||We get many questions from individuals
who are interested in having their own wind turbines. This web site
has an equation (see Wind Equation)
that tells people how much power can be expected from a wind turbine of
a given radius at a given wind speed. There is an example that is
apporpriate to the case, of a wind turbine of 7-m diameter in a 5 m/s wind.
A (nameless) lout has evidently never seen textbooks, for he complains about the choice of numbers in the example problem. EGAD! I should have used numbers for giant wind turbines! I quote: "Similarly, no serious industrial wind-power producer would build a wind generator with rotors only 7 meters long in a location where the wind speed averaged just 5 meters per second ... We would seriously question Dr. Hayden's choice of numbers." (I search in vain for where I said that this was meant to represent (A) average wind speed or (B) the power available from industrial-grade turbines.)
OK, let's do it. For a wind turbine of diameter 80 meters cenetered at 100 meters (328 feet) off the ground. Let the wind speed be 10 m/s (22 miles per hour). The power would be 1.0*(40^2)*10^3 = 1,600,000 watts, or 1.6 MW.
At a wind speed of 20 m/s, the power in the wind would be 1.0*(40^2)*20^3 = 12,800,000 W, or 12.8 MW. But wind speed is rarely that high, so one would normally use a 2-MW turbine that would produce constant power at 2 MW from about 11 m/s until shut-off at 25 m/s.
If the turbine rotated at 15 RPM, the tips would move at about 63 meters per second (136 miles per hour).
A wind farm of these machines would have them spaced at about 10 diameters in every direction, that is, 800 meters (about a half-mile) apart.
Note: When wind turbines are replaced by ones of double the diameter, the power per wind turbine quadruples. But so does the land area. Well, that's not quite the whole story. Larger wind turbines are put on taller pillars, and the wind speed up there is usually somewhat higher. Nevertheless, the power production per unit area of land is not particularly impressive.
Wind farms in the US produce power at the average rate of about 1.2 watts per square meter (about 5000 watts per acre). In order to produce an average of 1000 MW --- the power produced by any large conventional (coal, oil nuclear, gas) power plant --- would require about 833 square kilometers (300 square miles) of wind turbines. That's the area of a mile-wide swath of land extending from San Francisco to Los Angeles. Multiply that by about 30 and you have California's electricity.
In 1998, wind turbines in the US produced 3.5 billion kWh. The
US produced a total of 3,367 billion kWh, so the fraction from wind was
0.10 percent --- one part out of a thousand.