Method of calculating MH370's distance from satellite

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This is the basis for the preliminary analysis I am currently doing:

"Slant Range to target is measured by round trip delay in the received echo. It is the speed of light multiplied by the time delay and divided by two to account for the round trip." (Source)

Rp = Slant Range, Satellite to MH370
Dp = Distance, Satellite to MH370
Hp = Height, Satellite to MH370
Ep = Elevation Angle, MH370 to Satellite

Rg = Slant Range, Satellite to GES
Dg = Distance, Satellite to GES
Hg = Height, Satellite to GES
Eg = Elevation Angle, GES to Satellite

Hs = Height, Satellite to ground

T = (2 x (Rp + Rg) ) / c
T = round trip time of messages
c = speed of light

Rg = sqrt( (Dg x Dg) + (Hg x Hg) )

Rp = ((T x c) / 2) - Rg

Dp = sqrt( (Rp x Rp) - (Hp x Hp) )

Notes:

Drawing Not To Scale

Hp unknown, test for Satellite Height (Hs) minus MH370 Height (0 to 45000 feet)

delta times calculated from Inmarsat MH370 log file will include various overhead times that need to be determined and subtracted out, when computing Rp

Revision 1: Updated diagram on June 02, 2014. Updated blog post on June 03, 2014.

Diagram posted on May 30, 2014:

MH370's estimated maximum range, based on UAE343, with Inmarsat Arcs added

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I updated my MH370's estimated maximum range, based on UAE343 image, by adding the Inmarsat Arcs that were shown on a Malaysian Government image dated 17/03/2014. (I don't have the link for it.)

I'm still analyzing the Inmarsat MH370 Data Communication Logs (PDF), but I don't have anything ready to post yet.

In case you hadn't heard, today they said none of the underwater pings that they had detected were from MH370's black boxes. That came as no surprise to me, considering the fact that the signals they detected were outside of the black box tolerance specifications.

Inmarsat Data Plot with Estimated Burst Frequency Offset (Hz) values added

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I added estimated Burst Frequency Offset (Hz) values to Inmarsat's "MH370 measured data against predicted tracks" plot.

Various news organizations are quoting Acting Transport Minister Datuk Seri Hishammuddin Hussein as saying that the raw data from Inmarsat will be released on Tuesday, May 27: "This is what I have been told and that it will be released tomorrow."

My Estimated Burst Frequency Offset (Hz) values

Data   UTC    Hz
Point  Time   Offset
1      16:30   88.54
2      16:40  125.00
3      16:56  158.33
4      17:07  132.29
5      18:23  272.92
6      18:25  175.00
7      18:27  142.71
8      19:40  112.50
9      20:40  140.63
10     21:40  167.71
11     22:40  203.13
12     00:11  252.08

    Time margin of error: +/- 2 min
    Hz margin of error +/- 2.08 Hz

Notes:

1) In a previous post with time stamps added, I showed the xx:40 times as xx:41 because of MH370's take off time of 16:41:43. However, due to the granularity of the tool I'm using to estimate the values on the Inmarsat Data Plot, I am showing the times as xx:40 in this post. There is a margin of error of + or - 2 minutes for all of my time estimates.
2) There is a margin of error of + or - 2.08 Hz for all of my offset estimates.
3) I have seen various news reports about the total number of measured Inmarsat data points and the number of measured data points received after the ACARS was disabled. The plot released by Inmarsat shows a total of 12 measured data points from 16:30 UTC to 00:11 UTC.

MH370's estimated maximum range, based on UAE343

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At 18:22 UTC, UAE343 was flying at 34,000 feet in close proximity to where they identified MH370 as being at that same time (Last Air Defense Radar Point on their Preliminary Report map).

Based on that fact, I created a circle, with an origin at KUL,  to show the estimated maximum straight line range that MH370 could have traveled shortly before the last satellite communication at 00:19 UTC.

