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    Re: Semi-diameter in the Nautical Almanac
    From: Gary LaPook
    Date: 2009 Dec 22, 05:17 -0800

    I had written:
    "I am also curious why the sun correction table has only two tabulations 
    allowing for only two S.D. values when the S.D. of the sun includes six 
    different values during the year from15.8 to 16.3 minutes. This 
    unnecessarily limits the accuracy of the sun corrections. "
    
    
    
    -----------------------------------------------------------------------------------------------------------------------------------
    
    Frank wrote:
    
    "Yeah, this one has puzzled me, too. Clearly, whatever committee decided 
    back in the 1950s that those two columns were sufficient felt that this 
    was "good enough" for the accuracy of celestial navigation as practiced 
    at that time. It seems like it would have been "nice" to include a 
    monthly or bi-monthly table for the Sun, or, as you suggest, to provide 
    an alternate method allowing the calculation by separate steps. This 
    sort of table, as published in the N.A., combining refraction, parallax, 
    and semi-diameter was seen as a great improvement back in the middle of 
    the 20th century. This calculation had "normally" been done in three 
    separate steps for the previous fifty to one hundred years. Even 
    earlier, it was not uncommon to use an altitude correction that combined 
    dip with semi-diameter: +12' for a lower limb Moon or Sun sight, -20' 
    for an upper limb sight. You can find these corrections in most older 
    navigation manuals (especially for correcting the altitudes in lunar 
    observations since a few minutes of arc error in altitudes for clearing 
    lunars doesn't matter)."
    
    
    
    ----------------------------------------------------------------------------------------------------------------------------------------------------
    
    Well I decided to research this further and I was happy to find (not 
    surprisingly) that others had proposed the same types of sextant 
    correction tables that I described. I had proposed rounding the sun's 
    parallax in altitude correction to one-tenth of a minute and provide a 
    table of plus .1' for altitudes below 70 degrees and zero above. I have 
    attached an excerpt from Bowditch 1977 which says the same thing except 
    to use zero above 70º 07'.
    
    I have also attached excerpts from Norie's which has a parallax table 
    for the sun and also table 20 from Bowditch 1938 which has the same thing.
    
    I had also proposed that it actually made more sense to combine 
    refraction with parallax and handle S.D. separately to avoid the round 
    off error inherent in a separate parallax table. The attached Hughes 
    table has combined refraction and parallax and semi diameter but with 
    separate columns for the different values of semi diameter but labeled 
    by the dates when the sun has the different semi diameters. Table 23 
    from Bowditch 1938 has a combined refraction and parallax table for the 
    sun so you would account for S.D. separately. But table 40 from the same 
    book makes it even simpler, the sun correction table combines 
    refraction, parallax and semi diameter of 16' to the lower limb of the 
    sun and provides an additional correction to account for the changes in 
    semi diameter.
    
    I have also attached excerpts from Dutton's which reprints the sun 
    correction table from the 1939 Nautical Almanac and, guess what, it has 
    the same correction table as table 40 from Bowditch. Since this is a 
    more accurate way to handle all of the corrections for the sun and it is 
    simple, compact and had already been in the Nautical Almanac why did 
    they replace it with a less accurate table? This is especially curious 
    since the editors of the N.A. have no problem with having an additional 
    correction for the planets.
    
    I have also attached excerpts from Hughes and the 1939 Nautical Almanac 
    (in Dutton's) for the moon which I think are easier to use than the 
    current N.A. moon tables. I have also attached the inside cover of a 
    navigation notebook that I made 30 years ago by cutting out the several 
    P in A moon tables from the the daily pages of the Air Almanac which 
    makes another convenient way to deal with the moon.
    
    gl
    
    
    -
    
    
    frankreed@HistoricalAtlas.com wrote:
    >
    > Gary, you wrote:
    > "We are all familiar with the semi-diameter of the sun and of the moon 
    > being tabulated on each of the daily pages of the Nautical Almanac. My 
    > question is "why?" There is no place where you use this bit of 
    > information when using the N.A. "
    >
    > Because it's not perfect? :-) I'm serious. I think it's just that 
    > simple. The changes made during the 1950s resulting in the modern 
    > Nautical Almanac in 1958, very nearly unchanged right through the 
    > present, were mostly excellent, but they missed a few things, and 
    > there are some features which are either unnecessary or less than 
    > optimally presented. There's probably no point in changing it now, 
    > except in private substitute almanacs, since celestial navigation is 
    > essentially dead from a practical standpoint.
    >
    > There is one very small practical use for the lunar and solar 
    > semi-diameters. If you use the Sun and Moon to get an index correction 
    > by bringing alternate limbs together, you also simultaneously measure 
    > the diameter of the object (but only if side error has been rigorously 
    > eliminated which is otherwise fairly pointless). By comparing the 
    > measured SD with the tabulated SD, we get a sanity check on the index 
    > correction. This little trick was even known back in the 19th century.
    >
    > you also wrote:
    > "I am also curious why the sun correction table has only two 
    > tabulations allowing for only two S.D. values when the S.D. of the sun 
    > includes six different values during the year from15.8 to 16.3 
    > minutes. This unnecessarily limits the accuracy of the sun corrections. "
    >
    > Yeah, this one has puzzled me, too. Clearly, whatever committee 
    > decided back in the 1950s that those two columns were sufficient felt 
    > that this was "good enough" for the accuracy of celestial navigation 
    > as practiced at that time. It seems like it would have been "nice" to 
    > include a monthly or bi-monthly table for the Sun, or, as you suggest, 
    > to provide an alternate method allowing the calculation by separate 
    > steps. This sort of table, as published in the N.A., combining 
    > refraction, parallax, and semi-diameter was seen as a great 
    > improvement back in the middle of the 20th century. This calculation 
    > had "normally" been done in three separate steps for the previous 
    > fifty to one hundred years. Even earlier, it was not uncommon to use 
    > an altitude correction that combined dip with semi-diameter: +12' for 
    > a lower limb Moon or Sun sight, -20' for an upper limb sight. You can 
    > find these corrections in most older navigation manuals (especially 
    > for correcting the altitudes in lunar observations since a few minutes 
    > of arc error in altitudes for clearing lunars doesn't matter).
    >
    > -FER
    >
    > -- 
    > NavList message boards: www.fer3.com/arc
    > Or post by email to: NavList@fer3.com
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    -- 
    NavList message boards: www.fer3.com/arc
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