1 | P a g e Denver Cheddie, MH370 Prediction (September 5, 2014) www.bibleissues.org/mh370

Malaysian Airlines Flight MH370 Path Prediction

Denver Cheddie, PhD

September 5, 2014

Summary The disappearance of Malaysian Airlines flight MH370 has baffled everyone including the official team of investigators which has not been able to find the plane after six months of back and forth searching. Identifying the underwater search areas requires analysis of the INMARSAT satellite communication data, which is available to the public. This work reports my analysis of the satellite data and prediction of the path most likely flown by MH370. My model takes into account wind data and aircraft performance limitations, and seeks a realistic flight path that matches the satellite data. I predict that the plane took a southern route at 470 kTAS, slowing down by about 18% toward the end, before crashing in the Indian Ocean in the vicinity of 34.6°S, 93.5°E. I believe that the underwater search area should focus on a strip ranging from 34.2°S, 94.0°E to 35.3°S, 92.7°E. Background On March 8, 2014, Malaysian Airlines flight MH370 went missing en route from Kuala Lumpur to Beijing, and to this date (September 5, 2014) it has not been found. The ACARS system was disabled (deliberately or otherwise) less than one hour after takeoff, preventing communication with the aircraft. The plane was initially thought to have crashed in the South China Sea or in the Strait of Malacca. However, satellite data from INMARSAT suggested that the plane was communicating on the satellite network (independent of ACARS) up to seven (7) hours after the ACARS system was disabled. The INMARSAT team of investigators was able to use the satellite data to conclude that the plane eventually flew south and “ended in the Indian Ocean”. Purpose This work reports my attempt to reconstruct the unknown flight path of MH370 using the satellite data made available to the public, and to predict its final resting place. My model seeks to find a flight path that matches well with the satellite burst timing offset (BTO) and burst frequency offset (BFO) data, and is consistent with the prevailing wind patterns and aircraft performance limitations.

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Assumptions and Considerations 1. I do not hold to the pilot malice theory – that the pilots deliberately turned off

communication and flew the plane in a way that made it invisible to radar only to crash it in the Indian Ocean. If the pilots wanted to crash the plane, they could have done that anywhere. This theory is the political invention of the Malaysian government.

2. Instead I believe that the plane lost communication due to some electrical problem. The pilots then decided to fly the plane back to Malaysia without the help of ground control. The predicted flight paths suggest that they were trying to remain close to land lights. But at some point, they were no longer able to control the plane, which then flew unmanned until it ran out of fuel.

3. The reconstruction of the flight path revolves around a military radar location at time 1822

(UTC), followed by nine (9) distinct satellite communications. Seven (7) of these communications report a BTO value, which can be used to determine the distance of the plane from the satellite. All nine (9) report a BFO value which can give an idea of the plane’s speed and direction at the time of communication. Further details on BTO and BFO data can be found on pages 16-24 of the ATSB report – MH370 – Definition of Underwater Search Areas.

4. In between these ten (10) discrete times, I assume that the plane was flying at constant

groundspeed and heading, i.e. a rhumbline path. Turns are allowed at the satellite communication times. However, the turns should be systematic and not result in an unrealistically tortuous path. Also any speed changes should be systematically and not randomly implemented.

5. The true airspeed (TAS) and true heading represent the plane’s velocity relative to the air.

The plane’s true air velocity vector needs to be added (vector-wise) to the wind velocity vectors to determine the ground speed and actual heading of the plane. It is impossible to know the exact wind speeds and directions at the times and positions of MH370, but this model uses wind data available at earth.nullschool.net.

6. The plane was equipped with sufficient fuel for a six (6) hour flight beginning at 1642. It is

expected that there would be extra fuel for emergency. It was able to fly until 0019 (approximately 7.5 hours). Therefore the plane must have been flying economically – at a speed that minimized fuel consumption at the given altitude.

7. I use an ellipsoidal model of the earth – with equatorial radius, 6378.13 km and polar semi-

axis, 6356.74 km. All reported latitudes are geodetic latitude.

