>> 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.
Indeed, it's not as if they're trying to dodge.
However, doesn't a faster plane actually have a higher probability of intersecting the same space as a falling rock?
Comparable to: http://news.bbc.co.uk/2/hi/uk_news/magazine/4562132.stm ('...So running fast actually makes us wetter according to this analysis')