Is high propeller pitch inherently inefficient? For an airfoil, in general, the aerodynamic force is more or less perpendicular to the chord line.
A low-pitched propeller blade has it's chord line more perpendicular to the direction of flight, therefore, more of the force acting on it can have a greater component parallel to the direction of notion, and less perpendicular. If this force is acting forward, then this is efficient. But this may not be possible at high speeds and low rotation velocities. Thus:
A high-pitched blade has it's chord line more parallel to the direction of flight than the above. Therefore, the aerodynamic force acting on it is likely to have a greater component perpendicular and lesser component parallel to the direction of motion. This is always inefficient.
The above manifests itself in the higher-pitched propeller producing more energetic swirl than the lower pitched propeller.
So my conclusion would be that all else being equal, high-pitched propellers are inherently inefficient. Is this correct? Is this what is observed in practice?
Your conclusion is too simplistic. On aircraft, the difference between a cruise propeller and a climb propeller is rather small. However, in other applications, a low pitch propeller gives great acceleration but the engine will reach max RPM faster, which reduces top-end performance. A high pitch propeller will result in slower acceleration but higher top speeds.
This answer is also admittedly very simplistic -- there is a universe of math and engineering that goes into propeller designs. Sensenich, for example, produces more than 100 fixed-pitch propellers for aircraft, airboats and UAV's. McCauley Propellers produces thousands of constant-speed and fixed-pitch configurations for commercial, military, UAV, and general aviation applications.
If you want to get into the nitty-gritty of this, I have been told this book is one of the propeller design bibles for aircraft applications, &quot;Aircraft Propeller Design&quot; by Fred Weick, published in 1930.