Lambert’s Conformal Chart - 2 — Page 361, Lesson 318

Right, let’s pick this up where we left off. We’ve just dealt with plotting a bearing from a line drawn parallel to the aircraft’s meridian through the NDB. Now, the key point I want you to take from this first part is that chart convergence is automatically allowed for by drawing that line parallel to the aircraft’s meridian through the NDB. This method is always used in plotting. But what if you need the bearing to plot from the meridian of the NDB itself, rather than from that parallel line? Well, in that case, reference to Figure 22.12(b) shows that it’s equal to 090° minus chart convergence. Let me walk you through the example to make this concrete. An aircraft is flying in the Northern hemisphere on a heading of 330°(T) and measures a bearing of 090°(R) of an NDB. We’re asked two things: what is the bearing to plot on a Lambert chart, first from a line parallel to the aircraft’s meridian drawn through the NDB, and second from the meridian of the NDB, given chart convergence is 3°. For part (a), we add the heading to the relative bearing: 330° plus 090°(R) gives 060°(T). That’s the true great circle bearing of the NDB from the aircraft. So we plot 240° from a line parallel to the aircraft’s meridian drawn through the NDB. Notice we plot the reciprocal, 240°, because we’re plotting the bearing from the NDB back to the aircraft. See Figure 22.13(a). For part (b), the bearing to plot from the meridian of the NDB is 240° plus 3°, which is 243°. So the chart convergence is added here. Now, there’s a crucial note here about variation. In the case of bearings measured at the aircraft, it’s the aircraft’s compass which is used to add to relative bearing in order to obtain true bearing. So if the heading is magnetic and you need to correct it to True, you always use variation at the aircraft. But for bearings measured at a ground station — like VOR or VDF — you use variation at the ground station. For bearings measured at the aircraft — like NDB/ADF or AWR — you use variation at the aircraft. That’s a distinction you must keep straight. Now let’s move to the next set of examples, which deal with the relationship between the straight line on a Lambert chart, the rhumb line, and the great circle. Example 1: Two points A and B are plotted on a Lambert chart and joined by a straight line, which from the meridian of A measures 250°(T). Given that the chart convergence of the meridians through A and B is 6°, what is the rhumb line track from A to B, and what is the approximate great circle bearing of A from B, as given by the straight line, measured from the meridian of B? Assume Northern hemisphere. The key relationship here is that the angle between the straight line and the rhumb line is half the chart convergence, so 3°. For part (a), the rhumb line track from A to B is 250° minus 3°, which is 247°(T). For part (b), the rhumb line bearing of A from B is 247°(T) minus 180°, which is 067°(T). Then the straight line bearing is 067° minus 3°, which is 064°(T). Example 2: The straight line from A to B, both in the Northern hemisphere, is plotted on a Lambert chart and cuts the mid-meridian in the direction of 300°(T). Measured from the meridian through A, the direction of the straight line is 302°(T). We need the rhumb line track from A to B, the chart convergence of the meridians through A and B, and the approximate GC bearing of A from B. For part (a), the rhumb line and straight line are parallel at the mid-meridian. So the rhumb line track from A to B is 300°(T). For part (b), the straight line at A is 302°(T) and the rhumb line is 300°(T), so half the chart convergence is 2°, meaning the chart convergence is 4°. For part (c), the rhumb line bearing of A from B is 120°(T), and with half chart convergence of 2°, the approximate great circle bearing is 118°(T). So the pattern you should see is this: on a Lambert chart, the straight line between two points is the great circle, and the rhumb line curves toward the pole. The difference between them at any point is half the chart convergence. That’s the conversion angle, and it’s what we’re using in all these calculations.