Graviman,
The issue is still that you tend to see the blade as some static source of lift (as in the phrase "maintain constant lift throughout the azimuth") when in fact that blade is whipping about, getting its butt kicked by the relative wind (which changes its azimuth relative to the chord line at about 5 to 10 times per second) and also by the rotor controls, which are constantly changing its feathering in the hopes that the net lift averages out to 1/N of the aircraft's need.
At the hover, there is no N/rev because all the blades are experiencing almost no azimuthal variations, and the flapping across the revolution is approximately the same. As you build forward speed, the blade begins to see this varying velocity vector, varying as to speed and angle from the chord line.
At Vmax, the blade advancing abeam at precisely 90 degrees sees the "wind" as Vrotation plus Vairspeed. When that passes over the nose, it sees the "wind" as the vector sum of Vrotation and Vairspeed (which are 90 degrees apart). Each blade chord segment going out from the root sees the lateral angle of the "wind" differently. At the hub, the "wind" is along the blade, and no lift is produced. At 1/3 span, the "wind" is about 45 degrees to the chord line, at the tip it is about 20 degrees. Do the math for the confusion of the lift distribution, and the net wild spanwise swings of the center of net lift as that blade travels around. Then remember that this variability occurs at 5 to 10 times per second. In effect, the blade is bucked and kicked by its chore, which rings every natural frequency it has. Look up that classic blade movie to see the wild ride the blade takes.
Again, only a stolid ME with a feeling for static solutions could see this as a nice, solvable problem of statics!
If there were one blade, the pounding of the root shear is eye watering, with two blades it is less than half the variability, by 7 or 8 blades, the root shears approximate a steady flow of lift.
I have no idea how you showed the proof that you did, where 3 is the optimal number of blades, but I'd suggest two things :
1) Get a good book on helo engineering (Prouty, and Stepnewski + Keys are two that come to mind)
2) If you have a mortgage, don't quit your day job to run off designing a helo!!
