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Searching the Indian Ocean for a Plane Crash

Update: I was alerted to a miscalculation on this article. Tim Dierks wrote to warn me that my calculations aren't accurate unless I use the square root of the area when calculating equivalent lengths for search objects. Skip to new calculations.

In the last five days, the search for Malaysian flight 370 has achieved an almost supernatural status. Where did this giant aircraft disappear to?

A 777 is a huge aircraft, 200 feet long, but the Indian ocean has swallowed it up. It is gone.

To better envision the difficulty of finding an aircraft in an ocean, I re-scaled the task. I expected that it would be similar to finding a needle in Disneyland. Not very familar with the size of the Indian Ocean, that turned out to be understating the challenge.

The Indian ocean is 28,400,000 square miles in area. That is 105 times as large as the state of Texas (268,820 square miles). Finding a jet in the Indian Ocean is equivalent to finding a 1977 Lincoln Town Car in Texas.

If you aren't familiar with how large Texas is, that might seem possible.

To better comprehend the area, I shrunk the problem further. Consider Yosemite National Park in California. It is 1,190 square miles of forest. This is 1/23865th the size of the Indian Ocean. When people get lost in Yosemite, it can be very challenging to find them.

To find the equivalent size of a 200 ft jet in an area this large, you can divide 200ft. by the square root of 23865. I got 15 inches.

If you shrink a 777 down to 1/ 154th of its size, it will be about the size of one of LeBron James' shoes. Imagine trying to find a basketball shoe in Yosemite.

Next, consider the city of San Francisco. It occupies a mere 232 square miles of area. Shrink the Indian Ocean to this size and the missing jet is 7 inches long. Finding the jet in the Indian Ocean is equivalent to finding a pen in San Francisco.

It is also equivalent to finding a toothpick on the island of Manhattan, finding a pin at Burning Man, or finding a short grain of rice at Disneyland.

I won't promise that the aircraft will never be found, I just don't think anything supernatural is at work. It will be an astounding achievement if they ever find it. It will be a miracle.

Area Name Area square root of area fraction of I. Ocean equivalent target object equivalent target size
Indian Ocean 28,400,000 sq. mi. 5,329 miles full size Jet 200 ft long
Texas 268,820 sq. mi. 518 miles 1/10.3 a 1979 Lincoln Town Car 19.4 feet long
Yosemite Park 1,190 sq. mi. 34 miles 1/156 One of Lebron James' shoes 15 inches long
San Francisco 232 sq. mi. 15.2 miles 1/350 a pen 7 inches long
Manhattan 34 sq. mi. 6 miles 1/888 a toothpick 3 inches
Burning Man two sq. mi. 1.4 miles 1/3,806 a pin 16 mm
Disneyland 160 acres ½ mile 1/10,658 a grain of rice 6 mm


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