How to calculate in the right way the efficiency of a propeller?
If we know the engine power, speed of the plane and the thrust of its propeller, what is the correct method, (1) or (2), for calculating the efficiency of the propeller?
Assuming that Method 1 is the correct one, it appears that the efficiency of a propeller must satisfy the inequality:
Update:
It looks like Method 1 is correct and 2 is wrong as long as the page Performance of Propellers, MIT calculates the efficiency on an ideal propeller and gets the same inequality. If a propeller of diameter, d, delivers the thrust, T, while the plane travels at the speed, V, it always has a maximum possible efficiency that can be calculated, is below 1 and can not be improved. Not even an ideal propeller of diameter, d, has, in general, an efficiency that reaches 100%. The absolute minimum, reference power, is always $TV$ and not something else and the efficiency is always: $$TV/Power_{absorbed}$$ where the minimum absorbed power is calculated with Froude's Propeller Theory.