### MH370 Models

##### Main MH370 Flight Path Simulation Model

The latest version of the Doppler WGS84 model can be downloaded from: http://www.aqqa.org/MH370/models/BSMv7-9-4.xlsx

Updated 3rd March 2014.

##### Ping Ring Model

The ping ring model uses an explicit solution for the longitude of a position on a ping ring, given an input latitude, aeroplane ellipsoidal height, satellite position, BTO observation and BTO bias constant.

Version 3-7 is available from: http://www.aqqa.org/MH370/models/aqqa_pingv3.7.xlsx

You may wish to use our most recent BTO constant of -495679 microseconds (26th October 2014). See report below.

##### BFO Azimuth Model

The BFOs can be solved explicitly for azimuth values. There are in general either no solutions, a repeated solution or two unique solutions in azimuth for a given BFO, satellite position and velocity, and aircraft position and speed. The phase shift between each azimuth solution depends only on the aeroplane latitude. The majority of BFO observations occurring in the endgame period, 1828z onwards, coincide with a BTO observation. By examining only BFOs for which a BTO is also available it is possible to determine the aeroplane longitude given its latitude and height above the WGS84 ellipsoid. This model presents two R2 azimuth solution arrays for variable aeroplane speed and latitude, given a user-selected observation.

Version 3-5 is available from: http://www.aqqa.org/MH370/models/aqqaBFOazimuth_v3-5.xlsx

You may wish to use our most recent BTO constant of -495679 microseconds (26th October 2014) and BFO fixed frequency bias of 150.28 Hz, standard deviation 0.86 Hz), for R-channel CU 4 observations (12th December 2014). See reports below.

At the top of the *AzimuthSolutions* sheet are three cells in green intended for user input, as is the convention in all aqqa models. The first cell labelled OBS# which must be an integer [1 to 14] selects an observation from the *Observations* sheet. The observation time is shown for information in hh:mm:ss format in the cyan highlighted cell followed by the associated BFO, BFO components, BTO and the aircraft-satellite range corresponding to the BTO. The adjacent user input cell labelled altitude is interpreted as a height above the WGS 84 ellipsoid in metres. The arrays of azimuth solutions use a varying latitude down the rows and a varying ground speed across the columns. The step-size for latitude variation between rows, and for ground speed variation between columns, is controlled by the user inputs under the *array step sizes* label. Ground speeds are in knots (KTGS) while latitudes are in degrees. Azimuth solutions are presented in degrees east of true north.

Part of the first azimuth solution array is shown in the picture above. The ground speed associated with each column is presented for information in the first row bordering the array. The first entry in this border, highlighted in green, is a user-editable cell that controls the lower bound on ground speed. Likewise, the column adjacent to the array labelled *LAT* shows the latitude associated with each row. The first entry highlighted in green is user-editable. To the left of the latitude bordering column is a longitude (east) output shown for information. Each longitude, found using the analytic BTO ring function, for any given observation depends only on the aeroplane altitude (ellipsoidal height) and latitude.

A second solution array is presented in the same sheet below the first. This model uses the ATSB position vectors provided for integer multiples of five minutes, without correction, for each observation.

If an element within the array shows “*NoSolution*” then no azimuth solution exists for the associated inputs. This will often be the case when the latitude range is inappropriate for the observation under examination.

*Updated 28th Oct. 2014: version 3.5 now allows a rate of climb to be set.*

##### Radiosondes

Three radiosondes are available for 1200Z March 7th and 0000Z March 8th, 2014, for Kota Bharu (WMKC), Penang (WMKP) and Medan (WIMM), from the University of Wyoming online archive:

WMKC (station 48615): 12Z, 00Z

WMKP (station 48601): 12Z, 00Z

WIMM (station 96035): 12Z, 00Z

These 6 radiosondes have been incorporated into an Excel model available from: http://www.aqqa.org/MH370/models/aqqaRadiosondes02.xlsx

The radiosondes are required to determine the mapping between flight level and geopotential altitude during the early flight phase during which the ADS-B log records point-observations of the flight level. The transformation of flight level to geopotential altitude is necessary for a more accurate estimation of the early phase climb rates which act as explanatory variables in the BFO equation.

For example, a linear model for the geopotential altitude as a function of the flight level gives a coefficient of 106.2 ft per flight level. This is 6.2% larger than the mapping that would exist in a standard atmosphere, and consequently the rate of climb derived from the ADS-B log entries must be increased by this factor to transform them from rates of change of flight level to rates of change of geopotential altitude. The difference between a geopotential and geometric altitude is negligible and may be ignored.

##### Digitisation of Inmarsat graphs

Digitisations of several graphs in the Inmarsat paper are available.

Pilot Frequency Error – Figure 11

Satellite Related Frequency Variation – Figure 12 (data supplied by Sid Bennett)

BFO Validation (Amsterdam flight) – Figure 15 (document supplied by Assoc. Prof. Yap F. Fah, NTU, Singapore)

### REPORTS

Moved here.