I tried to do that once.
It seems like all the long math came out to about 35~40% of the swept area for a 55 gallon drum type VAWT, as related to HAWT math.
The returning bucket sees a higher "wind speed" than the working bucket.
Very confusing for me. My numbers were probably not very close, but the principle of subtracting power for the returning bucket is sound, IMHO.
G-