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bit A free teetering two blade rotor system doesn't tilt due to precession.

Gyroplane rotor blade control is rotor head induced and aerodynamic.*2
The flying of a gyroplane is not "weight shifting"
but rather "wait shifting" (pardon the pun).
bit A free teetering, two blade, rotor system on a gyroplane doesn't tilt for a direction change from a force on the rotor disc applied by the pilot. (Rotor disc only exists when the two blades are spinning)

"A gyroplane pilot only has control of the rotor head. The rotor head is in balance with the hub bar during sustained flight (fixed turn or level flight).
"To change the level of the rotor disc (to initiate a turn) the pilot puts the rotor head out of balance with the hub bar. This causes a difference in pressure on those areas of the rotation disc, which causes a change in level of the disc, applied about 90 degrees later.
"The overhead rotor disc changes it's level to balance again with the rotor head.
Because there is a momentary delay from pilot input to final movement (response), the pilot must learn to wait after making a control stick adjustment, then make another adjustment if necessary to complete the turn. This "wait" reflex on the part of the pilot is particularly important in learning to fly a gyroplane."

Precession response is triggered due to an aerodynamic force being applied by "vaning" of a rotor blade 90 degrees earlier on the rotor disc.
There is no way a stick input could directly force the rotor disc to change levels. over head stick arrangementThat's why older style rotor heads used an overhead stick down from the rotor head to change the rotor disc plane to a different angle. They did have to use brute force. Sometimes in recovering from a steep descent the pilot would apply too much direct change and the rotor plane would be aerodynamically "caught" in forward motion (drag), to over come the pilots strength.

With proper set-up you can fly a gyroplane hands free. The rotorhead and rotor hub bar always seek to remain in balance. The gyroplane is hanging from the rotor head and subject to "g" forces and aerodynamics as the rotor blade disc (plane) is flying through the air.
Regalpony logo image

Hub Bar,
Spindles and

precession diagram image
bit rotorhead, hub bar, linkages image
Bensen type
gyroplane bit
What is gyroscopic precession?

On any spinning wheel (disc / plane) there is a delayed reaction to change in levels. Even though a two blade rotor system is not a wheel, it becomes similar to one when spinning at a high enough rate. This creates gyroscopic effect and it behaves in like manner.
(see diagram)

Commentary: For some unknown reason, gyroplane designs have been moving away from "tried and true" to become more like aeroplanes.
What would "tried and true be"? Basically, the over head stick. The over head stick arrangement allowed easier input adjustments to the rotorhead, by a ratio of 13:1.
The tail area is also becoming larger as open frame moves to enclosed cabin. Unfortunately the tail design is ignoring "tried and true" and not considering the Cone Stabilzer.
The original Bensen style rotor head was not a offset gimbal type rotor head, rather it was a spindle head design taken right from Haffer's Rotachute glider. Although not really well designed for gyroplane use, it has not been on record as failing in use.*1
It's too bad more design work had not been made in the area of bearing support which is the spindle heads weak point.
However, the Offset Gimbal Head design is much better. It is self stabilizing in pitch. The Offset Gimbal Head almost balances the amount of lift created to the amount of drag that is being simultaneously produced.*1 A spring system is used to complete the balance.
  *1 Peter Lovegrove: Spindles and Gimbals, 1998, The British Rotorcraft Association  
Revisions: *2 According to D. McCoy, PhD