Hi Pierre:
Well good that you ran some numbers. A few things come to mind. One is that small wind turbines never seem to come very close to the Betz coefficient due to a low Reynolds number at smaller scales, which is an artifact of skin friction (viscous forces, or “air-as-glue”), versus kinetic energy and power effects which are more an effect of “air-as-a-frictionless-fluid”, which is an idealized abstraction. The smaller you get, the more surface area compared to volume, so the more “air-as-glue” effects enter the picture. Go to insect-wing size, and airfoils lose their magic which is why birds have airfoils but insects do not. So nobody in “small wind” should expect to come close to the Betz coefficient. But there is a way to “cheat”: Add more rotors. Same with the tilt, or skew, of a rotor: Add more rotors (cheat) and beat what Betz says a single rotor of the same diameter can achieve, even at a small size. Small-scale demos are perfectly valid, but you have to take what you get considering the scale. You realize at the scale you are at, the full Betz coefficient is unachieveable, or at least unlikely with what we know today. You compare to other small turbines, not so much to Betz. Also, please remember the generators are not 100% efficient, and smaller generators are less efficient than larger ones. Small ones are lucky to be 90% efficient, whereas large generators can be like 98-99% efficient. Still, there is good enough performance at small scales to prove theories and to power your home, farm, or ranch.
The advantage of ST technology is not specifically aerodynamic efficiency as compared to straight-on rotors.
What I like to say is an expression I stole from discount retailers, who like to say “We lose a little money on every deal, but make it up in volume!” (OK questionable math but you get the idea) Well with regard to ST tilted, partially-overlapping rotors, operating at a low Reynolds number, I say “We lose a little power at every rotor but make it up with an overwhelming number of rotors”. Aerodynamically-efficient? Not so much. Economically-efficient? Maybe a bit more so. Of course larger versions would operate at a scale further from insect wings stuck in glue, and we would expect better efficiency at larger scales, just as with aircraft wings. The wind turbines that are sometimes said to approach Betz are the largest ones - less surface area per unit volume served, less “aero-stickiness” involved.
1 Like