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How Many Windmills Does It Take to Power the World?
26 Feb, 2008 10:51 am
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.
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.
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I think it depends on not relying upon one solution (ie, strictly windmills) and decreasing energy consumption.
[Response] I wholeheartedly endorse your notion that we must reduce energy consumption. Of course, I'm not proposing just one solution to our energy challenges, but rather using windmills here as an illustration of the power density issue. That said, other renewables, whatever else their merits may be, suffer from the same lack of power density. Biofuels, for example, (which are represented by photosynthesis in the graph) are even less dense than windmills by an order of magnitude. Only nuclear energy would be able to approach power densities we enjoy today and even then the supply of uranium will turn out to be quite limited unless we build breeder reactors (which I count as highly unlikely because of the weapons proliferation implications).
This might mean that we should be using the vast sea areas.
[Response] I think you are correct. Certainly, wind and solar can both be deployed at sea and already are in some cases. But this will be at considerably higher cost than on land. Thus my concern that we will not get all the energy we want at prices we like.
It's important to point-out the sheer scale involved for renewables compared to concentrated forms of energy, e.g. fossil fuels or nuclear. For example, it can be worked out that to produce enough hydrogen to run a putative hydrogen economy for the UK would require the equivalent of a "belt" of 2 MW wind turbines around the entire UK mainland about 20 km thick.
I agree, we will end up with a mixture of resources, but cutting energy use through a greater efficiency in how we use it, must be a central part of the solution to the energy crunch that we can no longer avoid.
Ok this technology is not mature, stocking the energy produced remains an issue, and, Chris, I'm not sure this technology would be efficient in countries like UK...
First, you forgot to discuss the land for the coal mine, as well as the land for the ash and the tailings. There is mined land that is reclaimed well. Then there is land that is poorly reclaimed. And then there is West Virginia mountain-top removal.
You did not discuss the pollutants from the coal plant in any detail, which dwarf those from renewables by orders of magnitude.
And I am not sure the space from some renewables is as bad as you imply. For instance, it is estimated that Concentrating Solar Power technologies have 54,000 suitable square miles in the American desert (high insolation, low slope, away from cities, etc.) This is less than half the size of New Mexico. It is enough to theoretically provide several times more power than the country uses. (Whether we should actually have a national grid is another question.)
Regarding PVs, there is a good report that attempts to estimate potential on buildings given real-world limitations. (See ?PV Grid Connected Market Potential Cost Breakthrough Scenario? on the Energy Foundation?s Web site: www.ef.org/documents/EF-Final-Final2.pdf .) My estimate, derived figures in this report, is that in Texas, where I live, PVs would provide about 25% of the 2006 net generation in the state by 2010. (Sorry about the inconsistent years, but EIA does not have projected 2010 use.) This study analyzes buildings, and accounts for size, shading, and orientation. The study does not analyze the huge potential in non-populated areas.
Regarding your 110 miles of wind lines, if I did the math right, this is only about 6 SQUARE miles of rural area, which is the likely way such a wind farm would be organized. This is a lot of land, but in a rural area, it is not outrageous.
I agree with your point about efficiency, but land will not be the limiting factor for renewables in the foreseeable future, at least in the U.S.
[Response] Thanks for your thoughtful comments. You make many good points. Certainly, the pollution from wind and solar will be far less, even when you count the manufacturing processes. On the other hand, if you count the land area for coal mines then you must also count the land area for the myriad plants involved in the production of wind turbines and solar cells and any mines which are needed to mine the materials used to make these. Also, we should keep in mind that one coal mine may, in fact, be supplying many power plants so that only a fraction of most mines could be apportioned to any one power plant. This is not to excuse the tremendous devastation that often comes from coal mining. But I am attempting to isolate a prospective problem for renewables which I address in further detail below. Perhaps concentrating solar power technologies will turn out to be very compact and useful. Not every place in the world, however, has sites suitable for such technology. I'm not sure how you did the math on total land area for my hypothetical wind farm, but placing one wind generator in front of another in the path of the prevailing wind on your 6 square mile windfarm seems implausible to me. Typically, they are put in a line so as not to steal wind from one another. Of course, if the distance between them is great enough as they face the prevailing wind, as I have seen in some places, then this could be done. But I doubt that they could be crammed into the area you suggest and still retain 30 percent efficiencies. I agree with you that land is not the limiting factor, at least not in North America. But the main complication I see is the lack of public land. Most of the renewable energy generation will have be placed on private land. Of course many owners will welcome the opportunity to participate in generating renewable energy. But as we have already seen, many will not. Negotiating the necessary rights-of-way is going to be an enormous challenge and engaging in eminent domain proceedings where rights-of-way cannot be secured will be highly controversial and politically explosive. If we decide to site power generation close to users who are concentrated in the cities, our difficulty with rights-of-way and adequate land become far more pronounced. New York City simply doesn't have the necessary rooftop space to supply its buildings with solar-generated electricity. I'm not saying it is impossible to devote the necessary land space to renewables. I'm saying that there are complex land use, property rights, and governmental powers issues that will not be easily resolved.
