22/05/2015 MH370 End of Flight Modeling Final.docx Page 1 of 11

Stochastic Simulation of Hypothetical MH370 End-of-Flight Scenarios

Brock McEwen

May 22, 2015

Summary

This paper stochastically models MH370 end-of flight dynamics, and finds no evidence to support last month’s

announced continuation of status quo search strategies.

This finding is consistent with a documented pattern of decisions by MH370 search leaders which make no sense. A

rigorous, independent audit of both the Inmarsat data’s entire chain of custody and MH370 search leadership is

recommended.

Introduction

In a joint statement issued April 16, 2015, Malaysian Transport Minister Liow Tiong Lai, Australian Deputy Prime

Minister Warren Truss and Chinese Transport Minister Yang Chuantang indicated the search for Malaysian Airlines

Flight 370 (MH370) would continue to focus on the deep-sea search in the Southern Indian Ocean (SIO):

“Should the aircraft not be found within the current search area, ministers agreed to extend the search by an additional 60,000 square kilometres to bring the search area to 120,000 square kilometres and thereby cover the entire highest probability area identified by expert analysis,” they said in a joint statement.

“Ministers recognise the additional search area may take up to a year to complete given the adverse weather conditions in the upcoming winter months.”

In committing to this extension – described graphically as a modest search zone expansion in all four directions - search leaders appear to assume that

1) the Inmarsat data is sufficiently accurate and precise to permit interpretation by investigators AND 2) the officially assumed (and IG-endorsed) scenario* is correct, YET 3) the wreckage this conclusion predicts remains outside the areas already searched by side-scan.

* MH370 turns south by 18:40, takes a straight path at cruising speed/altitude until fuel exhaustion, and develops an (unpiloted) spiral to impact

This paper tests this hypothesis, via stochastic simulation of plausible post-fuel exhaustion flight paths.

Stochastic (or “Monte Carlo”) simulation

Stochastic (“involving random numbers”) simulation (“running of many, many trials”) is a well-recognized means of analyzing complex systems – in particular, whenever one or more of a system’s inputs is unknown (or “known” to vary within a range). Simulation involves building a model which treats the input as constant, but assigns it a randomly generated value (governed by distributional parameters which define the limits of plausibility). The resulting model (inputs and outputs) are referred to as a single “trial”. The model is then run again, with a different randomly generated plausible value – and so on.

The greater the number and complexity of variables driving a system, the more valuable a tool simulation becomes. The key output is no longer a single “best estimate” or “maximum likelihood” answer – rather, a distribution of results, from which statistical inferences can be drawn.

22/05/2015 MH370 End of Flight Modeling Final.docx Page 2 of 11

Model starting point: second engine fuel exhaustion

The compatibility of assumption 3) with 1) and 2) will be tested by assuming 1) and 2) are true, and developing the a priori probability of 3). We therefore begin the simulation from the point of fuel exhaustion for MH370’s second of two engines, as assumed under 1) and 2). This starting point (in time and space) is appropriate, as the flight path up to this point is relatively stable, while the flight path after this point will be relatively erratic.

Consider the assumed state of MH370 at second engine fuel exhaustion to be given by four attributes:

a) bearing b) speed c) altitude d) distance to 7th arc (FL0) in the direction of a)

a) 186 degrees is selected as a baseline, being representative of predictions conforming to 1) and 2).

b) While consensus under 2) is strong that a final major turn did send MH370 into the SIO, its timing (within a 12 minute span) remains in dispute. Accordingly, a range (albeit narrow) of assumed pre-exhaustion speeds is possible. We choose 480 KGS as a representative baseline speed, for consistency with parallel analysis.

c) FL350 is chosen as a baseline altitude; this is the consensus assumption under 1) and 2), and flight simulation experience conducted by Mike Exner, and reported by Brian Anderson - both members of the MH370 Independent Group (or “IG”) - suggest a 777 essentially maintains altitude for the first 4-5 minutes on one engine.

