The unsettling oddness was there from the first moment, on March 8, when Malaysia Airlines announced that a plane from Kuala Lumpur bound for Beijing, Flight 370, had disappeared over the South China Sea in the middle of the night. There had been no bad weather, no distress call, no wreckage, no eyewitness accounts of a fireball in the sky—just a plane that said good-bye to one air-traffic controller and, two minutes later, failed to say hello to the next. And the crash, if it was a crash, got stranger from there.
My yearlong detour to Planet MH370 began two days later, when I got an email from an editor at Slate asking if I’d write about the incident. I’m a private pilot and science writer, and I wrote about the last big mysterious crash, of Air France 447 in 2009. My story ran on the 12th. The following morning, I was invited to go on CNN. Soon, I was on-air up to six times a day as part of its nonstop MH370 coverage.
There was no intro course on how to be a cable-news expert. The Town Car would show up to take me to the studio, I’d sign in with reception, a guest-greeter would take me to makeup, I’d hang out in the greenroom, the sound guy would rig me with a mike and an earpiece, a producer would lead me onto the set, I’d plug in and sit in the seat, a producer would tell me what camera to look at during the introduction, we’d come back from break, the anchor would read the introduction to the story and then ask me a question or maybe two, I’d answer, then we’d go to break, I would unplug, wipe off my makeup, and take the car 43 blocks back uptown. Then a couple of hours later, I’d do it again. I was spending 18 hours a day doing six minutes of talking.
As time went by, CNN winnowed its expert pool down to a dozen or so regulars who earned the on-air title “CNN aviation analysts”: airline pilots, ex-government honchos, aviation lawyers, and me. We were paid by the week, with the length of our contracts dependent on how long the story seemed likely to play out. The first couple were seven-day, the next few were 14-day, and the last one was a month. We’d appear solo, or in pairs, or in larger groups for panel discussions—whatever it took to vary the rhythm of perpetual chatter.1
I soon realized the germ of every TV-news segment is: “Officials say X.” The validity of the story derives from the authority of the source. The expert, such as myself, is on hand to add dimension or clarity. Truth flowed one way: from the official source, through the anchor, past the expert, and onward into the great sea of viewerdom.
What made MH370 challenging to cover was, first, that the event was unprecedented and technically complex and, second, that the officials were remarkably untrustworthy. For instance, the search started over the South China Sea, naturally enough, but soon after, Malaysia opened up a new search area in the Andaman Sea, 400 miles away. Why? Rumors swirled that military radar had seen the plane pull a 180. The Malaysian government explicitly denied it, but after a week of letting other countries search the South China Sea, the officials admitted that they’d known about the U-turn from day one.
Of course, nothing turned up in the Andaman Sea, either. But in London, scientists for a British company called Inmarsat that provides telecommunications between ships and aircraft realized its database contained records of transmissions between MH370 and one of its satellites for the seven hours after the plane’s main communication system shut down. Seven hours! Maybe it wasn’t a crash after all—if it were, it would have been the slowest in history.
These electronic “handshakes” or “pings” contained no actual information, but by analyzing the delay between the transmission and reception of the signal— called the burst timing offset, or BTO—Inmarsat could tell how far the plane had been from the satellite and thereby plot an arc along which the plane must have been at the moment of the final ping.Fig. 3 That arc stretched some 6,000 miles, but if the plane was traveling at normal airliner speeds, it would most likely have wound up around the ends of the arc—either in Kazakhstan and China in the north or the Indian Ocean in the south. My money was on Central Asia. But CNN quoted unnamed U.S.-government sources saying that the plane had probably gone south, so that became the dominant view.
Other views were circulating, too, however.Fig. 5 A Canadian pilot named Chris Goodfellow went viral with his theory that MH370 suffered a fire that knocked out its communications gear and diverted from its planned route in order to attempt an emergency landing. Keith Ledgerwood, another pilot, proposed that hijackers had taken the plane and avoided detection by ducking into the radar shadow of another airliner. Amateur investigators pored over satellite images, insisting that wisps of cloud or patches of shrubbery were the lost plane. Courtney Love, posting on her Facebook time line a picture of the shimmering blue sea, wrote: “I’m no expert but up close this does look like a plane and an oil slick.”
Then: breaking news! On March 24, the Malaysian prime minister, Najib Razak, announced that a new kind of mathematical analysis proved that the plane had in fact gone south. This new math involved another aspect of the handshakes called the burst frequency offset, or BFO, a measure of changes in the signal’s wavelength, which is partly determined by the relative motion of the airplane and the satellite. That the whole southern arc lay over the Indian Ocean meant that all the passengers and crew would certainly be dead by now. This was the first time in history that the families of missing passengers had been asked to accept that their loved ones were dead because a secret math equation said so. Fig. 7 Not all took it well. In Beijing, outraged next-of-kin marched to the Malaysian Embassy, where they hurled water bottles and faced down paramilitary soldiers in riot gear.
Guided by Inmarsat’s calculations, Australia, which was coordinating the investigation, moved the search area 685 miles to the northeast, to a 123,000-square-mile patch of ocean west of Perth. Ships and planes found much debris on the surface, provoking a frenzy of BREAKING NEWS banners, but all turned out to be junk. Adding to the drama was a ticking clock. The plane’s two black boxes had an ultrasonic sound beacon that sent out acoustic signals through the water. (Confusingly, these also were referred to as “pings,” though of a completely different nature. These new pings suddenly became the important ones.) If searchers could spot plane debris, they’d be able to figure out where the plane had most likely gone down, then trawl with underwater microphones to listen for the pings. The problem was that the pingers had a battery life of only 30 days.
On April 4, with only a few days’ pinger life remaining, an Australian ship lowered a special microphone called a towed pinger locator into the water.Fig. 8 Miraculously, the ship detected four pings. Search officials were jubilant, as was the CNN greenroom. Everyone was ready for an upbeat ending.
The only Debbie Downer was me. I pointed out that the pings were at the wrong frequency and too far apart to have been generated by stationary black boxes. For the next two weeks, I was the odd man out on Don Lemon’s six-guest panel blocks, gleefully savaged on-air by my co-experts.
