Possible Flight Paths for MH370 from Inmarsat Data Not Supported by Scientific Calculations

Possible Flight Paths for MH370 from Inmarsat Data Not Supported by Scientific Calculations

Dr. Marvin Vestal CEO of SimulTOF Systems Sudbury, MA, has developed and applied methods for calculating the time shifts and Doppler Shifts for various possible flight paths of missing airliner MH370.  The distance determination depends on precise determination of the delay time between transmission and reception of radio transmissions and the direction determination is from Doppler shift of the frequency of the transmissions.   These calculations are compared to data produced from detection of hourly pings from the airplane by the satellite provider Inmarsat.  Results show conclusively that Inmarsat has misinterpreted these data to conclude that the plane flew south into the Indian Ocean.  Objective analysis of the Inmarsat data shows that the noise on the Doppler data is at least 20 times larger than the maximum signal consistent with a change in direction and the noise is 100 times larger than the signals that could provide definitive data on the flight path.   The massive search for the plane in the Indian Ocean continues even though there is no credible data that indicates that if will be found in the search area.

Calculation of Doppler Shift for Various Flight Paths

Summary of data relevant to flight path of MH370

Communication turned off 40 minutes after takeoff at 6.92 deg N, 103.5786 deg E

Satellite is on equator at 64.5 deg E

Last radar contact about 500 km east of initial position when plane turned west

Distance between satellite and initial position is 4336 km

Radius of earth at equator is 6353 km, diameter 39,943 km

Satellite is 35,800 km from earth surface

Ping 1 detected 1 hour 30 minutes after take-off and 4 minutes before last radar sighting

Doppler shift df/f=dv/v where dv is the dot product of the velocity of the plane onto the vector from the plane to the satellite.

                dv=v_psinacosb

            Where v_p is the speed of the airplane, a is the angle of the satellite position relative to the position of the plane, and b is the angle between the direction of the airplane and the direction to the satellite in the plane of motion of the airplane.

 sin a=d_p/d_s where d_p is the distance between the airplane and the satellite in the plane of the motion and d_s is the height of the satellite above the plane of motion.

b=arc sin(d₁/d_p) where d₁ is the distance in the plane of motion from the satellite perpendicular to the flight path. 

v=299,972 km/s

v_p=872 km/hr=0.242 km/s

df/f=0.8075sinacosb parts per million

Maximum value of sin a =0.12, thus maximum value of df/f=97.9cosb parts per billion.

Therefore the Doppler shift must be determined with a precision of about 1 part per billion to provide accurate information on the flight path.

This is possible with modern equipment, but Inmarsat has provided no information on the precision of their measurement.

Since the Doppler data, the process can be inverted and the Doppler shift expected can be calculated for any proposed flight path.  This calculation can then be compared with the actual data if and when it is available and the calculated trajectory adjusted as required. 

cosb=(df/f)/(0.8075sina) with df/f in ppm.

Calculation of Doppler Shift for Path Straight west at 7 deg N latitude

 

 

Calculation of Doppler Shift for 90 degree turn to south after ping 2

 

   Ping no.             west      turn to S        Inmarsat

Comparison of our calculations with data from Inmarsat  

 

Conclusion:

Noise on the Inmarsat data is about 20 times larger than the maximum expected change in Doppler shift and is at least 100 times larger than is required for meaningful measurements on flight path.  Inmarsat shows 3 values at ping 1 (only 1 shown above) apparently determined within a 2 minute period.  They interpret this as a change in direction at ping 1, but instead it clearly indicates the noise in their data. There is absolutely no credible evidence from the Inmarsat data about the direction that the flight may have taken following the last radar detection.

1.        Inmarsat data provided by Duncan Steel in the form of Burst Frequency Offset in Hz.  These have been converted to parts per billion by dividing by the base frequency of the transmitter 135.55 MHz.