
Did a meteor bring down Air France 447? - Anon84
http://blogs.discovermagazine.com/cosmicvariance/2009/06/04/did-a-meteor-bring-down-air-france-447/
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lutorm
The probability calculation is incorrect, you can't just multiply the numbers.
This should be obvious from the fact that if we wait long enough the
probability according to that expression will exceed 1.

If I have a probability of throwing a 6 on a dice of 1/6, throwing 6 dice
doesn't give me a probability of 1 of getting (at least) a six.

The correct calculation is:

If the probability of one meteor hitting an airplane is 5.7e-13, then the
probability of it missing is 1-5.7e-13. For no plane to be hit, all of the
750e6 hours * 125 meteors/hour must miss. That probability is
(1-5.7e-13)^(750e6*125)=0.948, ie the probability of at least one hit is 5.2%.

The answer is close to the same, but that's just luck. If the probability was
higher, it would be increasingly off.

~~~
tomsaffell
Thanks for pointing out the error in his math. But I think you got something
wrong too - thrown off big error on his part (~4000x). The correct calculation
is:

    
    
      p(one or meteor strikes) = 1 - ( (1 - p(strike of any meteor))^ (total # meteors) )
      
      (assuming statistical independence, etc).
      p(strike of any meteor) = 5.82e-13
      (total # meteors) = 3000 * 365 * 20     (for testing over 20 years)
    
      p(one or meteor strikes) = 1.3e-5 = 0.0013%
    

The error of multiplying 720e6 hrs (the total # of _flight_ hours) by 125
meteors/hr is that it does not give you the total number of meteors in the
time period (which is what you need), it gives you a number ~4000 times larger
(because at any one time, there are ~4000 planes in the sky...)

~~~
lutorm
Except that if there are 4000 planes in the sky, that does make (assuming the
planes are not overlapping, which seems largely safe) the probability 4000
times larger than for one plane.

As long as the planes don't overlap, the _flight_ hours is the correct number
to use, because more planes in the sky gives higher probability. It's not the
number of meteors that matter, but the number of "potential meteor strikes".

Equivalently, you can say that the probability of a meteor hitting _any one
plane_ at a given time is the fractional area taken up by planes, which if
there are 4000 planes in the air is 4000*5.82e-13. (Again assuming the planes
don't overlap, which since 5.82e-13<<1 is a safe assumption.)

~~~
tomsaffell
Ah, yes - I mis calculated p(strike of any meteor) by a factor of 3500 (the #
of planes in the sky, according to the article). I think this should be
applied to the probability, not the count of the occasions - but the numbers
are small enough that it doesn't make much difference.

    
    
      p(one or meteor strikes) = 1 - ( (1 - p(strike of any meteor))^ (total # meteors) )
      
      (assuming statistical independence, etc).
      p(strike of any meteor) = 5.82e-13 * 3500 = 2.04E-9
      (total # meteors) = 3000 * 365 * 20     (for testing over 20 years)
    
      p(one or meteor strikes) = 0.0436 = 4.36%

~~~
lutorm
Yeah, it doesn't make a difference until the planes cover a significant area
of the Earth, in which case just multiplying by the numbers of planes will be
wrong for the same case that the initial calculation was wrong. Then it would
be 1-(1-5.82e-13)^3500 in this case, too.

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tlrobinson
Birthday paradox strikes again?

I saw a meteor on a flight once. Granted it was pretty far away, but I also
only fly a few times a year. It's certainly not impossible.

~~~
frossie
Not that I want to give any credence to this theory, but actually the
statistics are better (or worse) than he thinks, because meteors are believed
more likely to strike at the equator than the pole.

[Horrid URL follows, sorry]

[http://articles.adsabs.harvard.edu/cgi-bin/nph-
iarticle_quer...](http://articles.adsabs.harvard.edu/cgi-bin/nph-
iarticle_query?bibcode=1964Metic...2..271H&db_key=AST&page_ind=5&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES)

~~~
lutorm
Wow, how on Earth did you find that article? The poor dude's been cited 3
times in 45 years...

~~~
frossie
No secret, just google. I speculated the distribution may not be symmetrical,
thinking there could be an excess of strikes along the ecliptic being fed by
the asteroid belt and guessed what terms would crop up in a paper that
discussed the topic (I find that is the best way to search for something -
don't ask the question, but search for what you think the answer would look
like).

Actually what I thought I would find is radar data showing actual counts of
meteor strikes, but no joy - I suspect the military knows what they are but
they are not saying.

Of course there could be more recent papers hidden behind a paywall, but ADS
didn't bring up any obvious abstracts.

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amichail
While I highly doubt this, I do wonder why we rely on black boxes for crash
investigations. Airbus already received some data from the plane after
problems developed. Why not develop this technology further to make black
boxes redundant?

And if you really do want to keep black boxes, why not develop an ejection
mechanism for them so that they would separate from the plane at the last
second and float in the ocean?

~~~
spitfire
Because it's simply not possible to make black boxes redundant.

You can fly into a storm or into a canyon where radio/satellite uplinks won't
work. Hence you need to store the data on sturdy local storage aka a black
box.

As much as people love to think that technology can completely tame mother
nature, it can't. It's still a brutal place, with nasty conditions. While the
uplink data is great, you still need backups (Higher resolution is a nice
bonus too)

~~~
ajross
A better way to explain it would be to point out that the remote telemetry and
the black boxes are _already_ examples of redundant design. The black box has
fewer failure modes _recording_ data, but requires recovery. The telemetry is
more easily disrupted, but can get data out even in the face of a total loss
of the aircraft.

Redundancy doesn't always mean the same thing as simple duplication.

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cameldrv
We know that the jet was in a severe thunderstorm when it crashed. Severe
thunderstorms have brought down many airplanes over the years.

~~~
quizbiz
This particular instance involved a very modern plane piloted by a very
experienced crew. Google the kind of stress tests they put plane wings and
such under. A wide body fuselage should not come apart in a thunderstorm.

~~~
cameldrv
Thunderstorms can kill in a variety of ways -- the turbulence isn't your only
problem, although I wouldn't bet that a storm as severe as this one (50kft
tops) couldn't have done it.

The kind of bumps you get in something like that aren't what you think of as
turbulence in a plane. Airlines have radar and always go around the big cells.
This one would have been strong enough to fling people out of their seats and
kill them from blunt force impact with the interior of the plane.

Second, in a thunderstorm, you have lots of rain, which if strong enough can
interfere with the engines. There is also hail which can do significant damage
to the skin of the plane and make it very difficult to handle. Third, there is
lightning, and while airliners are supposed to be able to take a lighting
strike, there are different types of lightning, and "positive lighting" has
been known to poke holes in airplanes otherwise believed to be protected.
Fourth, there can be lots and lots of ice. Airbus has already issued a letter
warning of the danger of pitot icing as a result of this crash, and they know
that at least one of the airspeed indicators wasn't working properly, probably
because it was iced over.

Furthermore, with extreme turbulence, it can be difficult to even read the
instruments. With lighting going off all around you, no visible horizon, and
you being vibrated and thrown around in your seatbelts, it is very easy to
become disoriented and lose control, possibly to the point of overstressing
the airframe and ripping it apart.

A thunderstorm like this is about the most dangerous place for an airplane to
be. I'm certain that one way or another, that is what did them in.

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jonsen
I think they haven't found any verified debris yet.

What's the probability that what those pilots saw was an up beam?

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qwertyqwerty
No.

