Wind Energy Conversion Systems Notes

Last reviewed 1 Oct 2026 · Facts as of 1 Oct 2026 · 7 min read

Wind as an energy source

Wind is air in motion caused by the uneven heating of the Earth's surface by the sun, modified by the Earth's rotation (Coriolis effect) and by terrain. Wind energy is renewable and pollution-free, but variable and site-dependent.

Wind measurement

Instrument	Measures
Cup anemometer	Wind speed
Wind vane	Wind direction
Propeller/sonic anemometer	Speed and direction (sonic gives 3-D turbulence)
Wind data logger, LiDAR/SoDAR	Profiles for wind-resource assessment

Beaufort scale classifies wind on a 0–12 scale.
Wind rose shows the frequency of wind direction; speed–duration curve shows hours for which each speed is exceeded.

Variation with height

Power law (Hellmann):

\frac{v _{2}}{v _{1}} = (\frac{h _{2}}{h _{1}})^{α}

where $α$ is the surface roughness (shear) exponent — about 0.14 (1/7) for open level country, 0.10 over smooth sea or ice, and 0.25–0.4 over forests or built-up areas.

Worked ExampleExample — wind speed at hub height

The wind speed at 10 m is 5 m/s in open country ( $α = 0.143$ ). At 80 m:

$v_{80} = 5 \times 8^{0.143} = 5 \times e^{0.143 \times 2.079} = 5 \times e^{0.297} = 5 \times 1.346 = 6.73 m/s$ . Since power varies as $v^{3}$ , the available power rises by $1.34 6^{3} \approx 2.44$ times.

Power in the wind

FormulaWind power

Kinetic energy flux through a rotor swept area $A$ at wind speed $v$ with air density $ρ$ :

P_{w in d} = \frac{1}{2} ρ A v^{3} A = \frac{π D ^{2}}{4}

$ρ \approx 1.225$ kg/m³ at sea level, 15 °C (it falls with altitude and temperature).
Power varies as the cube of wind speed — doubling the speed gives eight times the power — and as the square of the rotor diameter.
Power density $= \frac{1}{2} ρ v^{3}$ W/m².

Betz limit and power coefficient

A turbine cannot extract all the kinetic energy (the air would stop behind the rotor). Betz (1919) showed that the maximum fraction that can be extracted is 16/27 = 0.593 (59.3 %), when the wind speed falls to one-third behind the rotor.
Power coefficient $C_{p} = \frac{P _{r o t or}}{\frac{1}{2} ρ A v ^{3}}$ . Modern three-bladed turbines reach $C_{p} \approx 0.40$ – $0.50$ at the best operating point; Savonius rotors reach only about 0.15–0.25.
Electrical output $P_{e l} = C_{p} η_{g e a r} η_{g e n} \cdot \frac{1}{2} ρ A v^{3}$ .

Worked ExampleExample — turbine output

A wind turbine has a rotor diameter of 80 m. At a wind speed of 12 m/s with $ρ = 1.225$ kg/m³:

$A = π \times 4 0^{2} = 5027 m^{2}$ .
$P_{w in d} = \frac{1}{2} \times 1.225 \times 5027 \times 1 2^{3} = 0.6125 \times 5027 \times 1728 \approx 5.32 \times 1 0^{6}$ W $= 5.32 MW$ .
With $C_{p} = 0.42$ : rotor power $= 2.23$ MW; with gearbox and generator efficiency 0.90 the electrical output is about $2.0 MW$ .

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