MH370 Data Alignment Model

MH370 Data Alignment Model

Richard Godfrey
24th November 2015

(Updated 27th November 2015)

Many people are frustrated by the lack of a positive outcome in the search for MH370, and a determination of what happened onboard to cause its loss.

Matters (especially in the media) have been confused and confusing because there have been a large number of attempts to pin point the final resting place of MH370 based on the available data. This is understandable because we have information from a number of sources, as follows:
1. Physical Data (Location of Kuala Lumpur Airport, Gate, Runway and various waypoints).
2. Aircraft Flight Plan.
3. Aircraft Performance Data.
4. ATC Transcript.
5. ADS-B Data.
6. ACARS Data.
7. Primary and Secondary Radar Data.
8. Inmarsat Satellite Data.
9. Weather Data.
10. Debris and Drift Data.
11. Fuel Data.

Recognising this, and wanting to assist in clarifying what we know and what we don’t know, I have put together a MH370 Data Alignment Model (Excel spreadsheet, 540 kB) in order to see how many data points are confirmed by more than one of these sources.

A Single Location From Three or More Data Sources
One would think with all this data, we should be able to determine exactly what happened to MH370. However, there is only one data location that is confirmed by three or more data sources and that is the take-off point (which does not help us much to determine what happened to MH370):
a. The ATC Transcript gives the cleared for take-off communication at 16:40:38.
b. The ACARS Position Report at 16:41:43 shows the aircraft at an altitude of 103 feet but 505 metres right of the centre line of Runway 32R.
c. Primary Radar at 16:41:54 (11 seconds later) picks up the aircraft half way down the runway at an altitude of 2 feet above the centre line of Runway 32R.
d. The Inmarsat satellite BTO and BFO data at the time of ACARS Position Report approximately confirms the location given by the Primary Radar.
e. The Aircraft Performance Data also confirms the location (take-off distance) and ground speed (take-off speed) given by the Primary Radar.

As one can see from the above, even this set of data does not completely agree.

[Note on b and c above:
– The runway at Kuala Lumpur is not level, but officially the field elevation is 69 feet above sea level (ASL).
– The Primary Radar indicated an altitude of 2 feet, which may be interpreted to mean 71 feet ASL.
– The ACARS take-off report of 103 feet ASL is a pressure altitude and the calibration may be normalised rather than set against the actual local pressure.
– The difference between those two altitude values is 103 minus 71 = 32 feet.
– That is just half the physical height of the aircraft, and the pressure sensor on the aircraft might be 32 feet off the ground.
– Thus there is no inexplicable discrepancy between b and c in terms of the aircraft altitude, but the transverse discrepancy (ACARS indicating the aircraft to be 0.5 km to the side of the runway when it was obviously on the runway) remains.]

Only Three Post-IGARI Locations Based On Two Data Sources
Following take-off there are 70 data points where two sources agree. However, 67 out of those 70 data points are prior to reaching the waypoint IGARI. Therefore we do not have a problem thinking that MH370 flew 38.6 minutes to waypoint IGARI (which also does not help us much to determine what happened to MH370); it is what happened thereafter which is the problem, due to lack of data.

Near IGARI the mystery begins (no VHF, no handover to Vietnam ATC, no transponder, no ACARS, no SATCOM, departure from Flight Plan).

Let me consider now the remaining three locations (for which two data sources agree) post-IGARI.

A. The first location is in the Straits of Malacca, 67.7 minutes after waypoint IGARI, flying in almost the opposite direction at a point where the aircraft weight is finally down to the maximum allowed landing weight (assuming no fuel was dumped): (a) The Primary Radar data shows the aircraft 10 NM beyond waypoint MEKAR following Flight Route N571 at 18:22:12. (b) The Inmarsat satellite BTO data 195 seconds later matches the aircraft location, direction and ground speed extrapolated from the Primary Radar data. (c) The Inmarsat satellite BTO and BFO data another 168 seconds later matches the aircraft location, direction and ground speed extrapolated from the Primary Radar data.

B. The second location is in the Southern Indian Ocean some 5.8 hours later; this location is defined by: (i) The arc described by the Inmarsat satellite BTO data at 00:19:29 and (ii) the arc described by the fuel range, the intersection of the two arcs giving a location. There are two problems with the Fuel Range data however:
(a) Where is the centre of the arc (or how far did MH370 fly along or near Flight Route N571 toward waypoint IGOGU before turning south)? (b) The precise fuel consumption rates of the MH370 Rolls Royce Trent engines. In addition the data matches a SATCOM log-on at the same time (assuming one accepts the idea that the SATCOM log-ln was the result of fuel exhaustion causing a power interruption). If you wish to match the Inmarsat satellite BFO data, you have to accept that the aircraft had a rate of descent of 5,394 fpm (53 knots) representing an angle of 6.3 degrees below the horizon. The BFO data can be made to fit the other data sources and is therefore not an independent data source.

