Flight International - January 13, 2015

20 | Flight International | 13-19 January 2015 flightglobal.com

David Learmount offers his succinct views

on the complexities of aviation safety:

flightglobal.com/Learmount

NEWS ANALYSIS

A

n original geometric ap-
proach to the sparse data
available about the flight path of
missing Malaysia Airlines flight
MH370 suggests a final resting
place in the Indian Ocean just
outside the far south-western
edge of the core search area desig-
nated by the Australian Transport
Safety Bureau (ATSB) in the
southern Indian Ocean.
The Boeing 777-200ER has
been missing since 8 March 2014,
and no trace of it has been found,
despite an extensive multination-
al search.
Capt Simon Hardy’s calcula-
tions are based on a combination
of data which include Inmarsat
satellite communication “hand-
shake arcs” and his expertise in
777 performance calculation, as
well as some mathematical “re-
verse engineering” of the naviga-
tion geometry known to apply to
this flight.

Hardy currently works as a

senior 777 captain for a major in-

ternational airline. Like other

aviators he was distressed by

MH370’s loss, and his concern

that relatives of those on board

might never know what hap-

pened inspired him to begin a ge-

ometric investigation of known

navigational facts. He emerged

with a set of conclusions that en-

abled him to isolate what he be-

lieves to be MH370’s actual track.

REVERSE ENGINEERING

“Rather than picking speeds and a

route at random and making them

fit with the [satcom handshake]

arcs, I have managed to let the arcs

tell us both the speed and direc-

tion, and finally a location – the

exact track between arcs 4 and 6 –

where it was doing that speed and

heading,” Hardy says. His ‘reverse

engineering’ involved testing a se-

ries of plausible tracks southward

over the Indian Ocean from the

777’s last known position, and dis-

covering the only trajectory that –

uniquely – matches the ratio of ac-

tual elapsed times between the

consecutive Inmarsat/MH

“handshakes”. He then found that

certain known data made sense,

when tested against that naviga-

tional trajectory. For example, the

actual elapsed time between

“handshake arcs” would occur if

the 777 was flying at its long-range

cruise speed – possibly a coinci-

dence, but a likely choice by the

person directing the flight.

Hardy worked with one key as-

sumption: that, once set on this

southward cruise, the aircraft’s

true air speed and its track (based

on true north), remained the same.

He explains: “For the purposes of

this purely mathematical/geomet-

rical investigation I am making one

assumption: that in most scenarios

[hypoxia, fire, a hidden hand], the

track and speed of the aircraft from

2141Z [UTC/GMT at the 4th hand-

shake arc] to 0011Z [time at the 6th

arc] would be constant.”

INFORMATION

He continues: “In order to extract

the information from the arcs we

have to introduce some ‘what ifs’.

What if the aircraft crossed the

4th arc at some random posi-

tion... say Position A [see dia-

gram left]? And if it did, what

route could it have taken from

there? If a series of straight lines

are projected from point A

through arcs 4 and 5 to different

points on arc 6, only one satisfies

the ratio of 1:1.5.” That ratio is

derived from the 1h between the

satellite handshakes at arcs 4 and

5, and 1h 30min between 5 and 6;

the actual times for MH370.

“Line A shows the only straight

line from point A that satisfies

this ratio. If we now measure the

distance of the line from arc 4 to

arc 5 we will get the distance trav-

elled in that hour, hence the

speed required to fly Line A:

541kt [1,000km/h].” Using the

same elapsed-time ratio between

handshake arcs, he says the

speeds required to fly to random

points B and C would have been

428kt and 491kt, respectively.

All these lines appear to be

nearly parallel. “This is great

news,” says Hardy, “as we can

measure the angle of the lines.

We find that they only vary from

188 ̊T [track] to 192 ̊T.” This sug-

gests that the aircraft’s true track

between 2141Z and 0011Z was

190 ̊T, plus or minus 2 ̊.

The next task – again purely

using maths – was to try to find

out where MH370 actually

crossed the arcs, assuming it was

flying this approximately 190 ̊T

‘WHAT IF’ TRACKS BETWEEN THE 4TH AND 6TH SATCOM

‘HANDSHAKE’ ARCS

Tropic^ of^ Canc

er

A

C

B

4th arc

21:41UTC

5th arc

22:41UTC

6th arc

00:11UTC

7th arc

541kt

428kt

491kt

Not to scale

SOURCE: Capt Simon Hardy

Speeds inbound from ANOKO

601kt

485kt

601kt 443kt

S22 ̊

S37 ̊

S37 ̊

S42 ̊

S32 ̊

S27 ̊

Actual track 188 ̊T 488kt constant

SEARCH DAVID LEARMOUNT LONDON

Can maths solve mystery

of MH370’s resting place?

Senior 777 captain believes he has calculated crash site of missing Malaysian airliner