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, ᴫ 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
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 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.