When Malaysia Airlines Flight 370 disappeared on March 8, 2014, en route from Kuala Lumpur to Beijing, Andrew J. Schaefer, like the rest of the world, wondered absently about its fate.
What happened to the Boeing 777 and the 239 people aboard? Wouldn’t search parties eventually locate so large an aircraft? Won’t the “black box” be recovered and reveal what happened? After more than three years, small amounts of debris have washed ashore in Africa and on islands in the Indian Ocean but the mystery remains.
“We started thinking about it. What about the flight data recorder? Don’t they have a beacon that signals its location? What happened to it?” asked Schaefer, the Noah Harding Chair and Professor of Computational and Applied Mathematics (CAAM) at Rice University.
At the time, Schaefer was a professor of industrial engineering at the University of Pittsburgh. He graduated with a B.A. and master’s degree in CAAM from Rice in 1994 and joined the Rice faculty in 2015. With David J. Eckman, one of his undergraduates (now a doctoral student at Cornell), and Lisa M. Maillart, professor of industrial engineering at Pittsburgh, Schaefer decided to examine the search efforts mathematically.
The resulting paper, “Optimal Pinging Frequencies in the Search for an Immobile Beacon,” was published in an issue of IIE Transactions devoted to operations engineering and analytics, and later named the journal’s Best Applications Paper for 2017.
Since 1967, the U.S. has required all commercial airliners to be equipped with flight data recorders, devices that record and store the recent history of flights several times per second. Included is a cockpit voice recorder that preserves pilot conversation. The devices, now mandated internationally, are housed in a protective “black box” (though now painted bright orange) and fitted with an underwater locator beacon.
“What interested us was the beacon. They’re activated under water, produce ultrasonic pings about once a second, and have a battery life of about 30 days. Obviously, you have to locate the black box before the battery dies,” Schaefer said.
The multinational search for Flight 370, eventually focused on the southern Indian Ocean, was the largest and most expensive in aviation history. For more than two years, the search covered an expanse of ocean exceeding 46,000 square miles. Search vessels moving at two to three miles per hour towed signal-locators at a depth of about 1,000 feet above the ocean floor. The range of detection for the beacon signals is about 2.5 miles.
“We thought about proposing the addition of a second beacon, one with a lower frequency of sound and an increased range of detection – maybe eight miles – and extend the battery life from 30 days to 90 days,” Schaefer said. Instead, the researchers made a less costly recommendation – lengthen the time between successive pings.
“Assuming that the search speed is known, we formulated a mathematical model to determine the pinging period that maximizes the probability that the searchers will detect the beacon before it stops pinging,” Schaefer said.
In mathematical terms, Schaefer and his colleagues adapted the linear search problem to an immobile object. “The probability of detection,” Schaefer said, “becomes a function of the pinging period.”
At present, beacons are set to ping once every 1.1 seconds. Schaefer and the others determined that the optimal frequency of pinging should be about once every 12.4 seconds. “That’s a difference in scale of about 700,” Schaefer said. “The currently used pinging period is far too short.”