# Finding Flight 370 With A Little Deduction And Some Math

A Boeing 777 has a flight range of thousands of miles. Photo credit M42

A study of some critical numbers is helping investigators track down Malaysia Airlines Flight 370, which disappeared over a week ago on its way from Kuala Lumpur to Beijing.

All of the significant numbers have been looked at, but perhaps one more rehash with maybe a different perspective — and a couple of new numbers — will shed much-needed light on the search.

## Malaysia Airlines Flight 370: What Was The Range Of The Plane?

The Boeing 777 is designed to hold enough fuel to travel over 5,000 miles. However, airlines don’t fill the tank, as this would decrease efficiency due to the added weight of fuel.

Flight 370 was scheduled to fly from Kuala Lumpur to Beijing, around 2700 miles. A generous estimate would be that the plane carried enough fuel to fly 3500 miles. However, range may not be the most important metric for this flight.

## How Long Could The Plane Stay In The Air?

The Boeing 777 is designed to cruise at a speed of 562 miles per hour with a maximum speed of 590 miles per hour. At cruising speed, and with a range of 3500 miles, the plane would stay aloft for six hours and 12 minutes. However, if the plane flew at a considerably slower speed, it could remain in the air much longer

Consider a car. If you drive 30 miles per hour, you can drive twice as long as if you drive 60 miles per hour, though you won’t go any farther. A plane may not be exactly equivalent to a car, but the minimum speed of the Boeing 777, used on landing, is 160 miles per hour. At a speed of 250 or 300 miles per hour, the plane could stay aloft for at least a few hours longer than its time at cruising speed.

## The Path The Plane Traveled

At approximately 8 a.m., more than seven hours after takeoff, a geostationary satellite in the Indian Ocean recorded a signal from the plane. The satellite is only equipped to determine the distance to the signal –nothing more. Not the angle from the satellite to the plane, nor the speed or direction the plane is traveling.

The arcs that have been shown north and south of Malaysia are very misleading. If connected and continued, they would form a circle, the points of which are equidistant from the satellite. The arcs end because that is considered the maximum range of the plane. The plane was somewhere on that circle.

## Summing Up What We Know So Far

MH370 was diverted from its scheduled Kuala Lumpur to Beijing route by someone with intimate knowledge of the aircraft. This person had meticulously planned the theft of the airplane. If (s)he wanted to crash it into the ocean, (s)he wouldn’t have gone to such elaborate lengths to hide, and could have simply taken the aircraft down in the China Sea. If the plane had flown north over Asia, it certainly would have been spotted by radar.

The plane must have flown south, and was still in the air an hour after it would have run out of fuel if it had flown at cruising speed.

It is reasonable to assume that someone who has gone through this elaborate planning wants to land the plane. If the plane proceeded at cruising speed, it would have run out of fuel at 6 a.m. Kuala Lumpur time. The plane last sent a signal at 8 am. What happened between 6 and 8 am that would make the pilot want to keep the plane in the air? The sun came up.

Obviously this plane could not be landed at a commercial airport without the pilot being apprehended. Landing anywhere else would have to be done manually and require a decent view of the surroundings to have any chance of success.

Why would someone fly Malaysia Airlines Flight 370 to Australia? Image by Decoded Science

## Where Could Flight 370 Land?

Though other places in the Indian ocean have been suggested, the only sensible answer is Australia. It is only 2500 straight line miles from Kuala Lumpur to Perth in western Australia. Even accounting for the route, which may have been several hundred miles farther, the plane could have made it.

The Australian outback covers all of western and northwest Australia except for a very narrow coastal strip. The terrain is mostly flat and unpopulated. The Boeing 777 requires a landing distance of 7,000 feet; there must be many such stretches in the outback. The landing wouldn’t have been easy, and the plane surely wouldn’t be able to take off again, but there is no reason to think that an experienced pilot could not put the plane down there.

There are no military radars in western Australia. There are a number of meteorological radars, with ranges of around 200 miles. A pilot with knowledge of the locations could probably avoid detection; but even if one of the radars had recorded a signal, no one would have noticed.

## The Big Question: Why?

There are three possible reasons for wanting to steal this plane: there is a passenger of value; there is cargo of value; the plane itself has value. If it was a valuable passenger, a ransom note would have been received; the plane surely has no value (at least to the pilot) after the landing; so it must be the cargo. What it is and how it got there — that’s for somebody else to figure out.

