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those supersonic propellers max tip Mach is more than 1.3 while WWII p47 max tip Mach is below 1.15. quite different story.
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Come on man....
You understand the basic's of rotational mechanic's right?
On any radius of the circle, the point closest to the origin travels at a slower velocity than a point distal to the origin.
That is why as a generality, a smaller disc is better for Vmax performance.