Well, I beg to differ with the above supposition. The world is indeed a big place, and even a small amount of information can yield enormously useful constraints.
Start with the graphic below. While I make no claims for its precision, it is a useful approximation of the problem statement.
The graphic above shows the approximate maximum and minimum range associated with the fuel estimated to be on board MH370 at the time of the last radar contact West of Penang. The approximate radius of the maximum range, blue circle, is 2850 nm. The approximate radius of the minimum range, black circle, is 1100 nm. The red line is the 6th (00:11) Inmarsat arc.
The surface area between the maximum and minimum ranges is approximately 22 million square nautical miles. The distance along the 7th arc between 26S and 40S is approximately 1200 nm. If a very generous search width of 100 nm is used, the area of the 7th arc search as defined by the Inmarsat data is approximately 120000 square nm. It is clear that the Inmarsat data reduces the search possibilities by factor of almost 200, or a factor greater than two orders of magnitude. Two orders of magnitude is a huge reduction.
How can anyone possibly claim the Inmarsat is not extremely useful??
Tuesday, August 30, 2016
Sunday, August 28, 2016
Re: Iannello and Godfrey, “Possible Flight Path...”
Iannello and Godfrey
Very interesting. The narrative checks
a lot of boxes. Perhaps all of the boxes.
The points in the SIO on ZS's flight
simulator are certainly a compelling reason to believe that a flight
was simulated in that direction. Again, no hint of motive is
apparently provided by this new information. I say apparently because
it takes a little more thought, albeit speculative thought, to make
sense of it all.
Let's start with the Malay response to
the diversion in the first hour or two after the turn West near
IGARI. The response was below minimal standards. One could even
describe it as pathetic. Even the ICAO was critical of it, and that
is highly unusual for that organization(1).
Many people wondered why the response was not a “dialing until your
fingers bled” effort. A simple explanation is that the status (not
the exact location) of the aircraft was known. Third parties in KL
were attempting to negotiate concessions from the Malay leadership in
KL, with MH370 as the lever. The exact nature of those concessions
cannot be known, but there is certainly a large menu of options.
So ZS flew West from IGARI to play a
waiting game to the North and West of the Malay Peninsula – waiting
for word of success so that he could land the plane - Banda Aceh and
Car Nicobar being logical choices. That word never came, and the
“negotiation failed” response was to fly South and destroy the
aircraft in the SIO. While that action may seem extreme, it was the
only possible response. You cannot retreat from a situation like
that without carrying out the stated threat. Your chance of a
successful future negotiation is highly dependent on the other party
understanding that your ultimatums must be regarded very seriously.
So with the “negotiation failed”
result, ZS selected McMurdo Station as an AP destination, and
resigned himself to his fate. His ambition of becoming a national
hero was dashed, and he had to pay the price he knew full well was a
possible outcome of this bold plan. So why practice the route on his
simulator? Surely a pilot of his skill could execute that route
without practice. The simple and obvious answer was to indulge
curiosity. ZS wanted to know where the plane would run out of fuel,
and observe his final resting place on the planet.
The simulated route did not include the
turn near IGARI. The simulation was most likely done with the
assumption that the diversion would be performed on a route to
Europe. Scheduling and other constraints required a diversion from
the Beijing route. A European route would have been preferred, since
the diversion would not be noticed until the plane had flown well
past the Malay Peninsula.
I think the implication in the
“discussion” section of the latest IG narrative is excellent. A
logical place to look for the aircraft is where a flight path to
McMurdo crosses the Inmarsat 7th BTO arc. While the
precise location of the FMT in the actual route flown is a bit
“fuzzy”, the geometry reduces the spread in the 7th
arc crossing locations. Also the latitude of the crossing derived in
the IG narrative, ~27S, is far more consistent with the debris finds
(and lack of finds) than is ~38S.
Wednesday, August 24, 2016
More on Ping Ring Radii and Other Good Stuff
Found this data from Dr. Steel. Our values agree very closely so I'll just publish his table with attribution. Good reference, IMO, to 3F1 parameters including sat position, sat velocity, sub-satellite position on earth (Lat Lon columns), and ping ring radius (Approx Great circle distance).
Where is that Ring (18:25:27)
Wednesday, May 6, 2015
Obviously the accuracy of the handshake rings is of critical importance to the forensics related to the terminal location of MH370. My initial ring calculations (done a long time ago) were relatively "casual". The results were placed in a table which I have continued to use since. While these results have had no important bearing on modeling candidate flight paths, they would become important relative to directing search efforts or for use in comparisons with other data. One such comparison is the radar data obtained from Butterworth RMAFB. Of particular interest is the 18:25:27 ring which is very close in time to the last radar contact at 18:22. The 18:25:27 ring is quantified below.
Note: This value is correct only for analytics relatively close to the equator where the WGS84 earth radius is very close to 6378.
My ancient 18:25:27 calculation of 3630 is clearly astray by almost 100km. Not very useful for anything but flight path feasibility calculations. An earlier post made here relative to radar implications is obviously flawed, and will be revisited.
Figure 1 - GES / Satellite / Aircraft Geometry
(view is orthogonal to a plane containing R_s and (R_e +H))
Note: This value is correct only for analytics relatively close to the equator where the WGS84 earth radius is very close to 6378.
My ancient 18:25:27 calculation of 3630 is clearly astray by almost 100km. Not very useful for anything but flight path feasibility calculations. An earlier post made here relative to radar implications is obviously flawed, and will be revisited.
Friday, August 5, 2016
Tuesday, August 2, 2016
Saturday, July 30, 2016
Monday, July 4, 2016
MH370 Debris Analytics ("blue collar" version)
Elegant drift analytics have been performed by Brock McEwen, independent contributor, and Richard Godfrey of the IG.
McEwen's analytics can be found here:
Brock Study
Godrey's analytics can be found here:
Richard Study
This effort is not intended to replace or supplement the efforts linked above. It is simply another way to look at the problem. I would characterize it as being derived from common sense and complete. Complete in this context means everything is included below. Unlike the studies linked above where the heavy lifting from an analytical perspective is "under the covers", and you are presented with graphical or tabular output which cannot be checked (not meaning to imply that there is reason to believe checking is needed).
A table of the debris found as of this date (07/04/16) is presented below. Not all of these finds have been officially confirmed, but they are all compelling relative to being from 9M-MRO. No distinction is made by debris size, whether it came from the right or left side of the aircraft, or whether it was an internal or external part.
A LON - LAT scatter plot of these finds is as shown below.
Map view of debris finds below.
The finds show a significant clustering around latitude -20 to -26. Outliers are the Mossel Bay find and the most recent Pemba Island find.
Shown below is the Geomar reverse drift plot using "only" the flaperon finding on Reunion Island. Reunion Island is at -21 latitude, and is representative of the latitude of the debris clusters. I have no reason to doubt the validity of the Geomar model, and it saves the time and tedium of watching which way rubber ducks travel across the ocean.
It is clear from the Geomar graphic the preferred origin of the Reunion find is along the coast of Sumatra/Java. It can be inferred that other finds in the vicinity of latitude -20 to -26 would have a similar origin. It is reasonable to conclude, based on the Geomar model, that the 9M-MRO terminus lies between latitude -10 and -20 on or near the 7th arc.
The debris data lends absolutely no support to the current area being searched by the ATSB. The fact that no debris has been found on the coast of Western Australia further supports the notion that the current search area is not correct.
Edits July 7, 2106 - DW
Since posting the above on the JW blog several comments have been made by people with relatively little technical background or a flawed background that "beg" for additional commentary here.
First is the notion of forward and reverse drift calculation. All calculations are by definition reverse calculations since the objective of the calculation is the origin of the debris not the terminal locations of the debris which comprise the set of knowns. Now it is possible to use algorithms which reverse the forcing functions to arrive at a hypothetical starting point. It is also possible to use forcing functions that operate in the forward direction and use them act on debris at a variety of starting points and subsequently cataloging the results.
Second is the notion that additional debris finds add confusion and difficulty to drift calculations, especially in the reverse direction. The reality is that more data provides more constraining information that actually serves to "focus" possible starting points. More information is always better, that is an axiom of information theory as well as Kalman filtering.
Third is the notion that the new Geomar study should be used, and the above study to be discarded. I deliberately used the above study because it addresses the debris clusters at ~20S directly. No one, including Geomar, has indicated that the above study is flawed. Debris found at Pemba Island and Mossel Bay can only narrow the findings of the above study, not broaden them. A common metric in navigation mathematics is the notion of "dilution of precision". A narrow string of debris location latitudes significantly dilutes the precision that could be obtained if the debris were more scattered with respect to latitude. This statement applies particularly to the North-South precision of the starting point.
McEwen's analytics can be found here:
Brock Study
Godrey's analytics can be found here:
Richard Study
This effort is not intended to replace or supplement the efforts linked above. It is simply another way to look at the problem. I would characterize it as being derived from common sense and complete. Complete in this context means everything is included below. Unlike the studies linked above where the heavy lifting from an analytical perspective is "under the covers", and you are presented with graphical or tabular output which cannot be checked (not meaning to imply that there is reason to believe checking is needed).
A table of the debris found as of this date (07/04/16) is presented below. Not all of these finds have been officially confirmed, but they are all compelling relative to being from 9M-MRO. No distinction is made by debris size, whether it came from the right or left side of the aircraft, or whether it was an internal or external part.
A LON - LAT scatter plot of these finds is as shown below.
Map view of debris finds below.
The finds show a significant clustering around latitude -20 to -26. Outliers are the Mossel Bay find and the most recent Pemba Island find.
Shown below is the Geomar reverse drift plot using "only" the flaperon finding on Reunion Island. Reunion Island is at -21 latitude, and is representative of the latitude of the debris clusters. I have no reason to doubt the validity of the Geomar model, and it saves the time and tedium of watching which way rubber ducks travel across the ocean.
It is clear from the Geomar graphic the preferred origin of the Reunion find is along the coast of Sumatra/Java. It can be inferred that other finds in the vicinity of latitude -20 to -26 would have a similar origin. It is reasonable to conclude, based on the Geomar model, that the 9M-MRO terminus lies between latitude -10 and -20 on or near the 7th arc.
The debris data lends absolutely no support to the current area being searched by the ATSB. The fact that no debris has been found on the coast of Western Australia further supports the notion that the current search area is not correct.
Edits July 7, 2106 - DW
Since posting the above on the JW blog several comments have been made by people with relatively little technical background or a flawed background that "beg" for additional commentary here.
First is the notion of forward and reverse drift calculation. All calculations are by definition reverse calculations since the objective of the calculation is the origin of the debris not the terminal locations of the debris which comprise the set of knowns. Now it is possible to use algorithms which reverse the forcing functions to arrive at a hypothetical starting point. It is also possible to use forcing functions that operate in the forward direction and use them act on debris at a variety of starting points and subsequently cataloging the results.
Second is the notion that additional debris finds add confusion and difficulty to drift calculations, especially in the reverse direction. The reality is that more data provides more constraining information that actually serves to "focus" possible starting points. More information is always better, that is an axiom of information theory as well as Kalman filtering.
Third is the notion that the new Geomar study should be used, and the above study to be discarded. I deliberately used the above study because it addresses the debris clusters at ~20S directly. No one, including Geomar, has indicated that the above study is flawed. Debris found at Pemba Island and Mossel Bay can only narrow the findings of the above study, not broaden them. A common metric in navigation mathematics is the notion of "dilution of precision". A narrow string of debris location latitudes significantly dilutes the precision that could be obtained if the debris were more scattered with respect to latitude. This statement applies particularly to the North-South precision of the starting point.
Tuesday, June 28, 2016
Sunday, April 10, 2016
Friday, March 25, 2016
Reunion Flaperon Reverse Drift Graphics - Holding Area
From Brock's Drift Summary - Brock
From GEOMAR Study (2,000,000 "particles" used)
Sea surface temperature may be useful when/if French estimate flaperon barnacle age. The barnacles require a water temperature of 18C or greater to colonize flotsam.

