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Addendum #3 – New Analyses of

Proposed MH370 Routes

(The Location of MH370)

Dr. Bobby Ulich

B.S.E.E., M.S.E.E., Ph.D. Astronomy / E.E.

Bandera, Texas, USA

[email protected]

001-830-522-0839

October 15, 2014

mailto:[email protected]

Dr. Bobby Ulich Addendum #3 – New Analyses of Proposed MH370 Routes 2

TABLE OF CONTENTS

1 INTRODUCTION ................................................................................................................................................... 3

2 TEMPORAL VARIATION IN TRUE AIR SPEED ......................................................................................................... 4

3 SPEED SLOPE STUDY ............................................................................................................................................ 5

SPEED SLOPE STUDY RESULTS ................................................................................................................................... 6 3.1 SPEED SLOPE STUDY CONCLUSIONS ........................................................................................................................... 6 3.2

4 RMS RESIDUAL ERRORS OF BEST FIT ................................................................................................................... 7

ARE SMALLER RESIDUALS BETTER? ............................................................................................................................ 7 4.1 HOW TO BEST FIT NOISY DATA ................................................................................................................................. 7 4.2 NUMBER OF INDEPENDENT MH370 DATA POINTS ...................................................................................................... 8 4.3 NUMBER OF VARIABLES........................................................................................................................................... 9 4.4 EXAMPLE OF BEST FIT ............................................................................................................................................. 9 4.5 CONCLUSIONS ..................................................................................................................................................... 12 4.6

5 BFO DATA MODIFICATIONS AND DELETIONS .................................................................................................... 12

6 ASSESSMENT OF INMARSAT ROUTE .................................................................................................................. 14

7 ASSESSMENT OF AIRCRAFT RANGE FOR MY PROPOSED ROUTE ........................................................................ 14

9M-MRO FUEL DATA .......................................................................................................................................... 14 7.1 ROUTE INFORMATION ........................................................................................................................................... 14 7.2 FUEL BURN ANALYSIS ........................................................................................................................................... 15 7.3

8 DEBRIS SEARCH ................................................................................................................................................. 17

LIST OF TABLES

TABLE 1-1 REFERENCE LIST ....................................................................................................................................................... 3

LIST OF FIGURES

FIGURE 2-1 COMPARISON OF TRUE AIR SPEEDS FOR EACH LEG OF ROUTE .......................................................................................... 4 FIGURE 3-1 SPEED SLOPE STUDY RESULTS ................................................................................................................................... 6 FIGURE 4-1 POLYNOMIAL FITS TO 7 NOISY DATA POINTS .............................................................................................................. 10 FIGURE 4-2 RMS RESIDUALS VERSUS NUMBER OF FITTED PARAMETERS ......................................................................................... 11 FIGURE 5-1 MEASURED AND PREDICTED BFO VALUES AT FINAL TURN (REVISED FIGURE 5-9 IN BU1) ................................................. 13 FIGURE 5-2 MEASURED AND PREDICTED MH370 BFO VALUES (REVISED FIGURE 5-5 IN BU1) .......................................................... 13 FIGURE 7-1 BOEING 777-200ER RANGE CHART ........................................................................................................................ 15 FIGURE 8-1 AUSTRALIAN MARITIME SAFETY AUTHORITY SEARCH AREA MAP ................................................................................... 17


1 Introduction

This Addendum #3 to The Location of MH370 compares and contrasts the characteristics of MH370 routes proposed by the ATSB, the Independent Group (IG), and by Inmarsat with the route I have proposed.

Section 2 addresses the temporal variation of true air speed.

Section 3 addresses the potential presence of a "speed slope."

Section 4 addresses what the term "best-fit residuals" actually means.

Section 5 addresses the impacts of the recent revelations by Inmarsat regarding certain of the BFO data.

Section 6 assesses the likelihood that the route presented by Inmarsat is the correct MH370 route.

Section 7 assesses my proposed route in terms of the maximum aircraft range knowing the fuel on board early in the flight.

Section 8 compares the proposed end points with a map of the areas initially searched for debris.

