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When speed building up, what happens to P47/P51/Tempest? There airscrew tips reach/break sonic barrier??? howabout 109/190's airscrew?
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IIRC, the FW-190 tested is a G series by WerkNummer.
The maximum helical tip velocity is extremely important to any propeller design. At about mach .85 most propellers will begin to dramatically decrease efficiency as the normal shock formation disrupts flow. Yes, they break the sound barrier.
You can see the effect in any fast aircraft equipped with a CSP and the ability to over speed the propeller. Climb to about 12,500 feet, preferably on a hot summer day and set the aircraft for 75% cruise. If you increase to maximum rpm and manifold pressure, you will see a drop in your airspeed.
Maybe one could simulate the effect just by decreasing propeller efficiency sharply at Mach .85.
As you stated, propellers are extremely complicated and there are lots of trade-offs in design. For example, adding blades does increase the co-efficient of power but adding blades decreases propeller efficiency. The materials one chooses also has a large effect on propeller design. Metal blades have good power absorption but are fatigue limited. The primary reason for a metal propeller is cheap production and erosion resistance. Metal propellers have excellent erosion resistance so they be flown in the rain. Wooden blades have even better power absorption and unlimited fatigue life. Wooden blades can delaminate in the rain and require some sort of protection in order not to erode. The German wooden propellers were wrapped in metal mesh, fabric covered, and covered with a thick resin.
In the event of a prop strike, metal transferred more force to the engine resulting in more damage. Wooden propellers tend to act like a circuit breaker and disintegrate transferring less force to the engine. It is cheaper to replace a propeller than an engine.