From GEOMAR Study (2,000,000 "particles" used)
Sea surface temperature may be useful when/if French estimate flaperon barnacle age. The barnacles require a water temperature of 18C or greater to colonize flotsam.
Indian Ocean currents. Overview and closeup (near Madagascar and Mozambique)

Statement posted in "Crikey", March 24, 2016. Chester says the examination has been completed. No comments as of yet (March 27, 2016) relative to marine life or lack of it on this debris.
Interesting contrail below. Photo taken (just for the hell of it) 3/31/2016 ~ 130 miles North of San Francisco. Plane is flying straight South toward San Francisco.
Sunday, March 13, 2016
Blaine Gibson Find - Information Holding Area
The Hi Lok Fastener (HL1013-6)
In late February, 2016, Seattle attorney Blaine Gibson found a piece of aircraft debris near a sand bar off the coast of Mozambique (East coast of Africa). Gibson had traveled there with the intention of simply being a tourist, but decided to rent a boat to do a little beach combing in the hope of finding debris from MH370. In the unlikely short time period of an hour or so the boat's skipper spotted something, and Gibson and crew pulled it from the water. It certainly looks like aircraft debris. It should be mentioned that the sand bar area the skipper "guided" Gibson to was known to be an area where debris of all sorts tended to congregate.
Gibson and the debris find are pictured below. The inset map shows that the new debris find is almost directly West of Reunion Island where the first piece of confirmed MH370 debris, a flaperon, was found earlier. Gibson's find is believed (by knowledgeable bloggers) to be from the area of the right hand side of the horizontal stabilizer. Neither this location on the aircraft nor the fact that Gibson's find came from a 777 aircraft have been officially confirmed (as of March 17, 2016).
http://qz.com/630093/how-a-piece-of-flight-mh370-may-have-washed-up-on-a-beach-in-mozambique/

Very close to (just below) the 'N' in 'NO STEP' a fastener head can be seen which did not become dislodged from the debris.

