Vessbot, SFT, Meddlmoe et al. The problem here is that the real protagonist is not here to help square the circle. Here's what Nick Lappos had to say in 2005
In fact, many helicopters have control phase angles of less or more than 90 degrees, based on the hinge angle (delta 3) and the blade inertia vs its flap damping. I know of one helo that had a lead angle of almost 180 degrees, and the S-76 has a lead angle of 56 degrees, both not at all 90 degrees!
The way the blades flap as they whirl around, and the way the cyclic makes them flap is not gyroscopic at all, but a gyro and a rotor share the same need to make fundamental physics happy. The conservation of angular momentum is the key, so there is a bit of gyro DNA in a rotor, but not enough to make the lead angle precisely 90 degrees. In fact, it s almost never exactly 90 degrees in any helicopter. In fact, it is not even the same angle in one helicopter. let me explain:
The real phase angle of a helo can be easily found, just tilt the swash plate to the north, and watch where the rotor plane dips lowest after all settles out. The typical rotor will dip lowest somewhere around west, so we call that one a 90 degree phase angle (engineers call it gamma, the swash plate phase angle).
If you take a given helo and do that test at three different speeds, you will find three different gammas, because the airspeed has a strong effect. In other words, the "gyro precession" angle of a rotor varies with airspeed!
For a helo with delta 3, the gamma shifts for each degree of delta 3, so the Robbie, with 18 degrees of delta 3 has a gamma of 72 degrees. This has lost Lu a lot of sleep over the last few years, as he ponders the universal significance of that horrid 18 degree shortfall, all the while thousands of Robbies have flown millions of miles.
This has been beaten to death here on PPRuNe over the last few years.
Suffice it to say, the typical rigging angle of 90 degrees for most helos is an approximation, it works, it can be different for any model helos, and it is not due to gyroscopic precession.
And then a couple of posts later
It is how the rotor behaves as it flaps, it is approximated in some pretty hairy equations, and it is not generally 90 degrees.
Just because our helos are rigged that way does not make their gama exactly 90 degrees, but they are close enough so that it works. I would bet that a sizable percentage of production helos have gammas that are 10 degrees different than their controls are rigged, but it is so hard to notice, nobody cares.
When we build helos, we actually look to see what it s. I personally did it on the S-76 and Comanche. It is also not a constant for an aircraft, as slowrotor has observed, it changes with rpm (because it is a factor of the blade flapping inertia, centripital field, aerodynamic damping, hinge offset and several other things that escape me (phase of the moon?) Gamma even changes short term vs long term. If the rotor is rapidly flexed with cyclic, it dips in a different place than where it ends up long term. Boelkow drivers know this, and automatically compensate.
I suspect you would all enjoy a great debate using those hairy equations to work out how much of the behaviour of the rotor is 'gyro dna' and how much is something else.