d) 21 nmi is selected as the forced result, under 1) and 2), of

i. our selections of a), b) and c) ii. per Exner/Anderson, flight simulator result of a constant deceleration of 0.315 kts/sec while on one engine

iii. engine 1 fuel exhaustion time: deemed under 2) to have been very close to the signal sent at 00:11:00 iv. engine 2 fuel exhaustion time: assumed baseline of 00:15:49.42, based on the following reasoning:

a) signal data packet sent at 00:19:29.42 (7th arc) has been deemed to represent a log-on request b) trigger for this event is deemed to be engine two fuel exhaustion, causing total power loss c) time from power loss to log-on request has been claimed to be 3:40 (i.e. 220 seconds, +/-10)

By subtraction, the point of engine two fuel exhaustion is 00:15:49.42, +/- 10 seconds. 21 nmi is then simply 56 nmi (distance from first engine exhaustion to 7th arc (FL0) minus the 35 nmi MH370 would travel in time t=289.5s starting at velocity v=0.1333nmi/s, with acceleration a=-0.0000875 nmi/s2 (d = vt + ½at2 = 35 nmi)

ALL of the above baseline assumptions will be sensitivity-tested.

The frame of reference is shifted from geographic (putting MH370 at roughly [S38, E89] and bearing = 186 degrees) to

a Cartesian frame (x and y in nmi, z = feet) with initial position [0, 0, 35000], and bearing 180.

Model time-step: 10 seconds

The model recalculates all flight dynamics every 10 seconds. This value was chosen to strike a reasonable balance between the precision of each scenario, and model simplicity sufficient to permit generation of a large number of scenarios. In the notation that follows, the time index in parentheses represents units of ten seconds.

Number of simulated paths: 100,000

22/05/2015 MH370 End of Flight Modeling Final.docx Page 3 of 11

Model inputs: Flight Dynamics after Second Engine Fuel Exhaustion Note: “U(a, b)” = random variable with values uniformly distributed between a and b

Deceleration: a stochastic process was built, which begins at (and whose mean value is) -0.315, but then randomly walks, based on the formula:

a(0) = -0.315 KGS/s; a(t+1) = a(t) + U(-0.05, 0.05) v(0) = 388.8KGS; v(t+1) = max[100, v(t) + 10 * a(t)]

Turn rate: bearing, b, follows a left-biased random walk, with exponentially increasing (but capped) bias, :

b(0) = 180b(t+1) = b(t) – min[ -1, cap(t)] (0) = 1.15; (t+1) = (t) + U(-0.027, 0.033)

cap(t) = tan(10g/2.5v(t))

Horizontal position: is derived in straightforward fashion:

x(0)=0 nmi; x(t+1) = x(t) + 10 / 3600 * v(t) * sin(b(t)) y(0)=0 nmi; y(t+1) = y(t) + 10 / 3600 * v(t) * cos(b(t))

Vertical velocity, i, starts at -250’/min, and follows a complex random walk gravitating towards -10,000’/min:

i(0) = -250’/min; i(t+1) = min[0, i(t) + 25%(j(t) - i(t)) + U(-20, 20)

j(0) = -3600’/min; j(t+1) = j(t) + 12.5%(10000’/min – j(t)) + U(-45, 45) + 0.5b(t)

Altitude: is derived deterministically from prior vertical position, plus effect of vertical velocity, i:

z(0) = 35,000’; z(t+1) = z(t) + 10 * i(t)

The left bias reflects a consensus view under 2) that a left turn developed at t=0. While the model permits coming out of spirals - and even right turns - such events are infrequent, as the bias tends to produce increasingly tight left turns.

The cap on the change in bearing per second reflects basic principles of flight: the faster a plane is traveling, the harder it is to turn quickly. A basic relationship was developed, and calibrated to Exner-reported flight simulator results, with

respect to both terminal radius distributions (2-15 nmi) and maximum observed bank angle (1/sec).

While the vertical velocity formula may seem complex, a two-factor model was required to control vertical speed AND acceleration. Having vertical speed “chase” a target of j - which itself is “chasing” a target of 10,000’/minute - not only achieves this, but generates a much richer array of descent patterns than could be achieved by a one-factor model.

The last term in the “j” formula introduces a modest correlation between bank angle and vertical velocity. This additional term reflects the simple fact that altitude becomes more difficult to maintain as bank angle increases.

