Modern Haversine Sight Reduction

The cosine haversine Doniol sight reduction formula can be written as an all haversines formula to create the Modern Haversine Method of sight reduction. Only a single natural haversine table is needed and there are no special case rules.

http://fer3.com/arc/m2.aspx/Natural-Haversine-5-Place-Table-PDF-Rudzinski-jan-2017-g37790


Formula:

hvZD = n+[1-(n+m)](a)

Same Name
n = hv (L-d)
m = hv (L+d)

Contrary Name
n = hv (L+d)
m = hv (L-d)

L = Latitude
d = Declination
t = Meridian Angle
a = hv(t)
hv = Haversine
ZD = Zenith Distance
Hc = (90 - ZD) Calculated Altitude




Precision is 1' when done longhand to 4 places using natural haversines (see attached example). Azimuth is quickly done using the Ix graph (attached). A water resistant calculator watch such as the Casio CA 53W will make for ultra compact quick 5 place 0.1' precision as well as precise timing of observation. An Otis King slide rule will serve for quick non electronic 4 place precision.