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Wind speed distributions are described by a Weibull function with scale parameter c and shape parameter k, where k near 2 gives the Rayleigh distribution typical of temperate sites. Mean speed is c x gamma(1 + 1/k), and wind power density uses gamma(1 + 3/k) because power depends on the cube of speed.
Weibull mean
Mean = c x gamma(1 + 1/k)
Power density
Power density = 0.5 x rho x c^3 x gamma(1 + 3/k)
Because power varies with the cube of speed, so the distribution matters more than the mean. Two sites with the same average can differ by 20% in energy if their shape parameters differ.
Low k means highly variable wind with strong gusts and calms, typical of monsoon or thunderstorm-driven climates. High k means steady wind, as in trade wind regions, which is easier to harvest.