Power from Moving Air
Wind turbines convert the kinetic energy of moving air into electricity. The available power in wind scales with the cube of wind speed — doubling the wind speed means eight times more power. This cubic relationship makes wind speed the single most important factor in turbine siting. A site with average winds of 8 m/s has nearly twice the energy potential of one with 6.5 m/s winds.
The Betz Limit: Nature's Speed Limit
In 1919, German physicist Albert Betz proved that no turbine can extract more than 16/27 (59.3%) of the kinetic energy in wind. The reasoning is elegant: if a turbine extracted all the energy, the air behind it would stop, blocking incoming air. The optimal extraction slows air to 1/3 of its original speed, leaving enough flow to clear the rotor disk. This limit is as fundamental to wind energy as the Carnot limit is to heat engines.
Modern Turbine Engineering
Today's utility-scale turbines have blade radii exceeding 80 meters, swept areas larger than two football fields, and rated capacities of 10-15 MW. They achieve power coefficients of 0.45-0.50, capturing about 80-85% of the Betz limit. Variable-pitch blades and sophisticated control systems optimize performance across a wide range of wind speeds, from cut-in (~3 m/s) to cut-out (~25 m/s).
Exploring the Physics
This simulation lets you vary wind speed, blade radius, and power coefficient to see how turbine output changes. Watch how the cubic wind speed relationship dominates all other factors. Push the power coefficient toward the Betz limit and see how little room remains for engineering improvement. The animated turbine visualization shows blade rotation speed scaling with wind conditions.