Ever since the Independent Group first issued a public report offering guidance as to where search efforts for MH370 should be concentrated, people have been asking for details on group members’ calculated routes. Unfortunately, everyone is doing this work for free, in their spare time, and have other things to attend to as well, so providing explanations has not been a priority. At last, however, Richard Godfrey, one of the hardest-working of all, has gallantly stepped up and delivered a polished-up version of his latest theory so that all interested parties can have a look under the hood. Above is a screen shot of his model, which he dubs “MH370 Flight Path Model V13/1 Final,” as it appears in Google Earth. Details after the jump.
At left is a close up of the route’s end point, overlain on a map of the current underwater search.
Richard describes the basic parameters of the route as follows:
(1) the Auto Pilot was engaged and had waypoints such as ISBIX and S35E90 programmed, hence a constant track for the end game.
(2) the Auto Throttle was engaged and the Air Speed followed a Long Range Cruise simulation equation for Mach Speed provided by Victor.
(3) the True Air Speed is calculated from the Mach Speed taking the Air Temperature into account.
(4) the Ground Speed is calculated from the Air Speed taking the Winds into account.
Here’s an Excel file with all the data: MH370 Flight Path Model V13.1 Final
Some explanation of the image above from Richard:
The V13.1 End Point is 3.0 km further WSW than V13.0 and both are close to Victor’s latest End Point.
The Yellow lines are the Fugro Equator survey area and the V13.1 End Point is positioned centrally in the survey area.
The Light Blue lines are the Fugro Discovery search area and the V13.1 End Point is positioned within the current search area.
The two Red lines are Barry’s latest 7th Arc at 0 m (left) and 10,668 m (right) at 00:19:29 where I calculate MH370 is at a Geopotential Altitude of 35,166.9 feet or 10,718.9 m.
The V13.1 End Point is on Barry’s 7th Arc at 10,668 m.
The Brown line is where I place the Ping Ring at 00:19:37.443 at a Geopotential Altitude of 34,537.45 feet using a simple .kml circle generator centred on a sub-satellite point at 0.528261N 64.472083E with a radius of 4941.5787 km.
A new ATSB Video is available here:
youtu.be/F6ewJt83vJU
Maybe I am missing something in the sheet, “Keypoints”. First, I presume that column N is geodetic latitude, although later calculations use it as if it were geocentric. Column BJ is labeled “Aircraft WGS84 N (km)”. It seems the equation is intended to actually calculate the true earth radius at the aircraft location (since the altitude is added in in columns BK, BL, and BM). Now for row 22, at latitude -0.86 degrees (basically on the equator), the value is given as 6378.14, which is indeed the equatorial radius of the earth. As the latitude becomes more negative (e.g., row 25, latitude -25 degrees), the value should be dropping; I compute it should be 6374.34. However, the value given is actually bigger: 6381.95. Either the earth is prolate (and Cassini was right), or this equation is not correct.
sk999:
The earth radius math is correct. The earth is an oblate spheroid, so the surface height (radius) increases as you move north or south from the equator, as it should.
sk999:
Note that the geocentric radius decreases with latitude, but the transverse radius (N) increases. Perhaps this is a source of confusion?
sk999:
Barry suggests the following references:
Thomas, P. D. (1952). Conformal Projections in Geodesy and Cartography.
Special Publication 251, U.S. Coast and Geodetic Survey. Available online
at: http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no2511952.pdf
This model’s author is to be commended for applying so much effort and expertise, pro bono. Thank you.
It is a good model, postulating a route which, relative to that of Dr. Ulich, is almost as intuitive, and which fits the data almost as well.
We should search the hotspot along the 7th arc which encompasses BOTH models: E84-E88. We should do so BEFORE searching far less likely places (like the zone Go Phoenix has now spent several weeks searching).
If anyone thinks they should search E88 (V13.1) and NOT E84 (Ulich), I’d like to see their argument presented in this forum.
Any such argument CANNOT reference fuel feasibility; the feasible zone in Fig.3 specifies the SW extremity corresponding to an 18:40 FMT; if an 18:28 FMT is feasible, this feasibility zone moves 4 radial degrees clockwise (nearly 4 degrees longitude). This renders E84 FEASIBLE.
Despite its title, Fig.2 is NOT a useful reference for performance limits under an 18:28 FMT assumption. The feasible zone is strictly a reprint of the Fig.3 (18:40) zone, and its FL350 and FL400 paths were doctored and suppressed, respectively, so as to hide the fact that an 18:28 turn assumption must – MUST – push the feasibility zone out to E84.
Nor can any such argument reference BFO-indicated FMT time. An 18:28 FMT is JUST as feasible as 18:40. Jeff’s guest post early this week made an argument for 18:40 which has already been thoroughly “pre-butted” by the path-fitting principles and practices documented in Dr. Ulich’s white paper.
The timing of this guest post – which happens to muddy the waters just as the sharks of logic were homing in on the TRUE SW terminus of the feasibility zone – is curious. It reminds me of a similar publication a few months ago (“decompression scenario”) which happened to muddy the waters when those same sharks were homing in on the feasibility zone’s NE terminus.
Same author in both cases.
Probably just a coincidence.
Following up to my previous post, it is clear that column BJ on spreadsheet “Key Points” is intended to be the “geocentric radius” since that is how it is used in computing the aircraft x, y, and z components in columns BK, BL, and BM. However, the equation used to compute it is wrong. The proper equation is given here: http://www.mathworks.com/help/aeroblks/radiusatgeocentriclatitude.html and can be derived from first principles without difficulty. The Mathworks version uses flattening (1-b/a) as a parameter whereas the spreadsheet uses eccentricity (1-[b/a]^2) instead. Perhaps an error was made in converting from one form to the other?
It is also clear that the spreadsheet makes no distinction between geodetic and geocentric latitude. For example, on the sheet “Constants”, the geodetic latitude of Perth is enter in cell B3 and it is used in the equations to convert to WGS84 X and Y in cells M3 and N3, but those equations require geocentric latitude instead.
