Rhumb Lines and the Great Circle
Whenever I take a flight of any consequence, I inevitably pull out the airline’s magazine to flip through. I usually end up scanning the flight maps that appear in the last few pages of the magazine to see the arcs of the travel routes from various hubs. I’m not a navigator, and I’m definitely not a mathemetician, but I have a keen interest in travel and the most efficient way to get from point A to point B. Rhumb lines illustrates how that happens on a big blue ball, where we can’t very well cut through the middle. Instead, we calculate the great-circle distance, which is the shortest distance between two points on the surface of a sphere, as measured along the surface of the sphere. That dotted line that connects the two? That’s our friend the rhumb line.
On land rhumb lines don’t help much. You’ve got to follow the lay of the land, accounting for natural obstacles to progress like mountains, large bodies of water or the George Washington Bridge. Up in the air, or on the ocean where these types of obstacles are mostly eliminated (reefs and large continents excepted), plotting a course from say, London, latitude 51° :30 m:0 s N, longitude 0° :10 m:0 s W to Philadelphia, latitude 39° :56 m:58 s N, longitude 75° :9 m:21 s W is visually portrayed as a sweeping arc, as you’re flying from the smaller circumference northern latitude to the larger circumference southern latitude.
There’s a nice online resource for visualizing this, as seen in the image above. It comes from gpsvisualizer.com and allows you to enter either the longitude and latitude for your two points or simply plug in the airport codes for each as I did for London and Philadelphia. This site didn’t help those Portuquese sailors trying to show other sailors how to sail to the Gulf of St Lawrence for cod fishing, so navigation maps were drawn and copied with the rhumb lines to show sailors which heading would get them there and back.
I’ve made a few dotted lines across the world over the years, and hope to make many more. I think basic navigation should be a requirement for all kids in school, as it teaches not just math skills but also illustrates how small we are blipping across the fragile surface of the earth. Rhumb lines convey hope for the journey ahead, appreciation for how far we’ve come, and focus on the path we’re currently traveling on this great circle. I’m surely not the only one to pluck that analogy out of this fundamental of navigation, but I’ll celebrate having gotten here eventually.