C. The third location is in the Southern Indian Ocean just eight seconds later; it is defined by: (i) The point where the arc described by the Inmarsat satellite BTO data at 00:19:37 and (ii) the aircraft direction and ground speed extrapolated from the preceding location (B above). This is uncertain because the aircraft may have been turning. Flight simulations have shown that a turn develops after fuel exhaustion. The Inmarsat satellite BFO data can also be made to match, if you accept that the aircraft had a rate of descent of 15,873 fpm (157 knots), representing an angle of 18.8 degrees below the horizon. As mentioned before, the BFO data is not an independent data source.

In summary, we have a lot of data, but not much information based on two or more independent sources: thus there is very little data that helps us to determine precisely what happened to MH370.

We know that, if the aircraft speed profile was maintained between 18:28:12 and 19:41:03, the aircraft did not fly directly south from 18:22:12 to reach the arc described by the Inmarsat satellite data at 19:41:03.

How far the aircraft flew along or parallel to air route N571 toward waypoint IGOGU is the key to determining how far south the aircraft finally ended up.

We can have strong confidence that, for MH370 debris to wash up on Réunion when it did, the aircraft headed into the Indian Ocean.

We know there is a consistent set of single BFO data points indicating that the aircraft was headed southwards from 18:39:53 onwards.

We also know there is a consistent set of BTO and BFO data points from 19:41 onwards indicating that the aircraft proceeded in the same general direction and speed. Brian Anderson showed, in a post published last March (Deducing the Mid-Flight Speed of MH370), that the True Air Speed at the nearest point to the Inmarsat satellite (at about 19:52:15) was around 484 knots and consistent with the final reported ACARS value. Yap Fook Fah showed, in a post also published in March (Autopilot Flight Path BFO Error Analysis), that the BFO data from 19:41 onwards is consistent with an autopilot flight.

At the end of the day, our analysis has the same fundamental limitations as faced by the many others who have put forward their hypotheses. We are trying to connect the dots, except there are too few dots we are really sure about where it most matters. And that, essentially, is why the crash site of MH370 is yet to be identified.

Centaurs as a hazard to civilization

Centaurs as a hazard to civilization

by Bill Napier, David Asher, Mark Bailey and Duncan Steel

Summary: Assessments of the risk posed by near-Earth objects ignore the possibility of a giant comet entering the inner solar system. Bill Napier, David Asher, Mark Bailey and Duncan Steel examine the likelihood and potential consequences of the appearance of such a centaur.

This review paper is published in the 2015 December issue of the Royal Astronomical Society’s magazine Astronomy & Geophysics. A PDF (632 kB) of the paper is available here.

The movement of meteor shower radiants over aeons

The movement of meteor shower radiants over aeons

A PDF (368 kB) of this post can be downloaded by clicking here.

Various email messages have alerted me to some discussion of the Taurid meteor showers here, and of references to what I wrote in my book Rogue Asteroids and Doomsday Comets (Wiley, NYC, 1995). I have no desire to enter into a protracted debate on this – indeed, there is little to debate about – and so here I will just summarize a few pertinent points, whilst trying not to be impertinent and upset people. The reality of the universe, however, is that things are as they are, and not as anyone might wish or imagine.

What I wrote in that book is broadly correct. I used the word “broadly” there not to suggest that anything is wrong, as such, but rather to indicate that readers should recognise that in a popular-level book it is necessary for an author to simplify things somewhat, whereas in a refereed research paper the author(s) must be rigorous in giving the necessary detail. What I am trying to advise here is that if one wants to understand what is going on, a popular-level book is only a starting point: one must go back to the primary literature, and one must have the capability to understand it.

The core subject at hand here is the precessional movement of the Taurid meteoroid stream and therefore the shifts over centuries and millennia of the associated meteor shower radiants, and times of occurrence within a year. There are two types of precession involved: apsidal precession, and nodal precession. In order to explain what is going on, let me start with the Earth (although that involves a third type of precession: the precession of the equinoxes).

The precession of the equinoxes describes the shifting of the vernal equinox, and is due to the torque imposed on our non-spherical planet by the Moon, and the Sun, although there are minor contributions from other planets. This torque causes the spin axis of the Earth to swivel around, or precess. This has the effect of moving the positions of the equinoxes ‘backwards’ along the ecliptic (i.e. opposite in direction to Earth’s orbital path). From antiquity astronomers have termed the direction of the vernal equinox “the first point of Aries”, although that direction is now in Pisces, and in a few centuries’ time it will have shifted into Aquarius. A full rotation of the equinox locations around the ecliptic takes about 26,000 years.