Interestingly, even though the turn radius is capped at 1.5/second (to reflect the limits of large aircraft dynamics), typical spirals still tended to exhibit progressively smaller turn radii, due to decreasing velocity. Model output: distance between impact point and 7th arc

The trial ends when altitude reaches zero, at which point two positions are recorded:

1) coordinates (and other metrics) at 00:19:29, and 2) coordinates (and other metrics) at time of impact

The distance between 1) and the 7th arc (FL(z)) is then used to determine whether that trial “hit” the 7th arc. The tolerance for defining “hit” was set at 0.3 nmi in the y direction (or roughly 0.22 nmi crow’s flight).

For “hits”, the distance between 2) and the 7th arc (FL0) is computed: this is the value whose distribution we seek. (“Non-hits” are retained and plotted for the sake of perspective, and as a control on model fidelity.)

22/05/2015 MH370 End of Flight Modeling Final.docx Page 4 of 11

Results - summary

- 10.3% of paths “hit” the 7th arc - hits tended to do so at relatively high altitudes

o spirals tend to develop gradually, so most paths were relatively straight over the first 2 minutes o straighter paths tended to overfly the 7th arc (FL0), and thus only hit at higher altitudes

- of the paths hitting the 7th arc: o 61.1% impact OUTSIDE the 7th arc (FL0) o 99.1% impact within the area already searched (from 11 nmi inside to 27 nmi outside 7th arc (FL0) o 0.8% impact OUTSIDE the searched area o 0.1% impact INSIDE the searched area

Results – detailed

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10

0-1

10

11

0-1

20

12

0-1

30

13

0-1

40

14

0-1

50

15

0-1

60

16

0-1

70

17

0-1

80

18

0-1

90

19

0-2

00

20

0-2

10

21

0-2

20

22

0-2

30

23

0-2

40

24

0-2

50

25

0-2

60

26

0-2

70

27

0-2

80

28

0-2

90

29

0-3

00

30

0-3

10

31

0-3

20

32

0-3

30

33

0-3

40

34

0-3

50

35

0-3

60

36

0-3

70

37

0-3

80

38

0-3

90

39

0-4

00

40

0-4

10

41

0-4

20

42

0-4

30

43

0-4

40

44

0-4

50

45

0-4

60

46

0-4

70

49

0-5

00

50

0-5

10

55

0-5

60

Distribution GROUND SPEED (in knots) at Impact

Missed 7th Arc

Hit 7th Arc

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

<-1

80

00

-18

00

0--

17

50

0

-17

50

0--

17

00

0

-17

00

0--

16

50

0

-16

50

0--

16

00

0

-16

00

0--

15

50

0

-15

50

0--

15

00

0

-15

00

0--

14

50

0

-14

50

0--

14

00

0

-14

00

0--

13

50

0

-13

50

0--

13

00

0

-13

00

0--

12

50

0

-12

50

0--

12

00

0

-12

00

0--

11

50

0

-11

50

0--

11

00

0

-11

00

0--

10

50

0

-10

50

0--

10

00

0

-10

00

0--

95

00

-95

00

--9

00

0

-90

00

--8

50

0

-85

00

--8

00

0

-80

00

--7

50

0

-75

00

--7

00

0

-70

00

--6

50

0

-65

00

--6

00

0

-60

00

--5

50

0

-55

00

--5

00

0

-50

00

--4

50

0

-45

00

--4

00

0

-40

00

--3

50

0

-35

00

--3

00

0

-30

00

--2

50

0

-25

00

--2

00

0

-20

00

--1

50

0

-15

00

--1

00

0

-10

00

--5

00

-50

0-0

Distribution of VERTICAL SPEED (in ft/min) at Impact

Missed 7th Arc

Hit 7th Arc

Calibration reference: Anderson/Exner

flight simulator report (“descent rate

would be up to 15000 feet/minute”)

22/05/2015 MH370 End of Flight Modeling Final.docx Page 5 of 11

Averages - second engine exhaustion impact: Time: 7.0 min Distance flown south: 12.6 nmi Distance flown east: 8.8 nmi

Averages - at impact:

