Gridded Charts — Page 471, Lesson 469

We're moving into the heart of grid navigation now—the actual conversion between Grid and True headings. This is where the theory becomes a working tool. Let's start with the Northern Hemisphere answers you have in front of you, because they set the pattern. Look at the table for the Northern Hemisphere. For Aircraft 1, at longitude 90°W, the convergence is 90°E. The Grid Heading is 360°, and the True Heading is 270°. Notice the relationship: True is 90 degrees less than Grid. For Aircraft 2, at 45°W, convergence is 45°E, Grid is 225°, True is 180°—again, True is 45 degrees less. For Aircraft 3, at 45°E, convergence is 45°W, Grid is 315°, True is 360°—now True is 45 degrees greater than Grid. So the pattern in the Northern Hemisphere is: if you're west of the datum, you have east convergence, and True is less than Grid. If you're east of the datum, you have west convergence, and True is greater than Grid. That's the "Convergence East, True Least" rule in action. Now, the Southern Hemisphere is more of a challenge, and I want you to see why. The key difference is that True North points away from the South Pole. So on a South Polar Stereographic projection, the geometry flips. Let's take Aircraft 1: it's at longitude 90°W, and the answer gives convergence 90°W, Grid Heading 000°, True Heading 090°. The book walks you through a visual inspection: if Grid North is at the 12 o'clock position, then the datum meridian must be the Greenwich meridian—that's a Standard Grid. Aircraft 1 is at 90°W, which is west of the datum. From the diagram, in the Southern Hemisphere, being west of the datum gives you west convergence. And here's the new rule: "Convergence West, True Best." That means True is greater than Grid. So True Heading is 90 degrees greater than Grid—000° plus 90° gives 090°(T). Both the convergence formula and the diagram agree. Now look at the full Southern Hemisphere table. Aircraft 2 at 135°W has convergence 135°W, Grid 225°, True 360°. Aircraft 3 at 135°E has convergence 135°E, Grid 315°, True 180°. Aircraft 4 at 90°E has convergence 90°E, Grid 360°, True 270°. Aircraft 5 at 45°E has convergence 45°E, Grid 090°, True 045°. So in the Southern Hemisphere, the rule is reversed: west of datum gives west convergence and True is greater than Grid; east of datum gives east convergence and True is less than Grid. That's the "Convergence West, True Best" rule. Now let's move to the worked examples on Polar Stereographic Charts, because these tie it all together. Example 1: Aircraft position is 45°N 110°W. Grid Track is 132°(G). Datum is 060°W. We need the True Track. First, is the aircraft east or west of the datum? 110°W is 50 degrees west of 060°W, so the answer is West, 50 degrees. Now, is that east or west convergence? In the Northern Hemisphere, being west of the datum gives you east convergence. On a Polar Stereographic chart, the convergence factor 'n' equals 1. That's a critical point: for a Polar Stereographic projection, 'n' is 1, so a 50-degree change of longitude gives exactly 50 degrees of convergence. No scaling factor—it's one-to-one. Given "Convergence East, True Least," and Grid Track is 132°(G), we subtract: 132° minus 50° equals 082°(T). That's the True Track. You can also verify this with a diagram. Plot the aircraft position at 45°N 110°W—that's the blue dot. Draw the datum from 060°W to the North Pole and continuing—that's the red solid line, and it gives you the direction of Grid North. Draw Grid North through the aircraft position as a dotted red line. Then draw the direction of True North as the blue line. Compare the aircraft's True track with the Grid track, and you'll see the True track is about 082°(T)—matching the arithmetic. Now Example 2, which is the reverse problem. Aircraft position is 28°S 118°E. True Track is 042°(T). Grid Track is 133°(G). We need to find the datum meridian, the convergence, and whether the aircraft is east or west of the datum. First, the difference between Grid and True: Grid is greater, so we subtract—133°(G) minus 042°(T) equals 91° East. That's the convergence. Now, in the Southern Hemisphere, we look at the diagram: if the convergence is east, the aircraft is east of the datum. So the datum meridian is west of the aircraft's position. Since the aircraft is at 118°E and the convergence is 91°, the datum is at 118°E minus 91°, which is 027°E. So the datum meridian is 027°E, the convergence is 91° East, and the aircraft is east of the datum. Let me make sure you've got the two hemisphere rules locked in, because they're the heart of this. Northern Hemisphere: west of datum gives east convergence, and "Convergence East, True Least"—so True is less than Grid. Southern Hemisphere: west of datum gives west convergence, and "Convergence West, True Best"—so True is greater than Grid. And remember, on a Polar Stereographic chart, 'n' equals 1, so convergence in degrees equals the change in longitude in degrees. That's the clean, one-to-one relationship that makes these calculations straightforward.