## Thursday, March 24, 2011

### Blown Away

I was reading a discussion on green energy recently, in particular wind power, where the following claim was made
enough wind turbines to power the world would cover the surface of the world.
Now, this was quickly decried by supporters of wind power, but the claim has stuck with me. The question on my mind today is: How much of the earth's surface would have to be covered to power the earth with wind turbines?

We can't hope to put an exact number on this, the best we'll be able to do is an order of magnitude.  I also don't know much about wind turbines, so I'll be making liberal use of wikipedia as I go.  Let's start with the size of the wind turbine.  According to wikipedia the largest wind turbine has a rotor sweep diameter of 128 m.  To an order of magnitude, we'll say that our average wind turbine has a diameter of 100 m.  Next we need to know how much power this puts out.  The maximum power of this turbine is ~8 MW.  However, it certainly wouldn't be producing that at all times.  Current wind farms produce around 20-30% maximum capacity.  However, these turbines are careful placed in areas of high wind.  We're not going to get that lucky with our wind dose when we place our turbines haphazardly, so we'll assume they produce at 1% maximum capacity.

According to wikipedia, the world energy consumption in 2008 was 474 EJ (exajoules), or an average power use in 2008 of 15 TW.  To an order of magnitude then, the area we'd have to occupy with wind turbines to power the world would be:

$\left( \frac{(100\text{ m})^2}{1\text{ turbine}}\right)\left(\frac{1\text{ turbine}}{.01*8 \text{ MW}}\right)15 \text{TW} = 2\cdot 10^{12}\text{ m}^2$

That's 2*10^6 km^2, or, in english, 2 million square kilometers.  For comparison, the land area of the united states is roughly 10 millon square kilometers.  So we'd only have to cover 1/5th of the united states with wind turbines to power the entire world (in 2008, no doubt power use has risen since then)!

While that is a lot of space taken up, it is nowhere near the entire surface of the world.

There are, of course, other concerns about wind power.

Note:  maybe the wind turbines are less efficient overall.  Also, I assumed that the footprint was just the square area of the turbine diameter.  I know this is the size of the face of the turbine, but to an order of magnitude I imagine it is correct for the space occupied on the ground.

1. There are limits to how close wind turbines can be without interfering with each other too much. The optimal spacing varies based on prevailing wind direction and terrain -- they can be closer in the cross-wind direction than the down-wind direction, but when wind direction isn't unidirectional, they have to be spaced farther apart.

Your estimate of (100m)^2 works out to be about 2.5 acres. The paper at http://www.powernaturally.org/programs/wind/toolkit/13_windpowerproject.pdf gives two hypothetical windfarms, one using 27 acres/turbine (single wind direction, spacing 3diameters by 10 diameters ("3x10")), one using 59 acres/turbine (two wind directions 90 degrees apart, 7x7 spacing). That's an order of magnitude bigger than your estimate. That places it at 2 US areas to power the earth.

While the spacing allows for farmland use of the ground around the turbines, the landscape is still somewhat dominated by them.

2. Blaise,

Thanks for the information! As I said at the start, I'm rather uninformed when it comes to wind turbines, I was mostly just making up some numbers (a thing I'm remarkably good at). An order of magnitude there takes us to 2 US areas, as you say, which is still not the entire earth, but is a much more substantial piece of land than I estimated.

3. David MacKay's book/site 'Sustainable Energy: Without the Hot Air' has some good and relevant bits on wind power, though specific to the UK:
Wind (estimate of how much the UK could generate from onshore wind)
Offshore wind (similar for onshore wind)
Wind II (more details on how he made his estimates on wind power)
Wiki page on wind (wiki page extending the chapter with numbers from several real wind farms)
Wiki page on Wind II (another wiki page in which somebody criticises a part of his analysis, in a way which would underestimate the amount of wind power)

He estimated wind farms as giving 2.2W/m^2, depending on wind speed and height but not turbine diameter. For existing wind farms, a later blog post gathered some data, according to which "many Scottish wind farms, located on hilltops, have powers per unit area of about 4 W/m2. English and Welsh wind farms are in the range 2-3 W/m2 for the most part, though there are a few in England below 2 W/m2." (http://withouthotair.blogspot.com/2009/05/wind-farm-power-per-unit-area-data.html )

8 W/m^2 is not that much greater, but we'd end up with a somewhat larger fraction of US area if these estimates held for all wind farms. MacKay concluded that wind power would not be enough to give Britain its energy, but he was talking about all our energy use rather than just electricity.

There's a wiki page here - http://www.inference.phy.cam.ac.uk/wiki/sustainable/en/index.php/US - which looks at the US in a similar way, calculating based on individual states' wind data. The author of the wiki page is in agreement with you that
"If the other states were included it is likely that the U.S. could power the entire world (17,110 TWh per year, or an average power of 1.95TW) [6] and only have to use a fraction of its land." and that, as wind power doesn't greatly reduce the area of agricultural land, it would be realistic for the US to generate a significant fraction of its power by wind.

4. The distribution of wind on the earth is a difficult thing to estimate from first principles. Blaise and Bryn more or less get the answer correct (to order of magnitude): http://www.windpoweringamerica.gov/pdfs/wind_maps/wind_potential_80m_30percent.pdf

This is ignoring the issue of distribution, of course.

5. Or, if you look at off shore parks
http://www.lorc.dk/Knowledge/Offshore-renewables-map/Offshore-site-datasheet/Lillgrund-Offshore-Wind-Farm/000027

you can derive that the world must PRODUCE 3 Million single wind turbines. That is a lot of steel, which must be produced that manufactured.

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