Lambert’s Conformal Chart - 2 — Page 361, Lesson 314

Let’s pick this up right where the conversion angle left off, because that’s the key to everything on this page. Look at the three conversion angles in Figure 22.9. We have CA at 47°N equals half of 20° times the sine of 47°, which works out to 7.314°. At 45°N, half of 20° times the sine of 45° gives 7.071°. And at 43°N, half of 20° times the sine of 43° gives 6.820°. The point I want you to see is that these conversion angles are different for each latitude. The same 20° of longitude change, but the conversion angle shrinks as you move toward the parallel of origin. Now, here’s the clever bit. If you plot those conversion angles in at the other end of the line and join them up, you get the great circle track paths. That’s exactly why a great circle appears as a straight line at the parallel of origin, but is concave to the parallel of origin at any other latitude. The straight lines — those are the rhumb lines — always make the same angle to the rhumb line whatever their latitude. But the angle that the great circle makes to the rhumb line depends on its latitude. So the rhumb line is constant, the great circle bends, and the difference between them is the conversion angle, which varies with latitude. Now let’s look at Figure 22.10, the great circles, and then the next idea: lines parallel at the mid-meridian. If two positions are joined by a straight line, a great circle, and a rhumb line on a Lambert chart, they are all parallel to each other at the mid-meridian. That’s Figure 22.11. So at the midpoint of the track, all three lines run in the same direction. Now, the advantages of a Lambert chart. First, great circles can be treated as straight lines for all practical purposes. That’s huge. Second, radio bearings are great circles, so they can be plotted without applying a conversion angle. You still need to apply convergence by paralleling the NDB’s meridian from the aircraft’s DR meridian position, but no calculation is involved — I’ll explain that below. Third, if scale error is small, a graduated ruler can be used to measure distances. Now the disadvantages. Flying by compass gives rhumb line tracks, so if great circle tracks are to be flown, the aircraft must have a system which provides automatic continuous computation of desired track — that’s INS, IRS, FMS, or GPS — or the aircraft must be steered by gyro without transport wander correction. Also, the graticule is not rectangular, so plotting positions is not as simple as on a Mercator. And NDB position lines have to be plotted using meridian transfer — again, explained below. Finally, plotting on a Lambert chart. It’s less complicated than on a Mercator because great circles — radio waves — are straight or near-straight lines, so there’s no conversion angle to apply. However, there may be a correction for chart convergence to apply. And it depends on whether the bearing is measured at the ground station or at the aircraft. That distinction is the crux of the next part, so hold onto it.