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Can somebody explain to me how "pings narrowed the location of MH370 at that moment to one of two arcs"?

If a ping is picked up, shouldn't it be somewhat definitive of where it came from?

The satellite just recorded the time the signal took to get from it to earth and back. That gives you a circular arc of places.

The interesting bit in the article is to scroll down to "GOODFELLOW REBUTTAL...Interesting analysis of my analysis." in the comments.

Not really. Let's look at what is generally known:

1. We may if we are lucky know the time in transit.

2. We may know the signal strength.

Unless you have the same signal being intercepted by multiple (minimum number is 3) satellites, you can't triangulate. From a single satellite, you can probably extrapolate from either of these to some extent the location, however you can't do this with any precision beyond a full circle arc.

A good parallel might be earthquake detection and the location of an epicenter. Both these involve tracing a location based on the strength of weakening waves reaching detectors. To locate an epicenter, you need detection of the earthquake by three independent detections. One gives you very little information. Two gives you a line of possibilities. Only with three do you get a chance to determine exactly where the waves originated from.

Now if you know signal strength, and you have two detections, you know it is somewhere in a line based on signal strength, but you can trace it to two more precise possibilities if you have time in transit. Based on the information we have it sounds like they must have two satellites picking up on the signal and comparing times in transit.

It seems similar to how GPS is used to find location - you only know the distance from each satellite, not the direction. Contact with one satellite places you on an arc (or circle), two sats put you on one of the two spots where the arc around each intersects, and three isolates your position to a single intersection of three arcs at established distances from each satellite. (And four gives you altitude.)
There's only one satellite, so they only have (as far as we know) the delay time between sending out the ping and hearing a response to determine distance from satellite to aircraft, with no ability to triangulate the position as something like GPS (which uses many satellites) would do. So they can figure out a large curve around the satellite's position, and the aircraft could have been at any point (within the limits of its fuel capacity) when it sent out that final ping.
Distance alone should give you a full circle, but remember you also have processing time which is significant.

If they have two possible arcs, this suggests that the same ping was heard by two satellites (and no more), and that these are the places where the difference in time that the satellites heard the pings would work for both satellites.

You have basically three intersecting spheres (one is the earth and the other is based on the satellites' light cones). They all meet in two locations. If you had a third satellite, you should be able to determine which of the two locations was right.

You're misunderstanding. There is a single circle, which people are calling two arc. That is because they know the airplane can't fly more than a certain distance from its last known position (this reduces the circle to an arc) and because they know where the airplane isn't from radar data (that breaks the one arc into two pieces, which happen to be roughly the same size).
GPS relies on extremely precise timing as well, and extremely precise knowledge of the orbits of the satellites. If you have 10 millisecond timing on signals that narrows things down to a 3000km range of distances.
The theory was obviously wrong even when it was on the front page of HN two days ago:

1. It does not account for course changes made after the initial diversion from the flight path.

2. It does not account for the final known location of the aircraft along the infamous "arc" off of Australia and Kazakhstan.

The popularity of the theory was and remains puzzling.

Indeed. It's been so far very clear that the simple accident or suicide scenarii were a little too simple to explain all the data that was gathered so far.
And for this matter, it was no simple hijacking either.
A simple bungled hijacking is very much a possibility.
Flying into the middle of nowhere in the middle of the night with no transponder never to be seen again? If it is a bungled hijacking it is still not a simple "take me to this airport or I will start killing people" case.
"Take me to an airport in Australia, fly low over Malaysia and circumnavigate Indonesia to avoid radar. Disable all tracking tools so that the authorities don't shoot us down. I'm wearing a suicide vest so you must follow my orders."

Then the plane runs out of fuel in the ocean.

We can't rule this out completely, but I don't know, it kind of seems unlikely since there would have been attempts at communication from passengers in the plane once they would notice the plane flying very low.
Even if everyone on the plane were deceased, the phones which were left on should have picked up the network at 5,000ft over the Malaysian Peninsula.

The fact that they evidently did not connect to their networks is... yet another mystery.

It's possible that phone jammers were used.

Either way, mechanical failure theories can't explain the lack of phone-network connections (fire disables all aircraft communications AND all cell phones AND doesn't destroy the plane? Bizarro). Hijacking theories technically can, but only tenuously (jammers? seriously?).

Dunno. 1 and 2 could be experimental error. Here's his rebuttal cut and pasted:

GOODFELLOW REBUTTAL...Interesting analysis of my analysis.

New information surfaced today of several people in the Maldives seeing a large white airliner with three red stripes flying overhead at 6:15am the following morning. This coincides nicely with the 2000 nautical mile distance from the original turn made 5 hours before approx. 400 knots/hr. The Maldives lie on an extended line from the initial heading the plane took.

