Method of calculation

The calculation method used is mainly suited for horizontal axis wind turbines and delivers only a rough estimate of the annual energy output for this type of wind turbines. In practice big differences can occur, depending on the brand and type of the actual wind turbine.

The energy of the wind can be expressed with the formula:
P = 1/2 x Rho x v³ x A

Where:
P = the power of the wind in Watt
Rho = the density of air, in kg/m³
v = speed (velocity), in m/s
A = the area that is swept by the rotorblades, in m²

For a wind turbine with diameter D and operating at sea level and 15 degrees Celsius (an air density of 1,225 kg/m³) the power of the wind is:
P(wind) = 0,48 x V³ x D²

Betz’ law says that a wind turbine can extract a maximum of 16/27 (in other words 60%) of the energy from the wind :
P (Betz) = 16/27 * P(wind)

To get an estimation of the annual energy output of a wind turbine in kWh the follwing formula is used: E (kWh) = 0.48 * 8760/1000 x Cp x v³ x D²

Where:
E (kWh) = annual energy output in kWh
Cp = efficiency factor of the wind turbine
v = wind speed in m/s
D = rotor diameter of the wind turbine in meters

For this calculation an efficiency factor Cp of 0.6 is used. To get a result in kWh the number of hours in a year (8760) is divided by 1000.

Use a wind map to determine the mean wind speed in your region. In Western Europe mean wind speeds vary between 3.5 m/s and 7.5 m/s. On most wind maps the mean wind speed is obtained at a height of 10 meter in an open landscape.

Changes in hub height and roughness affect the mean wind speed. If we move further away from ground level, wind speed increases. And wind speed decreases if there are more obstacles in the neigbourhood of the wind turbine, for example buildings. The wind speed at a certain height above ground level is:
v_h = v₁₀ * log(h/z) / log(10/z)

Where:
v_h = wind speed at height h in m/s
v₁₀ = wind speed at a height of 10 meter in m/s
z = roughness length of the site in meter

The roughness length is defined in the following table:
Roughness length (meter), description
0.001: Ice, water surface
0.03: Grass, airports
0.2: Trees, hedgerows, scattered buildings
0.25: Rough terrain
0.5: Villages, very rough terrain
1: Cities, forests
2: City centre, skyscrapers

The map below is based on wind speed heights of 50 and 45 meter. We have corrected these wind speeds for a height of 10 meter above open grassland.

No rights can be claimed regarding these calculations.

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