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Energy Calculation

How many wind turbines?


Thomas M Crawford

8/3/2009

In my energy blog Understanding Energy Issues, I gave an example on how our current Secretary of the Interior gave a speech where he advocated replacing all the coal plants with wind power. Here are the portions of an Associated Press News Report dated 6 April 2009 that I quoted:

Wind turbine near Idaho Falls, ID - winter 2009.

"Windmills off the East Coast could generate enough electricity to replace most, if not all, the coal-fired power plants in the United States, Interior Secretary Ken Salazar said Monday. ... "
“'The idea that wind energy has the potential to replace most of our coal-burning power today is a very real possibility,' he said.  'It is not technology that is pie-in-the-sky; it is here and now.'”"
..... Salazar said ocean winds along the East Coast can generate 1 million megawatts of power, roughly the equivalent of 3000 medium-sized coal-fired power plants, or nearly five times the number of coal plants now in the United States, according to the Energy Department ....."
"...... Salazar could not estimate how many windmills might be needed to generate 1 million megawatts of power ......"

from: Salazar: Wind power can replace 3000 coal plants

In other words, Ken Salazar said, "Dah, I don't know." Obviously neither Secretary Ken Salazar nor the Associated Press did their homework on the subject. So I think I will help them out.

Yes theoretically it is possible to put up enough windmills to generate 1 million megawatts of power. The trouble is: How many windmills will it be? Where will they go? What is the environmental impact? We could go on. Following is an outline of my analysis on how many windmills or wind turbines it would take to generate one million megawatts of power (the output power of approximately 3000 medium sized coal plants).

Currently a reasonably sized state-of-the-art wind turbine is designed to have a peak output power of around 0.5 and 3 megawatts.  There have been a few cases of bigger ones being built, and there are a lot of smaller ones, but this seems to be the range of most of the commercial grade wind turbines.  A company called Vestas® Wind Systems has various models of wind turbines.  One of their bigger models is the Vestas® 112-3.0 MW (click to see their brochure).  This particular wind turbine has a 112 meter blade span (it sweeps out a disk 112 meters (367 feet) in diameter), and it has a maximum output of 3.0 megawatts in a 12 meter/second (27 miles per hour) wind.

Note - Wind speeds of 12 meters/second or 27 miles per hour are classified 6 on the Beaufort wind scale. At these wind speeds, wave heights of 9 to 13 feet or 3 to 4 meters are produced, large tree branches are in motion, power lines whistle in the wind, and umbrellas are difficult to use. This is a very stiff breeze, and is well above the average wind speed.

For 3 megawatt wind turbines, it would take more than 333,000 wind turbines = (1,000,000 megawatts / 3 megawatts per turbine) operating at their peak output power to produce 1 million megawatts of power.

BUT the wind is not a dependable source of energy.  The day I took the above picture, none of the turbines in the wind farm were turning.  This drives up the number of wind turbines needed.  Furthermore, the average wind speed at most locations is well below the speed needed to produce this peak output power.  The average wind speed at most locations is closer to or even less than 10 miles per hour (not 27 miles per hour). You can find some locations with a higher than average windspeed, but not over an area as large as the east coast. This means that the average output power from a 3 megawatt wind turbine will be about 0.2 megawatts (200 kilowatts) (see graph below). The number of wind turbines needed would therefore be about 5 million wind turbines = (333,000 turbines x (3 megawatts / 0.2 megawatts)).  Even if we could select sites to give us an average wind speed of about 15 miles per hour which would allow an average power output of about 1 megawatt from the wind turbine, we would still need 1 million wind turbines = (333,000 turbines x (3 megawatts / 1 megawatt)).  Obviously this is a stupendous number of wind turbines. 

Spacing between adjacent turbines needs to be at least several times the length of the turbine blades to prevent lowering the efficiency of the turbines due to one stealing wind from or causing turbulence for another.  One rule of thumb is that placement between turbines should be about 3 to 7 diameters between adjacent turbines in a direction perpendicular to the wind, and 10 diameters spacing in a direction of the wind. I use a factor of 5 in both directions in my calculations, meaning a turbine will have a footprint on the ground of approximately 1/2 kilometer by 1/2 kilometer or 1/4 square kilometers.  This seems reasonable from the wind farms I have seen.

Where would we place all these wind turbines?  Secretary Ken Salazar mentioned the east coast of the United States, so for illustrative purposes, let’s assume they are placed in the ocean a few kilometers from the coast.   The length of the east coast of the United States (tip of Maine to Miami) is roughly 2500 km.  If we space wind turbines 1/2 kilometer apart along the east coast, we could place 5000 wind turbines in a single row.  1,000,000 wind turbines (assuming 15 mile per hour winds (greater than average)) would require 200 rows of wind turbines along the east coast!  5,000,000 wind turbines (from the average 10 mile per hour winds would require 1000 rows of wind turbines!

The area footprint of 1,000,000 and 5,000,000 wind turbines is 250,000 square kilometers (97,000 square miles or 61,800,000 acres) and 1,250,000 square kilometers (483,000 square miles or 309,000,000 acres) respectively.  (For comparison, the area in ANWR Alaska that was proposed for drilling hand an environmental footprint of only 2000 acres or 3.1 square miles.)

The environmental footprint of this number of wind turbines is much much greater than the status quo, and even much much greater than drilling for oil on the same continental shelf proposed for these wind turbines.   Obviously from these numbers, wind is not the answer to our energy needs!  Wake up government and quit drinking the green kool-aid.


 


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