B407 delta3
Helisphere
I finally got to do the math for the tail rotor and beware...
Any delta3 is better than no delta3 !
Negative delta3 can be better than positive !
In approximate numbers (for a B407, without precise Bell data, just my best guesses)
I got a Lock number of 1.72
I computed a dimensional stiffness of 1% because of the bearing.
With a negative delta3 of 40° we get a negative stiffness 18% resulting in a normalized dampening of 12%, and a frequency response (amplifier) at the rotor base frequency of 300%. This is amplifier is relevant for disturbances that have the rotor frequency such as incoming wind.
Assuming a positive delta3 of 40° we get 400% ! This is worse.
Assuming no delta3 we get 500%. This is even more worse.
What happens ?
First: Tail rotors have small Lock numbers and are not very well dampened as compared to Main rotors.
By putting any positive or negative stiffness we gain more by taking the system away from the resonance frequency than by actually changing the dampening (looks a bit like the formula you quote, but this formula look a bit too simple and symmetric, but I did not verify that yet)
Second: both delta3's provoke phase shifts away from the center line of up to 30° (plus and minus)
Third: Tail rotors have also bearing stiffness. In particular this was a major modification Robinson did on the R44 (back in 2003?). Now this creates a positive moment bringing the rotor back to the center.
Putting 1 and 3 together could explain the less efficient positive delta3, because it works together with the bearing stiffness. So I would think that a TR with low bearing stiffness should go for a negative delta3 whereas a TR with some significant bearing stiffness should go for a positive delta3.
So why the change to positive delta3 :
the fact that TR's became mechanically stiffer.
m2c
delta3 (still learning...)