And since precession on a gyro is always 90 degrees later than where the force is applied, the fact that different helicopter rotor systems have phase lag angles of less than and more than 90 degrees rather puts the whole 'precession in a rotor system' argument to bed, once and for all. The precession argument is for people who don't understand flapping.
Not quite. If you play with a real gyro, its RPM determins the amount of force that gyroscopic precession will have, therefore the actual angle of tilt will be somewhere in between the orginal, and 90 degrees after.
Of course, as has been gone over again and again, the this force is so small on most helis that it's much closer to 0 than 90.
I know that a few people here are going to scream in horror if this topic goes on any longer, but I'd like to put across a perspective I haven't seen before:
If the 90 degree phase lag really was mainly because of gyroscopic precession, then surely the downdraft when applying the cyclic would preceed by 90 degrees. E.G. if your rotors spin clockwise, then appling forward cyclic should create the strongest downdraft on the right hand side. Seems like a fairly easy way to debunk the myth. How they conduct these experiments is their own problem. But playing with my RC heli (which probably feels gyroscopic forces more than most large helis) clearly shows the strongest downdraft at the back.