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How Many Windmills Does It Take To Power The World?

Power densities are a measure of the land required for both energy sources and energy users. The current infrastructure matches the small footprint of energy sources against the large footprint of energy users. With the drive toward renewable energy sources, this relationship is about to be reversed with consequences few people understand.

Though nowadays people sometimes rail against the deployment of wind generators because they mar the view, such deployments are the logical outcome of our desire to move away from fossil fuels. We may be concerned about the greenhouse gasses and toxic pollution emitted by coal-fired power plants, but most people do not worry about such plants ruining their view unless they live very nearby. Neither do they worry about coal mines unless, of course, they live in proximity to them, and only a very small segment of the population does.

But windmills can be put anywhere there is sufficient wind. And, that often conflicts with the aesthetic desires of people who must look at them and deal with the attendant disruption that servicing them causes. It’s not just that coal-fired power plants can be plunked down pretty much wherever we want them. It’s also that watt for watt they are far more compact than their equivalent in wind turbines.

Let’s take a 500-megawatt power plant which by itself can power a city of 300,000. (A megawatt is one million watts.) It will sit astride a fairly large plot of land. A coal-fired plant near me is just under that capacity (495 MW) and sits on about 300 acres. Most of that land, however, is essentially devoted to undeveloped transmission right-of-way filled with ponds, woods and streams. Only a small portion is covered by plant facilities including coal storage. I estimate less than 30 acres.

For new wind projects huge 5-megawatt wind generators are just now being deployed. If we take these as typical (and they are not), then using an estimate of the direct land footprint for wind towers of 0.38 acres per tower, we find that we’d need 100 towers covering 38 acres. But wind turbines run at only about 30 percent capacity because the wind doesn’t blow all the time. This compares to about 70 percent capacity for coal-fired power plants. So we need to multiply 100 towers by about 2 1/3 to get the number of towers we’d need to match the operating capacity of one coal-fired plant. That means we’d need about 233 towers with a direct land footprint of 87 acres. That doesn’t seem too bad. And, the land under the turbines is still available for farming and other purposes. The overall direct effects on the land and water are certainly less when compared to the coal plant.

But we’re not done. The spacing between towers is typically at least five diameters of the rotor. That doesn’t sound like much. But for the 5-megawatt towers in this example, the spacing would be 2,065 feet times 232–we don’t need to separate the last tower from another tower beyond it. Then we’d add the diameter of the rotors–413 feet times 233–and we get a distance equivalent to about 110 miles. So, we’d need a line of 5-megawatt turbines stretching 110 miles. In theory, we’d want to split them up and put them in various locations in which the wind blows hardest at different times. But the total length of the line would still be at least 110 miles. If we take the largest separation recommended between towers which is 10 diameters of the rotors, we’d have to just about double that distance.

By comparison most people who live 110 miles from a coal-fired power plant are rarely even aware that it might be a source of electricity for them. And, the plant is certainly not a direct irritation. The lesson here, however, is not one of aesthetics. It is an illustration of the disparity in power densities between those energy sources on which we currently rely and the alternatives now being proposed and deployed.

The power density problem for solar energy is no less daunting. Vaclav Smil, who has investigated the power density problem carefully, described it this way:

[I]n order to supply a house with electricity, photovoltaic cells would have to cover the entire roof. A supermarket would require a photovoltaic field roughly ten times larger than its own roof, or 1,000 times larger in the case of a high-rise building.

When we contemplate renewable energy sources, we rarely contemplate the land area required to deploy them. Just the problems involved in obtaining rights-of-way alone are beyond anything we’ve ever experienced. And, the enormous scale of manufacturing required to produce the panels and wind towers would dwarf our current energy industries. The coal-fired power plant by comparison seems like a wonder of compact energy generation.

This is not to make a case against renewable energy. We will need it and deploy it because we must–either because of the dangers that burning fossil fuels pose to the climate or because of increasing fossil fuel scarcity, or both. The real case to be made here is against business-as-usual. It is hard to see how a transition to a renewable energy society, however rapid and earnest, will give us all the energy we want at prices we will like.

In the graph which follows, it is glaringly obvious that the energy sources we rely on now are one to two orders of magnitude smaller by land area per unit of energy produced than the industries and buildings they service are per unit of energy consumed. That means it takes a relatively small land area to service the enormous area devoted to commercial, residential and industrial buildings. Just the opposite will become the case using renewable energy sources. We will be obliged to devote vast tracts of space–far more vast than the buildings they serve–to support the energy use of our current infrastructure.

This may not be impossible, but it will certainly be costly and socially disruptive. And, that brings us back to the windmills now increasingly dotting our landscape. We can certainly look forward to many more of them. But if we choose to oppose them on the grounds that they are “ugly” or “disruptive,” then we will essentially be choosing a much lower energy future, far below what we’ve come to expect from fossil fuels.

Scitizen, 26 February 2011