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Model Equations The full details of the BTO and BFO models can be found in Appendix G (page 54) of the ATSB report. Here I only present the equations that I used.

2

sat plane bias sat Perth

cRange BTO BTO Range

[eqn. 1]

, ,up down up comp down comp sat biasBFO f f f f f f

[eqn. 2]

L bandup sat plane sat plane

ff v v LOS

c

[eqn. 3]

, 0 groundL bandup comp plane geosat plane

ff v LOS

c

[eqn. 4]

C banddown sat sat Perth

ff v LOS

c

[eqn. 5]

,C band

down comp AFCsat AFCsat Perth

ff v LOS

c

[eqn. 6]

, 33.546 8.7525 1600down compf time [eqn. 7]

The bias values are chosen such that there is zero error between the measured and model predicted BTO and BFO values at 1630 when the plane was stationary at the Kuala Lumpur International Airport (KLIA). The satellite position and velocity are also obtained directly from the ATSB report. Since the public does not know the exact EAFC compensation model programmed into the ground station at Perth, it is difficult to use equation 6. However, since the ATSB report actually lists the relevant downlink compensation values (as opposed to the model which produced the values), we can use equation 7 instead of equation 6.

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Flight Path Prediction Algorithm For the known portion of MH370’s flight, there are four (4) satellite communication times that coincide with the known flight path data – 1630, 1642, 1656 and 1707. Shortly thereafter, there was a satellite blackout during which there was no satellite communication for over one hour. This coincided with the disabling of the ACARS communication system. So the flight path between 1707 and 1822 is sketchy, however this portion of the flight is not necessary to determine where it ended. The prediction of the unknown portion of the flight begins at 1822 when the plane was picked up by military radar @ 6.56°N, 96.3°E. I use the following algorithm to trace the path of MH370: 1. Start with a time when the position of the aircraft is known or determined.

2. Determine (by trial and error) the speed and heading that:

a. matches the BFO at that present time, and b. matches the BTO at the next communication time.

3. Follow the rhumbline path (prescribed in point #2 above) over the ellipsoidal earth and

determine the position of the plane at the next communication time. Note that my model does not require the plane to be on the satellite “ping ring” at the communication time. It acknowledges that there may be an error in the BTO value. However, it should be close to the ping ring to be considered a good fit.

4. Calculate the relevant parameters and errors. 5. Repeat until the final position is determined. Further, there are some ground rules that must be implemented to avoid an unrealistic flight path. I assume that the TAS remains constant for most of the path. Only at the end, I allow for a speed reduction as the plane runs out of fuel. I also only allow turns at two points – 1840 and 1941. Both of these turns must be in the same direction, i.e. no zigzag. After this, the true heading remains unchanged. The ground heading of course, may vary depending on the wind. These rules are intended to ensure consistency with the assumption that the plane was unmanned during its final hours. The predicted path is the one which best matches the BTO, BFO, wind data; and is consistent with aircraft performance limitations, i.e. how fast the plane could physically fly and how far it could go with the fuel it contained.

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Allowable Errors The allowable errors or tolerances indicate how much we allow the modeled parameters (BTO and BFO) to differ from the measured parameters to consider the predicted path a good fit. These can be estimated from a casual perusal of the satellite data. Usually there are multiple satellite communications, fractions of a second apart, for which there are variations in BTO and BFO values. On page 11 of the satellite data report, within a period of 1 second from 1606:59 to 1607:00, there are four (4) BTO values ranging from 14,780 – 14,900 μs on a single channel. Also on page 32 of the same report, during a 1 minute interval from 1706:53 – 1707:45, the BFO ranges from 132 – 138 Hz on a single channel. These give an idea of the errors inherent in the reported satellite data. Thus the acceptable errors are:

± 5 Hz for BFO

± 100 μs for BTO This represents a satellite – plane range error of ± 15 km. This error is the difference between the modeled satellite – plane distance and the actual satellite – plane distance derived from the measured BTO (equation 1). This is not the same as the distance between the plane and the ping ring, although it would be in the same order of magnitude.

