# Windmills

How much power can you get from a windmill? Windmills have long been used to pump water from wells, and are now being used to generate electricity on a somewhat wide scale. The most efficient windmills are a little under 50% efficient, and it is physically impossible to exceed 59%. For an excellent windmill (50% efficiency) the power available is given by the following formula:

where the R is the radius of the propeller (1/2 of the diameter), and the v is the wind speed. The symbol means that the power is approximately equal to the value calculated on the right; however, the formula is correct for only the very best wind turbines, and only for moderate wind speeds.

Most wind systems are designed to produce constant power above a certain wind speed.  For example, a 200-kW system will produce power according to that formula until the wind speed reaches, say, 14 m/s, after which the wind turbine produces 200 kilowatts for all wind speeds until, say, 25 m/s, after which the machine must be shut down lest it blow apart.

The formula is an overestimate for all but the very best wind turbines.  For example, one popular 1-kW unit produces only half as much power as the formula predicts.

Example