A related question: what's the probability of an aircraft being struck by a meteor. Seems this question was asked in the wake of the Air France flight 447 disappearance (since resolved as pitot tube freezing combined with pilot error and control feedback failures of the Airbus design).
But still, the odds of a strike on _an_ aircraft over the next 20 years are about 4%:
at any given time, airliners cover 2 billionths of the Earth's surface. There are 125 meteors an hour, each with probability 2x10-9 of striking some airplane. In 20 years, that's about 22 million independent possible impact events. The chance that every one of those meteors misses every airplane is: ppois(0,2e-922e6)*
(Using R).
So the odds of an asteroid flying past a skydiver aren't as infinitesimal as one might otherwise think.
It also makes one wonder at the possibility of space-junk collisions being the cause of past aviation accidents. There's little enough evidence this would leave, particularly for a flight which disappeared entirely without a trace, or whose wreckage was only found much later.
That would be under an assumption that the distribution of planes around the globe is even. Given most jetliners are flying in corridors, I would say the actual probability is much much lower. The same can be probably said about meteorites - I guess their geographic distribution is uneven as well.
If the meteorite strikes are evenly distributed, and if the planes aren't actually stacked (i.e., flying directly above one another) very much, then I don't think the plane positions matter for this calculation.
As others have said: the distribution of the planes over the Earth (and their speed -- one Yahoo site I ran across suggested they're harder to hit because they're moving fast -- that's also irrelevant, not to mention that pretty much everything on Earth is moving at about 20km/s relative to an asteroid) doesn't matter.
Because meteorites aren't aimed. Odds are they'll land pretty much anywhere on the planet.
I'm not entirely sure this is the case -- because the Earth orbits the Sun, the eastward-facing side should be sweeping through more debris than the west, which means that if you could concentrate your flights on that side, you'd be at higher risk. As it is, most flights tend to operate during daylight hours, with the before-noon flights being at greater risk. More reasons to catch the afternoon flight if you prefer to play things safe, or the morning flight if you feel like making history (or low-grade mysteries of the unknown TV programmes).
>> However, doesn't a faster plane actually have a higher probability of intersecting the same space as a falling rock?
I'm pretty certain thats true - against my intuition.
If a meterite will be crossing 35,000 feet at 300 km/hr it will be in the layer of the atmosphere the height of a Boeing for say 1/10th second. (300km/h ~ 8m/s, Boeing 747 about 8m tall in body if you squint)
so an aircraft that is stationary (!) in the air, will consume 1 airframe's worth of space in that 1/10th of a second.
A plane that travels its own length in 1/10th of a second will consume two airframes worth of space in the same 1/10th so doubling its chances of getting hit.
A Boeing 747 is approx 70m long which would mean to double its chances of getting hit it would have to travel 700m/sec or about twice the speed of sound (340m/s)
Running makes you wetter than walking over an equivalent time period. The main goal of running in the rain is to get to a shelter -- to minimize that time.
Something your link covers, and points out. [1]
So it would be with a plane: Flying faster means less time in the air, where meteorite strikes are particularly dangerous (as opposed to strikes while taxiing, or sitting idle). So while a faster-flying plane is more likely to encounter a meteorite than a slower-flying plane, if flying faster means less time in the air it's going to be "safer" overall.
[1] "So here we have it - more mathematical advice to avoid getting wet. Because we divide by VP in this equation, maximising our velocity now emerges as a good idea, assuming there is a shelter available."
>Flying faster means less time in the air, where meteorite strikes are particularly dangerous (as opposed to strikes while taxiing, or sitting idle).
That's a very good point: for a plane, reaching the ground is the equivalent of a runner reaching shelter from the rain.
But I suppose planes generally spend about the same amount of time in the air, no matter how fast they go. The faster plane just travels further in that time. There's no obvious reason a fast plane would spend more time safely on the ground than a slow plane.
Perhaps flying faster is safer for individual passengers, but more dangerous for the plane?
reaching the ground is the equivalent of a runner reaching shelter from the rain.
A meteorite capable of striking a plane in flight is just as equivalent of striking it on the ground. It's already passed through the ablative portion of its entry, and is falling at terminal velocity. So the probabilities of a strike don't actually change.
The implications for the aircraft, passengers, and crew, are rather different, however, when the plane is at-rest and on the ground.
>The implications for the aircraft, passengers, and crew, are rather different, however, when the plane is at-rest and on the ground.
Yes, that's so. A 300km/h 5kg rock striking any part of a plane in flight must have a very high probability of proving fatal for all aboard. On the ground the risk of injury for each passenger must be much lower - the plane might even be empty.
However, while the plane is in the air, it seems that a faster plane moves through a greater volume of space per unit of time, compared to a slower plane, therefore it is at greater risk of passing through the space occupied by a meteorite in any particular hour. So, assuming that faster planes spend about the amount of time airborne as slower planes, the risk of an accident is higher for faster aircraft.
The risk for an individual passenger is not increased in the same way (I guess it is not much affected by aircraft speed), because the faster aircraft gets them to their destination in less time, so they spend less time vulnerable to meteorite impacts on the aircraft.
roc is correct and, additionally, remember that part of the reason that you pick up more moisture per second while running is because while running you lean forward - by changing your orientation from the vertical, your cross section relative to the path of the rain increases as well.
whereas with a plane, it's exposing the same cross section to the meteor whether it's flying level at Mach 2 or sitting on a runway.
It's not the leaning forward (which reduces your forward cross-section), but your forward motion (which increases your _effective_ cross-section relative to the rain, which is the relevant factor in the running example.
In the case of an aircraft, since the frontal surface area is smaller than the topside area, the effect of velocity is to reduce the apparent interface.
If the distribution of meteors is perfectly even and all of the planes are parked next to each other in the desert, then the probability should be the same 4% expectation within the next 20 years of one of those parked aircraft being hit.
While staying within corridors would not matter, the distribution by latitude probably does, and my guess is that they align enough to actually increase the odds.
But still, the odds of a strike on _an_ aircraft over the next 20 years are about 4%:
http://blog.revolutionanalytics.com/2009/06/how-much-of-a-th...
at any given time, airliners cover 2 billionths of the Earth's surface. There are 125 meteors an hour, each with probability 2x10-9 of striking some airplane. In 20 years, that's about 22 million independent possible impact events. The chance that every one of those meteors misses every airplane is: ppois(0,2e-922e6)*
(Using R).
So the odds of an asteroid flying past a skydiver aren't as infinitesimal as one might otherwise think.
It also makes one wonder at the possibility of space-junk collisions being the cause of past aviation accidents. There's little enough evidence this would leave, particularly for a flight which disappeared entirely without a trace, or whose wreckage was only found much later.