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    Spur of the moment long by chron
    From: David C
    Date: 2018 Dec 15, 18:12 -0800

    Yesterday afternoon I checked a sun app to determine how near the sun was to
    the southern solstice. There was just 11' to go. Then I realised that in just
    20 minutes the sun would be due west. It was a perfect day for a sun sight with
    a clear blue sky and little wind to disturb the artificial horizon. A ideal
    moment to do a long by chron.

    Usually when I use my sextant I take lots of practise sights first. My eyes
    become tired and I find it hard to take the sight and then read the
    vernier. I decided to take just two sights. Five minutes before the sun was due
    west I took a test sight to make sure everything was set up correctly.
    Then at 1716 NZST I took the sight that mattered. I finished by
    measuring the index error.

     
    First the IE maesurement

    37' on
    28.5' off
    from which IE = 4.2' on
    Sun's SD = 16.4'

    From the Aeronautical Almanac  SD = 16.2' which confirms that I am  using
    the sextant correctly.


    Measurements were made with an AH. I am pretending that I do not know my longitude and my latitude is
    about -40°.

    15th Dec 2018   04 16 08  UT

    GHA =   243°  45.7'  +   1 ° 32'    =  245° 17.7'

    Dec  -23° 15.4'

    Ho  36°  58.3'

    I used an fx-82AU calculator and the formula

    cos t = (sin(Ho) - sin(lat)*sin(dec))/cos(lat)/cos(dec)

    To eliminate the need to think All Science Teachers Count and work out if the - sign should be a + I entered lat and dec as signed values.

    I calculated

    lat -40°         t  60° 24' 7"

    I then realised that if I calculated long for at least one more lat I would be
    doing a Sumner:

    lat  -41°   t  60°  24'  40"
    lat  -42°   t  60°  24'  10"

    long =  t - gha + 360 so

    lat -40°    long   175°  06.5'
    lat -41°    long   175°  07'
    lat -42°    long   175°  06.5'

    This demonstrates  why an accurate lat is not important for a long by chron if the sun is due west or east.

    For the record my gps long is 175° 05.2'  Given the relatvely poor optics of my
    sextant, the difficulty of reading a vernier, the use of an AH and my spur of
    the moment decision to perform a long by chron I am happy  to have determined
    my long to within 2' (1.5 nm at my latitude). The final part of my journey home can be by paper map and pilotage.

    The hardest part of the exercise was correctly typing the formula into the
    calculator. I kept getting an Error message whenever I pressed the  = key. It
    would have been so much easier if Blackburne had calculated his hour angle tables up to lat
    40!

    I suppose that if I wanted to follow tradition I could get my copy of Nories
    down from the bookshelf and calculate t using trig, log trig and anti log
    tables but there are limits to how fay I will go to avoid using electronic
    methods.

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