# Efficiency in Extracting Wind Power

Wind energy is one of the more efficient alternatives to fossil fuel energy. Wind power gives a significant Return On Investment (ROI) since it’s free energy that also has an endless renewable power source. **59%** efficiency is the BEST a conventional wind turbine can do in extracting power from the wind.

**Wind Power** depends on:

• amount of air (volume)

• speed of air (velocity)

• mass of air (density)

flowing through the area of interest (flux)

**Kinetic Energy** definition:

**KE**= ½ * m * v 2

Power is KE per unit time:

Fluid mechanics gives **mass flow rate**

(density * volume flux):

- dm/dt = ρ* A * v

Thus:

P = ½ * ρ * A * v 3

**Betz Limit & Power Coefficient:**

- Power Coefficient, Cp, is the ratio of power extracted by the turbine to the total contained in the wind resource Cp = PT/PW
- Turbine power output
- PT = ½ * ρ * A * v 3 * Cp
- The
**Betz Limit**is the maximal possible Cp = 16/27 - 59% efficiency is the BEST a conventional wind turbine can do inextracting power from the wind