Oggers,
The first point that we should note is that the author of that paper is not a universal authority on these matters. He has his point of view, but this cannot be used as an argument for rewriting all of the texts on these subjects.
The second point to note is that he was using a different equation because he wanted to know how much thrust the prop was producing when the aircraft velocity was zero. The final part of the essay is an equation for thrust produced.
But his equation cannot work out the efficiency of the propeller in converting power input into useful power output. And that is what the definition of propeller efficiency is all about. That is why his equation did not start with the words "Propeller Efficiency = "
But for some bizarre reason you have decided to argue that his equation is the one that should be used to calculate propeller efficiency.
Now if you wish to ignore all of the above then look at the essay a bit more closely. It includes the following equation
Substitute this into the equation for efficiency (1), and simplify to get:
The author had earlier defined VA as the aircraft velocity.
When the aircraft velocity is zero, the above equation shows that propeller efficiency is zero.
This entire thread has been about what is and what is not thrust horsepower. So there is nothing to be gained by introducing an equation that works out how much thrust a propeller produces.
If we look again at the basics:
Work is done when a force moves its point of application in the direction of the force.
Work = force x distance.
Power is the rate of doing work
Power = Force x distance / time
Power = force x velocity
From the above we can see that THP = Thrust x aircraft velocity.
Now look at your hovering model aeroplane and give us a logical explanation of why you believe that some THP is being produced.