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What are the chances that the propeller of a turboprop passenger aircraft like the Dash 8 will break and impale me when I’m sitting near it?

The chances are about as remote as those of you winning the state lottery jackpot sometime this week even though you don’t play the state lottery. It’s a simple question of mathematics. Let me show you…

In the first place you would have to be sitting in exactly the ‘wrong’ seat and on a Bombardier Dash 8 Q400 that’s about a one in 70 chance. Let’s say you’re an inveterate window seat hogger (though given your morbid fears of propellor blades, it’s hard to see why). That’s still a 1 in 35 chance.

And of course, the blade would have to separate from the engine on your side of the aircraft, a one in two chance. So we’re back up to one in 70.

Then the errant propellor blade would have to fly off at exactly the radial angle (to within no more than a quarter of a degree) required to hit you in that seat. So that’s a 1 in 1440 chance, multiplied by the previous 1 in 70. Already we’re up to 1 in 100,800 and we haven’t even really started yet…

Because it’s not just the radial angle at which the blade flies off that’s critical, it’s also the longitudinal arc that determines where the blade will strike the fuselage – and how.

Exactly where the blade will hit the fuselage is determined by a complex equation in which the variables include prop speed, blade pitch, aircraft speed, attitude and deviation, altitude at which blade separation occurs and even prevailing wind speed and direction. I am not even remotely qualified to attempt to formulate such an equation but would tentatively suggest they modify the previous chances by a factor of at least 500. So our previous one in 100,800 has now become 1 in 50 million.

Furthermore, the blade not only has to strike the fuselage exactly opposite the row of seats in which you’re nervously sitting but also at exactly the angle and with enough kinetic energy needed to penetrate said fuselage. Let’s assume the latter is a given but the former certainly is not and that adds a further factor of at least 1 in 25, reducing overall probability to 1 in 1,260 million, about thirty times less likely than you winning a five ball plus bonus lottery.

But wait, we haven’t even reached the biggest chance factor of all. All of the above presupposes that a blade is predestined to separate on the very flight you’re taking. But hundreds of Bombardier Dash 8s fly around the world on thousands of flights every day without blades flying off their propellors.

In fact no Dash 8 has EVER lost a propellor blade in flight. You’re probably thinking of that November 2014 incident at Edmonton International involving Air Canada Express Flight AC8481….

… or possibly an earlier one in 2007 involving Scandinavian Airlines Flight 1209 that crash landed at Copenhagen.

You’ll note that in both cases the aircraft are on their sides after main gear failures on landing. That’s right: the prop blades came off as they struck the ground – because the aircraft was already crashing.

In Canada, the problem was a burst tire and in Denmark, the gear failed to extend properly due to corrosion on an actuator. This latter problem actually was an issue on the Q400 model of the Dash 8 that caused the whole fleet to be grounded for a while. Fixes have since been implemented.

Even so, no passenger was killed in either case, although some were badly hurt.

So you can multiply the chances established above by your general chances of being involved in any kind of air accident, conservatively estimated at around one in 5.4 million. Now we’re dealing with (im)probabilities in the range of trillions to one.

Source: Quora

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