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

Right, let's pick this up. We've plotted the Great Circle track on the globe, and now I want to show you what happens when we transfer that same track onto a Mercator chart. Here's the key thing to understand first: on a Mercator chart, Rhumb Lines are represented by straight lines. A Rhumb Line, remember, is a line that cuts all meridians at the same angle — a line of constant direction. On the Mercator projection, that constant-angle property is what makes it appear as a perfectly straight line. Now, when we take the Great Circle track from the globe — the one we plotted by marking where it crosses various coastlines — and transfer it onto that Mercator chart, something dramatic happens. It doesn't appear as a straight line. It appears as a curve. And this is a dramatic illustration of the extent to which projections can introduce distortions. Here's the crucial point: it does not appear that way on the Mercator chart, but we know from plotting it on the globe that the Great Circle track is actually the shortest distance over the Earth between Moscow and Vancouver. So the chart is lying to us visually — the curved line on the chart is actually the shortest path in reality. But notice something else, and this is the second critical point: the track direction changes. Let's compare the Great Circle track direction on the Mercator projection with the meridians. As the track leaves Moscow, its direction is about 330°. As it passes near the North Pole, the track direction has changed to about 270°. And as it comes into Vancouver, the direction is about 210°. So over the course of that route, the Great Circle track has changed direction — in this case, quite significantly. It started heading roughly northwest, then it's heading due west near the pole, and finally it's heading southwest into Vancouver. Now, why does this matter for real navigation? Modern computer-based navigation systems can direct the aircraft along a Great Circle route and cope with the constantly changing direction of the Great Circle quite easily. The computer just keeps updating the heading. But in the early days of air and maritime navigation, compass and navigation equipment was less capable. It was found easier to navigate along lines of constant direction — Rhumb Lines. So the pilot would simply hold one compass heading for the whole leg, even though that meant flying a slightly longer path than the true shortest Great Circle route. So the contrast to hold onto is this: the Great Circle is the shortest distance but its direction constantly changes; the Rhumb Line is a constant direction but it's not the shortest distance. On a Mercator chart, the Rhumb Line looks straight and the Great Circle looks curved — and that's the distortion we have to be aware of.