when what actually happens is that auto begins when RoD exceeds induced velocity by enough to offset profile power.
As the collective is lowered the aircraft starts to descend and the induced velocity and the induced power both fall to zero. As the aircraft accelerates downwards the direction of the total reaction is tilted in the direction of rotation at some points along the blades and is tilted in the opposite direction at other points. It is only when a certain rate of descent has been achieved that the sum total of the different parts of the total reaction is sufficient to keep the blades rotating in the correct direction and to produce sufficient lift to support the weight of the aircraft. When the sum of lift plus vertical component of drag equals the weight of the aircarft the ROD becomes constant. The actual rate of descent depends upon a number of things include blade pitch angle and aircraft weight.
So even with a helicopter, the autorotative force does not become significant until a certain ROD has been achieved. But none of this confirms your argument that induced power is the same thing as THP
The actual mechanical arrangement is superfluous, this is about the over-arching physics. Simple momentum theory considers only that a 'disc' accelerates air. This does not tell you if the model is mechanically capable of going into auto, it tells you the theoretical relationship between induced velocity, RoD and thrust.
And
Any helicopter pilot will tell you that auto requires a healthy rate of descent, not merely a slight descent.
I have known several hundred helicopter pilots over the years, but none of them have flown theoretical discs. They have all flown real helicopters with real rotor mechanisms. You are using the behaviour of real systems to support arguments about theoretical physics, then you are saying that the actual mechanical arrangement of the systems is superfluous. That line of argument is clearly nonsensical because the behaviour of the real systems is determined as much by their physical characteristics as it is by the theoretical physics.
Throughout this thread you have made various assertions, including the following:
1. Propellers continue produce THP when the aircraft velocity is zero.
2. When an aeroplane is standing still on the ground with wheel brakes applied the THP is equal to Thrust x propwash velocity.
3. If propellers produced no THP when the aeroplane is standing still on the ground, it will be impossible for the aeroplane to accelerate when the brakes are released.
4. If THP is Thrust x TAS it will be impossible for aircraft to accelerate in flight.
5. THP is the same thing as Induced Power.
6. The propulsive efficiency equation is not the correct equation for propeller efficiency (though interestingly you have never actually stated what the correct equation is).
7. As long as a propeller is producing thrust its efficiency cannot be zero.
In each case your assertions have been incorrect. You have certainly demonstrated tenacity in pursuing these arguments for so long, but you have also demonstrated a very poor understanding of these subjects.