Airlandseaman, it is unclear why you provided references to conformal projections – they are of no use here.
In summary, while the spreadsheet is a fine piece of work, it still needs much scrubbing before one can use it to determine where to lower the towed sonar.
Brock McEwen:
I do not understand why you are bashing the “decompression scenario” described in the September 9 IG paper. It’s not that complicated. It was not put forward as the most likely scenario. It was put forward as a 2nd possible human factors driven hypothesis, but shown by the modeling effort to be less likely than the FL350 scenario, due to significantly higher BFO fit errors. It is discussed in part to show that we were not focused exclusively on a single human factors driven scenario. We looked at several and chose what we thought were the two most often considered by many people. How that muddies any water is a mystery to me.
Regarding the FMT, timing here is important, and just saying “[a]n 18:28 FMT is JUST as feasible as 18:40.” does not make it so. Ulich’s earlier analysis is not the final word on this subject. We can continue the discussion, but you can’t simply wave a wand and declare the two theories equal. They are not. It turned somewhere, and figuring it out is important.
Same for fuel. There are limits. We have conducted extensive fuel analysis independent of the ATSB, and we do not agree that the aircraft could have made it to 84E following Ulich’s logic. Again, we can debate the analysis, but you can’t simply deem the fuel analysis issue to be settled when it is not.
To be clear, I respect the work Ulich has contributed. He gets an A+ on documentation. And we agree with most, but not all of his assumptions and math. If I were in ATSB’s shoes, and I had a bit of extra money to spend, I would push the survey a bit further south-west before adding to the north-east.
sk999:
Sorry dude, but you are simple wrong on every criticism. Checked and double checked. All the math is correct. You seem to be confused on the various coordinate systems. Out of time to help.
Sk999,
If I may refer you once again to Thomas 1952, eqn. 152, for the transverse radius, the radius of the osculating vertical circle which is orthogonal to the meridional ellipse at the point defined on the surface of an ellipsoid in geodetic coordinates by (lon,lat).
Note the transformation provided in Thomas by system 155 uses the transverse radius to transform geodetic to ECEF Cartesian. It is perhaps too implicit, but the latitudes in RG’s V13 model are to be interpreted as WGS84 geodetic latitudes and therefore the transformations that model uses are entirely appropriate.
Kind regards,
Barry
@Brock: The fuel consumption analysis is a bit more complicated than you describe. Each Maximum Range Cruise (MRC) curve describes a path with a particular Mach number versus time, where the Mach number is a function of altitude and weight. If the plane is not flown at that Mach number, then the range will not be achieved.
In the last analysis I have seen of Bobby’s, the predicted air speeds correspond to Mach numbers higher than the Long Range Cruise (LRC) speeds. In fact, the LRC speed is higher than the Maximum Range Condition (MRC)speed, with lower range. (We have the Mach number as a function of altitude and plane weight for the LRC condition for what we believe is the correct RR engine. We do not have these values for the MRC condition, but we know the MRC speeds are slower and achieve a greater range, by definition.)
So basically, in order to say that a particular path and end point are consistent with a range using the MRC results, the speeds and position have to satisfy the BTO AND the speeds have to be consistent with the MRC speed profiles.
Also, Bobby only assumes a constant true air speed until 22:41, and then the speed drops, presumably due to an early flame out of one engine at some time before 00:11. The reason for an early flame out has not been explained. This would also reduce the achievable range.
One way to do the calculation is to show the Mach number along the path is consistent with the fuel consumption model. Knowing the temperature at the assumed altitude, the true air speed can be determined, and then the ground speed is determined knowing the wind speed and direction.
Airlandseaman,
I am willing to be shown wrong. I will publish my numbers for a sample time and how I computed them. It will take a bit of time to prepare.
sk999
@airlandseasman: the “decompression scenario” flew at a speed of 323KTAS – so slow that MH370 would have run out of fuel well below 00:19, according to the ATSB’s own published performance limits. It muddied MY waters because I was simultaneously attempting to prove the exact same thing regarding the only complete path search officials ever published which ended at the s21 site they chose to try to listen for acoustic pings. This path was precisely replicated by the “decompression scenario” – right down to the 323 KTAS.
I have no right to speak for Dr. Ulich – nor do I want to get between the two of you. I would vastly prefer if you experts achieved consensus on a reasonable confidence interval – in radial degrees – on either side of the BFO-indicated bearings. We could then rule objectively on the BFO-feasibility of his path (and yours). Do you disagree with the manner in which Dr. Ulich developed his BFO confidence intervals?
Mike, I believe your second paragraph derides me for supporting the ATSB’s assumption of record, which is precisely as I’ve stated it. I’ve also shown graphically how close the BFO-indicated bearings are to those of an 18:28FMT-then-500KTAS route. So it’s not like Dr. Ulich’s paper is the only thing in my corner.
Your derision becomes even more ridiculous in light of the fact that I’m the one who merely wants to respect BOTH points of view, and search the full RANGE (E84-E88). By contrast, the mere posting of your paper effectively attempts to REDUCE the chances of searching near E84, by (wrongly, IMO) implying MH370 “must have” blown range on the later FMT.
Having let off this steam, I confess I am impressed by – and grateful for – the openness you’ve shown towards SOME expansion west of the search area. Thank you. I offer in return my openness to being persuaded by your “turn in progress” analysis. If you can demonstrate statistically that an 18:28FMT-then-500KTAS path differs from the BFO-indicated path by a statistically significant margin – and that yours does not – I’m sold.
@Victor: if Mike gets to create an acronym (thanks, by the way), so do I:
S7P = Southwest intersection of 7th arc and Performance limit
Re: performance limits: Victor, do you deny any of these statements:
1. “if FMT @18:40 gives S7P=E88, then FMT @18:28 gives S7P=E84”
(Proof: 12 minutes = 100nmi on pre-FMT bearing = 125nmi further south on 19:41 arc = 4 radial degrees clockwise on this AND ALL subsequent arcs = roughly 3.9 degrees longitude to the west of E88.)
