Discussion
If 'a' is the fractional wind speed decrease at the wind turbine, the maximum extraction of power from the wind occurs when 'a' is equal to
Answer: B
Maximum power extraction from the wind occurs when the fractional wind speed decrease at the turbine is 1/3. Treating the turbine as an actuator disc, the power coefficient is proportional to a(1 - a)^2 (with a as the fractional speed decrease); differentiating and setting it to zero gives a = 1/3, and the corresponding maximum fraction of the wind power extracted is 16/27, about 59 per cent, the Betz limit. At a = 1/2 the coefficient is lower, 1/2 x 1/4 = 0.125 against 4/27 = 0.148, and at a = 1 the wind is stopped and no power is extracted.
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