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 the examiners love it, so we’re going to nail down the properties properly. I want to start with the summary of properties, because that's the core of what you need to know. Think of this as the definitive checklist for this projection. First, Scale. On a Lambert chart, the scale is correct on the standard parallels. That's the key reference. Between those standard parallels, the scale is contracted, and it's least at the parallel of origin. Outside the standard parallels, the scale is expanded. So you have a zone of contraction in the middle, and expansion beyond the edges. Next, Orthomorphic. Yes, it is orthomorphic. And remember, all charts used for navigation must be. Orthomorphic means it preserves shape — angles on the chart match angles on the Earth, which is essential for plotting bearings. Now the Graticule — the grid of meridians and parallels. 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. A crucial point: the pole is always off the map. You never see it on the chart itself, but the geometry all radiates from it. 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. So if your standard parallels are at, say, 40°N and 50°N, the parallel of origin sits at 45°N. Next, Chart Convergence. This is a big one. On a Lambert chart, chart 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. A rhumb line is a line of constant bearing. On a Lambert chart, the meridians themselves are straight lines. But all other rhumb lines are concave to the pole. That means they curve away from the pole, like the parallels of latitude do. Finally, Great Circles. A great circle is the shortest path between two points on a sphere. On a Lambert chart, the meridians are straight lines. At the parallel of origin, a great circle appears as a near-straight line. But at any other latitude, it's a curve that is concave to the parallel of origin. Now, I want you to look at that figure — Figure 21.12 — it shows part of a Lambert conical orthomorphic chart. You can see how the meridians converge and the parallels curve. That's the visual representation of everything we just covered. Let me just recap the key contrasts, because they're exam gold. Scale: correct at standard parallels, contracted inside, expanded outside. Rhumb lines: concave to the pole. Great circles: concave to the parallel of origin. And chart convergence: constant, calculated with that sine formula. That's the full property set. Now, the chapter goes on to cover constant scale, earth convergence versus chart convergence, great circle curvature, and the advantages and disadvantages of the Lambert chart. But for now, make sure you've got this summary locked in — it's the foundation for everything that follows.