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: Logarithms by Hand
    From: Hanno Ix
    Date: 2014 Jun 4, 12:08 -0700
    Hello,

    Peter and Noell

    Re: calculating sin()  and cos()  from scratch.

    Actually, CORDIAC is not a bad bet.
    You might do something like this  - written in an impromptu version of Pseudo Basic:

    x=0;
    y=1;
    L=157;           * equal to approximately pi/4*100

    for i = 1 to L

    dx = 0.01*y;   *  no calculation - just shift y two digits to the right ...
    x = x - dx;      *  and subtract from x
    X(i) = x;

    dy = 0.01*x;   * analogous to above
    y = y + dy;
    Y(i) = Y;

    end


    In "only" 157 steps you get sin() in -Y and cos() in X with the period 100*pi.
    That means the angles 0:90 deg are mapped into  0:25*pi.

    The error is less than 10^-4 which is sufficiently small for
    CelNav sight reduction using trig functions - not log-trig functions.

    Of course, you have also to transform the range 0:25 *pi of the angles
    into 0:90 deg or the other way around to match the sextant scale.
    This complexity is the prize for simplifying division by shifting.
    A subtle issue: the angles for sin() are located between the angles of cos().

    The process is actually very simple and easy to commit to memory.
    In particular, you don't have to memorize any constants or parameters.
    It would be certainly a laborious but not a hopeless task.

    I attach two graphs done in MATLAB. They are self - explanatory I think.

    H

    ____________________________________________________________________

    PS:

    Noell, I thought you did a very nice job in describing how to
    establish a log()  table.

    You realize the sight reduction by hand I recently described aims at
    NOT using log(), though.







    On Wed, Jun 4, 2014 at 5:56 AM, Noell Wilson <NoReply_Wilson@fer3.com> wrote:

    Hi Peter,
    No tables of any kind?! Wow! That would probably eliminate some of the index card cheat sheets also.

    If possible, I'd invoke the strict reading of "no tables" and pull out my trusty slide rule.

    If that's not legal, I'd probably run down a latitude line and approach the shore carefully.
    I'd probably make land before I could derive the formulas.
    Regards, Noell


    ----------------------------------------------------------------
    NavList message boards and member settings: www.fer3.com/NavList
    Members may optionally receive posts by email.
    To cancel email delivery, send a message to NoMail[at]fer3.com
    ----------------------------------------------------------------

    : http://fer3.com/arc/m2.aspx?i=127902


    File:


       
    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