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Final Two MH370 Communications Suggests Controlled
Eastward Descent
Vincent Lyne 1*
1 Retired Scientist
University of Tasmania
Hobart. Tasmania. Australia
* Correspondence: Vincent.lyne@utas.edu.au
Abstract
Official interpretations of Doppler Shifts from the final satellite communications of missing
Malaysian Airlines MH370 were based on a motion-decoupled “Up-Down Model”. That model
predicted an uncontrolled high-speed gravitationally accelerated dive following fuel starvation.
Here, I challenge that model using a more-realistic motion-coupled “Declination Model”.
Aerial, satellite, and underwater searches failed to find the predicted official violent crash-site
near the 7th arc. Meticulous re-examination of debris damage by air-crash investigator Larry
Vance concluded that the aircraft glide-landed under power with extended wing-flaps. The
trailing-edges was then damaged, broke off their mountings, flailing about, and retracted along
the guides to cause the observed wing-flap damage. Larry’s conclusions complement
interpretations from the “Declination Model” which we demonstrate here with three example
flight tracks. Our revised Doppler-Shift analyses support the hypothesis of a controlled
eastward descent. We conclude that the official theory of fuel starvation and a high-speed dive
are fundamentally flawed.
Keywords: Burst Frequency Offset; Burst Timing Offset; MH370; Doppler Shift
1. Introduction
Malaysian Airlines MH370, a Boeing 777-200ER equipped with the Inmarsat Classic Aero
system went missing on the 8th of March 2014 with 239 people on board (ATSB, 2017). As
described by Ashton et al. (2014), the Inmarsat Classic Aero system Satellite Data Unit (SDU)
used several different communication frequencies determined by the data rate plus an
allowance for environment and instrument errors. The transmitted frequency is altered by the
SDU which internally compensates for expected horizontal Doppler Shifts so that signals arrive
at the expected frequency. However, compensation errors arise from several factors, including:
the simplified satellite model used; aircraft location; track angle; and ground velocity.
Importantly, Doppler Shifts from vertical motions are uncompensated. Significant remnant
discrepancies, after all other factors are accounted for, as found for the last two MH370 satellite
communications, may be due to vertical motions—which are the core subject of this paper.
Our aim here is to provide a plausible reinterpretation of Doppler Shifts from those two signals.
They were so different and uncertain that various conflicting interpretations have been offered.
Indeed, as we discuss later, they were discarded as erroneous from the Bayesian model used to
guide the failed first search. Corrections to uncertainties in those data then led to an official
high-speed dive interpretation using a motion-decoupled model. This was used in part to guide
the failed second search based on revised fuel loads and drift model studies. But officials still
insist that the model and interpretations are correct. My aim here is to provide context for the
official theory so that we have a clear understanding of failures in the theory, model, and
interpretations. I demonstrate that there is a far more physically reasonable interpretation using
a motion-coupled model. Three possible tracks for the aircraft are then used to compare and
contrast interpretations from these competing models. An underlying key message I want to
make is that the wrong MH370 theory led to “irrational exuberance” by some experts/scientists.
Their interpretations, not just for the problem at hand, defy the laws of physics, and in some
cases common sense. At times, I will use the problem at hand to identify how such
“exuberance” was used to justify, what now appears to be, the wrong official theory. There is
no defying the Science Principle that analyses purporting to support a wrong theory are most
likely also wrong. That was indeed the impetus that led me to this reluctant investigation to set
the Science record straight. But first, let’s review the background context for later analyses and
comparisons.
As noted in the official report (ATSB, 2017), along its planned fight from Kuala Lumpur to
Beijing, MH370 was in normal flight up to the transition between Malaysian and Vietnamese
airspaces. The now infamous “Good Night, Malaysian Three Seven Zero” sign-off by one of
the pilots to Malaysian Air Traffic Control (ATC) marks the turning point for the most baffling
modern aircraft disappearance. Minutes later, before control passed to Vietnamese ATC,
MH370 disappeared from civilian radar screens. Malaysian military radar tracked the aircraft
for another hour, as it deviated westwards from its planned flight path and crossed the Malay
Peninsula and Andaman Sea. After rounding Penang Island from the east and south—which
some interpreted as a hometown “farewell” by the pilot—it left radar range at 18:22
Coordinated Universal Time (UTC) as it headed north-west along the Malacca Strait. Ground-
to-air telephone calls went unanswered, although at the request from Vietnamese ATC, a call
from a nearby aircraft heard “mumbling” and static (Campbell, 2014).
Inmarsat engineers identified regular monitoring “Log-on Interrogation” communications with
the Inmarsat satellite I-3F1 after each hour of inactivity, and two phases of specific “Log-on
Requests” from the aircraft near 18:25 and 00:19 UTC (Ashton et al., 2014). The relative
motion between satellite and aircraft caused Doppler Shifts in the satellite communication
frequency as signals travelled between aircraft, Inmarsat satellite, and Perth Ground Station.
The aircraft Satellite Data Unit (SDU) compensated Doppler Shifts from the horizontal aircraft
motion but small biases (from drift and ageing) and a track-dependent error, primarily due to
the SDU assuming a geostationary satellite (rather than geosynchronous), remained (Ashton et
al., 2014). Following correction procedures by Ashton et al. (2014), Holland (2018) (Figure 4)
determined aircraft speeds and track angles that minimized this error. Other uncertainties, such
as temperature variations within the satellite, and biases, were also carefully calibrated out
(Ashton et al., 2014). Detailed analyses of Burst Timing Offset (BTO – distance-based
measurement) and Burst Frequency Offset (BFO – relative speed-based Doppler Shift
measurement between satellite and aircraft) resulted in seven distance-based BTO global arcs
(Zweck, 2016) along which the aircraft was located at different times, centered around the
Inmarsat satellite undergoing a “teardrop” shaped geosynchronous orbit; located nominally
above the equator at 64.5oE (Ashton et al., 2014).
