To: Dave Jackson
The following is submitted to provoke interest, boredom, or a scathing rebuttal.
A. For a rotor that is freely articulated at the center of rotation, or a teetering rotor, the phase lag is 90-degrees.
Response:
There are no (to my knowledge) any helicopters that have articulated heads that flap at the centerline. The closest you can come to that configuration (to my knowledge) is a Sikorsky S-51 or a Boeing CH-47 or a CH-46. These helicopters have what is known as a spider and the blades are attached to the spider and flap about the hinge formed by the spider. This flapping takes place several inches from the center of rotation. These types of helicopters do have a 90-degree phase angle.
B. For rotor that is totally rigid, except for feathering, the phase lag is 0-degrees.
Response:
Possibly with the exception of the S-69 (?) which has a rigid head and blades there is no totally rigid system as all have some points where either the rotorhead deflects or, the blades bend. The precursor to the Cheyenne had a rigid head and it had a phase angle of 90-degrees. The Cheyenne was designed to have a similar phase angle but it didn’t work out that way due to both the aerodynamics of the blade and stiffness of the blade. The phase angle would vary due to speed, loading and air density. This variance was so severe on two occasions that the blades contacted the fuselage. On the first occasion the pilot was killed and on the second a wind tunnel was destroyed.
The conditions are;
The rotation is CCW, when viewed from above.
Azimuth-0 is aft; azimuth-90 is to the right, etc.
The flight maneuver is a transition from hover to forward flight.
In the case of A/, the higher blade pitches will be found between azimuth-181 and azimuth-359, with the highest at azimuth-270. The 90-degree phase-lag will result in the disk being high between azimuth-271 and azimuth-89, with the highest at azimuth-360. This will cause the rotor disk to 'drag' the helicopter's nose down about its pitch axis.
Response:
Your text should read the highest pitch is realized when the blade is at azimuth 270
And the highest point of flap is at azimuth 360 and the lowest point of flap (down) is at azimuth 180. This is true for a teetered rotor and an articulated or a flex rotor of some kind.
In the case of B/, the higher blade pitches will be found between azimuth-271 and azimuth-89, with the highest at azimuth-360. The zero-degree phase-lag, in conjunction with the absolutely rigid coupling of the rotor to the fuselage will cause the rotor disk to 'pry' the helicopter's nose down about its pitch axis.
Response:
Rigid rotor helicopters fly just like any other type of helicopter the only difference being the response to control input.
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An addendum to the forgoing is that this extremely rigid rotor must have higher than normal strength and thus greater mass. The mass will invoke gyroscopic precession. . However, the gyroscopic precession will be relatively small, and in the case of twin counter-rotating main rotors, such as the coaxial and intermeshing configurations, the opposing gyroscopic precessions should provide some static stability.
Response:
The rotors on a CH-47 can be viewed as individual rotors, both of which respond to control input. In forward flight up to about 60 knots there is no gyroscopic precession. Above 60 knots there is an automatic cyclic input and at this time there is gyroscopic precession or if you are a non-believer aerodynamic precession. Only when lateral cyclic or any other input that would cause the discs to tilt there is gyroscopic precession or the other thing if you are a non-believer. The fact that the blades are turning in opposition there is no stabilizing effect due to gyroscopic forces acting in opposition. I believe the same is true for coax helicopters and those like the Kaman.
Over.
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