Flying the meteoric skies

Over at Cosmic Variance, John Conway ponders the idea that a meteor might have taken down the Air France flight that crashed over the Atlantic the other day.

John’s a physicist, so he goes through the math. You have to make some assumptions, but most of them look solid to me, or at least not crazy. In the end, the odds of any one flight getting hit by a rock substantial enough to do catastrophic damage to a plane is extremely low. That should be obvious, because if the odds were high then we’d see it happen a lot!

But over time, the odds of one flight getting hit are just high enough to make a single disaster in the past 20 years just within the realm of possibility.

Still, I wonder. When it comes to meteoroids (the solid body that forms the meteor), smaller rocks are more common than larger ones. So for every rock that hits a plane that’s large enough to take it down, we should see lots of damage from smaller ones. Yet I have never heard of such damage being reported (and I think it would be huge news if it did, but to be honest I have not done the research).

But I continue to wonder. There is another complication I think people have forgotten. Airplanes fly at an altitude of roughly 10 km. Small meteoroids move at transsonic speeds when they enter our atmosphere, but slow rapidly, and become subsonic in seconds while they’re still about 100 km up. Once they’ve slowed they are no longer ballistic, and really just fall the rest of the way to the ground. By the time they’re at the same altitude as planes, they may only be moving a few hundred km/hr at most.

That changes the physics a lot. Why? Because of relative areas and speeds.

To calculate the odds of a plane getting hit, you need to know how many meteors burn up over the Earth per day, and what percentage of the Earth’s surface is covered by airplanes. If you have millions of airplanes in the air, the odds of them getting hit are pretty high, but if you only have one, it’s a pretty small target.

But that assumes the plane occupies a couple of hundred square meters of area; that is, that’s the area of an airplane as seen from above.

Imagine you are a rock moving at 25,000 km/hr. To you, the plane is essentially standing still, and the amount of area you see it occupy is really just its area as seen from above. In that case, the assumption is correct.

But now let’s imagine you have zero motion, and so you’re motionless, hovering in the sky. In that case, the plane hits you! You don’t see the plane from above at all, you see it coming head-on, and so it occupies less area, only a few dozen square meters.

That latter case is the one that is more physically realistic, because most meteoroids will be falling relatively slowly when they are in the air lanes. That means that the statistical odds of a plane getting hit by a meteoroid (or really the other way around) are far smaller, maybe by a factor of ten or more.

I suspect that may be why we have never definitively seen an airplane taken down by a meteor. Once you realize the rocks are moving slowly, planes are a lot harder to hit. And that might explain why we don’t see much damage even from smaller rocks. It really is a rare event.

And I should add that it’s incredibly unlikely in any case that this was the fate of Air France 447. We know it was flying into heavy thunderstorms, and in this case when you hear hoofbeats you think horses, not zebras. When you have such an obvious culprit, reaching for an incredibly rare one isn’t terribly parsimonious.

Still, as John points out, it’s really just a matter of time before a plane is hit. But because of relative speeds and cross sections, I suspect that time period is longer than most people think.

Airplane image from Marina Avila’s Flickr stream.