Ping Rings from the Inmarsat-3F1 Data

Ping Rings from the Inmarsat-3F1 Data

Duncan Steel, 2014 April 05.
duncansteel.com

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
(milliseconds)

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

1880

19:40

36741.0

122.555

55.80

1760

20:40

36786.5

122.706

54.98

1806

21:40

36959.5

123.284

52.01

1965

22:40

37243.5

124.231

47.54

2206

00:11

37838.5

126.216

39.33

2652

 

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.

 

69 thoughts on “Ping Rings from the Inmarsat-3F1 Data”

  1. Thermal satellite is fairly easy technology. If you look at weather satellites they give high-contrast color separation to cloud temperatures that vary by only a 125 degrees or so. The heat exhaust off the 777 engine would be hundreds of degrees against a -50 degree background and should be easily within existing technology. Especially when the aircraft was allegedly flying well out of normal flyways in the middle of nowhere. Especially with a 7 hour lead time post-9/11.

    1. Sorry, but you show there a total lack of understanding of the physics involved. According your comment a satellite sensor working in the thermal IR (say around 5 micron wavelength) should be able to detect the heat from a lighted cigarette from orbit. Before one can say anything useful one must understand far more about physics than you do.

  2. I will see if I can dig up an upper atmosphere wind map for southeast Asia at the time of the flight. Unfortunately, the map that covers the southern Indian Ocean does not extend anywhere near Kuala Lumpur, let alone north of there.

    I finished my short paper showing the inability to generate a constant velocity track for the final four ping times using the LOS ranges provided by GlobusMax. Happy to e-mail it your way if you want to look it over.

  3. Hi Duncan,

    Yes, my analysis is strictly ground speed, not airspeed. Fortunately, winds were definitely well under 100 knots for anywhere the plane could have been flying. (One of the first things I did was download the 300-millibar upper atmospheric winds for as close to the region as I could find.) Unlike what I’m accustomed to seeing over the U.S., the southern Indian Ocean and even much of the area between the southern Indian Ocean and Kuala Lumpur has comparatively light jet-stream-altitude winds. I doubt the winds reached even 60 knots anywhere along the flightpath.

    1. Thanks Rob. That is useful information.

      OK, what were the winds for possible northern routes? Let’s say Kolkata, Patna, Kathmandu and NW of there towards Xinjiang?

  4. Hi Duncan,

    Just saw your 2 replies regarding the discrepancies in the ping ring radii. (Checked last night around midnight my time, but you had not had time to respond yet; time difference between California and New Zealand means there are limited hours during the day when we’re both awake. ;-)

    “The reality as I wrote is that I placed those ping rings ‘by eye’ and you should not take them as being good to better than maybe 10 km on the equator in the east, but even less accurate elsewhere.”

    Okay, that makes sense (and I perfectly understand the demands on your time necessitate shortcuts here and there). You also wrote:

    “(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 at the places where those cones reached the Earth’s surface by eye.”

    Okay — yes, this introduces a little bit of slop at the earth’s surface. But ultimately your ring radii are dependent on your choice of the cone angle at the satellite, and that cone angle needs to be very precise. For instance, if the error is only 0.01 degrees on the cone angle, your ring radii will be off by over 10 km. Since your table is reporting the elevation angle of the satellite from the plane to two decimal places, I thought there might be a chance that you were only carrying two decimal places on the cone angle as well.

    So to recap, the ping ring radii are eye-estimates of the intersection of a cone from the satellite down to the ground, and that cone angle is derived from the satellite’s exact altitude, the plane flying at 35,000 feet, and the LOS range to the plane computed by GlobusMax. Some relatively small errors are introduced by the method, which is why the table numbers are not quite internally consistent. But ultimately the driving factor in the ping ring radii trace to the LOS ranges provided by GlobusMax.

    What my analysis shows is that GlobusMax’s LOS ranges for the final four pings cannot result in a flight path that both follows a great circle *and* has constant velocity. I’m finishing up a white paper I can send you that shows why this is the case, but the mismatch in velocities is large enough that it should be apparent just by drawing great circle candidate flight paths atop your final four ping rings.

    1. Thanks Rob.

      Don’t forget that in my analysis (and your own?) I might enter an assumed ground speed for the aircraft, but the speed (and heading) it makes through the air and thus its positions depends on (the unknown?) wind speeds, which may be of order 100 knots.

  5. Duncan

    Thank you for suggesting I do the analysis. Unfortunately the implication of what I said is that even if we assume the whole leg from sumatra was flown on one auto pilot setting there are an almost infinite number of solutions. Depending on speed and height.

    As they now seem to have located black box signals it would seem the approximate crash site is now known.

    Rory

  6. Hi Duncan,

    Was cross-checking some of the numbers in your ping-ring table, and there must be an error in there somewhere. For instance, let’s look at the last line:

    Aircraft-to-satellite LOS range: 37838.5 km
    Elevation angle from plane to satellite: 39.33 deg
    Range ring radius: 2652 nmi

    From this I calculate the earth central angle (alpha):

    Alpha = (2652 nmi * 1.852 km/nmi) / 6378.137 km
    = .77005307 radians = 44.12079 deg

    From Law of Sines, I can now back-compute your assumed satellite distance from the earth center (SatRadius):

    SIN (Alpha) / 37838.5 = SIN(90+39.33) / SatRadius

    SatRadius = 37838.5 * SIN(129.33) / SIN(44.12079)
    = 42041.8 km

    This is quite a bit smaller than the actual distance of the satellite from the center of the earth at 00:11 UTC. In a spreadsheet elsewhere you list Inmarsat’s altitude at that time as 35793.322 km, which would mean the assumed earth radius at the subsatellite point is only 6248.5 km — more than 125 km too small. So at least one of those three numbers — the LOS range, elevation angle, or ring radius must be off.

    The reason I uncovered the inconsistency is that I found it is not possible to have the aircraft fly a great circle route at constant velocity for the final four range ring radii (1806, 1965, 2206, and 2652 nmi). For instance, the speed solutions for 1806-1965-2206 are over 30 knots faster than the solutions for 1965-2206-2652.

      1. Rob: Can I refer you back to what I actually said in the post?

        “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 at the places where those cones reached the Earth’s surface by eye. 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.”

        That is, I did not CALCULATE the ping ring ‘radii’ in the final column: I estimated their positions by eye in my STK scenario, ONLY on the equator, and used that to insert indicative range rings.