The HL1013 is a standard marking specification for a Hi Lok (trademark owned by Hi Shear) pin type fastener. As shown in the Hi Lok specification linked below, the fastener is a titanium pin type. The -6 is a diameter designator which refers to the pin diameter in increments of 1/32". In this case -6 => 6/32" = 3/16" diameter.
http://www.aviaquip.com.au/pdf/hiloc/hl1013.pdf
From another specification control drawing it can be inferred that the VS marking designates the manufacturer to be Voi Shan, a well known manufacturer of hardware of this type along with installation tools of various kinds.

Note the "Arrangement optional" annunciation at the bottom of the drawing above. The manufacturers designated in the drawing are:
"hs" - HI-SHEAR
"VS" - VOI SHAN
"SPS" - STANDARD PRESSED STEEL
The V after the trademark indicates titanium, but omission of the V after the trademark is optional. Likewise the first dash number (i.e. -6) is most often placed after the HL1013 part number.
Voi Shan is no longer an independent active entity in California, but fasteners are still sold under the Voi Shan brand (see change of ownership progression in the last paragraph below).
http://www.corporationwiki.com/p/ovmre/voi-shan-manufacturing-company-inc
The company made news in the late 1980's due to alleged quality control lapses (and fraud).
http://articles.latimes.com/keyword/voi-shan-company
1994 earthquake damage and subsequent closure.
https://www.dtsc.ca.gov/SiteCleanup/Projects/upload/Voi-Shan_FS_dRAW.pdf
Direct calls to the phone numbers provided in the Voi Shan documentation were greeted with courtesy and respect despite the unusual nature of my questions. The initial contact phone numbers, of course, lead to people in a sales role. They promptly directed me to a technical support engineer.
Despite several changes of ownership (Voi Shan -> Fairchild -> Banner -> Alcoa) I was told that the markings on Voi Shan manufactured fasteners have remained the same. Voi Shan simply became the Voi Shan Division of the new owning entity. I was asked not to publish contact names because this type of information needs to be cleared by the legal department in order to constitute an official release of information. I will abide by that. So while I believe this information is accurate, it is not official.
In late February, 2016, Seattle attorney Blaine Gibson found a piece of aircraft debris near a sand bar off the coast of Mozambique (East coast of Africa). Gibson had traveled there with the intention of simply being a tourist, but decided to rent a boat to do a little beach combing in the hope of finding debris from MH370. In the unlikely short time period of an hour or so the boat's skipper spotted something, and Gibson and crew pulled it from the water. It certainly looks like aircraft debris. It should be mentioned that the sand bar area the skipper "guided" Gibson to was known to be an area where debris of all sorts tended to congregate.
Gibson and the debris find are pictured below. The inset map shows that the new debris find is almost directly West of Reunion Island where the first piece of confirmed MH370 debris, a flaperon, was found earlier. Gibson's find is believed (by knowledgeable bloggers) to be from the area of the right hand side of the horizontal stabilizer. Neither this location on the aircraft nor the fact that Gibson's find came from a 777 aircraft have been officially confirmed (as of March 17, 2016).
http://qz.com/630093/how-a-piece-of-flight-mh370-may-have-washed-up-on-a-beach-in-mozambique/

Very close to (just below) the 'N' in 'NO STEP' a fastener head can be seen which did not become dislodged from the debris.

The HL1013 is a standard marking specification for a Hi Lok (trademark owned by Hi Shear) pin type fastener. As shown in the Hi Lok specification linked below, the fastener is a titanium pin type. The -6 is a diameter designator which refers to the pin diameter in increments of 1/32". In this case -6 => 6/32" = 3/16" diameter.
http://www.aviaquip.com.au/pdf/hiloc/hl1013.pdf
From another specification control drawing it can be inferred that the VS marking designates the manufacturer to be Voi Shan, a well known manufacturer of hardware of this type along with installation tools of various kinds.

Note the "Arrangement optional" annunciation at the bottom of the drawing above. The manufacturers designated in the drawing are:
"hs" - HI-SHEAR
"VS" - VOI SHAN
"SPS" - STANDARD PRESSED STEEL
The V after the trademark indicates titanium, but omission of the V after the trademark is optional. Likewise the first dash number (i.e. -6) is most often placed after the HL1013 part number.
Voi Shan is no longer an independent active entity in California, but fasteners are still sold under the Voi Shan brand (see change of ownership progression in the last paragraph below).
http://www.corporationwiki.com/p/ovmre/voi-shan-manufacturing-company-inc
The company made news in the late 1980's due to alleged quality control lapses (and fraud).
http://articles.latimes.com/keyword/voi-shan-company
1994 earthquake damage and subsequent closure.
https://www.dtsc.ca.gov/SiteCleanup/Projects/upload/Voi-Shan_FS_dRAW.pdf
Direct calls to the phone numbers provided in the Voi Shan documentation were greeted with courtesy and respect despite the unusual nature of my questions. The initial contact phone numbers, of course, lead to people in a sales role. They promptly directed me to a technical support engineer.
Despite several changes of ownership (Voi Shan -> Fairchild -> Banner -> Alcoa) I was told that the markings on Voi Shan manufactured fasteners have remained the same. Voi Shan simply became the Voi Shan Division of the new owning entity. I was asked not to publish contact names because this type of information needs to be cleared by the legal department in order to constitute an official release of information. I will abide by that. So while I believe this information is accurate, it is not official.
Monday, January 25, 2016
Lipstick on a Pig
As time goes on it is apparent that something is very wrong with the search for MH370. This should come as a surprise to no one with any problem solving skills. The entire search was based on a flawed premise. Despite an abundance of advanced technical degrees in the mix, basic errors were made in the assumptions "guiding" the search. I put guiding in quotes because the term is used in the popular press and blogs, but it was anything but guidance. We are reminded once again that problem solving skills are not taught in school.
Duncan's prefatory remarks below.