BFO data from a "Log-on Request" at 18:25:27 UTC indicated the aircraft continued along the
north-west Malacca track. But data from an unanswered telephone call at 18:40 UTC suggested
that it was travelling south. So, between those communications, the aircraft turned south. A
similar request occurred at 00:19:29 UTC at the 7th arc, followed 8 seconds later by a "Log-on
Acknowledgement" at 00:19:37 UTC. This was the last communication as there was no
response to three handshake requests from Inmarsat at 01:15 UTC (ATSB, 2014).
Signals at 18:25:27 UTC and 00:19:37 UTC were part of a “Log-on Exchange” (LOE), whilst
other messages were part of a standard “Log-on Interrogation” (LOI) asking for a response.
Official interpretations of the two LOEs was that the first (18:25:27 UTC) preceded a track
change, but the second (00:19:37 UTC) was from the aircraft running out of fuel and crashing.
ATSB acknowledged that it could be due to the aircraft being readied for a “very unlikely”
controlled ditching (ATSB, 2017) (page 101). Our revised model and interpretation is that the
latter Log-on Requests reflect the aircraft being readied for a controlled descent and later
ditching.
Here, we compare BFO interpretations from Holland’s motion-decoupled model with our
model which couples horizontal and vertical motions. We aim to show that the fuel-starvation
model is incorrect, and that the decoupled model defies physics as it fails catastrophically into
a singular solution for finite declinations. Three example flight tracks are used to compare and
contrast the models.
In what follows, I describe official interpretations of BFO signals from the last two satellite
communications. I then explain why the first official search failed, and what went wrong with
the second search. These two theories are also differentiated by “fuel-starvation and flaps-up”
(Holland’s model) versus “fuel-available and flaps-extended” (our model and Larry Vance’s).
Hence context to the alternate “controlled ditching” theory is presented in relation to debris
damage and flap position by Larry Vance. I then describe the Penang Longitude Theory and
controlled ditching which complements the work of Larry. This theory’s prediction of MH370
veering eastward and descending by the 7th arc, also challenges the official high-speed dive. I
first discuss a surprising “break-through” development (since manuscript submission) of
riddles hidden in the Pilot-In-Command (PIC) home simulator track, which were discarded by
FBI and official investigators as “irrelevant” (ATSB, 2017).
The resolved riddles uncovered the probable very accurately planned flight track of MH370
(Lyne, 2023b; Lyne, 2023c). This track is now included belatedly as a third example track for
this study. However, it deviates marginally from the “Adelaide Track” (described later) so
conclusions are not critically altered. In yet another follow-up of this study (Lyne, 2022a), I
demonstrate that not only is our “Declination Model” capable of explaining the BFO signals
but it also demonstrates that Holland’s vertical death-defying gravitational-dive acceleration is
nothing more than apparent vertical acceleration from simple rotational-changes in declination
angle.
Potential flight paths from arc timings and BFO-estimated speeds/directions generally
supported a persistent southerly track down to the 6th arc (Ashton et al., 2014; Davey et al.,
2016). At the 7th arc, BFO anomalies remained after extrapolation of a statistical fit to previous
BFOs (Ashton et al., 2014) and resolved errors (Holland, 2018). However, for the first search,
the Bayesian model ignored Log-on Exchange BFOs (at 18:25:27 UTC, 00:19:27 UTC,
00:19:37 UTC) as settling errors could not be resolved and statistically assimilated into their
horizontal flight model (Davey et al., 2016)(Table 10.1). These deleted communications,
particularly the final two, allowed the Bayesian model aircraft to wrongly continue southerly
at the 7th arc. This resulted in a “heat map” crash region about 39oS. Searches of that area failed
(ATSB, 2017). Retrospectively (after search failure), the fuel model was also wrong, so Boeing
revised the fuel calculations and moved the Second Search further north.
For the Second Search, Holland (2018) (Bayesian-study co-author) carefully bounded errors
from power-up settling anomalies. Holland’s excellent work should have been used to update
the Bayesian flight model (assuming it had the correct flight dynamics that included vertical
motions). Instead, Holland used the Inmarsat decoupled BFO (not absolute velocity) model
(Ashton et al., 2014) for a solo effort to interpret the last two communications. We are here to
challenge these interpretations.
At the 7th arc discrepancies remained between a predicted BFO of 260 Hz and nominal
observed BFOs of 182 Hz and -2 Hz respectively at the last two communications 8 seconds
apart (Holland, 2018). Hypotheses on whether the SDU was started up from a power-off-on
engine-flame-out event (Hypothesis 1 – fuel-starvation scenario, long cold-start settling
behavior) or a warm-reboot electronic event (Hypothesis 2 – electronic switching, short-reboot
settling behavior as per the log-on BFO at 18:25:27 UTC) led to extended and extreme BFO
ranges (Holland, 2018). The extreme range produced unrealistic descent rates, so mid-point
values were used for the assumed-southerly track at the 7th arc.
Inmarsat’s decoupled BFO model (Ashton et al., 2014) assumes remnant anomalies are from
uncompensated up-down motions. This led Holland to conclude that, discounting the
unrealistic extreme range, a 0.68g (g is Earth’s surface gravitation acceleration constant)
acceleration took place during the 8 seconds leading to a nominal high-speed drop of 10,700
fpm (feet per minute). These conclusions, and the Boeing-revised fuel-starvation endpoints,
appeared to be supported by highly promising drift model analyses of recovered debris (Griffin
and Oke, 2017; Griffin, Oke and Jones, 2017). However, that “drift” model was in physically
impossible “sailing” perpetual motion in the turbulent open ocean (Lyne, 2023a). Extensive,
and highly detailed searches around these bounded locations were unsuccessful; with not even
a scrap of debris found (ATSB, 2017).
A significant positive outcome for ocean research was the huge volume of seafloor data
collected across 120,000 km2. Ocean Infinity donated this to the Nippon Foundation–GEBCO
Seabed 2030 Project, to update the global ocean seafloor map (Orr & Associates, 2018). It still
remains the most intensely mapped seafloor area of our Planet. MH370 was simply not there!
