THOSE relationships do not depend on wingspan! So many small models have been declared touchy, nearly uncontrollable, because the relationships of hand size, angle range, line separation and horn radii were shrunk too far.
Larger 'span' bellcranks are longer levers to operate controls as needed for heavier models, and the greater 'mechanical advantage' is useful to make the needed surface motions.
Thoughts, just IM(notso)HO.
Lou:
Everything you say is true and I certainly prefer a 4" if it will fit, however, the mechanical advantage comes from the length of the horns and the length of the connection arm. The force to drive it comes from the length of the bellcrank arms coupled to the line spacing. Equal force can be applied to the flap horn with any size bellcrank(within reason). To me the only reason to use a larger bellcrank is that you have a wider line spacing at the handle which takes some pressure off of your wrist.
I was out of the hobby for about 30 years and when I returned "everything" had changed. Few models used 4" when I left, in fact I don't think anybody manufactured them (I could be wrong since I wasn't looking for them). PA type planes were lighter, most around 40oz. Line pull was something we begged for. When I came back I quickly built two ships. One was a .35/40oz size since (I had an engine) with a 3" crank and the other was a .46/50oz with a 4" crank. Once trimmed, there is no real difference in response. Line spacing is quite different.
Personally I don't like my planes to require massive differences in control input to fly the pattern. The first thing I noticed when I flew the 4" was that I needed a whole lot more wrist to turn a tight corner. Since I am a "finger" type this was uncomfortable so I moved the line spacing out till it turned quick enough for me. Surprisingly, there was not enough difference in the pressure on my wrist to be noticeable.
This is NOT an argument against 4" cranks, quite the opposite, it is just that they don't make the plane fly any different. What they do is make it easier for us to make them fly the same which, in many ways was your point.
I don't see how this argument would be any different going from a 2" to a 3" on a 1/2a. I doubt seriously that any of us complain about line pull on a plane that small and the line spacing and horn height can easily be adjusted to give it proper response but like many things, my opinions are based on years of personal experience and are 100% open to being changed by a superior argument.
Ken