A quite different type of precession is apsidal precession. The line of apsides is the straight line connecting the perihelion and aphelion points of any heliocentric orbit. Gravitational tugs by the planets, in particular Jupiter, cause Earth’s line of apsides to swivel around, completing a circuit of the ecliptic in the ‘forward’ (prograde) sense in about 110,000 years. This is a long interval (i.e. this precession is slow) because Earth’s orbit is low-eccentricity (e = 0.0167 currently), and far from Jupiter.

The above two precessional changes of the Earth are simply described here.

Note that these two precessional effects combined produce a climatic cycle of duration t (the period of rotation of perihelion as referenced against the equinoxes) given by their harmonic sum:
(1/t) = (1/26,000) + (1/110,000) results in t = 21,000 years, this cycle being evidenced in the geological record.

Let us return now to the Taurid meteoroid stream. Its orbit is: (a) larger than Earth’s orbit; (b) of fairly high eccentricity; and (c) of low inclination. A consequence of these considerations is that the apsidal precession rate of that stream, dominated by Jupiter’s influence, is much faster than that of the Earth. Table AI in Asher and Clube (1993) – available for free download here – indicates a rotation interval for the line of apsides of about 7,000 years for orbital elements similar to Comet 2P/Encke (a=2.2 AU, e=0.85) and less still for orbits with larger aphelion distances (taking them nearer to Jupiter). See also Appendix B and Figure A2 in Asher and Clube (1993), in which numerical integrations of characteristic orbits are compared with the results from secular perturbation theory.

I hasten to add that this fundamental understanding is by no means new, and in the case of the Taurids was investigated by Fred Whipple over 75 years ago (see: F.L.Whipple, Proc. Amer. Phil. Soc., 83, 711, 1940).  Whipple established that the Taurid stream had to be at least 12,000 years old on the basis of its dynamics. Later researchers including myself have pushed out the necessary timespan to above 18,000 years (e.g. see various papers by Poulat Babadzhanov and colleagues, such as this), and likely 20,000–30,000 years.

The simple reason for this derived timescale is that, during each rotation of the line of apsides, the stream orbit intersects the ecliptic at Earth’s heliocentric distance (near 1 AU) four times: in the pre- and post-perihelion legs of the orbit, at both the ascending and the descending node. As a result, four annual meteor showers may be detected: an optically- and radar-detected pair of showers on the nightside of the Earth (at one time of year), only radar being feasible for the dayside pair (at a different time of year). Let me term this set of four showers a ‘quadruplet’.

One thing that often confuses people is the fact that the orbital inclination of 2P/Encke (almost 12 degrees) is substantially higher than the inclinations of Taurid meteoroids (only a few degrees). This is because, in the phases when Taurid meteoroids have orbital parameters resulting in them crossing the ecliptic near 1 AU (i.e. when collisions with the Earth and therefore observation as meteors are possible), their inclinations are small, whereas currently 2P/Encke is in a high-inclination phase of its evolution. These consistent inclination oscillations over millennia are shown in Figure A2 of Asher and Clube (1993).

An important thing to note is this. During the (say) 7,000 years it takes for a complete revolution of the line of apsides, the stream’s orbital plane also precesses, under gravitational perturbations again dominated by Jupiter. This is called ‘nodal precession’. (One can get some idea about this by looking here, although the examples given there are focussed on the nodal precession of satellites in geocentric orbit, the main cause in that case being Earth’s non-spherical gravitational field.)

The time for a complete rotation of the nodes around the ecliptic for an orbit like 2P/Encke may be obtained again from Table AI in Asher and Clube (1993), the answer being about 55,000 years. That is, in angular terms the nodal precession rate is about eight times slower than the apsidal precession rate (for that particular orbit).

The end result is that each time a rotation of the line of apsides occurs a new quadruplet of showers is formed, but these are separated from the previous quadruplet by about six or seven weeks (one-eighth of a year). Because we identify at least three sets of quadruplets (i.e. twelve distinct showers) we know that the Taurid complex has been developing for at least three times 7,000 years. Tentative identifications of other showers mean that likely the timescale is somewhat over 20,000 years. On these dynamical grounds and other lines of evidence my personal standpoint – always subject to revision in line with newer and better evidence – is that the Taurid Complex has formed in the inner solar system over about the past 30,000 years.

Comet 2P/Encke (around 5 km in size) is often considered the parent of the Taurids, but its present mass is only a tiny fraction (well below 1 per cent) of the overall mass of the complex, to which extent my opinion is that 2P/Encke is simply the largest lump remaining from an original comet 50–100 km in size that has undergone an episodic hierarchical disintegration, spawning a vast complex of material which we are yet to comprehend fully. This is the core subject of a forthcoming review by Napier, Asher, Bailey and Steel (Astronomy & Geophysics, 2015 December).