References in this white paper to other publications are provided in Table 1-1.

Table 1-1 Reference List

Author(s) Reference # Title Date

ATSB1 MH370 - Definition of Underwater Search Areas June 26 - August 18, 2014

ATSB2 MH370 - Flight Path Analysis Update October 8, 2014

DCL1MH370 Data Communication Logs

(Released by Malaysia Department of Civil Aviation)May 27, 2014

IN1"The Search for MH370" by Ashton, Bruce, Colledge,

and DickinsonOctober 8, 2014

IG1 MH370 Search Area Recommendation September 9, 2014

IG2Further Progress Report from the Independent Group,

and Updated MH370 Search Area RecommendationSeptember 26, 2014

IG3 Analytic Fuel Flow Analysis September 26, 2014

IG4Discussion of the MH370 Path Analysis by Dr Bobby

Ulich by Duncan SteelOctober 1, 2014

IG5EXCEL File: MH370 Flight Path Model V11.3 495

knotsOctober 2, 2014

IG6 EXCEL File: Doppler_WGS84_v7-6-7 October 2, 2014

IG7 EXCEL File: Doppler_WGS84_v7-3-4_090614-187h October 2, 2014

BU1 The Location of MH370 September 25, 2014

BU2 Addendum #1 – Error Sensitivity Analysis September 28, 2014

BU3Addendum #2 – Comparison of MH370 Route

Synthesis Methods and ResultsOctober 5, 2014

BU4Addendum #3 – New Analyses of Proposed MH370

RoutesOctober 15, 2014

The Independent Group

Dr. Bobby Ulich

ATSB

Inmarsat


2 Temporal Variation in True Air Speed

The first item to be compared is the temporal variation in true air speed along the route after the radar track ends. Figure 2-1 plots the average leg speeds versus the time at the end of each leg along the MH370 route. In this figure the black curve is the speed profile from just after takeoff until the last radar contact at 18:22 (from Table 5-1 in BU1).

The upper green curve is my proposed Maimun Saleh Airport route. You can see how the speed is constant between 18:22 and 22:41. Indeed, this is my figure of merit in synthesizing the route (BU3). It turns out that the average speed also matches the radar track speed within 1 %, although the radar track speed was never used in my route synthesis. The error bars on the black portion of the route before 18:22 are approximate one sigma errors.

Figure 2-1 Comparison of True Air Speeds for Each Leg of Route

The next curve down (blue) is a nearly identical 192.4 degree great circle route (BU1) which passes within several miles of Maimun Saleh Airport. It also has very steady true air speed with an average speed of 499 knots, again in agreement with the radar track speed.

I would suggest that the speeds between the 6th and 7th handshake arcs, plotted in Figure 2-1 at 00:19, are not very reliable estimates. The reason for this is that I have assumed, for lack of any overriding metric, the aircraft was exactly on those rings at the handshake times. This is undoubtedly not likely to be the case. The reality is that 9M-MRO was close to the rings, but unless we make some assumption about speed, we cannot calculate exactly where. The length of that leg is quite short and uncertainty in the end points results in a significant uncertainty in calculated speed for that leg only. The speed estimate at 00:11 is probably fairly reliable since it has a long baseline. In this case, using the exact location of the aircraft at 00:11 does not change the calculated speed for that leg very much.


The final (red) curve in Figure 1-1 is the 187 degree great circle route I analyzed in BU1, ending at 88.5 degrees east longitude. This is the great circle ending very close to the 88.75 degrees east longitude proposed by the Independent Group (IG2). The ASTSB's latest report (ATSB2 Figure 4:A1) indicates that they consider this same route (theirs ending at ~88.5 degrees east longitude) to have the highest probability among the "constrained autopilot dynamics" group. The red curve represents the steadiest-speed solution for that 187 degree great circle initial bearing, and its characteristics fairly represent both the IG's and the ATSB's proposed routes(that also match the BTO data).

