To get back on track, this thread is about the competence of CFIs.
A gyro CFI who does not understand the following is a danger to his student:
(1) A tilt head gyro is controlled by cyclic pitch input; in no respect different from swash plate tilt. It is not a weight shifter like a trike.
(2) A gyro rotor produces a line of thrust that is very nearly coincident with its the tip plane axis; in no respect different from a helicopter rotor or a propeller. It is not a drag chute.
(3) All rotorcraft with central flap hinges, i.e., teetering rotors, are controlled by rotor thrust vector orientation. When the rotor thrust vector is displaced relative to the CG, a pitch/roll moment is created that begins acceleration about the CG. This is no different, for instance, in the way space rockets are controlled; the engine nozzles are mounted on gimbals and the thrust line is vectored about the CG.
(4) Damping converts acceleration to rate. Without the damping provided by a horizontal stabilizer, pitch rate has no limit other than damping provided by the rotor itself.
(5) For any moving vehicle to possess stability, the line of disturbing force must trail the CG. Tail heavy aircraft respond to a disturbance in such a way as to increase the magnitude of the disturbance. Tail heavy automobiles spin out and go through the fence tail first. Tail heavy FWs can enter an unrecoverable flat spin. Tail heavy gyros are liable to tumble head over heels.
(6) Dangle angle is an aid to control centering but has little to do with CG. The primary determining factors of rotor thrust line to CG relationship are position of the line of propeller thrust relative to the CG and aerodynamic effects that tend to rotate the airframe.
(7) A rotor that flies at a 10º angle of attack under fixed conditions of airspeed and load will continue to do so whatever the dangle angle, except for the minor effects of the vertical component of propeller thrust.
Gyroplane CFIs who do not understand the basic principles outlined above ought to find another vocation.