How a Satellite Owner Failed MH370

This discussion focuses on the speed-of-light constant, c, as one of several distance metrics available for use in triangulation and trilateration. Things that travel at light speed have the advantage of moving at a constant speed through a given medium, such as earth’s atmosphere. That is a useful property when a plane’s conventional rate-of-speed, ground speed, is incalculable.

A good example is the MH370 airliner that vanished over the South Indian Ocean in March 2014. The pilot disabled all active outbound communication systems aboard the aircraft shortly after takeoff, including ACARS (Aircraft Communication and Reporting System). That prevented typical flight information like ground speed, air speed, altitude, and heading from reaching the satellite, its ground station, and search crews.

But unknown to the pilot, it seems, he failed to disable an emergency pinger that was programmed to activate one hour after everything else was turned off. Indeed, the emergency pinger self-activated as programmed and provided basic ground track and heading information for the final six hours of flight. While that ping information could have and should have allowed the satellite owner to track the plane in real time, no one employed by the company knew how to use basic geometry and light speed metrics [microseconds (μs)] to do that.

Loss of the airliner and all lives aboard was tragic, and the tragedy was compounded by the fact that the plane’s terminal location could have been determined within minutes using ordinary Eighth Grade geometry. In fact, a man named Daniel Liu published one of several simple solutions to MH370’s crash location in December 2015, 15 months after it disappeared. At the time, Mr. Liu may not have known his heuristic example was one of several equally simple solutions to that particular mystery; but now, years later, an overriding question is, why didn’t the MH370 search team include someone with applied expertise in geometry? [See:]

Mr. Liu’s important contribution, shown above, is one of a number of equally viable solutions to MH370’s terminal location. No matter which method one uses, the terminal location is always the same: that is, the math is consistent. A few of the other solutions are presented and discussed elsewhere on this website. Locating the plane should not have been a challenging or difficult task. It should not have consumed five years and ended in failure.

Rates of Speed Issues

If asked how far light travels in one millisecond (ms), there is only one answer: “300 kilometers”.  There is no variability in the speed of light through earth’s atmosphere. In two milliseconds light travels 600 kilometers; in three milliseconds, 900 kilometers, and so on. So, at the speed of light it is sufficient to know either time or distance.

But if asked how far a Boeing 777 travels in one millisecond, there are an infinite number of possibilities, depending on whether the plane is on the ground or in the air, serviceable or broken. So, all one can say is that more information is needed to answer the speed question for things not traveling at the speed of light.

Efforts to express the speed of a Boeing 777 in conventional units like kilometers per hour requires at least two pieces of information: distance and time:

      • Speed = Distance/Time;
      • Time = Distance/Speed;
      • Distance = Speed × time;

MH370 Geometry in Milliseconds and Kilometers

The two illustrations below show how simple the search for MH370 was. The information that was always available was gathered and stored by one satellite, known as 3-F1; everything was in microseconds (μs), which is a standard unit in satellite communication. Some of that data is shown in milliseconds in the first chart. (Milliseconds are simply three fewer decimal places and work nicely in this example.)

Corresponding information in kilometers.

Light Speed Metrics In Other Settings

Figure 1 below applies the same geometry used to locate MH370, but in a Central European setting. It helps show that it takes very little information to locate things when geometric patterns like these can be used. The only given, again, is the radius of the larger circle in milliseconds (4 ms). Answers are shown in milliseconds and kilometers in the illustrations that follow.

Figure 1: Grid of Central Europe. Diameter XY is perpendicular to Chord CI at F, and radius R from Berlin to Romania. The only available measurement is the radius from Berlin to Pin R in Romania. All distances are in milliseconds (light speed).

The solution in milliseconds.

Figure 2: This shows the values for each line and radius in milliseconds (ms). The only known value at the outset was the radius of the large circle (4 ms).

The solution in Kilometers.