Flight Path Predictions Here I present most-likely flight paths for high altitude (35,000 feet), low altitude (7,000 feet), and I also consider a possible northern path. The satellite data is weakly dependent on altitude. BTO is only slightly affected by altitude, since compared to the distance of the satellite from earth, there is very little difference between sea level and cruising altitude. The BFO is even more weakly dependent on altitude, however the BFO is strongly dependent on rate of climb (vertical component of velocity). So the satellite data alone cannot indicate the altitude of the plane. The major effects of altitude are wind patterns and aircraft performance factors. The wind speeds and directions are different at 35,000 feet and 7,000 feet above sea level. Also at lower altitudes, there is greater air resistance implying that the plane would not travel as great a distance, i.e. its speeds would have to be significantly lower than at high altitudes. For all paths, we note the following: 1. For the known portion of the flight, the BTO and BFO match very well with the satellite

data. The largest BTO range error is 6.7 km, and the largest BFO error is 2.6 Hz. Both of these are well within the allowable tolerances. See Table 1.

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2. The BFO value at 1828 strongly suggests that the plane was flying in a generally

northwesterly direction. Other headings simply do not fit the 1828 BFO. 3. The BFO at 1840 strongly suggests that the plane was flying south. So at or just before 1840,

the plane started to turn to the south. 4. Ideally I would like a single turn to the south at 1840 followed by a constant heading path

until 0019. However this does not produce a good fit at any speed. Instead I allow a final change of heading at the next satellite communication time, 1941.

5. Most paths result in an overestimation of the 2314 BFO (by >10 Hz which is above the

allowable tolerance). I have found that the only way to match that 2314 BFO is to impose a rate of descent. This is not unrealistic since the plane is estimated to have crashed shortly after 0019. Thus one would expect a slowdown and descent as the fuel supply to the engines began to dwindle.

6. Similarly the BFO at 0019 can only make sense if we apply a high rate of descent (~4000-

5000 feet/min). This would suggest that the plane was beginning to nosedive at around this time, and would have crashed very soon after.

High Altitude Path (35,000 feet) A Boeing 777-200ER has a fuel capacity of 305,000 lbs of jet fuel. We know that MH370 flew for approximately 7.5 hours, and on average burned fuel at the rate of 40,670 lbs/hr. Given that it burned fuel at a faster rate during take-off and ascent, we can assume that for the rest of the trip, its burn rate was in the order of 38,000-40,000 lbs/hr. At an altitude of 35,000 feet, this suggests a TAS of 460 – 480 knots. Figure 1a shows the flight paths at 35,000 feet that best fit the satellite and wind data. The black plot is for 470 kTAS with a 0019 location of 34.56°S, 93.48°E. An 18% TAS reduction is applied just after 2314 together with a 400 feet/min rate of descent due to reduced fuel supply to the engines. The points on the figure coincide with the satellite ping rings suggesting a good BTO fit. Figure 1b shows the BFO fit, which is also very good. Table 1 presents all the model parameters. The largest BTO range error is 10.5 km and the largest BFO error is 4.3 Hz which are acceptable. The plane flies at a 304° heading between 1822 and 1840, following which it turns south (186.2° at 1840 and 181.2° at 1941). These turns are realistic as they appear to be two phases of a single turn. Notice that in Table 1, the actual heading shifts to 171° toward the end because of the strong westerly winds (from the west) at the 35,000 feet altitude. This results in a curved trajectory in Figure 1a. This is what I consider to be the best fit.

