Great Circles, Rhumb Lines & Directions on the Earth — Page 28, Lesson 35

I want to walk you through a really important concept in navigation — the difference between a Great Circle track and a Rhumb Line, and how they behave when we transfer them onto a chart. Let's start with the scenario. Imagine we've plotted a Great Circle track on a globe — the shortest distance between Moscow and Vancouver. Now, we take that track and transfer it onto a Mercator chart. We mark where the Great Circle crosses various coastlines, and we plot those positions onto the chart. The result is Figure 2.5 — the Mercator projection with the Great Circle track added. Now, here's the key point: on a Mercator chart, Rhumb Lines appear as straight lines. But the Great Circle track — which is the shortest distance over the Earth — does not appear as a straight line on a Mercator chart. Instead, it curves. This is a dramatic illustration of how map projections can introduce distortions. It doesn't look like the shortest route on the chart, but we know from plotting it on the globe that it truly is the shortest distance between Moscow and Vancouver. But there's another critical feature to notice: the track direction changes continuously. Let's compare the Great Circle track direction on the Mercator projection with the meridians — the lines of longitude running north-south. As the track leaves Moscow, its direction is about 330 degrees — that's roughly northwest. As it passes near the North Pole, the track direction has shifted to about 270 degrees — due west. And as it comes into Vancouver, the direction is about 210 degrees — that's southwest. So the Great Circle track has changed direction quite significantly along the route. Now, here's where the practical navigation challenge comes in. Modern computer-based navigation systems can direct an aircraft along a Great Circle route and cope with that constantly changing direction quite easily. They recalculate the heading moment by moment. But in the early days of air and maritime navigation, compass and navigation equipment was much less capable. It was found easier to navigate along lines of constant direction — and those are called Rhumb Lines. So to summarise what we've just covered: a Great Circle is the shortest distance between two points on the Earth's surface, but its direction changes continuously. A Rhumb Line cuts all meridians at the same angle, so it has a constant direction — but it's not the shortest route. On a Mercator chart, the Rhumb Line appears as a straight line, while the Great Circle appears curved. And historically, before modern navigation computers, pilots and mariners preferred Rhumb Lines because they were easier to steer with the equipment available.