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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Accuracy of sextant observations at sea
From: Gary LaPook
Date: 2010 Sep 23, 02:57 -0700

```  Last year I had the opportunity to cross the Atlantic on the Royal
Clipper, a 437 foot long five masted full rigged ship as I reported at:

http://www.fer3.com/arc/m2.aspx?i=110827&y=200911

One of my goals on that sixteen day voyage was to evaluate the accuracy
of celestial navigation so I brought my Tamaya sextant along. I got up
early almost every morning to take the morning stars and took
observations of the sun during the day and then more stars at evening
twilight. Altogether I took 78 sights. I also had two GPS's with me and
I recorded GPS fixes within just several seconds of each celestial
observation so that I could use the GPS fixes as the assumed positions
and so could determine the accuracy of each shot. I did the sight
reductions with my Bygrave slide rule and then repeated the computations
with a calculator for maximum accuracy. The shots were taken from
several locations on deck and the height of eye varied from 24 feet to
33 feet. I had measured these heights by dropping a weighted line over
the side (actually a hotel complimentary small shampoo bottle) until it
hit the water and floated. I then marked the line off and measured it
off with my Ikea tape measure.

One one occasion I took 15 shots of Venus in 39 minutes and the
intercepts had a standard deviation ( σ ) of 0.876 NM. On another
occasion I took twenty sun shots in a 54 minute period and and the σ was
0.923. Combining these two series, comprising 35 shots, results in a σ
of 0.997.

I took another 31 normal sights. Leaving out the two worst shots in this
group for the moments results in a σ of 1.371 for 29 sights. Adding in a
3.8 and a 4.4 intercept (the two worst shots) brings the σ to 1.756 for
the 31 sights. Combining these 29 shots (again leaving out the two bad
ones for the moment) with the previous 35 shots produces a σ of 1.252
for the 64 shots. Adding in the two bad shots raises the σ to 1.433 for
66 shots.

Of these 66 shots 4 had intercepts of zero. Another 20 had intercepts of
0.1 to 0.5 NM making 24 out of 66 shots (more than one third) having
intercepts of 0.5 or less. Another 13 shots were in the range of 0.6 to
1.0 NM making a total of 37 out of 66 (more than half) with intercepts
of 1.0 or less. There were 11 in the range of 1.1 to 1.5 making 48 out
of 66 (72%) having intercepts of 1.5 NM or less. There were 9 more in
the range of 1.6 to 2.0 making a total of 57 out of 66 (86%) having
intercepts of 2.0 or less. There were 7 in the range of 2.1 to 2.8 and
then the two outliers of 3.8 and 4.4 NM.

In addition to the normal shots, I also took a series of shots in the
middle of the night with the horizon illuminated by moonlight. On
November 3, 2009 at 18° 39' north, 40° 36' west between 0024 Z and 0039
Z I shot Fomalhaut, Deneb and Vega three times each. The intercepts were
0.3T; 0.3A; 1.3T; 1.5A; 1.5T; 1.6A; 2.5A; 2.6T; and 3.8A making the σ
2.08 for these 9 shots taken in the middle of the night! Have others
tried this?

I also took 3 observations of the upper limb of the sun at sunrise
without a sextant, just watching the top of the sun appear to pop up on
the horizon with just my Mark one eyeballs. The intercepts for these
observations were 3.0A; 4.7 T; and 0.6A, a σ of 3.93 NM, not as good as
with a sextant at higher altitudes but still a useful level of accuracy.

I am curious what others have found when they have done this type of
investigation.

gl

```
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