# Wind Power

## Power generated from the wind

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The theoretically available power in air moving - wind - can be expressed as

P = 1/2ρA v^{3}

=1/8(1)ρπ d^{2}v^{3}

where

P = power (W)

ρ = density of air (kg/m^{3})

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

v = wind velocity (m/s)

= 3.14....π

d = wind mill diameter (m)

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

*20% increase in wind velocity - increases power generation with 73%*

Theoretical and rated wind power generation from 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)1/8ξρπ d^{2}v^{3}

where

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

### Example - Wind Power

The available power from a wind mill with diameter *1 m*, efficiency *0.2 (20%) *- in wind velocity *10 m/s* - can be calculated as

*P _{a} = 1/8 (0.2) (1.2 kg/m^{3}) π (1 m)^{2} (10 m/s)^{3} *

* = 94.2 W*

### 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 the 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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