To: Jave Dackson
I'm really confused by what you said that I said but I'll try to respond.
Lead/lag or conservation of angular momentum. First letís address a fully articulated rotor system. Assume the helicopter is in a hover and there is no correction for tail rotor translation. In other words the disc is parallel to the horizon. In this case the driving and driven axes are coincident with each other. This reference to two axes will be cleared up in just a minute. In this condition there is no leading and lagging. When the pilot moves the cyclic forward the disc will tilt forward and in doing so the driven axis will tilt forward in relation to the driving axis (rotor shaft).
With this tilting of the driven axis you will get leading of the advancing blade and lagging of the retreating blade and assuming a four-blade rotor system the blades over the nose and tail will be aligned with the longitudinal axis of the helicopter. If this is the case then why doesnít the rotor system go out of balance if the blades are not evenly disposed. I donít know the answer to that question but this is what a prominent aerodynamasist wrote in his book.
Quote: If you could stand in space and look down on the rotor system with your eye aligned with the rotor mast (driving axis) the blades would look as if they were not aligned like a cross. In fact the blade over the right side (Sikorsky) would be forward of the lateral axis of the helicopter and the retreating blade would also be forward of the lateral axis.
Now move your position in space with your eye aligned with the rotating axis (driven axis) of the rotor system and the blades would appear to be 90-degrees apart. I donít know if this explains why the rotor system is not imbalanced but I donít have the brainpower to explain this phenomenon any other way. So lead and lag is allowed on this type of rotor system and on other rotor systems that are soft in plane. On rigid rotors there is also a misalignment of the two axes but there is no lead/lag hinge. The blades flex inplane.
Now we go to a semi rigid head. Bell did not want to have their blades lead and lag as this would involve beefing up their blades and rotorheads. To counter lead and lag they dropped the rotorhead in relation to the teetering hinge. This was referred to as underslinging the rotorhead.
In the case of moving the cyclic forward with the attendant tilting of the disc the rotorhead would shift rearwards on the teeter hinge and although there was a misalignment of the two axes the driven axis would intersect the driving axis. By doing this the Bell engineers eliminated the tendency to lead and lag and any lead and lag that was there would be reacted by the drag link that attached the rear of the rotor blade to the rotorhead.
Now we get to the Robinson head. This design is also underslung so as to eliminate lead and lag. However this rotorhead also has cone hinges so when the blades cone or flap about this hinge there is a misalignment of the respective drive and driven axes resulting in leading and lagging. This movement of the blade is reacted by the cone hinges with the resultant force being transmitted to the teeter bolt and down through the rotor shaft to the final reaction by the fuselage. Although Robinson purists wold reject this writer opinion it has been proven by checking the cone hinges on some R-22s and you will see that the hinges are worn elliptically.
Here is another little known fact and I may get the terminology screwed up but here goes. Since it is very difficult to get the CP and the spanwise CG in perfect alignment with the pitch change axis designers will move the pitch change axis forward on each blade by as much as ľĒ in relation to the centerlines of the rotorhead. Because it is difficult to get these points in alignment the blade will bend inplane in order that the tip of the blade brings these points into alignment. This places a strain on the blade so by moving the pitch change axis ľĒ forward this movement of the tip is eliminated.
With that being said I will patiently await correction by those of you that went to engineering school as mathematics was not taught in the fine arts department when I went to school.