Welcome to the NavList Message Boards.

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    Name or NavList Code:
    Email:
       
    Reply
    Re: Nav exercise - ex-meridian
    From: Jeremy C
    Date: 2008 May 21, 00:54 -0700

        The purpose of the ex-meridian was to get a latitude line even if the
    body was obscured at the actual time of meridian passage in the days
    before accurate time pieces were the norm.  With an ex-meridian, you
    have to double interpolate the tables to get the �a� factor, even if
    you use the formula C=a*t^2/60 to get the actual correction.  I am not
    fond of this sight, and will just as soon not shoot an LAN then do an
    ex-meridian of one.  In my opinion, ex-meridians are next to useless
    these days at sea and are really only a good academic exercise.
    Frankly, in real life, I will just run a sunline calculation which
    would take me far less time, even if I did it by tabular methods.
        All types of bodies can be shot at ex-meridian, and at either upper
    or lower transit.  The most common is the sun near LAN, but stars,
    planets, and the moon can also be observed.
        My methodology of sight reduction of the ex-meridian is by the
    meridian angle (t) method.  This saves me from having to calculate the
    time of LAN at the actual position of the sight (if it is even known)
    or the DR, which would require a sailing and another iteration of
    calculating the time of LAN.
        The first step is to take the sight as you would a sunline, and mark
    the exact time.  Next you derive the declination and GHA of the sun at
    the time of the sight.  Next find the difference between the GHA of
    the sun and your longitude converted to GHA.  The number should be
    fairly small as the ex-meridian tables do not allow for too much time
    difference between LAN and the sight time.  The number can be either
    positive or negative.  Remember meridian angle is not always LHA.
    Meridian angle can be measured east or west of your longitude.  Use
    the arc to time table or formula for the sun; but for other bodies,
    the increments and corrections page in the Almanac should be used to
    turn this angular measure into minutes of time.  This will be a big
    source of error if it is done incorrectly.
        The �a� factor is found in the navigational tables (Table 24 in the
    2003 Bowditch) and is entered using the declination of the body and
    the latitude of the observer.   This table must be double interpolated
    in order to obtain an accurate value, especially as the declination
    and latitude values get  closer together.   This number is then
    entered into the formula C= a*t^2/60; where C is the correction to Ho
    that is added for upper transits and subtracted for lower transits,
    �a� is from the table, and �t� is meridian angle in minutes of time.
    As an alternative, you can enter and interpolate another table (table
    25 in 2003 Bowditch) to get the Ho or �C� correction.  Tabular values
    must be interpolated.
        Once Ho is corrected with the �C� correction, the problem is solved
    like an ordinary meridian transit problem.
        The tricky part about ex-meridians is that the table and the formula
    from which it is derived fails at high altitude sights.  If there is a
    blank spot where the declination and latitude meet, the formula can
    give error that may be too great for general navigation which usually
    occurs when the sun�s declination is the same name as, and very close
    numerically, to the latitude of the observer.  This can also occur
    when you are near the equator near the equinoxes.   In my example we
    have less than 5 degrees of difference between the declination of the
    sun and the latitude, so the �a� value will be very large and hard to
    calculate accurately.
        In the given example my solution is as follows:
    GHA hr      210-53.6
    t-corr        2-11.5
    GHA         213-05.1
    GHA-o       214-20.0 (360 minus East Longitude is the �GHA� of the
    observer)
    t             1-15.0 = 5 minutes (convert arc to time)
    �a� is interpolated from the tables, since it is borderline, it was
    only interpolated for Declination which will add a bit of error$, but
    since the latitude is fairly close to 15 degrees, the error should not
    be unreasonable for general navigation.  I got 22.5 for �a.�  Be sure
    to use the table that states Declination and Latitude are the same
    name.
    C= a*t^2/60 = 22.5*25/60 = 9.4�
    
    Hs           85-22.0
    IC             + 1.0
    Dip             -9.9
    T/P              0.0
    HA           85-13.1
    Body           +15.8
    Ho           85-28.9
    C               +9.4
    Ho�          85-38.3
    Z-dis (90deg minus Ho�) = 4 deg 21.7�
    
    Dec hr            19 deg 36.3� N
    Tcorr(+0.6)             + 0.1�
    Dec               19 deg 36.4� N
    Z-dis            -04 deg 21.7�  (sun dec is same name and > Lat, so
    Dec-Z-dis = Lat.)
    Latitude          15 deg 14.7�N
    Error 0.7 nm north
    
    When I ran a sunline using the given DR as the assumed position I
    computed an intercept of 0.8 towards an Az of 015 deg.  Very close to
    the ex-meridian latitude so the �a� correction and observation must be
    fairly accurate.
    
    Jeremy
    
    --~--~---------~--~----~------------~-------~--~----~
    Navigation List archive: www.fer3.com/arc
    To post, email NavList@fer3.com
    To , email NavList-@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Get a NavList ID Code

    Name:
    (please, no nicknames or handles)
    Email:
    Do you want to receive all group messages by email?
    Yes No

    A NavList ID Code guarantees your identity in NavList posts and allows faster posting of messages.

    Retrieve a NavList ID Code

    Enter the email address associated with your NavList messages. Your NavList code will be emailed to you immediately.
    Email:

    Email Settings

    NavList ID Code:

    Custom Index

    Subject:
    Author:
    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site