I will note here that the reason the IG and the ATSB "best" routes are essentially identical is because they have made equivalent assumptions to narrow down an infinite number of BTO/BFO solutions to a unique route (and not because they both necessarily have found the correct route). One assumption is necessary to get a single solution using their optimization functions (making BTO and BFO residual errors small). There are three equivalent assumptions for MH370 routes:

1. initial bearing after the turn, 2. southward turn time, or 3. average speed.

For the MH370 boundary conditions, you only need to assume one of these and the other two are then fixed. If one model assumes turn time, and another assumes a compatible average speed, the results are not really different. Knowing one of the three parameters, one can calculate the other two. So it really doesn't matter whether you pick an equivalent turn time or an average speed or a bearing, the resulting route will be the same.

In Figure 2-1 the speed profile of the IG/ATSB routes (in red) is, to put it mildly, highly variable. The average speed is (only) 473 knots. This doesn't match the radar track speed. The disagreement in the beginning of the fitted route after 18:22 is even worse, with a minimum of only 463 knots. To top it off, the speed must increase later in the flight up to ~485 knots. I am not aware of any speed control modes in a B777 aircraft that will automatically increase the speed by over 20 knots in a couple of hours.

The IG/ATSB route is not flyable on auto-pilot. It also doesn't match the radar track speed.

My proposed route does both.

3 Speed Slope Study

Michael Exner of the IG has suggested in a private communication that the true air speed might decay with time as fuel is burned off and the aircraft gets lighter. I did an analysis to see if this effect is present in any great circle route (including my proposed route). The results are shown in Figure 3-1 below.

First I modified my route fitter to best fit a "speed slope." That is, I assumed the speed changed linearly with time, rather than assuming a constant speed. I tried speed slopes between +5 and -5 knots per hour. This is the horizontal axis in Figure 3-1. The vertical axis is the standard deviation of the true air speed (again between 18:22 and 22:41). The blue curve is the result for 192 degrees initial bearing (my proposed route) with the condition that the aircraft is exactly on the handshake arcs. You can see the minimum is somewhere around -1 knot per hour. Next I applied a limit on the RMS radial errors of 0.67 NM (BU3). Now the speed errors (shown by the black curve) are much lower, even if you allow quite small BTO-

equivalent errors. This black curve is consistent with the BTO noise being quantization noise limited at 6

s RMS. The steadiest speed, with the smallest standard deviation of true air speed, occurs at zero slope. At the suggested slope of -2.7 knots per hour, the speed errors rise to ~1.7 knots RMS for the case of a fixed 192 degree initial bearing.


Figure 3-1 Speed Slope Study Results

Next, for each speed slope in Figure 3-1, I allowed the route fitter to find the initial bearing that best matched the assumed speed slope. This result is shown as the red curve in Figure 3-1. From -5 to +5 degrees per hour speed slope, the optimal initial bearings varied between 191.63 and 191.82 degrees, and the end-point longitudes varied by only 0.15 degrees.

Speed Slope Study Results 3.1

It is clear from Figure 3-1 that fitting a sloping speed produces the following results:

1. The best-fit slope is essentially zero knots per hour. 2. Between -5 and +5 knots per hour assumed speed slope, the same route is found very near 192

degrees (and with the same end point).

Speed Slope Study Conclusions 3.2

My conclusions are twofold:

1. Speed slopes of up to +/- 2 knots per hour will still provide 1 knot RMS standard deviation of true air speed and remain consistent with the satellite data.

2. Assuming any speed slope between -5 and +5 knots per hour does not noticeably shift the best-fit route away from my originally proposed route.


4 RMS Residual Errors of Best Fit

The ATSB, the IG, and Inmarsat believe that having BTO and/or BFO residuals (residual = predicted - measured value) smaller than the expected noise levels means that the route is more likely to be the correct one.

To quote the IG (in IG4): "The residuals (i.e. the differences between the measured BTO and BFO values and the corresponding values indicated by our model fit for each ping time) are minimized so as to derive the best-fit solution: that's what best-fit means! Those residuals are considerably smaller than those derived by Dr. Ulich for his assumed path, making the IG solution a better fit to the data, and therefore counting against his path."

