The most efficient propeller is one blade with a counterweight on the other side. Next most efficient is two blades, followed by three, then four, etc.
The real reasons to go to more blades are two:
1) There comes a point where the diameter of the propeller at the RPM in question approaches the sound barrier. You thenm opt for more blades at a lesser diameter to slow the prop tips.
2) There comes a point where the power to be absorbed by the propeller requires more blades or an increase in diameter that causes a) supersonic or transonic tips or b) unacceptable loss of ground clearance. (It is WAY easier to design a shorter prop than to fit longer landing gear)
The F6F and F4U make a really good comparison, and are the source of long-standing errors in performance estimates. They both had the same engine, same propeller at first and almost the same frontal area and, although the two planes had different performance numbers, they flew almost identically if flown side-by-side.
Grumman figured the Corsair had airspeed pitot installation errors causing it to be thought of as faster than it was. Naturally, Vought disagrees.
Famed Grumman test pilot Corky Meyer related that he flew an F6F-5 and an F4U1 side by side in 1943, alternating between the two, and there was no performance difference except in the main stage where Grumman did not use ram air and Vought did. Grumman did this to help prevent carb icing in cold weather, and MANY fewer F6Fs were lost to carb icing than F4Us. Both used ram air in high and low blower.
Anyway, the F4U was developed into the F4U-4 and had a much more powerful (2,600+ hp) P&W R-2800 than the F6F-5 (2,000 hp). Because of that, it needed more blades to absorb the power. Increased diameter was not an option since the landing gear was fixed.
Interestingly, the F8F Bearcat also had an R-2800. Later ... MUCH later ... one Bearcat used for racing owned by Lyle Shelton had (and Rare Bear still has) an R-3350 fitted. It was fitted with a propeller that requires the pilot to keep the plane in a 3-point attitude at all times. Lowering the noce will cause the prop to intersect the ground. So ... it works, but is quite a handful on the ground or when approaching a landing. Then extra power is also destabilizing.
More power without an attendant airframe modification is ALWAYS destabilizing, and results in a plane taht doesn't fly as well as one designed for the installed power. this is, of course, true for PISTON planes.
More powerful jets don't entail the addition of destabilizing blade area in front of the aerodynamic center of lift. Then again, jets can usually hit the airframe's critical Mach number more easily than can a propeller-driven plane. That is another story entirely, one that several early owners of Lear 25s discovered as they dived into the ground while pulling back futilely on the stick with all their strength. Geoffrey de Havilland also found that out when he died in his D.H 108 Swallow, I'm sure much to his regret. Therer were many more, both before and after these examples, some in WWII.
The Lockheed P-38 Lightning, among others, was known to get into Mach tuck at high speeds, though it wasn't called Mach tuck at the time. It was called "Compressability."
