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    Re: dip, dip short, distance off with buildings, etc.
    From: George Huxtable
    Date: 2006 Jan 7, 21:40 -0000

    Frank Reed wrote-
    | In Bowditch and elsewhere, there are formulas  for dip, dip short, Table XV
    | for distance based on measured height, maximum  visibility distance, etc., and
    | they all have various mysterious corrections for  "mean refraction". I've got
    | this stuff all figured out pretty well now, and it  turns out that there is a
    | really easy, though somewhat bizarre (!), way of  thinking about the effect of
    | refraction in terrestrial, or coastal navigation,  situations.
    | You can calculate dip or the altitude of a tall building  peeking up from
    | beyond the horizon using straight Euclidean geometry and  trigonometry ignoring
    | refraction completely. Then to include refraction, you  simply change the
    | radius of the Earth from R to R/(1-x) where x depends on the  temperature gradient
    | of the atmosphere. On average it's about 0.15 but it can  easily be anywhere
    | in the range 0.13 to 0.17 and sometimes it's as low as 0 or  as high as 1.0
    | (temperature inversions yield higher values of x).
    Comment from George;
    That's a perfectly valid way to assess refraction, but not a particularly new one. Indeed, in the
    very latest issue (Jan 2006) of the Journal of Navigation, which arrived in the post this morning,
    there's a short letter from F A Kingsley. This deals with the accepted formula for distance of the
    radio horizon between two elevated antennas. He is considering AIS (Automatic Identification of
    Ships) which employs channels in the Marine VHF band, at about 160 MHz as I remember. In that case,
    the cutoff figure that he uses is based on an enhancement of the Earth's radius from R to 1.3R,
    which is presumably the result of atmospheric refraction (though diffraction may play a part).
    Refraction varies with frequency, so it's no surprise that the enhancement of R by a factor of 1.3
    (or 30%) might differ from Frank's suggested figure for light, which amounts to 15 to 20%.
    It's of interest that the same technique of considering refraction, by enhancing the Earth radius
    appropriately, is applicable in such different circumstances.
    Frank went on to add-
    | This  works perfectly to derive the equations in Bowditch for dip, dip short,
    | Table  XV, and apparently everything else where terrestrial refraction is
    | involved.  Details upon request...
    I think the phrase "apparently everything else where terrestrial refraction is involved" is an
    overstatement. It's only concerned with refraction near to the horizon, and deals with the density
    gradient in the lower levels of the atmosphere. There's no relevance that I can see to calculating
    refraction of light that arrives at a large angle above the horizon, if I understand it correctly.
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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