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    Re: LOP by Sextant Box Shadow
    From: Gary LaPook
    Date: 2008 Jul 19, 16:52 -0700

    I remember one night in 1990 we were anchored in a
    long fjord on the east coast of Tahaa (an island about
    20 nm east of Bora Bora) and it was so still that I
    could see the stars reflected in the ocean around the
    boat. I got out my Tamaya and took a round of sight
    and got a fix that crossed on our anchorage.
    On Jul 19, 3:38 pm, Lu Abel  wrote:
    > In a similar vein, once on a very clear, calm night I looked aft of my
    > boat and saw a crystal-clear image of the moon on the water.   I
    > wondered if I could use the image as one would in an artificial
    > horizon.  I grabbed my sextant and tried it.  The result was pretty
    > reasonable -- my sight was off by about 10 miles, which I attributed
    > more to night vision challenges and/or my own shaky hand than
    > difficulties with the concept.
    > Lu Abel
    > frankr...@HistoricalAtlas.net wrote:
    > > Greg, you wrote:
    > > "My sextant box was sitting before me on the dock casting a shadow.  Could
    > > this shadow provide me with a LOP? The answer is yes. The inverse tangent of
    > > the sextant box height divided by the length of the cast shadow generates an
    > > hs. "
    > > The limiting factor in these sights is determining whether the surface is
    > > level. It would be interesting to test some built surfaces (houses, docks,
    > > parking lots, etc.) and find out what sort of typical scatter there is in
    > > leveling. When I was growing up, the scatter for dock surfaces was five
    > > degrees at least with some outliers at 20 degrees tilt, but they build 'em
    > > better now. :-)
    > > And you wrote:
    > > "I wasn't sure whether to treat this hs as an upper or lower limb so I just
    > > did the reduction as an upper limb to see what would happen."
    > > You can figure out which limb is associated with the different parts of the
    > > shadow by imagining what an ant would see. Imagine an ant behind the box
    > > where the Sun is completely concealed. As it crawls out (in a direction away
    > > from the Sun), it encounters a little "penumbral band" where the shadow
    > > tansitions from fully dark to fully light. If the ant looks over his
    > > shoulder just as he enters the penumbral band, he will see the Sun's upper
    > > limb just appearing. When he is dead center in the penumbral band, he will
    > > see the center of the Sun just clearing the top of the box. And as he
    > > finally exists the penumbra, he sees the lower limb of the Sun just clearing
    > > the top of the box. You can try this yourself with the shadow of a building.
    > > The order is reversed, of course, when the shadow is being cast by an
    > > overhanging eave.
    > > Shadow fringes and spots of light on the ground under trees contain some
    > > interesting information. Since the Sun's angular diameter is nearly
    > > constant, the width of the shadow fringe, or penumbral band, is related in a
    > > simple way to the distance between the object casting the shadow and the
    > > shadow itself. An angle of 32 minutes of arc is a ratio of 107:1. So if I
    > > see a tall building casting a shadow with a penumbral band that is five feet
    > > wide, then the portion of the building creating that portion of the shadow
    > > would be about 535 feet away. Note that you have to measure the shadow width
    > > in a direction that is perpendicular to the light rays from the Sun. If the
    > > shadows are faint or confused, you can do this also by walking back and
    > > forth. Find the spot where the Sun's limb first appears. Then walk until the
    > > whole disk of the Sun is clearly visible. The distance between those two
    > > places, multiplied by 107, gives the distance to the object in question.
    > > Similarly, if you're walking down a shaded sidewalk and you see circles of
    > > light on the ground along your way, each of those circles is a simple image
    > > of the Sun created by small gaps in the foliage above you. The gaps are not
    > > circular. It's the Sun's circular disk that makes the circular patches of
    > > light (and during a partial solar eclipse, you would find that the images
    > > match the partially obscured Sun). As with the penumbral shadow fringes, the
    > > distance to the gaps in the foliage creating the patches of light can be
    > > determined by multiplying by 107. This is an easy way to get the height of a
    > > tree. You find the end of the tree's shadow and then you look for the first
    > > few circular sun images inside the main shadow --they're created by gaps in
    > > the foliage near the very top of the tree. A little geometry then converts
    > > that slant distance to height. I figure it's accurate to about +/-10%
    > > without detailed measurements.
    > >  -FER
    > > PS: works with the Moon, too.
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