2. “FMT @18:40 gives S7P=E88”
(Proof: ATSB Oct.8 Update, Fig.3 S7P)
3. “FMT @18:28 gives S7P=E84”
(Proof: 1 + 2)
Re: Bobby’s scenario: I’m no expert (as has been demonstrated ad nauseam), so I invite Bobby to defend his modeled speed throughout. If you don’t like his PARTICULAR 18:28FMT-then-book-it-south scenario, just use the ATSB’s – it’s the theoretical line ending at S7P=E88 in Fig.3, shifted 4 radial degrees west.
My goal is not to force scientific consensus on a PATH, but on a SEARCH zone (extension).
(IF the signal data is valid, that is. If it is as doctored as was Fig.2 – or the “drifted west” directive – or the acoustic ping analysis – or the “passed near a NW point” claim – or the June “best estimate” of s30 – or the “preliminary report” paths – then the above goal happens to double as a means of denying the JIT the wiggle room to waste further months (years?) fabricating brand new insights.)
Would an early flameout of one engine necessarily reduce range? Some pilots on PPRUNE seemed to feel performance was MAXIMIZED by shutting down one engine – but this may not relate to the phenomenon you’re considering.
SK999,
Airlandseaman has already provided the reference above to Thomas, P. D. (1952). Conformal Projections in Geodesy and Cartography. Special Publication 251, U.S. Coast and Geodetic Survey.
Available online at: http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no2511952.pdf
Please take a look at the section on the Derivation of Mapping Formula and the sub-section on the Spheroid starting on page 58. In particular the 3 equations (155) and the equation (152)
x = (N + h) * cos(lat) * cos(lon)
y = (N + h) * cos(lat) * sin(lon)
z = (N*(1-e^2) + h) * sin(lat)
where:
N = a / sqrt(1-e^2*sin(lat)^2)
a = 6378137 metres
e = 0.0818191908426215
h: height above the ellipsoid along a normal to its surface
I have implemented these equations in the model.
This is the function required to map a geodetic latitude, together with a longitude, into the ECEF Cartesian components.
The model works in terms of geodetic WGS84 latitudes.
Nobody is claiming that a transformation from geodetic coordinates to Cartesian coordinates is in any way a conformal projection.
I apologise that the “look under the hood” does not include any description of the Excel Spreadsheet. I am still working on that.
The Excel Spreadsheet should open at the first Sheet called “Key Points”. This is the one to look at. You can ignore all the other Sheets as they just support various further investigations.
This path is one of many possible solutions. The methodology is generalised, but in this version a particular set of conditions has been chosen:
(1) the Auto Pilot was engaged and had waypoints such as ISBIX and S35E90 programmed, hence a constant track for the end game.
(2) the Auto Throttle was engaged and the Air Speed followed a Long Range Cruise simulation equation for Mach Speed provided by Victor.
(3) the True Air Speed is calculated from the Mach Speed taking the Air Temperature into account.
(4) the Ground Speed is calculated from the Air Speed taking the Winds into account.
As always, I am very grateful for any corrections or comments you may have.
Richard,
Many thanks – Latitude (column N) is indeed geodetic, and “N” (column BJ) is distance to the z-axis along a normal to the surface. As a cross-check, I derived the equation for geocentric radius from your x,y,z, converted geodetic to geocentric latitude, and reproduced the equations I have been using. Always nice to check that the equations in the book are correct.
Here is a summary of my cross-checks thus far of the V13.1 spreadsheet. I will just give the maximum difference between values I compute and what is in the sheet. I picked line 25, UT 22:41:21.9 longitude 91.116, geodetic latitude -25.0008, heading 185.5786 (column R), ground speed 472 (columns AO), altitude 37061 feet (column AQ). Exact agreement is not to be expected because I convert UT to hours and round to 3 decimal places (in order to use it as an index in various places.)
Satellite position (AZ, BA, BB) Maximum difference 0.2 km
Aircraft position (BK, BL, BM) Maximum difference 0.1 km
Satellite velocity (CH, CI, CJ) Maximum difference 0.3 km/hr
Aircraft velocity (CV, CW, CX) No difference
Doppler shifts are compared at the 0.1 hz level of accuracy.
Aircraft compensation (EA) No difference
Aircraft-satellite Doppler (EB) No difference
Perth-satellite Downlink (EC) No difference
We have differences in the EAFC+Sat and Offset values, but that is a separate discussion. My final BFO is 205.4 hz, compared with 205.1 in column EG.
So overall I find very good agreement, and the differences are small compared to the BFO errors (column EI) seen starting at 19:41.
@SK999, thanks for carrying out this work, which I think is very important.
@Brock: The MRC curves presented by the ATSB use an MRC speed profile while allowing turns at ping times to match the BTO data. As such, the paths are not straight, and rotating along the arc might not give you the right answer if you vary the turn time. For instance, when I compare the two results for 35,000 ft, I see a difference of about 2 deg latitude in where the curve crosses the 7th arc.
That is why I believe that in order to test a proposed path for acceptability, you have to demonstrate agreement with the BTOs/BFOs and also that the speed profile is consistent with fuel consumption needed for the required range and endurance. One way to do this is to develop a fuel consumption model, which is what was used in Richard’s v13.1 analysis for 35,000 ft.
Perhaps Bobby’s path, at his chosen air speed, is consistent with the a fuel consumption model. I have not seen that result.
Many thanks SK999 for the cross-check.
@Victor: if you enter the arcs x radial degrees clockwise at 19:41, then – all else equal – you exit the arcs x degrees clockwise at 00:19. You will have the same excess fuel you had before, and will thus exceed the 7th arc by the same margin. It does not matter what path was required to intersect the intermediate arcs.
This is a key point. Just visualize the problem from the perspective of the SATELLITE.
The only two things that could possibly DIFFER between the two FMTs in question are:
1) Wind effects: expected to be minor. Confirmed to be minor via earth.nullschool.net. If anything, they favour 18:28 fuel performance, due to reduce average headwinds.
