ORIGINAL: blw
I was talking about fixed pitch props, like we use on models, at varying RPMs and in flight. The best pitch and/or diameter to use is based upon figuring out the efficiency based upon a formula that includes airspeed. You can't have large diameter and a large pitch for most engines, so you have to make a choice. That would be what it is all about in the end. Getting the most out of an engine and airframe. You could call it calculating the pulling power of the prop, or whatever. A lot of people think that only the highest RPMs give the most power.
You can use a smaller diameter prop for faster RPMs and reach a point where it is the most efficient. If you get the tips near the speed of sound your performance will drop quite a bit. You can do the inverse and choose a larger diameter to reach peak prop efficiency. The large diameter wins out in efficiency if used on the same engine, same airframe, etc.
Prop efficiency is Thrust HP devided by Brake HP. Thrust HP is basically the thrust multiplied by the RPM, so you can basically divide thrust by the torque the engine is putting out. So airspeed is related only as far as it affects thrust. The low pitch prop will have little thrust at airspeed and will have a lower efficiency at speed than in climb and static. The high pitched prop is just the opposite. Since we are talking about increasing pitch and reducing diameter to keep the engine at the same RPM the high pitched prop will have more thrust and higher efficiency. Airframe and engine will not make a large differance here.