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    Re: The cocked hat
    From: Joel Jacobs
    Date: 2004 Apr 4, 15:02 -0400

    George Huxtable,
    You write so well, and your logic always sounds so reasonable, but I have to
    disagree with your theory that the horizon's visibility is the same around
    the clock.
    Here is a definition of visability from the Weather Network
    and then a similar one from a Vessel Reporting form. It seems I'm not alone
    in thinking that visibility can vary with azimuth. Something to mull over.
    The second site seems to have content pertanent to this group's subject.
    Visibility is defined as the greatest distance an object can be seen and
    identified. It is usually a visual estimate and is reported as prevailing
    visibility - the maximum visibility common to one half or more of the
    horizon circle. When visibility is uniform in all directions, prevailing
    visibility and visibility are the same. When visibility is not uniform in
    all directions, determine prevailing visibility by dividing the horizon
    circle into sectors of visibility. Estimate the highest visibility common to
    one half or more of the horizon circle.
    Go: http://athurtubise.com/weather_main.php
    Prevailing visibility Nautical miles This is the "maximum visibility common
    to one half or more of the horizon circle".
    Go: http://www.pangolin.co.nz/index.php
    Joel Jacobs
    ----- Original Message -----
    From: "George Huxtable" 
    Sent: Sunday, April 04, 2004 12:09 PM
    Subject: Re: The cocked hat
    > Robert Eno wrote-
    > >I was persuaded, some years ago, that the 3 star fix is overrated. Better
    > >take two observations of two stars.  This is not an an original idea on
    > >part: my inspiration comes from a little-known book -- Arctic Air
    > >Navigation -- by a former RCAF Air Navigator, Keith Greenaway:. In his
    > >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
    > >once, and the tables entered for two stars only. It is also easier to
    > >inaccurate computation or observation as shown in Fig. 27".
    > >
    > >Figure 27 shows two parallel LOP's spaced very closely and two parallel
    > >at right angles to the former, spaced far apart. The figure beside it
    > >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
    > >checked".
    > =============
    > Some comments come to mind here.
    > What if Robert had identified a wrong star (for example)? If so, no doubt
    > he would make the identical error on his second try, so everything will
    > SEEM perfectly consistent, a dangerous state of affairs. His technique
    > provides little cross-checking. There are many other likely sources of
    > error, which are likely to be exactly repeated if the first measurement is
    > simply measured again.
    > We have to remember that air navigators live under different constraints
    > those of us who sail. They are travelling so fast that unless they can
    > produce a quick answer, it may already be too late. On the other hand,
    > those of us that sail small vessels usually have plenty of time to put the
    > kettle on for a cup of tea, before we get round to tackling sight
    > reductions.
    > Why do we take a number of star observations, in that short twilight at
    > dawn and dusk? Well, partly because they are there, and we can, and they
    > can provide a good instantaneous fix. In the daytime, we have to use the
    > Sun, and as there is unfortunately only one Sun, we have to make do with
    > that, using transferred position lines as it moves round the sky.
    > But there's a more subtle reason. Generally speaking, the biggest error in
    > an altitude observation is not in our sight of the body itself, but in the
    > horizon, that we measure it up from. Except in a small vessel in heavy
    > weather, the biggest unknown in the position of the horizon is the dip.
    > Part of this dip is just due to geometry, the curvature of the Earth and
    > the height of the observer's eye, and that presents no problem. But
    > part comes from the bending of light rays as they skim just above the sea
    > from the horizon to the eye, which can be greatly influenced by
    > gradients close to the sea surface. It can vary from its normal value by
    > 2, or occasionally several minutes of arc, in either direction. When this
    > is bad, we call it "anomalous dip". If there's a ship to be seen on the
    > horizon, its image may be distorted by a "mirage" effect in an extreme
    > case, but often there is no way to know that anomalous dip is occurring.
    > However, anomalous dip is usually the same at all azimuths, so if it's
    > possible to observe three stars with azimuths 120 degrees apart (or nearly
    > so), the intercepts will be affected in such a way that the centre of the
    > resulting cocked-hat will not be displaced by anomalous dip. It's not
    > possible to treat Sun altitudes in that way.
    > This is exactly contrary to Joel's argument, in which he said-
    > >As everyone knows, the
    > >horizon at sea's definition varies with the direction you are looking due
    > >differences in light, sea conditions and cloud cover. Therefore, you have
    > >variables with which Greenway is not confronted since his horizon is a
    > >constant.
    > The reasoning I have presented above relies on the SAMENESS of the
    > behaviour of the atmosphere in different directions, not on its
    > Of course, from the air with a bubble-sextant, the dip of the horizon is
    > irrelevant.
    > George.
    > ================================================================
    > contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    > 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    > Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > ================================================================

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