The Australians lowered an underwater robotFig. 9 to scan the seabed for the source of the pings. There was nothing. Of course, by the rules of TV news, the game wasn’t over until an official said so. But things were stretching thin. One night, an underwater-search veteran taking part in a Don Lemon panel agreed with me that the so-called acoustic-ping detections had to be false. Backstage after the show, he and another aviation analyst nearly came to blows. “You don’t know what you’re talking about! I’ve done extensive research!” the analyst shouted. “There’s nothing else those pings could be!”
Soon after, the story ended the way most news stories do: We just stopped talking about it. A month later, long after the caravan had moved on, a U.S. Navy officer said publicly that the pings had not come from MH370. The saga fizzled out with as much satisfying closure as the final episode of Lost.
Once the surface search was called off, it was the rabble’s turn. In late March, New Zealand–based space scientist Duncan Steel began posting a series of essays on Inmarsat orbital mechanics on his website.Fig. 10 The comments section quickly grew into a busy forum in which technically sophisticated MH370 obsessives answered one another’s questions and pitched ideas. The open platform attracted a varied crew, from the mostly intelligent and often helpful to the deranged and abusive. Eventually, Steel declared that he was sick of all the insults and shut down his comments section. The party migrated over to my blog, jeffwise.net.
Meanwhile, a core of engineers and scientists had split off via group email and included me. We called ourselves the Independent Group,11 or IG. If you found yourself wondering how a satellite with geosynchronous orbit responds to a shortage of hydrazine, all you had to do was ask.12 The IG’s first big break came in late May, when the Malaysians finally released the raw Inmarsat data. By combining the data with other reliable information, we were able to put together a time line of the plane’s final hours: Forty minutes after the plane took off from Kuala Lumpur, MH370 went electronically dark. For about an hour after that, the plane was tracked on radar following a zigzag course and traveling fast. Then it disappeared from military radar. Three minutes later, the communications system logged back onto the satellite. This was a major revelation. It hadn’t stayed connected, as we’d always assumed. This event corresponded with the first satellite ping. Over the course of the next six hours, the plane generated six more handshakes as it moved away from the satellite.
The final handshake wasn’t completed. This led to speculation that MH370 had run out of fuel and lost power, causing the plane to lose its connection to the satellite. An emergency power system would have come on, providing enough electricity for the satcom to start reconnecting before the plane crashed. Where exactly it would have gone down down was still unknown—the speed of the plane, its direction, and how fast it was climbing were all sources of uncertainty.
The MH370 obsessives continued attacking the problem. Since I was the proprietor of the major web forum, it fell on me to protect the fragile cocoon of civility that nurtured the conversation. A single troll could easily derail everything. The worst offenders were the ones who seemed intelligent but soon revealed themselves as Believers. They’d seized on a few pieces of faulty data and convinced themselves that they’d discovered the truth. One was sure the plane had been hit by lightning and then floated in the South China Sea, transmitting to the satellite on battery power. When I kicked him out, he came back under aliases. I wound up banning anyone who used the word “lightning.”
By October, officials from the Australian Transport Safety Board had begun an ambitiously scaled scan of the ocean bottom, and, in a surprising turn, it would include the area suspected by the IG.13 For those who’d been a part of the months-long effort, it was a thrilling denouement. The authorities, perhaps only coincidentally, had landed on the same conclusion as had a bunch of randos from the internet. Now everyone was in agreement about where to look.
While jubilation rang through the email threads, I nursed a guilty secret: I wasn’t really in agreement. For one, I was bothered by the lack of plane debris. And then there was the data. To fit both the BTO and BFO data well, the plane would need to have flown slowly, likely in a curving path. But the more plausible autopilot settings and known performance constraints would have kept the plane flying faster and more nearly straight south. I began to suspect that the problem was with the BFO numbers—that they hadn’t been generated in the way we believed.14 If that were the case, perhaps the flight had gone north after all.
For a long time, I resisted even considering the possibility that someone might have tampered with the data. That would require an almost inconceivably sophisticated hijack operation, one so complicated and technically demanding that it would almost certainly need state-level backing. This was true conspiracy-theory material.
And yet, once I started looking for evidence, I found it. One of the commenters on my blog had learned that the compartment on 777s called the electronics-and-equipment bay, or E/E bay, can be accessed via a hatch in the front of the first-class cabin.15 If perpetrators got in there, a long shot, they would have access to equipment that could be used to change the BFO value of its satellite transmissions. They could even take over the flight controls.16
I realized that I already had a clue that hijackers had been in the E/E bay. Remember the satcom system disconnected and then rebooted three minutes after the plane left military radar behind. I spent a great deal of time trying to figure out how a person could physically turn the satcom off and on. The only way, apart from turning off half the entire electrical system, would be to go into the E/E bay and pull three particular circuit breakers. It is a maneuver that only a sophisticated operator would know how to execute, and the only reason I could think for wanting to do this was so that Inmarsat would find the records and misinterpret them. They turned on the satcom in order to provide a false trail of bread crumbs leading away from the plane’s true route.
It’s not possible to spoof the BFO data on just any plane. The plane must be of a certain make and model, 17equipped with a certain make and model of satellite-communications equipment,18 and flying a certain kind of route19 in a region covered by a certain kind of Inmarsat satellite.20 If you put all the conditions together, it seemed unlikely that any aircraft would satisfy them. Yet MH370 did.
I imagine everyone who comes up with a new theory, even a complicated one, must experience one particularly delicious moment, like a perfect chord change, when disorder gives way to order. This was that moment for me. Once I threw out the troublesome BFO data, all the inexplicable coincidences and mismatched data went away. The answer became wonderfully simple. The plane must have gone north.
Using the BTO data set alone, I was able to chart the plane’s speed and general path, which happened to fall along national borders.Fig. 21 Flying along borders, a military navigator told me, is a good way to avoid being spotted on radar. A Russian intelligence plane nearly collided with a Swedish airliner while doing it over the Baltic Sea in December. If I was right, it would have wound up in Kazakhstan, just as search officials recognized early on.
There aren’t a lot of places to land a plane as big as the 777, but, as luck would have it, I found one: a place just past the last handshake ring called Baikonur Cosmodrome.Fig. 22 Baikonur is leased from Kazakhstan by Russia. A long runway there called Yubileyniy was built for a Russian version of the Space Shuttle. If the final Inmarsat ping rang at the start of MH370’s descent, it would have set up nicely for an approach to Yubileyniy’s runway 24.
