NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2024 Jul 2, 05:38 -0700
(1) - Lars, thanks for mentioning Frank's previous results on Astronomical Refraction for [-3°, 0°] .
Frank, thanks for your subsequent detailed explanations on the way you achieved your results in this range of heights.
(2) - My turn now ... and it is an interesting and unexpected story as far as I am concerned.
Working from a Sunset Picture, and after performing the applicable Dip correction, I stumbled upon a negative Sun height, i.e. under the Astronomical Horizon. It triggered my following remark: " Obviously, no refraction tables exist for [invisible] heights under the horizon. ".
I nonetheless decided to squeeze the best of the available Refraction Tables, and - as per the Attachment - I decided to explore the concept of comparing the Refractions obtained in the usual Horizon Heights Scale with their counterparts obtained in Offset Heights Scales, .
This led me to Formula 2.4 (see Attachment) which is the backbone of my findings.
* I first explored a "Brute Force" Method from which I derived Tables (A) - unpublished then until to-day - which I was not fully happy with for the reason given in the Attachment: "Too big of a shortcut here" were my thoughts then.
** I then went for a "More in-depth Method" from which I derived Tables (B), not that far from Tables (A) results actually, but I did feel more confident about their expected "improved" results.
I used Tables (B) to solve my previous Canigou Sunset Quizz, and I subsequently published such Tables (B) in NavList.
*** The interesting if not "funny" thing happened when I compared Tables (A) and Tables (B) results with your own numerical integration, Frank.
- Over [-1°, 0°] the "Brute Force" Method , when applied to the NAL Refractions, yields results extremely close - by less than 0.5' - from your own integration results, i.e. Tables (A) results are closer from your own results, Frank, than Tables (B) results.
- Over [-3°, 0°] - a much more cumbersome "Brute Force" Method computation to implement here - this same "Brute Force" Method matches your results surprisingly well : less than 4' difference at height = -3° for Refractions then exceeding -165' !
(3) - Through 2 [almost totally] independent approaches yielding similar and compatible results, we can now reasonably consider that we now have at hand sufficiently accurate Standard Astronomical Refraction Tables for [-3°, 0°].
(4) - Still interested in looking up the Refraction Tables used on-board SEASHIPS. Any results here ?
(5) - BTW, would you mind disclosing to me a copy of the current - i.e. from 2004 and later - NAL Refraction tables, at least the ones pertaining to the Stars.
"Kermit"
[ my former USN A7(E) Pilot "tactical call-sign" :-) ]
