bookworm
Thanks for highlighting the bits you don't understand.
A sideforce from the fin, rudder central without sideslip ??? You have discovered something unknown in aerodynamics. Patent it quickly.!!
How can you possibly say " there's still substantial force coming from the vertical tail surface (without sideslip)" when there will be absolutely zilch except drag unless there are inequalities in the shape of one side with the other. I'll concede that slightly different airflows along the vertical tail resulting from one engine operating and the other closed down may have some effect. But skip this for now as it only complicates the case on which we seek a conclusion.
For ease of further discussion, which must be very illuminating to the thread visitors, let us just look at the wing down case where we have carefully adjusted the bank to result in a centralised rudder whilst we maintain balanced straight flight.
You say "And you want to ignore the force at the vertical tail..."
Please tell me how I am ignoring it when I have just said "and the one that most of you want to ignore which is the horizontal force generated by sideslip."
Does this not equate to your "the force at the vertical tail.."
This IS the force at the vertical tail which is ONLY achievable from sideslip unless we have a gremlin out there giving it a shove.
Don't forget that there is a reasonable contribution of force from the side of the fuselage to the balancing force at the vertical tail.
If the above does not convince please tell me where I have failed. I have a thick skin.!
We agree on one fact. That is that the total lift acts through the cg (ignoring any vertical component of thrust.)
Pardon me on my insistence on the use of cg intead of CG. It's the same as using MM for mm and maybe I'm a long way behind on an update.
The combination of a relatively small horizontal lift component and the small permissable fore and aft cg range results in there being insignificant effects of cg position on the stabilising couple with the tail force resulting from the sideslip. Because of its insignificance I have taken the liberty of ignoring it for the sake of simplicity.
Perhaps someone will come up with some typical numbers to illustrate that insignificance to satisfy the purists. That will involve complex multiple hieroglyphics.
Wings level, that insignificance disappears.
Incidently have you handled asymmetric situations?