Constraining Possible Routes for MH370
Duncan Steel, 2014 April 08.
duncansteel.com
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.
This says it all, and quite succinctly really…
http://www.reddit.com/r/MH370/comments/22k80s/duncan_steel_theory_revisted/
What that reddit post fails to say is that the author and its participants didn’t read this blog in its entirety and don’t understand the scientific theoretical process. Small minds generally have difficulty grasping how magnificent brains function. Duncan’s brilliant and he’s also human. Their loss!
Hello Duncan Steel,
I have read a few of your articles and they are very interesting although I havn’t studied it close enough to understand it fully.
I would like to ask a few questions which have probably been asked before but I can’t find answers.
1) Did Inmarsat use data from their Pacific region satellite and could they have?
2) Are the antennas on the plane directional and if so do they track the satellite?
3) Can the plane communicate with more than one satellite at a time?
I realize you are working from publicly available data but don’t you think the investigators have more information either technical or other that has given them a reason to search in the present area?
It is costing a lot of money and I would think they wouldn’t be spending all that just based on guess work.
There is a radio monitoring station in Tasmania that can hear any radio station or radio transmission in the world. They have a large antenna setup and very sensitive equipment.
Then there is the American Pine Gap facility and the Australian over the horizon radar.
Perhaps they have used some aditional sources of tracking.
Finally, in your opinion do you think;
4) Hijacking is still on the cards?
5) Drugging of pilots is likely?
6) Lightning could be the cause?
If you want some entertainment I’ve got a few good constpiracy theories I can post for you , but I wouln’t want to clog up your site unless invited.
Kind Regards.
All of what you ask has already been covered on this site; some of it many times. Read the posts.
Answers based on what I know/don’t know: (1) No and no; (2) No and not applicable; (3) Yes in principle (although should be “Could the plane…”)
Your next question: Yes, they might have, but I do not know that; and I also know (I think) that they have used a mistaken interpretation of the BFO graph.
Your surmise is just that. You show a vast level of gullibility and lack of understanding, I am afraid. On this site we (mostly) are trying to use only facts, and not introduce nonsense. For example “There is a radio monitoring station in Tasmania that can hear any radio station or radio transmission in the world.” is nonsense. It cannot “hear” my remote car opener when I use it. It cannot “hear” radio transmissions that propagate line-of-sight only (UHF and above) if they are below the horizon, or behind a mountain, or…
I have no opinion on your 4,5,6 because I have no information on which to base that opinion.
And no, your conspiracy theories are not wanted.
Rather I’d say there is no evidence that an uninterruptible autopilot as described in the patent has ever been certified for use in an airliner by the FAA/EASA.
So if it hasn’t been certified Boeing couldn’t offer it as an option for their airliners or as a retrofit to airliners built after certification approval was granted.
Your comment:
“Correct, there is no evidence that Malaysian Airlines retrofitted their 9M-MRO with uninterruptible autopilot.”
Implies that Malaysian Airlines had the option to retrofit such a system but there is no evidence that they did. When in fact there is no such option.
@LGHamiltonUSA is there any evidence that an “uninterruptible autopilot” has been installed and certified for use in commercial airliners?
I’ve seen references to the patent and talk from Boeing representatives at the time (2007) that it would be available in a couple of years time. But no references to Boeing actually implementing it and having it certified for use etc.
An earlier post from LGHamilton (on 07 April) said this:
Boeing was awarded a patent for an uninterruptible autopilot technology in 2006 and installations began a year later. Since tail number 9M-MRO (commonly referred to as MH370) was delivered on 2002-05-31 it would have required a retrofit. I do not have access to maintenance records to confirm such an upgrade. According to this article, the uninterruptible autopilot can be manipulated from the ground.
(Repeated here for the convenience of all)
@LGHamilton – “installations began a year later.”
Any evidence for this?
In addition to Duncan’s convenient reply, the following statements are excerpts from an interesting reddit discussion:
“A supplemental type certificate (STC) is an FAA approved major modification or repair to an existing type certified aircraft, engine or propeller. As it adds to the existing type certificate, it is deemed ‘supplemental’.”
“Couple of interesting things about the Boeing 777 Type Certificate Data Sheet.
First, there’s some accidental morbid humor. There’s a typo for Exemption CRI E-3. Instead of saying “Thrust Reversal Testing” it says “Trust Reversal Testing.” Hahah.