2) Amount of excess energy (fuel) spent in the FMT’s course change: expected to be minor. If anything, this favours 18:28 fuel performance, whose FMT is through fewer radial degrees.
QED.
Brock:
You seem to believe in the early FMT because it would be more consistent with your assumed final end point at 84E. I agree these two assumptions are interdependent. But this approach assumes the FMT time is unknowable, or known to be 1828. We do not agree with either of these assumptions. We believe the data supports a turn underway at the time of the 1840 data, and thus consistent with the 89E end point. Thus, it is important to resolve the question about this FMT if possible. It would be great if Bobby and the IG could agree on the FMT time like SK999 and Richard have come together on the math.
@Brock: I agree that once the position on the 19:41 arc is determined, the solution for the end point for different starting points on the 19:41 arc can be obtained by rotation (using the assumptions you made).
However, I am not seeing how you determine the position at 19:41 for the two cases. I considered an air speed of M=0.84, producing TAS of about 498 knots. I considered single turns at 18:28 and 18:40 and found the true track azimuth which produced a path that intersected the 19:41 arc at the appropriate time using this speed. (I neglected the rest of the path.)
I find that for the turn at 18:40, the position at 19:41 is -0.8881,93.7249 for an azimuth of 184.7 deg. For the turn at 18:28, the position at 19:41 is -3.1261,93.4541 for an azimuth of 193.8 deg. This represents a rotation of about 2.2 deg between the two cases. This is about one-half the value you cite.
A map of the two cases can be found here:
https://onedrive.live.com/redir?resid=361DBAA0F5CBE522!8202&authkey=!ABquF8vu2mZwZYk&v=3&ithint=photo%2cjpg
@Victor: thanks for taking the time and energy to fly my conceptual “path”.
I got 125nmi along the arc – you got 136 (which I obtained by plotting the 2 coords you supplied in my “Earth” app, and drawing a great-circle line between them). Suspect your pre-FMT route bears slightly north of mine (I tried merely to extend the primary radar track). But let’s take your 136nmi.
I am interested in how many RADIAL degrees around the arc this represents. I compute the circumference of the 19:41 arc:
2*pi*r = 2*pi*1,760 = 11,058nmi
% of full rotation = 136/11,058 = 1.23% * 360° = 4.4°
Victor, these are RADIAL degrees. These correspond perfectly to NEITHER latitude in the eastern quadrant NOT longitude in the south. I haven’t worked this out to anything clever, yet, so I’ll just point out the dangers of using latitudinal separation in the east to predict longitudinal separation in the south
Before publishing, I also double-checked longitudinal separation on the 7th arc via ratio analysis: the 00:11 arc radius is 50.7% larger than the 19:41 arc radius (2,652 vs 1761), so 136nmi on the smaller arc translates into 136*1.507 = 205nmi on the 6th arc. I then verified in my Earth app that this distance along the 6th arc is worth a shade under 4° LONGITUDE along the 6th arc.
@airlandseaman: no, I am not reverse-engineering a path to suit a pet search area. If you want to see how THAT process works, a stunning example is given by the JIT’s use of “passed near a NW point at 19:41” to fabricate the N7P (I get 2 acronyms, I guess) required to render s21 feasible.
I am being persuaded by Dr. Ulich’s work – and noticing that its one major criticism – “beyond MH370’s performance limit” – has been shredded by what we now know about
1) the range of possible altitudes at which MH370 could have flown, AND
2) the JIT’s (intentional?) understatement of its own S7P
I am open to being convinced of the greater probability of your later turn, Mike, if statistical tests show that your path has a greater BFO-based likelihood than does Bobby’s. I have not yet seen this test.
I recommend everyone read Dr. Ulich’s recent response on this important topic:
http://jeffwise.net/2014/12/01/occams-razor-is-overrated/comment-page-8/#comment-64030
@Brock: First, a bit of nomenclature. I don’t know what a RADIAL degree is, as you refer to it. I think you mean the arc length expressed in degrees. To me, a radius is an expression of length or curvature, not angle.
Second, the ping arcs are not circles because the earth is not a sphere, nor are they concentric as the subsatellite position moves. Your analysis needs to account for this.
Thirdly, I believe you need to include wind and temperature effects to get the correct ground speeds.
I ran a quick calculation to see what the effect of movement on the 6th arc would be due to an early vs. late turn for a constant Mach number of 0.83 at 35,000 ft, which is I believe faster than predicted by the MRC condition, especially for the end of the flight. Here is what I get:
Position on 6th arc for turn at 18:28: -38.5746, 85.6520
Position on 6th arc for turn at 18:40:
-36.9661, 88.6607
This translates to a shift of about 3 deg of longitude at the 6th arc.
I still have not seen an explanation of how Bobby’s speeds are consistent with the MRC analysis you keep touting. If you want to silence critics about range, that is the way to do it rather than making arguments about rotations about circles and claims of deception in the ATSB report.
Other shortcomings I see in Bobby’s analysis that I have cited include:
1. The requirement for an early flame out to be consistent with his assumption of constant TAS.
2. LNAV mode in which an overflown waypoint follows a great circle path rather than constant track or constant heading.
That all said, I never said that Bobby’s predictions are wrong, nor have I been overly critical. I just rate it at as a lower probability than predictions a bit further up the arc. If the search is unsuccessful in the current area, I would advise expanding the search area further south and west along the arc.
ALL BFO LOVERS:
I just posted an analysis of possible BFO “steps” in the other thread at:
http://jeffwise.net/2014/12/01/occams-razor-is-overrated/comment-page-8/#comment-64591
If real, the stability of the frequency and phase of the sawtooth “steps” during the 18:40 UTC BFO data sequence has implications regarding the possibility of a turn in progress at that time.
@VictorI,
Why do you think it is more likely that the southern route was flown using Track Hold or Heading Hold than using waypoint(s)?