Second is the matter of the "entropy subsidy" provided by fossil fuels. It is highly energy-dense fossil fuels which provide the energy boost needed to exploit low-density energy sources like wind and solar. A serious flaw in thinking in this area is the belief that nuclear has a high energy density. Nothing could be farther from the truth. Uranium ore cannot be used in its original state because the uranium is in far too diffuse a state to start and sustain a reaction. That is the reason that much energy is expended in the enrichment process. Again, fossil fuels to the rescue. A considerable amount of fossil fuel energy is expended in subsidizing this high-entropy energy source, from mining to enrichment, fuel fabrication, nuclear power plant construction and servicing, waste management, and ultimately the demolition of decommissioned plants.
Unfortunately, these points are almost totally ignored in the discourse on renewables and nuclear. And as you can see, this reality about our true dependence on fossil fuels makes our energy situation far more serious than people realize.
[Response] Sadly, you are correct about the huge subsidy that fossil fuels give to renewable production. I, like you favor, the quick and ubiquitous deployment of renewable energy generation while we still have the fossil fuels to do it. You are also correct about uranium and nuclear power which are highly dependent on fossil fuels for their production. I would add just one thing. It is conceivable to me that breeder reactors could overcome this problem by giving us very long-lived sources of nuclear-generated electricity (perhaps thousands of years) and assuming we electrify transportation and everything else that can be electrified. However, I suffer from no illusions that we will pursue this technology vigorously because of the weapons proliferation implications and the anti-nuclear sentiment in many countries. I do not think we should pin our hopes on a nuclear future of any kind, but rather I advocate proceeding directly to a renewable energy society.
Yes, many wind farms do place the turbines in a line. But my (exaggerated) point is that you are not going to locate these turbine lines 110 miles from each other. I have included a Web link to a picture exhibiting my point. The turbines are in a line, but there are several lines in the wind farm that are horizontal to each other.
RE: Concentrating Solar Power, you are correct that there are many areas of the country where these are not appropriate. CSP is mainly for desert areas with long periods of cloudless sun. At this point, I am skeptical of exporting CSP from the American Southwest to New England. But I will keep a (slightly) open mind to this strategy.
And yes, with our current infrastructure, all manufactured materials have some amount of fossil fuel, including renewable energy equipment. But if you want to get into Energy Return on Energy Invested, or Fossil Energy Return on Energy Invested, I think you will find much less embodied coal in a wind turbine than is used in a coal plant.
Regarding the lack of public land for siting renewables, in Texas, location on private land so far has not been a show stopper. There are plenty of farmers and ranchers that want the yearly royalties to supplement their income. Time will tell if this continues.
We can not, obviously.
So, there are environment friendly energy sources on one side, AND an intelligent way of life on the other.
Western way of life is actually very stupid, no doubt about that. Think about minimalism as a lifestyle. "As less as needed" unstead "as much as possible". This new approach allows humanity to change from the actual, self-killing behaviour to a futuristic, minimalistic economy.
It's the efficiency, stupid.
Back to your original subject, land area needed. The best solution is multiple use. It is easy to see this with PV mounted on roofs, and BIPV (Building Integrated PhotoVoltaics), here we are not increasing the anthropic area footprint because we were already using the area for other purposes. In the US we have already paved an area equal in size to a medium sized state. If we can find a way to utilize even some of this area for energy generation without compromising the original purpose (roads, and parking lots), then we have a very large available area resource. One such possibility: look up CoolEarthSolar. Their concept uses cable mounted mylar balloons for concentrated photovoltaics. The land underneath such a system is not used up by the system (although the aesthetic value will be affected). For instance, if such a system were deployed over a parking lot the main effect would beto partially shade it. Another really neat possibility for area dual use, is Nuclear and high altitude wind. The later uses kite type technology to harvest high altitude(500-1000)M wind. An objection is the need to exclude aircraft. The claim is made that the nofly zone around a Nuclear power plant contains about as much wind potential as the Nuclear output. If airspace were the only cost, it would be a no brainer to reuse the excluded airspace for high altiutude wind.
