A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2015 Jun 21, 15:29 -0700
Andrés Ruiz correctly points out that there is an ambiguity in the azimuth when using the Hanno diagram but this is not really a problem when actually navigating, only a problem when doing practice computations in your living room.
I posted this before:
We realize that in most situations there is no ambiguity as to which quarter the Zn lies since you know the approximate direction you are looking when you take the sight, The problem arises when the azimuth angle is limited to the range of zero to 90 degrees and the Zn is near 90 degrees or 270 degrees in which case the correct Zn might fall either side of the line so there is an ambiguity in converting from azimuth angle to Zn. (Example based on being in the northern hemisphere.) One easy rule to apply first is that if the declination is greater than the latitude then the azimuth can never be in the southerly semicircle. This rule handles the case Bob found since the declination was 56 N and the latitude was 41 N. To generalize this rule, if the declination has the same name as the latitude and the declination is greater than the latitude, then you start with the direction of the elevated pole (the nearer pole) when converting from azimuth angle to azimuth (Zn.) The second rule to apply is that if the declination is south then the Zn can never be in the northern semicircle. To generalize this rule, if the declination and the latitude have contrary names then you start with the direction of the depressed pole (the further pole) when converting from azimuth angle to Zn. These two rules take care of most of the cases, especially for navigators in low latitudes. The remaining ambiguity concerns situations in which the declination is the same name as the latitude but is less than the latitude. In this situation the azimuth of the body will be both north and south of the east - west line during part of each day.
The same problem exists when using the Rust diagram and Rust provided an auxiliary diagram which is used to resolve the ambiguity. I posted the Rust diagrams here:
Look at the auxiliary diagram to determine when the body is on the prime vertical.
Here is a better copy of the main Rust azimuth diagram: