13 December, 2005


Idle back-of-the-envelope calculations to save the world are a favorite pastime of mine, the product of, believe it or not, long road-trips with my family, where my dad would work us through calculations such as the circumference of the world at our latitude and the like. Here's a fun one:

In the latest New Scientist, a reader inquires about painting roofs white to increase albedo and thus prevent global warming. Someone responds to inform us that about 3% of the world is covered by buildings. A third says that we would do better to instead cover the world with photovoltaic cells.

Well, let's see how well we can do with this. Let's restrict ourselves to the U.S., so we can get plenty of data. Let's assume the U.S. has a proportionate number of buildings according to its population; probably more, but it's always better to be conservative. This is 5% of 3% of 510,065,284.702, which is the surface area of the Earth in km2. For some reason I happen to know off the top of my head that the average incident sunlight in the U.S. is 200 W/m2 (I don't know how this stuff happens to me). Which means, if we do some multiplication, that American rooftops are drawing, on average, 1.53e14 W. Let's say a photovoltaic cell has an efficiency of 16%; this allows us to produce 2.44e13 W, or in a year, 7.7e17 kWH. To put this figure in perspective, the U.S. consumes something like 3.6e12 kWH of electricity annually. In other words, even if we only did this with 0.1% of buildings, or if the process is a thousandfold less efficient, we would still be producing two hundred times as much power as we consume annually. Sounds like a good idea!


I have arrived with some stuff!
- Was it a joke? If 3% of the world is covered in buildings, that is 10% of the land area. Given the presence of what, a dozen? buildings in all of Canada, the Sahara, Antarctica, and Russia combined, the rest of the land must be like 20% buildings. Back of the envelope here, ok?
- PV cells are currently very low-albedo, even lower than normal roofs. So they cause problems. Solved by zinc-oxide or titanium dioxide PV cells, but not for a few years.
- There is not enough silicon to make nearly as many PV cells as you describe. Plus, Si cells are made with very polluting, energy-intensive, and worker-unfriendly vapor deposition techniques.

Better to cover the earth with CHEESE. mmmmmmm, cheese. 

Posted by hedgehog

so it seems like the better answer is to force passive solar at gunpoint. 

Posted by chromo

Hmm, your envelope is better than mine. I shoulda thought about that 3% more before I trusted it so foolishly. No matter! Let's come up with a minimal number:

Let's stick with homeowners in the US, since I can come up with figures for that. The average home is 200 sq m; say a third of this is roofspace. There's 73 million homeowners in the U.S. This gives enough roofspace to still put me about a factor of 150 from the figure I give above. I still maintain it's a good idea.

As to the photovoltaics, you're right - silicon is a shitty technology. But there are likely more reasonable, less polluting alternatives to microchip-grade silicon waiting to be discovered. Heck, photosynthesis is 12% efficient and it's purely organic. We'll just fill in that blank when we get to it. 

Posted by saurabh

following up on hedgehog, the total LAND area of the world is 1.5 * 10^8 km^2. 3% of this is 4.5 * 10^6 km^2. divide by 6 billion people and that's 7.5 * 10^{-4} km^2 or 750 m^2 per person.

this actually doesn't seem totally out of hand for the US if you include roads and commerical buildings. this site
http://phe.rockefeller.edu/tread/ says that 5% of non-federal land in the u.s. is developed, but that includes roads, and can include building cover as low as 30% (i think).

here's a quote that shows 750 m^2 is not so far off
In the 48 American states the covered land per capita falls from more than 2,000 m2 (about a half acre) in states where travel is fast, like Montana or Nebraska, to about 600 m2 in slower, more urban California or New York with their similar population densities. The covered land per dollar of gross state product is also less in the more populous states.
incidentally, i would say this supports my earler claim that urban america is less environmentally damaging than rural america, though i realize it doesn't account for trade.

Posted by aram

I have much else to say, later, but I wanted to note that the Earth is 15-25% Silicon---and extracting silicon from its natural form of silica (sand, say) isn't that hard. The pollution problem is not really navigable, though it needs to be fairly compared to nuclear and coal and even wind and damming, but the worker-friendiness is simply a matter of being careful and paying and treating people properly---it's not an innately dangerous job like coal mining. The energy payback is a major issue, but current technology makes up for its energetic cost in 3-5 years--ammortized over a conservatively estimated lifetime of 20 years, that's a .25 decrease in efficiency. By my sleepy count Saurabh had about 6 orders of magnitude to lose before the idea lost significance. If we trust his newer calcs, he's still got 3 or 4 orders of magnitude to play with, as far as math and physics go. That's good b/c there are still factors like the lack of flat roofing, the conflation of the distribution of sunlight with the distribution of appropriate roofing, the impact of temperature and moisture on efficiency, and of course the albedo that started it all. Economics is another matter, though I am deeply suspicious of all models and estimates that attempt to scale up costs from today's prices, ignoring the fact that we're in an absurdly high-entry and low demand regime. Clearly, still worth some thought.

