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    Re: good data from bad
    From: Eric Haberfellner
    Date: 2001 Dec 06, 11:14 AM

    A detailed description of this technique  (called Slope Fitting) can be
    found at the StarPath site at:
    -----Original Message-----
    From  Navigation Mailing List
    Sent: Thursday, December 06, 2001 10:48 AM
    Subject: good data from bad
    How to Turn a Series of Doubtful Observations Into an Excellent One.
    Sounds too good to be true, doesn't it. Let's start at the beginning.
    Making observations of celestial objects from the deck of a small boat
    out at sea, which never stops moving, using a horizon that is bobbing up
    and down, often as it is quickly getting too dark or too light, can be
    The conventional wisdom is to:
    1. Make a series of observations of the same body and average them out.
    But if one or two of them are wildly out (and we'll go into why that
    might be a little further on) then those wrong ones will ensure that the
    average will not be correct, even if most of the others are not bad.
    2. Make observations of many bodies. But this gives you lots of sight
    reduction to do, and I find it confusing to have lots of lines on the
    plotting sheet. For me, 3 lines of position is the right number.
    There is another way, one I've never come across anywhere else.
    It does add another step to the process, and some simple plotting on a
    graph sheet.
    First you make as many observations of the same body as you can during a
    5 minute period, or less, noting the changing Hs and times. Repeat this
    with your other bodies. Back at your Nav desk, calculate the change in
    altitude of your body in 5 minutes, according to its azimuth and your
    Latitude. This gives you a figure, say 30', either ascending or
    descending. This you draw on the graph paper as a straight line. Its
    actually an arc, which is why you shouldn't extend it beyond 5 minutes.
    The vertical side is altitude, the horizontal is time, the 5 minute
    period. Plot your observations as points.Then you draw a line parallel
    to your 'change of altitude' line which best fits your observations.
    Hopefully most of them will be fairly close, just above and below the
    You might have one or two that are wildly out. These you can ignore, so
    they won't pollute the others - but take another look, first. Are they
    exactly 1 minute of time out, or maybe 1 degree ? Its easy to write down
    the wrong minute, while you're concentrating on the seconds, or read the
    wrong degree, while you're peering at the micrometer drum. It may be you
    can adjust these to join the others. You can't do this by just looking
    at the numbers written down, it only becomes clear when its plotted, and
    becomes a picture.
    Then you take any point along this observation line and read off to the
    left the altitude, your Hs, and down to the time. For convenience you
    might choose a whole degree or minute of time, or any other point you
    like along the line. Then do your sight reduction and plotting as usual.
    I find it works well, and gives me feedback on how good or bad my
    observations are. You can end up with an observation which is better
    than any of the ones you actually made.
    I didn't invent this; it comes, complete with the required forms and
    graphs ready to be photo-copied, from a book 'The Complete On-Board
    Celestial Navigator', by George C Bennett. Its not a big book, but also
    includes a 5 year almanac and sight reduction tables, and much else
    besides - its supposed to be 'Everything But the Sextant' ! Published by
    International Marine, ISBN 0-07-007110-1. Its available in the USA and
    in Australia, and I don't know where else. There is also a web site,
    Peter Fogg

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