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    The cocked hat
    From: Robert Eno
    Date: 2004 Apr 3, 22:07 -0500

    I'll throw my two bits' worth in. I agree with Joel and in fact what he
    describes is more or less the method that I have employed for quite a few
    I'll take it a step further: I generally examine my intercepts before
    plotting them out, discarding the obviously wonky ones. I do, however,
    average out sights taken on land with a bubble attachment because bubble
    attachments are inherently inaccurate and in my experience, it is better to
    take multiple observations of a few stars and average them out.
    I was persuaded, some years ago, that the 3 star fix is overrated. Better to
    take two observations of two stars.  This is not an an original idea on my
    part: my inspiration comes from a little-known book -- Arctic Air
    Navigation -- by a former RCAF Air Navigator, Keith Greenaway:. In his book
    Greenaway writes:
    "Navigators who use asto continually prefer 2-star fixes with each star
    sighted twice, rather than 3 star fixes with each star sighted only once.
    Although an extra sight is required, time is actually saved, because only
    two stars have to be located, the course setting of the sextant changed only
    once, and the tables entered for two stars only. It is also easier to detect
    inaccurate computation or observation as shown in Fig. 27".
    Figure 27 shows two parallel LOP's spaced very closely and two parallel LOPs
    at right angles to the former, spaced far apart. The figure beside it shows
    a classic "cocked hat". The caption to the figure reads: "Comparison of a
    2-star and a 3-star fix. In the case of the 3-star fix, it is not obvious
    which sight may be in error, while in the case of the 2-star fix it is
    immediately apparent which star should be re-sighted or sight computations
    While it is true that I have quoted from a book pertaining to Air
    Navigation, I have used this technique, successfully both on land and at
    As for MPPs, I cannot argue with George and Herbert about the efficacy of
    performing the necessary statistical computations to arrive at this figure.
    I have read only a little on MPPs but I certainly agree that it is a very
    real and very valid concept. Nevertheless, for purposes of practical
    navigation, who is really going to perform this exercise while at sea? In
    reality, navigators will simply take the centre of the cocked hat or the
    intersection of two lines of position.
    I believe that the two times two star technique described by Greenaway is a
    reasonable compromise.
    ----- Original Message -----
    From: "Joel Jacobs" 
    Sent: Saturday, April 03, 2004 7:58 AM
    Subject: Re: The cocked hat, again. Was: "100 Problems in Celestial
    > In an off group exchange with Herbert Prinz, to which I have added a few
    > words to for clarity, I said this:
    > "It is really a matter of personal judgment. The navigator's selection of
    > MPP will vary as to how reliable or accurate the navigator thinks the
    > were based in the conditions he encountered when taking the sights. A
    > mathematical solution may not be appropriate."
    > I submit that this is what George is correctly introducing.
    > Let me add this thought. When I took the USCG Celestial Exam, year ago,
    > of the questions had a series of sights that when plotted, had one sight's
    > LOP distant from the others. If  you answered the question including that
    > sight in your calculations, even by averaging, you were wrong. If you
    > rejected it as a bad sight, you were right. As a matter of pride, I got
    > 100%. Of course I was a lot younger and sharper.
    > Joel Jacobs

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