Well, here are 3 credible definitions of THP:
<<The amount of horsepower the engine-propeller combination transforms into thrust.>> McGraw-Hill dictionary of aviation
<<THP: The horsepower equivalent of the thrust produced by a turbojet or turbofan engine>> FAA Handbook of Aeronautical Knowledge.
<<The amount of power that gets converted into thrust is referred to as thrust horsepower or thp>> Hubert C Smith Ph.D. Associate Professor Emeritus, Penn State
Well as far as I'm concerned none of them are precisely scientifically credible; words like 'equivalent' can be read as meaning 'exactly equal to' but this is not the case, the dimensions of the units involved are wrong. The discrepancy in all 3 cases, to make the units correct, is a velocity term. i.e. TAS. Which takes us right back to square 1.
really, none of those definitions is any more precise than saying
'well, its kind of like this.....'
I bet if you asked Hubert C Smith to give you a formula relating THP and thrust he would say: THP = Thrust x TAS.
pb