Delta-3 & Phase Lag

[NickLappos]

Dave,

You and Lu wonder where the 18 degrees go because you don't concieve of the way delta three changes the flapping geometry of the head. No matter how you two wonder, the head knows, that's why the controls must be phased differently, and that's why the S-76 and Robinson have appropriate phase angles, even if they seem wrong to you and Lu.
Every degree of positive delta three reduces the phase angle of the rotor by that same amount. That is a physical fact. The blade operates about an equivilent flapping hinge (the dual pivot points of the flap hinge and the blade pitch change horn) that allows it to flap earlier. You mix the concepts of blade movement with the concept of blade lift (thrust). We are talking about flapping as a physical movement of the blade. If the blade rises, it is moving, regardless if it produces any lift while doing so. Thus, when the blade rises earlier, it needs less phase angle.
The controls of the S-76 are almost perfect in regrad to phase angle, and the phase angle is about 57 degrees.

The use of delta three in the main rotor is almost always to reduce aircraft disturbence to those gusts and to relieve blade stress at the head due to gusts. I know this is true for the S-76 because I was one of those who helped introduce delta three into its design, back in 1974. We specifically chose it so that the ride was more stable, and it works that way, admirably. It also flattens out the cyclic pitch sensitivity, and makes things harder for the designer, who must figure out how to get more feathering angle for the blade because the delta three washes it out.

For the tail rotor, the delta three is not for gust alleviation. If the tail rotor had no delta three, it would build enormous flapping forces as the aircraft built up speed, due to dysymetry of lift, where the forward sweeping blade would have very high thrust, and would introduce very strong moment into the head and shaft. Delta three acts like an automatic stress relief for the tail rotor, that is why most tail rotors have about 45 degrees of delta three. This means that flapping of the tail blade reduces the increase in blade lift to almost nothing.