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1. Peter J Marshall says

Hi there I hope I am not to late, but my thought is, as a pilot myself and like to go on photographic trips, while flying over Bass Straight in a Beech craft Bonanza and wanted to get some good coastal shots… I would turn the aircraft into the prevailing winds slow down to 90 or 110 knots and quite often the air craft would slow down till almost stationary where my passengers would take photos…

If the MH 370 went down in the Indian ocean, where the weather was almost cyclonic, it could well have been ditched and not broken up… The fact that nothing has ever been seen or found makes me wonder… Because luggage floats

That’s if it went down in the sea at all… Still a very big Hmmmm ??

2. Paul Dunne says

Northern arc of MH370 travel possibility, in detail:- QingJiang Province Northwest China, where native Uighar Muslims are being subsumed currently under an avalanche of Han Chinese settlers as with Tibet, recorded an incident in early March (1/3/2014) when 39 Han Chinese were knifed to death in Hannim City, QuinJiang, China.
Northwest China is a high plateau desert with sufficient flat land to land a large passenger plane safely.
There is no debris field in the areas searched in the Indian Ocean to date.

• Jon Plotkin says

I won’t rule it out, Paul, but I find it hard to imagine that the Uighars could pull this off. And there are radars that should have picked up the plane if it went north. I’ve toyed with a different idea for a while now, and since the Malaysian government now insists the plane was on autopilot until it crashed, I might as well present it: The pilot was stealing something and he bailed out of the plane over the Andaman Sea. Radar reports the plane flew at 12,000 feet and that’s the height from which recreational skydivers jump. The plane is capable of going slowly enough. Of course there’s the question of what would be stolen. 20 million dollars worth of gold weighs about the same as the four tons of cargo, which the manifest said was mangosteens. Still, then the plane would be in the Indian Ocean and your point about debris is important. I’ll still go with Somalia, but the damn thing could be anywhere.

3. says

10°24’47.80″N 51°19’39.95″E

As good or better guess as any I have seen. The Somalians steal cargo vessels, why not an airplane? This is a deserted army camp and airstrip. It has been deserted for years. The Flight 370 could have made it there and no one would have seen it or picked it up on radar.
Jon Plotkin? Email me and tell me I’m crazy?

• Jon Plotkin says

You’re not crazy, Bob. If I had to pick a spot now, I’d pick Somalia too. When I wrote this article, I was willing to accept the word of Inmarsat and the Malaysian government. No more. I have read that the pilot is actually in charge of how much fuel is loaded. With a full tank, the plane had a range of over 7000 miles, more than enough to reach Somalia, or Oman, or many other places where friendly natives might await. As far as Inmarsat goes, they lost my confidence when they insisted that they could determine that the plane went south by doppler considerations of the transmissions. This is nonsense; their two arcs were precisely symmetrical — they couldn’t possibly have used doppler effects to tell the difference. As far as I ‘m concerned, the ‘handshakes’ aren’t worth the paper they’re not written on. The plane could be anywhere within 7000 miles of Kuala Lumpur. Somalia is a very good guess.

4. Wamuwi Changani says

Thanks Metin Gunduz
Whats the lowest a Boeing 777 is capable of flying and whats the slowest speed it can still attain airborne and whats the effect of that on fuel consumption and radar ?

5. mike RAL says

Someone could suggest that 2 good pilots were actually trying
to reach an extreme location.
An ice field landing may be possible.
Did any calculations correct for gravity deviation?
The engine ‘ping’ location may have directional veriance
due to atmospheric/ ionosphere divergence.
One Island location is/was possible.
70east x 50 south Kerguelen island
…just a guess :)

6. anti_nihilist says

‘Jon’ [sic.] picked the wrong type of 777.
Fuel estimates are unsubstantiated.
Assumes southern direction based on naive understanding of radar.
Claims “There are no military radars in Western Australia.”

Ha! That’s rich!
Cornell / MIT… so overrated.
I smell ignorant liberal.

7. MIke says

I would suspect the U.S. Military RADAR in
Deigo Garcia would have picked it up?

8. Metin Gunduz says

ESTIMATED LOCATION OF THE PLANE SHOULD BE: (Based on assumptions and reported sighting has to be correct )
Step by Step :
Take off from Kuala Lumpur 12:40 a.m. on March 8. And 8 hrs of fuel to travel at cruising speed of 562 miles/hr ( Boeing 777 is designed ) for 3500 miles travel distance , BUT if it is flying low speed at 250-300 miles and hour can stay on the air few more hours longer …(* ) .

