A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2021 Oct 13, 05:38 -0700
Good day to you, David.
In reply to your interesting remark, I have often noticed that if and when I start hearing a subsonic civilian aircraft at its cruising altitude, it is almost approaching its closest point from me, i.e. it is almost already reaching its highest elevation above the horizon for me.
I think that both our statements are compatible.
Let's verify whether they are actually.
As an example :
An subsonic A/C flies at 33,000' (FL 330) is heard by a sea level Observer. Average sound speed is 300 m/s over the slant distance from A/C to Observer. A/C speed is M.78, in other words, the A/C flies horizontally at 234 m/s. We need 2 extra assumptions to fully define our problem.
The A/C ground track minimum distance relatively to the Observer needs to be specified for each case. And :
This second assumption is subject to change (e.g. Engines noise intensity and Observer's hearing abilities) but - at least for me - the following one seems reasonable: on the average I have noticed that I can only hear Aircraft flying at 20 Km or less from me.
Hence, let us compute the following 2 cases :
A - The Aircraft overflies the Observer, i.e. A/C ground track minimum distance is equal to 0 km
(A1) What is initial sound direction elevation when Observer first starts hearing it ?
(A2) What is A/C elevation when Observer first hears it ?
(A3) What is the Distance between A/C position when it first becomes audible to the Observer and its actual position then ?
B - Same questions for an Aircraft with ground Track Distance minimum distance equal to 10 km.
(B1) What is initial sound direction elevation when Observer first starts hearing it ?
(B2) What is A/C elevation when Observer first hears it ?
(B3) What is the Distance between A/C postion when it first becomes audible to the Observer and its actual position then ?
Any taker for this computation ? Of course I will publish results.
Antoine M. "Kermit" Couëtte