Some very important points are being missed here.
Even if all other things are equal (which they are not), it must be remembered that Thrust, not Power, is required by the aircraft. Power is produced by the engine to drive the propeller and produce the thrust, and the useful thrust is the fore and aft component of the propeller reaction, the lateral component of propeller reaction is torque.
Seeing as some sample figures have been included in the last post, I’ll use them, i.e. 2000 R.P.M. and 2500 R.P.M. To provide a sample propeller of 4 feet radius, the mean propeller position (in terms of thrust production) is at 4 ft X 70.7% = Radius 2.828 ft.
Thus, at 2000 R.P.M. and 2500 R.P.M., propeller rotational speed at the mean position is 35,537.7 ft/min and 44,422.1 ft/min respectively.
Assuming that the propeller accelerates the incoming air flow by 60 knots, i.e. 6076.1 ft/min (about normal), the vector sum of the relative airflows over the propeller for the 2 engine speeds whilst the aircraft is stationary are –
2000 R.P.M. = 36053.4 ft/min : 2500 R.P.M. = 44835.7 ft/min
As the lift force generated by the propeller is directly proportional to the speed squared, the 2500 R.P.M. propeller is generating 1.55 times that of the 2000 R.P.M. propeller, or put inversely, if the 2500 R.P.M. propeller is producing 1 unit of reaction, the 2000 R.P.M. propeller is only producing 0.647 of a unit.
Now, assuming that both propellers are at an angle of attack of 4°, the blade angle of the propellers are –
2000 R.P.M. = 13.7° : 2500 R.P.M. = 11.8°
As the useful thrust equals the reaction force multiplied by the Cosine of the blade angle, the Thrust comparison becomes –
2000 R.P.M. = 0.647 Units X Cosine 13.7° = 0.629 Units : 2500 R.P.M. = 1 Unit X Cosine 11.8° = 0.979 Units
Thus, at zero speed and maximum power set in both cases, the 2500 R.P.M. propeller is producing 1.56 times the thrust of the 2000 R.P.M. propeller, or inversely, the slower propeller is producing only 0.641 times that of the faster propeller.
The “big chunks of air” theory, if put into effect, will lead to the loss of big chunks of performance.
Regards,
Old Smokey