Gridded Charts — Page 471, Lesson 469

We're moving into the heart of gridded charts now — the actual conversion between Grid and True headings. This is where all the theory we've built up gets put to work, and I want to walk you through the worked examples because they show you the exact reasoning you'll use in the exam and in the aircraft. Let's start with the Northern Hemisphere answers you have in front of you. Look at the table. For each aircraft, we're given the longitude, the convergence, the Grid heading, and the True heading. Take Aircraft 1: longitude 90°W, convergence 90°E, Grid heading 360°, True heading 270°. Notice the pattern — in the Northern Hemisphere, when you're west of the datum, you get east convergence, and the rule is "Convergence East, True Least." So the True heading is smaller than the Grid heading. 360° minus 90° gives you 270° True. That's exactly what the table shows. Now, Aircraft 2: longitude 45°W, convergence 45°E, Grid heading 225°, True heading 180°. Again, west of datum, east convergence, True is less. 225 minus 45 is 180. Aircraft 3: longitude 45°E, convergence 45°W, Grid heading 315°, True heading 360°. Here you're east of the datum, so you get west convergence, and the rule flips — "Convergence West, True Best." So True is greater than Grid. 315 plus 45 gives you 360. Aircraft 4: 90°E, convergence 90°W, Grid 000°, True 090°. East of datum, west convergence, True best — 000 plus 90 is 090. And Aircraft 5: 135°E, convergence 135°W, Grid 090°, True 225°. East of datum, west convergence, True best — 090 plus 135 is 225. Now, the Southern Hemisphere is more of a challenge, and I want you to really focus here because the reasoning is different. Look at Figure 27.19, the South Polar Stereographic Projection. Aircraft 1 — by visual inspection, the Grid heading is 000° and the True heading is 090°. Remember, in the Southern Hemisphere, True North points away from the South Pole. So True is 90 degrees greater than Grid. Here's the key reasoning. If Grid North is at the 12 o'clock position, then the datum meridian must be the Greenwich meridian — that means we have a Standard Grid. Aircraft 1 is at longitude 090°W, which means the aircraft is west of the datum. Now, from the diagram, in the Southern Hemisphere, when the aircraft is west of the datum, the convergence is west. And the rule is "Convergence West, True Best." So True heading should be 90 degrees greater than Grid — which it is. Both the convergence formula and the diagram give the same answer. Now look at the Southern Hemisphere answers table. Aircraft 1: longitude 90°W, convergence 90°W, Grid 000°, True 090°. Aircraft 2: 135°W, convergence 135°W, Grid 225°, True 360°. Aircraft 3: 135°E, convergence 135°E, Grid 315°, True 180°. Aircraft 4: 90°E, convergence 90°E, Grid 360°, True 270°. Aircraft 5: 45°E, convergence 45°E, Grid 090°, True 045°. Notice the difference — in the Southern Hemisphere, the convergence has the same name as the direction you are from the datum. West of datum gives west convergence, east of datum gives east convergence. And the rule is still "Convergence West, True Best" — so when convergence is west, True is greater; when convergence is east, True is less. Now let's move to the worked conversion problems on Polar Stereographic Charts. Example 1. Aircraft position 45°N 110°W. Grid Track is 132°(G). Datum is 060°W. What is the True Track? First question — is the aircraft east or west of the datum meridian? The answer is West, 50 degrees West. 110°W minus 060°W is 50 degrees. Now, is that east or west convergence? From the diagram, in the Northern Hemisphere, being west of the datum gives you east convergence. So we have east convergence. Now, with a Polar Stereo Chart, the 'n' factor equals 1. That's the convergence factor for a polar stereographic projection. So a 50 degree change of longitude equals 50 degrees of convergence. No scaling — it's one-to-one. Given the rule "Convergence East, True Least," and the Grid Track is 132°(G), the True Track is 132°(G) minus 50 degrees, which equals 082°(T). Now, you could also do this with a diagram, and I want you to look at Figure 27.20. Plot the aircraft position, 45°N 110°W — that's the blue dot. Draw in the datum, from 060°W to the North Pole and continuing — that's the red solid line. This gives you the direction of Grid North. Then draw in Grid North through the aircraft position — the dotted red line. Then draw in the direction of True North — the blue line. Now compare the aircraft True track with the Grid track. You can see the True track is about 082°(T) — which is the same answer as the arithmetical calculation. Both methods agree. Now Example 2 — this one is reversed. Aircraft position 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. 133°(G) minus 042°(T) equals 91° East. So the convergence is 91° East. Now, in the Southern Hemisphere, look at the diagram — the aircraft is east of the datum. And remember, in the Southern Hemisphere, east of datum gives east convergence. So the convergence is east, which matches our calculation of 91° East. Now, to find the datum meridian — since the aircraft is at 118°E and is east of the datum, and the convergence is 91° East, the datum must be 91 degrees west of the aircraft's longitude. 118°E minus 91° gives you 027°E. So the datum meridian is 027°E. Let me make sure you see the full picture here. In the Southern Hemisphere, the convergence has the same name as your position relative to the datum. East of datum, east convergence. And the rule "Convergence East, True Least" still applies — so True is less than Grid, which is why 133°(G) minus 91° gives you 042°(T). Now, I want you to notice something important about the 'n' factor. In Example 1, we used 'n' = 1 for the Polar Stereo Chart. That's the convergence factor. On a polar stereographic projection, the convergence equals the change of longitude exactly — one degree of longitude change gives one degree of convergence. That's why we could just take the 50 degrees of longitude difference directly as 50 degrees of convergence. The key relationships you need to hold onto are these. First, the convergence rule: "Convergence East, True Least" and "Convergence West, True Best." Second, the hemisphere rule: in the Northern Hemisphere, west of datum gives east convergence; in the Southern Hemisphere, west of datum gives west convergence. Third, the 'n' factor for a polar stereographic chart is 1, so convergence equals the change of longitude. Let me also point out the visual method from Figure 27.20 — it's a powerful cross-check. When you draw the datum line through the pole, that gives you the direction of Grid North. Drawing Grid North through the aircraft position, and True North through the aircraft position, lets you physically compare the two tracks. The angle between them is the convergence. This is exactly what you'd do on a chart in the aircraft, and it's a great way to verify your arithmetic. So, to summarise the whole process: you identify whether you're in the Northern or Southern Hemisphere, you determine whether you're east or west of the datum, you apply the appropriate convergence rule, you use the 'n' factor to convert longitude change to convergence, and then you apply the "True Least" or "True Best" rule to convert between Grid and True. Both the arithmetic and the diagram methods will give you the same answer, and you should be comfortable with both.