I suspect that the smartest minds hang out in this forum so here goes ...

Is there any formula for calculating the rpm for a prop given a single reference point (at least within a narrow range of prop sizes) ? For example given that a engine statically spins a 13 x 8 prop @ 9750 RPM what can one expect a 14x6 prop to spin at.

I have come across prop loading calculations that multiply the D x P to give a value but I think this breaks down for larger diameters.

If there isn't such a formula then what makes this such a difficult problem to solve theoretically ?