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    Sextant Accuracy: An Experiment
    From: Dan Allen
    Date: 1999 Mar 12, 2:09 PM

    A while ago I wondered how I was doing in terms of accuracy with my sextant.
    I have been doing celestial navigation for several years and thought I would
    measure my position with my most accurate sextant, so I performed an
    experiment...
    
    I took a series of sights with my Tamaya Jupiter sextant on my back porch.
    I used a Davis artificial horizon (which is a tiny pond of water with glass
    to prevent the wind from rippling the water), and averaged my position over
    30 minutes with my Garmin GPS III as a baseline to test how accurate I could
    measure my position with a sextant.
    
    I have written my own software in C for sight reduction and for the nautical
    almanac portion as well.  It runs on any Macintosh or Windows NT machine as
    a command line tool.  All of the calculations run through this tool.  I have
    done rather extensive checking with the nautical almanac and I am in very
    close agreement.
    
    For this experiment I took 11 sights done over 30 minutes starting around
    5pm on September 9th, 1998.  Looking at the sights individually, the
    intercepts were:
    
      Intercept: + 0.03097 deg  = 1.86 nmi
      Intercept: + 0.02124 deg  = 1.27 nmi
      Intercept: + 0.01720 deg  = 1.03 nmi
      Intercept: + 0.00948 deg  = 0.57 nmi
      Intercept: + 0.01074 deg  = 0.64 nmi
      Intercept: + 0.01953 deg  = 1.17 nmi
      Intercept: + 0.01754 deg  = 1.05 nmi
      Intercept: + 0.00826 deg  = 0.50 nmi
      Intercept: + 0.00981 deg  = 0.59 nmi
      Intercept: + 0.02469 deg  = 1.48 nmi
      Intercept: + 0.02494 deg  = 1.50 nmi
    
    My closest sight had a one half mile error.  A good sextant like this Tamaya
    Jupiter usually can get as accurate as 12" of arc, or 0.2 nautical miles, so
    I still have a ways to go.
    
    I have also adopted Tom Metcalf's "Overdetermined Celestial Fix by
    Iteration" software to obtain a fix by iterating over several sights.
    Iterating over the 11 fixes with Tom's nav.c program gives this table:
    
        GHA         DEC         ALT     ITER     LAT         LONG
    =================================================================
     183.63687     5.09272    22.55929
     183.87860     5.09247    22.39397
     184.07448     5.09226    22.26372   18    45.31649   120.86935
     184.24119     5.09209    22.14850   21   -39.80430   128.77931
     184.38289     5.09194    22.05832   20    45.52784   120.95796
     184.61628     5.09169    21.91637   19    46.47749   121.36912
     184.86634     5.09143    21.75271   20    46.87425   121.54800
     184.99137     5.09130    21.66252   20    46.78558   121.50773
     185.13307     5.09115    21.57234   20    46.81061   121.51905
     185.44981     5.09082    21.38195   20    47.18848   121.69127
     185.69987     5.09055    21.21994   19    47.40294   121.79058
    =================================================================
    
    The best iterated position via sextant was therefore:
    
      Latitude: N  47 deg 24.176' =   47.40294 deg
     Longitude: W 121 deg 47.435' =  121.79058 deg
    
    By GPS I averaged my actual position over 30 minutes as being:
    
      Latitude: N  47 deg 28.859' =   47.48098 deg
     Longitude: W 121 deg 47.941' =  121.79902 deg
    
    with a 50 foot error.  This gives a sextant error through iteration of
    
      4.70 nautical miles or 5.4 statute miles
    
    which is more than any single error.
    
    So I learned that I can improve, but I was also pleasantly surprised to
    realize that I am now getting proficient enough with a sextant that I could
    make my way to port okay when my GPS fails...
    
    Dan
    danallen{at}microsoft.com
    
    PS - I have actually had my Garmin GPS 40 just freeze on me.  Luckily it was
    on the highway just messing around, but if I had been at sea, I would have
    been up a creek.  Hence my interest in celestial navigation...
    
    
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