@Brock,
@VictorI,
Don’t forget that my proposed route is a great circle. Victor’s comments above are comparing 1828 and 1840 turns, both followed by a True Track LNAV mode. Mine uses a great circle, and below the equator it is to the west of a True Track route with the same initial bearing. That is why my end point (83.5E) is a bit west of Victor’s calculation assuming True Track.
@Victor: I appreciate the response. Always good practice to clarify nomenclature. Yes, you’ve seen through my poor usage to the correct concept. I had in mind the angular measure used in polar coordinate notation (with satellite as origin), commonly expressed as either degrees or radians. I chose “radial degrees” to distinguish from the degrees describing lat/long. Hereafter, I will use °ang, °lat and °long to disambiguate.
Having clarified: do you agree that your posted graphic shows that a 12-minute delay in the FMT is worth 4.4°ang clockwise on the 19:41 arc, and not the 2.2°(ang? lat?) you had posted earlier? I’m keen to ensure this key point is neither overlooked nor in dispute.
But to save a back & forth, I’ll also respond to your excellent criticisms:
Satellite: yes, I realize it is not stationary. In the five hours between arcs 2 & 6, it moves 50nmi. Failure to rotate this motion the same 4 degrees misplaces the satellite (and all arcs) +/- 1.7nmi (arc 2 should be shifted 1.7nmi east, 6th arc 1.7nmi west, with lesser adjustments for those in between). NOT enough to move the needle.
Sphericality: is even LESS relevant. Here again, my approximation error is not the entire error from circle to ellipse – it is my failure to account for the CHANGE in elliptical circumference from a 2°lat shift south in the path. My simple rotation implicitly assumes the earth’s radius exhibits the same ellipticality from -2° to -39°lat that it exhibits from 0° to -36°lat (6,378.1 to 6,385.6). The correction would increase radii by less than half a kilometer, which misstates path length of this path by less than 0.5nmi.
Wind: I posted the wind data days ago. If anything, it argues S7P further WEST, as average heading becomes slightly LESS directly upwind under the early FMT. Again: should be negligible, as the two paths are close enough in character to have similar wind profiles.
I’d added another: whether a late turn burns more fuel by virtue of the (say) 110°ang required for a late FMT, vs. the (say) 100°ang required of the earlier FMT. A FMT of fewer °ang might save fuel (albeit marginally), which again argues S7P further WEST.
You’re now at 3°long west along the 7th arc, and I’m at 4°long. I think if you move to the speeds implied by the JIT’s Fig.3 (500kgs at FL400) – and we both stop rounding – we’ll converge on around 3.8°long.
Of COURSE I’d prefer to compute fuel feasibility from first principles. I’d also like to play pro football, and sing at Carnegie Hall. But I can’t (believe me, Victor: I’ve tried. All three). So I rely on the ATSB’s published fuel limits – which should reflect every aspect you mention, and more. In anchoring to an ATSB-published fuel limit, I am not alone; in all of its published results, the IG itself anchors to the ATSB S7P/N7P’s.
My point is merely that the FL400 path depicted in Fig.3 says something very different about the JIT’s S7P than does the entirety of Fig.2. If you prefer to trust the JIT, can you and I at least agree that the portrayal of Figs 2 & 3 is ambiguous, and should be clarified, given that the performance limit (and thus the optimal search epicenter) hangs in the balance?
@Victor,
I published a fuel burn analysis for my route a month ago. It is available at:
https://drive.google.com/file/d/0BzOIIFNlx2aUMjhBWmk4ZlBBNEk/view?usp=sharing
See Section 7. At 0.84 Mach and with stepped altitude, the air miles to my proposed end point are exactly consistent with 1% engine PDAs. I believe there are uncertainties in such calculations of perhaps 2%, so I cannot prove it did happen or could happen. What I am saying is that, within a percent or two, using Boeing fuel burn tables (for RR engines, BTW), my end point could have been reached at fuel exhaustion.
All, @Brock:
WHAT IS WRONG WITH THE ATSB MAXIMUM RANGE BOUNDARIES ?
Looking at Figures 2 and 3 in the ATSB October report, I observe that the maximum range boundaries (the outer edge of the purple areas) shown intersect the 7th arc at ~88.5E for both the 1828 Turn (Figure 2) and for the 1840 Turn (Figure 3). I think Brock pointed this out earlier, but the implications of this are significant and did not fully dawn on me until now.
First, both can’t possibly be correct (I guess that means that Brock and I are in violent agreement on this point). That is because, for the 1840 Turn, 9M-MRO traveled approximately 100 NM NW before turning south compared to the 1828 Turn, so the mileage available after the 1828 Turn is approximately 100 NM farther than the same quantity for the 1840 Turn.
It appears that the SW performance limits shown in the two figures (in which they are plotted as being identical) are drawn from the same point and with the same radius for both turn times rather than from the two actual turning points which are separated by ~100 NM on a ~290 degree bearing (which puts the 1840 Turn point ~34 NM farther N and farther away from the 7th arc) and with different radii after the turn.
Second, the radius of the 1828 Turn boundary should be 100 NM longer than the radius for the 1840 Turn boundary.
These corrections reduce the difference in air miles traveled during the two cases (the 1828 Turn and the 1840 Turn) to reach the 7th arc. The 1828 Turn path is still a bit longer than the 1840 Turn path.
I will speculate that the performance boundaries may have been calculated by Boeing based on an initial assumption of turning point and time supplied to Boeing by ATSB. Then, later on, when the actual turn time limits (1828 – 1840) were selected by ATSB, perhaps the boundaries were not recalculated based on the two separate turning points. Since Figures 2 and 3 do not show the turning points assumed, it is difficult to say what location was used by the ATSB. It is not difficult to say that one of the figures must be wrong.
The performance limit intersection with the 7th arc (OK, we’ll call it S7P), for the 1828 Turn (at ~86ish E) must be farther west than S7P for the 1840 case (~88.5E). They cannot be the same.
I wonder if this realization might be part of the reason why the ATSB recently extended the Fugro Discovery search area farther SW along the 7th arc?
