Not sure whether this has been noted previously but both the 1995( http://fer3.com/arc/imgx/bowditch1995/chapt22.pdf ) and 2002 ( http://fer3.com/arc/imgx/Bowditch-American-Practical-Navigator-2002-(2004).pdf ) editions of Bowditch give the following formulas for the distance to the visible in nautical miles
D = 1.17 sqrt(
hf), or
D = 2.07 sqrt(hm)
depending upon whether the height of the eye of the observer is in feet (hf) or meters (hm).
Given that hf = 3.281 hm, the second equation is not consistent with the first and should actually be D = 2.12 sqrt(hm). This doesn't seem to be just a simple typo. The formulas above are however what you get using the conversion hf = pi hm
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