I will say up front that I am not a fan of Duncan Steel. Quite the opposite. However, his concern relative to a "conceptual error" misses the mark. I have provided a steady stream of criticism to the IG relative to the constrained AP flight dynamic assumption. While the IG is loathe to make any assumption relative to motive or causality, they seem quite ready to accept the constrained AP flight dynamic as a fact. Very strange.
I have a very high regard for the IG relative to their analytical skills. The latest retreat they have made, again very well executed, is not going to get it done. They are basically tweaking old ideas. They continue to use the same tired assumptions, and tweak them to the North. The error is a not a tweak away from being correctable. The entire IG conceptual framework is fundamentally flawed. The ISAT data is not a predictive tool. It is a qualifying tool. It can be use to eliminate the Maldives and Bay of Bengal. It cannot be use to predict where the aircraft terminated on the 7th arc.
Duncan's prefatory remarks below.

I will say up front that I am not a fan of Duncan Steel. Quite the opposite. However, his concern relative to a "conceptual error" misses the mark. I have provided a steady stream of criticism to the IG relative to the constrained AP flight dynamic assumption. While the IG is loathe to make any assumption relative to motive or causality, they seem quite ready to accept the constrained AP flight dynamic as a fact. Very strange.
I have a very high regard for the IG relative to their analytical skills. The latest retreat they have made, again very well executed, is not going to get it done. They are basically tweaking old ideas. They continue to use the same tired assumptions, and tweak them to the North. The error is a not a tweak away from being correctable. The entire IG conceptual framework is fundamentally flawed. The ISAT data is not a predictive tool. It is a qualifying tool. It can be use to eliminate the Maldives and Bay of Bengal. It cannot be use to predict where the aircraft terminated on the 7th arc.
Tuesday, January 5, 2016
Things We Do Not Know We Don't Know
"There are things we do not know we don't know. So when we do the best we can and we pull all this information together, and we then say well that's basically what we see as the situation, that is really only the known knowns and the known unknowns."
- Donald Rumsfeld
I am not now, nor have I ever been, a fan of Rumsfeld. However, even a blind squirrel finds an acorn once in awhile (my standard admonition to my direct reports on those occasions when they actually did something useful). So it goes, I believe, with the Rumsfeld observation above. Subsequent commentators, while agreeing with Rumsfeld, have described the language used as "tortured". I certainly agree with that as well.
Problem solving often resembles a random walk. As new information becomes available and old information is reviewed from a different perspective, we gradually home in on the truth. An appropriate metaphor is driving down the road to Solutionville while bouncing off the guard rails. As Jeff Wise implied recently, and I feel it also, we (independent investigators) are converging on the realization that we were perhaps more confident about our conclusions relative to an MH370 terminus than the information we had at hand warranted.
Consider a trivial example - flying from the 19:40 arc crossing to the Cocos. Of course, the location of the 19:40 arc crossing is subject to debate, and I have it further North than most everyone else (red line in Google Earth graphic below)

The spreadsheet describing two different ISAT solutions is presented below. As is my custom, the upper part is the calculation of a priori Doppler residuals - those elements such as satellite to Perth Doppler and BFO bias that do not change with flight path. Below that are shown two solutions for aircraft related Doppler. The middle part is for a constant heading, but variable speed solution (speed is selected to minimize Doppler residual at the arc crossings). The lower part is for constant heading and constant speed (the constant speed was once again selected to minimize residuals using a least squares metric).

The speed varying solution approaches perfection with respect to BFO residuals. The constant speed solution has residuals well below my own estimated bound of +/- 5Hz and the Inmarsat suggested bound of +/- 7Hz. In both cases the BTO errors are within the ATSB calculated two sigma limit.
The point here is NOT to suggest that the plane flew in a straight line (or any other path) to the Cocos, but it could have if one relaxes the ISAT data constraints or abandons the notion of fixed speed and heading or both. The purpose of this exercise is to raise the following questions:
1> Are we over-constraining our ISAT calculations?
2> What are reasonable bounds on residual BFO errors?
3> What are reasonable bounds on residual BTO errors?
4> Does a straight line and constant speed path deserve greater respect than a curved path with varying speeds?
I don't have any answers, but the questions seem legitimate to me in the context of trying to probe the unknown unknowns. It would be useful (to me, at least) if we had some degree of convergence on the answers to these questions.
Was the PIC heading to the Cocos before having a change of heart and diverting Eastward? Stay tuned for another ramble using a flight path to waypoint ketiv (a sort of crossroads in that region) before heading directly to CI (another waypoint). This latter exercise to address Jeff's "pesterings" on waypoint navigation.
Ah, nope. Could not make ketiv work. Also could not make a path from the Cocos back toward CI work out to my satisfaction, and I have a pretty low bar relative to most other ISAT data twiddlers.
- Donald Rumsfeld
I am not now, nor have I ever been, a fan of Rumsfeld. However, even a blind squirrel finds an acorn once in awhile (my standard admonition to my direct reports on those occasions when they actually did something useful). So it goes, I believe, with the Rumsfeld observation above. Subsequent commentators, while agreeing with Rumsfeld, have described the language used as "tortured". I certainly agree with that as well.
Problem solving often resembles a random walk. As new information becomes available and old information is reviewed from a different perspective, we gradually home in on the truth. An appropriate metaphor is driving down the road to Solutionville while bouncing off the guard rails. As Jeff Wise implied recently, and I feel it also, we (independent investigators) are converging on the realization that we were perhaps more confident about our conclusions relative to an MH370 terminus than the information we had at hand warranted.
Consider a trivial example - flying from the 19:40 arc crossing to the Cocos. Of course, the location of the 19:40 arc crossing is subject to debate, and I have it further North than most everyone else (red line in Google Earth graphic below)

The spreadsheet describing two different ISAT solutions is presented below. As is my custom, the upper part is the calculation of a priori Doppler residuals - those elements such as satellite to Perth Doppler and BFO bias that do not change with flight path. Below that are shown two solutions for aircraft related Doppler. The middle part is for a constant heading, but variable speed solution (speed is selected to minimize Doppler residual at the arc crossings). The lower part is for constant heading and constant speed (the constant speed was once again selected to minimize residuals using a least squares metric).

