# Wind Power

Theoretically power in moving air - or wind - can be calculated

P = ρ A v^{ 3 }/ 2

= ρ π d^{ 2 }v^{ 3 }/ 8 (1)

where

P = power (W)

ρ = density of air (kg/m^{ 3 })

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

v = wind speed (m/s)

π = 3.14....

d = wind mill diameter (m)

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

- 20% increase in wind velocity will increase the power generation with 73%

The theoretical and rated wind power generation from a typical windmill is 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.

### Actual Available Power

Actual available wind power can be calculated

P_{ a }= ξ ρ A v^{ 3 }/ 2

ξ ρ π d^{ 2 }v^{ 3 }/ 8 (2)

where

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

### Example - Wind Power

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

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

* = 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 over time depends on the wind mill potential 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 is indicated below.

## Related Topics

### • Environment

Climate, meteorology, sun, wind and environmental related engineering resources.

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Air - Density and Specific Volume vs. Altitude

Density and specific volume of air varies with elevation above sea level.

### Air - Density vs. Pressure and Temperatures

Air density at pressure ranging 1 to 10 000 bara (14.5 - 145000 psi) and constant selected temperatures.

### Air - Density, Specific Weight and Thermal Expansion Coefficient vs. Temperature and Pressure

Online calculator, figures and tables showing density, specific weight and thermal expansion coefficients of air at temperatures ranging -100 to 1600 °C (-140 to 2900 °F) at atmospheric and higher pressure - Imperial and SI Units.

### Air - Thermophysical Properties

Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.

### Efficiency

Efficiency is the ratio useful energy output to energy input.

### Power

Power is the rate at which work is done or energy converted.

### Wind Energy

Available wind energy.

### Wind Load vs. Wind Speed

Wind load on surface - Wind load calculator.

### Wind Shear

Wind slowed down at surface by trees and obstructions.

### Wind Turbine Power Calculator

Online wind turbine calculator.