Contributed By Eric Eggleston, 5 February 1998

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 V²

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 V³

where:
P = power in watts (746 watts = 1 hp) (1,000 watts = 1 kilowatt)
rho = air density (about 1.225 kg/m³ at sea level, less higher up)
A = rotor swept area, exposed to the wind (m²)
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 V³ 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/m³ at sea level, less higher up)
A = rotor swept area, exposed to the wind (m²)
Cp = Coefficient of performance (.59 {Betz limit} is the maximum thoretically 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 (depends, could be as high as 95% if good)

If there is any single equation that the beginning wind enthusiast should memorize, this is it.

IGET SS 524 N 21 66030 MOZZAGROGNA  CHIETI  ITAIA +39 0872 57123  e-mail iget@igetcol.it

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