        To do the whole thing properly I would need to do the LATITUDE and TIME-DEPENDENT calculations for the ring locations, and then enter each datum by hand in the STK scenario because the rings are not circles; whereas I can easily show ping rings as circles, which is what I did. They can easily be out by some distance, and looking at the windows in my STK scenario they are, at different latitudes (i.e. comparing the locations of equal elevation angle rings with equal radius rings). Caveat emptor, as always.

        The essence of making repeatability possible, in scientific pursuits: tell people precisely what you did! And I did.

        Maybe someone can use the essential derivative data (the satellite elevation angles from the aircraft) to derive (calculate) a set of latitude-dependent positions for each of the ping rings using WGS84 for the Earth’s shape and also remembering that I have used an aircraft altitude of 35,000 feet (i.e. the aircraft, when over the equator – if it ever was – was assumed to be at a distance 6388.805 km from the Earth’s centre, and at any other latitude it was at a distance equal to [Earth's radius at that latitude + 35,000 feet]). The sets of values are needed for each of the ping times, and don’t forget to use the positions and altitudes of the satellite which I posted here.

    1. Rob: Could you let me know if you have seen this and understand what I am saying/have said here. I need someone like you looking over my shoulder all the time. I spent a couple of hours repeating calculations and so on to ensure I had this right (I think!), but it is always possible that I have erred.

      The reality as I wrote is that I placed those ping rings ‘by eye’ and you should not take them as being good to better than maybe 10 km on the equator in the east, but even less accurate elsewhere.

  7. Thanks for the reply Duncan,

    I realize it doesn’t fit the current ping ring / Doppler analysis, however my understanding is that actual data is not available to confirm that analysis (in other words, it is not precise).

    Conversely, the known variables have somewhat more verifiable synchronicity, namely the known time and location of UAE343 (per FlightAware), the known location of MH370 (per radar plot) and the known (yet unexplained) series of ping *times* on the Inmarsat graph, all at 18:27 UTC (at 6.4812 N 96.5801 E).

    If the Inmarsat analysis (for which we have no actual data) is off by even a small margin, it would produce rather large errors in arc location. The suggested arc following UAE343 does generally go toward the satellite following convergence, reaching perpendicular somewhere further down the line, then increasing steadily away until completion, consistent with the constant speed and heading of UAE343 along Route N571.

    I would note the Inmarsat graph has a similar odd dislocation of points at 17:00 UTC. The ADS-B data on FlightAware shows that the plane did decrease in velocity at that time while maintaining physical direction away from the satellite en route to IGARI.

    Thanks,
    Phil

    (UWO will be lucky for the visit, no doubt.)

  8. Okay, since the planar solution was not all that different from the spherical solution, I opted to redo the planar equations *including* the satellite motion. This turned out to be more difficult than I thought. By introducing satellite motion, it turns out the velocity solution is no longer unique — it varies slightly with flight bearing. In other words, I can choose a flight bearing for the final 2 1/2 hours, and it will generate a unique velocity solution. It turns out that velocity solution is extremely constrained, but the flight bearing is not. These are all valid solutions based on (only) the final 3 ping rings:

    Bearing Velocity (knots)
    ———- ———–
    165.23 433.82
    170.15 435.12
    179.97 437.11
    189.76 438.27
    199.52 438.58
    209.25 438.03
    218.96 436.64

    (Bearing measured clockwise from north.) The take-away from all this is that if the velocity was constant for the last 2 1/2 hours, then it was somewhere between 433.8 and 438.6 knots.

    Repeating the exercise using the 20:40, 21:40 and 22:40 ping ranges would add some confidence that the methodology is sound if it results in similar velocities. Probably won’t have time to tackle that until tomorrow.

  9. Hi again,

    Just a quick follow-up; it was fairly easy to repeat the exercise using a spherical earth and great circles. As expected, the answer changed very little: 410.6 knots for the velocity from 21:40 UT to 00:11 UT. But I still need to fold in the effect of the moving satellite (which is NOT insignificant). Between 21:40 and 00:11 the subsatellite point has moved 0.815 degrees south, so the center of the final ping ring is shifted about 49 nmi south of the center of the 21:40 ping ring. That’s close to 5% of the distance the plane flew in that time, so that’s going to result in a significant change in the solution.

  10. Hi again, Duncan,

    Interesting analysis back-engineering the radii of the (as yet) unprovided ping rings prior to 00:11 UT. You realize that once you’ve done this, you have everything you need to determine
    the aircraft velocity (assuming it remained constant over the final several hours and flew a great circle route).

    To first-order, let me show you the solution to the flat-earth case, excluding the satellite motion. (Later, a full-blown solution can be done using a spherical earth and a moving geosat). For the final 3 pings you have three concentric circles of radii R1, R2, R3. The path of the aircraft is a chord that starts on the inner circle and ends on the outer circle. Call the chord length from the inner circle to the middle circle X12, and the chord length from the middle circle to the outermost (final) circle X23. By the cosine rule, you now have three equations:

    X12^2 = R1^2 + R2^2 – 2*R1*R2*COS(A)
    X23^2 = R2^2 + R3^2 – 2*R2*R3*COS(B)
    (X12 + X23)^2 = R1^2 + R3^2 – 2*R1*R3*COS(A+B)

    where A is the central angle corresponding to the first chord (X12) and B is the central angle corresponding to the second chord (X23). If we assume constant velocity, then we have a fourth equation:

    X23 = X12 * 91/60

    since the leg between the final two pings was 91 minutes vs. the prior ping delta of 60 minutes. So four equations, four unknowns. Fill in the values for R1, R2, and R3 from the back-calculated ping radii:

    R1=1965 nmi (@ 21:40 UT)
    R2 = 2206 nmi (@ 22:40 UT)
    R3 = 2652 nmi (@ 00:11 UT)

    With a little rearranging and substitution for X23, you get the following 3 equations in 3 unknowns:

    X12^2 = 8727661 – 8669580*COS(A)
    X12^2 = 5173088.274 – 5086613.501*COS(B)
    X12^2 = 1720081.768 – 1645563.616*COS(A+B)

    I’ll spare you the ugly details of how you solve this, and tell you that the solution for X12 is about 410.2 nmi, which means the plane was flying at 410.2 knots from the R1 ping circle to the R3 ping circle.

    It’ll take me some time to code up the spherical earth solution with a moving satellite, but this flat-earth approximation is probably not too bad.

