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.
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Power
Power is the rate at which work is done or energy converted.
Wind Energy
Available wind energy.
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