Great circles and rhumb lines

Get in loser, we’re making loxodromes

Figure 1

1. Download this csv file by clicking the link: rhumb.csv
2. Create a new ArcGIS Pro project
3. I removed the default basemaps and added a generalized countries layer from Living Atlas (World_Countries_Generalized)
4. Open the “XY to line” tool and run the tool twice with the following parameters, changing the “Line type” setting each time:
   1. Set rhumb.csv as the input
   2. Start X = “start_lon”
   3. Start Y = “start_lat”
   4. End X = “end_lon”
   5. End Y = “end_lat”
   6. Line type = first do “Rhumb lines,” then do “Great circles”
5. Add them to the map
6. For each feature class, do “Calculate Geometry Attributes”
   1. Create a new field called real_length
   2. Give it a type of “Length (geodesic)”
   3. Length units = “International Nautical Miles” (or whatever you want, I used this unit)
   4. Coordinate system can stay blank
7. Tweak the symbology, if necessary. I made lines thicker
8. Turn labeling on for each feature class. You might have to fuss with the labels a bit. I used this expression to render features:
   1. Great circles = Text($feature.real_length, 'Great circle length: #,###.#### km')
   2. Rhumb lines = Text($feature.real_length, 'Great circle length: #,###.#### km')

Now you have two feature classes, each displaying different lengths in kilometers of distance from three cities:

• Boston to London
• Norfolk to the Azores
• Antigua to Cote D’Ivoire

Great circles and rhumb lines

What the heck are these lines?

Here, we’ve got two different ways of calculating distance on the surface of the earth:

• Rhumb lines (or loxodromes) are lines of constant bearing. They cross meridians (vertical lines of longitude) at a constant angle. If we kept . Historically, this is useful for maritime navigation.
• Great circles represent the shortest possible path between two points on the surface of the earth. Ideal plane routes are great circles.

The descriptions below are from a great maritime navigation textbook (Dutton’s):

Figure 2: Great and small circles in figures

Figure 3: Great and small circles described

This short blog post has a nice explanation of the difference between great circles and rhumb lines.