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: The pedant's rhumb-line.
    From: Dave Weilacher
    Date: 2002 Oct 10, 12:53 -0700

    Well. Crap. Although this piece was entertaining, educational, and thought
    provoking, it will have everyone on this listed specifying "shortest"
    rhumb-line where just rhumb-line used to do :-}
    
    On Thu, 10 Oct 2002 20:31:54 +0100 George Huxtable 
    wrote:
    
    > Every now and again, rhumb-lines appear as a
    > topic on this list.
    >
    > Most list-members are aware that wherever you
    > start from on the Earth, with
    > whatever course, if you keep following a rhumb
    > line (constant course), you
    > will end up spiralling into one or other of the
    > poles. You will have made a
    > number (perhaps an infinite number?) of turns,
    > in longitude, to get there,
    > but will have travelled (in general) a finite
    > distance.
    >
    > Navigators frequently ask for the rhumb-line
    > course from A to B. Here I
    > wish to display my pedantry by insisting that
    > there is not just one
    > rhumb-line course between A and B, but many
    > (perhaps an infinite number?).
    > The one required by the navigator is the
    > SHORTEST rhumb-line course.
    >
    > This can be illustrated by a simple example.
    > Take a navigator on the
    > equator at position A, long = 0 degrees. What
    > is his rhumb-line course and
    > distance to a destination B, lat 10 deg North,
    > long 0 deg.? The obvious
    > answer is a course of zero degrees, which
    > happens to be identical with the
    > great-circle in this case. But what if he sets
    > off from A with a course of
    > about 88.4 degrees, that is, slightly North of
    > due East, and holds that
    > course? Well, that's a rhumb line, also, which
    > will also take him to B (or
    > it would if no continents got in the way), but
    > he has to go Eastwards,
    > right round the world, to get there. Similarly,
    > a course of about 271.6
    > degrees will also take him round the world to
    > B, but Westwards.
    >
    > He could set off with a course even closer to
    > due East, roughly 89.2
    > degrees, and if he sticks to that while making
    > two whole circuits of the
    > Earth it will take him to B. Again, there's
    > another corresponding rhum line
    > Westwards. Other courses, progessively closer
    > still to due East or West,
    > would take him to B after 3, 4, or more
    > circuits of the Earth, right up to
    > infinity.
    >
    > What's the practical importance of this? None
    > whatsoever. I am just
    > pointing out that these alternative, but quite
    > impractical ways of getting
    > from A to B are all genuine rhumb lines between
    > A and B, and each fully
    > meets the definition of a rhumb line. There is
    > no unique rhumb line. The
    > only rhumb line that's of any practical
    > significance, however, is the
    > shortest rhumb line.
    >
    > Just something to ponder over on a quiet watch.
    >
    > George Huxtable.
    >
    >
    > ------------------------------
    >
    > george---.u-net.com
    > George Huxtable, 1 Sandy Lane, Southmoor,
    > Abingdon, Oxon OX13 5HX, UK.
    > Tel. 01865 820222 or (int.) +44 1865 820222.
    > ------------------------------
    >
    
    
    
    Dave Weilacher
    .US Coast Guard licensed captain
    .    #889968
    .ASA certified sailing and celestial
    .    navigation instructor #990800
    .IBM AS400 RPG contract programmer
    
    
    

       
    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