Lambert’s Conformal Chart - 1 — Page 349, Lesson 309

Right, let's get into the Lambert's Conformal Chart. This is a big one for navigation, and I want to start by giving you the complete summary of its properties, because every single one of these points is examinable. You need to learn this table. First, the scale. On a Lambert chart, the scale is correct on the standard parallels. That's the fundamental anchor point. Between those standard parallels, the scale is contracted, meaning distances on the chart are slightly smaller than true scale. And importantly, this contraction is least at the parallel of origin. Outside the standard parallels, the scale is expanded, so distances appear slightly larger. So remember: correct on the standard parallels, contracted inside them, expanded outside them. Next, is it orthomorphic? Yes, it is. And here's a rule you must remember: all charts used for navigation must be orthomorphic. That's a hard requirement. Now the graticule — the pattern of meridians and parallels. On a Lambert chart, the meridians are straight lines, and they all originate from the pole. The parallels are arcs of circles, and they're centred on the pole. One key point: the pole itself is always off the map. You never see it on the chart. Then we have the parallel of origin. This is the mathematical basis of the projection. It's assumed to be halfway between the two standard parallels. This is the line that everything else is referenced to. Chart convergence. This is a critical one. On a Lambert chart, the convergence is constant across the entire chart. And the formula is: chart convergence equals change of longitude multiplied by the sine of the parallel of origin. So convergence = ch.long × sin(parallel of origin). That's a formula you'll use again and again. Now, rhumb lines. The meridians are straight lines, as we said. But all other rhumb lines — that is, lines of constant true bearing — are concave to the pole. The parallels of latitude are the exception; they're the rhumb lines that are arcs. Finally, great circles. The meridians are straight lines, so they're great circles. At the parallel of origin, a great circle appears as a near-straight line. But at any other latitude, a great circle is a curve that is concave to the parallel of origin. So let me tie that together. The parallel of origin is your reference. Scale is correct at the standard parallels, convergence is constant and depends on the parallel of origin, and great circle curvature is minimal at the parallel of origin. These are the core properties you must know cold. Now, let's look at what comes next in this chapter. We're going to build on these properties. The next sections cover constant scale, then the difference between earth convergence and chart convergence, then great circle curvature on a Lambert chart, then lines parallel at mid-meridian, and then the advantages and disadvantages of the Lambert chart, and finally plotting on it. Let's start with constant scale. This is where we see how the scale behaves in practice. On a Lambert chart, the scale is only truly correct at the standard parallels. Between them, it's contracted, and outside them, it's expanded. But here's the thing — over a limited area, the scale variation is so small that we can treat it as constant. That's what makes the Lambert chart so useful for navigation over large areas. The scale is effectively constant for practical purposes, even though it's not mathematically constant everywhere. Now, earth convergence versus chart convergence. This is a distinction you must understand. Earth convergence is the actual convergence of meridians on the real Earth — they all meet at the poles. Chart convergence is what the chart shows. On a Lambert chart, chart convergence is constant, as we said, and it's given by ch.long × sin(parallel of origin). But earth convergence varies with latitude — it's greater at higher latitudes. So the chart convergence is a fixed value, while earth convergence changes. This difference is what causes great circles to appear curved on the chart. Let me show you what happens with a great circle. On the real Earth, a great circle is the shortest path between two points. When we project that onto a Lambert chart, it doesn't stay straight. At the parallel of origin, it's a near-straight line. But at any other latitude, it curves — and it curves concave to the parallel of origin. That's the key visual you need to remember. Now, lines parallel at mid-meridian. This is a specific property. If you take two lines that are parallel at the mid-meridian — that is, at the midpoint of their longitude range — they will appear as straight lines on the chart. This is related to how the chart handles convergence. Then we have the advantages and disadvantages. The advantages of a Lambert chart are that it's orthomorphic, so shapes are preserved, and the scale is nearly constant over large areas, which makes it ideal for navigation. The disadvantages are that great circles are not straight lines except at the parallel of origin, and the scale is not exactly constant, so you have to account for the small variations. Finally, plotting on a Lambert chart. This is where you apply all of this. When you plot a track on a Lambert chart, you have to remember that a rhumb line is concave to the pole, and a great circle is concave to the parallel of origin. So the track you plot depends on what kind of line you're working with. That's the full picture of the Lambert chart. Let me know when you're ready to move on to the next part.