John Farley
Aircraft Axes. You prompt me to become more specific.
To say that all axes go through the cg is somewhat simplistic for convenience. The definitions become easier. OK for simple theory and non manoeuvering flight.
Throw in manoeuvre and things get very complex. The actual lateral axis during vertical manoeuvres normal to the wings will move around under the influences of wing/body lift and tail power.Trying to determine what the vertical and longitudinal movements of the lateral axis might be must be an aerodynamicist's nightmare.Too many variables.
Consider the vertical/yawing axis seperately. In steady flight this axis has no relationship to cg whatsoever. The symmetry or asymmetry of wings level flight is determined by the balance between three collective forces; Thrust, Drag along the longitudinal axis and the sideslip forces controllable by rudder acting through the Lateral centre of pressure. Weight/Mass doesn't get a look in as you cannot resolve weight through 90 degrees. Mass only comes into play during manoeuvre when you have lateral or other accelerations. Did anyone ever determine your axis of yaw when you rotated a Harrier around a fixed point on the ground in nil wind. Can't think of a reason for wanting to know that axis except that to rotate around it would require minimum control variations to hold position.
Then consider the Longitudinal Axis seperately. It would be a big coincidence if the actual longitudinal axis passed through the cg particularly its vertical position. If it did there would be less to worry about from cross coupling during rapid rolling.
Consider the three axes collectively and you have a a whole host of interactions to be sorted out by natural stabilities and/or the flight computers.
Conclusion. All steady state actual axes are influenced by the shape of the aircraft, the airflow around the shape and the cumulative direction of thrust and a few other incidental forces. Manoeuvres introduce accelerations on the mass of an aircraft usually represented at the cg. This cg has a three dimensional position with two of these dimensions (vertical and lateral) being conveniently brushed aside by most aviators.
I will be delighted if you can pick holes in the above.
Should I give up on trying to hang on to g for acceleration and hence cg for centre of gravity? It seems to be a lost cause!