There are lots of ways to harvest energy from our environment. Imagination is perhaps a more critical resource than land area.
It should be the patriotic duty of every American to reduce dependency on oil. Think of the money that would be saved and also the lives.
Also we could put sea platform up to place more turbines on.
As a rule you can site about 10 MWs of wind to the section (640 acres) and 100MW of solar to the section. Capacity ratios for wind are about 35% and solar capacity factors are about 20%.
Using 10% efficiency cells, A house will receive about 1700 Kwhs annually per 100 square feet. If the average annual consumption of a 1500 square foot house is 17,000 Kwhs (it can be much less), you will need about 1000 square feet, or a little more than 2/3rds of the roof .
Most coal plants have larger footprints than a half a section. Our 1800 MW plant is about 15 sections.
In my review of power plant footprints, I have found that the existing footprint of the power plant , cooling lake, the mine, and the extra roads is often the same order of scale as the solar power footprint.,
When you include using rooftops and parking lots, the solar footprint could actually be less.
I had been thinking about trying to calculate what your article presented.
I suspect the 110 mile long wind turbine array for 500 megs will open some eyes. (I think you were a bit harsh in assigning only a 70% capacity factor to your fossil fuel power plant?)
While I had suspected that super markets used much electicity I was still rather surprised at just how much it was.
Great article. Don Hirschberg
[Response] For coal, the only fossil fuel I mention, what the utility industry calls "capacity factor" was 73 percent in 2006 according the U. S. Energy Information Administration. An article in a major utility trade journal pegs that number at around 72 percent in 2003.
Everyone in my family are getting old they used to farm the land however now they are not doing anything. I live in the city and pay taxes on the and I am considering getting into the Wind Farming business.
What is the best way to get into the business?
A friend of mind told me that they have a friend who was getting paid 20 thousand a month for thier wind.
Is that realistic to be paid 20 k monthly?
What would be the best average wind conditions in a particular area to get into this business?
I figure the new economy the new government is proposing will make this a more attractive proposition for landowners ?
If interested in talking to me. Please call me at 2147537882. I have been contacted by other companies. I want to leverage some insight on this business or entertain offers.
The Department of Energy's National Renewable Energy Labs (NREL) suggests that a 13mph average is about the minimum threshold for commercial wind farms. However, an acquaintance of mine who actually develops utility-scale wind farms in Wyoming told me that even 18mph is barely break-even.
Other factors will affect your site's viability, such as altitude (lower altitude means denser air and thus more energy per swept area), temperature (low temperatures also make air denser), capacity factor (dependent on how steady the wind is), terrain, access to the site, and distance from the grid.
We've been measuring an average of 14mph and a capacity factor of 26%, but at an altitude of 8000 feet and 17 miles from the grid, we haven't generated much interest among developers.
What is not taken into account is volume...the Gulf Stream moves 5 Billion gallons per minute. Do a calculation and you will see that a drop of 0.5 degrees will provide all the worlds? energy needs.
The energy is there for the taking; of course it will not be easy; CERN Large Hadron Collider (LHC) is not easy.
This process will be on the scale of CERN. Who will step up to the plate?
Well actually it was 18m. It costs 190,000 euros or $CDN303,902.02. It's a machine, reasonably complicated one, and so probably takes a lot of mechanical work to keep going. Oh and there's land too, gotta buy land to put it on. Oh dear, need permits, yup we do, and the lefties have municipalities tied so tightly in red tape that ought to be another hundred grand. Then we need to tie it to the grid because the windmill doesn't actually squirt out the old 220v 60 cycle house current, no it does not. Wires, controllers, transformers, rectifiers, engineers, bric a brac, coupla hundred grand web design more. Then there is a bit of this and some that and plenty of so on. About another hundred grand I'd guess. And then after 10 years it's scrap, gotta have a do-over.
I would bet that windmill will cost a million to build, place and connect. I'll also bet that 2/3 or more of its energy comes out at night or some other time when it is useless. Why would I place such a bet? Because the left always lies.
My final estimate: Energy for 21 Dutch homes at a cost of 15 or 20 times any large scale competing energy source. By which I mean coal, oil, natural gas, hydro and nuke. And when I say 'cost' I mean environmental damage because money is how we measure stuff like that.