge. If it’s just the gov’t building one massive project in the Arizona desert you can bet it will be very, very expensive. Not least of all because every energy company would lobby like hell to get it shut down, and they should be willing to spend as much as they expect to lose from its construction. A.k.a., all their profits. A true cost calculation has to include those costs of rent-seeking.

    2. Could this be done via the private sector? The main advantage of a government actor would be the right of imminent domain. But note that the foregone value of the land should also go into a calculation of the total costs.

    3. Would we actually want a single such array, or would we want multiple ones with multiple owners to provide competition? Obviously, multiple arrays. Competition is one reason, diversification of risk is another. But on top of that, some of the electricity escapes as heat during transportation. That’s one reason power utilities tend to deal locally/regionally. Otherwise there would be no reason for local/regional blackouts, as a California utility, say, could buy power from a New York utility.

    4. If we did a single big array, what would be our backup source of energy, in case of accidents (whether terrorist, operator-caused, meteorite, whatever)? Why, optimism and rainbow kittens, of course!

    I should note that despite my snide tone I think it would be awesome if we could transition to cleaner, cheaper energy. I just don’t see this project as a prudent way of doing it.

  5. James Hanley says:

    imminent domain.

    I don’t believe I’m familiar with that concept. *grin*

  6. AMW says:

    You know, that’s when the government is just at the threshold of seizing your property. They’re going to do it any time now, but you’re just not sure when.

  7. Lance says:

    Economical large scale solar power has always been “just around the corner” much like nuclear fusion. That corner must be really big or really far away because we never seem to get any closer to it.

    As for the “would it really produce that much power?” question, yes. Give Ethan that, please: 35 miles square is a bit over 3×109 square meters, which receive about 1 KW/m2 solar input peak. Divide by pi for diurnal variation, tims cos(33 degrees) for latitude, about 20% efficiency, and you get just about 2*1011 watts average. 200 gigawatts. Not bad. – D.C. Sessions

    OK, I’m a math and science instructor (pulls out red pen) and I have a few issues with your numbers here. (We’ll get to the physics issues also.) What is 3×109 square meters and where did you get that number? 35 square miles is approximately 90.7 square kilometers which is (9. 07 x 10^1) x (10^3 meters)^2 which is 9.07 x 10^7 square meters.

    Then you say “…which receive about 1 KW/m2 solar input peak.” Check, but the important word here ispeak. That happens for a brief period each day, if the sun is shining and my Googling shows 220 sunny days/year in Arizona but we’ll pretend it’s always sunny in Arizona for these calculations.

    So using the 20% efficiency number, which is very generous considering that this assumes that ALL of the vast (and 90 square kilometers is sure as hell vast) array’s solar cells, circuits and other support devices, technicians and infrastructure are working at 100% capacity, a highly unlikely event, we arrive at peak power output of (2.0 x 10^-1) x (9.07 x 10^7 m^2) x (1.0 x 10^3 watts/meter). Which calculates to 1.81 x 10^10 watts or 18.1 gigawatts peak power.

    Then you say, “Divide by pi for diurnal variation”, huh, why?

    Is this supposed to convert the instantaneous peak power to an average value and if so how? What happened to the fact that the sun is, you know, on the other side of the planet half the day? We’ll get to more about this in a moment.

    Then you say, “…tim(e)s cos(33 degrees) for latitude”, uh, OK. That last one reduces the peak power number down to, cos(33degree) x (18 x 10^9 watts). Which is 15.2 gigawatts peak power.

    Averaging, over the year, daylight lasts 12 hours per day. So that cuts the average power figure in half without even considering the angle of the sun, and hence its energy intensity, varying as a function of time of day. Now it would take integrating that energy function of time over the actual length of daylight, and then also including the threshold efficiencies of the cells, circuits and other infrastructure and dividing it by the number of seconds in twelve hours, since watts is energy per second, to get the exact amount of average watts but I have been pedantic enough and I’m going to just use your “divide by pi” fudge, but then of course again diving by two to include the time when there is no sunlight because it’s night time.