Whether the plane went to Baikonur or elsewhere in Kazakhstan, my suspicion fell on Russia. With technically advanced satellite, avionics, and aircraft-manufacturing industries, Russia was a paranoid fantasist’s dream.24 (The Russians, or at least Russian-backed militia, were also suspected in the downing of Malaysia Flight 17 in July.) Why, exactly, would Putin want to steal a Malaysian passenger plane? I had no idea. Maybe he wanted to demonstrate to the United States, which had imposed the first punitive sanctions on Russia the day before, that he could hurt the West and its allies anywhere in the world. Maybe what he was really after were the secrets of one of the plane’s passengers.25 Maybe there was something strategically crucial in the hold. Or maybe he wanted the plane to show up unexpectedly somewhere someday, packed with explosives. There’s no way to know. That’s the thing about MH370 theory-making: It’s hard to come up with a plausible motive for an act that has no apparent beneficiaries.
As it happened, there were three ethnically Russian men aboard MH370, two of them Ukrainian-passport holders from Odessa.26 Could any of these men, I wondered, be special forces or covert operatives? As I looked at the few pictures available on the internet, they definitely struck me as the sort who might battle Liam Neeson in midair.
About the two Ukrainians, almost nothing was available online.Fig. 27 I was able to find out a great deal about the Russian,Fig. 28 who was sitting in first class about 15 feet from the E/E-bay hatch.Fig. 29 He ran a lumber company in Irkutsk, and his hobby was technical diving under the ice of Lake Baikal.30 I hired Russian speakers from Columbia University to make calls to Odessa and Irkutsk, then hired researchers on the ground.
The more I discovered, the more coherent the story seemed to me.32 I found a peculiar euphoria in thinking about my theory, which I thought about all the time. One of the diagnostic questions used to determine whether you’re an alcoholic is whether your drinking has interfered with your work. By that measure, I definitely had a problem. Once the CNN checks stopped coming, I entered a long period of intense activity that earned me not a cent. Instead, I was forking out my own money for translators and researchers and satellite photos. And yet I was happy.
Still, it occurred to me that, for all the passion I had for my theory, I might be the only person in the world who felt this way. Neurobiologist Robert A. Burton points out in his book On Being Certain that the sensation of being sure about one’s beliefs is an emotional response separate from the processing of those beliefs. It’s something that the brain does subconsciously to protect itself from wasting unnecessary processing power on problems for which you’ve already found a solution that’s good enough. “ ‘That’s right’ is a feeling you get so that you can move on,” Burton told me. It’s a kind of subconscious laziness. Just as it’s harder to go for a run than to plop onto the sofa, it’s harder to reexamine one’s assumptions than it is to embrace certainty. At one end of the spectrum of skeptics are scientists, who by disposition or training resist the easy path; at the other end are conspiracy theorists, who’ll leap effortlessly into the sweet bosom of certainty. So where did that put me?
Propounding some new detail of my scenario to my wife over dinner one night, I noticed a certain glassiness in her expression. “You don’t seem entirely convinced,” I suggested.
She shrugged.
“Okay,” I said. “What do you think is the percentage chance that I’m right?”
“I don’t know,” she said. “Five percent?”33
Springtime came to the southern ocean, and search vessels began their methodical cruise along the area jointly identified by the IG and the ATSB, dragging behind it a sonar rig that imaged the seabed in photographic detail. Within the IG, spirits were high. The discovery of the plane would be the triumphant final act of a remarkable underdog story.
By December, when the ships had still not found a thing, I felt it was finally time to go public. In six sequentially linked pages that readers could only get to by clicking through—to avoid anyone reading the part where I suggest Putin masterminded the hijack without first hearing how I got there—I laid out my argument. I called it “The Spoof.”
I got a respectful hearing but no converts among the IG. A few sites wrote summaries of my post. The International Business Times headlined its story “MH370: Russia’s Grand Plan to Provoke World War III, Says Independent Investigator” and linked directly to the Putin part. Somehow, the airing of my theory helped quell my obsession. My gut still tells me I’m right, but my brain knows better than to trust my gut.
Last month, the Malaysian government declared that the aircraft is considered to have crashed and all those aboard are presumed dead. Malaysia’s transport minister told a local television station that a key factor in the decision was the fact that the search mission for the aircraft failed to achieve its objective. Meanwhile, new theories are still being hatched. One, by French writer Marc Dugain, states that the plane was shot down by the U.S. because it was headed toward the military bases on the islands of Diego Garcia as a flying bomb.34
The search failed to deliver the airplane, but it has accomplished some other things: It occupied several thousand hours of worldwide airtime; it filled my wallet and then drained it; it torpedoed the idea that the application of rationality to plane disasters would inevitably yield ever-safer air travel. And it left behind a faint, lingering itch in the back of my mind, which I believe will quite likely never go away.
*This article appears in the February 23, 2015 issue of New York Magazine.
Oleksandr: When the first engine fails [the right engine] the asymmetric thrust is automatically compensated for by the TAC. Thrust is automatically increased in the left engine. The aircraft will remain precisely on track, and the speed will begin to reduce slowly. Altitude is maintained as the speed is reduced until the best single engine operating speed is attained.
It’s what happens after the 2nd engine fails that is the interesting bit.
Maldives – Don’t forget that Pakistan was ostensibly cooperating with the US on terrorism while it was hiding Bib Laden – for years, and that Iran has a lot of influence these days. Had they wanted to refuel an irregular flight discreetly it could have been arranged. Might it have been low to avoid electronic detection?
The Maldive govt is now a hardline outfit with known terror links(laundering). But I’ll put it down now if it’s making people uncomfortable.
@littlefoot, Thank you for being the voice of reason.
@Josh C, No, I hadn’t seen it before. Seems a worthy effort.
@Oleksandr,
@Benaiahu,
The formula for V_x seems to a duplicate of R_x and must be incorrect. Can you please supply the correct one?
Also, if anyone has a continuous formula for df(sat) + df(AFC) including the eclipse effect, could you please post it? Thanks.
@Jeff, thanks. I have to show that “voice-of-reason” quote to my husband 😉
@Matty, no – I found your article very interesting. And I believe that the Kudahuvadhooans have seen a noisy, very low and slow flying big plane with red stripes around sunrise. I’m just getting allergic if the very limits of reason are getting stretched here by throwing the Maldive sighting, the Curtin boom and the Diego Garcia angle plus a grand cover-up scenario for good measure into one big melting pot in the hope that somehow a plausible narrative will emerge. It won’t.
