Great Circles, Rhumb Lines & Directions on the Earth — Page 28, Lesson 33

I want to walk you through the foundational ideas of how we define routes and directions on the Earth's surface. This is absolutely core to everything we do in navigation, so let's take it step by step. First, we need to understand what a Great Circle is. The precise definition is this: a Great Circle is a circle on the surface of the Earth whose centre and radius are those of the Earth itself. Let me unpack that. Imagine slicing right through the centre of the Earth with a plane. Where that plane cuts the surface, you get a circle. Because that plane passes through the Earth's centre, the circle you get has the same centre as the Earth, and its radius is the Earth's radius. That's a Great Circle. Why is it called 'great'? Because if you cut a disc through the Earth in the plane of that Great Circle, that disc would have the largest possible area you can achieve with any such cut. It's the biggest possible circle you can draw on the globe. Now, here's the critical operational fact: the shortest distance between any two points on the Earth's surface is the shorter arc of the Great Circle joining those two points. If you have two cities, the most fuel-efficient, shortest route is along that Great Circle arc. There's a catch, though: given any two points on the Earth's surface, there is only one Great Circle that joins them. The only exception is if the two points are diametrically opposed—exact opposites on the globe—in which case there are infinitely many Great Circles that connect them. Let's look at the diagram for this. Now, let's contrast that with the Rhumb Line. A Rhumb Line is a regularly curved line on the surface of the Earth which cuts all meridians at the same angle. In other words, it's a line of constant direction. If you follow a Rhumb Line, your track—the angle you make with the meridians you cross—never changes. You hold one steady compass heading. This property was enormously important for mariners and aviators until about 40 years ago, when cheap, powerful computing became widely available. Before that, if you wanted to navigate from A to B, you would calculate a constant straight-line track—a Rhumb Line—and then simply hold the compass heading that would give you that track. This made the navigation problem relatively simple. However, and this is the key trade-off, unlike the Great Circle route, the Rhumb Line does not give the shortest distance over the Earth between the two points. Let's look at the example shown in the diagram. That's the Moscow to Vancouver Rhumb Line track. Now, consider the same route, Moscow to Vancouver, but as a Great Circle. You can see that the Great Circle track between those points passes very close to the North Pole, and it is much shorter. The diagrams compare them directly. So, to summarise what we have so far: a Great Circle gives you the shortest distance, but the track direction constantly changes as you cross meridians. A Rhumb Line gives you a constant, easy-to-follow direction, but it is a longer route. Understanding which one to use and when is a fundamental part of your navigation planning.