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Figure 1a also shows two other plots, for which the maximum BTO range error is 15 km (the maximum tolerable). As such they form the outer bounds of a range of paths falling within the allowable errors. The yellow plot is for 480 kTAS ending at 35.27 °S, 92.66°E, while the white plot is for 460 kTAS ending at 34.16°S, 93.98°E. I conclude that the underwater search for MH370 should be centered around 34.6°S, 93.5°E; and ranging from 34.2°S, 94.0°E to 35.3°S, 92.7°E. Low Altitude Path (7,000 feet) There were unconfirmed reports that the copilot’s cell phone communicated with a cell tower while the plane was close to Malaysian airspace. This would require the plane to be flying at a very low altitude, perhaps 7,000 feet. It is also consistent with the theory that the pilots were trying to communicate with ground officials. The Malaysian military radar @1822 indicated a very low altitude, but that was later discredited due to poor calibration. It was this low altitude assumption that caused the official investigators to move the search zone closer to Perth (in late March 2014). Now (September 2014) they are moving further south, closer to where they started. Nevertheless, it is worthwhile to construct a best-fit path at 7,000 feet. Figure 2 shows two low altitude flight paths. Both are problematic. The black plot represents 480 kTAS at a final true heading of 183°. This is my model’s best fit at this altitude. The largest BTO range error is 11.7 km, the largest BFO error is 5.1 Hz, and the 0019 location is 36.8 °S, 90.3 °E. This fits the satellite and wind data very well. The problem is that a plane flying at 480 knots at an altitude of 7,000 feet will run out of fuel long before 0019. This path is not consistent with the aircraft performance limitations. The plane must have been flying at a much lower speed at this altitude. The white path represents 400 kTAS. For this plot, a groundspeed of 400 knots is maintained, while the heading is manually adjusted to fit the BTO and BFO data. The predicted 0019 location of 29.57 °S, 98.54 °E is within what the official investigators consider the most likely zone. The satellite fit is very good, and this path is consistent with aircraft performance limitations. However, the large curve toward the east requires very strong westerly winds. The actual winds at this altitude are moderate easterlies. So this path is not consistent with the wind data. This wind would cause it to curve in the opposite direction, which would then result in a bad satellite fit. I conclude that there is no good fit at 7,000 feet, which most likely implies that the plane was not flying at such a low altitude.

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Northern Path – could the plane have flown north? I have included this section for the conspiracy theorists. Many believe that the plane landed in Diego Garcia or some secret island in the Indian Ocean. Diego Garcia is located at 7.3 °S, 72.4 °E which is far away from the 0019 ping ring. This final destination is not remotely consistent with the BTO data, unless you hold that the satellite data released to the public is erroneous. Others believe that the plane may have flown north. A northern route can be consistent with the BTO data. Figure 3a shows a possible north route ending in southern Kazakhstan. However it is not consistent with the BFO data. In Figure 3b, we see how significantly the modeled BFO for this path deviates from the measured BFO. The only way to make the modeled BFO fit is to apply a ridiculously high rate of descent (~ 2000 feet/min) from 1840 – 2241, followed by an equally ridiculous rate of climb (~ 3000 feet/min) until 0019 where it plateaus. This rate of descent would quickly take the plane under the ocean, where it continues to fly for hours. Then miraculously it rises out of the ocean and flies into space. Essentially MH370 is more likely to have been abducted by aliens. Conclusion My MH370 model aimed to predict the unknown portion of MH370’s flight path starting with the last radar location at 1822. It then used nine (9) satellite communications to determine that the plane flew northwest between 1822 – 1840, then south until 0019 just before it crashed. My predicted flight paths matched well with the BTO data and BFO data, as well as wind data. Aircraft performance limitations at an altitude of 35,000 feet suggest that the plane had to have flown at 460 – 480 kTAS in order to run out of fuel at 0019. These two speeds also happen to produce the two most extreme paths that just fall within the allowable tolerances of 5 Hz (BFO) and 15 km (BTO range). Their predicted positions at 0019 are respectively 34.2°S, 94.0°E and 35.3°S, 92.7°E. These form the outer bounds of my predicted search region where MH370 most likely went down. My best prediction (which minimizes the BFO and BTO errors) has the plane turning to the south around 1840 and flying at 470 kTAS, slowing down by 18% toward the end. Its predicted location at 0019 (shortly before it crashed) is 34.6 °S, 93.5 °E. Denver Cheddie is an Associate Professor of Mechanical Engineering at the University of Trinidad and Tobago.