  11. My comments are infrequent but I have been following the thread and have a few engineering observations.

    The Doppler analysis seems plausible and the 5 last pings give the radial range rate during that epoch. Regardless of the aircraft assumed speed and flight azimuth (but both being assumed constant), the range rate (Doppler vs time) times the time (actually integrated) between pings gives the radial change in ring radius from ping-to-ping. I have not studied the ring radius determination presented elsewhere, but it should be consistent with the Doppler-time history here. But, since the ring diameter (ping time) has not been released for the earlier pings, the determinations are likely to be redundant. If different analytical approaches were used, then this gives some confidence in the result.

    Since the Doppler data only give the radial range rate, the tangential range rate ( and thus the actual azimuthal angle) remains unknown. However for a great circle path from the last known point at a constant speed, there may be only one (or perhaps a few) paths that give a result consistent with the Doppler.

    To see this, consider a path that is from the first of the last five pings onward, and lies along a radius vector from the sub-satellite location. In this case the angle is zero and there is no tangential velocity. But since the Doppler shift (radial velocity) changes with time, and the path being evaluated would require the angle to remain zero, this path can excluded. (All I have done here is show that it may be a valid sorting criteria. The path directly away from the sub-satellite point has never been considered as plausible.)

    If the constant speed, great circle route is plausible, a fit would be found (ignoring the question of N/S). By doing the same for magnetic headings and rhumb lines similar paths could be evaluated.

    The Doppler data for the last 5 pings are unlikely to be biased by any human intervention in the flying of the plane during that period as it is unlikely that the ping times would be known to a person on the plane.

    I have left out some of the finer details as the work you are doing is a process of stepwise refinement and there is no point in applying second order corrections until you are close to a solution.

    Great work, thanks.

    Sid

    1. Thanks Sid.

      I follow all you have written there, and what you propose is essentially what I have been intending to do once we have the ping data available. Now we do: back-engineered. Pity we don’t have the data direct from Inmarsat.

      The/a problem is this. You wrote: “for a great circle path from the last known point at a constant speed, there may be only one (or perhaps a few) paths that give a result consistent with the Doppler.” Well, the last known point (i.e. military radar at 18:22) is outside the 18:29 ping ring; and at 18:29 the aircraft was moving away from the satellite (according to the Doppler data). And then the aircraft moved towards the satellite between the pings at 18:29 and 19:40 so as to be inside the 19:40 ping ring, but moving away from the satellite so as to cross that ping ring at that time from the inside.

      Thus the aircraft cannot have followed “a great circle path from the last known point at a constant speed”.

      I have all along been assuming (as a working hypothesis) that the aircraft did indeed follow a great circle path at a constant speed, but from some time shortly before 19:40. It appears that it cannot have done so between all of the time between 18:22 and 19:40.

      Any comments?

      Cheers,
      Duncan

      1. From a systems analysis pont of view – the distribution of the pings through time indicate to me that the aircraft supresses the hourly pings when it has got more important things to do (eg give out warnings, monitor manoeuvres). So in order to allow the first of the hourly pings to happen the system needs to monitor the steady state for a set time. Good practice would be to monitor for 30 mins then allow the first ping, but it could be monitored for up to an hour. Therefore there is a window of 30 mins when the great circle/constant speed could begin. (18:40 to 19:10)

  12. I put in rings at the distance the plane would have traveled at 450 k at each of the ping times and it produces fairly straight flight paths N and S symmetrical about a line from the satellite to the position at 18.22 corresponding closely to your 450 k Northern simulant path. As far as I can see no lower speed works. The doppler is close too if you postulate a turn to the west a bit at the start. Can’t sleep!

  13. Deriving a ground course from an assumed airspeed and known distance rings.

    Despite having read much on Pprune and elsewhere I am unaware of this particular analysis being publicised.

    It is based on a general knowledge of aero navigation not on the specifics of 777.

    Analysis shown so far seems to be based on constant ground speed but this is seldom ever the actual situation. Constant airspeed is a much more likely scenario although still by no means certain.

    As has been shown for each set of consecutive range rings there are two solutions for the second position based on an assumed first position. These merge to one in the case of the ground track directly away from the centre of the range rings.

    The wind velocity is generally significant particularly at altitude. The classic way of deriving ground track from airspeed and direction of flight is by vector addition. In this case mark the wind vector from the start point. In the case of 1 hour interval this is the wind speed in knot marked as nautical miles. This may be a different figure for the meterological area in the clockwise direction from the anticlockwise. Then with a compass draw a circle radius airspeed in knots as nautical miles (1 hour case) centred on the end of the wind vector and intersecting the second range ring. This gives the estimated second position and the ground speed and track achieved, also the direction of flight. Convert the direction of flight to magnetic heading (using local variation) for comparison with other time frames.

    Complicating factors are that windspeed varies with height so it will be necessary to assume a height for each unique solution.

    Two possible scenarios have been predominant that of constant magnetic heading and ground track towards a waypoint. If the above analysis throws up something close to one of these scenarios then that would act as an indicator that this may be indeed what took place.

    Rory

  14. A couple of hours ago I watched part of a live briefing by Malaysian officials. A reporter asked specifically for the last known position and altitude of the plane, and they refused to answer, instead disembling about cooperation between countries!

    Note that he did not ask for the source of the information, only for the position and altitude itself. I cannot imagine any reason they would try to keep this information secret, other than possible governmental problems they are trying to hide.

    There is a persistent rumor that the plane was last seen at 12000 ft. altitude (CNN quotes an “unnamed source”). If this is true, there is no chance that it went down anywhere close to the current search zone!

  15. Ping time is not calculated by the satellite which merely acts as a radio repeater/regenerator.

    The ping time is derived from four transit times – ground station to satellite, satellite to aircraft, aircraft to satellite, satellite to ground-station. Plus fixed times – aircraft processing time, ground-station processing times, and delays of the order of a bit period in the satellite signal regneration circuitry.

    The total fixed timing can be determined by pings at known locations – usually airport runways. It also depends on the choice of ground-station – which coincidentally is most likely a receiver in Perth.

    Your discussion does not seem to have taken into account the four-legs + fixed delay. Or at least has not mentioned them.

