Gridded Charts — Page 471, Lesson 467

Let’s pick this up right where the standard grid idea comes from. I want to walk you through why these charts are built the way they are, and then we’ll do the actual conversions step by step. First, the key property: on a polar stereographic chart, the meridians converge at a constant, predictable rate. That property makes these charts ideally suited for a standard polar grid — a grid printed on the chart for all users, so nobody has to draw their own. The whole point of a standard grid is to eliminate confusion over the alignment of those few VOR/TACAN stations which are not aligned with Magnetic or True North but with Grid North. So instead of aligning to True North or Magnetic North, those stations align to the grid itself. Now, the datum. In the Northern regions, the datum meridian used is the Greenwich meridian. Here’s the rule you must hold onto: at any True meridian, the chart convergency will be equal to the longitude, with the sign reversed. Let me show you with the examples. At 45°W, chart convergency = 45°E. At 45°E, chart convergency = 45°W. So west longitude gives east convergence, and east longitude gives west convergence — sign reversed, exactly as stated. Let’s apply that to a route from A to B in Figure 27.16. The Grid Track is 090°(T) — that’s the track measured against the grid, 090 degrees. At 45°W, the track is 090°(G) minus 45°E convergence, which gives 045°(T). At 45°E, the track is 090°(G) plus 45°W convergence, which gives 135°(T). Notice the pattern: west of the datum you subtract the convergence, east of the datum you add it — because the convergence sign flips with the longitude. Now the Southern hemisphere. The Greenwich meridian is again used as the datum meridian. And here’s the rule for the south: the chart convergency is always equal to the longitude when a standard grid is used. No sign reversal in the south — it’s just equal to the longitude. To keep the orientation with Grid North at the top, diagrams illustrating the standard south polar grid are normally drawn with the 180°E/W meridian at the bottom of the diagram. Let’s work the south polar example from Figure 27.17. Grid Track A to B is constant 070°(G). At point A, longitude is 45°W, so convergence is 45°W. The track is 070°(G) plus 45°W convergence, which gives 115°(T). At point B, longitude is 45°E, so convergence is 45°E. The track is 070°(G) minus 45°E convergence, which gives 025°(T). Now at point X, the track is 090°(G), and the convergence is 180°E/W — that’s the 180 meridian, which is the bottom of the diagram. So the track is 090°(G) plus or minus 180°E/W, which gives 270°(T). The plus-or-minus there is because at 180°E/W, the convergence is a full 180 degrees, and the sign depends on which side you’re on. Now let’s move to the conversion problems, and this is where the ‘n’ factor comes in. Figure 27.18 represents a North Polar Stereographic Projection. The ‘n’ factor — that’s the relationship between the inclination of the meridians and the change of longitude — is 1.00. So on this chart, the meridians converge exactly at the rate of longitude change; that’s what makes the standard grid work cleanly. Consider Aircraft No. 1. Just by inspection of the diagram, you can see its Grid heading is 360°(G) — that’s grid north, straight up — whilst the True heading is 270°(T). So the True heading is 90 degrees less than the Grid, by simple visual inspection. Now let’s work it out using convergence. If Grid North is at the 12 o’clock position, then the datum meridian must be the Greenwich meridian — we now have a Standard Grid. Aircraft 1 is at longitude 090°W, which means the aircraft is west of the datum. From the diagram: Northern hemisphere, aircraft west of datum, therefore convergence east. And here’s the rule you need to memorize: Convergence East, True Least. That means if the convergence is east, the True heading is less than the Grid heading. So the True heading should be 90 degrees less than Grid — which it is. Both the convergence formula and the diagram give the same answer. Now, the exercise continues with Aircraft Nos. 2 to 5 — you’d apply the same logic to each: identify whether the aircraft is east or west of the datum, apply the convergence sign, and use the Convergence East, True Least rule to check your True heading against the Grid heading.