I'm not an engineer or a pilot. I understand that tip speed means velocity at the tip of the prop and it's faster at the tip then near the center. Theres some formula that describes rotational velocity.
my point is when they built these planes, I imagine the didn't want the tip to be breaking the sound barrier all the time, so they put governors on the engines and design the props to keep it from doing that. if your in a dive and ram air is pushing your prop to rpm limits, I'm pretty sure the operators manual is going to tell you that isn't so good and you need to change the pitch angle and slow the rpms/reduce the tip speeds or something might break or do damage when you get near your never exceed speeds.
Going back to your tempest example, will the pilot not try to do something to mitigate the effects of sonic tip speeds? Or simply, the prop design specs try to engineer that out of the equation as much as possible? It seems in your analysis, you assume not, that it is simply a function of prop length, max rpms of the engine and forward velocity. I just don't know if that is realistic. To me, it seems that tips speed breaking the sound barrier would be a rare event. So, not sure why it needs detailed modeling.
But then again, I only learn aviation stuff from playing this game.
Edit:
Relates to what I was thinking about.
http://en.wikipedia.org/wiki/Scimitar_propeller
Quote:
This can be controlled to some degree by adding more blades to the prop, absorbing more power at a lower rotational speed. This is why some WWII fighters started with two-blade props and were using five-blade designs by the end of the war. The only downside to this approach is that adding blades makes the propeller harder to balance and maintain. At some point, though, the forward speed of the plane combined with the rotational speed of the propeller will once again result in wave drag problems. For most aircraft, this will occur at speeds over about 450 mph.
A method of decreasing wave drag was discovered by German researchers in WWII: sweeping the wing backward. Today, almost all aircraft designed to fly much above 450 mph (700 km/h) use a swept wing. In the 1940s, NACA started researching propellers with similar sweep. Since the inside of the prop is moving more slowly than the outside, the blade becomes progressively more swept toward the outside, leading to a curved shape similar to that of a scimitar.
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