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

    Greg,

    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.

    Example:

    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.

    Example:

    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!

    Matt

    File:
    Azimuth.pdf
    File:
    Height-Calculated.pdf
       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    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:

    Email Settings

    Posting 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