Second, the 777 200ER isn’t technically listed on any TCDS. The FAA considers it subject to the general 777 TCDS as an implied subtype: ”The FAA does not recognise the 777-200ER as a separate model, since it is not listed on the Type Certificate Data Sheet (TCDS). Any Airworthiness Directive (AD) that includes the 777-200 will also include the ‘-200ER,’ unless the effectivity is limited by airplane line number or some other factor.’’ But when Boeing was asked if the 2013 FAA directive for airlines to fix cracking and corrosion under satellite antenna on Boeing 777 planes had been addressed on MH370, it turned out that the “some other factor” clause applied to MH370. Boeing said the directive did not apply to MH370 because unlike all the other types of 777s which share that same TCDS and are actually listed on it, 777-200ERs do not have that type of antenna. It seems the 777-200ER has its own type of antenna which is not described in its TCDS.
So, while no Supplemental Type Certificates appear to have been issued for installing Uninterruptible Autopilot Systems in 777s, the “some other factor” clause that allows the 777-200ER to have (and continue to receive in new units) a different antenna than its cohorts without listing what it is doesn’t exactly fill me with confidence that everything is on the up and up.”
Although I’ve read that 9M-MRO’s antennae are commonly called the “shark fin style” I do not have access to any proprietary engineering design drawings or design change orders. It is also unknown to me whether or not a retrofit of any uninterruptible autopilot avionics package would necessitate a change in the antennae.
And then there’s this from the same authority who initially denied that 400+ pounds of lithium-ion batteries were stowed in the airplane’s cargo hold:
Asked whether the Boeing 777-200 (MH370) was equipped with Uninterruptible Autopilot System that can prevent hijacking manually from inside, he said: “The aircraft is equipped as standard. There is nothing additional on the aircraft.”
Okey-dokey-smokey. I’ll take that on advisement and dig a bit further.
In the meantime, please see this CNN video from this pilots’ forum for more discussion.
And, just for good measure, let’s throw a little satellite technology and Freescale Malaysia into the mix.
OK, back to science. Carry on! LG
Amazing the quality of some posts, compared to…
I’ll say no more.
Okay so no evidence then.
Did you watch the CNN video? It’s all future tense, “new technology COULD…” etc. And then “IF such a system…”
But it is useful for conspiracy theories!
Hi Sean ~ Correct, there is no evidence that Malaysian Airlines retrofitted their 9M-MRO with uninterruptible autopilot. Since I now don’t believe anything the Malaysian government says, I’ve got to investigate every reasonable possibility before excluding it from a hypothesis. I’m not interested in formulating a conspiracy theory; I’m seeking the truth, and right now I think the Malaysian government is lying through their collective pantat. And, while I’m on a roll, I’m beginning to think they’re complicit in this event.
Thanks LG.
Bringing this (the possibility of an uninterruptible autopilot) up was useful specifically so that it could be considered, and then excluded. I won’t quote Arthur Conan Doyle again.
A wonderful and thorough analysis, while 14 ships and 8 airplanes search the empty ocean off Geraldton, looking at 33 kHz pings. If a real physicist had access to those data to begin with, the plane might already have been found. Best, HRD
Thanks Horace, I type as my face goes red with embarrassment.
If the “pings” are at 33Khz, that too is puzzling. The specification for the underwater locator beacon says the operating frequency is 37.5 kHz +or- 1kHz.
http://www.radiantpowercorp.com/dk-series-underwater-locator-beacons.aspx
http://www.benthos.com/_doc/main/Brochures_Datasheets/elp362D__001815__rev_L.pdf
I would expect it to maintain that frequency under all the other specification conditions, such as temperature, acceleration etc. The pulse length is also required to be not less than 9mS, and the pulse repetition rate not less than 0.9 sec. One might make an allowance for the [carrier] frequency to be out of spec if the pulse period and repetition rate were within bounds, but being that far out is almost incredulous.
Duncan//
Back to my favorite graphic. I previously expressed my feelings (perhaps too bombastically) about the graphic. There’s no point in repeating things. I agree with your analysis entirely.
Whenever I review a report of any sort I always look for internal consistency. If a report is internally inconsistent either the report writers do not understand the topic (incompetence) or someone is diddling with the data. Either way the report becomes questionable. Let’s look at the graphic.
Up until about 1720Z this was a normal flight. The graphic shows four measured data points and four predicted data points. The measured points probably resulted from ACARS transactions rather than ‘pings’, though the results should be identical.
