Wind Turbine Power

Formula

Description

Wind turbine power output depends on the air density (approximately 1.225 kg/m³ at sea level), the rotor swept area, the cube of the wind speed, and the power coefficient. The cubic relationship with wind speed means that doubling the wind speed increases power eightfold, making site selection and tower height critical. The Betz limit sets the theoretical maximum power coefficient at 16/27 (approximately 0.593), meaning no turbine can extract more than 59.3% of the kinetic energy in the wind. Practical turbines achieve Cp of 0.35-0.45.

Variables

• P — Electrical power output (W)
• A — Rotor swept area (m²)
• v — Wind speed (m/s)
• Cp — Power coefficient (0-0.593, dimensionless)

Practical Notes

Air density decreases with altitude (about 1.112 kg/m³ at 1000m elevation) and increases with lower temperature. Small residential turbines (1-5 kW) typically have 2-4m diameter rotors, while utility-scale turbines reach 150m+ diameter with 5-15 MW ratings. Cut-in speed is typically 3-4 m/s, rated speed 12-15 m/s, and cut-out speed 25 m/s.