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

Right, let’s pick this up where we left off. We’ve just seen that the conversion angle isn’t a fixed number — it changes with latitude. Look at the three values in Figure 22.9: at 47° north, the conversion angle is 7.314°; at 45° north, it’s 7.071°; and at 43° north, it drops to 6.820°. Each one is half of 20° multiplied by the sine of the latitude. So the conversion angle is different for every latitude — that’s the key point. Now, here’s the clever bit. If you plot those conversion angles at the other end of the line and join them up, you trace out the great circle track path. That’s why a great circle appears as a straight line at the parallel of origin — the latitude where the chart is truly conformal — but it’s concave to the parallel of origin at any other latitude. The straight rhumb line always makes the same angle to the great circle, whatever the latitude, but the angle the great circle makes to the rhumb line depends on its latitude. So the great circle curves toward the parallel of origin, and the rhumb line stays straight. Now, there’s a very useful property called “Lines Parallel at Mid-meridian.” If you join two positions with 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 — the meridian halfway between the two positions. That’s Figure 22.11, and it’s the basis for measuring. Let’s talk about the advantages of the Lambert chart. The big one: great circles can be treated as straight lines for all practical purposes. That matters because radio bearings are great circles, so you can plot them 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 there’s no calculation involved — I’ll explain that in a moment. And if the scale error is small, you can use a graduated ruler to measure distances directly. Now the disadvantages. Flying by compass gives you rhumb line tracks, so if you want to fly a great circle track, the aircraft must have a system that 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 isn’t as simple as on a Mercator. And NDB position lines have to be plotted using meridian transfer — again, I’ll cover that below. So, plotting on a Lambert chart is 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 that depends on whether the bearing is measured at the ground station or at the aircraft. That’s the next piece we’ll dig into.