Further Statement from an Independent MH370 Investigation Team

Further Statement from an Independent MH370 Investigation Team

We have refined our analysis models over a period of time and have found no meaningful error in the assumptions or computational approaches that we have taken. We remain concerned that some information of importance may have been withheld for reasons that have not been made public. This has limited the scope of our analysis to exploration of a number of flight dynamics models and technical scenarios that appear to be simple and plausible. Recently we have attempted to confirm the selection of the current search area without presuming a specific set of events other than being consistent with the disclosed satellite data, radar data, and the aircraft technical performance characteristics.

We reiterate that our original proposed search area centred on 36.0S 88.5E has a higher probability of a successful search result than the presently envisaged official search area.

Endpoints near the final arc starting from about 39.7S 84.4E and moving along the ping arc to about 27.5S 99.9E can be computed using the same data set as we have used, depending on  hypothesized flight path scenarios (e.g., very low effective ground speed, or manoeuvring) during the interval between the satellite data obtained at 18:40 UTC and 19:41 UTC. However, unless further information becomes available, we consider such scenarios to be too speculative to pursue as a group.

Brian Anderson, BE: Havelock North, New Zealand
Sid Bennett, MEE: Chicago, Illinois, USA
Curon Davies, MA: Swansea, UK
Michael Exner, MEE: Colorado, USA
Tim Farrar, PhD: Menlo Park, California, USA
Richard Godfrey, BSc: Frankfurt, Germany
Bill Holland, BSEE: Cary, North Carolina, USA
Geoff Hyman, MSc: London, UK
Victor Iannello, ScD: Roanoke, Virginia, USA
Barry Martin, CPL (EASA-FCL Commercial Pilot Licence): London, UK
Duncan Steel, PhD: Wellington, New Zealand
Don Thompson: Belfast, Northern Ireland
Jeffrey James Wise, BS: New York, NY, USA


Previous statements from this team can be found here and here; these contain background material plus a variety of questions, many of which are yet to be answered.

This is not necessarily the final word on MH370 on this website, but any re-opening of discussions here will await the availability of significant new information.

In amongst the 6,000 comments and replies following the major posts concerning MH370 on this website are many invaluable suggestions and analyses from other able and generous people who have contributed in various ways. Anyone just tuning in: I suggest you look through those, because past experience has shown that the answers to many queries have already been answered therein.

My thanks to all for their interest and kind words – Duncan.


Radar Coverage of the Unknown Parts of the Flight of MH370

Radar Coverage of the Unknown Parts of the Flight of MH370

Duncan Steel, 2014 August 20.

There being a need for a fresh post here from me so as to start a new set of comments and responses from others, the length of the comment section under the previous post now being unwieldy, I turned my mind to what to put into that/this post. The obvious thing to focus on is that part of the flight of MH370 which is most unknown, and controls evaluations of where the aircraft ended up: I refer to its path northwest over the Malacca Strait and then its apparent turn to the south, this being at an indeterminate time after the final publicly-known radar detection at 18:22 UTC. There also being open questions with regard to the radar-tracked path prior to that time, I have now accomplished what I have been intending to do for the past three months: insert into an STK 3D scenario various military and other radars, and examine their potential coverages in the area in question. (I know it was three months ago that I started on this because when I searched for my ‘MH370_radar’ scenario I found that I had last saved it around May 20th; apologies for the delay.)

A set of radar sites was kindly supplied to me by Don Thompson, and others have also been helpful in this regard. Don’s list appears in the table below, and I added hypothetical radars located on Christmas Island and at the Cocos Islands airfield because many times the potential detection of MH370 from those sites as it flew southwards has been suggested.


As always, if any reader finds an error, please let me know. In the case of the final two locations I simply estimated likely coordinates and elevations for the radars.

In none of these cases have I made any attempt to identify and duplicate the functions of any specific radar installation: the only thing I am considering here is the locations of the radars, and their potential coverages as limited by their elevations/heights above the WGS84 ellipsoid at that latitude, and also putative altitudes for the aircraft (limited to four values here: 5,000, 10,000, 20,000 and 35,000 feet). In essence I am thinking about some generic radar (or other sensor) at each location, and asking: how far away might the aircraft be, and yet still be above the horizon so that a line-of-sight is viable?

Note also that I have not (yet) tried entering any topography in order to investigate the limitations on coverage it imposes, although this can be done in STK: this is a level of complexity that I have not yet addressed. Therefore it is distinctly possible, even likely, that in various directions from any particular radar the capability to ‘see’ the aircraft is limited by nearby terrain. For example, I placed the Christmas Island putative radar at the airport there, whereas the hills at the western end of the island would curtail any coverage along an arc at least from due west to southwest.

All I am doing here, then, is defining the furthest distances that a radar might be able to see the aircraft based on the WGS84 shape of the Earth, and the heights above that smooth Earth shape of the radar apparatus and the aircraft. The method I followed is very simple, as below.

Given the radar site’s latitude I calculated the terrestrial radius at that point, which I term R. Let the radar elevation/altitude be h, and the aircraft altitude be H. Assuming that R is constant across the whole of the radar’s coverage, the horizon as seen from the radar is at a distance x given by:

x = sqrt[sqr(R + h) ─ sqr(R)]

Since h is much smaller than R, to a good approximation one can use:

x = sqrt(2 R h)

The straight line from the radar to the horizon can then be extended to an altitude H which is an additional distance y away, where (as above) one can calculate y from:

y = sqrt(2 R H)

The total distance (x + y) then is the maximum possible range at which the aircraft would be above the horizon. These ranges for H = 5,000, 10,000, 20,000 and 35,000 feet are given for each radar site in the table above; all those ranges are given in kilometres.

Please be clear that this does not mean that any or all of the actual radars could or would have detected the aircraft out to those distances: these are simply maximum line-of-sight ranges. The actual radars would be limited by:

(a)    Detectability considerations: the power returned by a target drops off as the fourth power of its distance, and the detectability also depends on such things as the target’s radar cross-section at the wavelength used, aspect effects, the gains of the transmitter and receiver antennas (these have the same value for a monostatic radar), the power transmitted in each pulse, the background noise from natural sources (the cosmos, mostly), local radio noise sources, and so on;

(b)   The signal processing of the returned echoes; and

(c)    The range limits and gating used: obviously if a radar system is programmed to collect echoes only from ranges out to 200 km, it will not identify objects at 250 km.

All I am attempting to do here, then, is to provide some visualisations of the best possible radar coverage that would be feasible, based solely on the locations and elevations/altitudes of these radars.

Here is the coverage of all the radar sites in accord with the above descriptions, as a view of a 3D window in STK:


For each of these coverage rings I have produced KML files, which anyone can download from here and then display in Google Earth or similar tools. There are 52 KML files in total. For each ring there is a ‘wall’ of the appropriate height (i.e. from the surface to the relevant altitude). Although in my STK scenario the rings appear discrete, as above, in Google Earth I have found that the area interior to each ring seems to fill in with the colour of the ring itself. Apologies, but I have as of yet been unable to stop that occurring!

Here is a 2D map of all the 52 coverage rings:


For clarity, and for those wanting a quick look without using the KML files, in the 2D maps that follow I show the coverage rings selected a few at a time.

Thai sites: 


Malaysian sites:


Indonesian sites:


Australian sites: 


Interim Statement from an Independent MH370 Investigation Team

Since releasing our earlier statement of 17 June 2014, the Independent MH370 Investigation Team, an informal group of individuals with diverse technical backgrounds, has continued to collect information, improve our understanding of the data, and refine our models, in order to better estimate the final location of MH370.

We continue to seek any additional information that can be released by the accident investigation team that would help us. The official accident investigation teams can be assured of our continuing desire to collaborate and to share our work.

Information was released by the ATSB in their report “MH370 Definition of Underwater Search Areas,” 26 June 2014, which has assisted our work. We concur that the BTO data provides unambiguous and accurate arcs of position. We confirm that the BFO data and analysis cannot be used to determine precise tracks or the exact end point along the 00:19 arc. For this reason, we would like to better understand the ATSB assumptions. In particular, we ask the following questions:

  • Why do the downlink Doppler values change with aircraft latitude in Appendix G, Table 6?
  • Why is there only partial compensation of the downlink Doppler provided by the EAFC function in the pilot receiver?
  • Is it true that the coordinates of pilot source and/or the pilot receiver were incorrectly configured in the pilot receiver?

Other areas in need of clarification include:

a) Analysis A (p. 25) of the ATSB report begins the path computation at the 19:41, which is approximately the point of closest approach of the aircraft to the satellite. However, a complete solution of the flight path needs to account for the path of the aircraft between the last primary radar location at 18:22 and the start of the computation at 19:41. To better understand the ATSB results, we have computed a similar path starting at 19:41 that approximately satisfies the BTO and BFO data and terminates in the “priority” search area from the report. This leads to a location at 19:41 which is only about 195 miles from the location at 18:28, indicating a direct path speed of only 160 mph. Possible explanations are the aircraft path was a circling pattern or some other more complex path or scenario. Can the ATSB please provide further clarification of the possible flight paths during this critical time interval? (Please see Figure 1.) Interim Report Figure 1a Interim Report Figure 1b

Figure 1. Computed MH370 flight path that ends in the priority search area. (i) Entire path (ii) Path over Malaysia and Sumatra, Indonesia.

b) The BFO data is used by the ATSB to help narrow down the possible search area, for example in Fig. 29 of the ATSB report. However, the BFO data at 18:40 appears to be ignored. Including the 18:40 BFO data in the analysis would seem to significantly narrow the allowable paths of the aircraft, and reduce the size of the search area. Can the ATSB please clarify what assumptions were used to determine the location and time of the aircraft’s turn towards the south, and how the BFO value at 18:40 was used in this determination? (Please see Figure 2.) Interim Report Figure 2

Figure 2. Comparison of measured BFO data and computed values for an MH370 flight path that ends in the priority search area.

c) When the ATSB applied its BTO and BFO models to two known flight paths (Figs. 30/31), there were significant errors in the predicted location at the later times in the flights. The implication is there might be similar discrepancies between the predicted and actual path of MH370. Can the ATSB please provide an explanation for the discrepancies between the predicted and actual flight paths for the examples in the report and how that relates to defining the priority search area?

d) It would be particularly helpful if Inmarsat were to release the unredacted (raw) data relating to all message exchanges, including both the missing data line items and the missing data fields. Information that appears to have been edited out of the data logs released on or about 27 May 2014 could assist in determining much more about the aircraft movements throughout the whole flight. Can the ATSB please release a complete set of these satellite data?

e) It would also be helpful to know the Performance Degradation Allowance (PDA) for each engine, and then which engine was on the left, and which was on the right. This information would enable us to propose a more accurate end-point scenario which may help to further limit the extent of the search area. Can the ATSB please provide details about the assumed engine performance?

Our group intends to continue to improve our understanding of the models and the data. We will make further public updates when warranted. The following individuals have agreed to be publicly identified with this statement, to represent the larger collective that has contributed to this work, and to make themselves available to assist with the investigation in any constructive way. Other individuals prefer to remain anonymous, but their contributions are gratefully acknowledged.

Brian Anderson, BE: Havelock North, New Zealand

Sid Bennett, MEE: Chicago, Illinois, USA

Curon  Davies, MA: Swansea, UK

Michael Exner, MEE: Colorado, USA

Tim Farrar, PhD: Menlo Park, California, USA

Richard Godfrey, BSc: Frankfurt, Germany

Bill Holland, BSEE: Cary, North Carolina, USA

Geoff Hyman, MSc: London, UK

Victor Iannello, ScD: Roanoke, Virginia, USA

Jeffrey James Wise, BS: New York, NY, USA

Duncan Steel, PhD: Wellington, New Zealand

Addendum from Duncan Steel: Please all readers be aware that there are several others also conducting invaluable analyses of the available data pertaining to MH370, and they frequently post comments here.

Note added 2014/07/19: For reasons too tedious to explain, the original post carrying text and graphics as above were put up on this website on 2014/07/15 in a sub-optimal fashion. I have now updated the format and re-posted this material here in an improved form. However, the original post is still available here: Interim Statement… and it is followed by 57 varieties of comments and replies which interested readers might wish to peruse.  


Statement from an Independent MH370 Investigation Team


Shortly after the disappearance of MH370 on March 8th, an informal group of people with diverse technical backgrounds came together on-line to discuss the event and analyze the specific technical information that had been released, with the individuals sharing reference material and their experience with aircraft and satellite systems. While there remain a number of uncertainties and some disagreements as to the interpretation of aspects of the data, our best estimates of a location of the aircraft at 00:11UT (the last ping ring) cluster in the Indian Ocean near 36.02S, 88.57E.  This location is consistent with an average groundspeed of approximately 470 kts and the wind conditions at the time.  The exact location is dependent on specific assumptions as to the flight path before 18:38UT. The range of locations, based on reasonable variations in the earlier flight path result in the cluster of results shown. We recommend that the search for MH370 be focused in this area.

MH370 Best Estimate

We welcome any additional information that can be released to us by the accident investigation team that would allow us to refine our models and our predictions. We offer to work directly with the investigation team, to share our work, to collaborate on further work, or to contribute in any way that can aid the investigation. Additional information relating to our analysis will be posted on http://duncansteel.com and http://blog.tmfassociates.com.  A report of the assumptions and approaches used to calculate the estimated location is being prepared and will be published to these web sites in the near future.

          The following individuals have agreed to be publicly identified with this statement, to represent the larger collective that has contributed to this work, and to make themselves available to assist with the investigation in any constructive way. Other members prefer to remain anonymous, but their contributions are gratefully acknowledged. We prefer that contact be made through the organizations who have published this statement.

Brian Anderson, BE: Havelock North, New Zealand;
Sid Bennett, MEE: Chicago, Illinois, USA;
Curon Davies, MA: Swansea, UK;
Michael Exner, MEE: Colorado, USA;
Tim Farrar, PhD: Menlo Park, California, USA;
Richard Godfrey, BSc: Frankfurt, Germany;
Bill Holland, BSEE: Cary, North Carolina, USA;
Geoff Hyman, MSc: London, UK;
Victor Iannello, ScD: Roanoke, Virginia, USA;
Duncan Steel, PhD: Wellington, New Zealand


An immediate response to the Inmarsat information now released

An immediate response to the Inmarsat information now released

Duncan Steel, 2014 May 27

The data now made available appear to make sense. I was emailed the PDF of 47 pages by several people, to whom thanks are due; and LGHamilton gave me that link.

One can see no conceivable reason that the information could not have been released nine or ten weeks ago. There are many, many lines of irrelevant information in those 47 pages, but it is good that all have been published.

Having written that, there is no reason (as such) to criticize what has been issued. It took me just ten minutes to find the 18 (perhaps more?) lines of relevance. And there is a nice explanation at the beginning. So, credit to Inmarsat and others for now making the information available. In reality I believe that it has been the UK Government (rather than the UK company) per the AAIB which has delayed things.

The bit I have been looking at in detail (the time delays, or Burst Timing Offsets or BTOs in this tabulation) are in agreement with what we thought previously (i.e. we had managed to decipher from the various graphs shown to families). That is from immediate back-of-the-envelope sums; I will do more detailed calculations on the numbers now available on the morrow (well, later today in that it’s now 02:00 am).

I will be working on that to produce more precise ping rings, but expect no revolution as such.

More complicated are the Burst Frequency Offsets (BFOs), which had been much argued about. Others will be looking at that in detail over the next 24 hours. More information will doubtless be posted here.

On these BFOs the confirmation from this publication of information that the aircraft SATCOM system essentially is programmed to assume that the satellite is truly geostationary (i.e. does not wander from a fixed point above the equator: no satellites are truly ‘geostationary’) MAY explain the ‘symmetry breaking’ which leads to the belief that the aircraft went south (into the Indian Ocean) rather than north. But that awaits confirmation from the people looking into the BFOs.

Now that the basic information is available it should be possible to check on Inmarsat’s analysis and ensure that no mistakes were made. With this information the calculations are quite straightforward; but I hasten to add that this only narrows down the search region, NOT identifies precisely where the aircraft ended up.

I find 18 lines of potential interest, and some of those are either rejectable or else almost redundant in that they occur at almost the same time(s).

The only relevant lines, I think, are those that say “(R-channel)” [sic] at the end of the column that is headed “SU Type”. It’s only the two numbers in the final two columns that are wanted (the BFO and BTO values).

The relevant times are:
18:27:08.404  (Have I missed others near here?)
Approximately 18:40 – Attempted handshakes here indicate why and how the hourly handshake series was initiated.
00:19:29.416 (reject: BTO clearly incorrect, as anticipated)
00:19:37.443 (reject: BTO clearly incorrect, as anticipated)

Please check and verify. Any more to be added that I missed?


Updated KML Files for Ping Rings

Updated KML Files for Ping Rings

Duncan Steel, 2014 May 26.

Almost a lifetime ago (well, on April 29th) I promised in a previous post to make KML files available for the ping rings as derived from the fuzzy graph made public shortly before. Please refer to that post for the graph, and my original values for the radii of the rings.

Since then Brian Anderson has provided slightly-revised values for the first four ping ring elevation angles and therefore back-calculated radii. Adopting those four values I now present a revised table of the elevation angles and ping ring radii for ten of the twelve pings/handshakes involved:

Time UTC Elevation angle from aircraft to satellite (degrees) Radius of range ring on Earth’s surface (kilometres) Radius of range ring on Earth’s surface (nautical miles) KML
16:30:00 46.90 4138 2234 PR_16_30_BA
16:42:43 46.98 4130 2230 PR_16_42_43_BA
16:54:55 46.33 4193 2264 PR_16_54_55_BA
17:07:15 45.33

Update: should be 45.43


should be 4282


should be 2312


This KML file renders a ring that is 10 km/6 nm too large

18:25:26 None
18:26:53 None
18:27:47 52.2 3615 1952 PR_18_27_47
19:40:30 54.8 3361 1815 PR_19_40_30
20:40:26 54.1 3430 1852 PR_20_40_26
21:40:xx 51.6 3674 1984 PR_21_40_XX
22:40:19 47.3 4097 2212 PR_22_40_19
00:10:48 40.1 4813 2599 PR_00_10_48


The KML files listed in the final column of the above table are available in Dropbox here.