To quote the ATSB (in ATSB2): "For the analysis using constrained autopilot dynamics, the top 100 paths were selected on the basis of the match with the satellite data and the consistency with the autopilot behavior." The ATSB goes on to say "For the data error optimization method, the paths were weighted according to the root-mean-square (RMS) error of the BFO values at each arc crossing. The best 100 paths were coloured by probability at 0011."

To quote Inmarsat: "Each route was analysed and the error between predicted and measured BFO

evaluated to identify the route with the best match." and "This route crossed the 19:41 arc at 0oN and travelled south at a constant ground speed of 450 knots, matching the BFO measurements within 2 Hz at each of the five signaling data points between 19:41 and 00:11 UTC . . . ."

In the quotations above, the boldface emphasis is mine. It is apparent that the IG, the ATSB, and Inmarsat all assume that data fits having smaller residual errors have a higher probability of being the correct route.

Are Smaller Residuals Better? 4.1

This assumption, made by all three groups, is false.

Their conclusions are incorrect and demonstrate a fundamental lack of understanding of how to optimally extract the maximum amount of information from noisy data. A "fit" to noisy data with zero residuals in the fit is, in fact, guaranteed not to match the actual solution. Having zero residuals means that you have contaminated the fitted (output) parameters completely with the maximum available input noise power. In other words, you are fitting too many variables with not enough data. To get zero residuals, in general you must fit the same number of variables as you have data points. If the data are noisy (as is the case of MH370 satellite data), they are mistaken in expecting the transfer of noise power in the inputs to errors in the fitted parameter values as being beneficial. It is not. The optimal information extraction fit leaves the same amount of noise power as residual errors on the outputs as is present in the noisy input data. That is what I have done in implementing my fitting method. My BFO residuals match the known BFO noise level (5 Hz RMS). All fits that show smaller RMS values of residuals, by fitting too many variables, will provide a larger number of output parameter values, but each output will be uncertain by a larger than optimal factor that depends on the total noise power in the input data.

How to Best Fit Noisy Data 4.2

The "best" fit to noisy data is one that leaves output residuals equal to the input noise.

If you begin with D noisy data points at the input of a route fitter, and you fit P independent parameter values, you are left with (D – P) degrees of freedom in the output residuals (=output noise). A good example of this is the formula for standard deviation. You sum the squares of the D residuals, then divide that sum by (D-P), and finally take the square root. This formula recognizes that you start with D degrees of freedom at the input of the process. At the output, after the fit, the number of degrees of freedom is now (D – P). If P is nearly equal to D, you will have small output residuals because you have transferred most of


the input noise in D to output noise in the P parameter values. So the more parameters you fit, the less certain each one becomes. For "exact" fits, P = D and you have zero residuals. You also have very noisy estimates of P parameter values. Ideally, you want D >> P. That is, you want to fit the smallest number of parameters P consistent with extracting the type of information you are looking for. You also want lots of data (large D).

Number of Independent MH370 Data Points 4.3

For MH370, the number of data points D is not very large. The first handshake data adds very little in terms finding a route because that point occurs so close in time and space to the last radar contact. In addition, there is a turn after the first handshake. So we really have only 6 handshakes to work with. The BFO doesn't tell us much except that a southward turn occurred at some time between 18:25 and 18:40. That only limits the end point location to latitudes between 33 and 41 degrees south. The BFO is incapable of discriminating small course changes. The signal-to-noise ratio of a single value is simply too low.

The BFOs are not independent measurements from the BTOs. They are correlated, because the aircraft is "on the arc" for both. The BTOs are more valuable than BFOs because they tell us absolute distance from the satellite. Ignoring the very small effect of altitude, the BTO depends only on two variables: aircraft latitude and longitude. The BFOs give us a relationship between the aircraft location and its ground speed and direction (ignoring rate of climb). The BFO depends on four variables: aircraft latitude, longitude, horizontal speed, and bearing. Thus the BFOs are correlated with, not independent of, the BTOs. This fact leads to several conclusions.

