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Wind Turbines Swept Area  (Page 1)

 

<< Continue from previous page

Wind Turbine Swept Area

The wind extracting power of a turbine is directly proportional to the area intercepting the wind, all consideration given here will be for the conventional horizontal turbine as the one shown below:

 

The wind intercepting the area  is A =ᴫr2  where A is the area, is the constant 3.14159 and r is the radio.

 

 

 

 

 

 

 

 

 

 

From the picture above, it is clear that increasing the radio r will increase the swept area to the second power. Perhaps if the radio is one meter the swept area will be:

A = 3.14159(1)2 = 3,14159 m2

For a two meter radio the area will be:

A = 12.56 square meters

As consequence the power potential capability of the turbine was increased four times by increasing the radio “r” from 1 to 2 meters, this is the reason why bigger turbines are selected for economically viable projects, the bigger the turbine the lower cost per produced watt.

 

 

 

 

 

 

 

 

 

 

 

 

Solidity

Solidity is the ratio of the rotor blades area to the wind intercept area (the disc area defined by the blade radio). For a three blades rotor:

 

 

 

 

 

 

 

 

 

 

 

 

 

There is always an optimum solidity ratio for which wind power intercepted and tip speed can be maximized, for example rotors with many blades have a bigger solidity ratio and bigger torque but their blades rotate at lower speed, so depending on their applications and wind conditions the proper number of blades has to be selected, some multiple blades rotors can have up to 80% solidity ratio which produces high torque at low wind speeds, an efficient feature for water pumping applications but not so convenient for wind electrical power generators.

 

Continue on next page >>

 

 

 

 

 

 

 

 

 

 

 

Radio (meters)

Swept Area (meters)

0.5

0.78

1

3.14

1.5

7.06

2

12.56

2.5

19.63

3

28.27

3.5

38.48

4

50.26

5

58.53

Rotor blades area = A1+ A2 +A3

 Disc area = лr2

Where л = 3.14159

R = The blade radio

 

For a rotor with multiple blades, the blades area will be A1+ . . . +An

 

Radio r

A1

A2

A3

Radio to Swept Area Ratio

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