# Wind Power

## Power generated from the wind

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The theoretically available power in the wind can be expressed as

P = 1/2ρA v^{3 }(1)

where

P = power (W)

ρ = density of air (kg/m^{3})

A = area wind passing through perpendicular to the wind (m^{2})

v = wind velocity (m/s)

Be aware that the density of air decreases with temperature and altitude and that the major factor in power generation is wind velocity.

*a 20% increase in the wind velocity - increases the power generated with 73%*

Theoretical and rated wind power generation for typical windmills are indicated in the "wind speed-power curve" below. Cut-in wind speed, rated wind speed, shut-down wind speed and rated power for windmills with 20% and 40% efficiency are indicated.

### Actual available Power

can be expressed as

P_{a}= 1/2 ξρA v^{3 }(2)

where

ξ= efficiency of the windmill (in general less than 0.4, or 40%)

### Related Mobile Apps from The Engineering ToolBox

- free apps for offline use on mobile devices.

### Online Wind Power Calculator

The calculator below can be used to calculate available power from a windmill:

### Generated Wind Energy

The energy generated by a windmill depends on the power generation as indicated above - and how often, or how many hours the wind blows - or more scientifically - the "wind speed frequency distribution" at the actual location.

The total energy generated over a year can be calculated by summarizing the power generation for all velocities (ranging from the actual windmill cut-in speed to the shut-down speed) multiplied with the no. of hours the wind blows at the actual speeds.

A typical wind speed frequency distribution diagram with energy produced at the different velocities are indicated below.

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