Reference points at 00:13 UTC:
A) UAE343, DXB
B) AXM5878, KUL
C) CCA1877, PEK
D) Inmarsat-3 F1 Satellite

Notes:
DXB is Dubai International Airport in Dubai, United Arab Emirates
KUL is Kuala Lumpur International Airport in Sepang (near Kuala Lumpur), Malaysia
PEK is Beijing Capital International Airport in Beijing, People's Republic of China

Inmarsat-3 F1 Satellite is located at 0N 64.5E 35,800 km above sea level. It is a geostationary satellite, but it wobbles up and down over the equator, in a figure-8 pattern.

I captured the screen shot using FlightRadar24 and filtered on Callsigns UAE343, AXM5878, and CCA1877.

Airplane Traffic at 18:22 UTC (Last Air Defense Radar Point of MH370)

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I captured a screen shot of all of the airplane traffic at 18:22 UTC on FlightRadar24, and used the Preliminary Report Map Showing MH370’s Flight Path to add the flight path and approximate locations for MH370 at18:01:49 UTC and 18:22 UTC.

I also added certain waypoints and airplane call signs, as well as MH370's last approximate transponder location at 17:22 UTC.

At 18:22 UTC, UAE343 was flying at 34,000 feet in close proximity to where they identified MH370 as being at that same time.

Timeline of events, by the hour (Revision 2)

16:30    UTC Inmarsat plot satellite data (estimated time) [1]
16:41:43 UTC MH370 takes off [2] / Inmarsat plot satellite data

17:01:16 UTC MH370 reported maintaining FL 350
17:07:29 UTC last ACARS message (page 4) / Inmarsat plot satellite data
17:07:49 UTC last ACARS communication (page 3)
17:07:55 UTC MH370 reported maintaining FL 350
17:11    UTC 30 minute interval / No data point on plot
17:19:24 UTC KLATCC instructed MH370 to contact HO CHI MINH Air Traffic Control Centre (HCMATCC) on radio frequency 120.9 MHz. MH 370 acknowledged with "good night Malaysian Three Seven Zero". (pilot OR co-pilot says "good night Malaysian Three Seven Zero")
17:21    UTC transponder message (35000 feet 471 kts 6.97N 103.63E) [3]
17:21:04 UTC radar screen at KLATCC observed MH370 passing over waypoint IGARI
17:21:13 UTC radar label for MH370 disappeared from radar screen at KLATCC
17:2x:xx UTC HCMATCC radar contact was established over IGARI but there was no verbal contact
17:22?   UTC last transponder message HCMATCC observed radar blip disappeared at waypoint BITOD [2],[4]
17:28    UTC Thai radar detects "unknown aircraft" "in the South China Sea, moving southwest towards Kuala Lumpur and the Strait of Malacca" [5]
17:30    UTC True/False? Pilot bound for Narita, Japan (MH88/MAS88?) asked by Vietnamese ATC to attempt to contact MH370 gets "mumbling/static" reply from MH370, but no Mayday [6]
17:38    UTC HCMATCC made a query to KLATCC on whereabouts of MH370
17:41    UTC No data point on plot
17:57:02 HCM informed KL-ATCC that there was officially no contact with MH370 until this time. Attempts on many frequencies and aircraft in the vicinity received no response from MH370. (True/False? Were MH88/MAS88 and/or JL750/JAL750 asked by HCMATCC to attempt to contact MH370?)

18:11    UTC 30 minute interval / No data point on plot
18:22    UTC last Malaysian military radar signal of "unknown aircraft" 200 miles northwest of Penang at 29,500 feet
18:23    UTC Inmarsat plot satellite data (estimated time)
18:25    UTC Inmarsat plot satellite data (estimated time)
18:27    UTC Inmarsat plot satellite data (estimated time)
18:40    UTC later denied: Malaysian General Rodzali Daud says "unknown aircraft" detected near Pulau Perak at 29,500 feet [7],[8]
18:41    UTC No data point on plot

19:11    UTC 30 minute interval / No data point on plot
19:41    UTC Inmarsat plot satellite data

