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: Bermuda to St Helena on a North Atlantic Mercator Chart
    From: David Pike
    Date: 2021 Dec 28, 15:28 -0800

    Tony Oz you wrote:  "I'm suprised to read that there are difficulties with plotting a track aross the equator on the Mercator projection."

    Tony
    There isn’t a difficulty.  It’s proving the thesis that, if the great circle is north of the rhumb line in the Northern Hemisphere and south of the rhumb line in the Southern Hemisphere, then the great circle and the rhumb line must cross the Equator at the same longitude that concentrates the mind. 

    If indeed true, it’s hard to show perfectly using a numerical example, because meridional parts tables relate to the terrestrial spheroid and spherical geometry relates to a perfect sphere.  Moreover, the crossover longitude in the great circle case relies upon using information calculated in earlier equations, so rounding errors start to multiply, particularly at angles where trig functions change rapidly. 

    A closer match of GC crossover longitude might be gained using ellipsoidal geometry and the terrestrial spheroid.  Another method might be to consider the intersection of three discs, one containing the great circle through the start and finish points, one containing the Equator, and one containing the Greenwich Meridian.  I find these methods hard to imagine but I think there’s some scope in the discs idea, especially if I can show that the GC disc crosses the EQ disc in the ratio of the longitudes of the start and the finish points. Then it’s just like a 3D Mercator Sailing.  DaveP

       
    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