But yeah, I might go to extremes of sycophancy for the person who can figure out how to efficiently hook chloroplasts upto a battery, bypassing carbon altogether.


Posted by saheli

The earth might be 25% silicon, but the moon is 82% cheese.

mmmmmmm. cheese.

Flat roofs aren't as good as south or west-facing angled roofs. At the latitude where I'm sitting (37 degrees), you lose about 15% of the efficiency of a solar cell just by putting it on a flat roof. This is what I learned yesterday from a solar installer, though who knows. Maybe she didn't know what she was talking about.

I like chloroplast cheese. 

Posted by hedgehog

Flat roofs aren't as good as south or west-facing angled roof 

That's true, but it depends on the angle. You can always angles something up with a stick on a flat roof. It's more difficult to mess with angle and facing on a . At least I thought that's what my solar installer friend told me this summer, but that was a while ago. :-)

Saurabh, I think we need to feed Hedgehog more. Apparently  he needs to double his weight at this time of year and likes a treat of cheese, finely chopped. That might explain the subtle dropping of hints in comments.  

Posted by Saheli

You can always angles something up with a stick on a flat roof. It's more difficult to mess with angle and facing on a .  

On a sloped roof. sorry.  

Posted by Saheli

you can also put solar cells on a motor that tracks the sun. i think the energy investment would be trivial, but the increased complexity/cost of the device might make things worse.

also, under reasonable assumptions wind is already more economical than coal (i.e. if we remove various market distortions). 

Posted by aram

tracking the sun wouldn't have to be complex or require a motor. there are plenty of materials that can expand or contract based on heat or electrical activity or what not. an artificial plant stem would be pretty easy if the "leaf" weren't heavy. put out a grid of leaves in a basically level-to-path-of-sun position and let each leaf's "stem" determine its direction based on light hitting cells at the edges or something like that.

i've seen studies of ocean wave energy capture that say similar things about practical exploitable potential. are they BS? 

Posted by chromo

The best place to look for info on tidal energy is Mile Rock, just off San Francisco. There is a hazard to navigation in the area that is the result of an early tidal energy generator. It hasn't been maintained or removed -- because the ocean is scary. Working in frigid salt water is difficult.

Artificial plant stems -- nice idea. You could work on that after you finish the music collection? 

Posted by hedgehog

i was interested in the utility of portuguese sea monsters .

music collection status report. initial research: complete. methodology development: complete. listening time integration: complete.

so now all i need to do is get a suit and a chemistry degree and solar cells will spring up like petunias across north america. 

Posted by chromo

:-( No offense Chromo, but that seems like a big mess in the ocean, horribly perfect for entangling a pod of whales in. Let's stick to the solid-state petunias please. . . 

Posted by Saheli

NASA analyzed satellite imagery last year and concluded that 112,610 square kilometers of the contiguous 48 states are covered by buildings and roads (almost the size of Ohio). I don't know how much of that is buildings and how much is roads, but since you're doing back-of-envelope calculations you can probably assume a 50/50 split without affecting your accuracy much.

Incidentally, others have attempted similar calculations in the past. See, for example, http://www.nrel.gov/ncpv/land_faq.html . 

Posted by Alan

Hooray for Alan, real facts with sources and everything! Here's another fact: it's not a 50-50 split. Figure-ground drawings of the automobile-oriented landscape -- in which buildings are black and everything else left white -- show that the hard surface, the areas with buildings or road, can often be as low as 10% building. In downtown Albuquerque, that was true even 10 years ago before an urbanist renovation got going. In Houston, I've heard the number as being around 80% roads and parking lots.

Hey, how about a thermoelectric road substrate? It's the perfect place for it -- roads are very often warmer than the underlying soil. Thermoelectrics are very cool -- did you know that heat is often conducted with electrons? Somehow I did not know that until recently. Of course if thermoelectrics get cheap enough to put in roads, we will also have them in buildings, clothes, exhaust pipes, and all sorts of other places, so big installations like road beds won't be all that necessary. 

Posted by hedgehog

Once I read a proposal that we should just save the world by putting Sterling engines  everywhere. Might as well make use of these urban heat islands. 

Posted by saurabh

Saurabh, I think Sandia wants to put Stirling engines in the desert , and use parabolic mirrors to catch the sunlight. Their system looks excessively complicated enough to be only somewhat interesting to the lay reader.

I worry slightly about plans that want to use the ground as a giant heat sink, b/c I'm not sure we understand very well how small temperature changes will affect soil ecology. I suppose in very rocky, barren places it can't hurt as much as global warming is now. . .  

Posted by Saheli

(i don't take offense - in fact - a previous career has left me with a lifetime supply of it, which i am currently busy distributing for tax purposes to a variety of seasonal charities)

(however, as i can find no mention of concern for whales elsewhere, perhaps the possibility of decreasing the irradiation of the sea and the dilution of breathable air would offset the whales' additional discomfort) 

Posted by chromo

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