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: $$\left( \frac{(100\text{ m})^2}{1\text{ turbine}}\right)\left(\frac{1\text{ turbine}}{.018 \text{ MW}}\right)15 \text{TW} = 2\cdot 10^{12}\text{ m}^2$$ That's 210^6 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.

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