If you download those KML files and then drag them into your favoured GIS tool (e.g. Google Earth) then you will be able to visualise the positions of the revised ping rings; and several people are using these to estimate possible aircraft tracks.

Although these rings are drawn at ground level, in fact I computed them for aircraft altitudes of 35,000 feet above the WGS84 ellipsoid. Regardless of the fact that such ping rings are not truly circles on the ellipsoidal Earth model, I have drawn the KML files with constant radii (i.e. as circles). It might well be this, for example, that leads to the ring PR_16_30_BA passing slightly to the west of Kuala Lumpur International Airport when viewed in Google Earth. (Note that despite the name of that file, apparently MH370 left its gate at KLIA slightly before 16:28 UTC on 2014/03/07.)

Each of the circles is centred on the appropriate point (i.e. the sub-satellite point at the time of each ping/handshake). This means, of course, that their centres are different.

By now all should be familiar with the fact that the precise times for each have been altered slightly in the light of better knowledge since my post initially giving the ping rings. The times I have given above correspond to the times, so far as I know them, of each of the twelve events in the BFO graph.

I have been trying earnestly to get the times correct to the second for all events, but am a bit befuddled and in my haste to get this post up before retiring to the gym I may have made errors; and I can`t find the seconds for the 21:40:xx ping ring. Sorry!

For reference, here are two views of the ping rings from STK 2D and 3D windows.




Passages of the International Space Station over MH370: Update 2

Passages of the International Space Station over MH370: Update 2

Duncan Steel, 2014 May 20.

An astronomer in Portugal, Luis Plantier, kindly sent me an email suggesting that suitable instrumentation on board the International Space Station (ISS) might have detected MH370 during its flight.

Luis sent me a graphic showing a pair of tracks of the ISS over the Indian Ocean and south-east Asia during the time of the flight of MH370, computed using software designed specially to indicate to satellite-watchers when specific orbiting objects might be seen (generally around dawn and dusk, when the satellite is illuminated by sunlight but the observer below is in darkness).

In order to look for all opportunities/passes by the ISS over the area of interest I loaded its orbit for 2014 March 07 into STK and computed its ground tracks (i.e. the path of its nadir over the surface of the Earth). These are shown in the 2D STK-derived map below:


 In each case (each orbit pass) the ISS is travelling at an altitude of about 415 km, moving from the south-west to the north-east and passing its ascending node as it crosses the equator. The numbers in mauve show the orbit numbers: that is, the ISS completes about 16 orbits per day, and so by now has surpassed 88,000 orbits around our planet.

Those numbers increase from right to left (east to west) because precession is causing ISS’s orbit to swivel in that direction. The orbital pass over the Indian Ocean that might be of interest here is number 87560, which ends when orbit 87561 begins with the ISS over the island of Borneo.

In the following 3D view from STK I show the times at which each orbit begins (i.e. the times of the ascending node passages by ISS in the five orbits shown above).


In this 3D graphic I again shown the ground tracks of ISS, but with tick marks added every minute, those ticks marks being 400 km wide (i.e. stretching 200 km each side of the ISS ground track).

Orbit 87560 began at 19:58:53 UTC on 2014/03/07. The time of interest here is the last 15 minutes before orbit 87561 began at 21:31:39, and in particular between about 21:17 and 21:26 UTC. During that interval the ISS was passing over the general area of the Indian Ocean where MH370 has been suggested to have ended its flight.

At that time the ocean below was in darkness (i.e. it was night time). One might, therefore, not expect imagery collection to have been in progress then from the ISS. I point out the above, however, just so that others can go follow this particular rabbit in the hope that it might not be a pointless chase. Here is one place to start:




Duncan Steel, 2014 May 21.

After I posted the above two correspondents have commented that it might be feasible for MH370 to have been detected by satellites using optical cameras. First, gerry-AT has suggested that sunrise in the east of the Indian Ocean would occur about 30-40 minutes before 00:11 UTC and so the aircraft might have been in sunlight near the end of its flight (if that were where it was). This might make it feasible for it to have been observed from a satellite (although the passes of the ISS by that time were too far west).

Second, Rodney Small has suggested that, if the aircraft actually went north, then it might have been in sunlight when the ISS had its pass over eastern Asia on the orbit after the last one I shown above. Here is a map showing the path of the ISS:


As Rodney wrote, ISS orbit 87563 started at 00:37 UTC (on 2014/03/08), and it then swept up over India, eastern Nepal, and across the middle of China.

Here is a 3D view similar to that I posted earlier, but now with the initial part (i.e. the segment of interest) of orbit 87563 added (plus lines of latitude and longitude for reference):


That view ignored the effect of day and night, simply showing an ‘ideal Earth’ with no shadowing, no clouds, and so on. However, in STK I can ask for ‘true’ day and night to be shown, and here is the result at the time that ISS crossed the equator and started orbit 87563 at 00:37:11 UTC:


If you count the tick marks you will see that the ISS was over central China about 12 minutes after crossing the equatorial plane. It is conceivable, perhaps, that MH370 might have been detectable with optical cameras from the ISS if it were within range from about 00:45 UTC, when the ISS was passing just west of the city of Ranchi, India. At 00:46 UTC it was just starting to cross the border between India and the far east of Nepal as dawn was progressing below. It then passed over Sikkim, and at 00:47 UTC it was northwest of Bhutan. Twenty seconds later the ISS was just west of Lhasa, and it then continued northeast over China.

 Further Update

I have been asked for a KML file for the International Space Station’s orbital passes as shown in the above post. I have put file ISS.kml into this location on Dropbox. From there you can download the KML file and then drag it into Google Earth or whichever display tool you might prefer to use.

The Eclipse of Inmarsat-3F1 on March 07

The Eclipse of Inmarsat-3F1 on March 07

Duncan Steel, 2014 May 14.

Attention has been drawn in various comments under my previous post to the fact that the Inmarsat-3F1 satellite would have been in eclipse during part of the flight of MH370. That is, it would have been in the shadow of the Sun as cast by the Earth.

This matter has be raised as being of possible significance through: (a) Resultant conceivable temperature changes on the satellite causing drifting of its transmitter frequencies or related variations in other electronics; (b) The satellite switching to battery power during the hour-long eclipse (because its solar cells, obviously, are no longer generating power); and/or (c) The passage into or out of eclipse prompting, for some reason, a ping/handshake with the aircraft.

Whilst I am doubtful myself with regard to any of these possibilities – geostationary satellites have daily eclipses for several weeks each side of the equinoxes, and so are equipped to deal with these as a normal part of their operations – it was quite easy for me to calculate the times of the eclipse in STK for the contemplation of others.

Inmarsat-3F1 entered eclipse between 19:21:30 and 19:22:00 UTC on 2014 March 07, and left it again between 20:23:45 and 20:24:15 UTC. I have given time brackets of 30 seconds there due to the Sun not being a point source of light, and also the refractive effects of the terrestrial atmosphere at the limb(s). That is, it makes no sense to imagine that the sunlight is suddenly (on a sub-second-timescale) obscured.

For the interest of readers I show below the situation at the onset and termination of the eclipse. The 3D model I have used for the satellite is not completely accurate (and of course appears only as a silhouette in this geometry), but it is near-enough. And the Sun does not really look like that.



Out of interest, because we have talked about it a lot, here is an artist`s impression of one of the Inmarsat-3 series satellites, courtesy Lockheed-Martin:



Bolide over the Indian Ocean on May 08

I have noted previously that at present I am working at the University of Western Ontario for a couple of months on matters connected with meteors, spacecraft and astronaut safety, and so on.

My host here, Professor Peter Brown, has pointed out to me that on May 08 (actually on May 09 local solar time) there was a bolide (a very bright meteor, or fireball) entry over the Indian Ocean, detected by US Government sensors and just announced on a NASA website. It will also have been registered, I have no reason to doubt, on the global array of infrasound detectors. The location was above 36.9 degrees south, 87.3 degrees east: near midway between Perth and Kerguelen. The energy release involved was about 2.4 kilotons of TNT equivalent, around 15 per cent of the yield of the Hiroshima nuclear weapon.

Whilst it is true that the coupling between such a bolide and Earth`s surface is relatively weak – the altitude of 35 km for the main energy release is about three times as high as jetliners fly – it is an example of how large (natural) explosions occur from time-to-time with few people being aware of them.

If you look at the webpage cited you will see that on March 29 there was another bolide/fireball of about one-twentieth that energy (0.13 kilotons) about 30 degrees further east (over Western Australia). Such events are not uncommon. I would imagine that one would have been reported in the local newspapers.


The Circumlocution Office is Alive and Well

The Circumlocution Office is Alive and Well

Duncan Steel, 2014 May 06.

I was intending to put up a post here simply so as to enable a new thread of discussion, due to the huge volume of comments and replies that have made my preceding post unwieldy. I had failed to put up a new post for while not so much for a lack of anything to say, but rather the lack of time to say and write it whilst travelling and attending to a range of other matters; my apologies for this.

So, I was going to put up a post with a title saying simply “Here’s a new post you can file comments under” but I wanted to convey the spirit of the investigation, and therefore came up with The Circumlocution Office. This wonder (and all-too-common feature) of government had its name invented many years ago by Charles Dickens, in his book Little Dorrit, although it was by no means a new phenomenon in the middle of the nineteenth century. Dickens introduces it with this paragraph:

The Circumlocution Office was (as everybody knows without being told) the most important Department under Government. No public business of any kind could possibly be done at any time without the acquiescence of the Circumlocution Office. Its finger was in the largest public pie, and in the smallest public tart. It was equally impossible to do the plainest right and to undo the plainest wrong without the express authority of the Circumlocution Office. If another Gunpowder Plot had been discovered half an hour before the lighting of the match, nobody would have been justified in saving the parliament until there had been half a score of boards, half a bushel of minutes, several sacks of official memoranda, and a family-vault full of ungrammatical correspondence, on the part of the Circumlocution Office.

In the century-and-a-half since Dickens introduced the world to its existence, in a formal sense, The Circumlocution Office has grow’d like Topsy so as to have sub-branches and sub-sub-branches in every department of every level of government.

On Monday I sent the following email message to the Joint Agency Coordination Centre (JACCmedia@infrastructure.gov.au) in Canberra, Australia (a nation of which I am a citizen):

Dear Sir or Madam,

In the mass media today there have been various reports regarding a meeting of those investigating the loss of Malaysia Airlines flight 370, to occur on Wednesday in Canberra. For example, the following appeared in The Guardian (London):

Air Chief Marshal Angus Houston, said: “We’ve got to this stage of the process where it’s very sensible to go back and have a look at all of the data that’s been gathered, all of the analysis that’s been done, and make sure that there are no flaws in that.”

Might I ensure that you are aware of the analysis by a variety of people with knowledge of both the space/satellite sector and also the avionics and communications systems, all available on my website: duncansteel.com

As an example, on April 2nd I posted an analysis that indicated that the Inmarsat modelling of the satellite-derived information appears to be incorrect in that a northern path for MH370 cannot be excluded: http://www.duncansteel.com/archives/507

I have already discussed and critically reviewed this analysis with a wide range of colleagues, including aeronautics/aviation staff at NASA-Ames Research Center, where I work part of the year.

Duncan Steel

The following is the complete (obviously pro forma) reply that I received:

The ATSB’s MH370 search group has been established since Australia’s involvement in the search for MH370. The group initially based at AMSA is now at the ATSB.

This group has been working closely with the MH370 joint investigation team of experts and in particular, the satellite communication subgroup, who will be visiting the ATSB this week to continue the review of information that will assist in progressing future underwater search planning. The work of the groups will be ongoing in the coming weeks as the underwater search planning progresses.

The satellite communication subgroup comprises experts from the ATSB, UK Air Accident Investigation Branch, the US National Transportation Safety Board, Inmarsat and their respective technical advisers.

Joint Agency Coordination Centre (JACC)

Apart from telling us that The Circumlocution Office is alive and well and has been transported to the Antipodes, the above reply is not entirely devoid of information: it mentions only “underwater search”, apparently confirming that the view remains that the MH370 flew south, regardless of any review of the satellite data. Perhaps such a review will indeed demonstrate beyond doubt that the aircraft flew south.

Almost precisely a century after Dickens named The Circumlocution Office, in 1955 Cyril Northcote Parkinson introduced his eponymous law. It has various forms, and corollaries, but the commonest is perhaps that “work expands so as to fill the time available for its completion.” Unfortunately its application in the sorry case of MH370 is that there is no known time limit for the search for the last resting place of MH370, and so myriad public servants [sic] will continue to be paid to do worthless, obscurantist pseudo-work until such time as the aircraft is found, and then they will find something else to do that is both time-filling and self-serving, so as to continue to waste the public’s money.


We Now Have Confirmed Ping Rings

We Now Have Confirmed Ping Rings

Duncan Steel, 2014 April 29.

Many times I have bewailed the fact that the ping ring sizes (apart from the final ping ring at 00:11 UTC) have been kept secret by the influence of unknown parties. It now seems that they have been released (more than seven weeks after the loss of the aircraft).

A correspondent named Nathan has sent in a comment regarding a CNN Twitter feed here that apparently shows a (rather fuzzy) graph of the elevation angles for the satellite pings of MH370, issued a few hours ago by the Malaysian Government. I am assuming that this is a valid piece of information, and expect it to be confirmed by later reports and posts on the relevant Malaysian Government website.

Here is the graph in question:

Elevation angles

Obviously that image of the graph is difficult to read, but I think that I have managed to work out the values plotted with reasonable accuracy. The elevation angles I obtained are as in the following table. Using those elevation angles I then calculated radii for ping rings as shown in the final column in the table. Note that these are indeed ‘radii’ in that I have calculated here their sizes according to the method described in a previous post. That is, these are not ‘non-circular ping rings’ taking into account the non-sphericity of the Earth and therefore a radius changing with latitude, but instead I have simply calculated a uniform ring radius based on the aircraft-satellite range given the elevation angle and the satellite’s ephemeris (altitude, and the latitude of the sub-satellite point, the aircraft being taken to be at the same latitude in this simplified geometry).

These elevation angles and ping ring radii can be compared to those calculated previously on the basis of the back-engineering performed by GlobusMax.

Please anyone and everyone check my values read off that graph, and also check the results of my calculations for the ping ring radii. (Especially as I have jet lag at the moment.)

As soon as I am able I will enter these ping rings into my STK scenario and then make KML files available to all.

Time UTC Elevation angle from aircraft to satellite (degrees) Radius of range ring on Earth’s surface (nautical miles)
16:30 46.6 2250
16:43 46.5 2255
16:55 45.9 2287
17:07 45.0 2335
18:29 52.2 1952
19:40 54.8 1815
20:40 54.1 1852
21:40 51.6 1984
22:40 47.3 2212
00:11 40.1 2599


Developments in Investigations of the Route Taken by MH370

Developments in Investigations of the Route Taken by MH370

Duncan Steel, 2014 April 27.

A graphical technique for investigating the MH370 flight path

A correspondent I will refer to only as ‘Jim’ has sent the following suggestion of a graphical technique for investigating (and perhaps determining) the route taken by MH370. On my reading it seems to have some overlap of the ‘straight line’ path approach taken by myself (and VictorI), but is more formalised, as such. On the other hand, perhaps someone out there who knows far more than me of this will be able to identify it as a well-known process in geometry or graph theory, or something, and supply suitable references to published work. Here is what Jim wrote:

There is a graphical technique to verify the flight path of MH370 which does not rely on the aircraft velocity, nor the Inmarsat ping redshift values directly.  All one needs is a reasonably accurate map representation of the several Inmarsat ping “arcs”.  Given these arcs, the method allows one to determine where on a selected arc the aircraft was and its heading and its velocity as well.  By repeating the method across several arcs you can derive an aircraft flight path. 

The method requires one to assume only that the aircraft flew at a nearly constant speed (any speed) and nearly constant heading (any heading) across three (or more) of those arcs.  These can be any three (or more) arcs which are next to each other in time and distance.  I say nearly constant because not all that much accuracy is required to establish the flight path and headings.  Using this graphical method and the Doppler shift data that you provided in your posts, a couple of iterations should result in a very accurate flight path with derived (not assumed) velocities and headings at each of the arcs (not to mention the location along each arc). 

The Method:  Using three consecutive arcs, if the aircraft flew a constant speed and heading then there is only one straight line at only one specific tangent angle off the first arc that will result in equidistant spacing of that line as it intersects the second and third arcs.  It should not matter whether you work from the outermost arc inwards or the innermost arc outwards.  That line is a fixed data point characteristic of that first arc (in combination with its 2nd and 3rd arcs forming a triplet).  At any point along that first arc, this vector line (at the determined tangent angle) is still valid (true).  By repeating this process for additional sets of arcs you will establish additional vector lines for additional arc triplets (a total of five arcs would be required for three vector lines).  There will be only one point along each of those three arcs where those three vectors actually line up (are parallel, if not superimposed) on each other.  This convergence of the three vector lines is what establishes the exact point on the arc where the aircraft was, and thus also its heading at that time.  With these arc points and the heading, it is then easy to actually calculate the aircraft speeds at the time of each satellite ping.

This graphical technique will not yield mathematically perfect (precise) results, but it is valid and sufficiently accurate to independently substantiate a conclusion that the northern path was feasible for MH370.  This technique also establishes somewhat accurately where the aircraft was along each of the Inmarsat ping arcs, eliminating most of the uncertainty about where the flight ended.  Do note however that this technique is based upon the validity (and to a lesser extent the accuracy) of the reported Inmarsat satellite ping arcs.  Since these have not been publicly released, the arcs provided on your website are all that anyone has. The really critical assumption is the constant heading and constant speed.

In the case of MH370, it appears that the aircraft really did follow a pretty constant heading and speed for most of the period in question.  This is not all that surprising if the aircraft’s pilot/computer was actually trying to get somewhere.  It should thus not be surprising to find that you can draw a straight line with three equal length segments across the four arcs at 19:40, 20:40, 21:40, and 22:40 — which all have equal 60 minute time segments between each data point.  The very last segment (to the 24:11 arc) is a bit off, but the aircraft could have either changed heading a bit or slowed down during that flight segment.

