Total Leg Length = 78 — Page 208, Lesson 185

Let’s pick this up right where the arithmetic left off. We’ve got a 78 NM leg, and you’re 30 NM along it, so you have 48 NM to go. In practice, you won’t even need to work that out, because we normally mark our maps with distance-to-go, not distance gone. But for the calculation, we need that 48. Now, the key idea here is a single-step method to find the total angle to turn, instead of doing two separate calculations. Here’s the trick: take the proportion of your distance along track to the total leg length, and invert it. So for our example, the proportion is 30 over 78, and inverting it gives 78 over 30. Then you multiply your closing angle by that inverted fraction. We already worked out that 4 NM off track in 48 NM to go is 1 in 12, which is 5 in 60, so the closing angle is 5°. Now multiply: 5° times 78 over 30 gives you 13°. That 13° is the total angle to turn — the angle you need to head directly for the destination turning point. Now, an important point: this is not an approximation. You can prove geometrically that this method gives precisely the same answer as separately calculating the Track Error Angle and the Closing Angle and adding them together. In this example, we deliberately chose numbers that weren’t exactly a half, a third, or a quarter, just to show the arithmetic works even for awkward results like 13°. In practice, most of the time you’ll just estimate that you’re approximately, say, one-third of the way along your leg, so you need to alter by 3 times your Closing Angle. Now, let’s move on to using these methods practically. I should flag that this next material is not examined as part of the EASA ATPL exam, but it may be used in your flying training. So listen up, because it’s genuinely useful. In practice, you don’t have to carry out 1-in-60 calculations in the air to work out your Track Error Angle and Closing Angle. Instead, what you should do is, during preflight preparation, mark up the track on your map with 5° and 10° guide lines, as shown in Figure 11.12. With those guidelines, you can rapidly assess the Track Error Angle and Closing Angle of any visual fix you get on that leg. Then you just add the Track Error Angle to the Closing Angle to know the total angle to turn to head for the destination turning point. Practically speaking, though, drawing all those guidelines results in too cluttered a chart. So the recommended teaching is to draw just one guideline at each end of track, at 10°, as in Figure 11.13. Similarly, you don’t have to use a ruler in the air to assess your distances along and across track. Instead, mark up your map with distance-to-go using 10 NM markers. Do not use distance gone — that is of no interest to you. What you need to know is how many miles remain, without having to carry out subtraction in your head. So you mark up the map as shown in Figure 11.14. That figure shows a track of length 44 NM, and any time you get a visual fix you can instantly see how far you have to go. You also have a useful 10 NM scale to help you assess distances off track, if you need to. The recommended technique is a combination of these two methods: mark up the Closing Angle guidelines and the distance-to-go markers together. That way, with a single glance at a fix, you can read off both the angle to turn and the miles remaining, without any mental arithmetic.