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
    Re: Haversines with Logarithms
    From: Matthew Gianelloni
    Date: 2020 Oct 11, 18:10 -0700


    I totally concur on both points. These particular tables are 6 years old. I have a condensed version that is six digits instead of 9. Also, at the angles close to 0° and 180°, the closer you get, the less differentiation there is between haversine values per minute of arc using 5 or 6 digits. Thus the original 9 digits.


    On the Natural Haversine table you posted, the haversine values from 0°1' to 0°15' are all .00000 whereas on the 9 decimal CoValues table they each have a different value from .000000021 to  .000004760. The next angle, 0°16' is .00001 on the Natural Haversine table, which is rounded a good bit from .000005415 on the CoValues table.

    But really, how often will we actually encounter a situation that uses those values close to 0 or 180? Statistically not much. 5 digits is great for practical navigation. 

    The Daniol method is totally beautiful,  and I wonder why it's not taught as the standard sight reduction method instead of the H.O. 229 tables. It does, however, produce a result (Hc and Z) for use in the intercept (St. Hilaire) method to get a fix. 

    The intercept method requires precalculation. My goal in this was to dispense with precalculations for specific target stars and planets, and just walk outside and shoot the stars I knew, walk back inside and kick out a position in 10 minutes. Laziness has driven most of what I do on a daily basis.

    That being said, I am lazy about math too. I'd rather subtract two 9 digit decimals than divide them. On page 3 of the Daniol Method document you posted, it says "The draw back to this azimuth formula is a division step." The logarithm CoValues for each haversine and angle allow a subtraction to be done instead of that division.

    Next, the math will show how sometimes you will end up with angles in the spherical triangle calculations that need a haversine for angles greater than 180. This occurs when additions or subtractions of logarithms  yield doubled angles. I had to list those coresponding angles with each other for the algorithms to work.


    The angles 43°29' and 316°31' both have a haversine value of .137212713

    I haven't worked on these algorithms for Hc and Z for 6 years, so they're relatively untested compared to the one for Meridian Angle, but I've attached them here for use in the Daniol method. 

    Criticism welcome! Being wrong is how I  learn!


    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