italia: back to the helicopter problem. 'No THP in the hover' you say. The two main arguments you have provided go like this:
'The aircraft doesn't move therefore no work is done on it therefore there is no thrust horsepower, only thrust.'
'Power = Thrust x airspeed. There is no airspeed therefore there can be no thrust horsepower.'
Nobody at all is arguing with the equation you provide, and everyone will recognise the definition of work being a force x distance. They are basics. But it seems you are in denial when it is pointed out that work is being done on the downwash (as CYHeli stated). Your argument is a purely semantic one in which you insist on defining THP as that which moves the aircraft.
Because a helicopter can hover there is an alternative way of determining the efficiency of the rotor system that does not require airspeed of the vehicle. It is called Figure of Merit - not a phrase I was previously familiar with TBH. What is done is the 'power' of the so-called induced airflow is determined. It is the power that results from the thrust. The efficiency of the rotor is then determined by dividing the induced power by the sum of the profile power (from rtr drag) and induced power:
M = Pi/Pi+Po.
None of this requires the aircraft to be moving. It is explained in Basic Helicopter Aerodynamics by Seddon
pdf here. Ch 2.