    This gives (1/2 pi) x (15.2 x 10^9 watts) which calculate to 2.4 gigawatts average power over the day.

    This of course assumes that you could store all the energy and then evenly distribute it over the day and of course doesn’t include losses from transmission lines, regulating and conditioning the power etc. None of these things are possible but we’ll let that slide for the moment. So lets stick with the 2.4 gigawatt average power output just to be on the (very) high side.

    So your 220 gigawatts is way too optimistic even as a peak power output and really off when looking at average power output.

    Then there are all the other problems like obliterating all the living things in a 91 square mile chunk of Arizona desert. Now, it’s not a rain forest but lots of critters and plants live in 91 square miles of desert. I’d like to see the environmental impact study for that little proposition.

    There are plenty of other issues but I’ll save them for later posts. This one is long enough.

    (Disclaimer: I did these calculations while playing tug of war with my tiny dog Philo and drinking a beer so I’m cool with people checking my work.)

  8. James Hanley says:

    200 gigawatts, 2.4 gigawatts…what’s an order of magnitude here or there?

    Seriously, though, I hope D.C. respond, because I think it’s a fascinating issue, and one about which I so have to rely on others who know far more about it than I do. I can double-check the math well enough if I want to, but I am clueless about the assumptions built into them.

    One question, though, Lance. You say 35 square miles, when we’re actually talking about 35 miles squared. Did you based your calculation on square miles–which by itself would explain a large part of the discrepancy–or was that just a typo?

  9. Lance says:


    That would explain the biggest part of the discrepancy. I wondered if 3×109 square meters was supposed top be 3 x 10^9 square meters which is the correct number of square meters for a square 35 miles on a side..

    Yeah, and the original article says the less confusing “a square 35 miles by 35 miles”.

    So apologies to DC Sessions. Still, the term “35 miles square” can easily be confused with “35 square miles” especially if your drinking beer and playing with your dog while calculating.

    The other caveats I mention still apply, especially the “pi” business, but I guess I agree, within an order of magnitude, of his number given the many caveats I mentioned.

    And now your filing an Environmental Impact Study for obliterating 1225 square miles of Arizona.

    Not to mention financing, building, managing and maintaining a solar energyplant damn near the size of the state of Rhode Island!

  10. Lance says:

    Hey wait!

    DC Sessions says “…and you get just about 2*1011 watts average. 200 gigawatts. Not bad.”

    Uh, no. Using the 1225 square miles instead of my goof of 35 square miles means my number is low by a factor of 35. Multiplying 2.4 gigawatts by 35 gives an average power output of 84 gigawatts.

    So DC is still off by almost three times the actual amount but what’s a hundred and sixteen gigawatts among friends?

    Maybe he was drinking beer and playing with his dog when he made his calculations.

  11. Lance says:

    That unassailable source of scientific information (cough) Wikipedia gives an annual electrical production of electricity, from all sources, of 4.7 X 10^3 Billion kWh.

    Dividing by 365 and again by 24 gives average power generation of 460 gigawatts, so while 84 gigawatts is nothing to sneeze at, it would “only” supply about one sixth of the current US electrical generating capacity.

    Maybe we should cover the entire state of Arizona. It would reduce the need for a lot of air conditioning, if by nothing else shading the place with giant solar panels.

  12. Lance says:

    Also in the comment of that blog a “Laura” states,

    David MacKay extensively discusses our energy options in the book “Sustainable energy without the hot air”. He has a section on North America. He says that an array of solar panels 400 km x 400 km – about half the area of Arizona – would provide enough power to give 500 million people the average American’s energy consumption, which is 250 kWh per day. He explains his calculations and I think debunks the 35 mile x 35 mile claim somewhere.

    This jibes with my calcs. So I’m calling BULLSHIT!

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