The first conclusion is that all route fits that weight BTO and BFO residuals equally are suboptimal. BTOs are absolutely necessary to get any answer. BFOs are optional. For instance, I found my route without using the BFO data at all (except to justify a left turn instead of a right turn). In addition, all of the routes proposed by the ATSB, the IG, Inmarsat, and me "match" the BFO data, even though the routes vary widely in direction and in their end-point locations. One must conclude from this that the BFO data are certainly not very discriminating when it comes to identifying the southward route.

It is also clear that we have an advantage in fitting MH370 satellite data that may not always exist: we have independent measurements of the noise levels for both parameters independent of our handshake data. That is a significant advantage, especially considering we have such a small data set, because we now have the opportunity to compare our output residuals with the independent estimate of input noise (the separate measurements of BTO and BFO single-read noise before takeoff). Therefore, the optimal route fit will leave BTO and BFO residuals equal to the independently measured RMS noise values. If our fit has larger RMS residuals, we have fit too few parameters, and systematic errors remain. If our residuals are too small, we have fit too many variables, and each of them is a noisy estimate. With the optimal fit, the route is best determined and the output residuals equal the independently measured noise values.

Many MH370 route fits (by the IG, the ATSB, and Inmarsat ) produce small or zero residuals. This is not a good thing. It is not optimal.

No route with zero residuals in either BTO or BFO can be the correct route, and the correct route will have BTO and BFO residuals equal to their expected noise levels.

The error made by the ATSB, the IG, and Inmarsat is the assumption that having "best-fit" residuals smaller than the expected noise provides a higher probability of finding the correct route. This assumption is not correct, and it is a fundamental flaw in their route selection processes.

The reason for this is that these groups are fitting too many parameters with too little data. Most of the ATSB's routes, some of the IG's routes, and the Inmarsat route are not even consistent with any LNAV mode. These particular routes allow the bearing to vary independently from leg to leg over several degrees. The LNAV auto-pilot would in fact maintain a precise course that would not waver or drift. Yet


these groups all appear to be working under the assumption that after the southward turn the course was flown by auto-pilot.

Number of Variables 4.4

Auto-piloted navigation is a very useful condition that greatly simplifies our problem and reduces the number of variables needed to define a route. For instance, I need to solve for only four parameters to define the path flown by MH370 (the latitude, longitude, time, and initial bearing at the end of the southward turn). The only remaining task is to decide where the aircraft was at each of the remaining handshake times along the determined path. We have 6 handshake arcs to reach, so we have six range variables plus the four initial conditions. That gives a total of 10 variables that completely define the southern route. We have 6 BTOs, so that is not enough, by itself, to solve for 10 variables. We also have at least 6 BFOs, but they are not independent of the BTOs, so that is not enough data either. We still need at least one assumption to get a unique route solution. That assumption could be average speed (coupled with the radar track position and bearing). It could also be turn time or initial bearing out of the turn. My assumptions are the last radar time, latitude, longitude, and bearing and that I expect the speed to be steady.

It seems that everyone has to make at least one assumption that constrains all the legs. Then a single solution becomes possible.

Example of Best Fit 4.5

To demonstrate the truth of my statements above regarding the optimal fit to noisy data, I have prepared a demonstration of the errors in fitting too many parameters to noisy data. Here is the experiment. I start with 7 noisy data points representing a trajectory. These are shown in Figure 4-1. The horizontal axis is X . The vertical axis is Y. Each sample of Y data (the black dots) is the sum of a simple polynomial with 3 parameters:

Ytruth = 9.5 – 2 . X + 0.2 . X2

and (Gaussian) random read noise with a mean of zero and a standard deviation of 1.

The red curve in Figure 4-1 is the "truth" equation given above. The 7 noisy data points are the black dots, and they fall above and below the red "truth" line.

The purpose of fitting a model to the noisy data is to discover, as accurately as the data noise permits, the "truth." That is, we want to fit a model which most closely matches the red "truth" curve.

To accomplish this, we fit, by minimizing the sum of the squares of the residuals, the coefficients of a polynomial model equation:

YP =i=1i=P

Ci . X

i-1

In words, we sum terms given by a coefficient vector (to be determined by the fit) times the input data

vector (X) raised to the (i-1)st power. In this equation, P is the number of parameters (the coefficients Ci)

to be fitted.