The first question is, ‘Why is there a difference between measured and predicted?’ All four of these points should be congruent. The aircraft was on its normal flight path. Either their predictive model is inaccurate or they don’t know what they’re doing.
Moving on to what amounts to a set of three pings/transaction. I asked Tim Farrar if the Air Earth Station (AES) could initiate a ping. He said that he thought so and that a power cycle could easily cause it. He also thought that an aggressive turn could cause the AES antenna to break lock with the satellite and this could initiate a re-registration. Since the first of the three occurs about an hour after ACARS quit it could easily be a handshake request from the system because it hadn’t heard from the AES for an hour. The next two bother me. If a handshake had occurred and then, say, the aircraft went into inverted flight and then recovered, the antenna would have lost line of sight to the satellite. But, so what? The system could care less because of the recent handshake. The AES could also care less because apparently there are no constant transactions between the GES and the AES. So there’s no reason for a re-registration. The power cycle could make sense.
What happens after a power cycle? Would all of the aircraft’s computers reboot? Would the ACARS computer automatically reboot? Is the ACARS computer a standalone box or is the ACARS program hosted on another computer? Perhaps a better question is what happens to the aircraft in a power off situation? Could you even fly the airplane if the master switch is turned off? Would the engines shut down? How long does it take for all of the flight management computers to reboot? Somehow I’m having a bit of difficulty with a complete power off/power on cycle. Point is that two of these three transmissions really do not make any sense to me.
Why are they there? A possible turn? I don’t believe that. Why would any part of this system initiate two transactions/handshakes/pings simply because of a turn? Even if the aircraft completed a roll why would the AES re-register? Makes no sense. Is it possible that the first and third are not real points but were added by someone? Maybe that’s crazy.
Anyway, from my perspective this graphic has so many internal inconsistencies that its credibility is questionable.
Keep up the good work,
Bob
Possible Scenario:
Ping 1 ~ Forced power cycle reset
Ping 2 ~ Initiate uninterruptible autopilot*
Ping 3 ~ Registration to satcom via ground
*Assumes 9M-MRO was retrofitted.
@mung why can’t you imagine a partial ping being sent?
Even if the ping response from the aircraft is say only a transmission of 20ms why can’t say 10ms be sent from the Satcom unit before the power fails or it gets smashed?
While possible the chances of that event happening during that short time window is insane. The event, would have had to happen at the exact time of that hourly transmission. Can you even fathom the probability of that happening?
Now based on the very slight chance that it could have happened, how did they know it was MH370 and not something else? If they only had a partial ping, it couldn’t have possibly contained enough data to determine that it was from that system. You wouldn’t be able to decode the packet into text without the whole ping or at least a good portion of it.
Duncan: I’ve been through the aqqa analysis in a bit more detail. That BFO analysis is more detailed, but they came to the same conclusion I did on nearly everything. Our interpretation of the BFO values is the same, the 4 Inmarsat freqencies are the same, the total Doppler is the same (all within 1% anyway). One thing I do not understand is the satellite to LES L band correction. I assume that was mislabled. The final results are essentially the same for the last 5 points. They did the global solution for best fit to an assumed model which is what I have been advocating since the beginning (but unable to perform the math). I will look closer this evening, but from my first read, it looks good.
Mike
@Ole you mentioned:
@Sean. Nevertheless IMHO this part of you calculation has a problem:
—————-
So the satellite LOS velocity towards the aircraft is roughly:
159.6 * cos(50) * cos(45) ~= 72.5kts
—————-
IMHO it assumes the sat’s velocity is parallel to the earth surface at the position of the observer. Actually it is mainly parallel to the axis of the earth. So for the observer on the earth, the sat’s velocity vector points partly towards the observer but also partly into the sky.
————
At 00:11UTC the satellite’s velocity vector was:
Vx -> 1.5m/s
Vy -> -1.5m/s
Vz -> -82.1m/s
So for my napkin calculation I assumed that Vx and Vy were 0.
IMHO:
For the napkin it is OK to reduce the sat’s velocity to Vz .
_But_ Vz is not parallel to the surface of the earth at the position of the observer. If it were parallel, your calculation – i.e. taking the cosine of elevation and azimuth – would be OK.
Vz is parallel to the axis of the earth, and for observers at all latitudes other than the equator, the axis of earth is not parallel to the surface. For those observers Vz is pointing away from the surface, i.e. it is much closer to perpendicular to the line of sight than your calculation assumes.