The speed varying solution approaches perfection with respect to BFO residuals. The constant speed solution has residuals well below my own estimated bound of +/- 5Hz and the Inmarsat suggested bound of +/- 7Hz. In both cases the BTO errors are within the ATSB calculated two sigma limit.
The point here is NOT to suggest that the plane flew in a straight line (or any other path) to the Cocos, but it could have if one relaxes the ISAT data constraints or abandons the notion of fixed speed and heading or both. The purpose of this exercise is to raise the following questions:
1> Are we over-constraining our ISAT calculations?
2> What are reasonable bounds on residual BFO errors?
3> What are reasonable bounds on residual BTO errors?
4> Does a straight line and constant speed path deserve greater respect than a curved path with varying speeds?
I don't have any answers, but the questions seem legitimate to me in the context of trying to probe the unknown unknowns. It would be useful (to me, at least) if we had some degree of convergence on the answers to these questions.
Was the PIC heading to the Cocos before having a change of heart and diverting Eastward? Stay tuned for another ramble using a flight path to waypoint ketiv (a sort of crossroads in that region) before heading directly to CI (another waypoint). This latter exercise to address Jeff's "pesterings" on waypoint navigation.
Ah, nope. Could not make ketiv work. Also could not make a path from the Cocos back toward CI work out to my satisfaction, and I have a pretty low bar relative to most other ISAT data twiddlers.
Thursday, December 31, 2015
So What's Up with the French ?
People almost always do things for a reason, even French people. So why have the French not made public any information regarding the damage forensics of the flaperon recovered on La Reunion? There seems to be little if any discussion about this lack of disclosure. How the flaperon was damaged would seem to be important relative to whether the forensics support aerodynamic damage and in-flight separation (consistent with a high speed dive) or whether the forensics support damage and separation from impacting the water while extended (consistent with a controlled ditch).
As everyone knows, the French have opened a criminal investigation relative to the disappearance of 9M-MRO. This formality allows the French to claim that the forensic information is "sealed" as part of an ongoing investigation. OK, but why - unless the forensic information points to a scenario that involves parties that may be guilty of a criminal act even if that act was simple negligence? Withholding of information allows investigators maximum freedom to probe the periphery of this disappearance. Releasing information that does not support the status quo would alert guilty parties, and increase their sense of caution. It is difficult to postulate a reason for withholding information that supports the status quo.

My sense is that there may be evidence from the flaperon forensics that suggests something is or was going on that is inconsistent with publicly available information.
What this "something" might be is subject to speculation. Suppose the flaperon forensics support a controlled ditch. Suppose further that barnacle analysis makes the current search area even less likely than the drift modeling already suggests. If the forensics supports a controlled ditch well North of the current search area, the landscape surrounding this mystery would be altered substantially. Questions regarding that flight path would certainly be raised, and areas of inquiry would be expanded. Perhaps the French do not want this to happen, at least not yet.
As everyone knows, the French have opened a criminal investigation relative to the disappearance of 9M-MRO. This formality allows the French to claim that the forensic information is "sealed" as part of an ongoing investigation. OK, but why - unless the forensic information points to a scenario that involves parties that may be guilty of a criminal act even if that act was simple negligence? Withholding of information allows investigators maximum freedom to probe the periphery of this disappearance. Releasing information that does not support the status quo would alert guilty parties, and increase their sense of caution. It is difficult to postulate a reason for withholding information that supports the status quo.

My sense is that there may be evidence from the flaperon forensics that suggests something is or was going on that is inconsistent with publicly available information.
What this "something" might be is subject to speculation. Suppose the flaperon forensics support a controlled ditch. Suppose further that barnacle analysis makes the current search area even less likely than the drift modeling already suggests. If the forensics supports a controlled ditch well North of the current search area, the landscape surrounding this mystery would be altered substantially. Questions regarding that flight path would certainly be raised, and areas of inquiry would be expanded. Perhaps the French do not want this to happen, at least not yet.
Wednesday, December 23, 2015
Weapons of Math Destruction
The 30 November 2015 book draft, "Bayesian Methods in the Search for MH370", authored by members of the Australian DSTG (Defense Science and Technology Group) is an interesting document. Hereinafter I will refer to it as the BM. It is especially interesting to me. This short document addresses two issues in the BM that have received commentary, without clarification, by a number of independent investigators. I say without clarification since I am not aware of any published attempts to clarify them. Of course, I may have missed them, and apologies in advance if I did miss them.
The first issue has to do with measured BFO errors. There has been quite a lot of discussion relative to the accuracy that might be expected from the BFO data contained in the Inmarsat logs for the last flight of MH370. These discussions have been primarily between myself and Mike Exner of the Independent Group, IG. Until now there has been no way to quantify these errors directly since no data was available. The BM changes that, and Figure 5.4 from the BM is reproduced (without permission) below.

The BM comments on Figure 5.4 as follows:

The BM offers no additional data to support the claim of "geographic dependency" such as repeated flights exhibiting a pattern correlated with the data in Figure 5.4.
When I first read the BM, the data in Figure 5.4 did not really surprise me at all, and had questions not been raised by others, I would have probably not have given it further consideration. Without supporting data I mentally discarded the "geographic dependency" explanation, and applied my own explanation which is simply drift in the AES -> 3F1 -> Perth oscillator chain. I have long estimated this drift to be on the order of +/- 5Hz over the duration of the MH370 flight. Cut and paste below from a much earlier post in this blog, "BFO Errors (again)".

The errors shown in Figure 5.4 of the BM are certainly this order of magnitude. My estimate was based on a few decades of experience with oscillators of the type used in the Inmarsat chain. It was not based on a knowledge of specific part numbers and manufacturer's specifications of the oscillators used in the hardware associated with the MH370 BFO data. There is not much doubt in my mind relative to the source of the errors in Figure 5.4, but I stand ready to retreat from my explanation should the DSTG present data supporting their "geographic dependency" claims.
As a parting comment relative to this first issue it important to realize that BFO errors on the order of 1 Hz produce position errors along a range ring on the order of a degree of latitude per Hz (some 60 nautical miles of error).
The second issue has to do with the "anomalous" paths show in Figure 9.2 of the BM, and reproduced below.

The commentary offered in the BM relative to these anomalous paths is pasted below.

Basically if one draws a radial from the sub-satellite point to the aircraft flight path, the BFO data becomes ambiguous relative to a continuation along the flight path and a continuation at an angle equal to and on the "other side" of the radial to the sub-satellite point. While this statement is not quite true for satellite positions far from the extreme ends of the satellite "dither" (where the Doppler associated with satellite movement is significant), it is exactly true for times such as 19:40 data point in the MH370 log when the satellite was virtually standing still at the extreme end of its wobble. As some readers might recall, I pointed this phenomenon out on the Wise blog some time ago. It was met with the howls of protest normally associated with my blogs there. No matter. It is what it is (or is not).
Note: 12 February 2016
The text above was "struck" because it is incorrect. The bifurcations in the path for BTO are, as stated, about a radial to the sub-satellite point. The bifurcations in the paths for the BFO values are not about a radial to the sub-satellite point. They are about a N-S line, a meridian. My apologies to anyone who was misled or wasted time due to this error on my part.
The explanation from the BM above could have been worded better, but suffice to say that the three examples of flight path deviation are simply illustrative samples from a continuous "fan" of possible paths - "the true underlying pdf has support all the way around the arc. Without dynamic constraints the location of the peak of the pdf is simply a function of the measurement noise". What the quoted snippet in italics means is that without the assumption that the aircraft is flying in a straight line ("dynamic constraints"), the plane could be just about anywhere on the last arc while satisfying BTO and BFO.
Summary
The Inmarsat system was not designed to be a navigation system. It was designed to be a communication system. While I acknowledge the huge amount of effort put forth by various parties (including myself), that effort does not change the physics of the system. The simple truth is that this huge effort is akin to turning a sow's ear into a silk purse. It is certainly a very worthwhile effort, but it would be a mistake to think that the Inmarsat data can, in and of itself, be used to accurately estimate the terminus of MH370.
The DSTG BM adds little new to boost confidence in a terminal location. It is very "IGish" - assume a flight dynamic, find a path for your assumed dynamic that satisfies the ISAT data, and then conclude you have high confidence in the terminal location.

