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The available energy may increase as the cube of the velocity (see below),
but the transfer to the turbine is via momentum transfer and the air
momentum at the blades goes as the square of the velocity (mass per second
increases along with the actual momentum).
But then we have a torque
problem as well, as the wind is hitting different distances from the axis
of rotation (effective lever arm then 1/2 of the blade length?).
generator itself, doubling the rotational speed would double the rate of
flux change and therefore double the induced emf, but that should quadruple
the power through a fixed load V^2/R.
.... Published curves still look (to me) pretty
linear over an appreciable range of wind speeds.