MFT,
I have read your post several times, and you make a lot of sense - there is a lot of imagining of paper aeroplanes with a point mass as c.g. going on in my head.
(Sorry if you've been trying to say the same thing Milt - I can understand MFT's reasoning, but not yours. Perhaps the fault is mine? I understand your desire to say 'I told you so' anyway.)
As I'm not sure I understand the implications of your simultaneous equations, may I ask a question?
Cn(total) = Cn(beta)*beta + Cn(rudder)*rudder + Cn(OEI) = 0
It seems to me that Cn(OEI) does not depend on longitudinal c.g. position, but the other two coefficients do. It also seems to me that it's important that Cn(beta) is less than Cn(rudder) for the wings level case - much less, in fact, as Cn(rudder) has to oppose the other two put together in the wings level case.
If Cn(OEI) is independent of longitudinal c.g. (independent of whatever longitudinal reference point you choose to use), and Cn(rudder) is the dominant of the other two expressions, doesn't this mean that the longitudinal reference point is important? Otherwise we could pick the point
at the point of origin of force beta, making Cn(beta) zero. Or we could put the reference point far ahead of the aircraft, and Cn(beta) would approximate Cn(rudder). Either way the equation would cease to equal zero, simply by our apparently arbitrary choice of longitudinal reference point. In turn, this implies a fault somewhere in the reasoning.
Would you clarify this problem?
Tks,
O8