Here are two examples from Jim, which he overlaid on maps I had previously given:



Testing out the above graphical method

Due to various personal concerns I have not had the time to look into the above in any detail, and so I invite others to do so. In order to facilitate that I am making available to all my ‘best’ calculated ping arcs.

I have two sources for ping ring sizes:

(1)    For the final ring at 00:11 UTC only, the graphic/map from Inmarsat issued by the Malaysian Government on March 15th which indicates that the ping ring then was characteristic of the elevation angle of the satellite as seen from the aircraft being 40 degrees: this I take to be indicative of a separation of the satellite and aircraft of 37,786.588 km (see here), despite the satellite position apparently being falsely assumed to be at an altitude of 35,800 km directly above the equator. (Note that in all these calculations I have carried the figures as shown by those decimal places, but no-one should imagine that the true precision available from reading the positions off of a map or graph would be anywhere near that accurate; perhaps the ‘real’ precision is reflected in the tens-of-km digit.)

(2)    GlobusMax has back-engineered ping ring sizes from the Inmarsat Google Earth graphic, rendering satellite to aircraft separations as I have discussed most recently here.

For (1) I have taken the above satellite-aircraft range (37,786… km) and assumed that it can be applied to the real satellite position, which was above latitude 0.589 degrees North at the time in question. That gives me an Earth radius at that latitude (assuming the WGS84 shape for the planet), and from that I can calculate a range ring radius. In previous postings on this website except where I was investigating the effect of the non-sphericity of the Earth on the ping ring sizes I then inserted circular range rings into my STK scenario and presented these as indicative positions of the aircraft at the times of each ping/handshake. However, I do not need to assume circular ping rings/arcs: I can calculate rings which take into account the WGS84 form of the Earth, as I have shown previously: it is just the tediousness and the time needed for me to insert these into my STK scenario (because they consist of a large series of discrete points) that has led me to neglect them until now.

What I have done here is I have indeed calculated these discrete positions that define a ‘better’ ping arc, and am now making the coordinates available to all. What I have done, briefly, is to step through one-degree jumps in latitude, and at each latitude I calculate the Earth radius. Using that, plus the known altitude of the satellite, I can use the satellite-aircraft range to determine the longitude of the ping ring at that latitude. In each case I use the known latitude and longitude of the sub-satellite point as the ‘centre’ of the ping ring, and I also use the satellite altitude, all of which are shown here.

The result is not a circle. If I were to complete the calculations all around a loop surrounding the sub-satellite point then the shape would be neither a circle or an ellipse: because the satellite was north of the equator throughout the flight of MH370, the shape derived would appear close to being circular but would be slightly flattened at northern latitudes and asymmetric for reflection about a line of latitude drawn through the sub-satellite point. As I have noted previously, these ‘true’ shapes differ from the circular ping rings by 10-20 km; but remember that the overall inaccuracy may well be greater than this (due to the problems inherent in deriving the satellite-aircraft ranges in the absence of publicly-available information regarding these measurements).

For (1) above, then, there is just one CSV (comma-separated variable) file available, and I have named it I_PR_00_11UTC.csv. It is available here. If you download and look inside that file you will find it has five columns: (a) The satellite-aircraft range (which should be uniform: it’s the essential input parameter!); (b) The elevation angle from the ping ring position (defined in the next two columns); (c) The latitude of the point (in this case ranging from 43 degrees North to 41 degrees South); (d) The derived longitude of the point; and (e) The distance of the ping ring position from Earth’s centre. In making these calculations I have assumed the aircraft to be at 35,000 feet, and so the value in that final column equals the Earth radius at that latitude plus 35,000 feet.

A CSV file like this can be inducted directly into various spreadsheet applications, and in particular the Microsoft Excel tool.

For (2) above there are six ping rings and so six CSV files named according to the times of the pings/handshakes: from PR_18_29UTC.csv through to PR_00_11UTC.csv. In each case I have simply used the satellite-aircraft ranges as shown in this post, and calculated ping arc positions for one-degree steps in latitude as described above. Because the rings are of differing size, they cover different ranges of latitude, the smallest being that at 19:40 UTC. The six CSV files are available here.

What I would hope that someone will do is to use this set of ping ring positions to exercise Jim’s graphical method as described earlier. It seems quite straightforward. If someone could take the discrete points in my CSV files and produce smooth curves (rather than polygons) in KML files, that would be useful to all.


Progress in breaking the BFO code

Mike Exner believes he may, after herculean efforts, have broken the Burst Frequency Offset code. See his post here. This is important, and all (of course) subject to revision and update.


Personal notes

Apologies that my previous post had comments closed quite early. After a couple of dozen different posts on this website I found that several people were inserting comments under previous posts, and so these were getting lost in that people were not seeing them. Therefore I tried to close the facility to make new comments under those earlier posts, but that also resulted in comments being closed under the last post.

From now on I am setting an automated time limit of five days for comments after a post, such as this one. That should be plenty, I hope.

In any case comments do not appear until such time as I have approved them (or rejected them, in which case they never appear). There will be delays in this process from now on, because I need to do some travelling. Shortly I will be off to Mountain View in California for a while, and then on to Canada for an extended stay. One major reason for this trip is that I have not had a job for two years, and so now I need to find one because I am bankrupt and have two sons at university. If anyone has any good contacts in the Bay Area (e.g. with Google), please let me know! Actually, I would consider a suitable job anywhere, as I am quite mobile.



I was having coffee today at one of my favourite places in Wellington, a café called Plum in Cuba Mall, where the lovely staff treat me really nicely (and I’d also recommend the café called Felix). Anyhow, I was reading the local newspaper (such as it is), which on Saturdays has a block of quotations, some recent and topical, and some older. The final quote today read as follows:

“No-one who cannot rejoice in the discovery of his own mistakes deserves to be called a scholar” – Donald Foster.

Whilst there are a lot of negatives (an implied triple-negative?) in that statement, making one think hard about what was meant, in the end the implication seeps through; and I agree. It’s just that I would have phrased it as: “One who cannot rejoice in the discovery of his own mistakes does not deserve to be called a scholar.” Making mistakes, and falling for false assumptions, is part of the forward progression of fallible humanity.

But what do I know? I make mistakes all the time. As I have said to several kind correspondents, the only way never to make a mistake is never to do anything.


Further Notes on Ping Rings and the Search for MH370

Further Notes on Ping Rings and the Search for MH370

Duncan Steel, 2014 April 23.

How to calculate ping rings

My redoubtable correspondent LGHamilton, who has turned up all sorts of useful information, noted in a comment the appearance of a new blog post (English automated translation; or, here is the original version in Chinese) by Dr Yaoqiu KUANG which presents ping ring calculations and references this website. It was Dr Kuang who proposed the Beshtash Valley near Talas in  Kyrgyzstan as a possible crash location, as I described in an earlier post.

In his blog post Dr Kuang made his own calculations of ping ring sizes, and noted that I had not described in detail how I had made my own calculations of these, my values not being in agreement with his own. I have sent him an email message containing a description of how to calculate these ping ring sizes, but because I am unsure whether that might have reached him – and also because others might be interested – below I show the graphic that I have sent to him.


As can be seen, the calculations here are quite straightforward. If one has available the ping time delay (i.e. what Inmarsat actually measured, I presume) then one uses the speed of light to calculate the aircraft-satellite distance R and from that get the angle β and thence x, the ping ring radius. However, when I first looked at this problem I had only the elevation angle α from the Inmarsat map made public on March 15th, indicating α = 40 degrees. Using that I calculated R and then x as shown in the lower right of the graphic above. Later I have used values of R as determined by GlobusMax to calculate the ping ring sizes.

Note that in other early posts (here and here) I considered both the effect of assuming (incorrectly) that the satellite was truly geostationary, and so always directly over the equator; and also the effect of the Earth’s real shape, which is not spherical.

To account for the latter requires the solution of spherical (i.e. 3D) triangles rather than simple planar triangles as above, the distance r from the centre of the Earth varying with the latitude of both the sub-satellite point, and also (in particular) the latitudes of the series of discrete points that define the ping ring then. In this case of the real shape of the Earth, the ping rings are not circular. I discussed broadly how I did this in one of those earlier posts, but the full algorithm I will leave ‘as an exercise for the student’! Spherical trigonometry is good for the soul.

When I was preparing that post I was thinking that the attainable precision (or otherwise) of the ping ring locations might be dominated by the measurements of the ping/handshake time delays, but it has since become apparent that their precision is potentially much better than my first pessimistic estimate. In view of that it does turn out, as I noted right at the end of that post, that “analysis of the ping time delays aimed at deriving possible routes taken by MH370 must include the detailed shape of the Earth” because if one assumes the Earth to be spherical (rather than an oblate spheroid with the radius reducing with increasing latitude) then the circular ping rings one calculates will be increasingly inaccurate as one moves away from the equator. Remember, our planet’s polar radius is more than 21 km less than the equatorial radius, and that is why the top of Mount Everest is not the point on Earth’s surface that is furthest from its centre (that laurel being held by the summit of Chimborazo, an inactive volcano in Ecuador).

All the ping rings I have presented in recent posts have indeed been based on a spherical Earth assumption, because it’s just too time-consuming for me to enter in my STK scenario the geographical coordinates of the hundreds of discrete points that are required to delineate a ping ring for a true geoid.

All accounting should have a bottom line. So here it is:

The Bottom Line: Ping rings based on assuming a spherical Earth may be out by 10 to 20 km.


Resources and Ideas Concerning the Search for MH370

Resources and Ideas Concerning the Search for MH370

Duncan Steel, 2014 April 21.

Ranges as limited by fuel availability

At various places in these posts and comments/replies people have asked about limitations on the range which MH370 was capable of flying in the unknown (as of yet) portion of its flight.

Even given the known amount of fuel the aircraft was loaded with at KL, there are many considerations (see here and here and here and here and here for example) which limit our ability to say how much fuel was still available at (say) 18:29 UTC, when the aircraft crossed the ping ring associated with that time.

There are various reports of the aircraft climbing sharply, dropping abruptly in altitude, regaining (or not) a cruise altitude; and readers of my posts will know that I would not accept any such reports as being valid unless there was some quite solid information on which to move forward.

It does seem clear that various things happened during the first 100 minutes of the flight that would have led to fuel consumption being higher than would normally be the case for optimal (i.e. lowest) consumption, that being achieved by speeds above 480 knots at altitudes of 35,000 feet or more. From take-off at close to 16:43 through to the final complete ping (which might indicate fuel exhaustion) at 00:11 UTC is a shade under 7.5 hours.

Alain wrote that: [fuel] amount per hour averages the same: 250 knots/5,000 feet; 350 knots/10,000 feet; 400-420 knots/25,000 feet; 480knots/35,000 feet. [These are] B747 references but I guess the same for B777 even if new engines’ consumption is less.

Similarly Ed Baker has noted that regardless of the actual speed and thus total distance flown, the B777 performance tables indicate that the duration of flight is essentially the same whether it is a high-altitude/high-speed track or a low-altitude/low-speed track, with his answers coming out (for the 49,100 kg fuel load) at 7.6 to 7.8 hours.

Any abrupt altitude changes and so on would reduce that, so that a circa 7.5 hour flight seems a valid assumption. That is, it is sensible to think that the 00:11 UTC ping/handshake might have been due to either one or both engines running out of fuel, and the 00:19 UTC ping/handshake was due to either the second engine running out, or else an impending crash.

Now let me turn to the last ‘unknown’ part of the flight, between 18:29 and 00:11 UTC. That is precisely 5.7 hours. From my assumed position P_18_29 (which is at latitude 6.7 degrees north, longitude 95.3 degrees east) I can draw range rings which describe the distances that MH370 could have flown under the assumption of constant speeds along great circles (i.e. ‘straight paths’). These are as follows:
200 knots             1,140 nm
250 knots             1,425 nm
300 knots             1,710 nm
350 knots             1,995 nm
400 knots             2,280 nm
450 knots             2,565 nm

I can therefore draw range circles defined by the above distances, and I have done so for the use of all interested parties. The 2D maps and 3D views from my STK scenario are shown below. KML files for all six range rings are available here. Their filenames begin RR_…  




The two tracks from Victor

In the last post I wrote that Victor has been working on an interpretation of the Inmarsat information and the search region in the Indian Ocean in order to derive an alternative northern path: see his post about this. He has suggested that it might be useful if I could also put up graphics showing the southern track from which he derived his northern track, and that I do here.

Here are the coordinates and speed of the previous northern track:


Here are the coordinates and speed of his southern track (which he sent me directly):


Both are constant speed, constant heading. I put both at altitudes of only 10,000 feet (in view of the reduced speeds) but that is not a necessary part of the analysis here.

Here is a map of the two routes from the STK 2D window:


Here is a view from the STK 3D window:


The terminus of the southern route coincides (of course) with the location of the revised Indian Ocean search position, as supplied by Annette: it is on that position (and its possible implications) that Victor predicates his back-engineering. Both routes and Victor’s ping rings are available as KML files here for you to download and drag into Google Earth or some other GIS tool.



Yet More on the Search for MH370

Yet More on the Search for MH370

Duncan Steel, 2014 April 20.

Ping rings from the time delays

In a previous post I gave approximate positions/sizes for the ping rings based on back-engineering by GlobusMax from the Inmarsat Google Earth graphic. In that case I had placed the ping rings (and measured their sizes) solely by eye in my STK scenario. I have now calculated their sizes based directly on GlobusMax’s aircraft-satellite ranges, using an assumed uniform Earth radius of 6,378 km (the equatorial radius). My updated values are as shown below in the final column:

Time UTC Line-of-sight range  from aircraft to satellite (km) Ping time delay(milli-seconds) Elevation angle from aircraft to satellite (degrees) Radius of range ring on Earth’s surface (nautical miles)
18:29 36869.0 122.982 53.53 1881
19:40 36741.0 122.555 55.80 1762
20:40 36786.5 122.706 54.98 1805
21:40 36959.5 123.284 52.01 1962
22:40 37243.5 124.231 47.54 2199
00:11 37838.5 126.216 39.33 2642

All six ping rings are available here as KML files, for those who want to use them in virtual globes (such as Google Earth); they are called Ping_Ring_00_11.kml etc. Here is a map showing their locations. In terms of time, they progress from the darkest green through to the lightest.



Track and ping rings from Victor

Victor has been working on an interpretation of the Inmarsat information and the search region in the Indian Ocean in order to derive an alternative northern path. There are several comments from him on this website which contain detailed information about this. I have yet to catch up with all of that information, but for the time being I refer only to his latest (as I write). Please look up the details there.

I have entered Victor’s information for his hypothetical ping rings and aircraft track into my STK scenario, and produced KML files for those. All are available here for you to download and drag into Google Earth. These ping ring KML files begin with PR_VI_… and the aircraft track is MH370_VN_4_20.kml (V=Victor, N=North, 4_20 is today’s date [for me]). Note that I assumed an altitude of 10,000 feet for this aircraft track, reflecting its low speed of 257.4 knots (from Victor). That low altitude would result in a crash in the eastern Himalayas, as you will see as you zoom in within Google Earth.

Below is a map of the rings and track from my STK 2D window. I have coloured the rings from dark red through to pink in terms of a time progression. Note that in Victor’s interpretation all ping rings get larger with time, as shown.



Further Comments on the Search for MH370

Further Comments on the Search for MH370

Duncan Steel, 2014 April 18.

The situation as it stands

Several vital contributions have been received and shared via this website, from a handful of people ranging from experienced airline pilots through to wizened scientists and engineers. As I have indicated below, the ‘evidence’ that has been admitted as being usable in the analysis is very limited.

Without saying much more at the present time – other posts from me will follow, and there is a vast amount of useful material in the various comments received and archived on this website – at the present time I can see no reason to definitively choose one general route (north or south) for the aircraft after the final radar detection at 18:22 UTC on 2014/03/07. Arguments have been made here for the Inmarsat interpretation of the aircraft definitely heading south into the Indian Ocean being false, because there are northern routes and speeds that may fit the Inmarsat-derived information. An assumption in stating that – that the Inmarsat deduction of a definite southern path is wrong – is that there is no source of unrevealed information that would force that conclusion (e.g. the aircraft having been identified flying over the Cocos Islands).

The above does not imply that the aircraft headed north. It simply means that the available Inmarsat-derived information is not adequate to distinguish between northern and southern routes.

I will have more to say later in further posts about the excellent analysis that has been done by others and described in the many comments under my previous post, but although there is no inarguable position to be taken over north versus south there are various considerations that lead me to believe that a northern route was taken. On that, though, I need to clarify my thoughts and discuss things further with several correspondents, some of whom are fairly-well convinced of the veracity of the northern route (indeed due north) interpretation.


What is admissible as evidence?

I am continually bombarded with pet theories from various people who want to argue that their conspiracy theory has merit, and so on. Those just get deleted.

Please, let me repeat: we – and that is not Queen Victoria’s “we” as in “we are not amused” – are trying to apply scientific rigour to analysing where MH370 might have flown, using only evidence and information which seems reliable, and is in the public domain. Several people have made, and are continuing to make, vital contributions to this effort; especially over the past week whilst I have been only putting up their various comments for all to see, and making very little contribution myself.

By applying rather strict criteria as to what is admissible as evidence we might well be rejecting truthful information because we have no way to confirm its veracity at present; and it might well be that we are accepting as truthful various things that will eventually turn out to be wrong. For example, it might be that Inmarsat invented all their announced information: but I doubt it. I think they have made some slip-ups, but I do not believe that they have been malicious, or deliberately lied.

The guiding principle here, therefore, is that only ‘known’ things are used in shaping the investigation.


Absence of evidence is not evidence of absence

The phrase directly above I have repeated several times in my responses to comments. Please, everyone, try to understand what I mean!