    1. Charles: Please read earlier posts.

      I started out by back-calculating the ping delay time at 00:11 UTC from the only information publicly available: the range arcs published by the Malaysian Government on March 15th, but originating from Inmarsat. I just used the stated/shown 40-degree elevation angle to determine the aircraft-satellite distance at that time, and from that the residual ping time delay. Throughout the only “ping time delay” being discussed is that between satellite and aircraft, and I have consistently been using only the one-leg delay (rather than two legs which would be double that). All the other contributions would have been allowed for by Inmarsat, I assume. I also needed to make other assumptions about how they (at Inmarsat) worked the geometry. All described in earlier posts.

      Actually I do not care how the ping time delay was derived from the communications system. I am only looking at the other end of the problem: how to exploit the geometry so as to attempt to narrow down possible paths taken by the aircraft.

      With regard to using pings whilst the aircraft is at known locations, that is precisely what was done by Mike Exner (with input from Ari Schulman and myself) to reverse-engineer/decompose the Burst Frequency Offsets so as to get the Doppler shifts, and that includes all four transits.

      To repeat to all: Please read previous posts before commenting on technical things that have already been covered.

      Duncan Steel

  16. @Duncan (and others), there seems to be some confusion, because the ping rings for 19:40 and 20:40 UTC (blue and green ring) are at a nearer distance to the satellite than the dark red ping ring from 18:29 UTC. This seems to contradict the statement, that the plane was always moving away from the satellite at the time of the pings. But since the satellite isn’t stationary and is moving as well roughly on a North/South path, and the Doppler data indicate, that the plane was always moving away from the satellite at the time of the pings, I concluded that this means, the satellite and the plane were never moving TOWARDS each other: So, these Doppler data indicate, in which direction the plane was moving at the time of the ping. However, they don’t mean, each time, there was a ping, the plane was further away from the satellite than at the time of the last ping. Is that correct, or did I completely misinterpret this?

    1. Hi Littlefoot:

      “the statement, that the plane was always moving away from the satellite at the time of the pings” – I believe that statement was made by an Inmarsat spokesman (rather than directly the engineers, who may well be kept in a computer-infested dungeon and fed raw meat) and may not have reflected the reality of what the engineers may have found. My belief is that the statement was intended to apply only tho the pings from 19:40 onwards (in which case it is true: both the rings are larger/time delays are larger from 19:40 onwards, and also the Doppler shifts are all demonstrative of the aircraft moving away from the satellite).

      The ping at 18:29 indeed represents a greater distance from satellite to aircraft, and note also that this was soon after the last radar detection (18:22 UTC) which would also indicate the position at around 18:29 must have been further from the satellite than the positions at 19:40 and 20:40. However, part of the conundrum is that the pings at 18:25, 18:27 and 18:29 all show the instantaneous speeds of the aircraft to be AWAY FROM the satellite. That is, at those times it must have had (broadly) some significant EASTERLY component of its bearing, and that must be fitted against it being much further WESTWARD at 19:40.

      Duncan

      1. “That is, at those times it must have had (broadly) some significant EASTERLY component of its bearing,”

        Or, this may be where there is a downward motion….

      2. Actually, because of the geometry of where the satellite is, the Doppler is most sensitive to a change in altitude. Think that through again. If the plane were directly below the satellite (elevation angle 90), clearly there would be no sensitivity to change in velocity except for changing altitude. It is only when the plane is at the Earth limb as viewed by the satellite (elevation angle 0) that there is no sensitivity to an altitude change. At elevation angle 54, the sensitivity to change in altitude is still greater than for change of motion towards or away from the sub-satellite position.

        I would agree that using the satellite motion itself to discriminate altitude information would not work, but you are puzzling about a signal from the motion of the plane.

  17. Hi Duncan,
    Thanks again for your efforts and the time you take to explain in details what you do and how you do it.
    1) I don’t know SDK but I presume it’s possible to overlay on the globe a geo-referenced image. Since the daily AMSA search maps ( https://www.amsa.gov.au/media/incidents/mh370-search.asp ) are showing the Lat/Long, it’s easy to reference them. I am curious to see and compare where they are searching vs your ping rings and what you believe some possible flight paths could be
    2) In their daily media release, the JACC says :
    “… The Australian Transport Safety Bureau continues to refine the area … …. … based on continuing ground-breaking and multi-disciplinary technical analysis … ”
    They have been doing this for days without ” significant ” progress !
    How do you think they “refine” the area ? Do they “play” with the same “parameters” that you have ?
    Finally, what do you think is behind the words “continuing ground-breaking and multi-disciplinary technical analysis” as this seems a little pompous to me.
    Thank you.
    PS : I have seen you latest comments on ADO and AMSA. Hence my questions.

    1. Bonjour Louis, mon ami…
      (1) Yes. In STK one can induct any geo-referenced imagery (and indeed elevation data like DTED; and all manner of other GIS data: anything you can do with KML/KMZ files in Google Earth you can do better in STK) and I have done lots and lots of that in the past. But I *think* I need paid STK modules to do that. (In the past I was working for a company which had a full STK licence (‘license’ in the US); now I have just the free download, for which I am *very appreciative*.)
      (2) I would doubt that the JACC/AMSA has itself done anything like what I have been doing. All the AMSA search maps I have looked at (none in the past week) appear to be based on possible tracks supplied to them by the (US) NTSB. (If that is the case and the NTSB derives them itself from track modelling such as I have done, then I think it means that the NTSB has the Inmarsat ping data either directly or via the UK AAIB.) Sorry if I am doing them an injustice, but I would think that the JACC/AMSA is just plotting up the information/possible tracks that they seem to get from the NTSB and then picking areas nearby to search. In that regard the RAAF and AMSA is just acting as a wholly-owned client state of the US, which is likely for the best in this connection: I do not believe that they have the intrinsic ability to do anything useful and value-added themselves, apart from fly search aircraft around the Indian Ocean.
      (3) With respect to: “continuing ground-breaking and multi-disciplinary technical analysis” If you are going to tell a lie, make it a big one? This is laughable. Conceptually, the problem is not difficult. Nothing I have done is very complicated, I am just plodding through some matters that are quite straightforward. The major difficulty has been the lack of the original data (the ping time delays and Doppler shifts: twelve numbers). This has slowed me down immensely. I am serious that this is all quite straightforward. My two wonderful sons (aged 19 and 21) are both undergraduate students in physics, and if I had them here with me then they would have been able to do what I have done, with just a little nudging from me along the way. Although admittedly they are smarter than the average bear. My point is that I am just one bloke sitting in NZ making use of the internet, a simple years-old PC, one wonderful tool (STK), and collaborating with other good souls we can, perhaps, make some headway. Why the ‘authorities’ sucking up billions every year in taxpayers’ dollars cannot do likewise is not a mystery; it’s a tragedy.