The scenario of powered glide-landing with extended flaps is supported by comprehensive
finite-element modelling and simulation analyses by France’s MH370-Captio group (MH370-
Captio, 2019; Kamoulakos, 2020). These simulations used add-on models of realistic ocean
swell, waves, and wind. Predictions from these studies matched observed damage to trailing-
edges of the flaperon, and complement investigations by Vance (2018). These investigations
suggest the following evidence-based events at landing:
• During the powered level glide-landing with extended flaps, the right wing contacts a
wave, ripping off its engine (as per US Airways 1549 (Lyne, 2024b)).
• The trailing extended edges of the flaps and flaperon were then hydrodynamically
damaged (again, as per US Airways 1549).
• Downward crushing forces were created across the wing and rearward crushing from
frontal and upward impact with the wave. The fuselage is breached at the wing root
(Vance, 2018), indicating much greater forces at play than US Airways 1549.
• This crushed the inboard-end wing-flap seal-pan with the outboard end of the flaperon.
• The combined crushing forces breaks off the flaperon and the flap off their supports.
As shown in Lyne (2024b), this mimics damage to US Airways 1549 from a
“controlled ditching”—providing further support to interpretations by the Captio-
group and Larry Vance.
• The flaperon breaks away but the flap flails about whilst loosely attached to its internal
support track.
• Witness marks made by the support track inside the flap-pan suggest that the flap
retracted back beyond its fully retracted position before it was pulled back free of the
support arm and pulled through the front of the flap.
The thorough and meticulous examination of Larry Vance firmly refutes the incomplete and
inaccurate “flaps up” damage investigation of the ATSB. Further, the opposite finding of “flaps
down” also invalidates the ATSB theory of an uncontrolled crash because the aircraft could
only attempt a controlled ditching under full engine power (Vance, 2018) with flaps and
flaperon in extended positions; which then damaged the trailing edges (Vance, 2018; MH370-
Captio, 2019; Lyne, 2024b; Kamoulakos, 2020). Here, we show that official interpretations of
the satellite communications, which hinged critically on a “flaps-up” “Up-Down Model”, and
fuel-starvation, are all flawed. I demonstrate this using a much more plausible and realistic
alternative “Declination Model” to reinterpret the BFO signals.
Before we describe the MH370 tracks for the demonstration, one track was uncovered recently,
hidden in riddles in the Pilot-In-Command simulation track as shown in Figure 1. Details of
these riddles, one set for the northern PIC track and another for the southern, can be found in
(Lyne, 2023b; Lyne, 2023c). Those tracks were simulated most likely for very careful
calculations of fuel consumption (Lyne, 2023c) and to leave riddles to torment investigators;
who obliged and discarded the tracks as irrelevant (ATSB, 2017). Resolution of the riddles
showed simple waypoints and precise planning. Even the Decoy Tracks were chosen to reflect
a fictitious ending not just in Perth but at Perth Airport runway. JORN’s corner was cut to save
fuel. But here again, there was knowledge of the 3D dome nature of JORN’s range, because 10
km altitude at that location was above the 3D dome (Harris, 2017). Resolution of the northern
PIC track riddle, shown in Figure 1, involved simple measurement of planned and simulated
track lengths. An elementary task that could have been accomplished quickly in Google Earth.
Admittedly the southern track riddles were less obvious, but still solvable with critical thought
from the world’s most eminent analytical minds, who instead threw it all away. Suffice to note
that the PIC Track is similar to the “Adelaide Track” shown in Figure 2. Hence, findings
reported originally are not materially altered, but the mastermind careful planning did save
~100 km flight distance.
Two of the three tracks shown in Figure 2 concord with the PL Theory’s requirement to stay
outside the western boundary of the Australia’s Jindalee Over-the-Horizon Radar Network
(JORN) (Harris, 2017); the exception is the South Track. Further, no other theory has an
explanation for the inferred southerly tracks other than the utterly unbelievable official
explanation of an autopilot track with everyone onboard hypoxic (ATSB, 2017), and with no
reference to JORN at all. The aircraft had to stay outside JORN range (despite JORN not being
on at the time) if it was on a secret mission to not be detected in-flight or found. This implies
an eastward descent track at the 7th arc, heading towards the ultra-deep hole at the Penang
Longitude (PL) Location, which would be filled with sediments many hundreds of meters deep
(NCEI, 2021). A “perfect” hiding place.
Figure 1. Figure adapted from (Lyne, 2023c) comparing the respective northern and southern Pilot-In-Command
(PIC) simulated tracks (left-side purple labels) with the planned tracks (right-side green labels). The PL Hole is
near where the 33oS latitude intersects the longitude of Penang (thin brown vertical line) at a 6000 m deep hole.
The Decoy Tracks (to Southern Ocean and Perth Airport runway) were not executed but merely to cause confusion.
Track lengths are noted in the labelled track boxes. The Jindalee-Over-the-Horizon Radar Network (JORN) range
and southern boundary from Laverton are drawn in purple. The Decoy Track to Perth is inferred from the other in
the Simulator Track. Note that the map is not in equi-distance projection.
The example tracks in Figure 2 were derived with simple waypoints. In the “Adelaide Track”,
Adelaide is chosen as a waypoint past the southern boundary of JORN at (92oE, 31oS). This
path crosses precisely over the PL location and minimizes distance travelled to avoid JORN.
The “South Track” was southerly (up to 6th arc) for compatibility with the fuel-starvation theory
southerly tracks. This track cuts deeply into the south-west corner of JORN. The “PIC Track”
closely resembles the “Adelaide Track” except the JORN corner-cutting is further east and
north (92.5oE, 30oS) and more than 100 km shorter—a mastermind at work saving fuel.
Without this “safe” corner cutting (Harris, 2017), the hidden riddles cannot be solved exactly
as all planned lengths were very precise. However, for resolving BFO signals, deviations from
the Adelaide Track are minor.
