# Wind Energy - Physics

# Overview - Wind Power

The power *P *of a wind-stream, crossing an area *A *with velocity *v *is given by

It varies proportional to air density , to the crossed area *A *and to the cube of wind velocity *v*.

The Power *P *is the kinetic energy

of the air-mass *m *crossing the area *A *during a time interval

.

Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation

The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of () and behind the rotor area () is . The maximum power extracted is then given by

where is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of .

# Unit Abbreviations

m = metre = 3.28 ft. |
HP = horsepower |

s = second |
J = Joule |

h = hour |
cal = calorie |

N = Newton |
toe = tonnes of oil equivalent |

W = Watt |
Hz = Hertz (cycles per second) |

= p pico = 1/1000,000,000,000

= n nano = 1/1000,000,000

= µ micro = 1/1000,000

= m milli = 1/1000

= k kilo = 1,000 = thousands

= M mega = 1,000,000 = millions

= G giga = 1,000,000,000

= T tera = 1,000,000,000,000

= P peta = 1,000,000,000,000,000

# Further Information