Here is an example. Apparently the last radar detection of MH370 was by a Malaysian military radar at 18:22 UTC on 2014/03/07. That gives us a position for the aircraft at that time, in terms of latitude and longitude, with some uncertainty bars to be applied. (Depending on the specifics of the radar system, and the time stamp, the position might be out by several nautical miles [nm] from its actual position; and note that even if the vertical resolution were as accurate as the horizontal, that means that we can know little about the precise altitude of the aircraft at that time, except that it must have been above the horizon as seen from the radar site.)  So: we assume on that one that we have not been lied to, and we take that as a known fact; although always subject to re-examination.

Continuing the example. No subsequent radar detections have been reported. (a) Indonesia has apparently reported that MH370 did not fly through its airspace. I prefer to interpret that as Indonesia saying that they did not detect and identify it using their radars, because they are constrained by their own security concerns and so would not reveal that MH370 had perhaps flown through Indonesian airspace but either: (i) They were asleep at the time; or (ii) Their radars are not adequate to pick it up amongst the other air traffic. (b) There are no indications of MH370 having been detected and identified through radar systems in Myanmar, India, China and so on (i.e. plausible northern routes). (c) My personal knowledge of the JORN system (which I cannot reveal in detail) indicates to me that it is unlikely that it would have been detected and identified by that system, and that viewpoint has been backed up by others (offline here) including an experienced operator. Note how I have written “detected and identified” in connection with all the above systems: that is, there might be a signal returned to the radar receiver, and registered amongst the stored (or maybe not stored) data, but it may not have been identified either by automated systems or the human operators.

What is summarised in the preceding paragraph is an absence of evidence. However, that is not in itself evidence of absence. That is, regardless of MH370 not being identified using a variety of radar systems this does not imply that it did not fly a route passing near them. One can think of many reasons why it might have been missed.

The same applies to other means of detection and identification. Apart from the satellite-derived information, we have (at present) no direct evidence of where MH370 went. Before someone asks: no, the reported sound pings from the Indian Ocean are certainly not acceptable as evidence!


What is accepted as evidence?

The simple answer to that question is: herein, not much. For the early part of the flight we have tracks and speeds. Then we have evidence of the aircraft being west of the Malay Peninsula, and the last radar contact at 18:22.

After that the only evidence employed here is derived from the satellite (Inmarsat-3F1), and this consists of information that has been gleaned from: (i) The first Inmarsat ‘ping ring’ map issued on March 15th by the Malaysian Government; (ii) The BFO graph from Inmarsat dated March 23rd and issued on March 24th/25th by the Malaysian Government; and (iii) The Google Earth tracks from Inmarsat dated March 23rd and issued on March 24th/25th by the Malaysian Government.

Item (i) is available here amongst many other places.

Items (ii) and (iii) are available here or here or here amongst many other places.

Apart from the above we have evidence pertaining to the fuel load on MH370 on departure; fuel consumption rates and so ranges for different altitudes and speeds; information about the operations of such an aircraft and in particular its autopilot; and personal accounts from experienced pilots regarding possible scenarios that could lead, for example, to MH370 being left flying itself on autopilot until it exhausted its fuel and then crashed.


How does the B777 autopilot work in an extreme situation?

Several posts ago I posed a testable hypothesis for the possible route taken by MH370 based on an assumption about how the autopilot might function in an extreme situation of the crew and passengers all being incapacitated and the autopilot then being left to fly the aircraft with no further human input.

Since then I have received valuable information from several experienced airline captains and pilots regarding what they are taught about the autopilot functions; what the manual says; and what they have themselves experienced. As I wrote just above, that has been valuable information that has shown me that some of my assumptions were poor.

Strictly, though, my hypothesis has not been tested and shown to be wrong (which is what I might anticipate) because no-one has experienced a scenario like that which appears to have befallen MH370 (perhaps). Testing that hypothesis would require either a software test (run through the programs to see what the autopilot would really do, with information being welcome from the software coders who actually framed the autopilot algorithm) or a hardware test (take an identical B777 back to the early part of the flight of MH370, turn it westwards and then let it fly itself and see what happens).

Let me give a metaphor that shows you why I’d like this idea tested out. Imagine a hugely-experienced surgeon who knows precisely how hard (or soft) to press with a scalpel in order to make the necessary incision to start an operation. He is intimately familiar with scalpels, and how they behave, and how sharp they should be. He can tell me precisely how a scalpel would respond under all the possible situations he could imagine, in terms of operating on a human.

But could the surgeon tell me how the scalpel would behave if, instead of holding it gently between my fingers and thumb, instead I grasped it in my fist and violently tried to chip pieces off of a slab of granite? I could be wrong, but I think I might be better off asking the metallurgist who stipulated the metals to use in making the scalpel, and the craftsman who actually made it, rather than the surgeon. The surgeon would have valuable information of how the scalpel performs in the task for which it was designed, but might know little about how good it was at chipping away at solid rock, a situation for which it was assuredly not designed.


Another precedent from a US President

Thomas Jefferson is a name well-known to all, because he was one of the Founding Fathers of the USA and the third President.

Jefferson was a Southerner; late in life he founded the University of Virginia. There is a story, quite likely apocryphal, that when told of a report by a pair of academics from Yale University of a meteorite fall in Connecticut, Jefferson said that “It is easier to believe that those two Yankee professors would lie than that stones would fall from heaven.”

There is no proof that Jefferson said this, and one has every reason to believe that he had an open mind on all things philosophical.

Whether the story is true or not, it provides an instructive lesson. First, one might imagine that Jefferson’s origins and background would indeed bias him against the Yale academics. Second, the idea that meteorites are indeed stones falling from the sky was a novel one in Jefferson’s time, making him perhaps validly doubt a claim that would have seemed extraordinary, even bizarre, and even in our time I have had huge difficulty in persuading people that much larger stones fall from the sky from time to time. Third, he would be quite right to maintain a sceptical stance on the report until such time as he had verified it himself.

As I have pointed out previously, the motto of the Royal Society of London is Nullius in verba: Take no-one’s word for it. That’s what we should all be trying to do. I would add “within reason”, but it is clear that some people have far stronger reasoning powers than others, whilst many believe everything they read in the newspapers (or is announced by their Prime Minister).


Links to previous posts

Post       Date                      Title and link

01           March 23             Some Comments on the Final Ping of MH370 by the Inmarsat-3F1 Satellite

02           March 24             The Locations of Inmarsat-3F1 when Pinging MH370

03           March 25             Representations of the MH370 Ping Rings in the Media

04           March 26             Positions and Velocities of Inmarsat-3F1 During the Flight of MH370

05           March 27             Difference Between Inmarsat-3F1 Equal-Elevation-Angle Arcs and the Initially-Modelled Geostationary Satellite

06           March 28             The Range of Equal-Time-Delay Ping Rings from Inmarsat-3F1

07           March 30             Possible Flight Paths of MH370

08           March 30             Revised Possible Flight Paths of MH370

09           March 31             Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

10           April 01                 Revised Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

11           April 02                 The Inmarsat-3F1 Doppler Data Do Not Exclude a Northerly Flight Path for MH370

12           April 03                 Background Information on the Pinging of MH370 by Inmarsat-3F1

13           April 05                 Links to Previous Posts on the Inmarsat-3F1/MH370 Ping Analysis Saga

14           April 05                 Ping Rings from the Inmarsat-3F1 Data

15           April 06                 Information Pertaining to the Search for MH370

16           April 06                 A Testable Hypothesis for the Flight Path of MH370

17           April 09                 Constraining Possible Routes for MH370

18           April 10                More on the Possible Routes of MH370

19           April 11                 Information Available from the STK Scenario Involving Inmarsat-3F1 and MH370

20           April 12                 Potential Terminal Locations for MH370


Personal note

My apologies that it has been a long time between posts from me. This past week, for various reasons, I have been unable to do much more than approve comments from people and occasionally add responses.


Potential Terminal Locations for MH370

Potential Terminal Locations for MH370

Duncan Steel, 2014 April 11.

In my second-last post I presented hypothetical tracks for aircraft travelling generally northerly and southerly paths from my point P_18_29 (located near at 06.70 degrees North, 95.30 degrees East) and starting at that time (i.e. 18:29 UTC). The assumed speeds were 300, 350, 400, 460 and 500 knots, so that there were ten tracks in all. The routes taken by these hypothetical aircraft were defined by the requirements that:

(a)    They be located on each of the ping ring tracks at the appropriate times; and

(b)   They take great circle paths between the ping rings.

Thus any change of course would need to take place at the ping rings.

In various comments and replies I had said that of all these tracks the two I would tend to favour would be those at 400 knots northerly, and 460 knots southerly, based on the apparent fact that these were the ‘straightest’ of all the tracks plotted, requiring the smallest changes in course as they crossed the ping rings.

Victor Iannello kindly took the information I had provided and quickly did a best-fit analysis on possible routes. In essence he asked himself this question: “I want to know the assumed-constant aircraft speed which will render a single great circle path between P_18_29 and a final location on the 00:11 UTC ping ring, defined by minimising the ping arc error.” The ‘ping arc error’ is defined here as the distance the aircraft is from the ping ring arcs at the times of each of the pings. (This sort of least-squares fit is what good physicists do three times a day before breakfast, just for the heck of it; but not me.)

The point is that this renders two ‘most-likely’ speeds, one for a northerly route and one for a southerly route, based on the working hypothesis that the aircraft followed a constant heading great circle path after 18:29. The speeds Victor obtained were 421 knots for the north, and 481 knots for the south.

In the following tables I give Victor’s calculated positions at each ping time.

Northern Route: Constant Speed 421 knots, Constant Bearing 334.28 degrees

Time (UTC)


Ping Ring Centre

Aircraft Distance from Ping Ring Centre at that Time (nm)

Nominal Ping Ring Radius (nm)

Ping Arc Error (nm)

Latitude (degrees)

Longitude (degrees)

Latitude (degrees)

Longitude (degrees)


















































Southern Route: Constant Speed 481 knots, Constant Bearing 189.92 degrees

Time (UTC)


Ping Ring Centre

Aircraft Distance from Ping Ring Centre at that Time (nm)

Nominal Ping Ring Radius (nm)

Ping Arc Error (nm)

Latitude (degrees)

Longitude (degrees)

Latitude (degrees)

Longitude (degrees)


















































Regarding the final column in each table: I remind readers that I had placed my ping rings by eye in my STK scenario based on GlobusMax’s back-engineering of the satellite-aircraft distances, and had stated that I thought my ping rings might be out by 10 km/10 nm, or perhaps even more. Therefore the sizes of the ‘ping arc errors’ calculated by Victor are not surprising; and their signs are the same in each table, possibly indicating a systematic error (i.e. the ping arc errors are largely due to the inaccuracy of my ping ring sizes). If I had the time to calculate the sizes of the nominal ping rings more accurately then one might anticipate that Victor (or someone else) would be able to obtain an even better fit, and so a more precise termination point for each route, north and south.

The two tracks defined in the tables above I have entered into my STK scenario; here are the exact path definition tables:

Route MH370_VN (V for Victor, N for North) 


Route MH370_VS (V for Victor, S for South) 


These result in the following graphics.


Shots from 3D STK Window




Maps from 2D STK Window





The terminal points of the tracks I have marked with black spots. These were arrived at by assuming that MH370 flew on for about eight minutes after the reaching the 00:11 UTC ping ring, at the same constant speed it had previously. Obviously that is an assumption of doubtful validity, if it were just exhausting its fuel and beginning an erratic and largely-uncontrolled descent terminating in a crash.

Up until now I have had no reason, in terms of physics and aircraft performance, to favour a southern path over a northern one, or vice-versa. Now I do. Noting that the southern route shown above is longer (of course) than the northern route – they last for the same length of time, but the northern one is at 421 knots, the southern at 481 knots, so that it’s about 14 per cent longer – I thought that the southern route might be excludable by dint of there being insufficient fuel to complete it.

With this in mind I asked whether we knew the maximum possible range for MH370. Richard Godfrey answered as follows:

I have checked Victor’s routes with respect to your point about fuel .

The Northern Path is 3174.7 nm from KUL via IGARI, VPG, VAMPI, MEKAR, NILAM and Victor’s best fit co-ordinates.

The Southern Path is 3507.8 nm using the same assumptions.

As mentioned in a previous post, the maximum fuel range is 3336nm calculated based on a flight planned to Beijing plus 2 hours reserve (if MAS followed standard practice).

In this case, you would be right to exclude the Southern Path.

Richard’s calculations are yet to be repeated using the known fuel loading of MH370 at KL, which has been supplied by LGHamilton, but my present working position must be that – subject to the various assumptions that have perforce been necessary – MH370 most likely took the indicated northern route, and therefore would have crashed in the vicinity of Almaty.

Until this analysis has been refined in various ways there is nothing much further to be said, and so I will end this post now with the simple observation that there are several substantial mountains ranges to the south and south-east of Almaty that are still snow-covered and not easily accessible at this time of year.


KML files for induction to Google Earth

Earlier today (April 11) I informed readers that KML files were available for ten hypothetical aircraft tracks (five northern, five southern) plus all six ping rings, for pulling into Google Earth or other virtual globes/GIS software. In the present post I have been discussing two new aircraft tracks, with speeds 421 knots northerly (MH370_VN) and 481 knots southerly (MH370_VS), each of which follow single great circle tracks from a point located at 06.70 degrees North, 95.30 degrees East, and fly at constant speeds at 35,000 feet. Due to the way they were derived by Victor Iannello they each cross the ping rings at approximately the correct times. The two new KML files that result are available in Dropbox here.


Information Available from my STK Scenario Involving Inmarsat-3F1 and MH370

Information Available from my
STK Scenario Involving
Inmarsat-3F1 and MH370

Duncan Steel, 2014 April 11.

KML files for induction to Google Earth

Various people have placed (geo-located) my maps into Google Earth, which is good: thanks for that.

However, I thought it might also be useful for people to have access to some of my results as KML files for pulling into Google Earth (or NASA’s World Wind, or any other GIS tool). Therefore I have written out of STK as KML files both the ping rings and the aircraft hypothetical routes (from 18:29 to 00:11 UTC, as described in previous posts here and here). These can then simply be dragged into Google Earth so as to display the routes and ping rings. Note that the ping rings are drawn as ‘walls’ 35,000 feet high above the WGS84 ellipsoid (that is, they are not just lines along Earth’s surface); and the aircraft routes are all at altitude 35,000 feet above that height reference.

The sixteen KML files that result are available in Dropbox here.


STK scenario and VDF

Various people have asked whether they could have access to my STK scenario so as to make a start on their own modelling; my response has been that it was not feasible because an STK scenario depends on many (i.e. hundreds) of files spread around your C-drive. However, I have now realised (actually, remembered) how to make such sharing possible: package the scenario up into what is called a VDF (VDF = Viewer Data File).

This also has the advantage that others can use the VDF (essentially the data to construct a 3D scenario in which one can move around both in three spatial dimensions but also in time) without needing to use the STK tool itself. A VDF can be opened using either (a) The STK tool, which is complicated to use but would enable one to edit my scenario; or (b) The Viewer tool, which does not allow editing but does allow navigation as mentioned, plus the capability to record views as bitmaps, and so on.

So, as a start I would suggest that anyone who wants to try this should download the Viewer which is freely available from AGI, here. From memory, it’s about a 80 MB installation file.

Anyone who already knows how to use STK, or wants to try learning, can download the installation file from the AGI website here.  It’s close to 700 MB. You would then need to register with AGI and thence get a free licence/license file which would enable you to use STK.

My STK VDF file (my latest scenario file, all packaged up) is called MH370_I3F1.vdf and it is available here in Dropbox. It is about a 120 MB download.


More on the Possible Routes of MH370

More on the Possible Routes of MH370

Duncan Steel, 2014 April 10.

In my preceding post I gave possible paths for MH370 at uniform speeds of 300, 400 and 460 knots starting at 18:29 UTC at an assumed point just inside (i.e. west) of the 18:29 ping ring, that point being located at 6.7 degrees North, 95.3 degrees East. Feasible routes going both north and south were calculated and presented, being defined by the need for them each to cross the ping rings for 19:40, 20:40, 21:40, 22:40 and 00:11 UTC at the times in question.

It was suggested to me that I add a speed of 350 knots in order to see how it compares with the concentration of searches in the Indian Ocean, and I have now done that. I have also added a speed of 500 knots, so that I now have two sets (i.e. northerly and southerly) at 300, 350, 400, 460 and 500 knots. One might query why I used 460 rather than 450 knots, and the answer is that I wanted to use a path passing close by the Beshtash Valley in Kyrgyzstan, which has been suggested as being a possible crash location on the basis of satellite imagery showing both a temporary smoke plume and a localized thermal signature. As of yet I have seen no disproof of that suggestion, even though it might seem unlikely to be the actual landing/crash spot of MH370.

I will leave it to others to compare these graphics with the search regions in the Indian Ocean: please feel free to do so! Given the various assumptions made herein (e.g. great circle routes at constant speed, wind neglected) it would be entirely adequate for anyone to interpolate on the graphics for the locations at which routes at (say) 340 or 360 knots would appear, and intersect the final ping ring at 00:11 UTC.


Images from the STK 3D window





Maps from the STK 2D window





A note on the northern routes

As I have indicated in previous posts, at present my working position – supported by several others who have also looked into this matter in detail – is that there is no reason on the basis of the available information derived from Inmarsat (i.e. the Inmarsat-3F1 satellite pinging of MH370) to favour one direction of paths over the other. That is, the assertion by many in authority that the path definitely went south into the Indian Ocean is false, I believe.

That does not mean that it went north. The simple position here is that northerly and southerly routes should be considered equally likely, based on the available satellite information. I will be saying more below about this. This working position that I have adopted for several reasons involves a rejection of the Inmarsat BFO graph as being a reliable source of information: it is maintained to be incorrect in various aspects, until further evidence is released to support its validity (or not).

Under this heading the main thing I want to note is this. In a reply to a message from Rob Matson with regard to wind speed data at the time of the flight, after he had informed me of sources of wind speeds for southerly routes, I asked him whether he knew of similar sources of wind speed data for the northern routes. I specifically asked him for information covering the Xinjiang region of western China.

I expected that perhaps to start a bit of a discussion but it seems to have passed people by, likely for the best, but I have (maybe ill-advisedly) repeated the word above: Xinjiang.

