AnFI I haven't aligned myself with anyone. But I did make one mistake, I assumed that you were someone who was here, like a great number of users of this forum, to expand your own knowledge by interaction with others. I therefore chose not to directly post a refutation of your analysis, but instead gave you an opportunity to look at the conditions and statements that I and others had posted and see if it revealed to you where the inconsistency lay through your own exploration of the physics. From the tone, attitude and content of your post it is obvious to me now that that isn’t the case, so I won’t waste too much time here.
We'll use your equation.
κ = ρA©/2m
© used here by you to denote coefficient of lift, is a normalised value of lift, for any given aerofoil. An aerofoil has a curve associated with it, often obtained empirically, that links © to α. Assume we are in the linear part of the lift curve and we'll call dClbydalpha "a" and substitute.
κ = ρ.A.α.a /2m.
Unlike a fixed wing, a rotary wing is rotary. Therefore the "v" that any aerofoil element experiences relies on rrpm and the element's distance from the hub let's say Ωr . However the downwash the element is seeing is independent let's call it u.
Therefore
α = arctan(u/ Ωr)
Assuming a small angle
α = (u/ Ωr)
And substitute
κ = ρ.A. (u/ Ωr).a /2m.
As you can now see, there is a term for rotor speed in your equation. Q.E.D.
Last edited by dClbydalpha; 6th Oct 2016 at 14:23.