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    Re: Which Cocked Hat?
    From: Frank Reed
    Date: 2019 Aug 4, 12:27 -0700

    Bill L, you wrote:
    "I would suggest taking a point on the elliptical probability contour closest to the danger would make some sense rather than the corners of the cocked hat."

    Yes. Or just draw the error ellipse and use that. In addition, if there are dangers ahead, double it. Usually the error ellipse is drawn for some moderate level of risk, maybe a one standard deviation ellipse, which still leaves a not insignificant probability of being outside. So when at risk, move to the two s.d. ellipse. The ellipse is better because it's what the sights are really telling us. The analysis "dissolves" the lines of position and their crossing points and replaces them with a family of nested error ellipses. This point of view also emphasizes that the most probable position is only the center of the ellipses. It's not that a vessel is much more likely to be near that m.p.p. -- but rather the "thumbprint" on the chart should be centered there.

    The old method, described tepidly as "customary", a very weak recommendation, in vol.III of the Admiralty Manual (1938 edition) was a hack (a hack in one of the modern senses of the word). It was a bit of ritual to let navigators feel like they were doing something clever. I'll reiterate, though, that the hack did make sense in that one circumstance I described previously: when we have three lines of position, and a very wide triangle which makes it likely that one sight was a blunder, a serious mistake and should be thrown out, but somehow we don't know which of the three is bad. That leaves us with three possible two-line fixes and picking the one that will get you into trouble is a safer choice. Obviously it would be vastly preferred to get more bearings, in a piloting situation. Even more obviously, in the modern world, this is the moment when you stop playing olde-time navigator and you switch on the first GPS device you can find.

    Frank Reed

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