Horizontal speed: 260.6 kts Vertical speed: -8,896 ft/min Descent rate: 19.1

0

1000

2000

3000

4000

5000

6000

7000

8000

0-1

1-2

2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-1

0

10

-11

11

-12

12

-13

13

-14

14

-15

15

-16

16

-17

17

-18

18

-19

19

-20

20

-21

21

-22

22

-23

23

-24

24

-25

25

-26

26

-27

27

-28

28

-29

29

-30

30

-31

31

-32

32

-33

33

-34

34

-35

35

-36

36

-37

37

-38

38

-39

39

-40

40

-41

41

-42

42

-43

43

-44

44

-45

45

-46

46

-47

47

-48

48

-49

49

-50

>5

0

Distribution of DESCENT RATES (in degrees below horizon) at impact

Hit 7th Arc

Missed 7th Arc

0

1000

2000

3000

4000

5000

6000

3.5

3.7

3.8

4.0

4.2

4.3

4.5

4.7

4.8

5.0

5.2

5.3

5.5

5.7

5.8

6.0

6.2

6.3

6.5

6.7

6.8

7.0

7.2

7.3

7.5

7.7

7.8

8.0

8.2

8.3

8.5

8.7

8.8

9.0

9.2

9.3

9.5

9.7

9.8

10

.0

10

.2

10

.3

10

.5

10

.7

10

.8

11

.0

11

.2

11

.3

11

.5

11

.7

11

.8

12

.0

12

.2

12

.3

12

.5

12

.7

12

.8

13

.0

Distribution of TIME from exhaustion to impact (min)

Missed 7th Arc

Hit 7th Arc

Calibration reference: Exner flight simulator

report (“between 4 and 13 minutes”)

22/05/2015 MH370 End of Flight Modeling Final.docx Page 6 of 11

all axis units in nmi

Comment: the scatter plot of “hits” at 00:19:29 (above left) do not appear to follow the shape of any particular 7th arc (which, if plotted, would appear as a straight diagonal line). This is because the model does not constrain the altitude at which a hit could potentially occur: as a result, relatively straight paths will tend to intersect the 7th arc at higher altitudes, while relatively curved paths will tend to intersect at lower altitudes. Since the arc moves NW as altitude decreases, the curved pattern emerges. This relationship is further illustrated by examining the relationship between altitude and leftward bias (or x-axis position) at 00:19:29, as well as the scatter plot of hits by altitude band:

…and further demonstrated by an analysis of modelled 7th arc hits by altitude band:

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

0 2 4 6 8 10 12 14

Scatter plot:position at00:19:29

AllHits

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

-20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55

Scatter plot: position at impact

All

Hits

7th arc (FL0)

4000-5000

8000-9000

12000-13000

16000-17000

20000-21000

24000-2500028000-29000

32000-33000

0

10

20

30

40

50

60

70

<4

4.2

5-4

.5

4.7

5-5

5.2

5-5

.5

5.7

5-6

6.2

5-6

.5

6.7

5-7

7.2

5-7

.5

7.7

5-8

8.2

5-8

.5

8.7

5-9

9.2

5-9

.5

9.7

5-1

0

10

.25

-10

.5

10

.75

-11

11

.25

-11

.5

11

.75

-12

12

.25

-12

.5

Altitude (ft)

Leftward Displacement (nmi)

Distribution of ALTITUDE vs.LEFTWARD DISPLACEMENT at 00:19:29

-23

-21

-19

-17

-15

-13

-11

2 4 6 8 10 12

Scatter plot:position at00:19:29 - byaltitude band(in ft)

0-50005000-1000010000-1500015000-2000020000-2500025000-3000030000-35000

22/05/2015 MH370 End of Flight Modeling Final.docx Page 7 of 11

Despite the complex turn function formulation, the output - expressed here as a distribution of total number of

revolutions (360turns) from fuel exhaustion until impact - helps develop an intuition for the plausible range of spirals modelled:

Observations:

- the area searched appears to align reasonably well with the modelled distribution of distances

- the search to date thus appears to test (and, in fact, to emphatically reject) the hypothesis efficiently

- while some regions of the 7th arc FL(0) have not yet been searched fully out to 12 nmi inside, such “skipped” areas are over 40nmi to the east of even the easternmost of the IG’s newly revised best-estimate path predictions – the model suggests no material probability of spirals being able to stretch that far to the east.

