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: Yet another 4-place Nat-Haversine Table project?
    From: Greg Rudzinski
    Date: 2018 Dec 4, 13:05 -0800

    Roger,

    I will suggest adding or subtracting 1° to the assumed latitude for the few cases where the sums of latitude and declination are less than 1° when performing a longhand haversine sight reduction. For cases where the meridian angle (t) is less than 1° I will suggest doing an ex-meridian rather than a 4 place hav-doniol reduction. 

    Greg Rudzinski

    From: Roger W. Sinnott
    Date: 2018 Dec 3, 16:38 -0500

    Tony,

     

    Your haversine table looks quite nice, with no wasted white space!

     

    However, one problem, as it stands, is that 4 decimal places isn’t enough to preserve significant digits in very small angles.  So, for example, when you look up the haversine of 0° 48ʹ, the answer you get from the table is zero (not very useful).

     

    Some time back I made a set of 3-place tables, each the size of a business card and laminated, that I keep in my wallet.  I haven’t made one for haversines (yet), but I encountered a similar problem with significant digits in my 3-place sine table (picture attached).  My solution was to invent a new notation, where a negative exponent precedes the decimal value, so that the sine of 1° is

    given as -1.175 and means the same as 0.175 x 10-1, or 0.0175.  (I hope the superscripts I’ve typed survive this transmission by email!) 

     

    Note that this exponent could be anywhere from -1 up to -9 and not take up any more space in the table, so even a number like 0.000000000397 could be accommodated in a 3-place table.

     

    Roger

       
    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