Mercator Charts - Properties — Page 304, Lesson 268

Let’s start with the big picture. We’re looking at the Mercator chart and its properties. You’ve already met the idea of a projection — how we flatten the globe onto a sheet of paper. The Mercator is a special one, and its properties come straight from how it’s built. First, the scale. On a Mercator chart, the scale expands as you move away from the Equator. That’s why the figure shows “Examples of Mercator Scale Expansion” — the same physical distance on the chart represents fewer nautical miles near the poles than near the Equator. The scale is not constant; it grows with latitude. Now, the shape distortion. Figure 18.5 shows two projections side by side. On the left, you have a convergent projection, which is close to the shape you’d see on a globe. On the right, you have the Mercator projection, and it shows distortion of shape. Because the meridians are drawn parallel and the scale expands, shapes get stretched, especially at high latitudes. But here’s the practical point for you as a pilot: these distortions of shape are insignificant over small distances. So they have no effect on your ability to map-read. They also have no implications for rhumb line navigation at all. The only real problem is that they can give a false impression of the most direct routing, especially at high latitudes. That idea — that the Mercator makes a curved great circle look like a longer path than it really is — was covered back in Chapter 2. Now let’s talk about chart convergence. You already know Earth Convergence, or Convergency, from Chapter 14. That’s the angle of inclination of the meridians on the Earth — in other words, the change in direction of a great circle between two longitudes. But for each type of projection, we also have Chart Convergence. That’s the angle of inclination between meridians on the chart — the change in direction of a straight line between two longitudes. On a Mercator chart, all meridians are parallel. So their mutual inclination is zero. The change in direction of a straight line drawn on the map is also zero. A straight line will always cut all meridians at the same angle. And that is exactly why Mercator produced the projection in the first place — so that a straight line on the chart gives you a single track angle. Now compare that to the Earth. Earth convergency is zero at the Equator, but nowhere else. So Mercator convergence is correct at the Equator only, but it’s constant everywhere — always zero. That’s the key contrast: the chart says convergence is zero everywhere, but the Earth only agrees at the Equator. That brings us to rhumb lines. Because the meridians are parallel lines, a straight line track drawn on the chart will cut all meridians at the same angle. So a straight line track on a Mercator chart is a rhumb line. That’s the definition — a line of constant true track. Finally, great circles. Here’s the relationship you need to remember: the rhumb line between two points will always be nearer to the Equator than the corresponding great circle. Conversely, the great circle between two points will always lie nearer the Pole than the rhumb line. So if you’re planning a long route at high latitude, the great circle curves toward the pole and is actually shorter, but on the Mercator it looks like a longer, curved path. That’s the false impression we mentioned earlier. Figure 18.6 shows this visually — the rhumb line hugging the Equator side, the great circle curving toward the pole. That was covered in detail in Chapter 2, but the statement is simple: rhumb line near the Equator, great circle near the Pole. So to sum up the Mercator’s properties: scale expands with latitude, shape is distorted but only matters over long distances, chart convergence is always zero while Earth convergence is only zero at the Equator, straight lines are rhumb lines, and great circles always lie poleward of the rhumb line. That’s the whole picture.