@Bobby: “Why do you think it is more likely that the southern route was flown using Track Hold or Heading Hold than using waypoint(s)?”
I believe your supposition is that the plane continued flying after reaching the Maimun Saleh Airport waypoint. After the last waypoint is reached, the navigation mode is either constant track or heading, and possibly magnetic rather than true compass direction. I have not seen reference to continuing on a great circle path after reaching a waypoint discontinuity or terminating the route.
Thanks, Bobby. We’re in “violent agreement” on generalities, but “friendly disagreement” on details.
You translate a 100nmi shorter pre-FMT path into a 100nmi distance further west along the 7th arc. It in fact translates into a roughly 200nmi distance, because of two factors:
1) if the primary radar-indicated bearing is maintained throughout the pre-FMT leg, the required FMT is sharper than 90 degrees (MUCH sharper, for late FMTs). The additional 100nmi pre-FMT track thus costs MH370 130nmi or so by the time the 19:41 arc is reached. Victor has CONFIRMED this.
2) Because the problem BASICALLY (Victor is VETTING this) reduces from there to a simple rotation of the “Inmarsat arc dial”, then this 125nmi actually expands to around 200nmi along the 7th arc. Think “ratio of radii, 2nd–>7th arc”.
So, ~84ish E.
Unfortunately, I fear they’re extending the bathy survey 50nmi SW for the same reason they’re extending it SE – to accommodate the JIT’s “brand new insight #47”, which now puts MH370 as far as 50nmi beyond the 7th arc:
http://www.nzherald.co.nz/world/news/article.cfm?c_id=2&objectid=11373924
@Bobby: I’m curious about your use of the term True Track LNAV mode. My understanding is that the flight modes available are LNAV, HDG SEL, TRK SEL, and these are mutually exclusive.
I note that your track is a great circle to your end point. Again, I think that a great circle is appropriate only if the flight mode is LNAV, which means that the FMC is tracking waypoints. Hence to get right to the endpoint of your track there must be a valid waypoint in the FMC that is not yet reached.
If, on the other hand, the FMC runs out of waypoints, i.e. overflies the last one available, then the aircraft maintains its current [at that instant] heading. The track followed from that point cannot therefore be a great circle. Rather it becomes a loxodrome.
So my question is – – what waypoints have you chosen to allow the FMC to fly the great circle track?
If you have a different interpretation I would be grateful for an authoritative reference describing the flight mode.
@Brock: Wind does not affect the track in either LNAV or TRK Hold, but it will result in different groundspeed if the track azimuth is different for each case.
Dr. Bobby Ulich is to be commended for thinking outside the square and slide rule.
I encourage everyone to reconsider how credible the evidence is for MH370’s claimed deviation through the Straits.
Whilst it is asserted that BTO rings corroborate the turn north of Aceh in fact it is the other way around that the JIT used the Lido Hotel (alleged) radar image as a corroboration for the BTO signal delays.
The actual signal delays were estimated from 17 R-channel signals from MH370 on the ground before take off, but even these were variable. The truth is even the BTO rings are based on estimates for the signal delay.
Malaysia’s Government claimed their radar saw MH370 climb to 45,000ft perform a U-turn and dive below 23,000ft. The JACC used radar engineers to examine all the data and in June 2014 they officially concluded no Malaysian radar, civil or military saw this… So there’s one false claim:
The Malaysian Government claimed Thai radar from Surat Thani saw MH370 turn back at IGARI, but it is very easy to calculate the radar horizon. You can find several online calculators and calculate this yourself. Surat Thani radar could not see an aircraft over IGARI below 55,000ft and that is an impossible altitude for a Boeing 777… so there’s another false claim:
Next the JIT claim military radar at Butterworth saw MH370 over a small island called Pelau Perak at 18:02 UTC after it had flown around the heel of Penang island covering the distance in 41 minutes. That is a distance of 287nm. At lower altitudes the speed of a Boeing 777 reduces due to air density. MH370 could not have covered this distance within 41 minutes below 440kts and it could not fly such a speed below 22,000ft, so why was this not seen on radar? ….so there’s a third false claim:
Malaysian officials showed an image to relatives at the Lido Hotel in Beijing on 21 March, which they claimed was a radar image from the Butterworth military radar. Unfortunately the image did not include two other aircraft which should have shown up in the same area, UAE343 and SIA68.
Indonesian military radar at Lhoksumwae was watching the same airspace and did not see the aircraft which Malaysia claimed it saw and Indonesian radar did not see this aircraft.
Finally the Lido hotel image is not a real screen from a Thales Raytheon GM400 which is the actual radar used at Butterworth.
The Lido Hotel image which almost everybody believes proves this bizarre flightpath is actually photo-shopped image from the screen of a civilian SSR secondary radar…. so there’s the final biggest lie of all.
The search for MH370 along the so called Southern Arc is entirely based upon an interpretation of satellite tracking data which assumes the Lido Hotel image confirmed MH370’s position at 18:22 UTC was real, but if all those calculations are actually based on a photo-shopped hoax then everything you have been arguing about is unreliable and MH370 is not where they are searching.
@Brock,
We are closer than you think. I didn’t say the S7P point would move 100 NM along the arc. I did say the max range radius for the 1828 case must be 100 miles longer. I also said the 1840 turn point was about 34 NM farther N. Thus the allowable extra range south to S7P for 1828 is, as you say, more than 100 NM farther than the 1840 case.
Finally, I also said the S7P must move from ~88.5E to very roughly “~86ishE”. This distance along the 7th arc is also more than 100 NM.
So we are not that far apart after all. Our methods are different and produce slightly different S7P locations, both of which are considerably farther SW than shown in the ATSB’s Figure 2.
@VictorI,
The topic of the default FMC horizontal navigation method after the last waypoint is reached has been discussed previously. Other contributors stated as firm information that the FMC continues on the same great circle route if there is no further input. They said it does not default to a constant-bearing or constant-heading mode. I will search for the posts (they may be on Duncan’s blog or Pprune). Perhaps one of them contains a good reference. Have you got any authoritative reference that states the FMC does not continue the same great circle path?
