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The power determines the amount of blade area needed and the diameter possible determines the number of blades. The Germans stuck with 3-bladed props because they primarily used fuselage-mounted weapons and needed to fire through the propeller arc, Fewer blades means more ammunition can be fired in one revolution.
I remember asking a senior BAe aerodynamist about this some years ago. It was when civil prop planes with multiple 'cutlass' style props started appearing whether this was appearing now just because of new materials or was it unknown aerodynamics back then. He told me the most aerodynamically 'pure' solution was as few blades as possible but that new materials meant the compromise with more bigger blades was less. In short a 6 (or more) blade prop could have been made with similar profiles but the materials back then meant no advantage ( a lot of disadvantage - ie weight both of the unit itself it's controlling mechanisms) could be made from it. Maybe if jets had not appeared for several more years we might have seen the need drive the tech that way?
This is when Lyle Shelton was running custom blades cut down from P-3 Orion prop blades.
Good plane after the "fix" that never really WAS a fix ... but they DID learn to stay away from resonance in the props.
The Germans stuck with 3-bladed props because they primarily used fuselage-mounted weapons and needed to fire through the propeller arc, Fewer blades means more ammunition can be fired in one revolution. Many of their props had narrow hbs and very wide blades.