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    Re: Still on LOP's
    From: Peter Fogg
    Date: 2002 May 6, 08:46 +1000

    George Huxtable wrote:
    > I have some progress to report.
    > I have implemented a simulation of the "cocked hat" problem on my old Mac,
    > .... and has
    > confirmed that in 500 rounds of simulated bearings, the cocked hat embraced
    > the true position 133 times, and failed to do so 367 times. Close enough to
    > 1 in 4, statistically speaking.
    > ...If you have a significant compass error .. this will
    > displace all your bearings by the same amount in the same direction ...
    > must expand the average size of your cocked hat. If this systematic
    > compass error is greater than the scatter in the bearings, then EVERY
    > bearing would be in error in the same direction, and EVERY cocked hat must
    > then contain the true position. That would make Peter Fogg happy, but the
    > price to pay is that every cocked hat is correspondingly larger. Of course,
    > that doesn't conflict with my 1 on 4 contention, because the explicit
    > assumption there is that clockwise and anticlockwise errors must be equal
    > in number: not true when there's a systematic compass error.
    This is a masterful response, and I congratulate George on it. It seems to
    contain something for everyone, we should all be (at least partially) happy.
    On the one hand we have his computer simulation that he reports confirms his
    25% theory, and on the other he also confirms the 'enlarged hat' phenomenon,
    itself a variation of 'smudged lines'.
    We can all wish him sunny days in the Azores and hope he returns to the nav.
    list refreshed and as sharp witted as ever.

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