Duncan Steel
The first issue has to do with measured BFO errors. There has been quite a lot of discussion relative to the accuracy that might be expected from the BFO data contained in the Inmarsat logs for the last flight of MH370. These discussions have been primarily between myself and Mike Exner of the Independent Group, IG. Until now there has been no way to quantify these errors directly since no data was available. The BM changes that, and Figure 5.4 from the BM is reproduced (without permission) below.

The BM comments on Figure 5.4 as follows:

The BM offers no additional data to support the claim of "geographic dependency" such as repeated flights exhibiting a pattern correlated with the data in Figure 5.4.
When I first read the BM, the data in Figure 5.4 did not really surprise me at all, and had questions not been raised by others, I would have probably not have given it further consideration. Without supporting data I mentally discarded the "geographic dependency" explanation, and applied my own explanation which is simply drift in the AES -> 3F1 -> Perth oscillator chain. I have long estimated this drift to be on the order of +/- 5Hz over the duration of the MH370 flight. Cut and paste below from a much earlier post in this blog, "BFO Errors (again)".

The errors shown in Figure 5.4 of the BM are certainly this order of magnitude. My estimate was based on a few decades of experience with oscillators of the type used in the Inmarsat chain. It was not based on a knowledge of specific part numbers and manufacturer's specifications of the oscillators used in the hardware associated with the MH370 BFO data. There is not much doubt in my mind relative to the source of the errors in Figure 5.4, but I stand ready to retreat from my explanation should the DSTG present data supporting their "geographic dependency" claims.
As a parting comment relative to this first issue it important to realize that BFO errors on the order of 1 Hz produce position errors along a range ring on the order of a degree of latitude per Hz (some 60 nautical miles of error).
The second issue has to do with the "anomalous" paths show in Figure 9.2 of the BM, and reproduced below.

The commentary offered in the BM relative to these anomalous paths is pasted below.

Note: 12 February 2016
The text above was "struck" because it is incorrect. The bifurcations in the path for BTO are, as stated, about a radial to the sub-satellite point. The bifurcations in the paths for the BFO values are not about a radial to the sub-satellite point. They are about a N-S line, a meridian. My apologies to anyone who was misled or wasted time due to this error on my part.
The explanation from the BM above could have been worded better, but suffice to say that the three examples of flight path deviation are simply illustrative samples from a continuous "fan" of possible paths - "the true underlying pdf has support all the way around the arc. Without dynamic constraints the location of the peak of the pdf is simply a function of the measurement noise". What the quoted snippet in italics means is that without the assumption that the aircraft is flying in a straight line ("dynamic constraints"), the plane could be just about anywhere on the last arc while satisfying BTO and BFO.
Summary
The Inmarsat system was not designed to be a navigation system. It was designed to be a communication system. While I acknowledge the huge amount of effort put forth by various parties (including myself), that effort does not change the physics of the system. The simple truth is that this huge effort is akin to turning a sow's ear into a silk purse. It is certainly a very worthwhile effort, but it would be a mistake to think that the Inmarsat data can, in and of itself, be used to accurately estimate the terminus of MH370.
The DSTG BM adds little new to boost confidence in a terminal location. It is very "IGish" - assume a flight dynamic, find a path for your assumed dynamic that satisfies the ISAT data, and then conclude you have high confidence in the terminal location.

Duncan Steel
Saturday, December 19, 2015
Sherlock Holmes
'Eliminate all other factors, and the one which remains must be the truth.'
Sherlock Holmes Quote
-The Sign of Four
When one considers what may have happened relative to the disappearance of MH370 there are four broad categories of possibilities.
1> Suicide by someone on board - a not so broad category.
2> Downing by a sovereign state - intentionally or unintentionally.
3> Technical issue - fire, mechanical failure, explosion, decompression,...
4> Highjacking which may or may not involve a spoof or remote control.
5> Alien abduction, black hole, alternative dimensions, or the like.
I can't think of any other scenario or know of any scenario proposed on the WEB that does not fit into one of the above categories. I will eliminate 5> by fiat. Consider the others one by one.
Suicide
Neither the pilot nor the copilot have been assessed to have had suicidal symptoms. Numerous people in the mental health profession have weighed in on this possibility, and I have not read one opinion that would indicate suicide by either pilot. Background checks have not revealed that there was anyone else on board who could fly the aircraft. Suicide appears contra-indicated.
Downing by sovereign state
Possible, but a coverup of the magnitude required would be an incredible undertaking. Also, there is strong evidence to support that the aircraft flew until fuel exhaustion. Fuel exhaustion and intentional or unintentional downing are not compatible.
Technical issue
All of the explanations I have read in this regard are implausibly complex. While a technical issue cannot be ruled out, it would require a sequence of events that is three sigma or more improbable. Technical issues historically account for 20% of aircraft crashes. That probability is lowered in this case by the additional failure of all communication systems, and then lowered even further by the fact that the plane continued to fly until fuel exhaustion. Also, the flight path simply does not support this notion. Rather it supports an aircraft under the deliberate control of conscious pilot. A technical issue is a non-starter IMO.
Hijacking
The only explanation that has any credulity. What could be the motive for hijacking? The only ones I can think of are listed below.
1> To obtain something or someone on the aircraft.
2> To obtain the aircraft itself.
3> To architect a 911 type event.
4> To use as a "bargaining tool".
An aircraft has never been hijacked to obtain something or someone on board the aircraft in the history of aviation. MH370 could be a first, but it is far easier to obtain that someone or that something before it was placed on the aircraft or after the aircraft landed.
The aircraft itself is not the least bit unique. The same or comparable aircraft can be obtained from a number of online brokers. Orchestrating a hijacking for the purpose of obtaining the aircraft is perhaps the most complex way to do it. Not to mention the murder of more than 200 people in the process. It just does not hold together.
A 911 event requires a target. There were no plausible targets within the fuel range of the aircraft. A heading to Perth would require a speed that is incompatible with ever reaching Perth and simultaneously satisfying BFO and BTO. A heading to Perth at a BFO and BTO compatible speed would terminate well short of Perth. The 7th ping ring arc is a very long way from Perth.
That leaves the "bargaining tool" scenario. The only candidates I can think of are Chinese terrorists negotiating with the Chinese government or captain Shah negotiating with the Malay government. Take your pick. An argument can be made for either candidate. Personally, I lean toward Shah on the basis of background checks which are said to rule out the PAX. If this scenario is true, it is plausible that the aircraft was flown along the Southern coast of Sumatra and Java where there are several airfields that could accommodate a 777. Certainly a flight path to the ATSB search area in the SIO is not a path anyone would select for this scenario. It is also true that all the drift models associated with the flaperon finding greatly favor the area below Sumatra as a terminus.
I have a very difficult time understanding how the ATSB and their collaborators can possibly assess the primary search area identified in any incarnation of their analytics as an area of high confidence. It is simply not sensible.
I have a very difficult time understanding how the ATSB and their collaborators can possibly assess the primary search area identified in any incarnation of their analytics as an area of high confidence. It is simply not sensible.
Sunday, December 13, 2015
/// Clusterfuck ///
From the Wiktionary:
Noun[edit]
clusterfuck (plural clusterfucks)
- (slang, vulgar) A chaotic situation where everything seems to go wrong. It is often caused by incompetence, communication failure, or a complex environment.
Google defintion:

