Power generated from the wind
The theoretically available power in air moving - wind - can be expressed as
P = 1/2 ρ A v3
= 1/8 ρ π d2 v3 (1)
P = power (W)
ρ = density of air (kg/m3)
A = area the wind is passing through the wind mill - perpendicular to the wind (m2)
v = wind velocity (m/s)
π = 3.14....
d = wind mill diameter (m)
- 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
Pa = 1/2 ξ ρ A v3
1/8 ξ ρ π d2 v3 (2)
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
Pa = 1/8 (0.2) (1.2 kg/m3) π (1 m)2 (10 m/s)3
= 94.2 W
- 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.