The next point to which I turn attention is the nature of the Taurid meteor showers’ radiants. Most strong meteor showers have single, compact radiants, and the showers last only a day or so, perhaps a week at most. This is not the case with the Taurids, which have long been recognised to have prolonged activity stretching (for the present nighttime showers) at least from mid-October through to the end of November. In fact, one can make a case for a resumption thereafter into January or February, and also an earlier start.

In essence the Taurids have radiants that are a few degrees north and south of the ecliptic (in fact, arranged close to symmetrically about the orbital plane of Jupiter: remember that it is Jupiter that dominates their orbital evolution) but have a finite spread in ecliptic longitude on any particular night; and the mean radiant shifts along in ecliptic longitude by about a degree from night to night, as is to be expected (because the Earth moves by about a degree each day). Although there are many examples showing this in various papers published over the years, I will refer readers to an older summary, published in 1952: see Figure 1 in this report.

In view of this is would be a mistake to think of the Taurids having a discrete radiant. In any year for any night (or day, for the post-perihelion/daytime showers) one can determine a mean radiant, but that mean radiant moves from night to night, reflecting intersections with Earth by meteoroids which have followed slightly different orbital evolution paths by dint of their specific orbital parameters (again: see Table AI of Asher and Clube (1993)). Distinct initial orbits of the meteoroids result from such considerations as: (i) when they were released from the parent body/bodies; (ii) their velocities relative to the parent; (iii) the peculiarities of their particular evolution (e.g. close approaches to the terrestrial planets); (iv) various other physical effects such as the Poynting-Robertson pseudo-force; and so on.

What this means is that different quadruplets can have overlapping activity, in terms of the times of year in which meteors from different parts of the convoluted stream may be detected. For example, if we keep an assumed eccentricity e=0.85 but increase the semi-major axis to a=2.4 AU, it would take only about 4,000 years for a complete rotation of the line of apsides, so that in terms of precession this slightly-larger orbit would ‘overtake’ that with a=2.2 AU.

Apart from such considerations, the mean radiants for the showers in historical times will have been quite different from what is observed now. As explained above, secular perturbations (dominated by Jupiter) cause steady nodal precession such that in antiquity the showers will have occurred earlier in the year, and accordingly the shower radiants will have been in different locations.

Which locations? The answer is somewhat easy to state. In radar surveys of meteor radiants (and orbits) there are only a few dominant radiant regions recognised, the most prominent being termed the ‘helion’ and ‘anti-helion’ sources; for a recent example, see this paper.

These regions get their names because they are close to the directions of the Sun (on the dayside) and the opposite celestial location to the Sun (on the nightside), due the effect of compounding the Earth’s orbital velocity vector with the velocity vectors of the incoming meteoroids. Therefore, at any time in antiquity the nighttime showers we now associate with the Taurid Complex will have appeared to have been emanating from the direction opposite to the Sun, at whichever time of year they were occurring.

In fact it appears that at least 50 per cent (and perhaps 80 per cent) of the influx of small bodies to the Earth on an annual basis is derived from these helion and anti-helion sources, most of the mass being held in small meteoroids 1 mm and smaller in size.

We have various reasons, though, to think that the distribution of matter in the Taurid streams is by no means uniform and random. This would imply that in various epochs the conditions are achieved whereby meteor storms occur, for relatively brief periods (hours), and continuing for some centuries, but not occurring every year. Such storms may well contain larger objects, of the Tunguska/Chelyabinsk class. The celestial mechanics involved here is rather more complicated than what I have described above in qualitative terms, and so I must leave any explanation aside and merely encourage readers to see the various research papers published over the years by those working in this specific area, starting with Whipple.

An implication of this is that at various times in antiquity there must have been metaphorical fireworks in the sky, and I am confident that such events had a significant effect upon the civilisations existing in such eras. Understanding what they might have experienced, and how they might have interpreted it, is a worthy pursuit. Gaining such an understanding, however, would necessitate first developing a good knowledge of what we already know about the evolution of meteoroid streams and the celestial mechanics involved.

I hope that the above will prove useful to those interested in this area of study. Unfortunately I am pre-occupied with other matters (such as making a living) and so I am unable to provide any further answers to queries. I urge readers not to accept blindly what I have written above, but rather to dig out the vast literature available on this subject written by many excellent researchers over the past several decades: check what I have written, and verify it in primary sources (i.e. refereed research papers).

Duncan Steel
Nelson, New Zealand


Space Scientist, Author & Broadcaster