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Glossary of Terms ACARS Aircraft Communications Addressing and Reporting Systems ATSB Australian Transport Safety Bureau BFO Burst Frequency Offset BTO Burst Timing Offset c Speed of light EAFC Enhanced Automatic Frequency Control f Frequency INMARSAT Satellite company LOS Line of Sight Range Distance from Satellite to Plane Rhumbline Path followed by maintaining a constant compass bearing TAS True Air Speed UTC Coordinated Universal Time v Velocity

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Figure 1a. BEST FIT Flight Paths @ 35,000 feet

YELLOW: TAS = 480 knots from 1822- 2314, 384 knots from 2314-0019; True heading = 185.6 @ 1840, 182.7 from 1941-0019 BLACK: TAS = 470 knots from 1822- 2314, 385 knots from 2314-0019; True heading = 186.2 @ 1840, 181.2 from 1941-0019 WHITE: TAS = 460 knots from 1822- 2314, 404 knots from 2314-0019; True heading = 186.6 @ 1840, 180.2 from 1941-0019

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Figure 1b. BFO Fit for Black Flight Path in Figure 1a

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Table 1. Model Parameters for Black Flight Path in Figure 1a (TAS = 470 knots from 1822- 2314, 385 knots from 2314-0019; True heading = 186.2 @ 1840, 181.2 from 1941-0019)

WIND DATA PLANE VELOCITY PLANE LOCATION BTO DOPPLERS BFO

Time (UTC)

Wind Speed (knots)

Wind Dir.

Ground Speed

(knots) Actual

Heading

Rate of Climb

(ft/min) Altitude

(feet) Latitude Longitude

Mod. BTO (μs)

Meas. BTO (μs)

Range Error (km)

Up. (Hz)

Up. Comp

(Hz) Down

(Hz)

Down Comp

(Hz)

Mod. BFO (Hz)

Meas. BFO (Hz)

1629.8 0 140 0 0 2.745 101.710 14920 14920 0.0 -6.2 0.0 -84.8 29.2 89.0 89

1642.5 183 328 1000 1500 2.798 101.690 14900 14945 -6.7 192.7 -168.1 -80.3 27.3 122.4 125

1656.4 461 25 1400 26775 4.040 102.210 15240 15241 -0.1 -401.0 454.3 -75.1 25.3 154.2 156

1707.3 468 25 0 35000 5.287 102.800 15600 15604 -0.6 -460.2 487.9 -70.9 23.7 131.2 132

1822 470 304 0 35000 6.560 96.300 12692 601.3 -580.4 -38.5 12.8 145.9

1828 470 304 0 35000 6.999 95.648 12500 12441 8.8 584.1 -562.7 -35.7 12.0 148.3 144

1840 13.5 175.4 456.1 186 0 35000 7.900 94.341 11961 209.9 -251.1 -30.0 10.2 89.8 88

1941 13.9 192.5 475.8 183.1 0 35000 0.190 93.533 11500 11451 7.4 0.1 -44.8 0.0 1.3 107.4 111

2041 16.6 71.7 465.2 183.3 0 35000 -7.753 93.106 11740 11810 -10.5 -171.3 136.1 29.2 -7.4 137.2 141

2141.5 17.8 107.9 465.3 182.7 0 35000 -15.577 92.649 12780 12823 -6.4 -338.8 320.5 56.0 -16.3 172.2 168

2241.4 13.1 112.8 465.8 177.8 0 35000 -23.321 92.263 14540 14472 10.2 -543.6 548.0 78.3 -25 208.3 204

2314 28.4 260.9 389.4 173.1 -400 35000 -27.536 92.445 15752 -558.0 571.4 88.4 -29.8 219.0 216

0011 54.9 271.5 391.7 171 -400 35000 -33.650 93.302 18040 18013 4.0 -649.7 683.9 102.8 -38.1 249.7 252

0019.5 69.2 271.5 389.3 171 -4500 35000 -34.561 93.475 18400 18389 1.6 -726.6 692.0 104.7 -39.3 181.4 182

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Figure 2. Problematic Flight Paths @7,000 feet (Black: TAS = 480 knots, White: TAS = 400 knots)

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Figure 3a. Unlikely Northern Route

Figure 3b. BFO Fit for Figure 3a (zero rate of climb after 1707)