The writer says MH370 made several course changes at various waypoints. This is based on Malaysian radar data which may well have been tracking the other aircraft which is mentioned in the piggy back scenario while MH370 continued on in a southwesterly direction.

This morning I posted a new piece that calls for Rolls Royce to come clean with its data. I think they have the keys to the puzzle so to speak. After all it took two days for the information to filter out they had been collecting the databursts for a further six hours. (this was after I penned my original piece). The key to whether this was a "ghost plane" for 6 hours or a hijack is in their data. Again simple. If the data shows the engine parameters did not change - constant rpm - and normal cruise settings throughout the six hours then the aircraft for all intents and purposes was a ghost flight with no human input. If on the other hand as this writer asserts the plane maneuvered and changed direction and particularly if we were led to believe it performed a the piggy back operation to avoid radar as it moved up the Bay of Bengal there would be many power setting changes in the data. Rolls Royce needs to clarify this asap.

I would dearly love to be proved wrong and for this aircraft to have been hijacked and landed somewhere and the passengers although being held were at least alive. However, I cannot come to that conclusion on my interpretation of the scant facts. I still believe the craft flew on until fuel exhaustion somewhere west of the Maldives. The sighting, if correct, in the Maldives ties together the timeline and heading. The 777 when trimmed is a very stable plane and theoretically could just fly on if a heading was entered.

The New York Times has written that the initial turn south west was initiated by an entry into the Flight Management System and the plane was not manually turned. I don't know how they can determine this but I'll give them the benefit of the doubt. I too have GPS in my car and in two keystrokes I can hit go home and the route is plotted. Guess what? All the airports in the region of operations of this aircraft are already loaded in the FMS. All the pilot had to do was enter the identifier for Langwaki and they craft turned and headed for the initial approach waypoint. He may well have had time to do this before events overwhelmed him. In any event the plane took up a heading for Langwaki which appears incontrovertible at this point.. Many people wrote me about airports on the north coast of Malaysia. KBR in particular but this is a 6,000 foot strip with an approach over land and hills. Few pilots would opt to try and stuff an obviously damaged craft of this type at this point into a 6,000 strip at night. I still believe the turn was to initiate an approach to Langwaki where he had a long clear obstruction free approach over water. His craft was likely above max landing weight and he knew it. He couldn't dump fuel if he had fire. The best scenario is a very long runway.

Unfortunately I still think they were overcome by events.

I am an optimist and I believe we are going to have a resolution within the next couple of days because at least now I feel they are searching in the right place....namely at the place I said in the first post on an extension of the heading they had set up for Langwaki. I said it would be either at a point where the plane crashed becausefire destroyed the flight surfaces OR at the end of fuel exhaustion. We now know it motored on six hours. We now know ...

Thank you for posting that.

It seems that the rebuttal consists of claiming that the evidence we public thus far have been presented is wrong, people involved are not providing the entire truth, etc.

That's possible. But why not work with the information as presented instead of willing it away?

Also:

The change in direction was made at least 12 minutes before co-pilot Fariq Abdul Hamid said "All right, good night," to controllers on the ground, the sources said.

http://www.nbcnews.com/storyline/missing-jet/missing-jets-u-...

I think that one has to be clear about the possibilities here:

1. The plane was hijacked (this seems the most likely for now but let's see what develops)

2. The engine data and satellite ping data was erroneous, perhaps confused with another source.

3. You have a slow issue like slow decompression combined with an avionics failure which caused the plane to follow a long and complex course.

Under normal circumstances none of these three are reasonable explanations. For it to be a hijacking, someone has to have been interested not merely in takin the plane somewhere else but in stealing the plane and concealing it. And the other are remarkably complex.

At this point, though, those are the three scenarios we are discussing. The author of the theory suggests that investigators are using bad data. I wouldn't say it is impossible, and we are already talking about the margins of what is possible in all of our possible scenarios.

The hijacking and crazy pilot theories are most plausible. Hijackera were simply irrational and forced them to go to Australia or something like that. Has happened before.

Or the pilot wanted to commit suicide in a bizarre manner. Or he had a psychotic episode.

All of these are more plausible than Rube Goldberg mechanical failures or James Bond terrorist plots.

My problem though is that getting the plane onto the ground without anyone noticing (which is the only explanation I can think of that ties in the lack of the transponder to this as well as no followup sightings at, say, major airports).

That's a big question, and it suggests a level of clandestine resources I have trouble imagining being the case in Australia.

The ping data did not come from Rolls Royce, it came from the SATCOM provider. Rolls Royce did not receive data after the aircraft reached cruise altitude, despite early false reports that they did.