20:11    UTC 30 minute interval / No data point on plot
20:41    UTC Inmarsat plot satellite data

21:11    UTC 30 minute interval / No data point on plot
21:30    UTC Kuala Lumpur Rescue Coordination Centre activated
21:41    UTC Inmarsat plot satellite data

22:11    UTC 30 minute interval / No data point on plot
22:41    UTC Inmarsat plot satellite data

23:11    UTC 30 minute interval / No data point on plot
23:41    UTC No data point on plot

00:11    UTC Inmarsat plot satellite data (last complete message)
00:19    UTC last message received by satellite ground station (initiated by plane?)
00:41    UTC No data point on plot (plane no longer transmitting)


References:

[1] http://mh370research.blogspot.com/2014/05/inmarsat-data-plot-with-time-stamps.html
[2] http://www.avherald.com/h?article=4710c69b/028
[3] http://www.flightradar24.com/data/flights/mh370/#2d81a27
[4] https://www.facebook.com/media/set/?set=a.10152221414824355.1073741996.72613804354
[5] http://manilastandardtoday.com/2014/03/20/thai-reports-unknown-plane-blipped-its-radar/
[6] http://www.nst.com.my/nation/general/font-color-red-missing-mh370-font-pilot-i-established-contact-with-plane-1.503464
[7] http://www.reuters.com/article/2014/03/11/malaysia-airlines-military-idUSL3N0M835C20140311
[8] http://stream.wsj.com/story/malaysia-airlines-flight-370/SS-2-475558/SS-2-478603/


Notes:
Inmarsat plot satellite data times are estimated from their plot (see Reference [1]).

Every 1 hour interval at xx:41 is based on MH370 takeoff time and "ping handshake" being every hour. It corresponds to data point times shown on the Inmarsat plot

Every 30 minute interval at xx:11 (and xx:41) is based on Rolls Royce engines sending data every 30 minutes. It corresponds to the 00:11 data point time shown on the Inmarsat plot


MH370 playback data:

http://www.flightradar24.com/2014-03-07/16:30/12x/22.23,61.87/6

(I accidentally deleted the original Timeline post, which used to be here: http://mh370research.blogspot.com/2014/05/timeline-of-events-by-hour.html)

ACARS disabled at 1:07 am MYT (17:07 UTC)

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Based on official statements, and statements made by "unnamed U.S. officials," I believe MH370's Aircraft Communications Addressing and Reporting System (ACARS) was disabled at 1:07 am MYT (17:07 UTC).

March 13: ABC News [1]

"Two U.S. officials tell ABC News" The data reporting system, they believe, was shut down at 1:07 a.m. The transponder -- which transmits location and altitude -- shut down at 1:21 a.m.

March 15: Malaysian PM Najib Razak [2]

Based on new satellite information, we can say with a high degree of certainty that the Aircraft Communications Addressing and Reporting System (ACARS) was disabled just before the aircraft reached the East coast of peninsular Malaysia. Shortly afterwards, near the border between Malaysian and Vietnamese air traffic control, the aircraft’s transponder was switched off.

Preliminary Report [3]

17:01:16 UTC MH370 reported maintaining FL 350
17:07:29 UTC last ACARS message (page 4) / Inmarsat plot satellite data
17:07:49 UTC last ACARS communication (page 3)
17:07:55 UTC MH370 reported maintaining FL 350


Note: The screen shot was captured at FlightRadar24.


1. http://abcnews.go.com/International/malaysia-airliner-pinging-indication-crashed-indian-ocean/story?id=22894802
2. http://www.theguardian.com/world/2014/mar/15/malaysian-pms-full-statement
3. https://www.facebook.com/media/set/?set=a.10152221402889355.1073741995.72613804354

Pulau Perak sighting at 2:40am

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On Mar 11, 2014, Malaysian General Rodzali Daud was quoted as saying that at 18:40 UTC (2:40am) an "unknown aircraft" was detected near Pulau Perak, flying at 29,500 feet. He subsequently denied saying that.

