# Calculation of wind energy and wind turbine efficiency

The function of the wind turbine is to extract energy from the wind. The wind is flowing air, which has speed and therefore kinetic energy. When the wind flows through the wind turbine blades, part of the kinetic energy is transferred to the wind turbine to make it rotate. The wind turbine gains energy, and the wind loses energy, so the wind speed after flowing through the wind turbine will slow down. This article explains the calculation methods of wind energy and wind turbine power and efficiency, and provides a video to make it easier to understand.

The wind turbine rotates a circle, the area swept by the blades is called the “Swept area” (denoted as A), When the wind speed is V, the air density is $\rho$. Then the kinetic energy E in T seconds is：

Total wind energy： \begin{aligned} E&=\frac{1}{2}mV^2 \\ &=\frac{1}{2}\rho AVT \cdot V^2\\ &=\frac{1}{2}\rho AV^3 \cdot T \end{aligned}

But what we care about is power, so divide by time T to get wind power P：

Wind Power： $P=\frac{E}{T} =\frac{1}{2}\rho AV^3 ............(1)$

The function of a wind turbine is to convert wind energy into mechanical energy for the rotation of the main shaft. Its power P’ can be expressed by the rotation speed of the main shaft multiplied by the torque:：

Wind turbine power： $P' =$ Angular speed(rad/sec) × Torque(N-m)    ……………..(2)

The efficiency of a wind turbine Cp, is the ratio of the total wind energy converted to the mechanical energy of the main shaft of the wind turbine, The higher the efficiency, the more mechanical energy can be obtained, which is defined as follows：

Wind turbine efficiency： $C_p = \frac{P'}{P} ............(3)$

If the wind turbine efficiency is known, formula (1) can be substituted into formula (3) to obtain the wind turbine power P’：

Wind turbine power： $P' = Cp \times \frac{1}{2}\rho AV^3 ............(4)$

Therefore, the power of the wind turbine is proportional to the efficiency Cp, the swept area and the third power of the wind speed V. Therefore, in order to obtain more energy, in addition to improving efficiency, the wind turbines are also made larger and larger to increase the swept area, and set up where the wind speed is stronger. For example, higher altitude or offshore.