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    Re: Evaluation of H.O. 218
    From: Gary LaPook
    Date: 2011 Mar 15, 12:33 -0700
    I decided to complete my evaluation of the accuracy of the selected star section of H.O. 218. I had previously compared the Hcs computed with H.O. 218 to those computed with the Navy website for six stars selected at random. I found that none of the differences exceeded 1.0'.

    I decided to go further. The adjustment procedure for the change in date since 1941 only corrects for the change in declination due to precession of the equinoxes and cannot correct for each of the stars' proper motions in declination. To determine if we can safely use H.O. 218 for all of the twenty two listed stars in H.O. 218 I found the star with the greatest proper motion in declination and did the same comparison that I did for the previous six randomly selected stars since if this star produced accurate results then all the other twenty two stars will also.  Arcturus has the largest proper motion in declination which is almost twice that of the next star, Sirius.

    Doing this computation for Arcuturus,  for March 15, 2010, latitude 30̊ north, longitude zero, hour angle
    5̊. H.O. 218 returned the values of Hc = 78° 34', “t” = -17 and Z = 156 (ZN= 204°). To adjust
    the “t” value for the 69 years that had elapsed since 1941 I looked at my extended multiplication
    table
    and found the adjustment to be -20.2'', which added to the tabulated Hc produces 78̊ 13.8'.

    I then went to the Navy website and adjusted the time to 03:05:40 GMT (by trial and error)
    which produced a GHA for Arcturus of 4° 59.9', Hc of 78̊ 13.0' refraction correction of 0.2'
    and a Zn of 203.8°. Adding the refraction correction to the Hc produced 78̊ 13.2', which is 0.6'
    less than the value from H.O. 218.


    Based on this computation I it appears that using H.O. 218 for calculating computed altitudes for the twenty two selected stars will produce Hcs withing one minute of those calculated with the most accurate methods so are perfectly usable for practical navigation.


    Comparing the methodology for the selected star sections in H.O. 218 with H.O. 249 volume 1 shows advantages and disadvantages to each. With H.O 218 you must calculate the  LHA for each star while with H.O. 249 you need to calculate only one LHA, that for Aries, which you then use for all the computations for the entire round of sights. On the other hand, H.O. 249 volume 1 constrains your choice of stars to only the seven stars listed for the current LHA Aries while H.O. 218 allows you to use any of the 22 stars that may be visible at the time. H.O. 218 is a much more compact volume that H.O. 249 but each volume only covers 5° of latitude while H.O. 249 volume 1 covers all latitudes. But if using H.O. 249 you also need to carry at least volume 2 or 3 of H.O. 249 to cover the sun, moon and planets. If you are confining you sailing to a narrow band of latitudes then one or two volumes of H.O. 218 will work and be much more compact than the two volumes of H.O. 249 needed but if covering a great range of latitudes then H.O. 249 will be more compact. 


    gl



    --- On Tue, 3/15/11, Gary LaPook <glapook---.net> wrote:

    From: Gary LaPook <glapook---.net>
    Subject: [NavList] Re: Evaluation of H.O. 218
    To: NavList@fer3.com
    Date: Tuesday, March 15, 2011, 3:38 AM

    I decided to check the accuracy of the selected star pages in H.O. 218. These tables are entered
    with name of star, latitude and hour angle of the star not Aries as is done with H.O. 249. Because
    of this difference in procedure it is not convenient to compare H.O. 218 with H.O. 249 for
    selected stars.

    After entering the table you take out computed atltiude, “t” which is a correction factor for the
    change in the star’s declination since the date of the tables, 1941, and the azimuth angle which
    must be converted to azimuth for plotting the LOP. There is a multiplication table provided
    which is entered with “t” and the current year and the correction to computed altitude is taken
    out. This table ends in the year 2000 but since it is a simple multiplication table it can be easily
    extended to the current year or the correction could be computed with a calculator.

    The methodology I utilized was to first extend the multiplication table to the year 2010 I then
    chose a half dozen stars and computed their altitudes using H.O. 218 and the extended
    multiplication table. I then went to the Navy website at:

    and entered the date of March 15, 2010, a latitude of 30̊ north and longitude of zero. Since the
    website returns the GHA of the body, selecting a longitude of zero made the hour angle the same
    as GHA. I then adjusted the time to arrive at the same hour angle (GHA) as I had used in H.O.
    218 and took out computed altitude, azimuth and refraction correction. I then added the
    refraction correction to the computed altitude and compared the total with the altitude from H.O.
    218, they should be the same. In the case of Altair, where the Hc was about ten degrees, I also
    added the one minute additional correction from table VI in H.O. 218.

    The result of my tests showed that the H.O. 218 derived Hcs for the six cases I tried were within
    one minute of arc of the values derived from the Navy website. Since the “t” correction does not
    correct for the star’s proper motion I did not expect perfection but the results show that the
    accuracy is good enough for practical navigation.

    I will go through two examples. The first is for the star Fomalhaut, latitude 30̊ north, hour angle
    15̊. H.O. 218 returned the values of Hc = 28̊ 24', “t” = +18 and Z = 165̊ (ZN= 195̊). To adjust
    the “t” value for the 69 years that had elapsed since 1941 I looked at my extended multiplication
    table and found the adjustment to be + 21.4', which added to the tabulated Hc produces 28̊ 45.4'.

    I then went to the Navy website and adjusted the time to 12:26:11 GMT (by trial and error)
    which produced a GHA for Fomalhaut of 14̊ 59.9', Hc of 28̊ 44.5 refraction correction of 1.8
    and a Zn of 194.9̊. Adding the refraction correction to the Hc produced 28̊ 46.3', which is 0.9'
    greater than the value from H.O. 218.

    Going through the same steps for Altair, with an hour angle of 83̊, H.O. 218 tabulated Hc = 10̊
    27', “t” = +5, and Z = 86̊ (ZN = 274̊). The correction for 2010 for that value of “t” is 6.4'
    making the corrected Hc of 10̊ 33.4'. Using a time of 13:51:02 GMT produced a GHA of 83̊,
    Hc of 10̊ 27.7', refraction correction of 5.1' and a Zn of 274.3̊. Adding the refraction correction
    to the Hc produces 10̊ 32.8'. Since this is a low altitude we have to add one minute to this
    producing a total of 10̊ 33.8', only 0.4' greater than the value from H.O. 218.

    So it appears that even this many years after these tables were printed that they still produce
    altitudes that are within one minute of arc of modern tables and computer programs and are
    usuable for practicle navigation.

    gl
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