First, the Mercator projection — Page 447, Lesson 423

This is a fascinating page, and I want to walk you through exactly what you're looking at, because it's the heart of how we actually navigate across the surface of the Earth. What you have here is a departure chart — specifically, a grid of numbers that represents a great circle plotted on a Mercator projection. Let me unpack that for you, because every single number on this page has a specific meaning. First, the Mercator projection. This is a way of drawing the round Earth on a flat piece of paper. Its defining feature is that rhumb lines — lines of constant true bearing — appear as straight lines. That's incredibly useful for navigation. But there's a catch: on a Mercator chart, a great circle — the shortest path between two points on a sphere — does not appear as a straight line. It appears as a curve that bends toward the poles. So what this page is showing you is the great circle between two points, and it's giving you the data you need to fly it. The key insight is this: to fly a great circle on a Mercator chart, you don't fly a single constant heading. Instead, you fly a series of short rhumb line segments, each with its own heading, and you change heading at regular intervals. This page gives you the numbers to do exactly that. Now, let's look at the structure. The page is organized by latitude bands. You'll see labels like N 50, N 20, N 10, S 10, S 30, S 52, S 60. These are the latitudes, in degrees, of the parallel lines that run across the chart. The "N" and "S" tell you whether it's north or south of the equator. Within each latitude band, you have two rows of numbers. The top row is a sequence of longitudes — the meridians, running east to west. The bottom row, directly beneath each longitude, is the true track — the heading you need to fly, in degrees, at that specific longitude to stay on the great circle. Let me give you a concrete example. Look at the band labeled N 50. The longitudes run: 19 41, 19 45, 19 49, 19 53, 19 57, 20 00, 20 03, 20 05, 20 08, 20 10, 20 11, 20 12, 20 13, 20 13, 20 13, 20 12. And directly beneath each of those, the true tracks are: 45, 24, 27, 30, 33, 36, 39, 41, 44, 46, 47, 49, 50, 50, 51, 51, 50. So at longitude 19 41, the true track is 45 degrees. At longitude 19 45, it's 24 degrees. And so on. You can see the track values climbing and then peaking and coming back down — that's the curve of the great circle, expressed as a series of headings. Now, here's the critical part about true track. This is the heading measured clockwise from true north — not magnetic north, not compass north. True north is the direction of the geographic North Pole. When you're flying, you'll need to apply the local magnetic variation — the angular difference between true north and magnetic north — to convert this true track into a magnetic heading you can actually steer on your compass. But the numbers on this page are all true. Let me walk you through another band to reinforce this. Look at S 52. The longitudes are: 16 16, 16 12, 16 08, 16 05, 16 02, 16 00, 15 57, 15 56, 15 55, 15 54, 15 53, 15 53, 15 54, 15 55, 15 56, 15 58. And the tracks: 54, 16 08, 16 03, 15 59, 15 56, 15 52, 49, 47, 45, 44, 43, 42, 42, 43, 44, 45, 47. Wait — I need to be careful here. Let me re-read that. The tracks for S 52 are: 54, 16 08, 16 03, 15 59, 15 56, 15 52, 49, 47, 45, 44, 43, 42, 42, 43, 44, 45, 47. Hmm, that doesn't look right. Let me look again. Actually, I see the issue. The layout is: longitude, then track, then longitude, then track. So for S 52, the first longitude is 16 16 and the first track is 54. Then the next longitude is 16 08 and the track is 16 03? No — wait. Let me re-read the raw data. The raw data for S 52 reads: 16 16 16 12 16 08 16 05 16 02 16 00 15 57 15 56 15 55 15 54 15 53 15 53 15 54 15 55 15 56 15 58. And the tracks: 54 16 08 16 03 15 59 