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    Re: A noon fix inland with an peri-sextant
    From: Antoine Couëtte
    Date: 2018 Jan 7, 11:23 -0800

    Dear David,

    Thanks for your Noon Fix published on Dec 18th, 2017 which I could take adequate time to solve and study through a pure numerical "number crunching" approach this afternoon.

    I decided to perform all computations twice, with each full computation involving some 400 keystrokes. When it comes to manually keying in so many numbers that's the definite weakness of such numerical methods compared to graphic solutions such as yours or to folded paper solutions as advocated by Frank (posted on Dec 19th, 2017).

    Since I got identical numerical results between both full computations - and I am not sure I was ready for a third full sequence - here are these results:

    • Sun Local Apparent Noon (LAN) occurs at 11h59m00s, i.e. exactly your own result, which translates into an Observed Longitude of W000°34.5' . I am also getting an Observed Latitude of N53°07.6' which is 2.6 NM South from your published GPS Position (N53°17.2' and W000°32.3').
      • Your Observations "scatter noise" is 0.7 NM which I think is really excellent for a bubble sextant. It translates into a Latitude uncertainty of +/- 2.8' (4σ)  and a Longitude uncertainty +/- 12.6 ' (4σ) i.e. into +/- 7.6 NM East or West from true Position given your Latitude. Both such uncertainties are consistent with your published GPS position.
        • I also cared for scrutinizing the Time difference between LAN and Culmination and found it to be below 2 seconds of time, hence almost negligible in practice. I also computed this value through the Formula given in my 21 Dec post, to end up with an identical numerical result (Culmination Time - LAN Time = -1.7 s).

    I would therefore conclude here that :

    • Given your quite high number of sights (31 in total), a folded paper solution or a graphic solution is certainly a less risky approach than manually keying so many data. And :
    • All 3 methods - the Numerical, the Folded Paper and the Graphic ones - yield or would yield quite similar results when solving this case. Interestingly enough, the Longitude numerical determination is more accurate that the Latitude determination, probably because you "eyeballed" the Sun Center here, which also translates into your data set (e.g. shots 10 to 14). Most often, Longitude determinations are less accurate than Latitude determinations (as per the "4σ story" here-above).  And last but not least :
    • Your peri-sextant observations set is really excellent as it positions you within only 3 miles from your GPS Position. There are many cases when we do not or cannot perform equally well at sea from LAN Observations. Well done !
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