For bearings, at the 6th arc, the South Track bearing is less than 6o east from due-south. The
BFO residual from a track variation, relative to southerly, of under 6o is under 1 Hz (Holland,
2018) (Figure 4). At the 6th arc, the Adelaide Track and PIC Track veer east and cross at
bearings of 108.8o and 116.6o respectively, which potentially adds ~7 to 5 Hz (respectively)
BFO error.
Figure 2. Map features and example flight tracks. White curves are the 7 arcs. The purple curve and
inclined horizontal line are the Jindalee Over-the-Horizon Radar Network (JORN) range boundaries
(but ignore the curve past the southern boundary). Three flight tracks are shown: 1) in yellow (1: “South
Track”) the southerly track intersects the 6th arc near 94oE, then veers to 33oS, 95oE at the 7th arc, and
then proceeds east to the “Penang Longitude” Location (red circle); 2) in green (2: “Adelaide Track”)
the southerly path veers east towards Adelaide at 92oE and 31oS; in red (3: “PIC Track”), shown as a
dashed red line, is the Pilot-In-Command (PIC) track where the southerly track along 92.5oE veers
south-east once past the JORN southern boundary at 30oS. The bearing to the satellite is shown by the
light green northwest line. The light orange line running northwest is one of the simulation tracks from
the pilot’s home simulator. Other place marks are referred to in the main text, or for general background
information.
Our analyses will be as per Holland (2018) on the two final 7th-arc BFOs. We focus on alternate
explanations for anomalies from the “warm start” Hypothesis 2. The “warm start” refers to a
warm reboot from a power switching which is more compatible with the PL Theory’s
prediction that the aircraft was being prepared for descent—which the ATSB acknowledges
was possible (ATSB, 2017)(pg. 101). Precedence for this power-glitch assumption was
established by a previous such event (at 18:25:27 UTC) when the aircraft turned south, and
clearly did not run out of fuel. We will now analyse interpretations from the respective models.
2. Method
In our proposed analysis we allow the aircraft track to vary, and veer eastwards to the PL
Location. This contrasts with the fuel-starvation theory which, by extrapolation, required the
aircraft to maintain its southerly track (Ashton et al., 2014). We will also use a motion-coupled
flight descent model, where the aircraft descends at a declination angle to the horizontal plane.
This avoids the trap of assuming that the horizontal motion is compensated for by the SDU,
and hence need not be further considered. We add the appropriate small BFO differences due
to the horizontal deviation from a southerly track at the 6th arc as discussed above.
These changes are incorporated into the standard Doppler Shift model of equation (1) that
defines the frequency change observed from a moving electromagnet source:
=
∗
( − )
(1)
where speeds are in kilometers per hour (kph); frequencies are in Hertz (Hz); is the speed
of light (1,079,252,848.8 kph); V is the speed component of the aircraft velocity vector (kph)
that is aligned with the vector from the aircraft to the Inmarsat satellite (positive towards the
satellite); F is the uplink frequency from the aircraft to the satellite (1646.6525 MHz); and
is the received Doppler-shifted frequency (assuming no compensation).
The magnitude of velocity V was calculated from the aircraft track, heading, and elevation to
the Inmarsat satellite, and an assumed declination angle according to equation (2).
= ∗ cos(− ) ∗cos (−
)
(2)
Where, heading and track angles are measured clockwise from North in a 3D axis system; S is
the ground speed of the aircraft; is the aircraft to satellite elevation angle from horizontal
(positive and set to 38.8o for the 7th arc following Holland [4]); is the aircraft declination
angle (positive for descent); and and are heading angles at ground level for the satellite
and aircraft respectively (so 0o is a Northerly track, and 180o is a Southerly track).
The calculated velocity magnitude (V) is used in equation (1) following appropriate sign
conventions. The first cosine-term in equation (2) accounts for the satellite elevation angle
modulated by the aircraft declination, so when these angles are the same, the frequency offset
is at an absolute maximum—because the aircraft is proceeding directly to the satellite or away
from it. Likewise, for alignment of the satellite and aircraft headings in the second cosine term.
The two equations represent the model we used to calculate expected uncompensated BFOs
for various combinations of aircraft track angle () and declination angle (). Other
parameters were fixed as listed and referenced in Table 1.
Table 1 Ancillary parameters for the BFO calculations.
Parameter
Description
Value
Inmarsat Satellite Location (Ashton
et al., 2014)
Ground projected location of the Inmar-
sat Satellite at 00:19 UTC
0.5oN, 64.475oE
Inmarsat Satellite Elevation (Hol-
land, 2018)
Elevation angle from the aircraft location
to the satellite
38.8o
Heading of Aircraft Location to In-
marsat Location at the 7th arc.
(Note, this is not the aircraft track
heading)
Estimated by Ashton et al. (2014) Location: 34.70S, 93.0oE
Heading: 323.98o from North
According to the PL Theory
“South Track”
Location: 33.0oS, 95.0oE
Heading: 321.6o
“Adelaide Track”
Location: 32.13oS, 96.0oE
Heading: 319.8
o
Aircraft speed at 7th arc
In kph
“PIC Track”
Location: 31.72oS, 96.59oE
Heading: 319.03o
829 kph (Ashton et al., 2014)
First BFO at 7th arc: at 00:19:29
UTC (Holland, 2018)
Predicted for southerly track and ob-
served Predicted 260 Hz
Observed 182 Hz
Second BFO at 7th arc: at 00:19:37
UTC (Holland, 2018)
Predicted for southerly track and ob-
served
Predicted 260 Hz
Observed -2 Hz
BFO errors at the two times in Table 1 represent the difference between predicted BFO for a
frequency-compensated southerly track and measured SDU-frequency-compensated BFO.
Previous investigators interpreted the 7th arc mismatch as due to vertical motions, not accounted
for in the horizonal compensation by the SDU. This led to the official high-speed descent
conclusion (Holland, 2018). By contrast, in the PL Theory, BFO is not directly from vertical
motions, but from declination in the vertical plane. This also realigns the aircraft track more
closely with the aircraft to satellite direction (positive values implies the aircraft tracking away
from the satellite) and also affects the horizontal velocity component (hence SDU
compensation—wrongly assumed fixed in the decoupled dive-model).