      Au revoir,
      Duncan

  18. If you are able to do such fine analysis from such sparse data then I expect USA spy satellite data has told military exactly where #MH370 is. For me the question is why are they delaying telling the world where it is? Several scenarios are plausible.

    1. Thanks Bill.

      I work in the space field, and have worked for Defence/Defense. You are imagining spy satellite capabilities that do not exist.

      Thinking first about the optical/near-IR. The imagery comes mostly from low-altitude satellites with very narrow fields of view. They are powerful – the US has telescopes looking down from orbit with apertures almost twice that of the Hubble Space Telescope, and last year the NRO gave NASA two ‘surplus’ large space telescopes (on the ground) – but can only cover limited areas. They need to be targeted at specific places at times when they are accessible. (All this stuff on TV/in the movies about “we are just re-positioning our satellite” is bunkum.) Why would they have been even *trying* to follow MH370? And if they were, the access-availability times would only be a few minutes per orbit.

      On such spy satellites: look up ‘Keyhole’ and ‘New Crystal’ on Wikipedia.

      Turning to radar spy satellites from space: look up Lacrosse/Onyx. (Actually, you can look up into the sky and see Lacrosse! That and the other LEO spy satellites are easy to see with the naked eye near dusk and dawn because they are big! To find out when and where to look, go visit: http://www.heavens-above.com/ ) Radar satellites *must* be in low orbits because the radar equation says that the returned echo signal drops off as the range raised to the power four. One has similar limitations with radar (on LEO satellites) then as is the case with optical systems: you can only see your desired target a tiny fraction of the time.

      Now let’s go to high altitude and geostationary orbit. In the optical/near-IR there are whole-hemisphere imagers up there, but few of them. They are limited by their large range (> 35,800 km!) leading to poor resolution (pixel sizes) for their wide-field instruments. For narrow-field (spot beam) imagery systems you might get better resolution/smaller pixels in terms of ground-spot size, but you must know where to look.

      The final type of spy satellite are thermal IR systems which look for ‘hot things’: like ICBM rocket launch exhausts! I am familiar with these systems because of not only Defence applications but also because they detect lots of fireballs (bright meteors). Look up ‘SBIRS High’ (but also SBIRS Low might be of interest). These systems would be able to detect jetliner exhausts in principle, I think, but it would be difficult. Given so much jetliner traffic, one would have to be looking for one particular target, and even then doing some fancy manipulation so as to pull the signal (the jetliner exhaust) from out of the noise background. A military fast jet with its afterburner blasting would be a far easier target to pick up this way. And that is one of the things SBIRS was designed to do.

      Regards,

      Duncan Steel

  19. http://michaelsocalblog.tumblr.com/

    Link to a blog I posted few days ago of what I saw as ATC abnormalities in the ATC transcript.

    Also been corresponding with Jeff Wise from slate @manvbrain twitter

    Has been an advocate on CNN from moving search to north arc due to lack of known Indonesia and JORN radar track.

    To me don’t care if your reverse engineered ping arc radiuses disprove theory

    Just would appreciate a possible yes or no

    Thanks

    @socalmike_SD twitter

    1. Michael: I have no yes or no at present. I cannot give any answer until I have considered the question carefully. And there’s a queue/line!

      Duncan

      1. Thanks for the reply

        Apologize for multiple posts

        Got a little excited when I saw that possible match of flightpath

        Inmarsat always said each ping was further away from satellite than the first

        That’s why I somewhat discounted SQ68 theory…but pic 3 closer than further away puts it back into the possibility category

        Appreciate the consideration for further analysis

      2. Nil desperandum Michael. We’re getting there.

        Basic problem with much of this (science-based analysis) is we need to learn to WALK before we can RUN, whereas most people want to be able to JUMP to a conclusion!
        And I know that physicists can annoy others by our insistence in taking things step by step, proceeding in a way which WE think logical and the only proper way to do things, whilst others think that we are being obstructive, or worse.

        Cheers,
        Duncan

  20. Sorry meant sq68 instead of sa68

    Looking at arcs on pic 3 from top of page roughly matches to my eye SQ68. I’m an SEL instrument pilot and don’t pretend to understand all the math involved. However, the known evidence from an aviation POV seems to me that this theory is plausible. Starting at last radar contact at 1815UTC and proceeding NW roughly lines up with SQ68 flightpath across middle of India. Redbrown blue green arc..

    Really appreciate a reply

    Not a conspiracy theorist..try to apply circumstantial evidence to suggest plausible theory

    @socalmike_SD

  21. Twitter @socalmike_SD

    Dear Prof,

    Noticed your first few ping km distances move closer to satellite than further away. Was a proponent of Keith Ledgerwood’s theory from beginning of possible shadow theory of SA68. Concluded however need inmarsat ping arc radiuses to prove/disprove theory. Line up with SA68 flightpath. Made map to illustrate this. Does your data confirm or debunk theory?http://twitter.com/socalmike_SD/status/447683718707019776/photo/1

    Thanks

    1. Michael: Thanks.

      At present I am handling a few other things (e.g. making data, plus better graphics, available) so I do not have the time to look at that one.

      I think the graphics and information I have posted here should enable others to address that question. I encourage all to try.

      Duncan

  22. For conspiracy theorists the Northern 450 route is similar time and route to SQ62 on that night. I wonder if Inmarsat have the ping data for that plane?

  23. Hi Duncan,

    That view edge on is a nice touch and it has given me an idea. The best projection for line of sight velocity is actually altitude rather than the radius connecting the rings (though you run out of altitude rather quickly) so I wonder if the big changes in the closely spaced (in time) velocity data points might include a dive to make a low altitude sweep out to sea as the burgundy and purple rings are connected in a way that avoids Indonesian radar. That might explain how the Indonesian’s think they have good coverage, but the Earth’s curvature might still allow the plane to sneak past.

    1. Chris: I am not *sure* that I follow you, but I have just woken from a straight 11-hour sleep and am still feeling exhausted, hence no clarity of thought.

      (1) Remember that when I talk about LOS speeds I am referring to the LOS between the satellite and the aircraft, and NOT a range-rate in the usual meaning (here, between the sub-satellite point and the aircraft).
      (2) In a previous post (see the final two plots) I showed that a rapid change/drop in altitude has little effect on that LOS speed and hence the measured Doppler.

