Derivation of a Factor for Equilibrating the Blade Swept Area
of the Verticals Style of Wind Turbine to that of the Horizontals

by Anthony Chessick
IntegEner-W

 

The efficiencies of verticals blades are dependent on the component of the wind velocity vector that is perpendicular to them and the magnitude of this component varies throughout their rotational circuits.

The physical blade "swept" area of the verticals, that is, the cross section area seen by the wind in elevational views of the rotor, does not provide the same efficiency across it as can be said of the physical blade "swept" area of the horizontals. It is clear from the outset, for instance, that the conversion efficiency drops from its full value at the centerline to zero at the rightmost and leftmost edges of the blade swept areas. Certain assumptions and detailed qualifications apply but this can be considered a valid statement as a general rule. If so, then, some rough factor can be found from theory that may be used to convert the physical blade swept area of verticals turbines to an "effective" blade swept area that allows the two different rotor configurations to be compared properly. Here is a derivation for such a factor:

For the troposkein Darrieus turbine rotors the physical blade swept area cross section is something close to a circle in shape and so the "effective" blade swept area is found by first calculating the size of this circular or nearly circular area and then applying the factor determined above, i.e. 2/3, to it. For the H-Rotors and other straight-bladed verticals, the "effective" blade swept area is found more simply by just taking the blade length times 2/3 of the rotor diameter.

In effect, then, the physical blade swept areas of the verticals should be about one and half times those of the horizontals for an equivalent energy conversion capacity and a square meter or square foot of one is not equal to that of the other.

All wind turbines suffer various losses, some inherent, and the horizontals can not be said to take full advantage of their physical swept areas either. The portion of the horizontals blades nearer their roots and around the hubs is known to have less efficiency and wind redistribution towards the sides helps the verticals blades somewhat as does the concavity of the blade sweep on the back or downwind side.