Tip-speed ratio

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The tip-speed ratio, λ, or TSR for wind turbines is the ratio between the tangential speed of the tip of a blade and the actual speed of the wind, v. The tip-speed ratio is related to efficiency, with the optimum varying with blade design.^[1] Higher tip speeds result in higher noise levels and require stronger blades due to larger centrifugal forces.

${\displaystyle \lambda ={\frac {\mbox{tip speed of blade}}{\mbox{wind speed}}}}$

The tip speed of the blade can be calculated as ${\displaystyle \omega \cdot R}$, where ${\displaystyle \omega }$ is the rotational speed of the rotor and R is the rotor radius. Therefore, we can also write:

${\displaystyle \lambda ={\frac {\omega R}{v}},}$

where ${\displaystyle v}$ is the wind speed at the height of the blade hub.