Yep, not doubting that (that flapless stunters turn as tight as need be -- TaW). The calcs show what happens at incipient stall. We don't fly there. But what you can see from looking at the curves is that the flapped ship will need less angle-of-attack to make the corner, and it will look smoother on the entry and especially the exit of a corner since it doesn't need to over-rotate as much.
So the whole thrust of the thread is misplaced -- the effect of flap on the turn
radius is nil, because even with a flapless stunter the pilot is holding the aircraft back from turning as tight as it possibly can in an effort to achieve a smooth maneuver and to not lose too much speed to induced drag. So (assuming decent turn performance), neither a flapped nor a flapless ship is giving its all in this regard.
Thus, "flap effects on turn", or perhaps better yet "flap effects on turn aesthetics" is the better title for the thread (and direction of the analysis), with perhaps an introductory calculation that shows what you can do with a Skyray, Flight Streak or whatever.
I see the whole discussion of "how do I use flaps to turn tighter" (I think I even asked it myself) being asked, against a background of the guys who've flown flapless extensively stating that you don't need flaps to fly the pattern, and the top dogs giving occasional instruction on tweaking flap to elevator ratio to get a better
looking corner, and it all leads me back to thinking that if you think that you're putting flaps on your plane to turn tighter then you're doing the right thing, but for the wrong reasons.
As near as I can tell (and I'm definitely in the wilderness as far as my own direct experience goes, so I'm open to correction here), the tradeoff with flaps is not for maximum lift. The limitation on lift in the corners seems to be one of induced drag and turbulence, which means that that fight should be fought primarily with aspect ratio (and aspect ratio has its own problems, which is why there's not many semi-scale stunt YO-3's to be seen in the stunt circles). So thinking that you are aiming for maximum lift with your flaps, rather than for the look of smoothness in your corner, would mislead you in you design quest.