Tip-speed ratio
The ratio of the linear speed of a turbine blade tip to the undisturbed wind speed; three-bladed utility turbines are designed for values of about 7 to 10.
The tip-speed ratio (TSR, symbol λ) is the key dimensionless operating parameter of a rotor:
where ω is rotor angular speed (rad/s), R blade length and v the free-stream wind speed. Each rotor design has a TSR at which the power coefficient Cp peaks; if the rotor turns too slowly, wind passes through the gaps without being used, and if it turns too fast the blades act as a solid disc and flow is diverted around it.
Typical optimum values:
- Three-bladed utility turbines: λ ≈ 7–10
- Two-bladed rotors: λ ≈ 9–12
- Multi-blade water-pumping windmills: λ ≈ 1–2, high torque but low Cp
- Tidal stream turbines: λ ≈ 4–6, limited by cavitation
Variable-speed turbines track optimum TSR below rated wind speed by adjusting generator torque. Above rated speed the controller deliberately departs from it using pitch control.
The upper bound in practice is tip speed itself. Onshore turbines are usually limited to 75–90 m/s for noise reasons, since aerodynamic noise rises steeply with tip speed; offshore machines run at 90–105 m/s, constrained mainly by leading-edge erosion from rain impact. A 230 m offshore rotor at 100 m/s tip speed turns at only about 8 rpm.
Related terms
All terms →- Betz limit
The theoretical maximum fraction of kinetic energy an open rotor can extract from the wind: 16/27, or about 59.3%.
- Power curve
The relationship between hub-height wind speed and a turbine's electrical output, used with a wind speed distribution to estimate annual energy production.
- Pitch control
Rotation of wind turbine blades about their long axis to change the angle of attack, used to regulate power above rated wind speed, start up, and stop the rotor.
- Rated wind speed
The lowest wind speed at which a turbine reaches its nameplate (rated) power output, typically 10 to 13 m/s for modern utility-scale turbines.
- Swept area
The area of the circle traced by a turbine's rotating blades; wind turbine power output is directly proportional to it, and it grows with the square of rotor diameter.