## Wind Power Calculation

Because air has mass and it moves to form wind, it has ** kinetic energy**. You may remember from science class that:

**kinetic energy (joules) = 0.5 x m x V ^{2}**

*where:*

m = mass (kg) (1 kg = 2.2 pounds)

V = velocity (meters/second) (meter = 3.281 feet = 39.37 inches)

Usually, we’re more interested in power (which changes moment to moment) than energy. Since **energy = power x time and density** is a more convenient way to express the mass of flowing air, the kinetic energy equation can be converted into a flow equation:

*Power in the area swept by the wind turbine rotor:*

**P = 0.5 x rho x A x V ^{3}**

*where:*

P = power in watts (746 watts = 1 hp) (1,000 watts = 1 kilowatt)

rho = air density (about 1.225 kg/m^{3}at sea level, less higher up)

A = rotor swept area, exposed to the wind (m^{2})

V = wind speed in meters/sec (20 mph = 9 m/s) (mph/2.24 = m/s)

This yields the power in a free flowing stream of wind. Of course, it is impossible to extract all the power from the wind because some flow must be maintained through the rotor (otherwise a brick wall would be a 100% efficient wind power extractor). So, we need to include some additional terms to get a practical equation for a wind turbine.

*Wind Turbine Power:*

**P = 0.5 x rho x A x Cp x V ^{3} x Ng x Nb**

*where:*

P = power in watts (746 watts = 1 hp) (1,000 watts = 1 kilowatt)

rho = air density (about 1.225 kg/m^{3}at sea level, less higher up)

A = rotor swept area, exposed to the wind (m^{2})

Cp = Coefficient of performance (.59 {Betz limit} is the maximum theoretically possible, .35 for a good design)

V = wind speed in meters/sec (20 mph = 9 m/s)

Ng = generator efficiency (50% for car alternator, 80% or, possibly, more for a permanent magnet generator or grid-connected induction generator)

Nb = gearbox/bearings efficiency (could be as high as 95% if good)

*By Eric Eggleston, 5 February 1998*