Bill,
The answer to that is actually kind of simple. We need enough lift to support the weight of the airplane in the corner (weight X G force for the radius of turn). th eproper amount of lift will result in the CG of the aircraft pretty much following the desired radius.
Too little lift and the airplane will stall because the wing can't support the weight in the corner. The flight path will open up (nose down) as a result ... and, of course, if the stall happens in the wrong place you might break something!
Too much lift and the ship will accelerate perpendicular (roughly) to the desired flight path and the track of the CG will tend to be inside the desired radius (the appearance of turning aft of the wing and "leaping" into corners).
The results you mention (one to one with a heavy ship, 2/3 for a lighter ship, etc) fall neatly in line with that concept and are generally a pretty good place to start. then you use the slider horn to fine tune the response and flight track.
It does, of course, get a little more complex the deeper you delve into the issue. One of the consequences of cambering an airfoil (what happens when we deflect the flaps) is the airfoil produces a pitching moment in the direction the flaps are deflected; i.e. when the flaps go down the ship wants to pitch nose down (a negative pitching moment).
BEFORE THE ELEVATORS CAN DRIVE THE NOSE IN THE DESIRED DIRECTION (UP IN THIS EXAMPLE) THEY MUST FIRST PRODUCE ENOUGH DOWN FORCE TO OVERCOME THE NEGATIVE PITCHING MOMENT! THIS CAN BE A VERY BIG DEAL.
Thus, if you increase the flap movement on a given ship you will do two things.
First, you will increase the amount of lift from a given amount of control input at the handle.
Second, you will reduce the rate of pitch change because the pitching moment of the wing has increased (see the above).
The net result? More lift, less turn! Sheesh, who made up these rules anyhow?
No problem, if you need the lift (your airplane is heavy and may stall once in a while in hard corners) you can simply increase the spacing on the handle to regain the rate of pitch change you want and the wing will produce the additional lift necessary to avoid the dropsies. (I may just have had some experience with this phenomenom over the years).
It's even a bit more complicated than that. Let's look at another aspect of the lift/pitch conundrum.
The down load the tail produces to overcome pitching moments is exactly the same thing as adding weight to the airplane itself. Anything you do to the airplane that produces a negative pitching moment is precisely the same thing as making the airplane heavier. It's even worse because it compounds itself in corners.
(It is worth mentioning here that there is one more very real source of negative pitching moment that is very important in our stunters. That's right, Ted's favorite subject, the relationship between the Center of Gravity and the Center of Lift of the wing. The farther forward the CG is from the center of lift the more download is required by the tail to keep the nose from falling.
Every little bit of added G force (whenever we maneuver) accelerates that moment and, given enough Gs and enough distance between the CG and the CL and it is entirely possible that your stunter will not be able to stunt worth a darn ... if at all) So, if you combine excesses of these sources of negative pitching moments you can easily reduce the performance capability of the ship.
Lift in and of itself will not generate a tighter loop. The more lift you are capable of producing, however, the tighter the corner the airplane will be capable of flying given the necessary tail authority to drive the wing to the resulting G loads.
As others have said here, however, the ability of the wing to produce enough lift is seldom a problem on a sound stunter at a "reasonable" weight. The limiting factor has always been more the degree to which the pilot is capable of utilizing the performance he can build into the airplane and still present a pattern which will impress the judges.
The discussion on another forum regarding our eye/brain's ability to process visual data was a real eye opener. From my reading following a google search I can see that even if we could produce five foot corners we would have great difficulty in processing the result visually.
Fascinating stuff.
Ted
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