Nick,
Yes, there is difficulty understanding some of your points, but, your statement
"No matter how you two wonder, the [delta-3] head knows" can not be implying that a dozen pieces of metal in a delta-3 hinge has a higher cognitive ability than Lu or I.
Or does it?
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You say;
" the S-76 and Robinson have appropriate phase angles, even if they seem wrong to you and Lu"
Now you've really gone and done it.
Who said that the phase
angle was wrong. Hell, I've never even said that Robinson's use of delta-3 is wrong. The other thread is currently an attempt to understand his first reason for using it.
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You say;
"The use of delta three in the main rotor is almost always to reduce aircraft disturbance to those gusts and to relieve blade stress at the head due to gusts."
Now you've gone and got yourself into an argument with Frank Robinson.
He says;
" The R22 rotor system was designed with 18 degrees of delta-three to eliminate two minor undesirable characteristics ..... [1] In a steady no-wind hover, when forward cyclic pitch is applied, the 90-degree rotor disc will end up tilted in the forward direction ....... [2] The other undesirable characteristic in rotor systems having 90-degree pitch links is the lateral stick travel required with airspeed changes ..."
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You say;
"The blade operates about an equivalent flapping hinge ... that allows it to flap earlier."
I disagree on this point. The rotor's delta-3 is working in conjunction with the swashplate's phase-
lag. The Robinson's blade will start to flap (teeter) 18º
later.
To use an application of forward cyclic as the example, the control plane (swashplate) will be highest at 0º azimuth (the back) and lowest at 180º azimuth. This is in agreement with FR's statement;
"The lower non-rotating swashplate is aligned with the aircraft's centerline and always tilts in the same direction as the cyclic stick."
On a Bell-47, with its phase angle of 90º, it means that the blades minimum pitch will occur when the pitch-link - swashplate joint is at 180º azimuth and the blade is at 90º azimuth.
On the Robinson, with its phase angle of 72º, it means that the blades minimum pitch will occur when the pitch-link - swashplate joint is at 180º azimuth and the blade is at 108º azimuth.
In other words, all cyclic control (pilot) induced activity at the blade will take place 18º later on the Robinson than it will on the Bell.
In addition to what the swashplate's phase lag has done, the rotor's delta-3 will decrease the strength (angle) of that which was requested by the cyclic input.
Phase lag is used in conjunction with flapping hinge offset and with delta-3, but I believe that flapping hinge offset and delta-3 are two quite distinctly different activities. An example of this distinction is the fact that flapping hinge offset will reorient the disk faster then a basic teetering rotor, whereas delta-3 will take considerably longer then a basic teetering rotor.
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No argument with your last paragraph. My use of the word 'gust' was a lousy way of saying 'aerodynamic input'