I did already - but don't think you were receptive then...
1 Flapping as defined by the hub plane is great for seeing what a flapping hinge (or equivalent) has to achieve - but the flapping thus defined doesn't show us what is going on aerodynamically - it just shows us the difference between Tip Path Plane and Hub Plane.
2 Defining it against the Control Plane just shows us what the flapping would be if the pitch were not varying cyclically (Pitch Change and Flapping just being equal and opposite equivalents by that definition).
3 Personally I like Flapping as defined against the Tip Path Plane - just because it more purely indicates what is going on in a helicopter. This way any half-cycle asymmetries, which are not cancelled by cyclic pitch change, result in Flapping (to equality) - the beauty being that a pilot does not NEED to know this - he just sits there and makes the attitude look the way he thinks it should look - but he is infact (secretly
) making the lift equal around the disk, and de-facto applying asymmetric pitch which accounts for (almost) all effects known (and unknown - (DR))
4 Flapping as defined by the Horizon is a
possibility but doesn't make much sense in a wingover !!
AC!
The problem is - a helicopter is just much simpler than suits everybody - I think you (Crab) agree in cases like the (bogus) gyroscopic precession doctrine?