All very interesting.
Nick, your statement
" As predicted, the HP drops as Ct/sigma rises to .12 If you keep running the Ct/sigma up, the power will start back up again.' is certainly not being questioned. However, you picked a specific chord size and this changed the chord from a variable to a constant.
For the fun and the knowledge, another comparison is made. The turquoise is the [Chord: = 2.5'] column in first chart above. The yellow column is the same as the turquoise except that the Blade Pitch has been changed to 13º. This 13º is the pitch in the second chart where the [CT/Sigma] = 0.121.
The constants remain the same.
This third chart shows that changing the chord from 1' to 2.5' drops the horsepower further, from the 358 hp in the second chart, to 260 hp.
This suggests that a low solidity ratio is good for existing helicopters, for a number of reasons. One is the utilization of centrifugal force.
However very, very early attempts at hovering, were best served by a very high solidity ratio, to work with their slower rotational speed. Of course, to keep the weight down they used cloth for the airfoils and guy wires for the strength.
It appears that future helicopters will move back toward the earlier ones in that they will have large chords and slower speeds. Of course, the cloth and guy wires will be replaced by composite construction.
Any thoughts?
Dave