@Fitzer_Flyer,
Mea culpa. I did not use the proper acronym. What I meant to say was that the horizontal navigation mode I used was LNAV. I use Maimun Saleh Airport as my only post-turn waypoint. It is actually not assumed. My best-fit route happens to pass over it. That’s how I initially identified it.
@Bobby: Here is a few excerpts from an official Boeing B777 Operations Manual – –
LNAV maintains current heading when:
• passing the last active route waypoint
• passing the last waypoint prior to a route discontinuity
• passing the last route offset waypoint
FMC LNAV guidance normally provides great circle courses between waypoints.
If the airplane passes the last active route waypoint (or offset) or the last waypoint prior to a route discontinuity, LNAV maintains the current heading and a
scratchpad message displays.
There is never a mention of continuing on a great circle track after overflying a waypoint.
23:14 UTC BFO DATA FROM SECOND SATELLITE PHONE CALL
(This is a duplicate of my post on the Occam’s Razor thread)
Go here to see the sawteeth in the 23:14 (second sat phone call) BFO data:
https://drive.google.com/file/d/0BzOIIFNlx2aUTzlGQWZnSlpXb3c/view?usp=sharing
In this case the peak-to-peak amplitude is 7 Hz and the period is 22.5 seconds. The sawtooth residuals are less than +/- 1.5 Hz. That is a factor of 2X reduction compared to using just a straight line fit. This provides more evidence that sawteeth are real and probably present in all the BFO data when the aircraft is airborne.
The presence of sawteeth as seen in the BFO data but which are not included in current BFO models casts significant doubt on the notion that small BFO errors imply a higher probability of being the correct route. I think that any residuals smaller than 4-7 Hz peak are simply a result of over-fitting the BFO data with too many variables.
It seems Inmarsat was right when they advised accepting BFO errors up to +/-7 Hz.
@Flitzer_Flyer,
What do you think is meant by “maintains current heading”?
The language seems ambiguous to me. I don’t infer that it literally means that the aircraft will hold the current heading.
Please give a link to view the manual you are quoting from. Thanks.
@Bobby: Here is a link to one reference – – -http://curiozitydotnet.files.wordpress.com/2014/03/continental-airlines-boeing-777-flight-manual.pdf
See – –
777 Sec. 6.4 Page 35 Flight Manual Continental Rev. 11/01/00 #5
• LNAV maintains current heading when:
• Passing the last active route waypoint
• Passing the last waypoint prior to a route discontinuity
• Passing the last route offset waypoint
• Activating the inactive route or activating an airway intercept and not within LNAV engagement criteria.
It seems we have a whole bunch of numbers from Inmersat/Malaysia/Boeing. But if the Lido Hotel image is all made up we don’t have context to be data for finding MH370. Good work to everyone trying to figure out what these data means in terms of a B777 inflight. I guess the ping rings may need to be redefined as to expected locations to where mh370 went.
Simon Gunson: “The Lido Hotel image which almost everybody believes proves this bizarre flightpath is actually photo-shopped image from the screen of a civilian SSR secondary radar.”
It would be great if you could provide some background on how you have determined that the Lido Hotel radar image was derived from a secondary radar display. Do you happen to know which ATC radar?
I had previously assumed that the Malaysians had presented Thai radar data in the Lido image and never really claimed that it was from Butterworth, only having labeled it with the distance to Butterworth. Your summary, however, of their dissembling over the radar data in its totality, however, is quite troubling, both in terms of the behavior of Malaysia and the implications for the location science.
in sum, what we have is Malaysia not having contributed much in the way of anything regarding what they know of the flight. I suppose this can be attributed to ‘game theory’ and avoiding getting bit on the ass later via actually contributing real data/information to the search, but it does more than reveal their callous disregard the lives lost, as well as the commitments of others in terms of people, time and money. Rather, the Malaysian’s clunky and rather unsophisticated fleeing-felonesque behavior only further raises the probability of their actively working to inhibit the search and the development of any clear picture as to what has occurred. Perhaps the military/ADS people was only embarrassingly drunk at the screen that night. Than again, perhaps things are significantly more foul and rotten.
Simon, can you elaborate further as to what you know re the Lido image? Perhaps Nihonmama can dig up the record of Hisammuddin’s attributions re the image.
Simon,
Some time ago you posted the same description, as above, for the “Beijing Lido” RADAR image at metabunk.
RADAR systems have the ability to dump “raw” lat/lon or radial/range data for each target they detect.
The “Beijing Lido” image has been created using that simple data. It would also be very simple to filter out targets detected for any other aircraft as Mode-S interrogations returns would have been logged.
Malaysia does not operate a GM400 in the northwest region, a RAT-31DL is located on Penang Island.
The pattern of the returns depicted in this image suggest that they were sourced from Thailand’s two air defence surveillance sites at Phuket and Khok Muang. By presenting the data in this way Mlsia obfuscates its source.
It’s frustrating that the full context of the presentation in the Beijing Lido Hotel has never been explained but I believe that this data can be relied upon. The speed and times shown are consistent with continued flight from the turn back over Sth China Sea.
:Don
Further circumstances concerning in RADAR discussion.
Weather reports around the northern Str of Malacca for 1800-0000UTC show atmospheric conditions that typically create “ducting” effects for L-Band RADAR systems so limiting the systems’ range.
The returns plotted are consistent with the terrain impact on Phuket & Khok Muang’s horizon.
Indonesia, TNI-AU at Lhokseumawe & Sabang: it remains unexplained why they reported no sighting of 9M-MRO. However, the track depicted does not encroach their FIR, shows an aircraft flying away from Indonesia’s airspace and TNI-AU doesn’t have intercept capabilities in this region of the country.
:Don
Simon Gunson:
HIGH FIVE.