Fruitful theory building has to be more precise than that.
@Oleksandr,
@Benaiahu,
Here is a good closed-form approximation, including the eclipse effect:
deltaf(sat) + deltaf(AFC) =
coef1+coef2*(T -41705.8541666666)+coef3*(T -41705.8541666666)^2+coef4*(T -41705.8541666666)^3+coef5*(T -41705.8541666666)^4+IF( T > 41705.8541666666, coef6*EXP(-coef7*(T -41705.8541666666)), 0 )
where T is the (Excel) time in days (00:00:00 UTC on March 7, 2014 is 41705.0 days) and
coef1 = -8.934948935
coef2 = -237.2645232
coef3 = 35.44366355
coef4 = 1207.376023
coef5 = 4537.787655
coef6 = 11.90778249
coef7 = 33.06087047
The RMS error of this approximation is about 0.4 Hz, and the peak error is 0.7 Hz. It is useful for inclusion in a BFO model that uses arbitrary time as an input.
@jeffwise: you and I agree that the plane likely did not go to the SIO – DESPITE this being the signal data’s clear indication.
Your theory requires – REQUIRES – fully HALF the signal data to be faked (BFO’s – planted there by the Russians). (Last I checked, your theory also required multiple, non-aligned nuclear powers to have missed a jumbo jet flying through their territory, hijackers who are BFO-geniuses yet BTO-idiots, and a military-grade heist PLANNED to land on fumes, so I guess I find it mildly amusing to be lectured to – however indirectly – on the subject of reasonableness.)
My “theory” is that, having searched out the consensus location, we should explore other evidence – including both the Curtin event, and the Maldives mass-sighting.
Search leaders are KNOWN to have lied/messed up umpteen times in pursuit of this plane. Abandonment of the signal data altogether requires us merely to bump the counter to [umpteen+1].
I’m afraid the noose of logic is tightening slowly but inevitably around the notion that it remains reasonable to cheerlead for signal data US operatives took four days (Mar.10-14) to cough up in summary, and Inmarsat 11 weeks (Mar.10-May 27) to cough up in (redacted) detail.
Brock: There was enough information in one of the slides presented to the Chinese families in April 2014 to allow anyone to calculate the approximate position of the “ping rings” and to deduce that the aircraft was flying away from the satellite after take-off, then towards the satellite until about 19:41, and then away from the satellite again until after 00:11.
The “faked” data could have come from a flight from KUL to Perth or from SIN to Perth. There is a SQ flight that arrives Perth about 5:15am. I don’t know if it’s possible if these flights may approximate a path down to the SIO ….
While some here are pressing about the Maldives (read: the unreasonable crowd – and one multiple award-winning investigative journalist in Australia), and why a deeper exploration into ALL of the witness accounts should happen (even if, gasp, those accounts don’t line up with Inmarsat’s hallowed BTOs and BFOs) — and Brock — in Jeff’s Kazakhstan scenario, MH370 would not have landed on fumes, because it would have flamed out 100+ miles BEFORE reaching Baikonur (but please, ignore that pesky detail) — the (invisible) hand plays and another shoe drops:
Former leader Mahathir Mohamad demands that Malaysia Prime Minister Najib Razak step down to “save the country”. And Minister of Defense Hishammuddin Hussein could be his successor.
“The fact that [Mohamad] has come out so strongly, I think the current prime minister is now almost a dead man walking. It’s the end of his tenure”
http://t.co/eVxisT9RPA
What. Incredible. TIMING.
Well, that’s too bad.
If I rewrite the equation for you, does that help?
Vya = (BFO – 151.4) / 0.0927
Oleksandr
>My “constant thrust” version is still underway, but I am quite convinced that
>“constant thrust” mode (AT, TOGA, failsafe) conforming BTO and BFO does exists,
>and it ends up in the area around 27S.
I am dubious you can get a reasonably good fit to the later BFO points at that latitude, but I await your result.
>I also think that BFO = -2 Hz is a realistic value caused by the turn of the aircraft due
>to the moment, created by asymmetric thrust after flameout of the first engine.
So what causes the change of BFO from 182Hz to -2Hz in 8seconds? Anyway, the Inmarsat paper says the -2Hz measurement should be discounted, so why pursue it?
Littlefoot – I’ve left the Diego Garcia angle alone entirely and Maldives/Curtin boom probably don’t gel. The plane took risks and made a B-line for the Indian Ocean so you start to wonder why? If you accept that they saw a big low plane out there at 6.15 it would have been a simple matter to check out the local traffic which I’m sure they would have. It looks like an irregular flight, which is what MH370 was the moment it turned around. We can’t be at all sure what it was out there but I reckon we are dreaming to go and simply delete such events because a satcom link sprung back to life as it sailed away. I think it turned into a free for all because noone is responsible for the data.
@Nihonmama, thanks for that info about Mahathir Mohamad. I wonder how influential he still is. I also wondered often about his role in the mh370 drama – if he had any.
Don’t get me wrong, Nihonmama about the idea of exploring eye witness accounts, even if they don’t line up with the sat data. Since I belong to the crowd who doesn’t exclude a spoof I don’t regard them as dogma. And while I haven’t seen a scenario yet which IMO would really justify a very complicated cover-up on a multi-national level with many players involved – who then kept the most expensive search for a plane up for over a year now as a bogus operation , I would be foolish to completely discount such a possibility.
But if we try to connect the dots between several credible eye witness accounts of unusual plane sightings and observed phenomenons like the Curtin boom I demand some INTERNAl logic and consistency. That has nothing at all to do with the sat data. And it’s not a confidence inspiring procedure if someone points out on one hand how trustworthy the Maldive witnesses are only to meddle selectively with parts of their reports – like the timing of their plane sighting, or the observed plane’s height – because those accounts don’t line up with other observed phenomenons like time and location of the Curtin event. If you read the eye witness accounts it’s pretty clear to me that the islanders observed a low flying plane in the morning at daylight and not a high flying plane in semi-darkness -as would be necessary to give the plane even a remote fighting chance to miraculously recover from it’s low and slow flight path and transport itself very fast to the location of the Curtin event just in time to produce the boom. If I take the witnesses seriously – as I do – their reports make such a scenario almost impossible.
