
Let me walk you through this. We've just corrected an 8° track error by turning 8° right, which put us paralleling track — 4 NM to the left of it. But that's not good enough. We're not getting back to track, just not getting worse.
Why not just turn a bit more and map-read our way back? Two reasons. First, there might be nothing significant on the ground to tell us when we're back on track. Second — and this is the big one — we don't want a technique that demands continuous attention. As a single pilot you're already flying the aeroplane, monitoring weather, thinking about fuel, making radio calls, doing engine and electrics checks, and most importantly looking out for other traffic. We want to minimise the time spent actually navigating. So we want a measured, controlled turn that tells us when we're back on track without map-reading.
Here's the trick. Instead of turning just 8° right, we turn another 8° right — a total change of 16° right. By turning through exactly double the track error angle, we create an isosceles triangle. Look at Figure 11.6 — it's symmetrical about the cross-track error line, the line marked '4'. We're converging back to track at a closing angle of 8°. Because it's an isosceles triangle, the distance to get back on track equals the distance it took to get off track. So the times are the same — there may be a tiny difference because ground speeds aren't absolutely identical, but it's only a matter of seconds, certainly less than a minute.
So here's the practical picture. Suppose I start on track at 1000 hours and find myself off track at 1020. I turn by double the track error angle — 16° right. I'll be back on track at 1040. No continuous map-reading. All I do is look at my watch. That's the beauty of it — the geometry does the work.
But the story doesn't end there. Once we re-cross our planned track, having turned 16° right at our pinpoint, if we do nothing about it, we'll now diverge to the right of track. We've solved the original problem but created a new one — we're heading off the other side. That's what we'll deal with next.
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