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
To get you introduced see this link to my blog on the Doniol sight reduction method using sin, cosine, and haversine tables.
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.
d (A) (B)
L+d Hv Hv
L-d +Hv +P
1-sum Arc Hv sum
LHA * Hv Hc
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