It would be a very different story if Dr. Duncan et al would correct their time and location estimates of when and where exactly the boom happened yet again. But so far their tendency was to estimate the time rather earlier than later.
As to Jeff’s theory that the plane went North: Maybe the plane didn’t have enough fuel to reach Baikonur but there are plenty of other suitable landing sites on the Northern 7th arc which were well within reach of the plane with some fuel to spare. There’s no reason at all to declare the whole Northern route scenario implausible and throw it in the bin just because one proposed landing site might not work out.
@Matty , I wasn’t critizising you.
I was simply arguing against attempts to connect everything which happened in the Central Indian Ocean – no matter if it is even possible or plausible. But you were not the one doing that.
Bobby,
Thanks for the expression for deltaf(sat) + deltaf(AFC). Yes, you are right that R_x and V_x, which are the same. I was interested in 23:15 data as linear interpolation might be insufficiently accurate, but I haven’t got a chance to use Benaiahu’s expressions yet. Thus you are the first, who noticed this apparent copy/paste bug. Unfortunately I don’t have alternative formulations, so I hope Benaiahu can repost (or need to fit known data again).
Also, in my understanding the following should be satisfied: V_x = dR_x/dt, V_y = dR_y/dt, V_z = dR_z/dt, while it is not the case for Benaiahu’s polynomial expressions. May be it does not matter, but I hope Benaiahu can comment.
———–
Richard Cole,
Yes, BTO & BFO fitting is good, even probably better than for AP. The approach I took can be criticized for taking unknown parameters for optimization of the target functional, but I am getting surprisingly realistic values. For instance, the aircraft mass, which is also modeled, is predicted to be around 201-202 tons at 19:41 (I impose only 174 tons condition at the end of the flight). Generally, I am getting distance errors up to 15 km and BFO errors up to 4 Hz. But the model is sensitive to the parameterization of wind forcing, particularly to slip angle and nose angle.
With regard to -2 Hz, I would expect the aircraft to start turning and diving simultaneously in AT mode after the flame out of the first engine (in contrast to AP). If AES compensation stopped working after the flame out of the second engine, BFO = -2 Hz seems to be achievable by varying direction, speed and descent within physical range. But probably you are right with regard to it.
———–
Gysbreght,
1. What about Vya = (10000 x BFO – 1514000) / 927 ? What are you trying to do? Fit data from Yap’s BFO calculator? If yes, note that if you set column F to zeros, BFOs will not conform your formula quite significantly. Why?
2. I am not sure what you meant by duplicating some of my answers and comments on your questions. Answers without questions do not make sense in my opinion.
Try it.
Look here, I’m not accustomed to having my comments qualified as nonsense, and I’m tired of arguing against your ignorant criticism. If you still don’t get it, you never will.
Littlefoot – The search should be around 70% done by now(they have ceased updating that number) and if I had to bet I’d say that in just over a month Australia, Malaysia and China will agree to call it off. Australia and Malaysia certainly. Then people will be casting around and wondering and reassessing, and people will also start speaking out from various quarters. If you put the signal data aside for a moment, and you were an investigator, you would have been hard on the pedals to interview those Kudahuvadhooans. The fact is that data got eliminated from the investigation on the basis of a handful of pings that no one will stake their retirement funds on. It’s not like we are dealing with a fingerprint, DNA, or other tangible and accepted form of evidence. Rather it was a form of conventional wisdom that grew around MH370, and a momentary one at that. An orthodoxy set in quickly and breaking out of it involved personal attack as Jeff found out.
I know there are career scientists on this blog who seethe when Psychology/Lawyer types start speaking out of turn but they are themselves subjects in a strange landscape. A lot of them were sedately retired until this came and took hold of their lives, some of them even enjoy the publicity but none of them are responsible for the data or are culpable in any way if it’s a fruitless disappointment so it was irresistible intrigue. The data is good enough to attempt a search but it has been extracted with novelty or with very limited technical visibility and sits under the cloud of potential human contamination, so there are question marks. And those questions – anathema to some – will be flying around pretty soon I predict.
I agree with Matty (and others) that its high time that the Maldives reports of possible sightings were investigated thoroughly. I was going to post a link to Hedley’s article but Matty beat me to it 🙂 Also good to investigate other credible possible sightings such as Mike McKay’s; I think that Kate Tee has already documented her possible sighting comprehensively. I think this should be done in parallel with continued search in the SIO.
Just a minor point re: Maldives, the descriptions of the plane seen as reported in various news items are blue or white with red and/or blue stripes…Given Wills and Kate were holidaying there, apparently arrived via British Airways plane, apparently visited Diego Garcia one day arriving very early… could the plane seen by the locals have been a BA plane connected with this visit (colours blue underneath, mainly white with some red and blue markings)? I haven’t been able to find definitive dates for their visit (Daily Mail reported they arrived 6 Mar) and I recall ABC TV reporting their inspection of the DG base but can’t remember when. Does anyone have reliable sources for these dates please?
@Brock In a previous post you mentioned that the Curtin Boom was at 00:25 UTC at approx 2.1N,69.3E but I can’t find any good source for this time other than the Nature News Blog of 5 Sep which quotes: “On 3 September the researchers recovered data from another IMOS station at Scott Reef, off northwestern Australia. It contains a signal at 01:32:49 UTC that the researchers believe could correspond to the sound event they had detected earlier.” Could you please point me to any other sources.
@PM,
The sound generated by the Curtin event hit the underwater microphones at 01:32 UTC, if I understood it correctly. Which means the sound had to travel from the location where it originated to the location of the microphones.
Sound travels roughly 1.56 km per second in saltwater. So you can do some approximations yourself. I’m sure it’s complicated though. The debth of the sound’s origin might cause variances.
@PM: I asked Dr. Alec Duncan for information on the Scott Reef analysis, and he kindly e-mailed it to me.
If you know four things: detection time and location, for each of two detection stations (Scott Reef & Leeuwin) – plus the speed of sound through the deep sound channel – you can derive for yourself both the location AND time of the Curtin event to within a reasonable tolerance.
I’ll ask Alec whether he’s comfortable with me posting the Scott Reef report to this forum. The report also contained several standard deviations and confidence intervals – crucial considerations in the task of ruling paths and timelines in or out.