0

2000

4000

6000

8000

10000

12000

-0.1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9 2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9 3

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9 4

Distribution of REVOLUTIONS between exhaustion and impact

Hit 7th Arc

Missed 7th Arc

0

2000

4000

6000

8000

10000

12000

<-3

2

-31

--3

0

-30

--2

9

-25

--2

4

-24

--2

3

-23

--2

2

-22

--2

1

-21

--2

0

-20

--1

9

-19

--1

8

-18

--1

7

-17

--1

6

-16

--1

5

-15

--1

4

-14

--1

3

-13

--1

2

-12

--1

1

-11

--1

0

-10

--9

-9--

8

-8--

7

-7--

6

-6--

5

-5--

4

-4--

3

-3--

2

-2--

1

-1-0

0-1

1-2

2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-1

0

10

-11

11

-12

12

-13

13

-14

14

-15

15

-16

16

-17

17

-18

18

-19

19

-20

20

-21

21

-22

22

-23

23

-24

24

-25

25

-26

26

-27

27

-28

28

-29

29

-30

30

-31

31

-32

32

-33

33

-34

34

-35

35

-36

36

-37

37

-38

38

-39

39

-40

40

-41

41

-42

42

-43

45

-46

46

-47

47

-48

Distribution of DISTANCE from impact point to 7th arc (FL0), in nmi

Missed 7th Arc

Hit 7th Arc

Calibration reference: Exner flight simulator

report (“between 1 and 3 revolutions”)

Average rotation among “hits”: 370(1.03 revolutions)

Already searched:

from 12 nmi inside

to 27 nmi outside

of 7th

arc (FL0)

22/05/2015 MH370 End of Flight Modeling Final.docx Page 8 of 11

Sensitivity Testing

Scenario Impact relative to area searched*

Comment Inside Within Outside

Baseline 0.1% 99.1% 0.8% as above

Vertical acceleration +25% (-0.315-0.394)

0.0% 99.6% 0.4% Reduced minutes aloft, which reduces range

Initial altitude +5,000’ (FL350FL400)

0.1% 98.8% 1.1% Increased minutes aloft, partially offset by more southerly 7th arc intersections

Initial velocity reduced 20 knots (480460 KGS)

0.0% 100.0% 0.0% Origin moves 1.6nmi further from 7th arc and speeds drop (doubly hard to reach)

Logon sequence takes less time (3:403:30)

0.1% 99.2% 0.7% Origin moves ~1nmi closer to 7th arc and initial speed reduces ~3 KGS

Left-turn bias decreased

( (0), U each

x baseline)

0.1% 95.2% 4.6% OUTSIDE probability increases, but

average total rotation drops to only 212

Left-turn bias increased ( (0), U each 2 x baseline)

0.0% 100.0% 0.0% Paths curl too tightly to make it to 7th arc; only 8 of 100,000 trials “hit”

Arc 6 south of measured position (distance to arc 7: 2119 nmi)

0.1% 99.2% 0.8% Origin moves 2nmi closer to 7th arc

Arc 6 north of measured position (distance to arc 7: 2123 nmi)

0.1% 99.5% 0.5% Origin moves 2nmi further from 7th arc

Arc 7 south of measured position (distance to arc 7: 2123 nmi)

0.0% 99.1% 0.9% Same at “Arc 6 north” above, plus impact of searching 2 nmi further inside

Arc 7 north of measured position (distance to arc 7: 2119 nmi)

0.2% 99.5% 0.3% Same at “Arc 6 south” above, plus impact of searching 2 nmi further outside

* hits only; “area searched” is defined as a range extending from 12nmi inside to 27nmi outside of the 7th

arc (FL0)

Limitations

A stochastic simulator is not a flight simulator (and neither are “reality”): while built to proxy the behaviour of a real

plane under real conditions (by diligently calibrating to actual flight simulator results), it remains a mere model, whose

results cannot prove anything. This model could be wrong. Its builder hopes it is wrong.