The sighting reported by local residents at Maldives on March 8 morning at 6,15 local time “ The Residents of the remote Maldives island of Kuda Huvadhoo in Dhaal Atoll have reported seeing a “low flying jumbo jet” on the morning of the disappearance of the Malaysia Airlines flight MH370.”(**)

THIS IS IMPORTANT …! and QUITE SIGNIFICANT and SPECIFIC :
Local time of the sighting was 6.15 am (Maldive time ) which is 3hrs behind Kualo Lumpur time (** ) ( It means the MH370 was still on the air at 9.15 Kualo Lumpur time ) and 8hrs and 25 minutes after take off still on the air and the Cruising speed is 1950 miles( The `specific` distance between last transponder signal coordinates at 1.07 am to Maldives islands is ) it means from 1.07 am Kualo Lumpur time known coordinates of the plane –disappearance location- to Maldive local time 6.15 second sighting location by local residents of Kuda Huvadhoo in Dhaal Atoll is roughly 8 hrs … SO the calculated cruising speed is “roughly 250 miles/hour “….! With this 250 miles/hour calculated cruising speed and assuming 2 more extra cruising time due to low speed saved fuel and the –automatic pilot is on with set destination and direction – the plain should be at 500 miles west of Kuda Huvadhoo Atoll …! on the same straight trajectory – straight line- from the last known Coordinates joining the Dhall Atoll . EXACT COORDINATES ARE 1°20’4.66″N , 66°49’37.23″E Copy/paste this coordinates on Google Earth , and should be +- 100 miles radius circle of this
calculated location – Assuming 2 more hours flight time with calculated cruising speed of 250 miles/hr .

Assumptions made for this coordinates are :

1- Sighting at local time 6.15 (local time) on March 8 over Kuda Huvadhoo Dhall Atoll IS CORRECT and REAL SIGHTING

2- Calculated cruising speed(as above) is 250 miles/hour and on –AUTO PILOT IS ON-

3- 2 hours of extra fuel left after the last sighting with estimated travel distance of 500 miles westward .
References :
( * )http://www.decodedscience.com/finding-flight-370-little-deduction-math/43777

http://www.cbsnews.com/news/malaysia-airlines-flight-370-focus-shifts-to-flight-crew/ 7 hrs 31 minutes flight time confirmed

• Ryan says

My friend, I hope your realise just how close these co-ordinates are to the location of the pings thought to belong to MH370’s black box.

• Metin Gunduz says

Bryan , I realized you are talking about my earlier posting aove …(As you
may recall the witnessed sighting was `not true` and `not confirmed` by Maldives Coast Guard later on )..
Of course I recalculated when the sighting at Maldives was not confirmed ..
Than Read on below info : (I had Posted on March 27th )

HOW TO LOCATE THE PLAIN – LOGICALLY- AND NARROW THE SEARCH LOCATION ?

A- SIMULATED TEST FLIGHT`S ORIGINATING FROM THE LAST KNOWN LOCATION AND `MATCHING` THE PREVIOUSLY RECORDED PING DATA OF INMARSAT
B- CALCULATING THE BELT LIKE CURVE- MAXIMUM AND MINIMUM RANGE POSSIBLE BY THE 1- AVAILABLE FUEL AT THE TIME OF LAST CONTACT POINT 2- INMARSAT PING DATA (Total Number of Pings and Possible flight time AFTER LAST CONTACT POINT )

AND CROSSING THE A AND B SHOULD BE THE LOCATION OF THE MISSING PLANE

The `last Complete handshake ` was at 12.11 am UTC according released data from INMARSAT .
“ Possible Cause of `Partial Handshake` : Turbofan engines of Boeing 777 has one “rotating generators” at the each engine for electric power , when the engines stop one after another when the fuel exhausted there will be no `STOP` PING signals from the engines ; BUT during the Plunging fall stage and acceleration in air by the gravity –head on- the frontal air inflow through the turbofan engines will also accelerate and the Turbofan engine fans may rotate `PASSIVELY` this in turn may `Rotate the engine`s generators` very short burst prior to plunging and may generate
`Electric current` strong enough to give `PARTIAL HANDSHAKE` Ping Signal . Most
likely this happened .”
It also means the TIME ENGINES STOPPED `should be at or around 12.19 am UTC :

Than we can Recalculate the `Probable distance traveled from the `last known position ` over the Pulau Perak Island .

