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: Longhand Sight Reduction
    From: Peter Monta
    Date: 2014 Jun 12, 12:18 -0700
    Hi Hanno,

    The multiplications show each partial product separately in the array.  It's less compact than the usual method, but somehow I find it more reliable to add up everything at the end.  It's essentially the lattice method:

    http://en.wikipedia.org/wiki/Lattice_multiplication

    but turned on its side and with the low-order terms dropped.  The aim was to calculate one or two places beyond the least-significant digit of the inputs, then round.  Almost always this will give the same result as rounding the full-precision product (and for even lower expected error at very small additional cost, one can add a bias term before rounding to represent the dropped terms).  Computer arithmetic people worry about this sort of thing because the factor-of-2 savings is very attractive; I'm sure there was historical precedent too, before log tables took over the medium-precision market.

    Perhaps it's better just to do the full-precision multiplies.  The aim was to have a very robust, simple, desert-island-derivable method with no complications.  Your polynomial approximations sound fine, but our desert-island resident would have to devote time to reproduce them without high-tech aids (of course, if you're on a desert island, you have plenty of time).

    So no-table sight reduction seems tractable.  The other part of this is the almanac, and here we really have to memorize a few numbers.  The minimal set might be something like (ra,dec){at}J2000 of half a dozen bright stars plus the expression for sidereal time at Greenwich (including an estimate of the current delta-T).  The Sun seems a bit too complicated to memorize to any usable accuracy, let alone the Moon and planets; but any of these bodies could be used as "transfer standards" by measuring them against the stars.

    Here are my assumptions, which are of course pretty absurd:

    - available: sextant; chronometer showing UTC; pencil and paper
    - not available: tables or any other computational aid; almanac
    - known: micro-almanac of a few stars; sight reduction algorithm

    Hanno, just read your reply:  yes, exactly, Napier's bones.  The desert-island guy might well want to make a set.

    Cheers,
    Peter

       
    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