    2. Hi Duncan,

      I’m using “projection” in the sense that a vector can be broken down into components in a coordinate system. If we pick a convenient one: altitude, radius from sub-satellite position, and tangent to the ping circle, the LOS velocity will have no sensitivity to changing motion along the tangent, some sensitivity to changing motion along the radius, and large sensitivity to changes in motion in altitude. So, big rapid changes in LOS velocity could indicate an altitude change even more than a turn.

      Might have a crash position soon to test the idea that the last three pings could localize things assuming a great circle course: http://www.smh.com.au/world/missing-malaysia-airlines-search-chinese-ship-picks-up-pulse-signal-reports-20140405-zqrbc.html 25 degrees south latitude and 101 degrees east longitude.

  24. Thank you so much for the graphics provided!!!

    Strange thing – I wanted to ask you to do such analysis. Again thank you so much!

    Can you please add major cities for the close up picture – for our reference (pr-2d-b.png)?

    1. Thanks Alexander.

      (1) “I wanted to ask you to do such analysis” That is not because we are psychic; it’s because we are both thinking logically!
      (2) “Can you please add major cities for the close up picture” Some people will now be saying “That’s asking a lot.” But in fact STK has a built-in data bank of cities! Again, it’s a wonderful tool.
      I will do that ASAP.

      Duncan

  25. Fantastic! With pencil, paper and ruler the only route that I can fit that crosses the rings in the correct order and has the same speed between pings is the Northern 450 knot one. The Southern routes get too fast towards the end. Can’t wait for you to do it properly to see if you agree.

    1. Oops – I can fit the Southern route too with a tiny dog leg, much the same as the Northern route,and maintaining constant speed – again 450 Knots

  26. Good afternoon, Duncan,

    Thanks again for a comprehensive analysis while working with very scarce data!

    I’m still believing in a northerly path, and so would be quite interested in seeing a close-up covering area for the final part of the path, i.e., for the last 3 pings.

    As I pointed out in the thread to your post on 2 April, our “theory” (South Tibet theory) proposes that after crossing the Bay of Bengal the path followed the border between India and Myanmar (Burma). You have seen our revised path here:
    On 3 April, we have suggested a more detailed flight path:
    https://sites.google.com/site/mh370tibet/updates/03april2014

    The curvature of the part between Malacca straits and Myanmar coastline is “adjustable” – I haven’t had time to change it, but the initial post at
    https://sites.google.com/site/mh370tibet/home
    has the image with the path which is more consistent with the first three new rings you just reconstructed.

    Obviously, for the South Tibet theory, the crucial part is over the landmass, and so seeing where the suggested path intersects the last 3 reconstructed rings is important – if the intersection points are indeed correlated with twists of the border then the theory would gain some more plausibility, as its main assumption is that whoever was in control of the plane was trying to minimise radar detection by “tracing” the border, rather than completely embedding the path inside some territory.

    Thanks,
    Mikhail

  27. Dr. Steel,

    Thanks for your informative posts on these issues. Quick Question: do you know or trust that Immarsat or the investigators has those with a similar same level of expertise on these matters, in-house, as yourself, or that they have at consulted with those who do? I suspect you simply may not have the answer, but I think this whole investigation would really stink to high heaven if you know or suspect that the answer is no.

    1. Thanks for your support John.

      The engineers at Inmarsat are not idiots, but that does not mean that they have not made mistakes, and I have severely criticised (1) Their mistaken assumption in the ‘first week’ that their own satellite was at some set height directly above the equator, and not drifting; and (2) Their BFO graph (and indeed Google Earth track view), as repeated in the world’s media after being issued by the Malaysian Government, which was of a standard that I would find unacceptable in an experiment write-up by a first-year physics undergraduate. I mean, they drew lines between discrete points, misleading everyone! This is so daft I can hardly contain myself.

      Turning elsewhere, I worked for quite a few years with purported scientists from the Australian Defence Organisation (including DSTO) and in the majority of cases they were as much use as the proverbial one-legged man in an ass-kicking contest. I have worked with Australian Defence scientists, and American Defense [sic] scientists. To compare them would be a joke. And the Americans know that, they are just too polite to say so. In the ADO, incompetence is the rule, not the exception.

      Turning next to AMSA (the Australian Maritime Safety Authority [sic]). I worked for some time in the building (now demolished) next to the plush new AMSA building on Northbourne Avenue in Canberra. I often met and talked to AMSA staff in the cafe (called My Coffee Cup) out back of those buildings, on Mort Street. I did not form a high opinion of their capabilities. Being polite there.

      Duncan

  28. Dear Mr. Steel:

    I’ve found your work on MH370 to be the most informative, and apparently most trustworthy information available, and appreciate very much the effort and energy you are putting in. As an attorney, I have been bothered by the unreliability of information released over television news, and the lack of means to “test” the information released – cross-examine the matters, if you will. As a person born on 9/11, I’ve been quite taken up with this story, hoping the “disappearance” is not a new, developing chapter of what happened on my birthday. Your work is a welcome relief from all the tales full of sound and fury circulating among stations trying to keep the viewer tuned. Thanks for posting reliable, intelligent info. Thanks also for posting ring maps which I can print, and alter with my very own pencils. I’ve been waiting weeks to do just that.

    Michael Molinaro, Esq.

    1. Michael: Many thanks, I appreciate your comments.

      Might I suggest something to all readers? Make your local media people aware of these pages. The media are free to use my graphics on their TV programs or in their newspapers, and any or all the things I’ve written.

      Why do I say this? (1) Because there does need to be better information out there; and (2) This might shame the authorities into releasing the data needed (to improve the analysis here, and remove the need for various assumptions).

      Anyone and everyone can assist the overall effort by doing this. Be part of the crowdsourcing solution! Be part of the actual ‘game’, rather than a spectator!

      Duncan

  29. Holy azimuths! Duncan, I just had a major eureka moment:

    remember, earlier, I had measured with my protractor the headings of the Inmarsat tracks at the last ping ring, as well as the azimuth to the subsatellite ground position and obtained empirically a radial velocity away from the subsatellite point of 323.7 knots–for both flight paths. To be identical down to 4 significant figures when measuring with a mere protractor could not be a coincidence–most likely.