..and so it goes with the search for MH370.
History has taught us, or as Duncan Steel might say - should have taught us, that any product resulting from a group effort is subject to far more flaws than the output from a single well-qualified contributor or a small group of such contributors. This fact is especially true in an age where rapid electronic communication produces a segregation of ideas (lots of papers on this subject) and a polarization of thought (lots more papers) far more rapidly than a weekly or monthly face to face meeting. The current US political situation is a good metaphor. According to Pew Research, America has never been more polarized except perhaps (data not available) in the period preceding the US Civil War.
Among my favorite books is a relatively obscure effort by Dr. Frederick Brooks (Harvard PhD), "The Mythical Man-Month: Essays on Software Engineering". Basically Brooks chronicles his experiences and failures as manager of a large software project (Operating System for the IBM360) while employed at IBM. One of my favorite quotes from the book describes the evolution of a complex software system (and is applicable to any system or undertaking, IMO):

Does the above sound applicable to the current state of affairs in the quest for the terminus of MH370 - "Worn out as a base for progress."? The recent book draft, "Bayesian Methods in the Search for MH370", represents the high water mark in the evolution of the ATSB official search strategy. BTW, the authors claim that Springer-Verlag, which no longer exists (now simply Springer), will be the publisher. Springer has gone far down hill from their once respectable publisher position, and has been forced to retract a number of recent offerings due to flawed peer review and faked source material. Not trying to imply the DSTG effort is anything but sincere, it is simply based on the same tired assumptions that have not yielded any positive results, and are contradicted by lack of debris (surface or subsurface), drift models, and plausible causality.
Let's look at the starting definition above a little more closely to see how the terms fit.
Incompetence
Certainly a lot of that to go around. The principal contributors being the journalists supplying the conduit for disseminating information to the public. It is difficult to find an article in a mainstream channel that is not burdened by errors, misrepresentations, and attention grabbing tabloid style headlines. It is truly a pathetic reflection on the state of the journalistic profession today.
Communication Failure
The whole MH370 undertaking has been severely hampered by the refusal of virtually every party involved to release pertinent source information - be it radar data, flaperon forensics, cargo manifests, unredacted Inmarsat data,... The list goes on and on. I don't think anyone would dispute this point.
Complex Environment
No doubt. There is little to guide us, and it is a big ocean. The interpretation of the meager data we do have is subject to a lot of guess work and assumptions in order to derive a terminus. I could write a very long treatise on this aspect alone.
So, we have all the ingredients for a monumental clusterfuck. Is it any wonder we have reached the point where progress has halted (for some time now), and a restart (or serious consideration of alternatives) is both necessary and warranted as Brooks concludes above? What have we learned, and what could we have done better? My own opinion is that the search effort was "corrupted" by unfortunate timing. Had the flaperon been found before substantial expense was incurred searching what is now called the high priority area, events may well have evolved very differently. Sunk cost, both real and intellectual, is notoriously difficult to abandon. People will fabricate all sorts of reasons to continue down a path they have invested in long after it has become obvious that things are not working out according to plan.
No matter. Changes will not be made. The search will continue "in good faith" until people tire of tossing money into the ocean, and the whole affair quietly loses public interest. My own belief is that the aircraft will never be found. Blogs and tweets will go on in perpetuity, of course.


