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Frank,

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
distance"

Greg

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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