When I do the vector math the position of the currently detected pinger signals is in the ~6 m/s LOS speed cone. The southernmost track to the roaring forties previously proposed by inmarsat is in the ~10 m/s LOS speed cone.
Perth is in the ~8m/s cone.
Here is a question that bothers me. How did Inmarsat get a partial ping? Either they got a ping or they didn’t get a ping. We are talking about a very short message and if the message was sent, it was sent and they would have received it.
I have thought from day one that the Inmarsat results were very fishy and thanks to your work, I have proof to back up what my gut told me.
Thanks for the comment Mung. I have no answer to your question I am afraid.
It is just another point that makes one question the validity of Inmarsat’s statements. I have my Ham Radio license and I understand propagation and data transmission over radio. If what I have read about the Inmarsat system is accurate, the ping would be a single packet of data. Now, you have a computer on the plane that has to create the data packet and then it would key up the radio and transmit the packet. The only way that they could have gotten a partial packet is if the radio stopped transmitting in the middle of the packet being sent. We are talking about a time of milliseconds. What are the odds that something caused the radio to turn off right in the middle of that transmission?
Mung: At present we are all (well, most of us, anyway) working from a position of ignorance on that one…
A minor point about the end-of-run situation on board a 777. I understand that a 777 training pilot has put the results of a professional simulator run on the web. I haven’t read it or found it yet, but heresay suggests that this is what it says:
1 – First engine dies. Plane continues in same direction at reduced speed. The Automatic Thrust Asymmetry Rudder Trim system will ensure this.
2 – Second engine dies. All electrics fail, except critical battery back-ups. Thrust Asymmetry Rudder Trim is removed. Aircraft slows, but continues in same direction.
3 – Aircraft begins to dive, increasing speed. It also banks, up to 20deg, because there is no power to the automatic stability systems.
4 – As aircraft speeds up, the pop-up Ram-Air Turbine back-up power generator deploys. Power is restored to various circuits as the available power ramps up. The aircraft levels, then tries to automatically restart engines and climb. At this point a ping to the Inmarsat system might be attempted as the system reboots.
5 – Engine restart fails due to fuel starvation. Aircraft slows, and power provision from Ram-Air Turbine becomes insufficient. All electrics fail again.
6 – Stages 3-5 are then repeated, the aircraft descending in a series of phugoid oscillations, until it strikes the ground or sea. The impact is almost certain to be severe, and the plane will disintegrate.
If a conscious pilot were at the controls, it is likely that he would hold the aircraft in a shallow dive after stage 4, to maintain electrical power and controllability as the ground approached. In that case there would only be one ‘rebooting ping’. It is possible, though difficult, to land an aircraft in this condition on land or sea and maintain fuselage and wing integrity. If this happened on the sea, it is possible for the aircraft to then sink with minimal debris.
Thanks for that: very useful, very instructive.
You are clearly not a dodgy geezer at all, and so I claim my ten quid.
I have been looking out for this information, as Duncan knows.
In response to “DG’s” last paragraph & the rebooting of the satcom equipment/partial ping.
There wouldn’t be a ‘reboot’ for the satcom terminal, once power source is down to the main battery & RAT generator, electrical power would not be reinstated to the satcom terminal (& many other systems). Normal engine driven power generation delivers 240kVA, one engine plus the Aux Power Unit (APU) would be 210kVA whereas the RAT generator delivers only 7.5kVA plus the 47Ah battery.
Yes, I agree with your hypothesis that it was flying on autopilot since turning south. It looks like it was making a circle since then. Like if you start walking with your eyes closed, you would make circles of huge diameter. Looks like the plane was doing a circle.
Duncan
You are doing great work. It is focused on the STK modeling. Your sense of focus is sorely missing among those in the media with the access to ask Angus Houston questions.
What questions would you like to have asked? Maybe we can get some reporter(s) to act as your servant(s) and trained monkey(s). The nature of their business is to jump on the latest fad. I know you are busy, so you probably are unaware of what those daily fads are. One recent one was that the flight was using stealth tactics to avoid Sumatran radar. Could the Sumatrans simply be covering up that they turn their radars off in the wee hours and therefore don’t know whether or not MH370 crossed through their airspace? The discipline of Occam’s Razor seems to elude the reporters thought processes.
