Delta-3 & Phase Angle
This new thread has been started to explain two specific subjects. It is separated from the [Cyclics, Semantics and Teetering Rotors ~ A question] thread so that both can stay on topic, which is/are different.
IMAO (In My Arrogant Opinion) the following is a valid description of these two subjects. Of course, the thread is always open for a scathing rebuttal.
Delta-3 & Phase Angle:
The following is an explanation of delta-3, followed by an explanation of phase-lag. It should be noted that these are two different subjects. The action of the rotor's hub, due to delta-3, and the action of control system, due to phase-lag, are then related.
Please note that phase-lag is also used in conjunction with 'flapping hinge offset'; but not in this thread.
In a conventional teetering rotor, the application of 10º of cyclic stick will result in the swashplate [control plane] having a 10º tilt. This, in turn, will change the plane where an observer sees no variation in cyclic pitch [no feathering plane] so that it will have a 10º tilt. This cyclic pitch of the blades will then result in a 10º tilt of the disk [tip path plane]. It should be noted that the stick input [control plane] and the rotor output [tip path plane] have identical values. It should also be noted that if the cyclic stick was somehow instantly advanced by 10º then the disk will tilt by 10º within one revolution.
A teetering rotor with delta-3 operates differently. To set the boundaries of delta-3 it should be mentioned that 0º of delta-3 will be the same as no delta-3. In other word, the amount of flap equals the amount of pitch, and the scenario in the previous paragraph will take place. We could say that 100% of the change in cyclic stick pitch gets through to the blades.
If there happened to be 45º of delta-3 then every degree of flap will remove one degree of pitch. This means that none (i.e. 0%) of the change in cyclic stick pitch gets through to the blades.
Lets now assume that the rotor has 20º of delta-3. This means that approximately 70% of the cyclic stick pitch get through to the rotor. In other words, the application of 10º of cyclic stick will result in the swashplate [control plane] having a 10º tilt. This, in turn, [b]through the modified pitch horn[/b], will change the plane where an observer sees no variation in cyclic pitch [no feathering plane] so that it will have a 7º tilt. This cyclic pitch of the blades will result in a 7º tilt of the disk [tip path plane]. In other words, the stick input [control plane] and the rotor output [tip path plane] are not identical.
It should be noted that if the cyclic stick was somehow instantly advanced by 10º then the disk will have tilted by 7º within one revolution. There is still a discrepancy of 3º. This means that the tip path plane will tilt 70% of the 3º in the next revolution, which is 2.1º. This means that the tip path plane will tilt 70% of the 2.1º in the next revolution, and on, and on, to infinity. In other words, with delta-3 the tip path plane will have a slower response to the instruction from the control plane.
In an articulated rotor, the phase angle is related to the frequency of blade flapping. A greater flapping hinge offset means a shorter blade, which means a higher frequency and a faster flap to position. Because the blades flap to position sooner the instruction to flap must be delayed, so that orientation of the cyclic stick and the orientation of the disk are in the same direction.
In a teetering rotor, delta-3 does not change the frequency of the blade flap (teeter). All that delta-3 does is reduce the amount of flap (teeter), not the speed at which it flaps. In other words, the teetering hinge with or without delta-3 has a frequency matching that of the rotor.The forgoing three sentences may not be correct. See the graph midway down the page Pitch-Flap Coupling; (delta3) If the phase lag angle is reduce by 20º, from 90º to 70º, then the location of lowest and highest teetering will be 20º further around the mast. There will still be 180º of increased pitch and 180º of decreased pitch.
The following two graphs, which were stolen from Ray Prouty and Shawn Coyle without permission, may help explain the activity.
The graphs are rough approximations but it is interesting to compare them. Both show very little lateral cyclic stick near hover and both show a reasonable amount of left cyclic stick at fast forward speed. The obvious difference between the two is the opposite lateral cyclic at moderate forward speed.
It is assumed that the left-hand graph represents articulated rotors and basic teetering rotors. As the forward velocity increases, the craft will experience 'transverse flow effect' and then the effect of coning. Both effects require the application left lateral cyclic.
It is assumed that the right-hand graph represents a teetering rotor with delta-3, such as the Robinson. In this situation, the phase lag has biased the teetering to left. Therefor at moderate speeds there is a need for a small amount of right lateral cyclic, whereas at fast forward speeds there is a need for a small amount of left lateral cyclic.
Delta-3 and Phase Lag are two distinctly different functions. Delta-3 'softens' the response of the rotor to the cyclic control. Phase Lag repositions the radial orientation between the cyclic stick and the rotor disk.
In addition, I can see no reason why the delta-3 angle and the reduction in the phase angle need be the same, other than that of keeping the pitch link vertical.