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    Re: Navigation in Fog
    From: Gary LaPook
    Date: 2007 Feb 17, 18:13 -0800

    To follow up on my previous post about the "sky compass."
    As an experiment I cut out a small rectangle of celophane and laid it
    on top of a polaroid camera filter. I then balanced this on top of my
    astro-compass and placed a small mirror below it so that I could look
    through the celophane-polaroid filter combination up at the zenith. I
    used the astro-compass because it has a base that can be leveled and
    it rotates against an azimuth scale so that I could make  accurate
    readings. I waited for the sun to be setting and then rotated the
    astro-compass to cause the light to match on the filter and celophane.
    This match point is very distinct. Rotate it slightly to the right and
    the celophane portion is darker than the uncovered part of the filter,
    too far left and the celophane was lighter than the other part. By
    rotating the compass both right and left and reading the azimuth at
    the match point I determined that the repeatabliity of this reading
    was plus or minus only two degrees, close enough for practical
    navigation. If anyone is intersted I took some pictures of this
    operation and I could scan the relevant pages from H.O. 216. and could
    send them to you.
    Gary LaPook
    On Feb 17, 10:50 am, "Marcel Tschudin" 
    > I could imagine that this information would be useful for the authors
    > of the paper. Of interest to me would be how such a "sky compass"
    > would look like manufactured with the skills of the Vikings.
    > The article which I read was written by one of the co-authors and
    > appeared in a Swiss newspaper. For those of you who are interested
    > (Wolfgang?), you can find it herehttp://www.nzz.ch/2007/02/14/ft/articleEV4VN.html
    > Marcel
    > On 2/17/07, glap...@pacbell.net  wrote:
    > > This technique was used in the "sky compass" (invented in 1948) which
    > > mounted in the sextant mount of aircraft for polar navigation. It
    > > works by determining the polarization of light directly overhead, at
    > > the zeneth, which then shows the azimuth to the sun even though the
    > > sun is not visible and possibly several degrees below the horizon.
    > > These "twilight periods" can last for weeks in high latitudes. The
    > > sky compass is completely discribed in "Air Navigation" H.O. 216
    > > (1962) and is also mentioned in "Bowditch" (1962.)
    > > You can experiment and see how it works. Get a polarizing filter,
    > > either for a camera or a polarized sun glass lens. Hold it overhead,
    > > looking through it at the zenith and rotate it in azimuth and you will
    > > see the sky alternately lighten and darken as the polarizer
    > > alternately lines up with the polarization axis of the sun light, it's
    > > azimuth, and then crosses it. The light and dark points are 90º apart.
    > > Although this can give you a general azimuth to the sun the change in
    > > intensity is hard to judge accurately. So the next step is to get a
    > > piece of cellophane from a craft shop (or they may still use it on
    > > cigarette packs). Cut a piece to cover half of the poarizer and place
    > > it on top of the lens, between the lens and the sky, then try the
    > > experiment again. The two halves of the view through the polarizer
    > > will lighten and darken out of phase with each other. (You may have to
    > > try different orientations of the cellophane.) You will find four
    > > points where both sides will be the same intensity and this is very
    > > sharp and can be judged accurately but this causes a 90º ambiguity. By
    > > adjusting the orientation of the cellophane you will end up with four
    > > match points but two will be darker than the other two. This leaves
    > > you with an easy to manage 180º ambiguity.
    > > It works.
    > > Gary LaPook
    > > On Feb 14, 7:40 pm, "Peter Fogg"  wrote:
    > > >  Marcel Tschudin wrote:
    > > > > Just read in German a summary on a published paper. The author(s?)
    > > > > investigate(s) whether it was possible for the Vikings to use the
    > > > > polarised light of the sky for navigation, this with the help of the
    > > > > "sun stone" (Sonnenstein). Those of you who are interested in this may
    > > > > read the original paper in English:
    > > >  Polarising filters can indicate the direction of the sun, even under
    > > > overcast skies, and have proved useful for this, especially in Arctic
    > > > regions.
    > > > Here is that abstract, 
    > > > *Abstract:*
    > > > In sunshine, the Vikings navigated on the open sea using sundials. According
    > > > to a widespread hypothesis, when the Sun was occluded by fog or clouds the
    > > > Vikings might have navigated by skylight polarization detected with an
    > > > enigmatic birefringent crystal (sunstone). There are two atmospheric optical
    > > > prerequisites for this alleged polarimetric Viking navigation under
    > > > foggy/cloudy skies: (1) the degree of linear polarization *p* of skylight
    > > > should be high enough and (2) at a given Sun position, the pattern of the
    > > > angle of polarization *α* of the foggy/cloudy sky should be similar to that
    > > > of the clear sky. Until now, these prerequisites have not been investigated.
    > > > Using full-sky imaging polarimetry, we measured the *p*- and *α*-patterns of
    > > > Arctic foggy and cloudy skies when the Sun was invisible. These patterns
    > > > were compared with the polarization patterns of clear Arctic skies. We show
    > > > here that although prerequisite (2) is always fulfilled under both foggy and
    > > > cloudy conditions, if the fog layer is illuminated by direct sunlight,
    > > > prerequisite (1) is usually satisfied only for cloudy skies. In sunlit fog,
    > > > the Vikings could have navigated by polarization only, if *p* of light from
    > > > the foggy sky was sufficiently high.
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