I really wish Dr. Duncan himself would break this unfortunate mental connection which has taken hold of the public imagination between the “Curtin Boom” and the sighting of the big plane over Kudahuvadhoo.
I re-read Hedley’s vivid article again. According to his quotings of the islanders’ reports the plane was seen more around 06:30 local time than 06:15. Which corresponds well with the quotes of some witnesses of this having been a bright day. So, it’s even possible that the plane was spotted AFTER or at the same time when the boom happened (if the estimation of 00:25 UTC – which would be 06:25 local time – is correct).
Sorry to be so persistent about this one point. But if one isn’t inclined to do the math it’s simply too tempting to connect these dots erroneously because of the proximity of the area where the sound came from to Kudahuvadhoo. The journalist Hedley re-inforces this mistake, too unfortunately. And it doesn’t help that the articles about the Curtin Boom always give the time when the sound hit the microphones but don’t give any estimates about the time when the sound was generated.
Thanks Brock and littlefoot for your replies. I must read news articles more carefully. It would be good to have the “Curtin Boom” info from Dr Duncan if he is OK about that. As to a possible connection between the “Curtin Boom” and Maldives sightings, IMO this is highly unlikely (even if the timeline allows for it) but I wouldn’t yet rule out either one from connection with MH370.
@PM,
This idea about the plane from Kudahuvadhoo having been a British Airways plane is certainly interesting. What the islanders describe – the low flight and the banking – corresponds well with a pilot offering some good glimpses at a wonderful early morning scenery. These islands are stunningly beautiful from above. German tourists have described those pilot stunts being done regularly over the Maldives. It seems to have been very unusual over Kudahuvadhoo though. The islanders were clearly not used to it. So it might’ve been indeed a special charter flight of some sort.
The question arises of course if the pilot wouldn’t have come forward by now and said: yeah I did show off a bit that morning. Hard to say. Would any pilot fear repercussions because of such a stunt?
@PM,I was confused about the boom’s timing, too, at first.
I agree with you that a connection to mh370 isn’t likely. But while it is probably impossible that BOTH events are connected to mh370 I wouldn’t completely rule out that one of them has something to do with the mystery.
@ Oleksandr:
I’ll give it one more try.
The general equation is: BFO = k1 + k2 * Vya, where Vya is the latitudinal (north-south) component of airplane groundspeed.
That equation expresses the fact that for each time and location there exists a linear relation between the BFO and the latitudinal component of groundspeed. The effect of the longitudinal (east-west) component on the BFO is so small that it can be ignored for practical purposes. Your counterarguments about radial and tangential components of groundspeed are therefore demonstrably wrong.
It has been clearly stated that coefficients k1 and k2 depend on time and location. Their values can be determined with the complex expressions embodied in Yap’s spreadsheet. My thanks to Yap Fook Fah for making it so easy to apply those expressions for everyone with a basic understanding of EXCEL. I provided an example of the equation for a particular time and location which were explicitly stated.
BFO = k1 for groundspeed = zero. For given location k2 varies with time. As Jeff Wise observed correctly, k2 is largest when the satellite is farthest from the equator, i.e. close 19:41 UTC, and reduces to zero when the satellite passes the equator, because the AES computes the Doppler compensation for the equatorial position of the satellite.
@PM
I remember reading somewhere William and Kate left Maldives on Thursday 13 March 2014. Indeed they arrived just before the weekend of 8 March. Note their holidays were announced at short notice (William had to cancel some examinations) and there was a lot of consternation because the left little George at home.
I will dive in my archive to see if I can find back dates of travel. I remember them being on a regular BA flight going there (?) However it was difficult to find any info on how and when exactly they went back.
I have been considering the possibility that they were in fact evacuated to DG when it became clear an unknown a/c was heading in the Maldives direction, as an explanation for the unusual noisy morning flight observed.
Niels.
@Everybody,
It’s worth re-reading the results of Rand Meyer’s personal telephone inquiries on that matter at the Maldives . He posted them here in a comment on December 21, 2014 at 09:01 am.
He actually formed the opinion that the whole story doesn’t hold water and that especially Marc Dugain didn’t really make the necessary formal inquiries.
It has to be noted that he didn’t speak personally to the witnesses. But his keen insights are interesting as always. Especially his remarks about the origins of the stories and his insights on the language barrier are important. He contends that the English translations of the islanders’ descriptions of the size and the type of plane are probably not only translations but also potentially distorting interpretations of their narratives by the English language journalists.
Gysbreght,
Once again: BFO is affected only by relative radial (“ping-sphere”) component of the velocity in 3D space (Note 3D, not 2D! In ECEF system, if you wish). This is where you have to start from if you want to understand your mistake.
Once you add all the terms detailed in ATSB report, you will get BFO. Some terms will be partially cancelled due to AES compensation term.
However, first you said BFO=151.4+0.0927*Vya, which is obviously wrong. Then you said that these coefficients are not constants, but depend on the time and space coordinates. Then you are saying that “The effect of the longitudinal (east-west) component on the BFO is so small that it can be ignored for practical purposes”. How small in your estimation?
In the very beginning you had to say that BFO can be approximated by the expression 151.4+0.0927*Vya, and provide its accuracy and the validity interval. Indeed, it does not invalidate more accurate formulation.
Your coefficient k1 may change in a wide range. Once you change ground speed in Yap’s calculator to zero (column F), you will get BFOs from 90.63 Hz to 261.55 Hz. How useful is the expression BFO = 151.4+0.0927*Vya?
It appears to me that you are trying to simplify already simple math, right?
@PM
Two links from very reliable sources 😉
(however the dates can be found in several sources)
Kate and William arrived on March 6th 2014 on Maldives:
http://www.royal-fans.com/kate-middleton-prince-william-jet-relaxing-break-maldives-ahead-royal-tour/
They were back in UK at 13th March 2014:
Next posting
@PM
Kate and William were back in UK at 13th March 2014:
http://www.dailymail.co.uk/news/article-2581316/Wills-Kates-6-500-night-luxury-hideaway-royal-couple-stay-minus-Prince-George-cut-price-course.html
Indeed no details given on how they went back.
Niels
No.
