Gridded Charts — Page 471, Lesson 471

Let’s pick this up right where the worked example leaves off. We’ve got an aircraft at 28°S, 118°E, and we’re told its grid track is 133°(G). The question is: where is the datum meridian? And the key to this is the relationship between grid track, true track, and convergence. First, let’s set the scene. On a gridded chart, we overlay a grid of parallel lines, and the grid is defined relative to a datum meridian. The datum meridian is the one meridian where grid north and true north coincide. Everywhere else, the grid and true north differ by the convergence between that meridian and the datum. Now, in this example, we’re given the true track as 042°(T) and the grid track as 133°(G). The difference between them is 133 minus 042, which is 91 degrees. That 91 degrees is the convergence between the aircraft’s meridian (118°E) and the datum meridian. So the rule is: grid track equals true track plus convergence, when the grid is oriented such that grid north is east of true north. Here, grid track is larger than true track, so the convergence is applied in that direction. Now, to find the datum: if the aircraft is 91 degrees east of the datum, and the aircraft is at 118°E, then the datum is at 118°E minus 91 degrees, which gives us 027°E longitude. That’s the numerical answer. But let’s also walk through the diagram method, because it helps you see which way to apply the convergence. On Figure 27.21, you’d plot the aircraft position at 28°S, 118°E — that’s the blue dot. Then you draw in the direction of true north at that position — the blue line. Next, you draw the true track of 042°(T) — the green line. That’s the direction the aircraft is actually moving relative to true north. Now, the grid track is 133°(G). That’s the direction of the aircraft’s path measured against the grid lines. So you draw that as the red dotted line. The angle between the true track and the grid track is that 91 degrees of convergence. To find the datum meridian, you parallel the grid through the South Pole. Why the South Pole? Because on a polar stereographic projection, the meridians converge at the pole, and the grid lines are parallel to the datum meridian. By drawing a line through the pole parallel to the grid direction, you locate the datum meridian. Now, a very important note: these diagrams are sketches, not scale drawings. They’re meant to help you visualize the situation and decide which way to apply the convergence. Once you’ve done that, you do the numerical calculation — which is exactly what we did: 118°E minus 91 degrees equals 027°E. So the datum meridian is at 027°E. That’s the answer. And the key takeaway is: grid track minus true track gives you the convergence, and you apply it to the aircraft’s longitude to find the datum.