Figure 4-1 Polynomial Fits to 7 Noisy Data Points

The purpose of fitting a model to the noisy data is to discover, as accurately as the data noise permits, the "truth." That is, we want to fit a model which most closely matches the red "truth" curve. In other words, the "truth" is the signal we want to extract from the noisy data.

To accomplish this, we fit (by minimizing the sum of the squares of the residuals) the coefficients of a polynomial model equation:

YP =i=1i=P

Ci . X

i-1

In words, we sum terms given by a coefficient vector (to be determined by the fit) times the input data

vector (X) raised to the (i-1)st power. In this equation, P is the number of parameters (the coefficients Ci)

to be fitted.

For P = 1, we only have one parameter to fit:

Y1 = C1

For P = 2, we fit

Y2 = C1 + C2 . X

For P = 3, we fit

Y3 = C1 + C2 . X + C3

. X2

and so on until we reach P = 7.


I have done these seven fits to these seven data points. The residuals of these fits are shown in Figure 4-2, and they demonstrate my point.

Figure 4-2 RMS Residuals Versus Number of Fitted Parameters

The black curve in Figure 4-2 is the RMS residuals of the fit to the noisy data (shown in the vertical axis) as a function of the number of fitted parameters P (the horizontal axis). In order to provide a general result, I have plotted the RMS values normalized to the known standard deviation of the noise, which in this example was simply 1. Starting at the upper left, you can see from the black curve that the fitted residuals

with P = 1 (just one constant value) are larger than unity (1.4). That immediately tells us that higher order terms are needed to produce smaller residuals. Referring back to the first plot, Figure 4-1 above, we see the green dashed horizontal line that is the P = 1 fit, and it does not match the red "truth" curve.

Moving down the black curve in Figure 4-2, we see that it crosses the horizontal black dashed line. This dashed line is where the fitted residuals equal the data noise. We also see that the nearest value of P to that intersection point is P = 3. That tells us we need 3 parameters to extract all the useful information in this data set. Again, referring back to Figure 4-1 above, we see that the P = 3 fit, shown by the black dashed curve, matches the red "truth" curve rather well, confirming that higher order terms (P larger than 3) are not needed in the fit (and, as we shall see shortly, are actually deleterious).

Continuing down the solid black line in Figure 4-2 all the way to P = 7, we see that the fitted residuals, with respect to the noisy data set, become zero. This is because we have fit 7 parameters to 7 data points, and we have exactly zero residuals remaining. This 7-parameter fit is shown as the blue dashed curve in Figure 4-1. Note how it matches all the data points exactly.

The last step in my demonstration is to plot the residuals between the fitted curves and the "truth" curve. These residuals are shown in Figure 4-2 as the red solid curve. Making these as small as possible is the goal, since we desire our "best" fit to match the "truth" curve as closely as possible given the noise in the data. Thus we seek the minimum value in the red curve, which signifies the "best fit" to the "truth." We see in Figure 4-2 that this minimum occurs at P = 3, and that should be no surprise to us since the "truth" curve


has three coefficients. Note that we get poorer information extraction on both sides of P = 3. Smaller P than 3 is incapable of matching the "truth" because there are not enough parameters used in the fit. Larger P than 3 is also worse because we are determining a larger number of coefficients, but their values are contaminated with more noise than is the optimal P = 3 fit.

Conclusions 4.6

The takeaways from Figure 4-2 are the following:

3. Fitting too many parameters (P too large) produces smaller residuals with respect to the data but larger residuals with respect to the "truth."

4. Fitting too few parameters (P too small) produces larger residuals with respect to the data and also larger residuals with respect to the "truth."

5. The optimal (best) fit best matches the fitted curve to the "truth" curve which is "disguised" by the noise.

6. The optimal (best) fit leaves residuals equal to the noise level of the input data.

Generating route fits to BTO/BFO data with residuals smaller than the expected noise levels, which is viewed by the ATSB, the IG, and Inmarsat as indicating a higher probability of being correct, is not the best extraction of information. Having small residuals means that, while you have extracted all the information, it appears in the outputs with additional noise superimposed on the parameter values, and this results in a lower probability of being correct. My route fitting method extracts all the information but does not add unnecessary noise power to it, leaving the residual fitting noise equal to the expected BTO/BFO noise.

