NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andreas K
Date: 2014 Apr 22, 06:09 -0700
Hi Greg,
haversine is half of 2*sin^2(1/2*x). This versine equation was introduced to navigation, as far as I can see, by Cornelis Douwes 1747 with his method for finding latitude by two altitudes of the sun and the elapsed time. You can find the logs of this equation in the Tables Requisite 1767 and later. Here it is called "Log Rising". It was also used to determine the local apparent time using the formulae
2*sin^2(1/2*LHA) = (cos(B-Dec) - sin(Alt))/(sin(B)*cos(Dec))
with B=90?- Lat.
An early table of haversine you can find in David Thomson's Lunar and Horary Tables 1831. Using the formulae
sin^2(1/2*LHA) = (cos(1/2*(P + Lat + Alt))*sin(1/2*(P + Lat - Alt)))/(sin(P)*cos(Lat))
with P=90?- Dec.
For some years I made both tables very simple and quick with Excel (see att. files). Since then I used them with much fun and success. So I am curious what method you use to compute your tables!
Kind regards
Andreas
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