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    Latitude + Longitude calculations
    From: Henry Halboth
    Date: 2005 Jul 24, 22:38 -0400

    Again, have spent a couple of weeks at NC beaches and was able to
    indulge myself in a number of celestial observations for Lat + Long.
    By testing oneself in a known position, some idea of personal accuracy
    can be obtained, as well as a real feel for the reliance which may be
    placed on observations based on a sea horizon. For those who may be
    interested, the following are offered .
    
    In all, a Plath vernier sextant was employed. IC = 00'24" on the arc.
    HE = 20-Ft. ZD = +4
    
    July 5, 2005: Latitude by meridian transit - Sun's LL
    LAN = 13-12-37 LMT + 4 = GMT 17-12-37
    DEC = 22-43-42 N
    hs 77-53-10 + corr 00-11-00 = ho 78-04-10
    LAT = 89-59-60 - 78-04-10 + 22-43-42 = 34-39-32 North
    
    July 6, 2005: Latitude by meridian transit - Sun's LL
    LAN = 13-12-47 LMT + 4 = GMT 13-13-47
    DEC = 22-37-40 N
    hs 77-47-10 + corr 00-11-00 = ho 77-58-10
    LAT = 89-59-60 - 77-58-10 + 22-37-40 = 34-39-30 North
    
    July 8, 2005: Latitude by meridian transit - Sun's LL
    LAN 13-13-07 LMT + 4 = GMT 17-13-07
    DEC = 22-24-21 N
    hs 77-33-15 + corr 00-11-00 = ho 77-44-15
    LAT = 89-59-60 - 77-44-15 + 22-24-21 = 34-40-06 North
    
    July 10, 2005: Longitude by time sight - Sun's LL, bearing about
    111 drgrees, true
    LMT = 11-36-04 + 4 = GMT = 15-36-03
    DEC = 22-10-03 N
    LAT = 34-40-06 N by previous meridian transit
    hs 63-22-20 + corr 00-10-48 = ho 63-33-08
    LHA = 26-39-15 E, by time sight formula
    GHA = 50-21-42 W, by NA
    Long = 77-00-57 West
    
    July 10, 2005: Latitude by meridian transit - Sun's LL
    LAN = 13-13-24 LMT + 4 = GMT 17-13-24
    DEC 22-09-32 N
    hs = 77-20-20 + corr 00-11-00 = ho 77-31-20
    LAT = 89-59-60 - 77-31-20 + 22-09-31 = 34-38-11 North
    
    July 12, 2005: Latitude + Longitude @ LAN by equal altitudes
    + reduction to meridian
    
    1. For the Longitude
    AM obs @ chro time = 17-00-12; Sun's LL = 76-42-00
    PM obs @ chro time = 17-26-59; Sun's LL = 76-42-00
    Mean chro time of obs = 17-13-35.5 = GMT of LAN
    GHA Sun @ 17-13-35.5 = 76-59-06 West = Longitude
    
    2. For the Latitude
    hs Sun's LL @ 17-00-12 = 76-42-00
    DEC = 21-53-12 N
    GMT of LAN by equal altitudes = 17-13-35.5
    Time of obs before LAN = 17-13-35.5 - 17-00-12 = 00-13-24
    Altitude corr to meridian - Bowditch Tabs 29 + 30 = + 00-19-36
    hs 76-42-00 + 00-11-00 + 00-19-36 = ho 77-12-36 @ transit
    LAT = 89-59-60 - 77-12-36 + 21-53-12 = 34-40-36 N
    
    3. Position @ 13-00-12 LMT = Lat 34-40-36 N + Long 76-59- 06 W
    
    Note:  If one were to "analyze the analyzed analysis", and, if the
    assumed correct Longitude given below is absolutely correct,
    there is roughly a 4.5 sec discrepancy in this solution, indicating
    possibly some unaccounted for chronometer or sight timing error -
    perhaps a combination of both.. However, as subsequently stated,
    I cannot be absolutely sure of the charted Longitude, nor can I deny
    the possibility of a small error in timing. There are a number of ways
    to resolve this error, but they seem to be beyond the purpose of
    this posting.
    
    July 14, 2005: Latitude by meridian transit - Moon's UL
    LTT = 19-13-36 + 4 = GMT 23-13-36
    DEC = 10-55-40 S
    hs = 44-06-20 + corr 00-19-24 = ho 44-25-44
    LAT = 89-59-60 - 44-25-44 - 10-55-40 = 34-38-36 North
    
    I was in position 34-40.073 N + 77-00.097 W. I cannot vouch for
    the accuracy of this position, as the location is somewhat off
    the beaten path, and may not be well charted on the map program
    available to me. Unfortunately, I do not have a GPS to verify it.
    Regardless, it is my opinion that these results demonstrate the
    average accuracy + repeatability attainable by celestial navigation,
    under good to average conditions, utilizing the sea horizon.
    As previously reported, the horizon used, at the edge of the
    Gulf Stream, is plagued with a light haze which may have induced
    a bit of foreshortening, with resultant altitudes a somewhat greater
    than true.
    
    I am surprised at the apparent accuracy demonstrated in the
    equal altitude solutions shown. I did experiment with equal
    altitudes many years ago at sea, and it is my recollection that
    results were comparable. It might prove interesting and informative
    if some of our members who employ an artificial horizon would
    give equal altitudes a try and report accordingly. Their value may
    be being understated in available literature as well as on this List.
    
    Henry
    
    
    

       
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