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
    2017 Bowditch Errata
    From: Antonio Sauci
    Date: 2018 Jan 21, 13:49 -0800

    Hi everybody,

    I downloaded this evening the new 2017 edition of publication no. 9, published by the National Geospatial.Intelligence Agency. While scrolling down volume 2,for a possible print-out of its tables, I was surprised to find in the entry for "Cardiod", in the section entitled "Glossary of Marine Navigation",on page 312, no actual figure which depicts what a cardioid looks like. The figure in the book only depicts three concentric circles in different colours and radii and another fourth circle tangent to the innermost one and of the same radius and with center also laying  on the same x-axis.

    Regarding the definition,although accurate, is only part of the problem. Let me expand on this topic. If a generating circle of radius r rolls along the exterior (or the interior) circunference of a fixed circle of radius r1,then each point of the first circle describes a simple (general,normal) epicycloid (or hypocycloid),respectively.The parametric equations  are:

    x = (r1+ or -)· cos(t) - or + r ·cos ((r1+r)/r) t          and   y= (r1+ or -)· sin(t) - r· sin((r1+r)/r)t

    The (+) signs for epicycloid; the (-)sign for hypocycloid.. Only when r1 = r,  we get the cardioid of equations: x = r(2cos(t) -cos(2t))  and  y=r(2sin(t) - sn(2t)) , while if we let r1=2r,then we get another epicycloid,called a nephroid, and whose equations are: x =r(3cos(t)-cos(3t))   and  y=r(3sin(t) -sin(3t)).

    For someone interested in visualizing a real cardioid,it is much easier to use its polar coordinates  equation:  ro=2r(1+cos(phi)).

    I infer from my very quick inspection of the edition that the two books need a good proof-reading.

     

       
    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