In these posts I have tried to follow a strictly-scientific approach, but from time to time have thrown out discursive comments. So, whilst not wishing to spawn a whole new set of hijack or conspiracy theories, I note that a large fraction of the arc of northerly routes (the part between, say, 320 and 400 knots) end up in the southern part of Xinjiang. That’s the home of the Uyghur people.


Clarification of a point made in my previous post

In my last post I wrote the following, in describing my line-of-sight speed plots:

“… please … imagine a line that smoothly follows the general trends in the lines.

                If you do that you will see that they are essentially identical, whether the paths go north, or south. (And before someone asks yet again: yes, I have included the satellite’s velocity in the calculations.)  

                An implication of this, if it is correct, would be devastating given that the searches have concentrated upon the Indian Ocean. The implication, of course, is that the LOS speed(s) of the aircraft do not favour one direction (north or south) over the other. Unless I have made a serious error somewhere, the Inmarsat engineers made a mistake in their analysis.

                The lines in my plots also have slopes rather higher than that indicated by the BFO/Doppler information (i.e. the six discrete points). I cannot find a solution that will fit the ping rings and the indicated Doppler shift/LOS speeds from the BFO graph.

                Further, the fact that all six graphs show essentially the same slope indicates that somewhere amongst the analysis a circular argument has been made.

There is a limited number of explanations for this:

(1)    I have made an error somewhere;

(2)    Mike Exner made an error somewhere in his de-composition of the BFO graph; or

(3)    The Inmarsat engineers have erred somewhere.”

Some correspondents have interpreted my words “There is a limited number of explanations for this” as referring only to the preceding sentence (“Further, the fact that…”). They don’t. The “this” in “There is a limited number of explanations for this” was intended to refer to all the preceding text quoted above, which together (and with other considerations) lead me to reject the Inmarsat BFO graph as being a reliable source of information. Sorry for any confusion.


Other reasons to believe that the BFO graph is wrong

I have said (several times) that I believe at present that the Inmarsat BFO graph is incorrect, and have given various reasons. Here I discuss another reason that I should have covered in my preceding post.

Here is that graph yet again:



The Inmarsat model that renders the two sets of predicted BFOs for north and south tracks are common until 19:40 UTC (i.e. they must follow the same paths at the same speeds). However, the path actually taken by MH370, and its speeds, are known through to 17:07. Therefore one would expect the modelled BFOs to agree with the measured BFOs, and they do not. Which obviously brings the accuracy of the modelling into question, shall we say?

In making the above observation I have assumed that Inmarsat did not use 450 knots as the input speed for their model during that first part of the route taken by MH370 (through to 17:07), when it is known that it was not travelling at such a uniform speed.


Explanation of my line-of-sight speeds

Someone commented:

Your LOS plots look wrong. It is counter-intuitive for example, that for the southerly path, the final segment shows about the same LOS for the three different air speeds, which increase by over 50%.”

I understand what is meant there, and yet the intuition and connected belief are wrong.

Look at the five southern routes, in the first of the 2D maps above. You can also see the sub-satellite points for different times, that cluster of dots SW of India. All five paths are consistently moving away from the sub-satellite points, as they must (given that the vertical speed of the satellite is relatively small). The contribution of the aircraft’s velocity to the LOS speed in each case will depend upon not only its speed (a scalar) but also its direction, which here we can think of just in terms of the azimuth of its heading. The higher speeds are cutting across the radial direction from the sub-satellite points, and so their contribution to the LOS speed is reduced somewhat; whereas the lower speed paths gradually turn until one (the 300 knot path) is moving radially away from the sub-satellite point cluster. Thus although the 300 knot path has a lower speed, its velocity component away from the satellite compensates. And in the end the LOS speeds turn out the same for all the paths/speeds.

Another point to be made. The (changing) azimuths of the northern paths are rather different to the azimuths of the southern paths. For example, compare the 460 knots paths, north and south: the former ends up (on the white ping ring pertaining to time 00:11 UTC) about 20 degrees of longitude further west than the latter does. Similarly one might note that the 300 knot northern track does not end up pointing radially away from the sub-satellite points, whereas above we saw that the 300 knot southern track does so. This is not a trivial observation, because it is precisely this that results in the LOS speed for the northern tracks matching the LOS speeds for the southern tracks, despite the fact that the satellite is moving southwards throughout the time from 19:40 to well beyond 00:11 UTC. (Actually, it continues moving south for about half a sidereal day from 19:36 UTC.)

This symmetry in LOS speeds north and south despite the lack of geometrical symmetry in the paths is what leads me to suspect that there is some circularity in the Inmarsat calculations/models rendering the BFO graph.


Constraining Possible Routes for MH370

Constraining Possible Routes for MH370

Duncan Steel, 2014 April 08.

The physicist always asks, “Do I know this?” “How do I know this?” and “Is this still true?”                       Luis Alvarez (1976)


After the diversion represented by my last post, I now return to the scientific (I hope!) analysis of the information that is publicly available with regard to the path taken by MH370.

In previous posts I have examined how the range of possible flight paths might be narrowed down based on the information that was available to me at the time of those posts. That information has now been expanded with more ping rings being available, through the good work of GlobusMax, and so one would anticipate that with both ping rings (from the ping time delays) and line-of-sight speed/Doppler shifts (de-composed from the Inmarsat Burst Frequency Offset graph by Mike Exner) the range of feasible routes for MH370 could be narrowed down. But, as I will show here, that anticipation might be mistaken, at least in part.


Plausible aircraft tracks inserted into STK

In several previous posts I have been considering, to greater or lesser degrees, the path taken by MH370 during the early part of its flight: through to the final radar detection at 18:22 UTC, the apparent (from the BFO hence Doppler information) rapid turn around 18:25 to 18:29, and then the position somewhere on the 18:29 ping ring. Now I leave behind considerations of that early part of the flight, and consider only the path from 18:29 onwards.

What I do, then, is to assume the aircraft was at a certain position at that time which I will call P_18_29, and examine the possible paths from then onwards. I chose latitude 6.7 degrees N, longitude 95.3 degrees E for that point, just inside the 18:29 ping ring:


From that point I allow paths to go either north or south, although not directly (i.e. they do not start off with headings at either azimuth 0 or 180 degrees). The paths from P_18_29 are defined only by the following requirements:

(a)    The assumed speed is to be constant for each path; and

(b)   Each path must cross the ping rings for 19:40, 20:40, 21:40, 22:40 and 00:11 UTC at those times and from the inside (that is, the satellite-aircraft distance must be increasing at each of those times).

Note that I am ignoring all effects of the wind, including increasing or decreasing the aircraft speed (i.e. tail or head winds) or changing its path through the air (i.e. cross winds). As I have explained previously: Ockham’s Razor dictates that I should start with the simplest approach.

Note that requirement (b) above is in essence dictated by the BFO/Doppler information, and as explained later I have reasons to doubt its veracity; nevertheless I think that requirement (b) is correct in that the aircraft does indeed cross all the ping rings from the inside from 19:40 onwards. But that presumption is subject to possible disproof.

In a previous post I concluded, based on the information available at that time, that a track going generally northwards at about 250 knots would be a good fit to the Doppler information. With no availability of ping rings other than that at 00:11 UTC I was later able to indicate that the aircraft speed must have been at least 300 knots. As discussed later in the present post, that does not (again) exclude a northerly path. (It does not, also, exclude a path taken with variable speed.)

Before coming to that, I must first present paths that satisfy requirements (a) and (b) above, and only paths with speeds of at least 300 knots will do that, due to the separation in distance and time of the ping rings for 22:40 and 00:11 UTC.

With that in mind I have so far modelled plausible aircraft paths for uniform speeds of 300, 400 and 460 knots, turning either northwards or southwards from P_18_29. That makes six paths in all, as shown in the following image obtained from my STK scenario 3D window:


Here is an expanded view of the northern paths:


(The figures at lower left simply define my effective viewing position in this 3D environment.)

Here is an expanded view of the southern paths:


The small white symbols apparent along each of the paths simply indicate the points at which I had clicked to define effective waypoints in the STK route definitions, these being decided upon by trial and error with the criterion being that the path/route (at constant speed) should reach the appropriate ping ring within a minute of the time defining that ping ring. It is this that leads to the paths displaying sudden angles/heading changes at the ping rings.

I caution again that my ping rings positions were themselves entered by eye, and so may be erroneously placed by 10 km/10 nm, perhaps more.

For the convenience of readers, I will now show also the path locations in the STK 2D window (i.e. as maps):





Line-of-sight speeds for these paths

For each of the six paths shown above I have calculated LOS speeds for the aircraft relative to the Inmarsat-3F1 satellite across the time of the flight between 18:29 and 00:11 UTC. The resultant plots are shown below. In each plot there is included an identical set of six dots, representing the LOS speeds that would be required on the basis of the decomposition of the BFO graph and thus the evaluation of Doppler shifts, which can then be converted into LOS speeds.







In each plot the line showing the LOS speed satellite-aircraft demonstrates fairly-sudden changes or steps. These are due to the angles (or changes in bearing) at each of the ping rings as seen and discussed above. They are not of concern. The actual trend of the LOS speed for a smoothly-changing path would also be smooth, so please ignore the steps and imagine a line that smoothly follows the general trends in the lines.

If you do that you will see that they are essentially identical, whether the paths go north, or south. (And before someone asks yet again: yes, I have included the satellite’s velocity in the calculations.)

An implication of this, if it is correct, would be devastating given that the searches have concentrated upon the Indian Ocean. The implication, of course, is that the LOS speed(s) of the aircraft do not favour one direction (north or south) over the other. Unless I have made a serious error somewhere, the Inmarsat engineers made a mistake in their analysis.

The lines in my plots also have slopes rather higher than that indicated by the BFO/Doppler information (i.e. the six discrete points). I cannot find a solution that will fit the ping rings and the indicated Doppler shift/LOS speeds from the BFO graph.

Further, the fact that all six graphs show essentially the same slope indicates that somewhere amongst the analysis a circular argument has been made.

There is a limited number of explanations for this:

(1)    I have made an error somewhere;

(2)    Mike Exner made an error somewhere in his de-composition of the BFO graph; or

(3)    The Inmarsat engineers have erred somewhere.

Having checked my own analysis multiple times, and also having had access to Mike Exner’s analysis, I am hereby adopting a working hypothesis that (3) is what has occurred. I think there has been some significant mistake made by the Inmarsat engineers in their interpretation of the raw data so as to derive their BFO graph, and either that or some other error has also led to their model for the aircraft’s path – leading to the southern route(s) being favoured over the northern route(s) – being invalid.

We all make mistakes under pressure; and that statement also applies to me, perhaps here. But at this juncture I do not believe that the BFO information is correct.


DIKUW hierarchy

At this stage of my discussion I insert a little note with regard to some laxity that has appeared in debates on this thread, with me being responsible for some of the lapses (mea culpa). I have already mentioned it in one or two of my replies to comments received.

The DIKUW hierarchy or pyramid (sometimes simply DIKW) should be second nature to anyone who wants to analyse complex situations, or indeed conduct scientific research. I like to think of it this way:

Data < Information < Knowledge < Understanding < Wisdom

There are many little examples that could be given, a frequently-cited one being that you might understand that a tomato is a fruit, but it takes wisdom not to put it in a fruit salad.

In this instance we only have information about constraints the satellite engineers have placed on the path of MH370, we do not have the data. I interpreted the first ping ring graph (issued March 15th) to get the radius of that ring subject to various assumptions, and also pointed out on March 23rd various false assumptions apparently made by the Inmarsat engineers. Later GlobusMax has used publicly-available information (in particular the Google Earth graphic from Inmarsat, made public on March 25th) to derive all the ping ring positions. Mike Exner, aided by Ari Schulman and myself, de-composed the Inmarsat BFO graph to get Doppler shifts and thus the LOS speeds I have used here (i.e. the identical six dots in each of the preceding six graphs).

From the above information we have tried to develop knowledge and thence understanding, in the hope that the wisdom will result to narrow down the search.

But what if the information is false in some way? Without the data we cannot check the first transition, from data to information. And that forces me to assume that in some important aspects the information is wrong.

To some extent my adopted assumption henceforth, until proven incorrect, is that the Inmarsat BFO graph and deductions based on it are false. It may well be that the aircraft went south, but I no longer believe the analysis/information that led to that conclusion.

In coming to the decision to reject the Doppler shift constraints my thoughts have been shaped somewhat by the apparent performance of the Inmarsat engineers both early on (the March 15th graph) and later (the BFO graph itself). The impression I gained from those is not of a professional organisation. Sorry, but that’s the way it is, and I stated at the start of this series of posts that I was trying to give an explanation for each decision I made. Advance apologies to them if they have been correct all along, but paramount at present is finding out what happened to MH370.


A precedent involving a President

The quotation from Luis Alvarez I showed at the start of this post, and also that from that same person in an earlier post, comes from a paper he wrote entitled A physicist examines the Kennedy assassination film (American Journal of Physics, volume 44, page 813, 1976).

One of the things he showed in that paper is that, contrary to all previous assumptions by others, the camera that recorded the famous Zapruder film of the assassination was not running at the nominal 24 frames per second. If I recall correctly, his conclusion was that the framing rate was near 17 frames per second (i.e. it was running slowly, which means that when played back at the usual 24 frames per second it is shown too fast). The way in which Alvarez got suspicious about the film speed is quite surprising: he noted how fast spectators were clapping their hands as the presidential cavalcade approached, and showed that it was quicker than normal human clapping rates. The point is that there is a natural rate (or range of rates) at which we applaud. Do it a little faster and the power required is tiring, and you soon slow down again.

On that basis Alvarez was able to reject some information that had previously been generally accepted, including by the Warren Commission. The data were still valid – you can never argue with data – it was the information derived from the data that was wrong, due to a false assumption and so a mistake in the analysis.

To repeat: The physicist always asks, “Do I know this?” “How do I know this?” and “Is this still true?” In asking myself those questions I have come to the conclusion that there is something fundamentally wrong with the Inmarsat BFO graph, and so I reject it. I may well be wrong to do so.


Where is MH370?

I do not have an answer to that. All I can try to do is to narrow down the possibilities. Paradoxically, if I am correct in what I have written in this post then I have actually widened the possibilities: I do not see a valid reason to favour the putative southern routes over the northern routes.

Dependent upon the speed, the aircraft seems to have ended up somewhere close to the ping ring for 00:11 UTC. Above I have shown fans of arcs (in the north and the south) limited by assumed speeds of 300 to 460 knots. I have no reason to exclude speeds higher than 460 knots, and will likely look at (say) 500 knots tomorrow.

One might presume that the aircraft continued outside of the 00:11 UTC ping ring for several minutes and the reported ‘partial ping’ at 00:19 UTC might represent the engines shutting down, the aircraft descending, or hitting the ground/ocean; I do not know.

One should not assume, however, that the aircraft continued on anything like its previous course once its fuel was exhausted. That is, it might have done so; but unless one has definitive evidence for that (e.g. that the autopilot would have maintained course after fuel exhaustion) I think it best not to assume such a thing.

Indeed I have assumed herein, perhaps incorrectly, that the aircraft continued at the nominal speeds I have given it for each path, and one might easily imagine that not only would it slow as fuel was running out, but also that each engine would have its own fuel exhaustion time and that would result in the aircraft not only slowing but also deviating from its nominal course somewhat.

I note also that I have ignored the effects of the wind at different positions and times on the aircraft. One must start somewhere, and so I started without multiplying complexity by adding in wind factors about which I know almost nothing.


A suggested location for MH370’s crash

I wrote above that I do not have an answer for where MH370 ended up. But I do have a suggestion for where it might be.

Quite early after I began this series of posts I received an off-the-record email message from someone who, through a misunderstanding on my part, I thought to be a Chinese man. In fact later emails revealed it to be an American woman. She has posted comments several times as LGHamilton, but I have no reason to believe that she would want her identity revealed to the world.

LGH drew my attention to a series of three posts on a Chinese website: here, and here, and here. The posts are apparently in Han Chinese (not one of my languages), but Google translates.

The posts, by Dr Yaoqiu Kuang, a professor at the State Key Laboratory of Isotope Geochemistry of the Chinese Academy of Sciences, draw attention to imagery from NASA’s Terra satellite which indicate a smoke plume rising from the Beshtash Valley (about 30 kilometres SSE of the town of Talas in Kyrgyzstan), and also thermal emission from the source location of the smoke. The Aqua satellite, which obtained imagery of the same area a few hours later, showed no such smoke plume.

Whilst the area is fairly densely covered in trees, it is at a high elevation and at this time of year covered in snow, so that a forest fire is contra-indicated. Dr Kuang also indicates evidence for rapid snow melting causing the river in the valley to rise.

The locations of Talas and the Beshtash Valley are shown in the graphic below, and can be seen to be fairly close to the termination of the hypothetical 460-knot northern path I have presented earlier in this post.


A web search from here in my apartment far away in Wellington, New Zealand, fails to indicate any further information with respect to the above suggestion. Perhaps someone has already gone to take a look on the ground and found no evidence of a jetliner crash. If this has not yet been done, given the amount of time, effort and money being spent on scouring the Indian Ocean it would seem to be a sensible step to go and take a look in the Beshtash Valley.

I’d invite readers to alert the mass media to the potential for a scoop as being perhaps the quickest way to get a reconnaissance accomplished. Unfortunately I can proffer no advice with regard to the availability of snowmobiles for hire in Kyrgyzstan.


A Testable Hypothesis for the Flight Path of MH370

A Testable Hypothesis for the Flight Path of MH370

Duncan Steel, 2014 April 06.


The present post concerns the flight of MH370, but has nothing directly to do with the Inmarsat-3F1 satellite. It (this post) is not part of any logical sequence following from my earlier posts on this sad topic. It introduces a new idea which is not dependent on anything I have written here before. It involves a testable hypothesis for the flight path of MH370.

I have not seen this suggested anywhere else before, but I would be surprised if it had not been discussed and debated elsewhere, because it’s so obvious. I am kicking myself that I did not think of it weeks ago.

