Harvest the Wind
(Page 2 of 7)
June/July 2002
By Michael Hackleman and Claire Anderson
THE MATH OF WINDPOWER
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Several variables—including the wind plant's size and design, and the site's wind speeds and duration—determine how much energy you can harvest from the wind. Power from wind is calculated using the formula:
Power = Swept area of rotor x Wind velocity3 x 1/2 Air density
You can increase power either by using a wind plant with a larger rotor or by placing your plant where it will receive stronger winds—usually on a hill or taller tower. (The third variable in the power formula, air density, doesn't vary much and isn't something you can control.) Note the total power in the wind is a function of the cube of the wind's velocity; just a small increase in velocity results in a much larger increase in power. For example, a 2.6 mph (a 26 percent) increase in wind speed from 10 mph to 12.6 mph will give you a 100 percent increase in power. To achieve this same increase using a larger rotor is usually a more expensive choice than placing a smaller rotor on a higher tower where it will receive stronger winds.
TOWER POWER
In general, wind plants should be installed on a tower at least 20 feet taller than the tallest object within 400 feet. A tall, lightweight, guyed tower topped with a small (1-kilowatt to 10-kw) wind plant usually yields more bang for your buck than a larger wind plant positioned on a shorter tower.
There are several reasons to mount a wind plant on a tall tower. One is to gain clearance above trees, houses and other obstacles that create turbulence and reduce the power of the wind reaching the wind plant. Wind acts like water in the way it flows across any topography. It is slowed by obstacles such as trees, ridges and rocks, and is channeled by the overall shape of the terrain.
Not only does the wind get smoother at higher distances above the ground, it also increases in velocity. Most windspeed measurements are taken at a height of 6 feet because that's where wind affects us. But the wind speed is always greater higher above the ground. For example, a wind of 8 mph measured at 6 feet indicates a speed of 11.4 mph on a 36-foot tower and 13.9 mph for a 96-foot tower. So what, you say, we've raised the tower 60 feet higher, only to increase the wind speed by a mere 2.5 mph?
Remember the wind power formula: The power of the wind increases with the cube of the wind's velocity. So although the wind speed on top of a 96-foot tower increases just 25 percent compared to the 36-foot tower, the power of the wind reaching the taller wind plant increases 100 percent. The cost of an additional 60 feet of tower and rigging is generally less than the larger wind plant needed to give the same power increase. (To calculate wind power at different heights, visit the Windpower Web site.)
SIZING YOUR SYSTEM
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