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: Bermuda to St Helena on a North Atlantic Mercator Chart
    From: Robin Stuart
    Date: 2021 Dec 29, 10:23 -0800

    David,

    Your thinking of the great circle equator crossing problem in terms of discs (or slices through the sphere) has merit but I don't see how it gives your stated result. If the latitude and longitude for the departure point are L1, λ1 and for the destination L2, λ2 then I get the longitude, λ, of the equator crossing point is
    tan λ = ( sin λ2 tan L1 - sin λ1 tan L2 ) / ( cos λ2 tan L1 - cos λ1 tan L2 )
    This equation has 2 diametrically opposite solutions and you need to select the one that applies.

    This was derived by working in 3D coordinates. A pole of the great circle can be found as the vector cross-product of the departure point and the destination. The longitude of the equator crossing point is the longitude of the pole ± 90°. To show that it works here's a plot of the great circle from Auckland to New York City; a route that Air New Zealand was planning to start around the time the pandemic hit. The red dot is at 135.2°W.

    Regards,
    Robin

    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