Going even further on this, it is true that the TSR often taken for the horizontals, that is the TSR at the blade tip, or the "tip" TSR, is the
maximum TSR for the blades, everything else along their lengths being less.
It is the opposite for the verticals. The TSR often taken is the tangential speed of the H-Rotor blades divided by the wind speed and this only holds at the dead centers of the upwind and downwind faces of the swept area. Everywhere else it is greater and so it is the minimum TSR for the rotor.
The horizontals struggle, in other words, to keep their TSRs high and the verticals have little need once they gain a rotor speed 1.5 or 2 times the wind speed of going any faster than just this set speed. Their TSRs are plenty high already.
The other reason for a fast rotational speed, that is, the need to slice up the wind into thin slices like cheese, is at least partly helped in the verticals by the blades' traversing their swept areas twice each rotor rotation. It is sort of double duty, unlike the horizontals blades. Some recent efforts have been resurrected about the past contra-rotation horizontals in which a second rotor placed just behind the first rotates in the opposite direction. For the verticals, of course, the blades already do this on the back side without the added complexity of such an arrangement.
Contra-rotation, be it known, still has its adherents and even Federal and State governmental energy agencies have demonstrated a soft spot for it. It can be easily understood as just a turbine that combines upwind and downwind rotors on its nacelle, sort of two turbines in one. Trouble is that blades going at TSRs over 1.5 or 2.0 have shown good efficiency and even theory says they can be over 90% efficient in doing so, obviating much of the need for this feature.
The question remains, though, why most all modern turbines, even the best, do not approach the Betz limit any closer than they do and this is forms a puzzle and opportunity for those who can understand these problems and suggest solutions. It certainly can be useful to look at some of these details.
Anthony C.
www.integener.com