Typical airfoil blade turbine deflects the wind outward downstream, loosing power.

According to mathematical analysis, wind power is proportional to the cube of the wind speed, or doubling the speed of the wind gives 8 times the power. It has also been analysed by Betz that  a maximum of 59% of the mass momentum of the wind molecules, or wind power density (WPD), can be harvested from the wind by reducing the velocity of the wind by up to two thirds. This is theoretical, without any losses from turbulence or bypassed air molecules.  In actual performance, efficiencies of existing wind turbines have been significantly lower, as shown in the chart below.  However, these calculations do not take into consideration other mechanisms of power transfer not present in conventional propeller blades.

By these calculations, the wind power density at a velocity of 10 meters/second (22 miles per hour) is around 613 watts/sq.m Therefore, the theoretical maximum energy that can be extracted from this wind at 10m/sec is 613 x .59 = 362 watts/sq.m.  At 9.5 sq.ft (0.883 sq.m.) wind shadow our first prototype must extract less than 320 watts from the 10m/s wind. According to analysis of real wind turbine performance, the actual power generated is probably less than 35% of the power in the wind, or less than 189 Watts.

I postulate that, due to the advantageous wind deflection profile downstream, the involute turbine can be more efficient than the airfoil blade turbine.  The turbulence behind a fast-moving and relatively fat propeller blade not only looses power by flinging the wind outward down- stream, but also from accelerating a fat propeller through the air at several times the wind speed, an increasingly turbulent wake is generated behind the prop, robbing it of power.

In contrast, an involute shaped turbine, with paper-thin vanes smoothly catches the wind and spins it into the center, gaining power, instead of loosing power as when propeller blades throw the wind out.  The involute vanes act like an ideal venturi shroud, diverting the wind mass continually into a low pressure leeward zone.

The mostly laminar flow throughout should also improve power-transfer efficiencies, especially at higher speeds.  This needs to be tested in a wind tunnel, along with the other variations mentioned.  Some intriguing questions come to mind ~ is a spinning low-pressure vortex created in the center? ~ What would happen if you open up a center hole in the bottom disk - will it suck in?  - will efficiencies improve or drop?  Ribbons placed in the flow path indicate that there is no upward or downward air-flow tendency, only cross-flow.

The potential application of this geometry for quiet, efficient high-pressure fans should be investigated immediately. It could provide the ultimate Tesla Engine design!  and what about water power?

Top View of Involute-vaned
Vertical-axis Wind Turbine.

Postulate:

Involute vanes deflect the wind inward downstream, gaining power from adjacent air outside turbine wind shadow, further decreasing downstream pressure and increasing power extracted from the further-accelerated wind as it leaves the turbine.  This does not contradict Betz’s 59% maximum efficiency calculations, but changes the input/output pressures, volumes and acceleration numbers, theoretically to increase the maximum efficiency potential.

Betz’ law is based on analysis of fluid flow through a disk-shaped actuator, whereas this VAWT has active energy transfer throughout the volume of the cylinder or cone of impeller surface.  The actual flow and pressure profiles of this shape are complex and need to be further simulated and tested. For instance, is it possible to harness the wind, not just passing through the vanes, but also in the vicinity of the turbine to increase the power density transferred to the turbine?