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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@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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