    Thus, I was highly perplexed when I tried it on the next ping ring and the radial velocities were significantly different. However, I now realize I was laboring under the assumption that then next ping happened at 23:11, rather than 20:40. When I redid the analysis again, guess what: both empirically measured radial velocities were 280 knots.

    Again, this cannot be a coincidence. The Inmarsat folks who produced those flight paths clearly took into account the Doppler data and made sure that the headings when crossing the ping rings were consistent with the Doppler data.

    Which led me to think that the published Doppler “offsets” were actually, honest-to-god, corrected red shifts, with an “effective frequency” of 600 MHz. IOW:

    LOS speed = FBO * c / 600,000,000

    So, I recalculated the expected subsatellite radial velocities for the 00:11 and 22:40 ping rings using red shifts of 250 and 200 Hz respectively: I got 314 and 288 knots radial velocity from the subsatellite point respectively. This is within 3% of my empirical measurements with my plastic protractor, after copying by hand the Inmarsat flight paths to my Google Earth program.

    Time presses, as you say, and I haven’t yet had time to look at the other ping rings, but I suspect they will pan out as well.

    Cheers,
    Warren

  30. What I just did id the follow. Assuming everything is 2D on a Eucledian plane, use cosine theorem to calculate angle when pont a is n circle #1, point b is on concentrical circe #2, and the angle is the turn required to move point a to point b (the point also moves to a new circle with a different radius). Then if we move with constant speed from circle 1, to circle 2 and so on to circle 6, we have combined angle of turn.
    Speed n knots ; Angle in degrees
    295 32.8
    310 37.8
    330 42.7
    350 47.0
    365 50.1
    380 53.1
    400 57.0
    425 61.8
    450 66.4

    Unfortunately, I do not have a printer and cannot measure the angle to the point where the plane turned south to the point where they are looking for it.

  31. So now we are at the point where what I proposed earlier could be done.
    One could try to draw several great circle arcs starting a the same point and going to different points on the 2652 circle. Assuming constant speed, at the points where each big circle crosses the colored circles, we could draw radial speed component from Doppler affect and compare it with the radial speed component that comes from the assumption of constant speed and going along the great circle. Also, we could marks the points of intersection and by measuring the distance between them, verify how the speed was really close to constant one.
    Second try would be with lines of constant magnetic bearing (versus great circles), marking the same points and calculating speeds and comparing them to assumed constant speed.
    Third try would be more complicated – trying to draw paths that are neither parts of great circle nor having constant magnetic bearing. However, if we have success with first two types of lines, the third one might not be needed.

  32. Further to my previous post, the recent comment on the TMF Blog at strikes me that I should add a parametric approach to how I assume the BFO data should be used.

    I have prepared a “Outstanding Questions” sheet on my TMF/DS MH370 investigation crowdsourcing solution summary Google Doc at

    1. Thanks Steve.

      This is good stuff. Crowdsourcing works!

      Please everyone be aware of certain assumptions that have perforce been made in all parts of this investigation, and the results can only be as good as the assumptions. The decomposition of the BFO is an area of debate still, and I know that ‘Eugene’ does not agree with Mike Exner’s decomposition (which requires assumptions about the aircraft path). However, in that specific case (BFO to Doppler translation) I do not have the background or clarity of thought to judge which is the better solution; give me a week of doing nothing else and maybe I would, but I am pondering other things which I already have better knowledge about (e.g. simulation in STK).

      Duncan

    2. It seems my links did not get posted on the previous comment so here they are (without the HTML).

      …TMF Blog at “http://tmfassociates.com/blog/2014/03/24/understanding-the-satellite-ping-conclusion#comment-22814″

      …summary Google Doc at “https://docs.google.com/spreadsheet/ccc?key=0AqgaSUc7Mmn3dHZrODJJTVZuRXNGRUxEaDBlQk1lNWc&usp=sharing” rel=”nofollow”

  33. Duncan,

    Awesome work (as always).

    The data that you, GlobusMax, Mike/Ari have created is the data that I was planning to calculate as the starting assumptions for my partially-created model to attempt to iterate through potential speeds/headings to match the best-estimate for range-rings (ping-rings). I suspect I need more sleep than you seem to need but I hope to stop watching these blogs this weekend and crunch through this model.

    I do find it interesting that the plotted ping arcs have the 19:40 and 20:40 ping arcs outside the “18:22″ = “18:29″ ping arc which contradicts what the Inmarsat spokesperson was quoted as saying by Jeff Wise. (Is this yet another inconsistency in the public record or was the best fit that was itself based on the Inmarsat-provided Google Earth graphic from Annex-1 incorrect?)

    I have a number of hypotheses but for some reason (call it a EWAG for educated WAG instead of Scientific WAG) I have a “favorite” (I know I shouldn’t but I do) that the heading bug was set hurriedly to 180 (for the moment, I am taking the radar plot as true so I have to explain why an a/c on a heading of ~320 True changes course to 180) and the a/c was travelling at cruising speed so TAS was in the range of 460 to 470 kn (light 5 – 15kn winds for most of the route until around 45 minutes before the final ping). I don’t know if a B777 would maintain or return to cruising speed if the autopilot was instructed to make a course correction based on a rapid-response-based movement/setting of the heading bug.

    I will have to download STK too but based on your description of the GUI, I will not have time to become proficient in it this weekend. Skyvector, Excel and Google Earth will have to suffice for now I think.

    Steve

  34. Hi Duncan,

    Thank you for all your hard work, and your excellent posts.

    I wanted to let you know I sent an email to the Inmarsat Maritime Support , and they responded. I asked them to “Please release the raw satellite data that is related to the Malaysian Flight MH370. There are many good people around the world that are eager to help with the analysis of the data, or if nothing else they could help to provide peer review of the analysis (Doppler / burst frequency offset) of the data.”

    Their reply was:
    —————————-
    “The data recorded by Inmarsat in relation to MH370 is being used in an international investigation and, as such, is governed by international law relevant to such an investigation.

    If you believe that you are able to be of assistance to the investigation, may I recommend that you direct your request to the investigation authorities in Malaysia or the NTSB, which is part of the investigation team.”
    —————————-

    I don’t know if this information helps in any way, perhaps there are other individuals out there that could help with making contact with the Malaysian Ministry of Transport or the NTSB to request the raw data.

    Regards,
    Duane

    1. Hi Duane,

      I think the best chance of getting the pings is from JACC under the Australian, Freedom of Information Act.

