9478

Comparing Loxodromes and Great Circle Routes

This Demonstration plots both the great circle route and the shortest loxodrome route between selected cities on the globe. A great circle on a sphere cuts the sphere into two congruent halves. A loxodrome, also known as a rhumb line, is a path on a sphere that cuts all meridians at the same angle (not 90°).
Although historically loxodromes were widely used for navigation, the loxodrome route is not the shortest one. The shortest route is the great circle route, as used in modern air traffic and navigation.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The loxodrome equations used were derived from the article by J. Alexander, "Loxodromes: A Rhumb Way to Go," College Mathematics Journal, 77(5), 2004 pp. 349–356.
From the snapshots you can see that the difference between the routes is greatest on East-West routes or routes close to the poles. The difference gets smaller on North-South routes or routes closer to the equator.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics



 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+