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Old 28th Oct 2014, 22:25
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Back of the envelope, worst case scenario math here.

I'm assuming that it's just the very tip of the prop that separated (as that's rotating the fastest), and I'm not incorporating any aerodynamic drag or other effect here (if that prop bit becomes a glider-like object, then it can travel for tens or hundreds of miles).

I'm also assuming that the prop tip at redline RPM is near-supersonic speed (300 m/s), but in reality it will be less, perhaps just 90% of that number. And if a significant bit of the prop is broken off, like you said, the initial speed of that separated bit will be some sort of weighted average of the whole separated bit, not the speed of the tip.

Having said that, here's the math:

If the prop tip is separated and goes straight up, the altitude reached is v^2/2g = 90000/20 = 4.5 km. But obviously you'd eventually find the prop tip back, right next to the plane. The time it takes to fly up and fall back down is 2 * ( v/g ) = 2 * 300 / 10 = 60 seconds.

If the prop tip separates on a 45 degree angle (more or less the optimal angle to get maximum distance) the initial vertical speed is 300 / sqrt(2) = 212 m/s. The altitude reached is 2.25 km and the time it takes to fall back to the earth is 42 seconds. In that 42 seconds the tip can travel a horizontal distance of 8.9 km. (Again, I'm not considering a deceleration due to aerodynamic drag here.)

So that 8.9km is your absolute upper limit. But in reality it will be far, far less than that. A wooden prop tip will incur significant drag, especially when traveling at near-supersonic speed and while tumbling. How to calculate that is beyond my ability, unfortunately. Still, I would not be surprised if you eventually find the prop tip maybe half a kilometer away.
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