First, please be clear that in science a ‘hypothesis’ is not what people usually think that word to mean. In the Popperian philosophy of science progress is made by proposing testable hypotheses which are falsifiable; that is, capable of being demonstrated to be wrong. One can never prove anything in science, one can only say that it has not yet been shown to be incorrect. We are fairly sure that the ‘law’ of the conservation of momentum is correct, but only one replicable experiment showing that it is not quite true that momentum is always conserved is needed to bring it down. Thus, for example, Newton’s Law of Gravity seemed fine for almost 200 years, but was then superseded by Einstein’s General Theory of Relativity. That is, the Newtonian formula for gravity is a really good approximation, but is not absolutely precise, and its failing is most apparent in the case of large masses and small separations.

My hypothesis, then, should not be imagined to be something I ‘believe’. It is a suggestion. If it is correct then trying to test it will lead us to the aircraft, perhaps. If it is incorrect then it represents a matter that we do not need to worry about again, in this context.



About an hour before starting to type this I responded to two comments from Brian Anderson and Mark Poidvin. In replying to Mark’s enquiry I went off on a bit of a tangent from the specific matter in hand, and wrote the following:

[begin quote from me]

Although I have not looked hard, I have seen no reliable statements with respect to the operations of the autopilot on MH370 (and also on other B777s?). By that, I mean statements from the people who made it, designed it, wrote the software code and so on. I have heard directly from airline captains/pilots with regard to how they use the autopilot, and that’s been instructive to me. But what I mean here is a set of definitive statements from the autopilot experts who could say how their system would operate in a default mode subject to certain assumptions. Things like: “Imagine the autopilot had been set to fly at speed X at altitude Y along a great circle path to waypoint Z. Now, if the aircraft reaches point Z and there has been no further input (i.e. crew are incapacitated) then what does the autopilot do?” One presumes that the answer is not “Tip the nose downwards and crash into the ground*”, so what is the default? Fly ever onwards along the same bearing with the same speed and altitude until the fuel runs out?

*”Tip the nose downwards and crash into the ground” is in fact the default autopilot command for the Global Hawk UAV (Northrop Grumman RQ-4), should its operators lose contact with it. I am not joking, and it has already occurred at least once  (that was 1999; I believe that the loss at the end of 2001 was perhaps similar).

[end quote from me]

Then I turned to Brian’s comment. I note in particular that Brian wrote:

“My inclination is that the pilot flew standard waypoints to get to this position. The times and speeds seem to match pretty well, and I think the locations and directions do not violate the constraints of LOS in Duncan’s table.”

To this I replied:

[begin quote from me]

“I just posted a reply saying that I have seen little/nothing about the default mode(s) for the autopilot if the crew is incapacitated. Perhaps it heads for the nearest (or some other consideration giving the decision) waypoint, and after that skips on to other waypoints in accord with (a) The distance(s) to them; and (b) Its heading as it reaches them? That is, it would not make a 150-degree turn to go to a waypoint that is 100 nm away when it could make a 20-degree turn to go on to a waypoint that is 120 nm away. And then on it goes… If this were the case then one could definitely solve for the route of the aircraft! (In physics/maths this might be termed a Markov Chain analysis.)

To me, it would make a lot of sense if that were what defined the algorithm in the autopilot code.

Any autopilot experts out there? I do not mean pilots (users of autopilots), necessarily. I mean people who actually design autopilots and know what the software would be designed to do in the absence of any human input on the flights and a waypoint (the last one humanly-entered during the flight) being reached. On the other hand, perhaps airliner pilots get detailed instructions on what the autopilots would do under different circumstances? Me being me, if I were training to be a commercial pilot I would keep asking questions until I was satisfied that I knew what the autopilot defaults were.”

[end quote from me]

Brian’s sentence that read “My inclination is that the pilot flew standard waypoints to get to this position” prompted a Eureka! moment for me. Perhaps. I just thought: what if the autopilot flew standard waypoints?


Suggested scenario

It is known that MH370 made a turn to port/westwards soon after the last secondary radar contact at 17:21, if indeed it was just west of the Malay Peninsula at 18:02 and 18:22 (last military radar contact). Various people, including experienced airline pilots, have suggested possible scenarios involving some emergency in the aircraft and in particular in the cockpit, maybe a fire. Such pilots have said that they would hit the autopilot so that the autopilot flies the aircraft whilst they concentrate on saving themselves, the passengers and crew, as it were. I am not using the correct aviation technical terms there I am sure, but I would hope that readers will understand what I am saying.

In my scenario (part of my hypothesis) the pilots do not save the aircraft, as such. They threw the aircraft heading westwards with an emergency landing in mind (as has been suggested by other pilots as being the thing that they would do in the above emergency circumstance) but were incapacitated before they could execute such a landing. This would have left the aircraft under the control of the autopilot, with no further human intervention possible, assuming that all passengers were also incapacitated by whatever catastrophe had occurred on board.

When I was a child I read a comic every week which had a page headed What would YOU do? and beneath that some dramatic scenario was outlined and pictured. The point was that you had to come up with a viable solution to the quandary posed.

And so now I ask the autopilot: What would you do? In the awful circumstances of the scenario I have posited above, what would the autopilot do?


What did the autopilot do?

In my analysis in all these postings so far, once I turned my attention to the aircraft (rather than simply the satellite) I have been assuming that the aircraft would end up on a long great circle route according to what was entered in the autopilot; for example, heading from wherever it was after the pilots were incapacitated towards the South Pole, never reaching that destination because the aircraft runs out of fuel. I stated this as being an assumption in various places, I think. I was also assuming that during the part of its flight over the Malay Peninsula and around the Malacca Strait it was still under human control. I think those assumptions may have been incorrect.

Under the hypothesis I am proposing here, the pilots were incapacitated (or at least took no further part in flying the aircraft) within a short time after 17:21. That ‘short time’ may have been 10 or 15 minutes. After that, and until it crashed, the autopilot was flying the aircraft.

So, what did the autopilot do? Well, I don’t know for sure, or even vaguely, and that is why I posed the questions I did in my replies to Mark and Brian, and said that I’d like to know from an autopilot expert just what the autopilot on this B777 would do.

Wikipedia, the font of all knowledge (perhaps), says this about autopilots:

The hardware of an autopilot varies from implementation to implementation, but is generally designed with redundancy and reliability as foremost considerations. For example, the Rockwell Collins AFDS-770 Autopilot Flight Director System used on the Boeing 777 uses triplicated FCP-2002 microprocessors which have been formally verified and are fabricated in a radiation resistant process.

Software and hardware in an autopilot is tightly controlled, and extensive test procedures are put in place.

So with that in mind I tried instead putting myself in the place of the person designing the autopilot software. It’s like when you lose a horse and you don’t know where to look; what you do is you say to yourself: “Well, if I were that horse, where would I go?” and the answer might be “That shady spot down by the river to get some water and have a nap out of the sun before that bastard tries to saddle me up again.”

What I would do if I were the autopilot software engineer is I would think to myself: “well, the human pilot last inserted instructions to head to this waypoint, which implies this direction/bearing, and so I will assume that he wants to keep heading that general way/that bearing despite the fact that he’s reading the newspaper and forgotten to update the autopilot to the next waypoint.” I would also assume that the human pilot wanted to maintain the same speed, and the same altitude, unless the autopilot were told otherwise.

In an emergency the pilots might have entered VPL as the waypoint to head towards as they (or the autopilot) turned port/westwards soon after 17:21, and the precise choice might be important in the testing of this hypothesis and also finding the aircraft (see below). All aviation waypoints in Malaysia are listed here, and the same website also gives waypoints in other countries. Soon after passing IGARI MH370 might first have headed to VPL, or TASEK, or DALAN, or GOMAT, or GUNIP, I don’t know.

Once it started on the above process – going to the indicated waypoint and then, as it approached it, by default automatically updating the next waypoint to be that which is indicated by some formula combining both the bearing and the distance – it would continue until its fuel was exhausted and it crashed: perhaps in the southern Indian Ocean, I know not.

I would presume that if it did take such a southerly path then there would be few waypoints over the ocean and so, once it left the region just west of Sumatra, if it turned south its next waypoint may even have been Kerguelen.

On the other hand, if the sequence of waypoints in the Malacca Strait and west of there led to it heading across the Andaman Sea and then the Bay of Bengal then the higher spatial density of aviation waypoints would lead to much more frequent changes in heading and a greatly convoluted path, perhaps. Then again, maybe the autopilot software code prohibits the choosing of a next waypoint that is less than some set distance away from where you are now, because the whole idea of the autopilot is that the aircraft flies on a smooth, near-direct path with minimal human intervention.

Above I wrote “see below.” I would anticipate that the actual route the aircraft took, if this hypothesis is correct, will be contingent upon the first waypoint entered (and indeed the bearing the aircraft was on as it approached that waypoint, because that would affect the next waypoint that the autopilot might choose). To repeat: the actual route will be contingent on that first waypoint and bearing, just as the evolution of all life on Earth over the past 65 million years has been contingent upon an asteroid striking our planet way back then and not just missing it; and your own existence is contingent on your great-grandfather having missed his train to work one day and consequently he met your great-grandmother on the next scheduled departure.


Testing this hypothesis

Two ways of testing this hypothesis come to mind.

(1)    Work through the autopilot algorithm and the data it has associated with it pertaining to waypoints, for a variety of start conditions (first post-emergency waypoint and heading as it approaches it); and/or

(2)    Take an identically-equipped B777 to waypoint IGARI heading NNE, turn it sharp left, engage the autopilot and enter a waypoint (e.g. VPL), and see what happens, although one might not want (or need) to fly it to fuel exhaustion.

A complicating factor might be that the pilots had entered as the next location for which to head a geographical latitude and longitude rather than a standard aviation waypoint. However, especially considering comments and messages received from experienced airline pilots, in an emergency it is more likely that a familiar waypoint (like VPL) would have been entered.



I have proposed a testable hypothesis for the route actually followed by MH370 based on a scenario in which all on board were incapacitated soon after the aircraft passed waypoint IGARI, with the aircraft being left flying under control of its autopilot and heading westwards towards some waypoint around the Malay Peninsula. A core feature of this hypothesis is that the path taken thereafter by the aircraft was defined by the autopilot software code making decisions on successive waypoints based on built-in presumptions regarding the headings to be taken, the choice of those successive waypoints being dependent on the bearing and distance of the next waypoint from the waypoint that the aircraft is approaching; that is, the autopilot, in the absence of human intervention, makes its own choice as to the direction to fly the aircraft next based on various criteria defined by the software algorithm and the input data (the array of aviation waypoints).

This hypothesis can be tested by flying an identically-equipped aircraft along the same initial route as MH370 and then letting the autopilot take total control soon after waypoint IGARI is reached, perhaps after steering the aircraft hard to port.

This hypothesis can also be tested by simulating the autopilot’s issuance of ever-changing path instructions using the actual autopilot code.

Members of the public with suitable coding skills could also try simulating the autopilot by writing programs that make decisions regarding the choice of ‘next waypoints’, inducting the global array of standard aviation waypoints (all available on the internet), and flying their simulant MH370s through that array using a range of start conditions (the initial waypoint chosen, and the heading on which you approach it). Think of it as being similar to a bagatelle, pinball or pachinko game.


Information Pertaining to the Search for MH370

Information Pertaining to the
Search for MH370

Duncan Steel, 2014 April 06.

In this post I present various pieces of information, and in particular graphics and maps, intended to assist in the search for the path taken by MH370 and so its final resting place.

In my last post  I showed the locations of the ping rings based on the back-engineering of the Google Earth graphic, and other materials, by GlobusMax. Here I present other graphics that might assist people involved or interested in the search.

Let me first summarise what is required, based on the best-available (to my knowledge) information.

(1)    The final radar detection of MH370 was at 18:22 UTC on 2014/03/07, at which time the aircraft was located near the aviation waypoint MEKAR, about 200 nautical miles from Butterworth on a bearing of 295 degrees from the military radar there. I have adopted a geographical location of latitude 6.50 degrees North, longitude 96.5 degrees East for that final radar-detected point.

(2)    All LOS speeds after that time as measured through Doppler shifts in the ping signals received back by the Inmarsat-3F1 satellite appear to have been characteristic of the aircraft moving away from the satellite. The decomposition of the Burst Frequency Offset graph from Inmarsat has been accomplished by Mike Exner, resulting in values for the LOS speed satellite to aircraft as shown in the table below. I have previously shown these same data, but with the times of the pings in minutes and the speeds in km/sec. For your convenience, here they are in hours and minutes (UTC) and knots.

Time (UTC)

Line-of-Sight Speed (knots)













(3)    The ‘ping rings’ represent a range of possible positions for the aircraft at the times of the pings. That at 18:29 is outside of those at 19:40 and 20:40, but inside those from 21:40 onwards.

The requirement for any plausible path taken by MH370 must therefore encompass all of the following:

(a)    A start at near 06.50 N, 96.5 E at 18:22 UTC

(b)   The direction of motion of the aircraft at the times of all pings being away from the satellite and producing LOS speeds in accord with the above table.

(c)    Movement inwards from the 18:29 ping ring and then consistent movement outwards thereafter, crossing the rings at the correct times.

Note that this means that despite MH370 apparently moving away from the satellite at 18:29, by 19:40 in had shifted rather closer to the satellite and was again moving away from it so as to cross the 19:40 ping ring from the inside.


Views from the STK 3D window

People have asked for some cities to be inserted as reference points, so here they are: x_3D_1

Close-up of one possibility for the initial part of the flight (orange path). The trajectory after waypoint IGARI is not securely known. The location at 18:22 UTC (final radar detection) is labelled as ‘P_18_22’. x_3D_2

A wider view showing the ping rings: x_3D_3

Southerly parts of the ping rings: x_3D_4

Northerly parts of the ping rings: x_3D_5

Relevant parts of the globe with lines of latitude and longitude added (in ten-degree steps): x_3D_6

Equal-distance rings centred on P_18_22 added in bright green, at distances from 1,000 to 3,500 nautical miles in steps of 500 nautical miles: x_3D_7

Close-up of the southerly portion of the possible paths of MH370 with bright green range rings: x_3D_8

Close-up of the northerly portion of the possible paths of MH370 with bright green range rings:  x_3D_9


Views from the STK 2D window (i.e. maps)

Detail of the initial (possible) path of MH370:  x_2D_1

Map of the general SE Asia region with ping rings: x_2D_3

General map of the full limit of possible locations for MH370: x_2D_4

Southern region of possible locations for MH370: x_2D_5

Northern region of possible locations: x_2D_6

Wide-area map showing range rings centred on P_18:22: x_2D_7

Detailed map showing range rings, southerly part: x_2D_8

Detailed map showing range rings, northerly part: x_2D_9

Someone complained to me that the images were too small to see any detail. To make any image appear larger, just left-click on it. You can then right-click on it to save it.

The 2D maps I have shown here are the full spatial resolution that I produced from STK, although stored as 8-bit PNG files rather than the original bitmaps.  The 3D window views were also stored as 8-bit PNG images, converted from bitmaps, although the original bitmaps had pixel scales four times larger (i.e. I reduced them from 6,000 pixels wide to 1,500 pixels wide).


Ping Rings from the Inmarsat-3F1 Data

Ping Rings from the Inmarsat-3F1 Data

Duncan Steel, 2014 April 05.

Most readers will be aware that there is, shall we say, considerable unhappiness amongst many of us concerned about the apparent loss of MH370 with regard to the lack of publicly-available data from the Inmarsat-3F1 satellite. I have discussed this in previous posts, and in amongst the comments and emails received many people have expressed their outrage at the situation. If the data were available then a crowdsourced attack upon the problem of narrowing down the search region would be feasible, and recent history has shown how powerful crowdsourcing can be: there are many people out there with useful skills who could work together over the internet so as to generate perhaps useful outcomes.

However, it appears that the powers-that-be prefer to preserve their power, to the detriment of the search programs and also the suffering friends and families of the passengers and crew, and others. I would hope that this will backfire in the faces of the culprits; to the best of my knowledge, the major offender is the UK Air Accident Investigation Branch (AAIB) of the Department for Transport.

The data required are quite simple: (a) The measured time delays (around 120 milliseconds for each leg) from each successful ping between Inmarsat-3F1 and MH370; and (b) The measured Doppler shifts in the pings, which would render the satellite-to-aircraft line-of-sight speed at the time of each ping. There are twelve pairs of such ping data. Four of those pertain to early in the flight. The other eight cover the time after MH370 disappeared; three are in quick succession (perhaps indicating that MH370 was in trouble and initiating pings itself) so in essence there are six ping times involved.

In a recent post I gave a decomposition of the Burst Frequency Offsets (BFOs) due to Mike Exner, which rendered those Doppler shifts; that is, they were reverse-engineered from an Inmarsat graph, with some input from Ari Schulman and myself. One other person has carried out a verification of that process (Rob Matson). However, there is still an ongoing argument/discussion as to whether the decomposition is correct; plus there are some assumptions that must be made in the process. Obviously if the original data were made available, rather than readings off a (rather poor) graph, things would be better.

Amongst the comments after a couple of posts I have noted that the other type of data, the ping time delays, have now also been reverse-engineered by a person with an online name of GlobusMax. His relevant posts are here and here. His work and brief write-ups are exemplary. When there is so much junk on the internet, it is heartening to see things like this being done. I most strongly recommend that people take a look at his analysis and conclusions.

For verification purposes, and assuming that the Inmarsat data is not going to be made available any time soon, I am going to assume that GlobusMax’s values are ‘correct’. The essence is that he gives a set of ranges from the satellite to the aircraft at the six ping times, with a range of best-fit values. I have interpolated his values to give the ranges as in the second column of the following table.

Time UTC

Line-of-sight range  from aircraft to satellite (km)

Ping time delay

Elevation angle from aircraft to satellite (degrees)

Radius of range ring on Earth’s surface (nautical miles)
































For each of those line-of-sight ranges I have calculated:

  • A ping time delay (just the range divided by the speed of light);
  • An elevation angle from aircraft to satellite, assuming an Earth radius of 6378.137 km (i.e. the equatorial radius); and
  • After inserting those elevation angles into my STK scenario I placed range rings with radii as given in the final column above.