At 18:33 UTC, KLM836, another 777, passed very close to Pulau Perak, flying at 30,000 feet.

Information about airplanes in that vicinity at 18:33 UTC:

KLM836 777-206(ER) 30,000 ft
UAE405 777-36N(ER) 33,300 ft
UAE343 777-36H(ER) 34,000 ft

One article about Daud's statements can be read on Reuters.

The screen shot was captured at FlightRadar24.

MH370 and UAE343 at 18:22 UTC

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I used the Preliminary Report Map Showing MH370’s Flight Path and overlaid a screen capture of UAE343's position at 18:22 UTC with it, to show that MH370 and UAE343 were in close proximity of each other when the last military radar sighting of MH370 was made. (Note: the maps didn't overlay exactly, so UAE343's position is approximate.)

In the Inmarsat plot I created, I estimated the 3 measured Inmarsat data points on their plot to be at ~18:23, ~18:25, and ~18:27. (There has been no official explanation for where those measured data points came from, nor what they are.)

My current thoughts about the explanation for those data points is that MH370 had to adjust its speed (slow down or speed up), to line up with UAE343, so it could shadow it, then flew at the same speed as UAE343. Because of the speed adjustments, the Rolls Royce engines sent data values during that time. The investigators have denied that the Rolls Royce engines sent any data, but I think the Inmarsat plot proves otherwise.

(Note: The shadow theory mentions SIA68, but I believe if MH370 shadowed another plane, it was UAE343.)

Inmarsat Data Plot with Time Stamps added

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I added time stamps to Inmarsat's "MH370 measured data against predicted tracks" plot.

The investigators claimed the only data they received from MH370, after it vanished, were hourly pings. Yet as can be seen on the Inmarsat plot, there were 3 measured data points in quick succession just before 18:30 UTC. There is also a 1.5 hour gap of time between the last (00:11 UTC) and second to last ping (22:41 UTC), which is coincident with Rolls Royce (RR) engine data being sent every 30 minutes.

Another discrepancy that has been pointed out by scientific experts is that every (Doppler Shift) Burst Frequency Offset value is positive. The Burst Frequency Offset is the Expected Frequency minus the Actual Frequency. The value will be positive if the object is moving away from the observer, and negative if the object is moving toward the observer.

We know at the beginning of MH370's flight, it was moving away from the Inmarsat satellite, and those values are positive on their plot. Yet when the plane allegedly turned back and headed West, it should've been traveling toward the satellite, yet those values are also positive. A less positive number only means the plane wasn't traveling as fast away from the satellite; it does not mean it was traveling toward the satellite.

The original Inmarsat plot can be seen here.

MH370 Preliminary Report Discrepancies

The MH370 Preliminary Report has two mistakes in it, yet I haven't seen any news organization mention them, nor question the investigators about them:

Mistake #1:  They state two different times for the last ACARS message.

01:07:29 MYT last ACARS message (page 4)
01:07:49 MYT last ACARS communication (page 3)

If there truly were two different events that occurred, they should make that clear. Otherwise, if one of those times is a "typo" one has to question their failure to have anyone proofread this important report.

Mistake #2: They state the first ACARS/satellite communication occurred prior to MH370 taking off, while it was still on the ground, yet the time they say it occurred is after MH370 took off.

00:41:43 MYT MH370 took off (page 2)
12:56:08 MYT first ACARS/satellite communication (page 3)

12:56:08am is the same as 00:56:08, which is after the plane took off, and therefore incorrect. We know from the Inmarsat plot that the first communication was around 12:30am MYT.

(Note: Links to the report are on the side of this blog.)

MH370

MH370 "vanished" 10 weeks ago today, after taking off on March 07, 2014, from Kuala Lumpur, Malaysia, heading to Beijing, China.

Myself and others have questions that aren't being answered by the investigators. Other than CNN, I don't see any news organizations asking questions.

I decided to create this blog, to post facts and links from reliable sources, as well as to post some of my own research based on facts that are in the public domain.