Figure 3 schematically portrays motion-coupling differences between the Up-Down model and
the Declination model. In the Up-Down model the two components are decoupled based on the
assumption that there is no need to be concerned about the motion-compensated horizontal
track. However, in the Declination model, for finite declination, the horizontal compensation
varies. Therefore, the BFO horizontal-compensation deficit, plus the BFO from the vertical
motion, must be considered in explaining the overall BFO. Hence, the fundamental flaw in the
Up-Down model is exposed when the aircraft undergoes declination. Unless of course the
cruise speed is zero and then we have the valid but singular solution of Holland’s that depends
only on the gravitationally accelerated drop speed. This is the stopping in mid-flight and
dropping from the sky “solution” whose BFO only depends on the elevation angle to the
Inmarsat satellite as explained in considerable detail in Lyne (2022a).
Figure 3. Comparison of horizontal and vertical motion coupling between the Up-Down model of previous
investigators (left model) with the model of coupling between horizonal and vertical via a Declination Angle
from the horizontal (right model). The Up-Down horizontal Doppler Shift is assumed to be compensated by the
SDU, so BFOs are attributed solely to the vertical dive motion.
The uncompensated BFO was calculated by subtracting the compensated horizontal component
using equations 1 and 2 and the declination angle. For a level/horizontal flight with declination
angle = 0, this value is zero but with positive (or negative) declination the component due to
horizontal velocity (whose speed is the aircraft speed times cosine of declination angle) is
subtracted off the total BFO. Note, as discussed previously there are BFO discrepancies with
track angle due to incomplete horizontal BFO compensation by the SDU. These amounts are
to be added to the BFO errors shown in Table 1.
3. Results
BFO changes, compensated for horizontal motion, by track angle and declination angle are
shown in Figure 4 and Figure 5. With no declination (horizontal motion only), the difference
is zero and increases as the declination angle increases. For any declination, the BFO is
maximal at a track angle in-line with the direction of the satellite to the aircraft. These angles
are (141.6o, 139.8o, 139.03o) respectively for the tracks (South, Adelaide, PIC). For
convenience, the satellite track angle in Figure 4 of 141.6o should be shifted to align with the
respective satellite track.
For the South Track, the mismatch at the first 7th arc communication is approximately 80 Hz
(80 Hz = Predicted 260 Hz – Observed approximate 180 Hz). The mismatch would require a
minimum declination of 6 o at the satellite track angle, and 8o at the southerly track. There is a
slight advantage in veering to the east but overall, the first BFO mismatch is explainable by a
declination of under 8o at the assumed cruise speed of 829 km/hr. The second communication
mismatch was nearly 260 Hz and again the minimum declination is where the aircraft track is
aligned to the satellite direction, for a declination of under 19o. The aircraft has veered to a
heading of about 123o at the 6th arc, so during the 8 seconds between communications at the 7th
arc, it needs 20o of declination to explain the BFO error. This demonstrates clearly that track
angle does matter in explaining the “vertical” component of the BFO changes as evident from
the curvature of the BFO contours (Figure 4). In the case of the first BFO error, the track angle
effect is small at about 2o declination, and it increases to 6o declination for the second BFO
error. For the Adelaide Track, the required declinations are 8o and 22o for the first and second
BFO errors respectively, and the PIC Track is slightly less for the first and about 20o for the
second.
Figure 4. Variation of BFO error (Hz), compensated for horizontal motion, with track angle in degrees
clockwise from North, and declination angle down from horizontal. The approximate aircraft to satellite
direction is at 141.6o track angle (and elevation angle of 38.8o) where BFO changes are at a maximum across
track angles for any given declination angle. At this track angle, BFO changes of over 325 Hz are possible for a
declination angle of 25 degrees. Dashed lines refer to the different tracks in Figure 2: yellow is the “South
Track”; green is the “Adelaide Track”; and, red is the “PIC Track”.
BFO (Hz)
Figure 5. Variation of BFO with declination angle. Black line is for a nominal flight track heading directly to the
Inmarsat satellite—representing the maximum BFO possible by track angle. Other tracks are as shown in Figure
2.
For comparison, at the satellite track, 19o of declination produces 260 Hz BFO decrease—a
change that requires 15,300 fpm (280 km/hr) downward motion according to Holland’s Up-
Down model; a speed at which the entire aircraft would obliterate in well under one second.
This is higher than the nominal 10,700 fpm estimated by Holland to explain the nominal BFO
error at the last 7th arc communication—which requires just 14o declination. Finally note that
the Up-Down model requires the arcs seen in Figure 4 to be straight (horizontal) as vertical
motions in that model are independent of horizontal-compensated motions, and BFO error just
depends on vertical speed as calculated above. This is clearly not realistic, especially where the
track angle is closely aligned to the satellite track. To summarize this point, Figure 6 shows
how BFO errors are invariant with track angle, and further that there is difference of almost 75
Hz at the satellite track angle for a declination of 25 degrees.
0 5 10 15 20 25
050 100 150 200 250 300
Declination (degrees)
BFO (Hz)
Tracks
Inmarsat
South
Adelaide
PIC
Figure 6. Variation of BFO (Hz) according to the Up-Down model where horizontal speed is invariant with
track angle, hence horizontal compensation does not vary with track angle. For comparison with the Declination
model we used the horizontal speed at the 180o track (a track angle has to be chosen for comparison as the main
point of this comparison is that horizontal compensation in the Declination model does vary with track angle for
positive declination angles—Figure 4).