Rand:
What HH said about the Lido image I don’t know, but here’s something else forgotten I just found that should also trouble people (posted in another thread earlier today):
Matty, Rand (and Neils):
““Malaysian officials admitted that Malaysia has no access to Inmarsat’s raw data and algorithm in terms of how Inmarsat gained the southern corridor conclusion”
http://www.duncansteel.com/archives/751/comment-page-4#comment-4154
[From “The Circumlocution Office is Alive and Well” (Duncan Steel) – trying to find the rest of it in that permalink maze]
Simon, Rand:
Take that sketch Lido image (which has never looked legit) and Simon’s comments, add my previous post (Malaysia admits it wasn’t privy to how the SIO conclusion was reached) and now, top it off with what NYT’s Keith Bradsher told us (very clearly) happened (which I keep posting, hoping it will wake somebody up):
“Their conclusion, reached in the past few weeks, helped prompt the decision to move the focus of the search hundreds of miles to the southwest…
‘The primary radar data pertaining to altitude is regarded as unreliable’ said Angus Houston…Martin Dolan, the chief commissioner of the Australian Transport Safety Bureau, agreed with Mr. Houston. ‘There’s nothing reliable about height’…
Mr. Houston and Mr. Dolan declined to discuss any details about the Malaysian radar readings…
SO THE DISMISSAL OF THE RADAR ALTITUDE DATA PROMPTED A CHANGE IN THE FOCUS OF THE SEARCH.”(CAPS mine).
http://www.twitlonger.com/show/n_1sd7gtn
“Malaysian officials admitted that Malaysia has no access to Inmarsat’s raw data and algorithm in terms of how Inmarsat gained the southern corridor conclusion”
That is a direct quote from ‘Haxi’. Here’s the new link:
http://www.duncansteel.com/archives/743/comment-page-1#comment-3156
And if I recall correctly, wasn’t Haxi in the room when that statement was made?
GuardedDon: Thanks for the provenance on the Lido Hotel radar data projection.
Nihonmama: We could conclude that the Malaysians are deliberately avoiding providing any substantive/material data re the search. Whether indicating Inmarsat or the Thais, or by way of simply not providing information, the Malaysian authorities seem to be bereft of knowing virtually anything about the flight.
Again, it appears the Malaysians are cocooning themselves within the ‘mystery’ of MH370, so as to avoid making public what they know concerning the flight. I would suggest that what they are not providing in terms of chunkier elements, e.g., radar data, is indicative of a broader directive to withhold any and all data/information concerning the flight. And so the question then again arises: why? Is is simply political anxiety re the potential surfacing of charges of incompetence, or is it something nastier and more corrosive? Regardless, they are certainly not pulling out the stops to locate the debris, much less discover what actually transpired. It’s not any sort of smoking gun, but the lack of genuine remorse or concern and the general projection of Malaysia as some sort of victim in this tragedy reminds me of your prototypical murdering spouse feigning unconvincing innocence. No horror, no wringing of hands, no demands for justice; only a look of bewilderment and a deadpanned, “what?”
@Rand
Sorry Rand I do not have a twitter account but I do read what others say reasonably often. If you wish to re-post these images on Twitter for me then feel free.
You asked about the Lido Hotel image. The best way I can answer Rand is to suggest some links to images in my photobucket:
http://s257.photobucket.com/user/727Kiwi/library/MH370?sort=3&page=1
Many of my oldest images are superceded by new disclosures and therefore not relevant but not deleted either.
Here is the Lido Hotel image referred to, first leaked by a Chinese blogger in Mandarin. I re-posted it and now it is common knowledge.
http://i257.photobucket.com/albums/hh212/727Kiwi/MH370/Lido_Hotel_Beijing_21March_zps2eb1b3f1.jpg
Next is the same image superimposed with the concurrent flight paths of UAE343 & SIA68:
http://i257.photobucket.com/albums/hh212/727Kiwi/MH370/UAE343Overlay_zps49d145d2.jpg
So you asked about military (primary) radar versus civilian SSR (secondary) radar?
SSR of course only tracks the Mode-ES transponder also called the ADS-B or in the case of MH370 actually an ADS-C. If the transponder was not working Secondary radar could not see the target. Primary radar is the old conventional type.
In longer range (ie 200nm) primary radar the antennae has to slow to about 5 RPM to allow the distant signal reflections to catch up. Civilian Primary radar only found around airports has a range of about 90nm and the antennae rotates much faster about 15 RPM.
The bunching of radar hits on the LIDO image seem too thick and bunched up to me. Here is a screen shot from a sister Thales Raytheon GM400 unit at Kuantan, which incidentally covers IGARI. Another sister Thales Raytheon GM400 was located at Kota Bharu and both of these would have seen MH370 turn back if the account was real. Malaysia has never claimed either of these units spotted MH370 turn back:
http://i257.photobucket.com/albums/hh212/727Kiwi/MH370/ActualButterworthradarimage_zps9ca910e6.jpg
…also the GM400 coverage profile
http://i257.photobucket.com/albums/hh212/727Kiwi/MH370/Thales-GM400_TRS_2009-Envelope-1S_zps0c15f4ba.png
You only have to look at the GM400 screen to see the difference. Below is an image from a Selex Aton-S radar training screen for the civilian SSR radar which Malaysia uses:
http://i257.photobucket.com/albums/hh212/727Kiwi/selexsquared_medium_ATON_s_zpsdeb788b8.jpg
This Malaysian SSR screen shows Penang in the bottom left corner:
http://i257.photobucket.com/albums/hh212/727Kiwi/SATCAS_s_02_zps3684773e.jpg
…and this is an image from their actual control centre:
http://i257.photobucket.com/albums/hh212/727Kiwi/MalaysianATC_zps547d4886.png
Keep in mind too that Malaysia originally claimed their Butterworth Royal Malaysian Air Force Base radar tracked MH370 flying VAMPI-GIVAL-IGREX like this plot:
http://i257.photobucket.com/albums/hh212/727Kiwi/MH370/GIVALIGREX_zps91917a4d.jpg
They have never explained why they changed their story to Pelau Perak – VAMPI -MEKAR?
Hope this helps?