ONLY REVISION TO THE ORIGINAL CALCULATION IN ORDER – TO NARROW THE CURVED STRIP SEARCH AREA FURTHER OVER THE INDIAN OCEAN – WILL BE THE ENGINE STOP TIME – OF 12.19 am UTC = LAST PARTIAL
HAND SHAKE . ( 8 minutes AFTER THE 7th PING …! )

( 1 ping at the start of engines + 7 pings on the air + 1 last Partial HANDSHAKE at 12.19 am UTC )

So from the known Last Focal Point (Over the Pulau Perak Island) at 1 hr 34 minutes into the flight ; the plain CAN FLY ONLY 5 hrs 57 minutes (5.95 hrs) + 8 minutes until LAST PARTIAL HANDSHAKE = 6 hrs and 5 minutes (EXACT ) ..= 6 ( 5/60) = (6.08 hrs )

GROUND SPEED ASSUMPTION :

Flight height should be 18,000 or below due to previous Depressurization and Oxygen need to breath and the Air Speed 275 KIAS (Knots in Air Speed) and Calculated corrected(conversion factor is x1.3 for the 18000 feet height )(** ) Ground Speed (No head or Tail Wind ) 410 miles/hr . This height of 18,000 feet and Speed of 275 KIAS is the `OPTIMUM` speed for the Minimum Fuel Consumption – Above or Below this optimum speed of 275 KIAS (Knots in Air Speed) the fuel consumption increase so the TRAVEL DISTANCE DECREASE .(Flight manual page 27 ) (* ) IF there was `Depressurization` which indeed the `Radar data confirms that very high altitude of 45,000 feet flight early on ` than the rest of the flight has to be `Below 18,000 feet to breath Oxygen ` and the fact is below this height the Fuel Consumption Increase from 6300 to 6600 pounds per engine per hour and the KIAS speed decrease also .

So ; Time X Estimated Speed = 6.08 (Exact time engines were running ) X 410(Estimated ground Speed)= 2492 Miles (ground) distance from the
FOCAL POINT(Over the last known locatıon Pulau Perak Island)
*******
FUEL CONSUMPTION POSSIBLE MAXIMUM AND MINIMUM FLIGHT DISTANCE CALCULATIONS UNTIL FUEL EXHAUSTION : (NO CHANGE NEEDED)

108200 pounds of jet fuel , the starting Fuel (54.1 ton) of MH370 at the Kuala Lumpur Airport before the take off and engines started running 29 minutes on the ground before the take off at 00.41 am . According to the Boeing 777-200 Flight Manual , each jet engine uses 3000 pounds jet fuel per engine per hour X 2 engines X 1/2 hr (29 minutes) = total 3000 pounds of fuel used on the ground before the take off . (Manual page 27 at the link below ) (* )

And 6300 pounds per engine at 275 KIAS 18000 feet ( assumed the Oxygen need to breath at this low altitude after the Depressurization occurred at 45,000 height reported by the Military radar ) 6300X 2 engines = 12600 pounds jet fuel / hr both engines uses in 1 hr (Manual page 27 ) (* )

1 hr and 34 minutes after take off ( 1.566 hr. ) – on the air time after the take off – to the Last Contact focal point with military radar above the island of Pulau Perak 6300 to 7200 /per hour each engine fuel consumption range ( maximum and minimum`s average of 2 fuel consumption range in different heights and speeds possible ) (Average 6750 pounds hr per engine for the initial 1 hrs and 34 minutes after the take off ) 6750 X 2 engines x 1.566= 21141 pounds of fuel consumption until the Last Contact Focal Point by the Military radar ..

So at THE LAST CONTACT POINT ..Maximum fuel left = 108200 (start fuel) – (3000 on the ground fuel used before take off + 21141 pounds of fuel used on air until Last Contact by Military Radar) = 84059 pounds of fuel left at the point of LAST CONTACT …

Assuming flying at 18000 feet for adequate Atmospheric Oxygen (Because of previous Depressurizing occurred at previous 45,000 feet which is far out of range recommended height of 41,000 feet ) at the 374 KTAS (275 KIAS) with OPTIMUM fuel consumption of 6300 pounds per hour per engine THE MAXIMUM RANGE OF FLIGHT POSSIBLE UNTIL FUEL EXHAUSTED IS 84059 : ( 6300 x 2 engines) running 6.67 = 6 hrs. and 40 minutes of flight possible with 275 KIAS Knots In Air Speed – Assuming no tail or head wind condition – Actual Ground speed Altitude Conversion Factor (multiple) should be around 1.3 (**) than the Ground Speed should be 357 Knots which is equal to 410 miles and hour speed at Ground Level .

( THIS IS THE OPTIMUM FUEL CONSUMPTION FOR THE MAXIMUM DISTANCE THAT CAN BE TRAVELED)

Please notice the fact that : Below or Above height or Speed the FUEL CONSUMPTION INCREASES …( Please look at the Manual at the page 27) (* )

For example at 12,000 feet the consumption increase to 6600 pounds per hour per engine .

