Lambert’s Conformal Chart - 1 — Page 349, Lesson 307

I want to walk you through the Lambert's Conformal Chart, and we're going to start with the heart of it: chart convergence, and then how rhumb lines and great circles behave on this projection. Let's begin with convergence. On a Lambert chart, the meridians are drawn as straight lines. Because they're straight, the angle between any two selected meridians — what we call the chart convergence — does not change with latitude. In other words, chart convergence is constant on a Lambert chart. That's a key property to hold onto. Look at Figure 21.14 in your mind: we have meridians through points A, C, and E, and we've drawn parallels through B, D, and F. The angles marked 'CC' — that's chart convergence — are all equal to each other. So no matter where you measure it between those meridians, the convergence is the same. Now, rhumb lines. A rhumb line is a line that crosses every meridian at the same angle — a constant true track. On a Lambert chart, except for the meridians themselves, which appear as straight lines, rhumb lines are curves that are concave to the pole of the projection. The parallels of latitude are also rhumb lines, and they too are curves concave to the pole. Now let's talk about great circles. A great circle is the shortest path between two points on a sphere — the intersection of the Earth's surface with a plane through the Earth's centre. On a Lambert chart, except for the meridians, great circles appear as curves concave to the parallel of origin. A straight line drawn in an east-west direction most nearly represents a great circle when it's drawn between two positions on the parallel of origin itself. Let me explain why, step by step. Imagine a spherical Earth — the real Earth, or a Reduced Earth, which is just a scale model of it. On that sphere, the meridians converge towards each other as latitude increases. Now imagine three great circle tracks at different latitudes — one near the equator, one mid-latitude, one high latitude. Now, what happens when we project this real Earth situation onto a Lambert chart with a parallel of origin of 45°N? The Earth's curved meridians are straightened out into straight-line chart meridians. That straightening means the formerly straight-line great circles get stretched outwards at latitudes higher or lower than the parallel of origin. So the great circles become straight lines exactly at the parallel of origin, and curves concave to the parallel of origin at any other latitude. Here's the crucial practical point: the amount of curvature shown in the diagrams is exaggerated to make the explanation clear. In reality, there is very little curvature compared with a straight line. For all practical purposes — including plotting — great circles on a Lambert chart may be treated as straight lines. That's a huge simplification for navigation. One more contrast to note: the amount of curvature on a rhumb line is far greater than on a great circle. We'll come back to that in the next chapter. So to summarise what we've covered: chart convergence is constant on a Lambert chart because meridians are straight; rhumb lines are curves concave to the pole; great circles are curves concave to the parallel of origin, but so close to straight that we treat them as straight for plotting. And the parallel of origin is the key reference — it's where the projection is most accurate.