NavList:

Hello to all,

On Friday morning Oct 8th 2021, in France and shortly before Sunrise, I happened to watch for a long time the condensation trail of a long haul Aircraft flying an easterly track. This "contrail" immediately followed the Aircraft and was very short, to an extent that - given our relative configuration - it was showing as a very bright slowly moving spot. I even thought of Mercury for a few seconds ... And by no means could I see the Aircraft herself since she was so far away.

This Aircraft - or at least its contrail - went all the way downwards until it became hidden by and behind my "local horizon" itself. As the result of the small elevation of some nearby terrain 3 miles away my "local horizon" in the Aircraft Azimuth shows slightly above my "true horizon" at an angular elevation which I accurately measured to be at 0.76° .

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For fun, I decided to compute this Aircraft distance and I got a bit surprised at the results.

Interesting computation, and not utterly difficult.

Let "α" be the elevation of the "apparent horizon" above the "true horizon" and let "h" be the aircraft altitude in units of the Earth Radius which makes computations easier.

What is the Aircraft Distance "d" ?

(1) - Numerical example assuming that there is no refraction. With h = 42,000' (FL 420) and α = 0.76°, what is the oblique distance "d" - in Nautical Miles - of the Aircraft to the Observer ?

(2) - Same numerical example with the previous values and assuming this time that the refraction is equal to 19'. This refraction estimate seems a reasonable starting point since "full refraction" would be close to 26' if the Aircraft were outside the atmosphere at an infinite distance. A significant part of the atmosphere has been crossed obliquely from the Aircraft downwards to the Observer as the static Air pressure around the Aircraft is close to 1/4 of its sea level value.

Hope this has not been addressed in NavList before ...

Please publish your own solutions altogether with comments if any.

I will publish mine, altogether with pictures showing the unusual and funny manner I measured my local horizon elevation to be at 0.76° ... in a quite windy day yesterday.

Enjoy !

Antoine M. "Kermit" Couëtte

antoine.m.couette[at]club-internet.fr