Tip-speed ratio

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, ${\displaystyle v}$. 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 larger centrifugal forces.

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

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

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

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