FYI – Angus Houston reported that they now have four separate instances where they have gotten what seem to be sonar pings consistent with those emitted by the “black boxes” using the equipment towed by the Ocean Shield.
http://www.foxnews.com/world/2014/04/09/malaysia-plane-search-teams-relocate-signals-in-indian-ocean/
They have moved the search box several times, due to refined data. You are a critical piece in that data refinement! My suggestion is to write your questions down for the trained monkeys to ask. The pings are getting softer, as expected due to limited battery life. You may have done a great deal to locate the wreckage in the nick of time.
Well done!
Thanks for that Bruce, appreciated.
I am just not that interested in fads, as you can imagine!
If you would like to alert media (in Australia and elsewhere) to this website (plus other good ones like http://www.aqqa.org/ ) then that would be useful, perhaps, in getting appropriate questions asked.
For example, the media might be asking Houston:
(1) Why has there been no withdrawal of the definitive statement that the aircraft must have flown south and into the Indian Ocean now that it has been demonstrated that there is no leverage in the Inmarsat data to favour one direction over the other?
[Note, again, I am NOT saying that it went north; I am simply saying that the analysis that led to the announcement made by the Malaysian Government on 24/25 March was flawed]
(2) Does any part of the Australian Government have direct access to the raw data from Inmarsat-3F1, or is it privy directly to the analysis done by Inmarsat’s engineers?
(3) Given that none of the analysis of the satellite-derived information has been done within Australia, why do you continue to work on the basis of the crumbs of information made available to you by your overseas sources (the UK AAIB and the US NTSB) rather than attempt your (Australia’s) own analysis of the satellite information?
(4) Why do you ignore the crowdsourced analyses of the possible aircraft routes, given that the people involved have demonstrated that they are able to duplicate the Inmarsat results, and also have demonstrated that Inmarsat made errors in some aspects of their analyses?
I believe we all agree on this. The public need to know that there is basis for the searches that are performed. More debris and more assumed FDR pings are not “more clues” or “more evidence” or “best ever lead” if this cannot be linked to a wreckage.
Alex look at my earlier comment about doing a napkin check where I show calculating the LOS speed between the satellite at the 00:11UTC ping and the aircraft at a specific point on that ping arc.
You’ll see that the satellite had a speed of roughly 159kts heading due south.
Now given the elevation angle between the satellite and the aircraft that means it’s speed down the cone in effect is roughly:
159 * cos(50) ~= 102kts
So if the aircraft was stationary on the 00:11UTC ping arc and was exactly due north of the satellite then the LOS speed between the satellite and the aircraft would be 102kts.
As you move the aircraft along the ping arc from say due north towards the east the LOS speed will only drop, e.g. assuming it was on the arc NE of the satellite then the LOS speed would be:
102 * cos(45) = 72kts.
So there is nowhere on the 00:11UTC ping arc that you could place a stationary aircraft and get to see a LOS speed of 125kts.
Now don’t forget Duncan has mentioned he’s not confident on the BFO data and therefore the calculated LOS speeds that you quote.
Thank you Sean for helping to preserve my sanity. It gets quite exasperating at times…
Sean,
I posted a comment to your earlier calculation.
Sean, Ole,
Thank you for the replies. However, what the two of you are saying doesn’t seem to correspond with what Duncan had said in his March 26 2.50 comment in the TMF blog. So either Duncan was wrong in his comment or the two of you are wrong in your calculations.
I have no mathematical training but if I understand Duncan correctly, the satellite component would be equal to vz cos 45 or approximately 0.7vz.
Duncan, sorry to keep pestering you.
According to Mike Exner, the LOS values for the 6 successful pings are as follows: 39.77, 39.14, 60.80, 79.85, 100.64 and 125.35 knots. U have given a formula in your March 26 2.50 comment in the TMF blog, regarding the calculation of the satellite component of the LOS at any one time (approximately 0.7 of the satellite speed at that moment in time).
Applying your formula, it would appear that Mike’s LOS values were derived solely from the movement of the satellite. In other words, the plane was not moving during all 6 pings.
I would be very grateful if u can spare a few moments to explain any flaw in the foregoing reasoning or the conclusion reached.
“(approximately 0.7 of the satellite speed at that moment in time).”
Duncan as everybody else is only human (at least I hope) 😉
And he always preaches to doubt everything.
You can draw a small 2 dimensional sketch of a cartesian coordinate system. Put the center of the earth at (0,0), the surface of the earth will be at (0,6) and (6,0) the satellite at (0,42). Draw the sat velocity vector as (0,42)->(1,42).
