oggers:
But, he is careful to point out that it cannot be used to determine the efficiency of a prop in the static thrust situation. It is - according to him - "invalid" in that situation. So, he uses a different equation for that.
Exactly, because it's a different kind of efficiency - i.e. a measure of how much STATIC thrust can be had, compared to some theoretical "perfect" static thrust. That's altogether different from propulsive efficiency, which is
= 100% x (Thrust horsepower) / (engine output hp)
In other words, efficiency = output / input !