A writer recently used Thrust = $\eta \frac {P}{V}$ here to determine the maximum forward airspeed of an aircraft for a given set of conditions.
While efforts made to answer were very impressive and reflected a lot of effort, there was a nagging question that seems difficult to reconcile:
does thrust always decrease when airspeed increases?
Wouldn't a better expression of prop thrust be:
RPM × AoA$^1$ to the relative wind?
Before the mass flow argument comes in, let's consider that specific impulse of props are in the thousands while the best (mass flow) rockets barely top 400. Props pull by making lift, and loss of $\Delta$ mass flow velocity will have far less effect on thrust than non-optimal AoA at higher airspeeds.
The drag of the prop is consuming the engine power, not the planes forward speed!
Which leads us to:
jets are constant thrust, props are constant power?
Really? Isn't engine power strictly a function of fuel flow?
As an aircraft gains airspeed, prop pitch must coarsen to maintain optimal AoA. Thrust loss is only cosine of this angle, in other words, not much at all at lower angles, especially if prop RPM is high, which brings us to this, courtesy of Stipa and Caproni from the 1930s.
I know, too slow, not enough power, too much drag. But if the propeller were recessed into the duct where air was slower and higher pressure, might this not be an analog of today's fan jets? Could ram pressure at increasing airspeeds eliminate the need for variable pitch?
$^1$ as part of a prop "lift equation"