You can see the LOS component of the sat’s velocity toward any point on earth will never get greater than roughly 6/42=1/7 of the sat’s total velocity (in y-direction in this 2d example)
I’ll let someone else tell Ole about resolving cartesian velocities as opposed to angular velocities…
No need for that (I hope).
The cartesian coordinate system was just to describe a sketch which one can then use to split the sat’s velocity vector into radial and tangential component to get a ballpark figure of the radial (LOS) component.
Angular velocities (dphi/dt) not yet involved here.
“Applying your formula” – Applying my formula incorrectly.
The wrongness of what you have done is simple to see. The satellite changes direction (from N-S to S-N) at 19:36 UTC. According to your (wrong) thinking with the aircraft speed zero that would imply a LOS speed that is negative prior to 19:36. Do you see that in my graphs?
Please, Alex, no more comments. I will delete all incoming unread from now on.
Time for another napkin to try work backwards.
Assuming the LOS speeds you have derived from the BFO data are correct then for a given position on a ping arc and an assumed aircraft ground speed then there is only one angle between the aircraft’s ground track and the vector between the aircraft and the satellite that will result in matching the LOS speed for that ping arc.
So for example in my earlier napkin calculation of your southern 400kt route intersecting the 00:11UTC ping arc the angle needed to be about 60 degrees between the aircraft’s ground track and the vector between the aircraft and the satellite.
Resulting in 2 possible ground tracks at that point, 195 or 75 versus the rough 155 degree track that your 400kt route has at that point.
So my idea is to choose an aircraft ground speed, e.g. 400kt then sample positions on the 00:11UTC arc (say 50 in 1 degree increments) and work out what the resulting aircraft ground track would have to be for each of the sample points and then see if flying back for 91mins at that aircraft speed and that ground track results in an intersection with the 22:40UTC ping arc.
“Assuming the LOS speeds you have derived from the BFO data are correct ” – My working position right now is that the assumption you’ve stated there is incorrect, because the BFO graph is wrong in itself.
“So my idea is to choose an aircraft ground speed” – Go for it, and tell us the outcome.
Duncan
2014/04/03 AT 9:03 AM
“presumably because Duncan’s chart does not account for the motion of the satellite in the same way?”
So Inmarsat got the motion of their satellite wrong?
POSSIBLY IMPLIED:
Angus Houston, JACC, 2014/04/06
“The correction arises from new information about the state of the satellite itself when it received transmissions from MH370 during its flight.”
NOTE TO THE UK-AAIB:
~ “Oh what a tangled web we weave, When first we practise to deceive!” – Sir Walter Scott, Marmion, Canto vi. Stanza 17 ~
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 think the problem is the first segment. From the BFO data, the plane plausibly headed west after some manouver, then went south (or north) before the next ping. In other words, a straight heading is not plausible for the first segment. This throws the rest of the flight paths off.
You would need to make a best guess starting point for 19:40 UTC and take things from there …
Joe.
Joe: I am afraid that your intuition is wrong. Sorry!
As you wrote, consider the 3 southerly routes. In the latter stages of the paths shown, the slower aircraft (300 knots) has a path almost radially away from the sub-satellite position (but remember that the LOS speeds are from the actual satellite position to the aircraft: I am just here describing things along Earth’s surface for ease of understanding), whereas the 400 and 460 knot routes have far lesser angles compared to the sub-satellite position. Thus although their SPEEDS are different, their VELOCITIES relative to the satellite are much the same, and so the calculated LOS speeds are the same.
This is why I suggested that somewhere in amongst Inmarsat’s analysis a circular argument has been made, and they did not realise it.
Hi Duncan,
No worries, what you say about LOS speeds for the different air speeds makes sense, although I still have the same reservations about the first (18:29-19:40) segment.
Another thing that occurs to me, is that the smoother flight paths (and consequently, LOS plot) produced at 460 knots, means that this air speed is the best match for the ping data (reverse-engineered ping rings). Then again, the Immarsat Doppler plot mentions 450 knots in its heading, so that’s possibly why?
Joe.
Joe: Yes, good observation (and I was thinking much the same thing which is why I am just writing up a post that includes a 500 knot route, to see whether that is ‘smoother’ still!).
That is, for others: One might expect, if the aircraft were continuing on some heading under autopilot control following a great circle, that the path taken would NOT be curved. I/Joe are not saying due north or due south (necessarily), just not curved. And the 460 knot path is that which is ‘straightest’.