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    From: Antoine Couëtte
    Date: 2021 Nov 5, 16:13 -0700

    Dear Peter,

    Thank you for your quick reply

    I fully agree that Hc is the Body Center Altitude. But it is the Geocentric Body Altitude. It cannot be otherwise, because in the process of height reduction you compare the Geocentric Body Center altitude derived from Observation to the Geocentric Body Center altitude derived from your DR position. From that you get Intercept and Azimuth.

    How does it work ? You do know it, but le's have a close look again.

    (1) You measure Body LL Topocentric apparent altitude from which you subtract Dip. Therefore you are considered from now on as an Observer right on the ocean surface.

    (2) You add the overall "Sum" correction published by ICE and you then get Body Geocentric Altitude. Very simple !

    In other words for an Observer with 0' height, Body LL Topocentric Altitude (as seen in the sextant) + ICE overall Correction = Body Center Geocentric Altitude.

    Let me further elaborate on the following example very close from the one which has triggered this long NavList thread : Moon LL very close to the Horizon with HP close to 1° .

    The standard sequence of corrections is as follows, and ICE does exactly that:

    1st Correction: Approximately - 34' for Refraction in this example (see attachment). Such "Refr" correction is always negative. There you get the LL height if seen from sea level in your sextant but with no atmosphere. (see note)

    2nd Correction- Then from that "no atmosphere" LL topocentric altitude you "proceed" towards the "no atmosphere" Body Center topocentric altitude through adding the Augmented SD, close to 16.3' in our case (for HP = 1°) . So this second "SD" correction is Positive since we just shot the LL.

    3rd Correction - Finally from such Topocentric Body Altitude, i.e. the "bright dot" you would get in your sextant if no atmosphere and no SD, you proceed to HP correction, close to 1° here to end up to the Geocentric Body Altitude. This Parallax correction "P" is always positive.

    To recap 1st, 2nd and 3rd correctiosn here-above, and with Sum = Refr + SD + PAR :

    Body LL topocentric Height + ( Refr + SD + PAR) = Body LL topocentric height + (Sum) = Hc (Body Geocentric Center height)

    This is exactly what the ICE says in its definite paragraph about Hc.

    QUOTE : Sum = Refr + SD + PA.  If Sum is subtracted from Hc, the apparent altitude (that comparable to observation) of the lower limb of the object is obtained UNQUOTE

    In other words this Explanatory Documentation statement is exactly equivalent to : "If Sum is added to Lower limb observation, the observed Geocentric Body Center height is obtained" which I have just herebaove.

    This makes the Beauty of ICE (which actually I have almost never used). And I do insist that the Refraction correction given by ICE is for the Apparent Topocentric (seen from "Earth Surface") LOWER LIMB (as being the 1st correction step right after getting rid of dip) and not the for the Geocentric Body Center which is our final target directly comparable to Height computed from DR with the help of Ephemeris and UT.

    Therefore, I am in full agreement with the ICE documentation you just let me discover. You claim that you too are also in full agreement with this document.

    Why we are not singing the same music then remains a mystery to me.

    In the cockpit during real world emergencies under environments which permit some different strategical options (e.g. if over the south mid-Pacific fly back or continue ...) if different viewpoints / arguments raise between Captain and First Officer, the most difficult - especially for the Captain - is to ask himself the following question :"What is the right solution" raher than "Who is right in our verbal fight". Incidentally and to Passengers, only the first question is relevant ...

    As a recap and after reading you last post over and over, and mulling over it I think that:

    (1) - The Explanatory Documentation is very poorly worded. I agree that ICE Delta-T shortcomings have led you towards writing your own Software. Since a good number of us has done it, "Welcome to the Community" then.

    (2) - When you state that Hc refers to a Body Center Height, through insisting that "The paragraph Hc is definite", I have agreed to that view point from the onset.

    (3) - I am simply adding 2 things:

    (3.1) - Hc refers to the Geocentric Body Center height which you cannot directly / immediately measure with any sextant I know of.

    (3.2) - ICE - after some hidden reverse engineering computations - see (5) and (7) - publishes Corrections (Refr + SD + PAR) directly applicable to the LOWER LIMB value recorded from a Sextant and not to a Body Center "unreachable" in any usual Navy Sextant.

    As an example : ICE publishes a -34.5' correction for a LL at less than 2' above the horizon. This is perfectly in line with the US NAL refraction tables. If such refraction correction were applicable to Body Center - i.e. at some 16' above the horizon - then you would get some Refraction correction close to -31' but - again - this is a quite different story (Ref 1 and Ref 2).

    As earlier mentioned, there is absolutely no shame in temporarily "erring".

    If you "defeat" (3.1) and (3.2) here-above, I will readily acknowledge that the explanation I have described and supported therein is not a right one. 


    As a concluding smiling note, by the way, I LOVE music as I have been an organist for decades and have had the extreme chance to play all over the world (Washington Saint Patrick, Melbourne Saint Patrick, Sydney Opera house, South America, Quebec ...) all over my long haul flights trips.

    All my wishes that we both actually can sing the very same music at least in Heavens, but certainly as soon as possible here on Earth.

    Best Navigational Regards

    Antoine M. "Kermit" Couëtte

    and just in case : antoine.m.couette[at]club-internet.fr          :-)

     (Note) : Not giving here any details on the extra correction named "refraction induced parallax" which is almost negligible for the MOON but quite sizable for Artificial Satellites.

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