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    Re: Review of the Longhand Haversine Sight Reduction method
    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:

    http://fer3.com/arc/img/103383.rust%20diagram.pdf

    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:

    http://fer3.com/arc/imgx/Rust-diagram-left-part.pdf

    http://fer3.com/arc/imgx/Rust-diagram-right-part.pdf

     

    gl

     

     

     

     
       
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