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I'm not quite sure if this is the correct SE, but what is the probability for a plane crash on one m^2 in one second?

Yep, I know it's very low and this is rather for fun than scientific, but it would nice to know.

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  • $\begingroup$ Collect some statistics about plane crashs total (world-wide / on land / in your home country) over a reasonable period (long enough to have significantly many crashs, but do not include pre-Linder´nberg days) and divide. Hm, on second thought: One neeeds to consider the number of square meters affected per crash $\endgroup$ May 6, 2014 at 14:44

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So, I did some research myself.

According to this, we had a total of 773 plane crashes in the past 5 years.

5 years have $((365*5)+1)*24*60*60 = 157766400$ Seconds (+1 because of the leap year '12), arround 157,77 million.

The Earth has a surface of $5.1*10^14 m^2$ (src, couldn't find more exact). Estimating the space a plane crash affects is much harder, but if you scroll through B3A's list (see link 1), you'll note that most crashes are small passenger planes (and that I'm not gonna enter a Rockwell Aero Commander 500, 120 crashes with 202 fatalities on record). I tried to get the breaking distance of a previously mentioned Aero Commander 500, but I couldn't find data about friction coefficient of steel on earth and my time is a little limited so I'll do a guess:

The wing span of an AC 500 is 14.95m, when it slits it'll take a little more, so I'll use 30m to include flying parts and a factor for bigger planes. For the breaking distance I'll take 127.2 m, two times the length of a boeing 777. The reason for this is that big planes seem to slit less and if they do, it'll most probably be on an airport where the threshold between landing and (start of the) crash is fluid, so 127.2m should be a sufficient damage area length.

Summarizing, we have an average damage area of $3816 m^2$ or $0.003816km^2$; so for 773 crashes we have a total affected area of $2949768m^2$ or $2,9 km^2$; $5,784*10^{-7}%$ of the earth surface (click here for the full number). Areas which were affected several times had been left out, though.

For the sake of simplicity, we'll make another assumption and say that a plane crash only takes one second (actually the question kinda already says that) because nobody's running into a burning plane part.

So, at the end we have a $5,784*10^{-7}%$ chance to have an affected square meter and a chance of $157766400^-1$ to be there in the exact second. Typing this into wolfram alpha we get

$\frac{2949768}{5.1×10^{14}} * 157766400^{-1} *100 = 3.6660903865014424901030145537587... × 10^{-15} %$

This is the approximate chance to have a plane crash.

So, next time someone says life isn't too short ... add that there's also a chance of 1 to 27.28 quadrillion to be killed by a crashing plane every second ;)

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