Wind Power
The power P of a wind-stream, crossing an area A with velocity v is given by
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It varies proportional to air density ρ, to the crossed area A and to the cube of wind velocity v.
The Power P is the kinetic energy
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of the air-mass m crossing the area A during a time interval
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.
Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
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The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (v1) and behind the rotor area (v2) is v1 / v2 = 1 / 3. The maximum power extracted is then given by
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where cp.Betz = 0,59 is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of cp.Betz = 0,5.
Unit abbreviations
m = metre = 3.28 ft.
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HP = horsepower
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s = second
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J = Joule
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h = hour
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cal = calorie
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N = Newton
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toe = tonnes of oil equivalent
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W = Watt
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Hz = Hertz (cycles per second)
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10 − 12 = p pico = 1/1000,000,000,000
10 − 9 = n nano = 1/1000,000,000
10 − 6 = µ micro = 1/1000,000
10 − 3 = m milli = 1/1000
103 = k kilo = 1,000 = thousands
106 = M mega = 1,000,000 = millions
109 = G giga = 1,000,000,000
1012 = T tera = 1,000,000,000,000
1015 = P peta = 1,000,000,000,000,000
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