Note, in connection with this final step:

(a) The centres of those rings are the sub-satellite points at each of the times stated, and of course the satellite moves (mostly north-south) across this set of times; and

(b) The process I followed was actually to have cones of the appropriate angle projected down from the satellite for each of the ping times and I then placed the range rings by eye at the places where those cones reached the Earth’s surface. This may have caused the radii in that last column to be out by a few kilometres, but I needed to do things this way for reasons of personal time and energy constraints. Sub-optimal, but that’s life.

Before we go further, note the order of the values in the final column in the above table. After 18:29 the aircraft moved inwards in that it shifted to a lesser range from the satellite (but also note, from earlier posts, that the Doppler data indicate that at 18:25, 18:27 and 18:29 the aircraft was moving away from the satellite, although at a rapidly-reducing rate; that is, it appears that it was quickly turning at those times, forcing me to put tight aircraft turns in my recent simulations). But then, from 19:40 onwards, the aircraft is consistently moving away from the satellite (the ranges are all increasing); and the Doppler is always in accord with this (moving away from the satellite and indeed increasing its recessional line-of-sight speed).

Note also that the satellite-aircraft ranges above are expressed in kilometres, whilst the ping ring radii are in nautical miles (so as to facilitate speed calculations in knots).

I had hoped to be able to put some possible aircraft tracks into this post but this has proved too time-consuming to get done overnight, and so I will limit myself now to publishing images below that show the ping rings, followed by a few pertinent comments.

First, two views from the STK 3D window:

PR 3D b

Next is a side-on view which I think may help people to understand what a ping really actually represents.

PR side on

Now I shift into the 2D STK window (i.e. ‘maps’). Here is a large view that covers all feasible end points for MH370. Note that in this projection the ping rings are by no means circular: all maps are distorted in one way or another, and this projection keeps all meridians (lines of longitude) equally spaced regardless of the latitude. Note also the black dots showing the sub-satellite points at the different times: yes, the satellite moves/drifts.

Ping Rings 2D

Finally, here is a close-up covering the area of the early part of the flight of MH370, with a good margin around, just in case it is useful to people thinking about a path taken that did not go very far.

PR 2D b

Now, some concluding comments.

Having these range rings early on would have helped to stop some wild speculation, and also suggested paths that can now be seen to be non-viable with fuller information (assuming that these ping rings are correct).

For example, consider the final two range rings, at 22:40 and 00:11 UTC. They are not quite concentric, but for present purposes it is adequate to assume that they are. Their radii are 2206 and 2652 nautical miles. The difference between those figures is 446 nautical miles, and the aircraft took 91 minutes to fly between those rings. That means that the lowest speed it could have had at that time would have been near 294 knots. For that to be the case, it would have needed to be flying such that it was taking the shortest route between each ring (i.e. flying perpendicular to each).

At any other angle the speed would have been higher. Taking into account the approximations made, one might take 290-300 knots as being the minimum speed in the latter part (the last 90 minutes or so) of the flight. Following from previous posts and considerations, it is perhaps a valid assumption that the aircraft was being flown for the last several hours of its flight by the autopilot; and at a constant speed, which we have seen was at least 290-300 knots.

This is itself imposes useful constraints on possible paths. If we were to assume that it was following a great circle route, then the geometry for crossing the last two range rings (i.e. the feasible angles for crossing them at any assumed constant speed above the minimum derived above) limits the overall path.

Similarly the other pairs of range rings impose limitations. The pair of 21:40 and 22:40 are 241 nautical miles apart, and so the minimum speed between them was 241 knots; but the previously-determined minimum of 290-300 knots results in a requirement that the angle at which those two rings were crossed was greater than a certain value (i.e. the aircraft could not have crossed between those two rings at 90 degrees, assuming a constant aircraft speed across the final hours of the flight).

From this one gets the idea of a path which, compared to the ping rings, is gradually turning (but is also a great circle from its start point) so as to cut the rings at increasing angles, culminating in the largest angle being at the outermost rings. This would also be in accord with the Doppler evidence: the speed away from the satellite keeps increasing.

Anyone interested: get out a pencil and paper, and try sketching possibilities! If you print out the images above it might assist: but remember that the 2D map is distorted (as can be seen from the great circle paths in previous posts – effectively straight paths across the curved Earth – being bent in those 2D maps).

I will have more to write about interpreting these ping/range rings, and the constraints they impose, later. Maybe within 24 hours.


Links to Previous Posts on the Inmarsat-3F1/MH370 Ping Analysis Saga

Links to Previous Posts on the
Ping Analysis Saga

Duncan Steel, 2014 April 05.

This set of posts from me has become somewhat complicated to navigate. To date I have put up twelve posts about the subject given in the title above.

I started out on this investigation simply because I realised that in their initial analysis of the ping time delays between their satellite and the missing airliner the Inmarsat engineers had assumed the satellite to be stationary above the equator at an altitude of 35,800 km, and that is not correct, with the satellite’s movement (its changing position and drift velocity) varying significantly across the time frame of the flight of MH370. Because of this my first six posts were concerned only with the importance of the Inmarsat-3F1 satellite’s orbit (or, more correctly, its ephemeris) across the time of the flight (between outside limits of, say, 16:30 UTC on 2014/03/07 and 01:30 UTC on 2014/03/08).

It was only with the seventh post that I turned attention to trying to narrow down possible paths for the aircraft (i.e. the flight of MH370) with the obvious eventual aim of restricting possible final locations for that aircraft.

Unfortunately quite a few correspondents have seen only the later posts, and assumed that the analysis/simulation that I have conducted is wrong because (they imagine) I have not allowed for the satellite’s motion, and that is not the case; as I wrote above, this was the very consideration that started me on this investigation.

That does not mean that I imagine my analysis to be faultless, by any means; but I am doing the best as I can as an individual with access only to certain public information.

To make things easier for people to navigate around this series, hereunder I am making available clickable links to each of the posts.

Another notable point is as follows. Much useful information has been made available from various commentators in messages that follow these posts; but each post has its own set of comments and in many cases those comments refer more closely to matters covered in other posts! In fact, there is some important information in comments which appear at the bottom of my About Me and Contact Information page. (Advance apologies that the first thing you see if you go there is my ugly face.) Therefore I would just say here that readers wishing to access all the information/comments need to check after each of the posts, plus that page mentioned in the preceding sentence.

Post       Date                        Title and link

01           March 23             Some Comments on the Final Ping of MH370 by the Inmarsat-3F1 Satellite

02           March 24             The Locations of Inmarsat-3F1 when Pinging MH370

03           March 25             Representations of the MH370 Ping Rings in the Media

04           March 26             Positions and Velocities of Inmarsat-3F1 During the Flight of MH370

05           March 27             Difference Between Inmarsat-3F1 Equal-Elevation-Angle Arcs and the Initially-Modelled Geostationary Satellite

06           March 28             The Range of Equal-Time-Delay Ping Rings from Inmarsat-3F1

07           March 30             Possible Flight Paths of MH370

08           March 30             Revised Possible Flight Paths of MH370

09           March 31             Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

10           April 01                 Revised Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

11           April 02                 The Inmarsat-3F1 Doppler Data Do Not Exclude a Northerly Flight Path for MH370

12           April 03                 Background Information on the Pinging of MH370 by Inmarsat-3F1

Apart from the above posts on my/this personal website I have also made a number of comments in the following discussion threads, all hosted at TMF Associates (Menlo Park, California), and there are many other useful contributions there from knowledgeable people:

Understanding “satellite pings” …

Locating “satellite pings”…

Understanding the “satellite ping” conclusion…


Background Information on the Pinging of MH370 by Inmarsat-3F1

Background Information on the Pinging of MH370 by Inmarsat-3F1

Duncan Steel, 2014 April 03. duncansteel.com

In this post I am just giving some information that followers of this saga might/need want to know.

The Inmarsat briefing to the AAIB thence the Malaysian Government 

In a comment following a post of March 23rd  a correspondent ‘Andy’ wrote, several days later (2014/03/29 at  2:03 am), to say the following : 

There was a PDF document on the Inmarsat site which gave some details of the work involving the doppler effect: 


It does not appear to be there any longer, but the document is present in internet archives. 

Andy sent me the PDF. I present it below as images (screen grabs from the PDF). The second, third and fourth pages are the pages that formed the ‘Annex I’ issued by the Malaysian Government on March 25th (see also this web page). The cover sheet (page 1) shows that the origination of those three pages was a briefing by Inmarsat to the UK AAIB. Nothing new there, but I put it in for completeness. p1 p2 p3 p4 Everyone will surely have seen the above three images previously; but likely not the first of the four. 

Deciphering the Burst Frequency Offset (BFO) graph to get Doppler shifts  

The three contributions to the BFO are explained in p.2 above. The idea here is that component D3 can be calculated, knowing the satellite ephemeris and the location of the ground station; D2 is derived from the BFOs (i.e. is time-dependent); and values of D1 can then be inserted and tested against possible paths and speeds of the aircraft. The fact that the initial path and speed of the aircraft is known (including being stationary on the ramp at KL) allows a calibration to be achieved.

Mike Exner, with some assistance from Ari Schulman, has deciphered all this and so derived time-dependent values for the Total Doppler, as in the first diagram below. I calculated the LOS speeds (hence time-dependent Doppler shifts D3) between the satellite and the Perth ground station and supplied those to Mike for incorporation in his analysis.

From the Total Doppler Mike pulled out just the L band Doppler (red dots in the first diagram) as shown in the second diagram below. From those Doppler shifts Mike calculated speeds of the aircraft relative to the sub-satellite point (i.e. Range-Rates in usual ground-based radar observations) and based on an assumption that the elevation angle from the aircraft to the satellite was 40 degrees. That is what is shown in the third diagram below.

At the time he was doing these calculations shortly before going on vacation, Mike only had that angle (40 degrees: the ping ring elevation at 00:11 UTC) to use. We now have others (which I will be posting on this webpage in a while). Anyone with a calculator should be able to derive the aircraft speeds relative to the sub-satellite point for any other elevation angle by back-calculating, using an assumed altitude for the satellite (35,790 km is near enough).

Mike inserted comments regarding his method and assumptions into each diagram. His time frame was MYT = UTC + 8 hours. Following are the three pertinent graphs that result; Mike Exner specifically asked me to make these public here. 

All_Doppler_2014-04-02 L-band_Doppler_2014-04-02 MH370_Radial_Velocity_2014-04-02 

Please, I am simply unable to explain anything further about these plots. If you don’t understand them, apologies. Let me close by repeating the line-of-sight speeds that I gave (based on Mike Exner’s analysis) in my previous post. In my own analysis, this is all I need.

Time (minutes)

LOS Speed (km/sec)


























The Inmarsat-3F1 Doppler Data Do Not Exclude a Northerly Flight Path for MH370

The Inmarsat-3F1 Doppler Data Do Not Exclude a Northerly Flight Path for MH370

Duncan Steel, 2014 April 02.

“It is possible to disprove a theory, but never to prove one; no matter how often a theory has given a correct prediction in the past, a single (repeatable) counterexample invalidates that particular theory… a documented counterexample is now available to disprove the assertions of many writers…”                    Luis Alvarez (1976)


The search for the missing Malaysia Airlines flight MH370 has concentrated upon the Indian Ocean due to an assertion by Inmarsat personnel that the Doppler data could only be fitted by a southerly route of the aircraft. The announcement of this was made by the Malaysian Government on 24th March, with it coming an expression of certainty that the aircraft must have crashed unseen into the Indian Ocean.

I assert here that the assertion by Inmarsat is wrong. I do not assert that the aircraft definitely took a northerly route. However, I present evidence hereunder that a northerly route cannot be excluded on the basis of the satellite data, and that a northerly track remains viable in terms of what the satellite data can tell us.

Note that I make this assertion despite a lack of access to certain data that Inmarsat will only give to the “proper authorities.” My only sources of information with regard to the satellite data are:

(a)    The graphic/map issued by the Malaysian Government on 15th March, showing the ‘ping ring’ with elevation angle from aircraft to satellite of 40 degrees; and

(b)   The following graph, drawn up by Inmarsat and issued by the Malaysian Government on 24th March.


I have made various comments on that graph in different places, for example amongst my posts on this website itself and also at the TMF Associates blog site on this matter.

For background on my investigation and likely answers to most of your questions please read the previous posts I have published here. This is the eleventh post in a series. I regret that I cannot respond to queries and questions that cover things I have already discussed in these posts. Please also check the many comments and my responses to them after each of the posts.


The method I have applied here is precisely the same as that employed in previous posts, in particular this one and that one. (I caution again, though: read all of this sequence of posts from the beginning!)

Here is a sample simulant aircraft track:


In my preceding post I had six aircraft following common routes at the same speeds until they diverged following the sixth line in the table above. After that they continued on southerly routes across the Indian Ocean at assumed speeds of 200, 250, 300, 350, 400 and 450 knots. The simulant aircraft in the table above is that which flies at 300 knots; that 300 figure is replaced by the other considered speeds in order to get different paths.

In that analysis I included a tight turn over the northern entrance to the Malacca Strait, about 320 km to the NW of Penang, so as to fit against: (i) The last known (to me) radar detection of MH370; and (ii) The apparent turn indicated by the Doppler data (as in the Burst Frequency Offset graph shown above).

After that tight turn I had all my six simulants taking shallower turns to port/left and continuing at their own speeds south to the equator following identical routes. At that point (equator crossing) I had them follow different routes which were defined by being great circles from that point on the equator to the locations (latitude and longitude) at which they would cross the ‘ping equal time delay ring’ at 00:11 UTC, as indicated by the satellite ping data. Because each simulant aircraft has its own constant speed, this led to a fan of possible paths.

This was in my previous post, for southerly routes. Now I am interested in investigating possible northerly routes. What I have done here is as follows. At the exit from the tight turn described above (precisely, at latitude 07.25 degrees North, longitude 97.5 degrees East) I have my six simulant aircraft continuing north along diverging paths which are again defined by the requirement that they reach the ‘ping equal time delay ring’ at 00:11 UTC.

Tracks of the six northerly simulant aircraft

Here is a map from the STK scenario 2D window:


Here is a view from the STK scenario 3D window:


As might have been anticipated, there is again a fan of paths starting from the 200 knots track at furthest east and culminating in the 450 knots track at furthest west.

All simulant flights I put at a constant altitude of 35,000 feet (5.79 nm) apart from the initial take-off and climb. This does not significantly affect the results obtained here in terms of paths, line-of-sight (LOS) speed calculations and so on, although in the real world obviously the altitude does affect the aircraft through fuel consumption rates and so on.

Graphs of line-of-sight speeds satellite to aircraft

These six simulant aircraft render line-of-sight speeds (which easily can be converted into Doppler shifts) which vary during the simulated flights as shown in the plots below. These are of the same form as those that I published in my preceding post and so I will not detail again what they depict.

A reminder: the black diamond-shaped symbols across the top of each plot indicates the times at which data are available from successful pings of MH370 via Inmarsat-3F1; that is, they are the times at which measurements were available and so plotted in the very first graph in this post (i.e. the Inmarsat-derived ‘Burst Frequency Offset’ graph).








Negation of Inmarsat’s argument

Because Inmarsat has refused to make the basic data (i.e. ping time delays and Doppler shifts directly) available to the public I must go on various open statements made by the company, either directly or through the AAIB and thence the Malaysian Government.

What has been stated is that for all pings the aircraft (i.e. flight MH370) was moving away from the satellite. What this means is that I require the LOS speeds between satellite and aircraft as shown in the six plots above to be positive at all times at which data are available (i.e. at the times indicated by the black diamonds).

Looking at those plots above, one can see that this condition is met by the first four speeds (200, 250, 300 and 350 knots), but not by the final speed (450 knots); and at 400 knots the LOS speed at 1180 minutes is marginally negative, enabling one to understand that if that speed had instead been set as, say, 380 knots then a positive LOS speed would have resulted at that time.

Based simply on that inspection of the plots one can therefore say that:

(a)    A northerly route is possible, and so Inmarsat’s assertion is negated/falsified; and

(b)   The speed was likely below 380 knots.

However, please note clearly that the second statement there is based on a particular routing prior to the divergence point at latitude 07.25 degrees North, longitude 97.5 degrees East. I could easily invent other paths that do not contravene the apparent facts of the initial part of the flight and derive some different limit than 380 knots. My point here, though, is that Inmarsat’s assertion that a northern route was not possible or likely was based on a model predicated on an aircraft speed of 450 knots, as shown above the Burst Frequency Offset (BFO) graph at the start of this post; and I believe that assertion is incorrect.

Actual values of Doppler shifts

Inmarsat has been less than forthcoming with the data obtained from the pings from its satellite; in fact it has been outright obstructive, which is inexcusable in a situation such as this.

In view of the above it has been difficult to derive a solid interpretation of what the Burst Frequency Offsets (BFOs) mean in terms of the more usual expression of a Doppler shift, which of course translates directly into a LOS speed.

I am indebted to Michael Exner and Ari Schulman for the following table of values for the LOS speed (or range-rate) for each of the times at which ping data are available, which they have derived using their own relevant expertise. I assume validity for the figures given; I also assume responsibility should they be wrong, because of caveat emptor considerations.


LOS Speed

























The data in that table can now be plotted in a graph, and overlaid with my calculated LOS values (from the preceding six graphs). Here is the result:


First, I am not much concerned about the measured Doppler shifts underlying my calculated LOS speeds at the start of the flight. That initial part of the flight I entered in my STK scenario just with a few clicks on different positions. As I wrote in earlier posts here, the early part of the flight is not really of great concern to me. By altering the trajectories in my simulation to be slightly nearer north than NE the calculated LOS speeds will drop and come into accord with the actual measurements, I believe. Also, it has been pointed out to me by Jeffrey Wise that a pretty good path for MH370 is known from military radar in this pre-disappearance phase of the flight, with transits from near the waypoint IGARI to VAMPI to GIVAL and then loss of known path somewhere between there and IGREX. I can fix all these things once I have had some sleep!

One important part of such a revision of the early part of the actual flight MH370, however, will be as a check on the Doppler values. Note that both the Inmarsat models (vide the Burst Frequency Offset graph at the start of this post) underlie the measured BFOs.

