The Physics of Wind Power

Moving air carries kinetic energy, and the power available to a wind turbine is P = ½·ρ·A·v³: density times swept area times the cube of wind speed. The density term is small but constant; the area grows with the square of blade length; and the cubed speed dominates everything.

Why v³ Changes Everything

Because power scales with the cube of speed, a site averaging 7 m/s produces nearly twice the energy of one averaging 5.5 m/s — and a 14 m/s gust carries eight times the power of a 7 m/s breeze. Turbine placement, hub height, and cut-in speeds are all engineered around this cubic sensitivity.

The Betz Limit and Reality

Albert Betz showed in 1919 that a rotor can capture at most 59.3% of the wind's power — extracting more would stop the air completely. Real turbines achieve 40–50% of the available power, and their annual energy output lands at 30–45% of the rated figure due to wind variability. Both corrections are visible in the calculator's output.