= ρ π d 2 v 3 / 8 (1)
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 .
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 wind power can be calculated
P a = ξ ρ A v 3 / 2
ξ ρ π d 2 v 3 / 8 (2)
ξ = efficiency of the windmill (in general less than 0.4 - or 40%)
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
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The calculator below can be used to calculate the available power from a windmill:
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.
Climate, meteorology, sun, wind and environmental related engineering resources.
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
Density and specific volume of air varies with elevation above sea level.
Air density at pressure ranging 1 to 10 000 bara (14.5 - 145000 psi) and constant selected temperatures.
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.
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 is the ratio useful energy output to energy input.
Power is the rate at which work is done or energy converted.
Available wind energy.
Wind load on surface - Wind load calculator.
Wind slowed down at surface by trees and obstructions.
Online wind turbine calculator.
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