Let me set the scene — Page 457, Lesson 458

Let me walk you through how navigation actually works in practice, because the theory of flying a perfect straight line on a chart is only half the story. We've been talking about the idea of a straight line on your chart being 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. But here's the key point: most non-automatic navigation is done using the other option, which is the great circle track. That's what this chapter on gridded charts is really about. Let me set the scene. We're flying a leg, and 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 take position fixes at intervals, compare where we are to where we should be, and make corrections to get back on the straight-line track. After a certain time, we take our first fix. There will probably be some cross-track error — that's the distance we are sideways off the intended track. This error is mainly caused by a combination of components. The first is changes in the wind from the forecast value — the wind we actually meet differs from what we predicted. The second is 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). Why does the straight-line track alter? Because we're flying a great circle, and the track direction relative to true north changes as we move along it — that's convergency, the way meridians converge toward the poles. But this component is completely swamped by the other random navigation errors, of which the wind and heading errors are far the greatest components. In fact, we do not even notice the cross-track position error caused by convergency because it is 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. Here's the clever bit: we locally measure the track near the fix, using the local meridian — the meridian at our current position. By doing that, we automatically correct for the convergency. We don't need to calculate it separately. During the course of the leg, the datum track — the reference track we're trying to hold — will change from 082°(T) to 098°(T). That's a 16-degree change over the leg. But the process happens simply by correcting back to the straight-line track on the chart and measuring using the local meridian each time. We don't chase a fixed bearing; we chase the straight line on the chart, and the local meridian does the convergency correction for us. So the whole art of practical great circle navigation is this: set off on the initial track, fix, correct back to the straight line using the local meridian, and repeat. The track direction changes under you, but you never have to think about it explicitly — the chart and the local meridian handle it. That's the essence of flying the great circle track.