The key idea here is the straight line on your chart — Page 457, Lesson 458

Let me walk you through how navigation actually happens in practice, because the theory we just covered isn't how most flying is done. The key idea here is the straight line on your chart. That line is supposed to be the track you're trying to fly. If you wanted to fly a rhumb line track — that's a line of constant bearing that crosses all meridians at the same angle — you'd use a Mercator chart, because on a Mercator projection a rhumb line appears as a straight line. But most non-automatic navigation is done using the other option, which is the great circle track. So here's the practical scenario. We set off on an initial track of 082°(T) — that's 082 degrees true, measured from true north. We then settle into our normal regular cycle of fixing and correcting back to track. That means we periodically take a position fix, compare it to where we should be, and make corrections to get back onto the line. After a certain time we take our first fix. There will probably be some cross-track error — that's the distance we've drifted sideways off the intended track. This error is mainly caused by a combination of two components. First, changes in the wind from the forecast value — the wind we actually encounter differs from what we predicted. Second, inaccurate heading hold — we don't maintain our heading perfectly. Now here's the subtle part. The cross-track error will also include a small component caused by holding a track of 082°(T) whilst the straight line track has actually altered to, say, 083°(T). This is the effect of convergency — the meridians converge toward the poles, so the true track of a great circle changes as you move along it. But this component is completely swamped by the other random navigation errors, which are far the greatest components. We don't even notice the cross-track position error caused by convergency because it's usually so small at low to medium latitudes. So what do we actually do? We plot our fix, then use our protractor to make a normal correction to get back to track. We locally measure the track near the fix — that is, we measure the angle using the meridian closest to our position — and this automatically corrects for the convergency. During the course of the leg, the datum track will change from 082°(T) to 098°(T), but the process happens simply by correcting back to the straight-line track on the chart and measuring using the local meridian. That's the beauty of this method. We don't need to calculate convergency explicitly. By measuring the track locally at each fix, using the local meridian, we automatically account for the changing track angle. The straight line on the chart is the great circle track, and our local corrections keep us on it without us ever having to think about the mathematics of convergency. This figure shows the fundamental geometry — A is at longitude 70°W, and the line defining True North is the line joining A to the North Pole. That's the meridian through A, and it's the reference we use when we measure our track locally.