Friday, March 14, 2014

MH370: the accidental π-day wisdom of NPR

Please find this exchange six minutes into the show:
ANCHOR: "How big is the search area, or areas, Tom?"
CORRESPONDENT: "Well the defined search area is about 31,000 square miles. But if you take into the possibility that this plane may have flown another four or five hours, then you're looking at a potential distance of 2500 miles, and then you've got to've got to get some mathematician from MIT to figure out every single direction from the point off South Vietnam, all the way in every possible direction, you seems to me the possibilities are endless there..."

But seriously. Where the plane could have gone depends not only on its headingairspeed, and endurance, but also on the wind. And at an airliner's cruising altitude, the wind commonly blows at 50-100 knots - faster than you drive down the freeway, and a severe hurricane at ground level. Not only that:

The wind vector field is actually four-dimensional, varying with altitude and time. By the way, the ground speed and endurance also vary with altitude. Integrating over a multidimensional infinity of possible flight paths, we'd need to find the maximum range when they're projected down to the surface of the Earth - accounting for its curvature and coriolis effect - and calculate some kind of polar integral over the resulting surface. If we're searching for debris, what about those ocean currents?

In conclusion, contingent on a certain understanding of "endless", the correspondent is entirely correct. Godspeed to all those searching for MH370.

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