@B. Ulich
the following coefficients to a polynomial of sixth degree (t^0..t^6) describe satellite position and velocity well, where t is the time in seconds since 2014-03-07T00:00:00 (r,v in ecef in m or m/s, resp.):
rx = [25390482.8946,-603.709190215,0.0202346407905,-3.51527772866e-07,3.336001796e-12,-1.62943435432e-17,3.16666502295e-23]
ry = [52828180.6019,-1335.18772729,0.0498326103051,-9.79751909045e-07,1.06955367164e-11,-6.14815083023e-17,1.45432521871e-22]
rz = [-13999389.4178,1383.34310161,-0.0643188230889,1.55178847604e-06,-1.92854573249e-11,1.17064142086e-16,-2.75704174714e-22]
vx = [589.937962045, -0.0634348200486, 2.70332163472e-06, -5.89252174093e-11, 6.97853792222e-16, -4.27753510762e-21, 1.06352790169e-26]
vy = [-1689.70257166, 0.143905678484, -4.9795915624e-06, 8.966832853e-11, -8.86971097191e-16, 4.57247710665e-21, -9.60218377943e-27]
vz = [1009.11103215, -0.103087216501, 3.97737381779e-06, -6.86620866226e-11, 5.40993469347e-16, -1.65772106007e-21, 5.90565435208e-28]
Gysbreght,
The last attempt:
1. Read some stuff on red/blue shifts, for example here: en.wikipedia.org/wiki/Redshift.
2. Assume two points with coordinates (x1,y1,z1) and (x2,y2,z2), which depend on the time t. The distance between points:
D = sqrt ((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2).
The relative speed is
Vr = dD/dt = {(x1-x2)* d/dt(x1-x2) + (y1-y2)*d/dt(y1-y2) + (z1-z2)*d/dt(z1-z2)}/sqrt ((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2) = (x1-x2)/D*(u1-u2) + (y1-y2)/D*(v1-v2) + (z1-z2)/D*(w1-w2),
where u1=dx1/dt, … – velocity components for each of the points.
In the vector form:
Vr = (R1-R2, V1-V2)/|R1-R2|=((R1-R2)/|R1-R2|, V1-V2),
where R1={x1,y1,z1}, V1={u1,v1,w1}, etc. Note that Vr (scalar) is the projection of the movement of the source w.r.t. the receiver into the line-of-sight.
3. Insert relative speed into the equations summarized in Wiki with appropriate sign. You may ignore small terms of order (Vr/c)^2, where c is the speed of light.
4. Apply obtained formula individually for each of the respective terms in ATSB’s Eq. (2), p55. Prior that you will need to transform the aircraft velocity in a local coordinate system (West-East, South-North) into ECEF. This depends on what shape of the Earth you assume. Note you will need to consider several ‘points’: aircraft, satellite, fictitious geostationary satellite, and GES. For the AES compensation term take local horizontal velocity components of the aircraft with the opposite sign.
5. Add all the terms in ATSB Eq. (2), and you will obtain BFO.
You may wish to do it analytically and then simplify by neglecting small terms. I believe you may get an approximate formulation you are talking about for the area of interests, but I have no idea about its accuracy. I found it easier to compute exact expression “as is”.
If you still think this approach is wrong, tell me why.
Also, I would like you to explain, how you derive 4 unknowns (longitude, latitude, speed and heading) from 2 equations without additional assumptions? Basically, I have already asked this question in a different form, but you ignored it. Jeff has also pointed out to you the impossibility to derive location and velocity of the aircraft in a unique way, but it seems he also did not succeed. Your response was: “I believe I made it plain that finding MHH370 is not trivial because, firstly, we don’t know the airplane location at 18:40, 19:41, etc. and secondly, we don’t know who or what controlled the airplane after fuel exhaustion, we only know it was not the autopilot.”. No, these are of secondary importance and do not pose a significant difficulty to find the terminal location.
Thanks Niels
Littlefoot/PM/Brock – The good work of Dr Duncan was virtually done on the quiet which could point to the weird politics surrounding the search. Ordinarily this would have been great publicity for Curtin and did anyone else go under the radar? Back when it was just rumoured I remember now arguing with Littlefoot that there is no way Curtin would be so discreet about it. Well, they were. Curious thing about scientists – they claim all the time to be scientists but engage in all kind of petty stuff at the same time – many of them anyway. The LANL group were discreet but were not official. A peculiar climate set in around the search.
Obama has handed out a few free passes to Putin in the last couple of years and I think we now know he intended to do the same for the Iranians. I thought Obama looked remarkably disengaged from the MH370 question – did he duck it for a reason? He is relentless about pursuing “deals” and ignoring the actual stuff. His climate deal was worthless, the Iranian deal is the same – is this someone just building their legacy.
It’s in the SIO, everyone go home. It’s pretty much all he said, meanwhile volunteers were doing a lot more lifting than they should have. Dad’s army to the rescue. It has always looked odd.
@Matty
Sorry to disagree but generally I would expect academic researchers to be pretty cautious re: their data. They are often working towards a journal publication and/or there may well be IP and other considerations.
PM – keeping the data/findings close is one thing but if they are involved officially in the search? Doesn’t seem like a shocking disclosure to me. I feel it had a bit to do with the optics of the whole affair. How can you say the data is “excellent” and investigate a noise in the opposite direction at the same time?
I forgot the link to previous post –
http://www.powerlineblog.com/archives/2015/04/daniel-pipes-the-obama-doctrine-serves-up-one-disaster-after-another.php
Up to date ship tracks here:
https://www.dropbox.com/s/e8xtas5hx6027w2/MH370%20Track%20and%20Search%20Area%20Update.pdf?dl=0
Reminding folks…the PAR5 vectors are available here:
https://www.dropbox.com/s/lq36itei6kals1m/PAR5_I3F1_Vectors.xlsx?dl=0
These second by second satellite positions and velocities were derived from a close fit to the ATSB/Inmarsat vectors provided at discrete times. I recommend these over vectors computed from any of the TLE files. Inmarsat had the best ephemeris for I3F1.
@ Oleksandr:
RE YR items 1 through 5: why on earth would I do such a thing when Yap’s wonderful spreadsheet does that for me at the drop of a hat?
Of the six terms that compose the BFO, two are affected by the airplane’s location and speed. The BFO can tell us only the sum of delta.F.Up and delta.f.comp. Yet you keep hammering on the Doppler shift between airplane and satellite, and seem to forget about the frequency compensation for the airplane movement performed in the AES which is three times as large as the bit you are fixated on.
