Please share with us the infallible math you are using Phil.
Well it was a serious point actually. I'm not sure to what extent you may or may not agree with any of this but it was discussed to some extent on another thread with talk of tip speed ratio i.e. the speed of the rotor at its tip v the speed of the aircraft as read from the ASI.
If you consider your very own point made just a moment ago:-
In my opinion a two blade semi rigid gyroplane rotor becomes divergent when the critical angle of attack of the retreating blade is exceeded.
There are many ways to achieve this.
Contributing factors are not enough rotor rpm for a given indicated airspeed, disk angle and turbulence.
Suggests that you have some recognition of the same, yet there are a mixture of issues in your view.
If we deal with what actually creates the issue of blade sailing in your two blade teetering rotor; it is merely because the flapping required in the rotor to "equalise" the disymetry of lift is constrained by the teeter stop, that gives some feedback via the stick and because its onset is very fast [usually because the pilot has pulled the stick back creating more alpha to flap out and rotors have become slow] the aircraft rolls due to disymetry of lift [now unable to have been equalised via normal flapping/teetering [language] action of the rotor] and the aircraft thrashes itself to some form of damage on the ground.
The alternative is the rotors are very slow but so is the airspeed [ground speed] and the rotors smash the tail to pieces.
I can not find a case where the combination is such that the rotors have flapped, the aircraft didn't roll or the blades were fast enough to get airborne but we had smashed the tail to pieces and then we fell out of the sky. [if someone can point to an investigated accident that contradicts that view please refer me to the report].
That doesn't happen because once the rotor has accelerated it will keep doing so to flying speed as long as the tip speed ratio is favourable.
Edited to add the quote from the prior thread in September on same subject:-
As you know, the divergence of the flapping angle is due to the stall of the retreating blade. Therefore the acceptable limit of tip speed ratio also depends on this angle.
Unfortunately, the angle of attack of each blade element changes periodically during rotation, which creates an hysteresis: Later stall and re-stall. The stall angles then become difficult to predict for me, and thus also the critical ratio of divergence.
But to give you an order of magnitude, I find that in a situation quite usual for our gyroplanes (A.o.A disk at about 20°, aerodynamic pitch of the blades at 3°, and assumed stall angle of 13°) the calculated divergence seems to appear to me as soon as the speed ratio of 0.2
If one accepts that number roughly then the average modern 2 seater pre-rotated to 200RRPM could see 40mph on the ASI before a problem occurred. If you also accept that the same aircraft will likely "wheel balance" at 300RRPM and 60mph becomes an issue. The paradox comes when you see an aircraft seemingly take off in a normal fashion at a normal attitude but then suggest that it had rotor to tailplane contact - which can only occur with slow rotors and large backstick inputs [assuming design]. You don't strike the tail with a flat rotor....and if its too flat you don't get RRPM and neither do you get airborne.
Elsewhere a view was given on the inability to keep the stick fully back on a Magni... well thats not technique thats just arm strength!