Wind Turbine TSR & Cp

The Tip Speed Ratio (TSR) is the ratio of the blade tip speed to the free wind speed: TSR = (ω × R) / V_wind. It is the most important dimensionless parameter in wind turbine design — it determines the power coefficient (Cp) and hence how efficiently the turbine extracts energy from wind.

The theoretical maximum power coefficient is 0.593, known as the Betz limit. No wind turbine can extract more than 59.3% of the kinetic energy in wind, regardless of design. Modern large wind turbines achieve Cp values of 0.45–0.50 at their design TSR.

Each turbine type has an optimal TSR. High-speed, low-solidity turbines (like 3-blade HAWT) operate efficiently at TSR of 6–10. High-solidity slow turbines (like multi-blade water pumpers) operate at TSR of 1–3.

TSR by Turbine Type

TSR and Blade Design Connection

Higher TSR means the blades move faster relative to the wind. At high TSR, blades need a smaller chord (width) and lower pitch angle. The number of blades also drops — single or two-blade turbines can operate at higher TSR than three-blade designs. The trade-off is noise and fatigue loading: high TSR turbines have higher blade tip velocities, increasing aerodynamic noise significantly.

For small wind turbines (under 5 kW), a TSR of 5–7 is practical. Going above TSR 8 on small turbines causes structural and noise issues that outweigh the marginal efficiency gain.