On 3 November the Australian Transport Safety Bureau resumed the deep sea search for the lost Malaysia Airlines flight MH370 [but see update at end of story].

Refuelled, replenished and ready to go, the ATSB’s survey ship Fugro Discovery has arrived on station once more in the southern Indian Ocean (see footnote for an update).

For those seeking a reason to be optimistic following a discouraging 20 months of searching the ocean without a result, there is definite cause for renewed hope this time.

Since it began the search the ATSB has been scrupulously methodical, scanning the ocean floor within a long, slender curved rectangle that encompassed what became known as the “7th arc”. This is a long line on the earth’s surface established by vestigial radio responses from the fatal aircraft to Inmarsat satellites just as it was running out of fuel.

Theoretically the Boeing 777 could have come down anywhere close to it, but working with the aircraft’s last radar position the ATSB identified the arc sector where the aircraft could realistically have come down, and has searched almost all of the identified curve and its close vicinity.

Since it has now trawled almost all the 7th arc’s viable sector and not found the wreckage of MH370, there is not much more to search. Logic says they must be getting close.

But not only logic.

For those who doubted MH370 came down in the sea at all, the fact it did so was established in July when one of its flaperons was washed up on a beach on the Indian Ocean island of La Reunion. This fact was forensically confirmed more recently by the French air accident investigation agency BEA.

But there’s another reason for optimism: on 22 December last year Flightglobal published a mathematical/geometric calculation by Boeing 777 captain Simon Hardy, also a mathematician, which indicates precisely where, according to his calculations, MH370 came down.

The search sector that Fugro Discovery has just begun to trawl encompasses Hardy’s predicted position for MH370. His recent refinements to the aircraft’s final descent profile put it at S39 22′ 46″ E087 06′ 20″. He adds, however, that depending on how long the aircraft floated, the main wreck could have drifted some time before sinking, and even during the descent could have travelled laterally. At this location he would expect to see mainly “some moveable aerodynamic surfaces, like the missing part of the flaperon that we already have, and parts of slats and flaps and maybe even the RAT [ram air turbine].”

This could be said to be the last chance for the search under present estimated criteria, because 777 performance dictates that the aircraft could not have flown further than this extreme southern end of the 7th-arc-defined potential ditching area.

Anyone who has published material on the web knows that it may receive praise, but it will certainly receive criticism. The impressive fact about Hardy’s mathematics is that, despite hundreds of thousands of hits on the article containing his calculations, nobody has been able to blow a hole in them.

By 3 December Fugro Discovery expects to have completed the search of the area containing, according to Hardy’s calculations, the wreck of MH370 and the remains of those who went down with it.

Hardy says he says he is excited about the next month’s search, having invested more than a year of mental and emotional energy into working out where MH370 flew, and why. He wants it found.

He’s not alone.

Watch this space for more on MH370.

LATE NEWS: On 5 November Fugro Discovery had to suspend the search and return to Fremantle, Western Australia, according to Australia’s Joint Agency Coordination Centre, because one of the crew developed suspected appendicitis.

UPDATE: Fugro Discovery was due to arrive back in the search area on 3 December.