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    Re: The cocked hat
    From: Henry Halboth
    Date: 2004 Apr 4, 00:15 -0500

    In my experience at sea, before other means of position finding were
    available offshore, conventional wisdom suggested the EFFORT to observe
    at least four stars (including planets), one each bearing respectively
    south, north, east, and west, or as close thereto as possible, so as to
    average out opposing horizon conditions. The sea horizon is seldom
    consistent at all points of the compass and discrepancies readily show up
    in utilizing this method - judgement being of course necessary in not
    using a portion of the horizon which may be obviously unsuitable.
    Obviously conditions do not always permit of such niceties and one must
    do what one can. It was, however, quite customary to pre-compute and
    observe at least five bodies, even if only to have a reserve in the event
    that some proved obviously in error, i.e, wrong body, poor horizon, time
    error, sextant reading error, etc. By the way, pre-computation is
    essential to accurate star sights - if you wait until you can see them
    it's too late to expect a good horizon on average, telescope power
    With a well calibrated sextant, a good horizon, the correct time, and
    careful calculation, "cocked hats" of any great significance or magnitude
    were not the usual thing - if they occasionally were, judgement as to the
    value of the individual sights and as to the reliability of the fix as a
    whole were seen as more of a consideration than efforts to calculate, by
    whatever means, an MPP. If two sights are correct and a third is in
    error, calculating an MPP by any method is not going to provide a more
    correct position, especially if one can be evaluated out. If it is a
    matter of serious concern, it seems the careful navigator will carry
    his/her (almost slipped on that one) reckoning forward from each
    intersection of the fix to insure s/he is not standing into danger -
    assuming of course a "cocked hat" of a magnitude requiring calculation of
    an MPP.
    Just thought I'd put my oar in.
    On Sat, 3 Apr 2004 22:07:05 -0500 Robert Eno  writes:
    > 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
    > years.
    > 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
    > checked".
    > 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
    > sea.
    > 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.
    > Robert
    > ----- Original Message -----
    > From: "Joel Jacobs" 
    > To: 
    > Sent: Saturday, April 03, 2004 7:58 AM
    > Subject: Re: The cocked hat, again. Was: "100 Problems in Celestial
    > Navigation"
    > > 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
    > an
    > > MPP will vary as to how reliable or accurate the navigator thinks
    > the
    > sights
    > > 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,
    > one
    > > 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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