Betz Limit Wind Turbine Aerodynamics

Energy Engineering

How It Works

Wind turbine rotors extract kinetic energy from moving air masses, causing downwind stream-tube expansion and flow deceleration. Betz's law establishes that the theoretical maximum aerodynamic power extraction coefficient is 16/27 (approximately 59.3%) at an optimal axial induction factor a = 1/3. Any attempt to extract more momentum chokes the airflow around rather than through the rotor.

Governing Equation
C_p = 4 · a · (1 - a)² ≤ 16 / 27 ≈ 0.593  |  P_wind = (1/2) · ρ · A · v³ · C_p