Welcome to the NavList Message Boards.


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

Compose Your Message

Add Images & Files
    Time Sight and Ex-Meridian by Bygrave
    From: Brian Walton
    Date: 2021 Apr 6, 02:49 -0700

    1.   CV19 means that I have not flown or done astro from a moving boat for 6 months. I am therefore now an armchair pundit.

    2.    Maskelyne used log versines or haversines, plus log secants and sines to derive a longitude from lat, dec and Ho. This method (involving about 8 lines of math, plus 5 look ups and additions of 5 figure tables) then called long by chron, together with a noon lat, endured in the mechant marine for over a hundred years. Azimuth could be found by sinAz=cosDec. sin t . sec Ho, but was not needed.

    3.    The Bygrave cylindrical spiral slide rule uses lat, dec and t with 6 movements, and some math, to find Az and Hc, and thus Zn and intercept. The operator does not need to look up trig logs. I have long wanted to use a Bygrave to work out a time sight by reverse inputs, but failed because of the need to input azimuth as raw data, and that required a separate slide rule to work the formula given in para 2.   I then found that given azimuth and intercept by Bygrave, simple plotting gave long by chron, ex- meridian, and  Sumner lines, with no extra calculation. See the attached plot, made on an exercise book I use as a deck logbook.

    4.    A Mercator plot is constructed using the exercise logbook lines. Only the black lines are needed; the blue lines are for explanation. I have chosen 50°N. A scale is formed as shown. 10 miles per line works well for a boat averaging about 6 kts, rather more for an aircraft, but I have chosen 1 mile per line to illustrate the principle.

    5.   If a Bygrave solution gives a towards intercept of 3 miles, on an azimuth of 150°, it is plotted from DR to SH, and a PL is drawn at 90°; black lines.

    6.   If the St Hilaire PL is extended to the DR lat, position T gives the longitude by time solution, and is in effect a Sumner line.  If the St Hilaire PL is extended to the DR long, position M gives the ex-meridian correction. This can be checked by rearranging Maskelyne's formula.

    7.   So, by simply extending the St Hilaire PL, one can find Long by Time, Sumner's line, and ex- meridian corrections without any need for logs or trig !!    Any other PL from any source can be plotted directly from DR to get a fix, provided the DR is worked correctly, and the azimuth differs by more than about 25°.

    Brian Walton


    Browse Files

    Drop Files


    What is NavList?

    Join NavList

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

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

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

    Email Settings

    Posting Code:

    Custom Index

    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