5 BFO Data Modifications and Deletions

Inmarsat's paper on October 8, 2014 (IN1) revealed that the BFO data between 18:25:27 and 18:39:55 and at 00:19:37 may not be valid. I have therefore removed these values from comparison with my BFO model. In addition, very small changes were made to the "Satellite and AFC Effect" values (see Table 1 in ATSB2).

There are several implications of Inmarsat's conclusion:

(1) the complex maneuvers (multiple turns or a climb) near the southward turn that the IG and I created to fit the BFO data at that time are no longer required, (2) the BFO data cannot precisely determine the turn time, except that it occurred at some time between 18:25 and 18:40, (3) the very high apparent descent rate at 00:19:37 may be unreliable, and (3) the high descent rate at 00:19:29 is reliable.

Figure 5-1 shows the revised BFO data and my model prediction (now just a simple turn and no climb) for the time near the final turn.

One can see in the figure that the remaining, trustworthy BFO data define a window for the turn, but that window is 15 minutes wide. There is no apparent possibility of obtaining a more precise turn time estimate from the BFO data. My predicted and the measured BFO values are in agreement.


Figure 5-1 Measured and Predicted BFO Values at Final Turn (Revised Figure 5-9 in BU1)

Figure 5-2 shows an updated Figure 5-5 from BU1 with the untrustworthy data removed. This is the measured and predicted BFO for the entire flight. The BFO Bias required to make the mean error at the 12 epochs where we have measured BFO data (between 16:10 and 00:19) is 148.2 Hz. The BFO match is excellent, and the RMS residual value is 5.3 +/- 1.6 Hz (which is consistent with the 5 Hz RMS noise figure provided by the ATSB (ATSB1).

Figure 5-2 Measured and Predicted MH370 BFO Values (Revised Figure 5-5 in BU1)


The BFO data is not very restrictive for selecting MH370 routes. Even including the restriction on turn time to occur between 18:25 and 18:40, the range of allowed end-point latitudes is quite large – from 33 S to at least 41 S.

6 Assessment of Inmarsat Route

Table 9 in Inmarsat's recent paper (IN1) contains their example route information. This route turns as late as possible consistent with the 18:40 BFO data. The average true air speed is about 440 knots, which is 60 knots below the radar track speed. It is impossible to independently evaluate the BTO errors, because the aircraft positions are only listed with 0.1 degree resolution in Inmarsat's table. It is possible to evaluate the True Track errors. Their Table 9 shows the bearing varying from 179 to 186 degrees after the turn. This is not flyable with the True Track LNAV mode. One should see very small fractions of 1 degree track variations along the route. It appears that the bearing has been allowed to vary for each leg so that a constant speed is obtained.

The Inmarsat route has two shortcomings:

1. It is not consistent with True Track auto-piloted flight after the turn because the bearing variations between handshakes are more than an order of magnitude too large.

2. Its speed is 60 knots slower than the radar track speed.

I therefore conclude that the Inmarsat route is very unlikely to be the correct MH370 route.

7 Assessment of Aircraft Range for My proposed Route

One test of a proposed route is to determine if it is reachable using the known quantity of fuel on board 9M-MRO on this particular flight. In this section I calculate the aircraft range using Boeing data for the 777-200ER aircraft and compare that to the distance traveled along my proposed MH370 route.

9M-MRO Fuel Data 7.1

Here is what we know:

1. The MH370 aircraft dry weight was 174,000 kg (zero fuel weight). 2. At 16:41 brake release at takeoff, the fuel on board was 49,200 kg, and the gross takeoff weight

was 223,200 kg. 3. At 17:07 (i.e., the last ACARS data) the remaining fuel on board was 43,800 kg (ATSB2), and the

gross weight was 217,800 kg.

