MOSTAFA,
Thanks for the questions, I redid the post above to more clearly show the progression to more descent. I hope the new organization is helpful. If the group can follow all this, I will transplant it to my web site to add to the more general stuff there.
Your daughter sounds wonderful, when will she start making enough money so you can retire, buy that helicopter and just fly around? Unfortunately, the unsteady nature of the helo rotor wake make it a candidate for simulation, and not equations, as Dr. leishman has done. His work does include a family of helicopters all with different chords, radius, etc. They have different properties, but follow the general behavior I have extracted here. Pass the web link for Leishman's site to her, she will blast right through it, I am sure.
As a note, in flight test I have descended vertically through vrs to vertical autorotation several hundred times, so I can confirm that this sequence IS what rotors do.