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: Azimuth and Declination formulae
    From: Henry Halboth
    Date: 2005 Jul 20, 11:55 -0400

    Many thanks Lu - you saved me the trouble. There is probably no modern
    use to the formul;a posted - just, in may opinion, an interesting
    historical note and perhaps part of one's math education.
    On Tue, 19 Jul 2005 21:05:42 -0700 Lu Abel  writes:
    > Whoa on the haversines.  It's not half of a sine, it's half of a
    > versine.
    > A versine (x) = 1 - cos (x).   Note that vers (x) has a range from 0
    > to 2.
    > Haversine (x) = vers (x) / 2.   This just makes hav (x) have a range
    > from 0 to 1.
    > The whole reason for versines and haversines was to allow sight
    > reductions to be done using logarithms (and therefore the requisite
    > multiplications become additions); but logs are not defined for
    > negative
    > numbers, hence the need to shift everything to have a positive
    > value.
    > Versines and haversines can also be expressed in terms of sine
    > squared,
    > vers (x) = 2 sin^^2 (x/2).
    > As a side note, the traditional formula for the great circle
    > distance
    > between two points breaks down into finding the difference between
    > two
    > nearly equal large quantities for small distances.  This can produce
    > inaccurate answers because calculators and computers only carry out
    > calculations with a limited number of digits.  The equivalent
    > haversine
    > formula is well behaved, subtracting two small numbers.  Therefore
    > all
    > GPS's actually use the haversine formula for calculating the
    > distance
    > between two points.
    > Lu Abel
    > Peter Fogg wrote:
    > >>From: Henry C. Halboth
    > >>A bit more complicated, but generally employed with the Time Sight
    > is ...
    > >>
    > >>hav Z = sec ho x sec L x sin 1/2S - ho x sin 1/2S -L, where ...
    > >>
    > >>Z = azimith, named according to Latitude + meridian angle, E or W
    > >>ho = corrected altitude
    > >>L = Latitude
    > >>pd = polar distance
    > >>S = ho + L + pd
    > >
    > >
    > > Interesting. Presumably 'hav' stands for haversine, which I
    > vaguely recall
    > > is a half sine? And 'sec' is secant? I don't know what that is.
    > >
    > > What do I need to be able to use this formula? Scientific
    > calculators I
    > > have. Do I need tables of havesines and secants?
    > >
    > > What is the advantage of this formula?
    > >
    > >

    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