Wind effects: are not modelled. Below are wind speeds by

altitude at 37.8S, 88.4E on Mar.8, 2014 at 00:00 UTC:

Altitude Wind

hPa ft (kts)

250 34,000 49

500 18,000 39

700 10,000 25

850 5,000 22

1000 400 16

Sfc 0 14

Source: http://earth.nullschool.net

While wind effects depend on modelled altitude, attitude,

bearing and speed - all of which vary greatly - a reasonable

time-weighted average wind speed is conservatively

estimated at 30 knots. Acting over an average spiral time of 7 minutes, this might be expected to drift a spiralling

plane up to 3 nmi - in a direction parallel to the 7th arcs. Accordingly, none of the conclusions below are expected to be

sensitive to this omission.

22/05/2015 MH370 End of Flight Modeling Final.docx Page 9 of 11

Conclusions

1) Model results point to a stark conclusion: if both the Inmarsat signal data and its interpretation by search officials is valid, then the search should have turned up wreckage by now (99% probability). This offers strong circumstantial evidence that either the Inmarsat data or its interpretation is invalid.

2) Accordingly - unless search officials know something we don’t - the announced decision to spend another year searching around the improbable edges of a discredited theory (while this paper does not address surface debris, its absence likewise serves as strong Bayesian counter-evidence) appears to be an extremely poor one.

3) Yet another poor decision would be entirely consistent with the string of counter-productive decisions search leaders have made since March, 2014. A careful comparison of these decisions to the actual DATA on which they have been based raises suspicions, frankly, of a search which is not being conducted in good faith.

Recommendations

1) A rigorous audit of the entire chain of custody of the Inmarsat data should be conducted, to determine whether any data have been altered, by accident or design, and either before, during, or after its synthesis and dissemination by Inmarsat.

2) A rigorous audit of all key search decisions since March, 2014 should be conducted, to determine with certainty whether blunders have been due to incompetence or malfeasance. Such an audit should include all agencies which at any time reported either directly or indirectly to the MH370 Joint Investigation Team (JIT).

3) Each audit should be conducted under the direct supervision of a government with a) superior experience and expertise in air accident investigations, b) a strong record of impartiality, and c) no representation on the JIT.

Epilogue

If wreckage is found in the 60,000 km2 extension whose search this model counter-indicates, its author will celebrate the possibility of being wrong. He will then work to verify the authenticity of such a find - a task made necessary by its incompatibility with his understanding of the physical laws governing both surface debris and pilotless, gliding aircraft.

Sources

Anderson, Brian: “The Last 15 minutes of Flight of MH370”. MH370 Independent Group, April 2015 Exner, Mike: personal communications, as well as contributions published to jeffwise.net, circa November, 2014 This paper’s model is available at MH370 Impact Simulation (downloadable standalone 43Mb Excel 2013 xlsb file; set workbook calculation to “automatic except for data tables”) Prior concerns raised by search: MH370: Time to Investigate the Investigators (viewable/downloadable 2Mb pdf file) Acknowledgements

The author wishes to thank the members of the MH370 Independent Group for their expertise, flight simulator hours, and careful analysis, whose interpretation by the author underpins this model’s calibration.

The author also wishes to express his gratitude to Duncan Steel and Jeff Wise for their skilled moderation of online forums in which dedicated people from all over the planet continue to crowdsource the unravelling of one of modern history’s greatest mysteries.

22/05/2015 MH370 End of Flight Modeling Final.docx Page 10 of 11

Appendix: sample stochastically-generated flight paths

(origin = point of second engine exhaustion; down = pre-exhaustion bearing)

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

22/05/2015 MH370 End of Flight Modeling Final.docx Page 11 of 11

Appendix: sample stochastically-generated flight paths (cont’d)

(origin = point of second engine exhaustion; down = pre-exhaustion bearing)

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute

-40

-35

-30

-25

-20

-15

-10

-5

0

0 5 10 15 20 25 30 35 40

0

10000

20000

30000

40000Altitude (ft)

by minute

0

100

200

300

400Velocity (KGS)

by minute