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 its track. Since I know the exact path, and 我的位置的座標 my coordinates, let's see all the things I can compute as a simple ground observer.

[2013 update: I used programs/3d to make m750_3d.kml. See also ../routes/programs.]

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.)

knots km/h m/s mph mach ang-20C 150 278 77 173 0.23 14 200 370 103 230 0.31 19 250 463 129 288 0.39 23 300 556 154 345 0.47 28 350 648 180 403 0.54 33 400 741 206 460 0.62 38 450 833 231 518 0.70 43 500 926 257 576 0.78 48 550 1019 283 633 0.85 53 600 1111 309 691 0.93 58 650 1204 334 748 1.01 63

True when the position of the sound and plane form an isosceles triangle. Distance is not a factor.

Given a airplane at speed 600 knots, whose track at its closest point passes by one at 15 kilometers away (elevation angle not important,) what are the formulas that would describe the shape of the decibel readings over time? (which are something like 25 25 40 40 40 38 36 34 30 25 25, with 25 dbA being the background.) Discussion in sci.physics.acoustics, answered in askthephysicist.com with graph too.

d | horizontal distance of closest approach |
---|---|

v | speed |

t=0 | time of closest approach |

The dB level relative to the maximum is given by
10*log_{10}(d^{2}/(d^{2}+v^{2}t^{2})).

It turns out the speed of the plane has nothing to do with the imbalance over time, but instead it is the fact that standing in front of a jet plane with its motors running even still stationary on the ground, is less noisy than standing behind it...

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

That gives

100FT METER DEG FL410 12496 61 FL390 11887 60 FL370 11277 58 FL350 10668 57 FL330 10058 55 FL310 9448 53 FL290 8839 51 FL270 8229 49

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; 2013: the web flight tracker sites show that they often are close to 600 knots!

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...

有時韓國下來的飛機很多改由 APU → TNN. 其半路點為中橫公路的天冷。

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

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...

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.

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...

積丹尼 Dan Jacobson

Last modified: 2019-05-06 14:48:50 +0800