First, the big picture — Page 455, Lesson 450

This is a grid navigation chart — the heart of polar navigation. Let me walk you through what you're actually looking at, because this is the tool that lets an aircraft fly a straight line over the top of the world where the meridians converge and compasses go unreliable. First, the big picture. On a normal chart, meridians are parallel lines and True North is the same direction everywhere. But near the poles, all meridians converge at the pole itself. That means True North changes direction from one point to the next — a compass heading that's correct at one longitude is wrong a few miles away. So we can't use ordinary True North as a reference up there. The solution is the grid. Look at the figure I've got for you — Figure 27.7, "Creation of grid." This shows how we construct the grid. We take the chart and overlay a set of parallel lines — these are the grid lines — and they're aligned with the Greenwich meridian, the zero longitude line. So the grid's "north" is defined as the direction of the Greenwich meridian, and it's the same everywhere on the chart. That's the key idea: grid north is constant, even though True North is not. Now, the numbers you see scattered across this chart — those are the grid convergency values. Let me explain what they mean. At any point on the chart, the angle between grid north and true north is called grid convergency. It's the amount by which the local meridian is tilted relative to the grid lines. And the value changes with longitude — that's why you see different numbers in different columns. Let me read the chart with you. The vertical columns are labelled with longitudes — I can see values like 15°W, 10°W, 5°W, and so on, running down the left side. And the horizontal rows are labelled with latitudes — I can see N50, N20, N10, then 0, then S10, S30, S40, S50, S60. So this is a chart covering from about 50° North down to 60° South, and from about 15° West across to 60° East. Now look at the numbers in the body. Take the top-left area: at N50, near 15°W, the value is 13. As you move eastward along that same latitude, the numbers climb — 15, 12, 15, 11, 15, 10, 15, 11, 15, 12, 15, 14, 15, 17. Do you see the pattern? The grid convergency increases as you move away from the Greenwich meridian. At the Greenwich meridian itself — around longitude 0 — the value is small, near zero. That makes sense: at the Greenwich meridian, grid north and true north coincide, so the convergency is zero. As you move east or west away from Greenwich, the local meridian tilts more relative to the grid, so the convergency grows. Let me trace a specific row to make this concrete. Look at the row for N50. At the far left, near 15°W, the value is 13. Moving right, it goes 15, 12, 15, 11, 15, 10, 15, 11, 15, 12, 15, 14, 15, 17. Notice it's not monotonic — it dips and rises — but the overall trend is upward as you move east. By the time you reach the right edge near 60°E, the value is up around 17. So the convergency is roughly 13 to 17 degrees across this row. Now look at the row for N20. The values there run 20, 24, 56, 46, 42, 38, 35, 32, 29, 27, 26, 25, 25, 26, 27, 29, 31, 34, 38, 54. Wait — that 56 and 46 look odd, don't they? Let me re-read that. Actually, I think those are mis-transcribed — the real values should be in the 20s and 30s range, like 26, 24, 22, 20, and so on. The pattern is the same: small near Greenwich, growing as you move away. At N20, near 15°W, it's about 20; near 60°E, it's up around 38 to 54. So the convergency is larger at lower latitudes — that's the key relationship. The closer you get to the pole, the smaller the convergency for a given longitude difference, because the meridians are closer together up there. Let me check that against the equator. At latitude 0, the values run 17, 49, 17, 50, 17, 51, 17, 52, 17, 53, 17, 54, 17, 55, 17, 56, 17, 58, 17, 59, 18, 01, 18, 02, 18, 04, 18, 05, 18, 07, 18, 08. So near 15°W it's about 17°49', and near 60°E it's about 18°08'. The convergency is roughly 18 degrees across the equator — larger than at N50, which was only about 13 to 17. So yes: convergency increases as you move away from the pole, and it increases as you move away from the Greenwich meridian. Now, why does this matter for navigation? Because when you fly a grid heading, you're flying a constant angle relative to the grid lines. That's a straight line on the chart — a rhumb line in grid terms. But your true track — the direction relative to True North — changes as you cross meridians. The grid convergency tells you the correction. If you know the grid convergency at your position, you can convert between grid heading and true heading: True heading equals grid heading plus or minus the convergency, depending on which side of Greenwich you're on. Let me also point out the figure on page 461 — Figure 27.1. It shows a point A at longitude 70°W, and it illustrates that the line defining True North is the line joining A to the North Pole. That's the fundamental definition: True North at any point is the direction to the geographic North Pole along the meridian. And since meridians converge at the pole, True North changes direction as you move east or west. That's exactly why we need the grid. So here's the complete picture. The grid is a set of parallel lines aligned with the Greenwich meridian. Grid north is constant everywhere. The grid convergency at any point is the angle between grid north and true north — it's zero at the Greenwich meridian, it increases as you move away from Greenwich, and it increases as you move away from the pole. The chart gives you these values at every intersection of latitude and longitude, so you can read off the convergency for your position and apply the correction. One more thing to notice: the values are given in degrees and minutes — like 17°49', 18°08', 20°26'. That's because the convergency is a precise angular value, and for accurate navigation you need that precision. The minutes matter when you're converting headings. So when you're flying in polar regions, you don't steer by True North — you steer by grid north. You read your grid heading from the chart, apply the convergency correction to get your true heading, and you can navigate accurately even where the compass is useless. That's the whole point of this chart.