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    Re: Standard Astronomical Refraction Tables [-1°,0°]
    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    * I first explored a "Brute Force" Method from which I derived Tables (A) - unpublished then until to-day - which I was not fully happy with for the reason given in the Attachment: "Too big of a shortcut here" were my thoughts then.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.


    [ my former USN A7(E) Pilot "tactical call-sign" :-)  ]

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