Differences between the two models are illustrated by variations in the speed factor applied to
the horizontal and vertical components in the Declination Model, shown in Figure 7. For
declinations up to 25o, horizontal speed varies with declination (~10% at 25o declination). For
the vertical component, declination contributes over 40% of the cruise speed. In 8 seconds, the
Up-Down aircraft falling out of the sky at 0.68g (Holland, 2018) reaches ~200 km/hr, whereas
the Declination model has a vertical speed component of 350 km/hr at 25o—under controlled
descent. Declination, achievable by manipulation of control flaps, under power, confers
vertical velocities and BFOs more than that achievable by stopping the aircraft in midair and
dropping it out of the sky. Further explanations of the mathematical and physics discrepancies
are detailed in Lyne (2022a), where I show that the 0.68g acceleration is simply explainable as
an aircraft in high-speed normal flight undergoing a declination change. This declination
rotation results in an apparent vertical acceleration of (ω V), where ω is the declination rotation
rate and V is the aircraft speed; equivalent to: ω V = 0.7g for our example (Lyne, 2022a). This
about matches what Holland derived as “gravitational acceleration”.
Lastly, the different tracks are of different lengths between the 6th arc (at 00:10:58 UTC) and
the final communication (at 00:19:37 UTC). These horizontal lengths are:
Adelaide/PIC Track: 113 km
South Track: 110 km
0
50
100
150
200
250
300
350
100 120 140 160 180
0
5
10
15
20
25
Track Angle (degrees)
Descent Angle (degrees)
BFO (Hz)
Southerly Track: 147.5 km (southerly from South Track at 6th arc)
Implying that the horizontal speeds necessary to cross between the arcs are:
Adelaide/PIC Track: 783 km/hr
South Track: 762 km/hr
Fuel-starved Southerly Track: 1023 km/hr
Both PL tracks have the aircraft slowing down (horizontally) from the previous southerly track
cruise speed (necessary to cross the arcs at the right times but these horizontal speeds will
decrease with declination angle—as per Figure 7) of 829 km/hr (Table 1). However, the fuel-
starvation southerly track requires the aircraft to slow down (horizontally) to undertake the
vertical dive, but the track crossing requires the aircraft to in fact speed up to over 1000 km/hr
(horizontal) whilst it impossibly runs out of fuel. The only way for the aircraft to decrease its
speed is for it to veer east from the southerly track and it still needs a minimum speed of over
750 km/hr to cross the arcs at the right times. This compares to a speed of about 254 km/hr
before the aircraft stalls and drops (Marks, 2013). Realistically, this is not the scenario of an
aircraft stopping in mid-flight. There is no way for it to achieve that whilst it must cross the
arcs at the right times. The evidence is overwhelming that MH370 did not run out of fuel and
fall out of the sky. That scenario just simply does not fit the available evidence, nor physics.
By contrast, the PL tracks suggest slower horizontal speeds and eastward veering compatible
with the predictions of the PL Theory of an eastward turn and descent.
Figure 7. Variation of the speed multiplicative factor with declination angle. Horizontal speed varies simply as
the cosine of the declinaton angle, and vertical speed as the sine.
To bring this demonstration to a close, Figure 8 shows the horizontal compensation applied by
the SDU model for the declination model which varies with track and declination angles. As
shown previously, the greatest variations and compensations are applied at the satellite track
angle. To summarize, the coupled declination model is a more realistic and accurate model of
BFO changes due to changes in track and declination angles. Further we can explain the
apparent gravitational acceleration of Holland as merely due to declination rotation, and not
gravitational high-speed dive.
Figure 8. Variation of horizontal BFO (Hz) compensated by the Satellite Data Unit (SDU) (hence BFOs are
negative) for the Declination model. Some variation with declination angle is seen at the South track (180o) but
the greatest variation is at the satellite track angle (~141o).
The PL Theory predicts that at the 7th arc, there is about 30 minutes before landing on an
unfamiliar ocean surface where wind, waves, and swell, need to be monitored carefully to affect
a precise controlled-ditching. The landing time estimated by Lyne and Lyne (2021a) was about
0:53 UTC, and descent at 00:19 UTC was past sunrise estimated at 23:34 UTC (NOAA sunrise
calculator: https://gml.noaa.gov/grad/solcalc/sunrise.html). The final track was towards east to
southeast on a very cloudy day with limited visibility from standard altitude (Lyne, 2022b).
For secrecy the aircraft needed to descend as low as possible to just below, or within, the clouds.
In a very recent update, I report the discovery of a 300 km trail of cloud anomalies that align
well with the expected final PIC track of MH370 (Lyne, 2024a). These anomalies were visible
in five satellite images from three satellite passes. These observations confirm the predictions
of our model, and the PIC Track flight path.
The observations also justify the aggressive nature of the descent predicted at the 7th arc.
Although an alternate explanation, proposed by Lyne (2023c), is that it may be near the end of
a controlled “glide phase” to conserve fuel so that, as concluded by (Vance, 2018), fuel would
remain for the failed (debris was emitted) powered near-level landing attempt in the wild
Southern Ocean. This strategy fits a mastermind plan, whereas others would assume the glide
occurs at the end. But in this case, the lack of fuel and engine power would make a “controlled”
ditching very difficult as the plane must be kept as level as possible as explained by Vance
(2018) and Captain Mike Glynn (pers. comm.).
A summary of the evidence against the high-speed crash and the evidence for the controlled
eastward descent is presented in Table 2.
Table 2 Summary evidence against high-speed crash (left column), and for controlled eastward descent (right column).
