What is a straight line?

There are two basic interpretations of what a “straight” line is:

  1. A line in a cartesian grid of latitude and longitude (a loxodrome)

  2. The shortest connection of two points on earth surface (a geodesic)

Background

Because the earth is a globe, fitting its surface onto a rectangular shape (for instance a computer screen) requires stretching out areas towards the poles. This is called a mercator projection and is responsible for notable distortions in the size of various parts of the world (visualization). A straight line on a mercator-projected map is called a loxodrome or rhumb line. Loxodromes always cross meridians in the same angle.

However, since meridians aren’t parallel (at least on the globe), a loxodrome isn’t the shortest path between two points on earth’s surface. The acutal shortest path is called a geodesic and is a section of the biggest circle on a globe (great circle). See this website for examples.

Relevance

Loxodrome and geodesic don’t differ on the equator and meridians, since they are great circles. However, when moving in other directions, the difference between a loxodrome and a geodesic between identical points becomes more important when:

  • moving farther to the poles and

  • crossing bigger distances.

To find out whether the difference between geodesic and loxodrome is relevant in context of the expected devatiations of a straight line mission, this map might be helpful.

Linesman’s understanding of a straight line

By default, linesman always uses a geodesic as reference line. Using a loxodrome as reference line might be implemented in a future release.