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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Greg Rudzinski
Date: 2014 Nov 13, 07:53 -0800
Gary,
To get you introduced see this link to my blog on the Doniol sight reduction method using sin, cosine, and haversine tables.
https://gregrudzinski.blogspot.com/2014/06/longhand-sight-reduction.html
Hanno Ix has modified the original formula so that just haversines are used thus only a single table is needed to derive the zenith distance. My contribution is the formating of the modified haversine Doniol formula into a 2 column reduction for practical use. There are three natural haversine look-ups for L+d,L-d,LHA and a natural arc haversine look-up for zenith distance. No logs are used. There is a single multiplication step done longhand. There are five summing steps.
L
d (A) (B)
L+d Hv Hv
L-d +Hv +P
1-sum Arc Hv sum
sum ZD
LHA * Hv Hc
P
L=latitude, d=declination, Hv=haversine, LHA= local hour angle (converted to meridian angle for LHA>180°), P=product, ZD=zenith distance, Hc=calculated altitude
Greg Rudzinski