The early maneuvering was seen on military radar and is confirmed (Malaysia flew another 777 along the same route and monitored it on radar and the signature matched). The positional arc that has been frequently shown is from the final SATCOM ping the aircraft responded to, roughly 7 hours after takeoff.

>Rolls Royce did not receive data after the aircraft reached cruise altitude, despite early false reports that they did.

It casts much doubt on Goodfellow's ability to analyse this case if he didn't know basic facts about it, such as this.

He also referred to the supposed sighting in the Maldives, which appears to be wrong, as it was nowhere near any of the final positions indicated by the SATCOM pings, and occurred about an hour after the plane should have run out of fuel.

#2 (the arcs based on the final SATCOM reading) would have to be radically wrong for the Maldives sighting to be a genuine MH370 sighting, or for the straight-west-until-the-end theory to be correct at all. I suppose it's possible that someone got the calculation based on signal strength (or was it latency?) horribly wrong, but wow what a big clanger it would be.

(The Maldives report and SATCOM conflict under any theory of the incident, btw: a 777 simply can't cover the distance from any point on the arcs to the Maldives in an hour.)

For perspective, it seems there are now reported could-have-been-MH370 sightings more or less wherever you want them in the region, such as as south and east of where the transponders were switched off: http://www.countercurrents.org/jkp180314.htm .

Oh, and speaking of eyewitness reports, IIRC the Thai authorities don't believe that MH370 ever entered Thailand (based on their radar data). It's hard to draw a straight line from just south of Thailand to the Maldives without clipping southern Sri Lanka or western Malaysia around Aceh.

#1 is easier to try to knock down, at least partly. One aircraft could be mistaken for another, the readings must have margins of error, and it's not clear that the charts showing a VAMPI -> GIVAL -> IGREX path for the aircraft aren't based on reading something into the radar data which isn't fully supported there. OTOH, supposedly the radar traces attributed to MH370 were verified against the SATCOM readings, though I can't find a good source for that so caveat emptor.

As far as the trajectory is concerned, isn't going near Maldives just about right (let's not forget about map projection and the shape of the earth).
My problem with Goodfellow's theory, and what really makes this disappearance so intriguing, is that they never found any wreckage anywhere. I would figure with the plane crashing in the ocean somewhere(which would be the most likely scenario in Goodfellow's theory) I would figure they would find SOMETHING by now considering how many resources are being poured into this search.
In Goodfellow's hypothesis the wreckage will be found west of the Maldives shortly. It wouldn't have been found up to now because they have been searching in the wrong places. I have not been blown away by the Malaysians efficiency in doing the search and analysis.
Any onboard fire fast and strong enough to suddenly disable the crew would almost certainly also bring the plane down in short order, rather than letting it fly on for hours (as the supposed satellite data shows).

See Swissair Flight 111 and ValuJet Flight 592 as past examples.

http://en.wikipedia.org/wiki/Swissair_Flight_111

http://en.wikipedia.org/wiki/ValuJet_Flight_592

It might be possible to find a Goldilocks explanation. Maybe a smaller fire, located in the cockpit, which the crew eventually extinguish only to find that the cockpit instrumentation is destroyed? Or maybe which they successfully extinguish, but only after both pilots are unconscious from smoke inhalation, and no-one else knows how to fly or use the radios? Sounds a bit contrived, but this is an unusual situtation.
Sure he's an experienced pilot, but he doesn't seem to have access to any better information than the rest of us. There are plenty of other aviation experts and informed amateurs doing equally interesting analysis and speculation.

So what did Goodfellow do so right to get everyone buzzing about "his" theory?

There's something that particularly bothers me about Goodfellow's article. He condescends about crazy theories while making ridiculous assumption after ridiculous assumption while acting very authoritative about each one. Just because his theory is less "sexy" (it doesn't involve hijacking or terrorists or suicide) doesn't make it any more valid. I'm appreciative of commentary that urges a more prudent approach, not a condescending and equally implausible theory that happens to be boring.
Half of the article is an ad hominem style attack against Goodfellow. It would be nice if it was 50% shorter, with only real content. Wise up Jeff.
I absolutely think a fire theory would be valid, after all the plane was carrying a large load of lithium batteries.

However, that's precisely the factor that calls Goodfellow's fire theory into question (for me). If a fire broke out that was strong enough to disable comms and/or knock out pilots, then it was strong enough to set off those batteries.

No way the plane flew seven more hours in that scenario. Even if the fire was contained to the cabin and there wasn't a pilot left to fly the plane, someone at some point in those seven hours would've found a cell signal to call for help.

Unless, of course, there was no 7 hours and that satellite ping was for another plane. In that case, I'm thinking is the plane would've gone down soon after the transponder went off and the wreckage would've been found by now.

Personally, I have no clue what happened to this plane.