*** So the RADIUS of MAXIMUM RANGE OF FLIGHT DISTANCE POSSIBLE UNTIL THE ENTIRE FUEL EXHAUSTED IS 410 x 6.67 =2735 miles (ground distance ) from the LAST CONTACT POINT .

PS : Assumptions : Flight height should be 18,000 or below due to previous Depressurization and Oxygen need to breath and the Air Speed 275 KIAS (Knots in Air Speed) and Calculated corrected(conversion factor is x1.3 for the 18000 feet height )(** ) Ground Speed (No head or Tail Wind ) 410 miles/hr . This height of 18,000 feet and Speed of 275 KIAS is the `OPTIMUM` speed for the Minimum Fuel Consumption – Above or Below this optimum speed of 275 KIAS (Knots in Air Speed) the fuel consumption increase so the TRAVEL DISTANCE DECREASE .(Flight manual page 27 ) (* ) IF there was `Depressurization` which indeed the `Radar data confirms that very high altitude of 45,000 feet flight early on ` than the rest of the flight has to be `Below 18,000 feet to breath Oxygen ` and the fact is below this height the Fuel Consumption Increase from 6300 to 6600 pounds per engine per hour and the KIAS speed decrease also .

So we CAN FURTHER NARROW THE CURVED STRIP the the PLANE SHOULD BE 2492 MILES TO 2735 MILES RADIUS – RANGE OF “CURVED BELT LIKE STRIP IN THE INDIAN OCEAN” – FROM THE LAST CONTACT POINT AS THE FOCAL POINT WHICH IS OVER THE “PULAU PERAK “ BY THE MILITARY RADAR . BEYOND 2735 MILES NOT PROBABLE IF DEPRESSURIZATION OCCURRED .

RETROSPECTIVELY :
My calculations ON MARCH 27th was The minimum distance traveled from the Focal Point of Pelau Perak should be 2492 MILES TO MAXIMUM OF 2735 MILES …! Current Pinger locations Chinese Ship`s at the Coordinates 25.58 ° S,
101.26 ° E which is exactly 2550 miles (ground) travel distance from the Focal Point Pulau Perak Island –When the radar detection avoidance course taken around the outskirts of peninsula of Indonesia (Yesterday April 6th ) they revised their data also that the Indonesian Military Radar confirmed that there was no Radar detection of the MH370 over the peninsula) . So it is roughly 300-320 miles distance North-West trajectory `traveled` from the Focal point Pelau Perak Island (Last Confirmed Coordinates) than the MH370 apparently and presumably made Sharp –SOUTH turn and the Auto pilot straight course was set at low altitude may be it was programmed earlier? –also remain to be Confirmed when black box analyzed of course ) so I am assuming the actual location will be in between 2492 miles minimum – ( 2550 miles PINGER DETECTION location 25.58 ° S, 101.26 ° E ) – maximum 2735 range . As
calculated on March 27th ..

Retrospectively ; I am glad I had Posted on my Facebook with picture explanation as well as details of the calculations ( which was tagged over 40 times different people repeatedly ) –at that point they have been `searching the wrong place – floating garbage/debris whirlpool like natural currents area – 550 miles Southerly location as you may recall ` then of course they changed the search location after so called ` credible new lead` . Thanks noticing and paying attention my post …What is really important is `The relief and final closure for the families and the loved ones – I was motivated by `Empathy` I felt – as well as the Search crew of thousands of people
and experts involved Worldwide and 20 odd number of Nations ..
These are documented facts `Bryan` , sorry you were not well informed and updated about my postings

9. Anon90017 says

Thanks, MP. I expect that the majority of experts trying to figure this out don’t have the technical expertise to know the precise specs of the different systems in each jet. Am looking forward to hearing more thoughts and information through what I expect to be the next year or two.

10. Bryan Dennis says

I have to say this was an interesting read as it was a major diversion from the majority of the reports covering this topic. I don’t think I’ve heard this Australian outback theory yet, but as to the “why” I found the omission of a political motivation. The highlighted motivation of “valuable cargo” seems ludicrous to me. Is this referring to valuables in the checked luggage? If so, get a grip brother!

• Jon Plotkin says

Reported cargo on this flight is 4 tons of mangoes. But valuable cargo is not ludicrous if a baggage handler is a co-conspirator. Ever hear of money laundering?…….The author

11. Mark says

Thanks Jon. The plane was apparently spotted over the Maldives at 6.15am heading from the North to South East. This is in the direction of Australia but way too far.

The last satellite ping was at 8.11am It was either on the ground then or in the water within the next hour as the gas tank would be very low after 7~8 hours flying.

Any more thoughts about the final resting place?