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    Re: Line of Position Fix
    From: Lu Abel
    Date: 2012 Oct 18, 16:18 -0700

    I totally agree on taking a run of sights.  I know of no text (either standard ones such as Dutton's or celestial navigation specific texts) that doesn't suggest this.  Some books even suggest plotting them on graph paper; where a consistent rise or fall in the curve and "outliers" are easily spotted.  In fact one can push beyond that and do a least-squares fit of a line to the data (impracticable in real life, but gives the mathematicians joy). 

    I also agree with "the more, the merrier" implied in your quote from Dutton's.  I think that a "starburst" of LOPs will quickly show any LOPs that are outliers and should be eliminated.

    But nowhere in Duttons can I find a suggestion that one not trust two LOPs or that one's position must be in the center of the cocked-hat formed by the intersection of three LOPs.     And there was heated discussion on this list about the latter, starting with the simple fact that if one assumes there's a 50/50 chance of one's true LOP being on one side or the other of the plotted LOP then there's only a 1 in 8 chance of the fix being inside the cocked hat.

    Last but not least, Debra said she's a beginner in celestial navigation.  I've taught a lot of beginners and in my experience it's a whole lot easier to help them see the magic of celestial when they can start with sights taken during daylight (ie, sun or moon).  I remember when I reduced my first sight 30 years ago (a sun shot) and I felt like Christopher Columbus when I reduced to an LOP only a mile or so from my KP!   (Okay, no list comments on the fact that Columbus didn't practice celestial, I only learned that later)

    Celestial has a steep learning curve -- handling the sextant properly, reading it properly (especially the vernier), measuring IE, bringing a body down correctly, rocking the sextant, etc, etc, not to mention timekeeping, and sight logging.  (In the last celestial class I taught we did Sun shots three hours apart and the second set of sights was for almost every student better than the first set for consistency and closeness to our KP).   So why make it more difficult by insisting that even a beginner has to take shots at twilight?

    My 0.0153 Euro's worth.


    PS - my Dutton's, which is the 1976 edition, seems to have lost a chapter -- your quotes are in my paragraph 2509.   Any reader have an idea what was dropped between 1972 and 1976?

    From: Brad Morris <bradley.r.morris@gmail.com>
    To: NavList@fer3.com
    Sent: Thursday, October 18, 2012 3:07 PM
    Subject: [NavList] Re: Line of Position Fix

    Hi Lu
    Dutton's Navigation & Piloting
    Twelfth Edition
    Naval Institute Press
    PARAGRAPH 2609
    A fix is obtained when two or more lines of position are crossed,adjusted to a common time. ... At twilight, in clear weather, he will observe a minimum of five stars, well distributed in azimuth.  He will make 3 observations of each body. ... This gives a check on the consistency of observations and therefor their probable reliability.
    End quote
    The purpose of taking 15 observations of 5 bodies is to provide a more reliable fix, consistent for each body (3 observations), and consistent among bodies (5 stars). 
    If it was good enough for US Navigational Officers at the height of celestial navigation, then that's good enough for me.
    In deference to your considered opinion, you may follow the practice you see fit.
    Brad Morris
    On Oct 18, 2012 5:42 PM, "Lu Abel" <luabel@ymail.com> wrote:
    I agree that even on land LOPs are likely to be off by a mile or even more and so fixes have that uncertainty; it's just the nature of celestial navigation.

    But I have to question the claim that getting three LOPs will give a better fix.  As someone pointed out in a discussion on this list a few years ago, there's only a one in eight chance of a fix even being inside the cocked hat and there's no certitude at all that the fix will be in the center of the hat.

    From: Brad Morris <bradley.r.morris@gmail.com>
    To: NavList@fer3.com
    Sent: Thursday, October 18, 2012 12:45 PM
    Subject: [NavList] Re: Line of Position Fix

    Hi Debra
    The best two times of the day are the civil twilights.  Those are just before dawn and just after sunset.  The best bodies to use are the 57 navigational stars.
    Just as a note, you will want 3 bodies in your fix.  It is unlikely that 2 LOPs will cross at your position, in general, and 3 will produced a 'cocked hat'.
    Best Regards
    Brad Morris
    On Oct 18, 2012 3:23 PM, "Debra Hillman" <wombatroo@hotmail.com> wrote:
    Could somebody help me with my problem . I am learning on my own at present from books on celestial navigation.I need to get a fix with two lines of position but not sure which celestial body other than the sun and the best times of the day to achieve the fix.

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