SR71
You must be psychic. Just when I was going to ask you to pull Octas8's castle down.
Octas8
Must butt in here before you pass on too much duff gen. You left the other thread on Yaw and Sideslip too soon.
When considering Vmca and directional stability you cannot use the cg as the axis. Weight and cg don't get a look in until you use a little bank to help with the asymmetric yaw. Even then it is an indirect relationship Try resolving weight through 90 degrees and what do you get? Longitudinal stability is the one that has serious concern with the cg.
The axis for considering forces in the horizontal is the lateral centre of pressure unless manoeuvre is also considered.
The only participation of the cg arises from the fact that total lift acts through a point close to the cg ( vertically displaced).
Consequently when you use any bank to assist in asymmetric control the small resolved portion of lift acts from the centre of total lift most often with its centre above the cg. The effect into the horizontal plane is so insignificant that for practical purposes it can be ignored.
So one can delete all reference to cg entirely.
The text books are seeing the errors of their ways and will be corrected in due course.
Wings 777
You should now be able to work it out for yourself.
If any of the above does not yet make sense to you then you may learn a lot if Octas8 is challenged.