Turning to the vital part of the above graph, that to the right of 1100 seconds (18:20 UTC), one can see that the measured Doppler shifts appear to be in close agreement with the red line, which pertains to the northern route at 250 knots.

This does NOT mean that MH370 travelled on this path, at this speed. It merely means that this northerly route (or something quite like it) at a relatively low speed is in accord with the information I have in hand.

As soon as I am able I will be repeating the above analysis (again) for:

(a)    These northerly routes with the early part of the flight (as known) properly entered into my STK scenario (although I do not expect this to affect the core conclusion of this post); and

(b)   The southerly routes, such as those I investigated in my last post, to see how they compare with the measured Doppler shifts I now have, given the above table of LOS speeds (range-rates) versus time courtesy Michael Exner and Ari Schulman.

The Bottom LineA northerly route for MH370 deep into central Asia cannot be excluded on the basis of the publicly-available Inmarsat-3F1 satellite data.


Revised Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

Revised Doppler Shifts between Inmarsat-3F1 and
Possible Flight Paths of MH370

Duncan Steel, 2014 April 01.

Continuing now on attempts to narrow down the path taken by (and thus the appropriate search area for) MH370. In my post yesterday I presented some preliminary results on the line-of-sight (LOS) speeds between the Inmarsat-3F1 satellite and possible paths of MH370 based on what I knew at that stage. Chong Meng pointed out something to me that I find to be important: all of my LOS speed plots showed monotonic increases from minute 1110 (18:30 UTC) onwards, yet the Inmarsat Burst Frequency Offset (BFO) graph – as below – shows a decrease between pings at 18:30 and 19:40. This is indicative of a change of path.


This observation has prompted me to try to derive plausible routes for my MH370 simulants which can mimic the features of the BFO graph. This is apparently a form of coding of LOS speeds and hence Doppler shifts, but as “BFO” says they are offset. It is not clear which datum in the measured BFOs corresponds with zero LOS speed. When the aircraft was at the gate at KL airport at 16:30, the BFO was 87 Hz, and at that time the LOS speed (due solely to the satellite motion) was about plus 0.021 km/sec. At take-off at 16:41 the BFO was about 125 Hz, but it is not clear whether this was whilst the aircraft was stopped or crawling along, or else actually during the take-off acceleration or initial ascent stage.

In the absence of definitive knowledge on my part, I will assume that the zero LOS speed value of the BFO is near 125 Hz. Larger values mean positive LOS speeds, and lower values imply negative LOS speeds (i.e. the aircraft reducing its range from the satellite).

Next I edited my paths within my STK scenario so as to attempt to mesh against the handful of LOS speed measurements represented in the above graph. For example, there is a small peak at 16:55 followed by a dip at 17:07; this could be explained by an alteration of the route between those times from one close to NE to a path slightly closer to due north.

A major feature to mimic in the graph above is the large value at about 18:27, followed by a rapid reduction in the BFO over the next two minutes. As the annotation on Inmarsat’s graph says, this is indicative of a possible turn. This would have occurred a few minutes after the last radar detection of MH370, the location of which I discussed in my preceding post. And so I have inserted a sharp turn there in my simulation, for all aircraft tracks.

Here is the set of input data for one of those tracks:


This is the simulant to be known as 300 knots. For all simulants (200, 250, 300, 350, 400 and 450 knots) I used precisely the same paths and speeds until about 18:22 UTC. At that time I had them start a downward spiral from 35,000 feet to 12,000 feet, and a change in speed from 400 knots (see above) to their respective speeds (200, 250, 300, 350, 400 and 450 knots) for the whole of the rest of their simulated flights.

Here is a close-up view of that early part of the tracks and the spiral from the STK 3D window:


As I have just noted, I had all simulants follow their respective speeds from the start of that downward spiral. However, I had them continue on identical routes until they reached the equator a while later; when they each reached the equator of course depended on their speeds.

Here is a view of their complete routes from the STK 3D window:


For completeness, here is the 2D map view:


As before, the orientations of the paths over the Indian Ocean were determined by requiring that the time that the paths crossed the ‘ping equal time delay arc’ (the bright green curve) be 00:11 UTC on 2014/03/08. This produces the fan of paths seen in the previous two graphics.

The point at which I made the routes diverge I fixed to be on the equator at longitude 95 degrees East. This was decided on simply by convenience and the need to have southerly tracks that might mesh against the BFO values.

Note that the ‘200 knot’ simulant did not have the capability to reach the ‘ping equal time delay arc’ by 00:11 UTC; it was just too slow, given the above divergence point on the equator. However, this is an unreasonably-low speed to employ anyway (cf. stall speed).

The above process resulted in LOS speed graphs as shown below. The black diamonds across the tops of each plot I have positioned so as to indicate the times at which measured BFOs are available (as in the Inmarsat graph at the beginning of this post).

For all these plots the early parts are identical, because I had the simulant flights following the same paths at the same speeds. The plots only differ to the right of minute 1102 (i.e. 18:22 UTC).

There is a small anomalous spike at minute 1015 (16:55 UTC), the time I introduced a small change in path as mentioned earlier. I believe that the spike is a numerical artefact produced by the STK engine through having that turn occur precisely then. Just smooth it out with your eyes.

If you compare each plot with the BFO graph you will find qualitative agreement, except in the middle of the plots for the lower speeds. The spike at near minute 1110 is slightly too far right (we require a large positive LOS speed followed by a precipitous drop) and the LOS speeds at minutes 1200-1260 (20:00-21:00 UTC) are near zero whereas the BFO plot indicates a LOS speed that is increasing. The requirement for a speed near zero at minute 1180 (19:40 UTC) followed by a monotonic increase thereafter forces me to think that the 400 knot speed appears to give the best fit to the BFO values. I can see why Inmarsat used 450 knots in the published BFO graph, but feel this is likely too high. As has been pointed out elsewhere, 400 knots seems an unreasonable speed for an altitude of 12,000 feet, but altering that altitude to 35,000 feet would not make significant difference in my STK simulation.

Regardless, there is more that could be done in terms of deciphering these plots, and I welcome input. In particular if anyone can interpret the Inmarsat BFO graph and translate it into a set of LOS speeds for the twelve instants in time indicated in that graph, that would be very helpful.

Finally, several people have asked me about the effect (in terms of LOS speed/Doppler shift) of a rapid decrease in altitude by the aircraft. As noted above, these simulant flights include a quick downward spiral. In order to illustrate the effect of this in terms of LOS speeds, right at the end of this post I include a plot for a simulant flight identical to the 400 knots simulant except that I keep the aircraft at 35,000 feet throughout (i.e. the path now involves a level circle rather than a downward spiral. I will leave the reader to spot the difference!









Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

Doppler Shifts between Inmarsat-3F1 and Possible Flight Paths of MH370

Duncan Steel, 2014 March 31.

My last post resulted in a set of possible flights paths for MH370 based on the last apparent radar detection and the satellite ‘ping equal time delay arc’, for different assumed speeds of the aircraft (200, 250, 300, 350, 400 and 450 knots).

To summarise, here are the paths in a 3D view of an STK scenario:


And here are the tracks in the 2D map:


These fans of tracks begin with the 200 knot path being that at furthest east, culminating in the 450 knot track at furthest west.

For each of these paths one is able to calculate within the STK scenario a line-of-sight (LOS) speed between the Inmarsat-3F1 satellite and the simulant MH370 aircraft, that LOS speed rendering an expectation of a Doppler shift between the transmitted and received frequencies. The frequency shift Δis related to the carrier frequency f as:

Δf = Δv / c

where Δv is the LOS (relative) speed and c is the speed of light. Δv can be thought of as having two components, due to the satellite’s motion relative to the Earth, and the aircraft’s motion relative to the Earth. Within STK Δv can be derived directly; and that is what I did.

The following six graphs show Δv in km/sec for the six paths in the STK maps/screen grabs shown above. The paths all start at 16:55 UTC on 2014/03/07 (minute number 1015) and overflow by eleven minutes into the next day (UTC). As can be seen, the paths assumed are identical until the final radar contact at 18:22 UTC (minute 1102).










The initial interest here is a comparison with the Inmarsat-produced ‘Burst Frequency Offset Analysis’ graph as issued by the Malaysian Government on 24th March (but previously available on the Inmarsat website). Here is that graph:


My analysis is not concerned with the initial parts of the flight, and so starts from 16:55. From that time onwards there is a cluster of frequency offsets just before 18:30 UTC and then five further frequency offset measurements. The LOS speeds that I calculated for my six different paths/constant cruise speeds of the aircraft at each of those times are shown in the following table.

Line-of-Sight Speeds in km/sec

Time (minutes, UTC)

200 knots

250 knots

300 knots

350 knots

400 knots

450 knots


























































The information in the above table I have plotted below, with colour-coding of the dots:


Two immediate observations on the above plot:

(a)    The slopes depend upon the aircraft speed (no surprise there!);

(b)   Dependent on the speed, the Doppler shift could be positive or negative around the time of the last radar contact: that last contact was at 18:22, whereas Inmarsat apparently received ping data soon thereafter at 18:27-18:29 (the latter being minute 1109 in the above plot).

Apart from the modelling of the flight above, I also examined the Doppler shift that would be expected when the aircraft was stationary on the tarmac at KL. This I did by putting in a time of 16:30 UTC into the STK scenario. The LOS speed then (which is, of course, entirely due to the satellite’s motion) was near 0.021 km/sec. It varies in the third decimal place over the course of 20 minutes.

For a variety of reasons is seems clear that the speed of MH370 as it traversed the Indian Ocean moving southwards was somewhat less than the 450 knots assumed in the plot shown above from Inmarsat. My own plots shown at the start of this post indicate that such a speed would necessitate a path far west of Australia down through the middle of the Indian Ocean, moving SSW. A lower speed is therefore preferred in terms of my perception of what is likely.

On the other hand, quite low speeds (200 and 250 knots) are perhaps excludable on the basis that they would imply a route either directly down the length of Sumatra, or else very close to its southern coast, and no detection of MH370 there has been made public.

The above considerations direct me towards suspecting that the speed of MH370 during the great circle automatic pilot route that I have assumed here was near 300 knots, perhaps 350 knots at the outside.

This also meshes against my immediate response to my calculated LOS speed graph above as compared to the Inmarsat Burst Frequency Offset measurements (and Inmarsat’s modelled values based on a 450 knot speed). I think that 300 knots seems to offer the most likely fit. I could explain more, but am so tired at the moment (03:35 here in Wellington, New Zealand) that I will leave further thoughts until the morrow.

Anyone who would like Excel spreadsheets of the LOS speeds for each of the six aircraft speeds should let me know by email and I will oblige as soon as I am able.


Revised Possible Flight Paths of MH370

Revised Possible Flight Paths of MH370

Duncan Steel, 2014 March 30.

In my last post I investigated plausible flights paths for MH370 based on the last apparent radar detection and the satellite ‘ping equal time delay arc’, for different assumed speeds of the aircraft.

Several correspondents have pointed out that the time of the final radar detection was at 18:22 UTC rather than 18:15 UTC, which I had assumed; and also that the location of the aircraft at that time was apparently further northwest of Penang than Pulau Perak, a matter of ambiguity to which I alluded.

What I have done here is to repeat my analysis with MH370 now located further northwest at that time (18:22 UTC on 2014/03/07). However, the location at that time has been variously stated as being (06.533 N, 96.383 E) and (06.868 N, 97.339 E), and perhaps other values too. What I have done is to arrange that my simulant MH370 passes mid-way between these two points at that time, using a route as shown in the view below (a screen-grab from a 3D window in my STK scenario).

y3Db small

That route is as shown by the data hereunder:


I have repeated my analysis as described in that previous post. For each assumed speed from 18:22 UTC onwards (200, 250, 300, 350 and 400 knots; plus 450 knots also now) I used input data identical to that in the preceding table except that the speed in the second-last line (given as 400 knots in that table) was adjusted to take each of those assumed values in turn, these rendering the speed from that location through to the location in the final line; and then, for each, I searched for the location along the ping equal time delay arc at which the aircraft would arrive on that arc at 00:11 UTC on 2014/03/08, as was actually observed in the interpretation of the satellite pings.

The locations for those final points on the arc were as follows:

Assumed Speed (knots)

Latitude (degrees)
(all South)

Longitude (degrees)

(all East)




















Note that the final location (for the newly-introduced 450 knot speed) is not actually on the arc I calculated, because I only took that calculation as far south as latitude 35 degrees; nevertheless it was straightforward to locate a suitable position by eye in the STK 2D window, as shown by the last of the maps included below.

The following six maps, then, pertain to possible routes for MH370 from its last radar-detected position, following great arcs at constant speeds equal to those stated on each map. Some of these might be excludable on the basis of other considerations, such as the 200 knot route covering the length of Sumatra (and that for 250 knots being not far off), but that is outside of the considerations I have been applying in my analysis.







Possible Flight Paths of MH370

Possible Flight Paths of MH370

Duncan Steel, 2014 March 30.

In previous posts I have been investigating the interpretation of the time delays in the pings/handshakes from Inmarsat-3F1 to MH370. That is what might be termed the ‘space sector’. About five hours ago I started to take a look at the ‘aviation sector’. As I have said in previous posts, although I know some things about space, I cannot claim to be an aviation expert. But here goes anyhow.

I am using STK throughout here, and I much recommend that others should use it! (No, I don’t work for Analytical Graphics, Inc.) All the features I have used have been part of a free STK download.

I think we (the general public) know the following from open sources:

(1)    At 17:21 UTC on 2014/03/07 MH370 was at altitude 35,000 feet, latitude 6.9208 degrees North, and longitude 103.579 degrees East.

(2)    The last radar contact with MH370 was apparently at 18:15 UTC when MH370 was either “200 miles (320 km) NW of Penang” or “near Pulau Perak”, the two not being quite the same location.

(3)    There have been disagreements with regard to the route taken between those two locations; the altitude that MH370 was at by the time it neared that second location; and various other matters regarding whether the flight path involved more than one turn.

Being a scientist I must apply Ockham’s Razor and look for the simplest solution. I think that simplest solution is that something went wrong with the aircraft and as a result the pilots followed the “Aviate; Navigate; Communicate” mantra and turned the aircraft to head for the nearest known airfield which would enable them to put down, with their immediate response being governed by their professional knowledge and experience. That would imply (rightly or wrongly) a turn to port/westwards, back towards Malaysia. It seems that they were able to aviate, and navigate, at least for a while; but they were not able to communicate (with the ground) whilst taking emergency action, and were subsequently incapacitated in some way.

What I have done inside my STK scenario is that I have inserted an aircraft, simulating MH370 (perhaps), and made it follow different paths. Here is a picture of the aircraft (just for fun):


That’s a Boeing 777-200. The thin blue line indicates its path, in the STK scenario.

Next, here is a 3D view from the STK scenario:


Now, the route I chose for the next part of the flight is as shown here:


For my present purposes, the precise route taken is not important, because the aim of my investigation now is just to delineate possible paths of MH370 south over the Indian Ocean and not during this curved-path part of the overall trajectory. My requirement here is just to have MH370 passing Pulau Perak at 18:15 UTC. In order to achieve that I gave the aircraft a series of gradual turns in the STK simulation. The precise parameters I used are as shown here:


Looking at the figures given in that table:

(a)    I put the aircraft at 35,000 feet initially (=5.76025918 nautical miles) but brought it down to 12,000 feet (1.97494600 nm) after commencement of what I have assumed to be emergency action by the crew, based on various reports in the media; however, that altitude does not affect any other factors in my simulation. (Yes, in reality a lower altitude means faster fuel consumption, but I am not considering fuel consumption here.)

(b)   I had the aircraft initially travelling at 430 knots, increasing to 450 knots as it reached cruise altitude, but then reducing after emergency action was initiated.

(c)    The ‘Turn Radius’ in the final column simply adjusts the sharpness of the turns.

(d)   In STK, the speed given (i.e. 430, 450, 425, 400 knots) in any line pertains to the speed from the geographical location in that line to the location in the next line.

(e)   The matter which is of concern to me here is the speed from soon after the aircraft passed Pulau Perak (the third-last line in the above table) through until it reached the ‘ping time delay arc’ at 00:11 UTC on 2014/03/08; that is the arc delineated by the bright green dots in the 3D view above, the derivation of which I described in a preceding post.

(f)     I chose an arbitrary point about a degree south of Pulau Perak (the second-last line in the above table) as the start of an assumed path for the aircraft flying in automatic pilot at a constant speed (which I could adjust), a constant altitude (this is inconsequential here), and following a great circle (which is the shortest route between any two points); essentially I have assumed that the crew were incapacitated.

(g)    I could adjust the speed in that final part of the simulated flight (i.e. that between the two last points in the table) by altering the speed inserted in the second-last line in the table.

(h)   I gave that speed values of 200, 250, 300, 350 and 400 knots, and in each case then adjusted (by trial-and-error) the geographical location of the final point by requiring that it be on the ‘ping time delay arc’ at 00:11 UTC.

(i)      The locations for those final points were as follows:

Assumed Speed (knots)

Latitude (degrees)
(all South)

Longitude (degrees)
(all East)

















Because I have made use of great circle routes between all waypoints within STK (excepting that the turn radius limitations increase the distances ‘flown’ between points) these represent minimum distances to be covered. In particular the route between the last two points in the table of positions (i.e. that just south of Pulau Perak through to the intersection at 00:11 UTC with the ping equal time delay arc) is a pure great circle with no turns; consequently it is the minimum flight distance. That is, if the autopilot instead followed a path based on a magnetic bearing then slow changes of direction would be involved, increasing the distance travelled. This would result in the effective speed being slightly reduced, and so an intersection with the ping equal time delay arc further north than the values given above for each assumed airspeed.


The actual routes calculated in this way are shown on the maps that follow. I hope they will be of interest to those charged with searching for the aircraft in question. Of course my work might well be wrong, or too simplistic, or misguided. I’m just trying to help a bit.

My main conclusion has to be that this was all rather simple. It was the work of just one person, making use of information available on the internet and free software. Why has there been so much confusion and disinformation in the media?












Space Scientist, Author & Broadcaster