Wind power

📚 Theory¶

Theoretical wind power is the maximum amount of energy that can be extracted from the air flow passing through the area swept by the wind turbine blades. This calculation is based on the assumption of perfect efficiency (ignoring losses), i.e. it is the upper limit of the available energy.

Understanding this value is important for:

assessing the potential of an installation at a specific location,
preliminary comparison of different turbines and their diameters,
optimizing the location of wind turbines.

Tip

In practice, some energy is lost due to mechanical, aerodynamic and electrical factors, but the theoretical power serves as a starting point for calculations.

Formula¶

$$ P = \frac{1}{2} \cdot \rho \cdot A \cdot v^3 $$ Where: - P is the theoretical wind power (W), - ρ is the air density (kg/m³), typically about 1.225 kg/m³ at sea level and 15°C, - A is the area swept by the blades, $A = \pi \cdot \left( \frac{D}{2} \right)^2$, where D is the rotor diameter, - v is the wind speed (m/s).

🧠 Explanation

The turbine blades rotate and sweep a circular area.
This area is critical because it defines how much wind energy can be captured.
If you double the rotor diameter, the swept area increases by a factor of 4:

\[ A \propto D^2 \]

So even small increases in blade length can significantly boost potential power output.

This formula demonstrates a cubic dependence on wind speed: a small increase in speed significantly increases the power.