Evidence Against High-Speed Crash
Evidence for Controlled Eastward Descent
The aircraft did not run out of fuel (Vance, 2018)
Aircraft had fuel till landing (Vance, 2018)
The flaps and flaperon were extended, not retracted, at
landing (Vance, 2018)
Aircraft had functional flaps to veer and de-
scend (Vance, 2018)
Minimum stall speed was not reached (Marks, 2013)
Minimum eastward horizontal speed of 750 km/hr required
to traverse 6th and 7th arc
Aircraft was travelling at cruise speed eastward
and descending at 7th arc
Estimated horizontal speeds consistent with air-
craft travelling near cruise speed and descend-
ing
Eastward veering requires fuel and functional flaps
Controlled eastward veering and descent ex-
plains BFO discrepancies
Southerly track requires horizontal speed over 1000 km/hr
to traverse arcs with no fuel
Eastward track horizontal speeds consistent
with veering and calculated declination angles
Crash speed would be horizontal speed plus about 200
km/hr vertical speed (min 950 km/hr). At those speeds, air-
craft disintegrates within “the blink of an eye” (Vance,
2018)
No debris or aircraft discovered at 7th arc from
two extensive searches
Southerly track requires higher vertical speeds than east-
ward track, but Up-Down Model is incorrect and has them
the same
Calculated track and declination angles possible
in Declination Model with fuel and control of
flaps
No explanation possible for high-speed crash, or southerly
track past 7th arc
Aggressive descent was necessary as sun had
risen, or it was the end of a glide phase. East-
ward veering once past JORN necessary to
reach PL location
4. Discussion
Our revised model and analyses provide compelling evidence that MH370 did not run out of
fuel and fall out of the sky. This assessment is supported by the extensive failed searches that
did not find one shred of debris evidence within the hugely extended official crash zone.
Instead, careful detailed expert investigations by Vance (2018) confidently suggests a powered,
piloted, controlled landing, incompatible with a high-speed nosedive that would have crumpled
the leading-edge nose (MH370-Captio, 2019) and obliterated the aircraft into many pieces
within the blink of an eye (Vance, 2018). For example, the crash of Swiss Air Flight 111
resulted in over 2 million pieces of small debris—see pictures of such catastrophic devastation
in Figure 5 of Larry’s book (Vance, 2018).
A controlled landing at the 7th arc is also clearly at odds with the suggested uncontrolled high-
speed descent demanded to explain the BFO changes with the fuel-starved theory. Despite the
reconciliation of all other evidence by the PL Theory there were no previous analyses to support
the predictions of this theory that MH370 veered eastward at the 7th arc to follow an easterly
track. That however changed with the discovery of the hidden riddles in the PIC Track, and
more recent discovery of a cloud anomaly trail aligned with the final PIC Track.
Results of our coupled Declination Model for the three tracks suggests that the first BFO is
explainable with declination under 8o for the first BFO mismatch. The second communication
mismatch required a minimum declination of between 19o and 25o. Veering is completed by
the 6th arc for all tracks, so changes at the 7th arc were primarily to do with descending for the
landing, and possibly the end of a low-fuel-consumption glide-phase.
The Up-Down Model decouples horizontal and vertical velocities; hence it relies upon a
dropping-from-the-sky vertical velocity to explain BFO changes. But the Declination Model
shows that those changes are from a simple declination of the aircraft. We also demonstrate
that the track angle does matter, and more so with greater declination – a point entirely missed
by the Up-Down model as further demonstrated by Lyne (2022a). This scenario also cannot
explain the large horizontal speeds necessary for the aircraft to cross the 6th and 7th arcs at the
correct time. We also now have a very plausible explanation for the “gravitational acceleration”
as being simply due to controlled declination rotation of a high-speed aircraft.
The other point to make is that in the most likely situation where the aircraft continued to glide
along, the velocity at the last communication will have a much larger component than the
vertical speed—perhaps less than the assumed 829 km/hr (but not zero) versus 200 km/hr
vertical. How else can claims be made that the dive model was used to calculate bounds for the
7th arc? This combination, particularly the assumed vertical-drop speed, is unrealistic. Simply
put, the aircraft is not a gravitationally accelerated lead-weight when it runs out of fuel; despite
what a decoupled (BFO) model might lead some to believe. Yes, as far as BFOs are concerned
we do not need to worry about the compensated horizontal component, which changes because
the aircraft is now descending, not diving. Hence, for an actual dive scenario vertical velocity
is from momentum (and BFO) transferred from the horizontal cruise speed plus gravitational
acceleration. As I explain in Lyne (2022a), an air-crash in 2022 shows that under such
circumstances, which is facilitated by a belly-up dive (otherwise the controlled forward dive
levels out to a phugoid), speeds can approach supersonic levels, as lift forces are reversed and
now acts downwards with gravity. We do not need supersonic dive speeds to explain the BFOs
from MH370, nor does it explain why not one shred of debris was discovered within the
expansive 7th arc search zone. But it is a real worry that students can now read authoritative
out-of-context claims in an educational reference that the diving aircraft simply slipped without
trace into the ocean (Gregersen, 2021). Let them all prove this “blink of the eye”
disappearance!
There are two elements responsible for this: 1) the assumption that the aircraft ran out of fuel,
and 2) the mathematical independence afforded to analysts by the Up-Down model. These two
may have been the disastrous pairing that wreaked havoc in the search for MH370. But the
original culprit was the blinded conclusion that the recovered flap was retracted. No, they did
not see the obvious trailing-edge damage. Here’s a short list of the main potential disasters of
these incorrect assumptions, and irrationally-exuberant attempts by scientists to reconcile
evidence to the wrong theory:
1. Misled the excellent technical analyses of debris drift to a fictitious 7th arc location
(Griffin, Oke and Jones, 2017). The official drift model resorted to a misapplied added
10 cm/s perpetual motion, to in effect illegally (in Physics) and forcibly “sail” the
recalcitrant flaperon to Réunion Island on time from the 7th arc—as explained by Lyne
(2023a). No such mysterious force was required from the PL Location (Lyne, 2023a)
using the same model with a standard drift formula (Lyne, 2023d). The implications
are obvious.
