Milt,
The only way I know of to get a side force from the fin, rudder central, is with sideslip
The rudder doesn't have to be central though...
In fact, throughout this discussion, apart from the flight condition
alf5071h's notes refer to, it won't be.
To my mind, it is quite possible to attain banked, zero sideslip flight when asymmetric with rudder deflection.
Regards the effect of CG location on V_mca...
We need force
and moment equilibrium for an unaccelerated flight condition.
The point about which you consider these two forces to act makes a crucial difference to whether \sigma
M = 0! It won't remain unaccelerated for long.
You can fix your axes system anywhere on the a/c and define things accordingly.
Agreed, for lateral force equilibrium, balance them about whichever origin you like on the a/c x-axis.
Having chosen this point, you then fix the required sideload required by the fin/rudder because presumably your airframe is not aeroelastic and the distance to the fin is fixed.
But, having chosen that point, if you then change it, whilst it does not change the size of the thrust related yawing moment, I cannot see how you won't change the required sideload that needs to be generated by the fin/rudder?
How do you otherwise propose to size your fin/rudder?
I see an analogous relationship between centre of pressure, aerodynamic centre, CG and AOA in the vertical sense and their lateral equivalents, except that, of course, you can't decouple lateral/directional stability.
My $0.02.