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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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