Route Information 7.2

From 16:41 to 17:07 the aircraft consumed 5,400 kg of fuel in 26 minutes of takeoff roll and climb to FL350. The average fuel burn during this period was 12,500 kg/hr.

From 16:41 (takeoff) to 00:16 (fuel exhaustion), my proposed MH370 route includes approximately 3,709 ground nautical miles and 3,738 air nautical miles (= ESAD = Equivalent Still Air Distance). The ESAD is greater than the ground miles covered because of net headwind conditions.


From 17:07 (last ACARS data) to 00:16 (second engine flameout), my proposed MH370 route includes approximately 3,541 ground miles at an average ground speed of 495 knots. During this same period, MH370 flew 3,591 air miles (Equivalent Still Air Distance) at an average true air speed of 499 knots.

Fuel Burn Analysis 7.3

Based on my proposed route, the average fuel burn rate from 17:07 to 00:16 would have been 6.13 metric tons per hour. Based on the information currently available, it appears MH370 maintained a high altitude

during this period ( FL350) and a high air speed (at least Mach 0.84).

We have to be careful in using standard aircraft range tables to figure fuel burn because they typically include fuel reserves for headwinds, a go-around, change to alternate airfield, and low-altitude holding

pattern. The extra fuel for additional landing maneuvers adds 25,000 pounds (11,340 kg) to the dry weight (zero fuel weight) of the aircraft. This extra fuel weight is carried for the entire trip through landing, increasing the fuel burn rate. In addition, the range tables include a 10% fuel reserve, to allow for headwind conditions and engine performance degradation (=Performance Degradation Allowance, or PDA).

Figure 7-1 provides fuel burn rate information for an aircraft of the same type as 9M-MRO: a Boeing 777-200ER aircraft with Rolls Royce Trent engines.

Figure 7-1 Boeing 777-200ER Range Chart

We start by selecting 174,000 -11,340 = 162,660 kg effective zero fuel weight on the Y-axis (remember the chart assumes you land with 11,340 kg of fuel remaining; see the last note at the bottom of the chart).


Selecting the ESAD for my proposed route of 3,738 NM on the horizontal axis, we find the intersection occurs right on the contour for 217,700 kg gross weight at brake release. Subtracting the 162,660 kg effective dry weight, we find the takeoff fuel load needed to fly my route is 217,700 – 162,660 = 55,040 kg. This has a 10% trip contingency factor built in, so the actual amount of fuel needed is 90% of 55,040 = 49,540 kg.

The uncertainty in reading the graph is about 2%, plus the engine performance factors (=Performance Degradation Allowances) should be included. The chart also assumes a step climb to maintain optimal efficiency (but does not provide any information with which to estimate the degradation of non-optimal altitudes).

The PDAs for the 9M-MRO engines are known but have not been publicly released.

We next need to estimate the uncertainty in this fuel/ESAD calculation. Readings on the range graph are probably uncertain to +/- 2%. The PDA's are also uncertain, and affect the fuel requirement by approximately +3% to -0%. Adding these errors leads to an estimated uncertainty of +5% and -2%. Thus the fuel required to fly my proposed MH370 route is estimated to be 49,500 +2,500 and -1000 kg, or from a minimum of 48,500 kg to a maximum of 52,000 kg. The actual range could be even larger depending on the altitude effect previously mentioned.

The fuel consumed was in fact 49,200 kg, which is consistent with the estimated requirement of 48,500-52,000 kg. This estimate of the fuel requirement for my proposed route is about 1 % more than the

available fuel, and it would match it with 1% average engine PDAs. In any case, even with known PDA's,

the uncertainties in such range versus fuel calculations are probably not much better than 2-3%.

I therefore conclude my proposed end point is in fact reachable (within the uncertainties of such calculations) using the Boeing range information for this type aircraft.


8 Debris Search

Figure 8-1 is a map of the areas initially searched for floating debris in the aftermath of the incident (using manned aircraft). The locations of the IG's and my predicted positions are also marked. You can see that the IG (and the ATSB's) most–likely position was initially searched. My proposed location was not searched. Perhaps that is why no floating debris was found.

Figure 8-1 Australian Maritime Safety Authority Search Area Map

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