The flybar paddles are two small airfoils (one on each end of the flybar) in a Hiller or Bell-Hiller head design. When the flybar twists (due to swashplate inputs), the pitch angle of the paddles change, changing the amount of lift they generate and tilting the flybar disk in the direction the helicopter should go.The main rotor disk then follows the flybar's change of plane.
A helicopter can be made slightly more stable by angling up the paddles a few degrees (called adding dihedral); with a small amount of dihedral, as the flybar disk moves away from horizontal, the paddles will tend to create forces that push the disk back to horizontal. Especially on fixed pitch helicopters, this may limit forward flight top speed due to retreating paddle stall, causing the helicopter to pitch nose up dramatically.
The paddles play a large part in determining the 'feel' of a model helicopter. Paddles come in different weights (some can even have their weight changed); the heavier the paddles, the slower the cyclic rate and so more stable the helicopter. Different airfoil shapes also affect the feel: sharper edged paddles will tend to "catch" the air more, and so lead to faster cyclic rates, but can lead to the nose pitching up in forward flight or wind.
Share your opinion