55 horizontal axis wind turbine wing one full exterior end on view
 

This design applies the curveset:

X = If [ f <= 1 , Cos [ pi + f pi ] , Cos [ 2 pi + ( f - 1 ) pi ] ] ;

Y = If [ f <= 1 , -Sin [ pi + f pi ] times Sin [ pi / 3 + f pi / 3 ]^n times Sin [ pi / 6 + f pi / 6 ]^n , (* plot underside for f values 0 to 1 *)

-Sin [ 2 pi + ( f - 1 ) pi ] times Sin [ 2 pi / 3 + ( f - 1 ) pi / 3 ]^n times Sin [ 2 pi / 6 + ( f - 1 ) pi / 6 ]^n (* plot upperside for f values 1 to 2 *) ] .

Here, n is varied across the radius : from 3/4, (at 3/4), to 5, (at 5), where the wing closes .

Below 3/4, the wing is cosine blended into its cylindrical hub, which then expands into a 'whale' mounting flange, (which i quite like), modeled from a lift neutral 5th degree variation of the equations above ; wrapping around the driveshaft at a radius of slightly over 1/3 .

Rotation is upward, (as shown, from the end of wing one, where it is designed to turn as fast as 5 times the speed of the incoming air) .

Wings are expected to cross eachothers' wake effects near (2, 4 and 6) fifths pi ; making them comparable in this regard with three wing turbines, which i expect encounter wake effects near (2 and 4) thirds pi .

Under steady wind conditions, the wings are expected not to fully create, (or thus to fully encounter), a denser wake at 8/5 pi, (numerically about 5.02) .

However, such a wake should appear in variable winds when the turbine overruns 5x windspeed at its tips .

Under such circumstances, the wake would act as a brake ; though in doing so it could cause some shudder .

Yet, because of the shape of the airfoil curveset used, with a nose which points, (upwind in this case, leftward as shown), slightly below their line of travel ;

and because its release of air gets more gentle as radius increases, these wings may be well formed to handle the wakes they make .

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The angular width of the wing is halved as radius is doubled .

The pitch is shallowed from about 53.5°, (at radius 3/4, where the wing is hoped to rotate at 3/4 the windspeed), to 9°, (at the radius of 5) .

The mounting flanges reach about 71.3° .

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( Banding on the mounting flanges is a display artifact . Red lamp on the wing tip is not . )

 

 
13 May 2010
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