      1. My information is (as noted in other comments from me) that the UK AAIB has refused to make the ping data to others. I do not mean ‘the public’. Specifically, I have been told that the UK AAIB has refused to make the ping data available to the relevant French authority (the BEA: Bureau d’Enquêtes et d’Analyses pour la sécurité de l’aviation civile) despite the French transport ministry making a direct request. The BEA – which I am again told was invited to be involved in the overall investigation by the Malaysian Government due to the fact that it was the BEA that was investigating the last event even vaguely like this, the Air France crash into the Atlantic a few years ago – apparently sent a team to KL but after waiting for ten days for the ping data they gave up and went home to Paris. Of course, the information I have been given by someone who wishes to remain anonymous might be wrong, but s/he is an experienced airline captain with close contacts to the BEA.

        The above might mean that the JACC does not have the ping data; or perhaps the British would give the data to Australia and not to France?

        Whichever, I’d suggest to readers that they might prompt some decent investigative journalists to follow that lead and shake it until it hurts. Not your local media. I am talking about the NY Times, the Washington Post, Le Monde, Der Spiegel, The Times, The Daily Telegraph (London), The Guardian.

        Cheers and best of luck,

        Duncan

  35. Duncan,
    You have done a lot of impressive analysis. However, most of the analysis is based on the “ping rings” whose data have been supplied by Inmarsat, which you and I have both evidently found no hard evidence on. I have been questioning the accuracy of this data for some time, and believe your assumed error of +- 0.3 ms may be far to low.

    My understanding of the pings in question is that these were routine transmissions from the ACARS system ground station in Australia to the plane ACARS system, to ascertain whether the plane was still active and able to receive data. I would assume a ping would consist of the following steps:

    A.Ground station composes ping message and sends it to the satellite
    B. Satellite rebroadcasts ping on a different frequency
    C. Ping is sent from satellite to aircraft SATCOM receiver
    D. SATCOM receiver determines it is an ACARS ping and routes it to ACARS unit
    E. ACARS determines it is a ping and formulates a reply
    F. Reply is sent to SATCOM
    G. SATCOM transmits reply to satellite
    H. satellite rebroadcasts reply and sends to ground station
    J. Ground station receives reply and records transit time.

    Note that each of these steps have uncertainties.

    Step A, the transit time for the signal to satellite, would depend on the actual distance between the ground station and the satellite, which in turn depends on the actual position of the satellite at the time and the accuracy of the surveyed location of the ground station. Even if the errors are very small for these, we are still faced with uncertainty, call this time +-T1.

    Step B time may or may not be inconsequential, but call the uncertainity +-T2.

    Steps D, E and F are where I have the most problems. We are dealing with two pieces of equipment made by different manufacturers. How each reacts to the message is not known, but may have significant variation. The SATCOM receiver has to decide the message goes to ACARS, then send it there. That unit has to decide that it is a ping message, not some other type of message, and produce a ping reply. It then has to send the reply back to the SATCOM receiver, who then transmits it back to the satellite. Now both of these units are probably running software to control these functions, and software can sometimes be doing something else before it gets to our task. I think there could be a large uncertainty Call this +-T3.

    H is the same as B, i.e. +-T2.

    We then get to J, where the total transit time is measured, also with some error, call this +-T4.

    So we compute the C and G times (which should be identical) by subtracting times B+D+E+F+H from result J. This is the actual transit time for the signal and determines the distance of the plane from the satellite and the diameter of the ring. Of course this time is subject to all of the possible errors, T1+T2+T3+T2+T4.

    Although you are assuming that Inmarsat knew what these errors were and compensated for them, I would think from an engineering standpoint some may just be approximations, especially D,E and F. Now they say they calibrated based on the signals received from the plane at known points, but remember the normal signals received from the plane as a result of ACARS transmissions, which were NOT triggered by the ground station, are of no use for calibration, since it would be unknown EXACTLY when they were sent. In fact any transmissions originated by the plane would not be useful for this purpose, although they could be used for Doppler calibration.

    The other thing I noticed. They have shown three data points very close together around time 1830 UTC. If pings were random on approximately an hourly basis, where do these data points come from?

    I could easily see where the total error in the transit time could exceed 1 millisecond, and my rough calculations say a 1 MS error would result in about a 1000 mile error in ground position of the ring, or to put it differently, +- 1 MS makes the ring into a 2000 mile wide band!

    What do you think?

  36. A pointer to those three, closely timed, comms events. I’ve been analysing detail of why messages are exchanged at various phases of the flight.
    We are told by MoTM/DCA that ACARS data transmissions from the aircraft were disabled. It’s my understanding that while outbound aircraft to ground messages may be disabled, inbound ground to aircraft messages are not. Malaysian Airlines subscribes to SITA’s ‘FMS Wind Uplink’ service for their A380 and B777 fleets (various sources state 40 aircraft, A380s + B777s number about 40). The data for that service comes from World Area Forecast Centres (WAFC’s), at NOAA & Met Office UK, with the forecasts issued at 00:00, 06:00, 12:00 and 18:00. With processing and distribution time through SITA’s data centres, 18:30 is a feasible time for data associated with that service to be relayed to the aircraft.

  37. Well done !

    Perhaps 290-300 knots is also on the low side. The B777 in normal cruise would be between M0.8 and M0.84. So speeds up to around 500 knots may still be possible.

  38. Based on the Elevation angle from aircraft to satellite (degrees), can we conclude that the airplane is holding a steady altitude for the whole flight? Or is there a change. At a steady altitude, moving away from the satellite would naturally bring a lower angle correct? However we would need the elevation of the satellite to calculate this I believe. This would help us answer if the plane was on a steady altitude (autopilot), or controlled altitude (pilot control).

    1. Hi Chris:
      (1) “Based on the Elevation angle from aircraft to satellite (degrees), can we conclude that the airplane is holding a steady altitude for the whole flight? ”
      No. The aircraft altitude makes no significant difference to the elevation angle to the satellite. Aircraft at 0 to 12 km altitude, satellite around 35,800 km altitude.
      (2) “At a steady altitude, moving away from the satellite would naturally bring a lower angle correct?”
      Yes. That’s what the ping rings delineate. See the table in the post above.
      (3) “This would help us answer if the plane was on a steady altitude (autopilot), or controlled altitude (pilot control).”
      No. The satellite data provides no information about the altitude. I showed this in earlier posts.

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