A Google Earth image shows the radius outward from a geosynchronous satellite in which the lost MH370 flight might be found, based on complex forensic mathematical analysis of the final automatic signals generated by the falling plane. Image: Ian D. Holland/, Open Access

The search for the disappeared flight MH370, still missing for nearly three years, was called off last month by investigators from multiple countries.

Now the forensic mathematics which helped guide the unsuccessful underwater search have been published.

The paper, which describes the methodology based on Doppler physics, satellites and automatic contacts between the plane and Earth-based trackers, is published at the open-access site

Of most interest is an eight-second window between two contacts, showing the plane was falling fast—and should be somewhere close to that last radius, writes Ian Holland, of Australia’s Defence Science and Technology Group.

The calculations are called a “burst frequency offset,” or BFO, which “provide an estimate of the direction and velocity of the plane on the assumption of a given location.”

“The results of the oscillator analysis, combined with direct Doppler analysis based on the vertical velocity of the aircraft, suggest that the final two BFOs recorded show that flight MH370 was rapidly descending and accelerating downwards at the time of the associated SATCOM transmissions,” Holland writes.

Essentially, the calculations are made from an assumption of where the plane was, based on geosynchronous satellites and the contact the plane was making with ground earth stations back on the ground.

The two scenarios that triggered the automatic signals for the login attempt were either a SATCOM outage due to a lack of fuel, or due to lost contact from some other reason (including sabotage and mechanical failure), according to the paper.

In the final eight seconds, based on the nuances of the changing signal, the plane fell 10,500 feet — roughly 1,300 feet per second.

The calculations plotted seven rings across the globe, based on radius outward from satellite contact—and the mathematics determined it had to have been a long and narrow strip stretching across the Indian Ocean, Holland concludes.

“The derived bounds and approximate downwards acceleration rate are consistent with simulations of an uncontrolled descent near the so-called 7th arc … This suggest (the plane) should lie relatively close to the 7th BTO arc,” he concludes. 

Image: Courtesy of Australian Transport Safety Bureau

The Boeing 777 disappeared off radar screens on March 8, 2014, during a flight from Kuala Lumpur to Beijing, with 239 people aboard.

The plane made a hard turn over Malaysia in the middle of the night on March 7, 2014, investigators believe. Authorities also believe someone deliberately turned off the plane’s transponder before turning it thousands of miles off course, to the west.

The governments of China, Australia and Malaysia announced they were giving up the search on Jan. 17, saying they had run out of leads in their massive search, which had included 1.8 million square miles of surface waters in the first six weeks of the hunt, and 120,000 square miles of the underwater terrain in the years to follow.

“Despite every effort using the best science available, cutting-edge technology, as well as modeling and advice from highly skilled professionals who are the best in their field, unfortunately, the search has not been able to locate the aircraft,” the three governments said in a joint announcement. “Accordingly, the underwater search for MH370 has been suspended.”

The plane is almost assuredly destroyed, and all aboard dead. Two summers ago, a piece of debris that washed up on the French island of Reunion in the Indian Ocean was confirmed to have been part of the wing flap of the Boeing 777. Experts said the serration damage to the piece could be evidence of damage from an excessive speed from a purposeful dive of the plane—or from it running out of fuel and plunging back to Earth.