Hmm, I can imagine a 2 meter blade intercepting 4x the area of the moving air column and capturing 4x the kinetic energy. KE is proportional to the square of velocity. I'm having trouble imagining how a column of air moving 2x the speed generates 8x the power. Does it mean 2x the speed mean 8x the energy that can be captured?
I can't actually remember the explanation but thinking about it E=1/2mv² but when the air is moving twice as fast the mass of air passing the wind turbine would also double. Sounds plausible at least.
That's exactly the reason why. Kinetic power of each air molecule scales with the square of its speed, and the number of air molecules passing over the wing scales linearly with speed.