2. Misled the important hydroacoustic discoveries by Alec Duncan (Butler, 2014) and
Usama Kadri (Kadri, 2019). They tried hard but neither could find any 7th arc source
using either Duncan’s water-borne model, or Kadri’s novel, and very clever, hybrid
Acoustic Gravity Wave (AGW) model. Anomalous sound data comprised four very
accurate atomic-clock timings and two very accurate directions from two
Comprehensive Nuclear-Test-Ban Treaty (CTBT) International Monitoring System
hydroacoustic stations (HA08: Diego Garcia, HA01: Cape Leeuwin) and two marine-
life listening stations of Australia’s IMOS program (Perth Canyon, Scott Reef) (Lyne
and Lyne, 2021b). Precise resolution (within-seconds timing and one-degree
direction) of all data (4 timings and 2 directions) was only possible from the precise
PL Deep Hole location with sound propagating within the seafloor (the PL Hole is
about 1.5 km below the general seafloor level at that location) before emerging into
the ocean Sound Channel from special seamounts at the end of continental plates
(Lyne, 2022b)—the so-called “MH370 Mechanism” dedicated to MH370 victims.
Although for Diego Garcia the sound appears to have had an uninterrupted path all
the way as a seismic signal bouncing off the hard vertical plate structure of
Madagascar. Kadri thought Madagascar might have been the actual source, as he did
with the Batavia Seamount (using the AGW model). He proposed two separate
sources for the conflict. In fact Batavia was the seafloor exit point for sounds heard at
Perth Canyon and Cape Leeuwin as explained in Lyne (2022b). However, neither
Duncan nor Kadri could reconcile the Scott Reef sound which emerged from Exmouth
Plateau (shown in Figure 2). Paradoxically, the sound from there to the more distant
Scott Reef (at 1:32:49 UTC) arrived before the sounds heard at Perth Canyon (1:33:44
UTC) and Cape Leeuwin (1:34:50 UTC). This paradox can only be resolved by the
near-double speed of sound in the seafloor compared to the water-borne speed (Lyne,
2022b); a phenomena also noted for the ARA San Juan submarine where a precursor
implosion-sound propagated within the ice-shelf before exiting to the ocean 20
minutes before the arrival of the direct but slower water-borne sounds (Vergoz et al.,
2021). Here again, the wrong official theory led to failed interpretations by those
contracted to desperately search in vain along the 7th arc.
3. Misled the analyses of other debris damage reported in (ATSB, 2017) that was
corrected by Vance (2018) in his careful, competent, and thorough reassessment. Such
damage was visibly apparent in the damage to flaps and flaperons from hydrodynamic
forces as US Airways 1549 landed on the Hudson River (Lyne, 2024b), after its
engines were taken out by a bird-strike (see the film Sully (2016)). Evidence of
ditching-damage was there all along, as was Larry’s illustration of what a high-speed
dive did to Swissair 111. Compare and contrast which theory you would select after
seeing those images. Perhaps officials thought they could get away with the no-blame
fuel-starvation idea (possibly to minimize grief/trauma), despite obvious evidence to
the contrary, and rammed it into failed submission (Lyne, 2023a).
4. Most importantly, misled the second extensive search, and stymied hopes of a future
search. In science we make mistakes but we (some of us anyway) admit those mistakes
if we want to move forward with alternate explanations; as I did with my first
wayward explanation of the MH370 sound heard at Perth Canyon (Lyne and Lyne,
2021a). No admission, no progress.
5. Quashed other scenarios by insisting that only the official narrative is correct. “Due
diligence” of other theories, or a new search proposal, always finds its way back to
officials (my bitter experience). How these failed officials are able to do “due
diligence” credibility assessments on scientists and scientific analyses that go beyond
prevailing studies and expertise is beyond comprehension. Here, science journals must
play a part to set the record straight.
We also note that the short disturbance SDU power after the 6th arc (Hypothesis 2) may have
been from preparation for the descent, predicted to be underway by the end of the 7th arc.
Whereas the fuel-starvation theory assumes the power-up was from engines flaming out and
the cold SDU restarting sometime later – the extreme Hypothesis 1 scenario. Vance (2018)
conclusively demonstrates that the aircraft did not run out of fuel, and our calculations also
imply that the aircraft was powered to affect the veering and aggressive declination.
To sum up, we can safely, with absolute confidence, say that the fuel-starvation high-speed
dive theory is not supported by the available evidence. We can also say that MH370 was most
likely in a controlled descent at the 7th arc along a very accurately planned and plausible
premeditated PIC Track, to its secret resting place in a deep hole at the PL Location.
5. Conclusions
Whilst valid for horizontal motions only, the official decoupled “Up Down” model fails
comprehensively and catastrophically by attributing vertical velocities from declination as
being due to a fictitious “gravitational acceleration” following fuel-starvation. Instead, the
baffling BFO changes at the final two communications from MH370 at the 7th arc are more
plausibly due to the aircraft veering eastward, in a controlled descent, and undergoing apparent
vertical acceleration from declination rotation. These revised interpretations accord with
predictions by the Penang Longitude theory which also uncovered the precise PIC Track hidden
in riddles in the Pilot-In-Command simulator track. These new interpretations of BFO changes
provide mutual support for the PIC Track taken by MH370 (presumed, till proven) to its precise
mastermind secret final location. We can now safely ditch the very troublesome official 7th arc
fuel-starvation high-speed dive theory, and all analyses supporting it.
Funding: This research received no external funding.
Acknowledgments: Many keen scientists indirectly contributed to this study, which would not have been possible without
their remarkable technical detective work on diverse aspects of finding MH370. We are all deeply indebted to all the brave
folks who took part in the search for MH370 in one of the most inhospitable, but ecologically unique, ocean environments on
the Planet. Despite not finding MH370 your work has contributed to detailed seafloor mapping and excluding vast areas of the
ocean from further searches. I am particularly indebted to Larry Vance for his advice and independent expert thorough inves-
tigations of debris damage; a quiet voice of reason lost in the cacophony of contrived misinformation. Thank you also to
Captain Mike Glynn (former RAAF and Qantas Pilot) for his expert thoughts on questions I had on the simulated flight tracks.
To the Editors and Reviewers of JN, thank you for your suggested improvements, and your valued indirect contribution to
finding MH370. Finally, a sincere thank you to the unknown voices for providing the insights. Rest in peace.
Conflicts of Interest: The author declares no conflict of interest.
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