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Question: consider a wind upstream speed u0 passing through the rotor...

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Consider a wind, upstream speed u0, passing through the rotor of a turbine, with n blades each of length R turning at angular velocity W. Assume that this movement disturbs a length d of the airflow, which passes in time tw. i) Calculate the time tb, for a blade to move to the position of the previous blade. ii) If maximum power is extracted when tw=tb, show that the tip-speed ratio del=(2piR/nd). iii) If wind tunnel tests on certain model turbines show that max power extraction occurs when d=R/2, show that the max power coefficient occurs at del=6 for a two-bladed model, and at a del=3 for a four-bladed model.

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