I’m not going into your last paragraph. That is the simple part, but as long as you consider my understanding to be nothing but nonsense and mistakes you’re obviously not quite ready for it yet.
In the meantime you can perhaps help me understand what you mean by radial and tangential components of groundspeed. What are the headings of these components in the situation of the example at 19:41, and at say 500 kt what are the corresponding BFO’s compared to the BFO for zero speed?
Sorry that it took me a few days to contemplate that problem – I was distracted by other issues.
I think you possibly went wrong when you considered only the speed of satellite but not its position. For the sake of argument, let’s for a moment ignore the physical reality and assume that the satellite can be held at a position at 10° North of its geostationary reference position. There would then be a difference between the distances of the airplane to the satellite and to the reference position, and hence between the speeds of the airplane relative to those points, and the sum of ΔFup + δf comp would not be zero.
Does that help?
@ALSM: thanks very much for the search track details – wonderful to have actual speed data embedded, and precise paths preserved.
The southern search map finally confirms what I tried (without success) to get M. Chillit to check out: that Supporter did indeed seem to lay down one lone swath well SOUTH of the priority area (centred on a region due south of IG/ATSB spot). Interesting.
My questions:
Request #1: would it be easy for you to post a map of the region WEST of what you’ve provided so far? I think some scanning was done out there, as well (again, WELL outside the priority area).
Request #2: in your report, you make the statement: “Current post fuel exhaustion path models suggest MH370 is at least as likely to be inside the 7th ARC”. Why JUST as likely, when (I’d thought) the ATSB had already deduced that the first turn was to the LEFT? If the first turn was to the left, then the centre of the probability distribution would certainly be centred BEYOND the 7th arc. Because (math).
More to the point: do we KNOW what direction MH370 was heading as it crossed the 7th arc? I thought we were now to disregard key 00:19 BFO values. To the extent we’re now unsure of 7th arc heading, some forward (i.e. southward) momentum would seem to me to be a reasonable baseline assumption.
Thanks.
@Oleksandr, Gysbreght
For several reasons it’s a pitty you seem to disagree to agree. In principle it is helpful to have a pragmatic approximation, though we should know when it is valid. I had a look at the analytics and the point that bfo is not much influenced by v_lon and more by v_lat is due to the fact that sat position has a major z-component for the time interval we are considering (Innerproduct of sat pos and ac velocity). I expect k2 to decrease when sat moves to equator plane, but also for the more southerly a/c positions (z component of v_lat decreases)
Regards
Niels
Ref:Henrik’s residual doppler analytical model
Gysbreght,
Re: “RE YR items 1 through 5: why on earth would I do such a thing when Yap’s wonderful spreadsheet does that for me at the drop of a hat?”
I can name at least two reasons why you would need to do it:
– To understand how BFO is derived, particularly in Yap’s spreadsheet.
– To understand errors in BFO estimates, when you use the approximation BFO = k1 + k2*Vya instead of the accurate math.
“In the meantime you can perhaps help me understand what you mean by radial and tangential components of groundspeed”.
Sure. I think I did not use the word ‘groundspeed’, but I said in 3D space, which you constantly omitting. Once again, under the ‘radial’ component I implied the projection of the relative velocity of the aircraft with respect to the satellite on the direction of the direction of the line-of-sight. Tangential components are the two other components, which are in the plane perpendicular to the line-of-sight. It is the plane tangential to a ping-sphere, with the satellite in its center. All in 3D space. The only ‘radial’ component affects BFO, but you disagreed with this. I do not evaluate tangential components because they do not affect BFO.
To compute ‘radial’ component, you first need to convert ground speed {u,v,w} in a local coordinate system, in which u is parallel to longitudinal axis, v is parallel to latitudinal axis, into {U,V,W} in the ECEF system (if you want, I can give you formulation to convert). As well as you need to convert coordinates. Then compute projection according to the formulation I gave you in Step 2 above (Vr). Sounds difficult? Well, in the reality it is not. You need to do some programming only once.
Re: “BFO can tell us only the sum of delta.F.Up and delta.f.comp.”.
Yes, finally you got it!
Re: “Yet you keep hammering on the Doppler shift between airplane and satellite, and seem to forget about the frequency compensation for the airplane movement performed in the AES which is three times as large as the bit you are fixated on.”
No, I am not forgetting. See my Step 4, particularly last sentence. In more details: when you compute AES compensation term, you need to take local horizontal velocity components of the aircraft with the opposite sign, set vertical velocity component to zero, use assumed constant location of the geostationary satellite, and set velocity of the assumed geostationary satellite to zero. You may even use some ‘fictitious’ components of the aircraft in such an algorithm, assuming that INS supplied data different from the real aircraft’s location and velocity (in other words you can experiment with hypothetical INS failures).
Re: “Sorry that it took me a few days to contemplate that problem… and the sum of ΔFup + δf comp would not be zero”.
I am happy that you have finally realized this! I said the same to Peter in the post on April 2, 2015 at 5:15 PM.
Niels,
Thanks for your comments. There are a few issues we are arguing with Gysbreght. We have principal disagreements in a few things:
1. Is the set of (BTO, BFO) is sufficient to derive the trajectory in a unique way, both location and velocity, assuming that the location at 18:40 is known, errors in BTO and BFO are absent, and the altitude is constant?
2. Is it necessary to make a hypothesis about the mode of the flight / how the airplane was steered or not?
3. Whether “latitude is obtained from the north-south component of groundspeed defined by the BFO” or it is obtained from the two equations for BTO and BFO supplemented by a hypothesis about flight mode?
4. Whether formulation BFO = k1 + k2*Vya is a simplified approximation of the accurate expression for BFO or “The general equation”?
@littlefoot, Niels
Thanks, I did re-read Rand’s posting and it was useful. Seems most likely that a low-flying plane over Kudahuvadhoo was just there for scenic purposes. Niels, I also wondered whether the Royal couple were evacuated to DG that morning but if so can’t see a reason why their plane would fly so low and slow.
So far the only agreement I can see in witness reports from various sources is that the plane was large and flying low; plane type, colours, time, direction are unclear. In summary I think its extremely unlikely to have been MH370 and won’t post further on this topic.
PM – scenic purposes is absolutely plausible but troubling still to me that the only such occurrence on record for these people(apparently) is in the MH370 window.