Tip-speed ratio

The tip-speed ratio, X, 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, ${\displaystyle v}$. The tip-speed ratio is related to efficiency, with the optimum varying with blade design. Higher tip speeds result in higher noise levels and require stronger blades due to large centrifugal forces.

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

when wind speed is specified in meters/second. –

The power coefficient, ${\displaystyle C_{p}}$ is a quantity that expresses what fraction of the power in the wind is being extracted by the wind turbine. It is generally assumed to be a function of both tip-speed ratio and pitch angle. Below is a plot of the variation of the power coefficient with variations in the tip-speed ratio when the pitch is held constant:

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