15 56 15 52 49 47 45 44 43 42 42 43 44 45 47. Hmm, I'm confusing myself. Let me be very precise. The format on this page is: for each latitude band, you have a row of longitudes, and directly beneath each longitude, a true track. So the first longitude in S 52 is 16 16, and the track beneath it is 54. The second longitude is 16 12, and the track beneath it is 16 08? No — that can't be right, because a track of 16 degrees doesn't make sense next to a track of 54. Let me re-read the raw data one more time, very carefully. The raw text for S 52 is: 16 16 16 12 16 08 16 05 16 02 16 00 15 57 15 56 15 55 15 54 15 53 15 53 15 54 15 55 15 56 15 58 And then the next line is: 54 16 08 16 03 15 59 15 56 15 52 49 47 45 44 43 42 42 43 44 45 47 I think I misread the structure. Let me look at the N 50 band again, which is clearer. The longitudes there are: 19 41, 19 45, 19 49, 19 53, 19 57, 20 00, 20 03, 20 05, 20 08, 20 10, 20 11, 20 12, 20 13, 20 13, 20 13, 20 12. And the tracks: 45, 24, 27, 30, 33, 36, 39, 41, 44, 46, 47, 49, 50, 50, 51, 51, 50. Wait, that's 16 longitudes and 17 tracks. That doesn't match either. Let me count again. The longitudes: 19 41 (1), 19 45 (2), 19 49 (3), 19 53 (4), 19 57 (5), 20 00 (6), 20 03 (7), 20 05 (8), 20 08 (9), 20 10 (10), 20 11 (11), 20 12 (12), 20 13 (13), 20 13 (14), 20 13 (15), 20 12 (16). So 16 longitudes. The tracks: 45 (1), 24 (2), 27 (3), 30 (4), 33 (5), 36 (6), 39 (7), 41 (8), 44 (9), 46 (10), 47 (11), 49 (12), 50 (13), 50 (14), 51 (15), 51 (16), 50 (17). That's 17 tracks. So there's one more track than longitude. That makes sense! Because the track at the start of the segment applies until you reach the next longitude. So you have 16 longitudes defining 15 segments, but the page gives you 17 tracks — the initial track, then a track for each segment, and the final track. Actually, let me reconsider. Actually, the standard format for these great circle sailing tables is: you have a series of longitudes, and at each longitude, you have the track you should be on as you cross that meridian. So the track at longitude 19 41 is 45 degrees, meaning when you cross the 19°41' meridian, your true track should be 45°. Then at 19 45, it's 24°, and so on. But the count mismatch — 16 longitudes and 17 tracks — suggests the page might have a slightly different layout. Let me look at the very first line of the excerpt: 20 48 20 50 20 50 20 24 20 50 20 49 54 19 59 20 04 20 08. Hmm, that's the top of the page, and it's a bit garbled in the extraction. I think I'm overcomplicating this. Let me step back and give you the conceptual understanding, which is what matters for your exam. The core concept is this: a great circle track on a Mercator chart is flown as a series of rhumb line segments. At each meridian crossing, you adjust your true track to the value given in the table. The table gives you, for each latitude band and each longitude, the true track you should be flying. The reason the tracks change is the convergence of meridians. As you move away from the equator, the meridians get closer together. On a Mercator chart, this distortion means a great circle — which is a straight line on a globe — appears as a curve. To follow it, you must continuously change your heading. Now, let me look at the overall pattern. At the top, N 50, the tracks start around 45 and climb to about 51, then drop back to 50. At N 20, the tracks are lower — around 30 to 35. At N 10, they're around 14 to 25. At the equator — well, there's no equator band here, but you can see the pattern. At S 10, the tracks are around 17 to 20. At S 30, they're around 28 to 32. At S 52, they're around 42 to 54. And at S 60, they're around 14 to 21. Wait, that last one — S 60 — the tracks are: 15 36, 15 29, 15 24, 15 18, 15 14, 15 09, 15 06, 15 03, 15 00, 14 59, 14 58, 14 57, 14 58, 14 59, 15 01, 15 04. Hmm, those look like longitudes again, not