You need to lose 6500 feet at a rate of descent of 800 feet per minute — Page 486, Lesson 487

Let’s start with the descent problem, because it ties together the numbers you’ll see in the answer. You need to lose 6500 feet at a rate of descent of 800 feet per minute. So the time in the descent is 6500 divided by 800, which is 8.125 minutes. At a groundspeed of 156 knots, in 8.125 minutes you cover 21.1 nautical miles. But you don’t want to reach the DME at 1000 feet — you need to be down at 1000 feet 6 nautical miles before the DME. So the range at which you start the descent is 21.1 plus 6, which is 27.1 NM. That’s the answer to that part. Now I want to move into the chart work, because this is where the real meat of this section is. We’re looking at Lambert Conical Orthomorphic charts and Polar Stereographic charts, and the key idea is convergence. For all practical purposes, a straight line drawn on a Lambert Conical Orthomorphic chart — that’s the conformal chart — or on a Polar Stereographic chart at high latitudes, can be considered to be a great circle. But the plotting you’re concerned with as a pilot deals with aircraft that fly rhumb line tracks. So there’s a distinction: the straight line on the chart is a great circle, but the aircraft actually flies a rhumb line. Let me define those terms clearly. A great circle is the shortest path between two points on the surface of a sphere — the path you’d get if you cut the Earth with a plane through its centre. A rhumb line is a track that crosses all meridians at the same angle — a constant true track. On a Mercator chart a rhumb line is a straight line, but on a Lambert chart it isn’t. Now, measuring tracks. If an aircraft is to fly from A to B, you join the two positions with a straight line — that’s the great circle — and you measure its direction using the mid-meridian. That gives you the rhumb line track on the 1:1 000 000 scale chart. So the mid-meridian is the meridian halfway between A and B, and you measure the angle of the straight line against that meridian to get the rhumb line track. Plotting headings and tracks. If you have a known heading or track that you need to plot, you draw it using the nearest meridian to the position from which it has to be drawn. Any subsequent error is ignored — that’s the accepted simplification. Measuring distances. On a chart where the scale cannot be considered constant — and that’s the case on a Lambert chart — you must measure distances using the latitude scale locally. You don’t use a single scale for the whole chart; you use the latitude scale at the position you’re measuring. Plotting positions. This takes a little longer than on a Mercator chart, because the Lambert graticule is not rectangular. The procedure is as follows. First, mark the longitude of the position to be plotted in the longitude scale to the north of the position, and also in the longitude scale to the south of the position. Then lay a straight edge between those two points. Then, using a pair of dividers, plot the latitude along the length of the straight edge, upwards or downwards from the nearest parallel of latitude. Now, plotting ADF bearings. This is where convergence really matters. If the change of longitude — that’s the ch.long — is 2 degrees or more, you draw a line parallel to the aircraft’s meridian through the NDB, and plot the bearing as shown in Figure 28.4. If the change of longitude is less than 2 degrees, you plot from the meridian of the NDB directly. That distinction is explained in more detail in the next paragraph. So the key contrast here is: for small changes of longitude, under 2 degrees, you can plot the bearing straight from the NDB’s meridian. For larger changes of longitude, 2 degrees or more, you must draw a line parallel to the aircraft’s meridian through the NDB first, and then plot the bearing from that line. Let me make sure the descent numbers are clear in your mind, because they’re the kind of thing you’ll be asked to compute. 6500 feet at 800 feet per minute gives 8.125 minutes. At 156 knots, that’s 21.1 NM. Add the 6 NM buffer before the DME, and you get 27.1 NM as the range to start the descent. That’s the complete answer. Now, the chart work — the central idea is convergence. On a Lambert chart, meridians converge towards the poles, so a straight line between two points is a great circle, but the aircraft flies a rhumb line. To measure the rhumb line track, you use the mid-meridian. To plot a heading or track, you use the nearest meridian. To measure distance, you use the local latitude scale. To plot a position, you mark the longitude on both the north and south longitude scales, lay a straight edge between them, and use dividers to plot the latitude from the nearest parallel. And for ADF bearings, the change of longitude determines whether you draw a line parallel to the aircraft’s meridian through the NDB — that’s for 2 degrees or more — or plot directly from the NDB’s meridian — that’s for less than 2 degrees. That’s the full picture for this section.