M-750 air route trail across my sky

Here in central Taiwan, the M-750 air route from Hong Kong to Japan passes near me. From a pilot's point of view, I am 3.5 nautical miles (6.5 kilometers) southeast of track. Since I know the exact path, and my coordinates, let's see all the things I can compute as a simple ground observer.

Source of X,Y points air defining the air route

My netnews query results gave me confidence that planes follow their routes well. So, looking at the charts on Vatroc and also maybe looking up individual points, e.g. PILOX, I got a pretty good grip on the X,Y of M-750.

Location of point closest to me on route

Using makefile, section: point_closest_to_dan, we find it is 6.5 km away at bearing 314 degrees.

Computing the speed of the aircraft

Taking the number of seconds between when a plane passes directly to my west, and then north, we can compute the speed, as we know the length traveled. Using the makefile, section length_of_points_90_degrees_to_dan, we find the length is 13.0 km. We then divide this by the time elapsed (makefile section "speed").

On our first observation, it seems the plane took about a minute to fly the 13 km. So we get 780 km/h; 421 knots; 484 mi/h; 0.65 mach;

Angle between where the plane is vs. sounds like it is

The eye and ear have different impressions of where the plane is. (Here the speed of light is much greater than sound, so we ignore it.)

(makefile, section see_hear_angle)

km/h, knots, angle(deg)
278 150 13.0
370 200 17.4
463 250 22.0
556 300 26.7
648 350 31.6
741 400 36.7
833 450 42.3

True when the plane, or its sound, are at the point closest to me on the route.

Arc length of aircraft

Let's compute the arc length of say a Boeing 747-400, 70 meters long, against the sky. (makefile, section arc_length.) We use the point on the trail nearest to us.

height(ft, km), length(arc minutes)
25000  7.6 24.0
30000  9.1 21.5
35000 10.7 19.3
40000 12.2 17.4

For comparison, the full moon is on average "just over half a degree" wide.

Actually, the heights that mostly matter according to Mar. 2004 Taiwan government aeronautical publications are flight levels 410, 380, 370, 340, 330, 300, 290, where 1 flight level is 100 ft., also depending on atmospheric pressure...

Tracks for astronomy or satellite programs

I should enter route M-750's path across the heavens in star charting software.

A satellite TLE file to describe the air route?

I want to make a satellite TLE file for the air route, if possible, so I can say plug it into various software. It seems I must fake one of the parameters, say rotations per day, to get the altitude down to where I want, at the price of making times unreal ... but my focus is on the path across the heavens anyway. I got as far as Kepler's third law.

Try just plotting it as an "horizon"

A simpler option would be for me to use simple trigonometry to compute an elevation angle for the air route at each degree of azimuth from me, and plug this into star charting software as a "horizon" line. See target "horizon" in the makefile.

Supposedly I will notice a plane crossing very close to some star one day, and plugging in different heights' horizons, see which height matches.

Distance from azimuth

As a side effect of our horizon calculation, we get the horizontal distance from us as a function of azimuth, which is independent of altitude. Looking at a map, we notice that M750 leaves the island of Taiwan 143 km from us NEward, and 106 km SWward. The azimuth of the latter is 227.5 deg...

Dan Jacobson

Last modified: 2006-03-14 12:50:27 +0800