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    Re: Range by height beyond the horizon
    From: Greg Rudzinski
    Date: 2009 Nov 16, 16:03 -0800

    Sounds very familiar ;-)
    A good explanation of ranging beyond the horizon is described by US
    Navy Captian H.H. Shufeldt in his book SLIDE RULE FOR THE MARINER on
    page 29:
     "In clear weather , an object such as a mountain, can be seen even
    when it is well beyond the horizon. If its height is known, its
    approximate distance can be determined with a sextant. The first step
    is to correct the sextant altitude for any index error, for the dip of
    the horizon, and for refraction. For this purpose refraction is found
    by dividing the estimated distance in nautical miles by 13.75 : it is
    obtained in minutes and tenths of arc, and subtracted from the sextant
    altitude. Next, correction must be made for the curvature of the
    Earth. This is done by multiplying the square of the estimated
    distance in nautical miles by .907 ; the product, which is in feet,
    has to be subtracted from the height of the object. The corrected
    height is then divided by the corrected sextant altitude, stated in
    minutes of arc, and the quotient is multiplied by the factor .566 to
    obtain the distance in nautical miles. When the distance thus found
    varies considerably from the estimated distance used to obtain the
    refraction and in correcting for the curvature of the Earth, the
    problem should be reworked, using the distance found as the estimated
    On Nov 16, 2:29�pm,  wrote:
    > Here's a story from USS Growler, the diesel sub formerly armed with nuclear 
    cruise missiles, now a museum ship in New York City:
    > "Growler's first deterrent patrol began on 12 March 1960. [...] Lieutenant 
    John J. "Joe" Ekelund, Executive Officer and Navigator, developed an 
    innovative method to determine the submarine's position in the assigned 
    operating area. The technique was quite simple and similar to that used by 
    submarines to determine the range of a target ship. Using navigation charts, 
    Ekelund identified mountain peaks and their height as listed. He then 
    observed the mountain through the periscope and, utilizing the built-in 
    periscope stadimeter, he could superimpose the image of the base of the 
    mountain on its peak. This double image and known peak height provided a good 
    approximate range to the mountain that was read on the stadimeter dial. Using 
    the range so determined, one can could calculate the amount of height which 
    was not seen (was below the horizon) and correct the charted height to the 
    observed height. Using the observable height a second, more accurate range 
    could then be measured. Three iterations of this sequence would yield a 
    navigationally useful range. Using more than one peak, he could accurately 
    determine his position. "
    > That should sound familiar! Greg?
    > -FER
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