Sunday, December 6, 2015
Controlled Ditch ??
The Australian Defense Science and Technology (DST) Group claims (see AE-2014-054) the evidence from the Inmarsat data "is inconsistent with the plane making a controlled ditch". They offer no compelling explanation for that claim other than the assertion that engine power is needed to execute such a maneuver, and the evidence strongly indicates a dual flame out. Wow. How did Scully manage the "miracle on the Hudson" with both engines inoperable due to bird impacts? Does the DST not read newspapers or do they know something we don't know?
My guess is the latter. What would it take to make such an outrageous claim that flies in the face of a very recent and well-publicized event? The only answer I can come up with is that the French have provided flaperon forensic data to the Aussies, and have not shared it with the rest of the world. If the French have concluded that the flaperon damage is consistent with aerodynamic flutter, as originally suggested by Mike Exner, then the DST assertion makes perfect sense. The damage forensics would be THE key piece of information needed to rule out (or support) a controlled ditch.
Also the implicit DST rejection of a long terminal glide associated with an assumption of pilot control inputs is consistent with a flutter damage scenario.
Edit 12/14/2015:
On second thought, it really is conceivable that the DSTG pulled their conclusion out of some place other than their brains. Nothing would surprise me anymore relative to the MH370 "science".
My guess is the latter. What would it take to make such an outrageous claim that flies in the face of a very recent and well-publicized event? The only answer I can come up with is that the French have provided flaperon forensic data to the Aussies, and have not shared it with the rest of the world. If the French have concluded that the flaperon damage is consistent with aerodynamic flutter, as originally suggested by Mike Exner, then the DST assertion makes perfect sense. The damage forensics would be THE key piece of information needed to rule out (or support) a controlled ditch.
Also the implicit DST rejection of a long terminal glide associated with an assumption of pilot control inputs is consistent with a flutter damage scenario.
Edit 12/14/2015:
On second thought, it really is conceivable that the DSTG pulled their conclusion out of some place other than their brains. Nothing would surprise me anymore relative to the MH370 "science".
Saturday, September 26, 2015
Christmas Island Revisited
A great deal has been written about the terminus of MH370 by "experts" of all persuasions, some very good and some not so good. The prevailing theory among the cognoscenti is that the plane travelled pretty much directly South into the Southern Indian Ocean, SIO. Problems with this scenario arose almost immediately. There is no plausible motive or causation hypothesis, and no debris from the aircraft has been found there. That did not deter the expenditure of tens of millions of dollars searching the ocean floor in that region. As we all know, nothing has been found. What most people do not realize is that the SIO hypothesis is flawed - the major flaw is the assumption relative to the fixed AP flight dynamics after the turn South. This turn is often referred to as the final major turn, FMT.
This fixed AP flight dynamic assumption has taken on a life of it's own. Too much has been invested to retreat from it. A few people, Dr. Victor Iannello and Jeff Wise among them, have proposed viable alternatives. However, they have not been seriously regarded by the people advising or conducting the search operation. The reality is the plane could be virtually anywhere on the last range ring. A competent analyst can create a set of flight dynamics to support a location North or South of the equator. While these flight paths might seem contrived, they are certainly not far removed conceptually from the flight dynamics used by the ATSB and "consensus" IG. The observables suggest that MH370 was actively piloted prior to the FMT. To assume that everything was "hands off" after the FMT is logically unsustainable (for me).
I have taken a somewhat more holistic approach to the problem. An approach that invokes the notions of motive, lack of radar sightings, and lack of debris. When one considers the totality of information, some of it nuanced, it becomes clear that the SIO terminus is tenuous at best. Neither pilot displayed any suicidal tendencies. Suicide is usually not the result of a spontaneous decision. It evolves over a long time period (i.e. the German Wings case), and warning signs are almost always evident. It is more likely that Captain Shah simply wanted to make a political statement or negotiate a political concession from the Malaysian government. Shah had several landing locations available with a more Northern flight path depending on the status of "negotiations" going on in Malaysia between the government and his co-conspirators - Banda Aceh, Cocos, Christmas Island, Bandung,... Certainly flying into the SIO toward the current search area provided no opportunity to land the aircraft. Flying along the Southern coast of Sumatra/Java offers a diverse set of landing opportunities.
With that as background, I have constructed a revised flight path below which satisfies all the BTO and BFO data after and including the 19:40 handshake. The revisions from earlier postings are based on:
- Carefully derived BTO range rings using a WGS84 ellipsoid and correct sub-satellite centers. My original rings were made in haste using a spherical earth and centered at the nominal sub-satellite location over the equator.
- More care relative to speed and heading selection to better match the BTO and BFO data without the need to include arbitrary altitude variations.
- The conclusion that the PIC intended to land from North to South instead of South to North. This change was the result of considering surface winds from the Southwest at that time.
- The conclusion that the PIC did a flyby South of the Island to verify a clear runway before turning North for the final approach.
- It has been pointed out to me by a very sincere source that it is also possible that the PIC turned North to land at Bandung, and the intention was not to land on Christmas Island.
The Inmarsat BTO and BFO data were used in accordance with the vector diagram below.
The revised flight path is shown below along with the supporting data in spreadsheet form. The spreadsheet continues to be shown in two parts. The upper part calculates Doppler residuals based on the known observables. These residuals would be the same for any flight path. The lower part of the spreadsheet shows the aircraft location, speed, and heading used to match the residuals. The area inside the white circle will be the subject of additional discussion below.
Note that no altitude variations were used to reconcile the BFO data with the aircraft position, speed, and heading.
Note that no altitude variations were used to reconcile the BFO data with the aircraft position, speed, and heading.
Edit 2/23/2016 to table below:
A 23:15 data point was added at the request of Oleksandr. No other changes were made.

In the table data above D2 refers to the aircraft and satellite Doppler, and D1 refers to the Doppler compensation produced by the AES. The heading lag is associated with the turn North and the Doppler change associated with this lag is quantified in an earlier post in this blog. A three degree per second turn was assumed with an inertial update interval of 0.25 seconds. Two values are shown for the 00:10 Doppler - one with no ROC or heading lag, and one with an ROC of +2 meters/sec OR a heading lag of 0.7 degrees (either accounts for the additional 7Hz of Doppler).
The aircraft speed at 19:40 was based on a calculation made in another post in this blog "Mid-flight Speed - MH370" below.
The aircraft speed at 19:40 was based on a calculation made in another post in this blog "Mid-flight Speed - MH370" below.
The conclusion is that the aircraft ran out of fuel during or shortly after the turn North, and went into the ocean almost due East of Christmas Island. Please take a look at "Coincidences - Are You a Believer ??" elsewhere in this blog.
The graphic below shows an enlarged version of the white circle area in the first graphic above.
The area inside the circle (with the exception of the 19:40 location) represents residual confusion. The radar data presented by the Malaysian government showed a last contact at a range of 200nm on a 295 degree radial. This contact was time tagged at 18:22 UTC. This location and time are not compatible with reaching the 18:25 UTC range ring location. The aircraft could not fly that fast. Other analysts have concluded that the radar data presentation was made in haste, and that the labeling was incorrect. They have used overlays to infer a last radar contact range of 250nm on a 285 degree radial toward Mekar. An "official" correction to the radar data has never been made. It is also true that the GM400 radar at Butterworth has a manufacturer specified detection range of slightly more than 200nm, and that the radar data showed by the Malaysians did not come from a GM400 display. Until revised and officially certified data is available, I won't speculate on the flight path prior to 19:40.
A final comment is that the flight path associated with my analytics lies too far West to have been the sighting described by Kate Tee. Kate could have seen the plane, but at a distance of some 70nm.
Of course, the usual disclaimers apply. While I believe the calculations above are correct, history has shown that making errors is virtually inevitable.
Update 20 November 2016
The flaperon found on Reunion Island has been confirmed by the French to have come from 9M-MRO (MH370). This finding and confirmation allows drift models to be created in an attempt to narrow down the likely terminus of the aircraft on the last ping ring. The most credible such model has been created by Geomar, a Research Institute in Germany.
Dr. Jonathan Durgadoo and Prof. Dr. Arne Biastoch from GEOMAR Helmholtz Centre for Ocean Research Kiel used a state-of-the-art ocean model in combination with observational data. This provides a coherent realistic dataset for their drift analyses to determine the possible origin of the flaperon. To do so, they release virtual particles around La Réunion and compute their trajectories back in time. "Of course it does not make much sense just to track only a few particles within the model," Dr. Durgadoo explains. "We have traced back almost two million 'virtual' particles over a period of 16 months," Durgadoo continues. "For each month back, we subsequently calculated the probable region of the particles positions."
There is still no word from the French relative to the flaperon damage forensics or the pathology of the barnacles.
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