I would like to ask some clarifying questions regarding the moments acting on a flying airplane.
My understanding is that there are following force:
Weight (pointing down and applied to the CG of the plane)
Lift from the wing (pointing up and applied to the aerodynamic center AC)
Lift from the horizontal stabilizer in the tail (this resultant force is pointing down, it is smaller than Lift_wings, and it is applied to the AC of the tail).
The airfoil, on its own, also has an aerodynamic moment (positive) which would make the wing rotate nose-up about the CG of the wing itself if the wing was placed free in the wind stream. However, the aerodynamic moment about the aerodynamic center is constant negative (nose down). Is that correct? The physical effect is the nose up intrinsic moment of the cambered wing due to the fact that the force on the bottom and the force on the top of the wing do not act along the same line of action.
For longitudinal stability, are the participating moments the moment due to Weight, the moment due to the wing lift and the moment due to the horizontal stabilizer that need to add to a zero resultant moment? Can the positive aerodynamic torque of the wing be ignored because much smaller in magnitude than the other torques?
In most planes, starting from the leading edge of the wing, the aerodynamic center AC of the wing is placed behind the plane's CG. How far behind CG should the wing AC be placed? The placement of the tail's AC should easily derives from the moment equilibrium equation (sum of moments equal to zero). I realized that some big airplanes have the CG behind the wing AC. In that case, the lift from the tail is force always directed upward and not downward like when the CG is in front of the wing AC.