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Wind Energy, Energy in the Wind

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Energy in the Wind

The energy that a turbine can extract from the wind depends basically on these factors:

- Wind speed
- Air density
- Turbine type and blade design

But before going into more details some basic definitions must be understand, in sake of simplicity all constants and variables will be limited to the MKS system.

Standard International Atmospheric Conditions

Reference Conditions for Wind Turbines

These conditions are used as reference conditions for the design of wind turbine generators for extreme conditions like very high terrain and extreme climates will not work and the proper calculations for air density must be performed.

Sea level pressure (p) = 760 mmHg

Sea level temperature (T) = 15 oC

Air density = 1.225 kg/m3

Power Density in the Wind

(Given the reference conditions above)

Power density (P/A) in watts per area for wind flows at 15 OC and for a given air density of 1.225kg/m3

P/A= 0.6125 (V3), power P is given in Watts, area A, is given in m2 and Velocity V is given in m/s

Wind Energy and Wind Power

From physics we know that the kinetic energy is given by 1/2(mV2), where m the air mass is given by:

m = ƿAVt

where:

ƿ = air density

A = The sectional area in which the air pass through at any given period of time t

Substituting m in the kinetic energy formula we have the power in the wind meaning the energy that flows through a given area in a given period of time.

Power in the wind:

P = 1/2ƿAV3

So from this equation we can see that power in the wind is dependant on the air density, the area in which the wind pass through and the wind speed. Changes to any of these variables will result in different power outputs. From this equation It is very important to note that the power available is a function of the cubic power of the wind speed, so at only small differences of wind speed the available power can be much greater, without doubt one the most important consideration in wind turbines location selection.

The air density as function of the pressure and temperature is :

ƿ = p/RT where:

p = Pressure in Newton/m2 or N/m2 = Pascal

R = Gas constant specific for the air mix = 287.04 J/kgK

T= In Kelvin degrees = 273.14 +/- OC

This equation is very useful to calculate the air density at different height and temperatures

Wind Height Speed and the Terrain Shear Factor

As was mentioned earlier the wind increases with the height in a similar way as the water flows faster in the center of a river than at the edges. This increase in the wind speed with height is related to the roughness of the surface related to tress, rocks, crops, hills, bushes and any type of obstruction natural or man made as building, structures etc.

The Shear Factor Exponent (Sf)

For each one of this terrain conditions experimental wind shear factors exponent (sf) have been established. This shear factor exponent varies with the terrain type but also during the day, the season and the atmospheric conditions.

The German engineer Jean Molly proposed a simplified experimental formula to calculate the shear factor exponent from measurements of roughness of a surface:

Sf = 1/ln(S/So)

Where:

So = Surface roughness length in meters

S = The reference height

Example:

Calculate the wind shear factor exponent for a given roughness length of .02 meters and a height of 10 meters.

Sf = 1/ln(S/So) = 1/ln(10m/0.02m) = 1/ln(500) = 0.1609

Continue to:

Energy in the wind related to the height >>

Terrain Type |
Surface Roughness Length in m |
Wind Shear Exponent Sf |

Ice |
0.00001 |
0.07 |

Calm Sea |
0.0001 |
0.09 |

Cut Grass |
0.007 |
0.14 |

Hedges |
0.085 |
0.21 |

City Suburbs |
0.4 |
0.31 |

Woodlands |
1 |
0.43 |

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