Power generated from the wind
Theoretically power in moving air - or wind - can be calculated
P = ρ A v3 / 2
= ρ π d2 v3 / 8 (1)
P = power (W)
ρ = density of air (kg/m3)
A = wind mill area perpendicular to the wind (m2)
v = wind speed (m/s)
π = 3.14....
d = wind mill diameter (m)
- 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
Pa = ξ ρ A v3 / 2
ξ ρ π d2 v3 / 8 (2)
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
Pa = (0.2) (1.2 kg/m3) 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:
ρ - density of air (kg/m3)
ξ - efficiency of windmill
v - wind speed (m/s)
d - windmill diameter (m)
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.