General Chart Properties — Page 288, Lesson 257

Let's start with the big idea. People make charts for all sorts of reasons, not just navigation. A farmer, for instance, might want to know whether 1000 hectares in Kansas produces more wheat than 1000 hectares in Azerbaijan. For that job, the map must represent area accurately — but it wouldn't matter at all whether bearings were accurate. So, from the huge range of projections available, we have to select only those which are orthomorphic, or conformal. Those two words mean the same thing. An orthomorphic chart is one that preserves shape and, crucially, preserves angles — which means bearings are represented correctly. Now, there are two fundamental conditions that must both be met to achieve orthomorphism, or conformality. Condition 1: The meridians and parallels on the chart must intersect at right angles, exactly as they do on the Earth. Let me show you why this matters. Consider a rectangle on the Earth's surface, and take the bearing of position X from position 0 — that bearing is 056°. Now, if the chart graticule has been distorted so the meridian/parallel intersection is not 90°, two things go wrong. The shape is incorrect, and the bearing from 0 to X is now shown as 028° instead of 056°. That chart is not conformal. So the first rule is simple: meridians and parallels must cross at right angles. Now, look back at the graticules we've discussed so far — they all meet that 90° intersect rule. So condition 1 alone isn't enough. Condition 2 relates to the scale at a point on the chart. Imagine a square on the Earth, with a line 0Y that has a bearing of 045°(T) — that's 045 degrees true. Now, on the chart, suppose the north-south scale has changed, but the east-west scale has stayed the same. The overall effect is that the square becomes a rectangle, and the bearing 0Y is now shown as 035°(T) instead of the correct 045°(T) on the Earth. That chart is not orthomorphic or conformal either. So the rule for condition 2 is this: on an orthomorphic chart, scale at a point should be the same in all directions. Now, you might look at that and think, "Doesn't that mean the chart should have constant scale everywhere?" And you'd be right to wonder — but constant scale is only true on a globe. On a flat chart, scale will change. So condition 2 gets modified to its final form: at any point on a chart, scale should be the same in all directions, or should change at the same rate in all directions. Let me tie this back to the simple cylindrical projection we saw earlier. The shapes there were distorted — stretched in the north-south direction, because the N-S scale was changing at a greater rate than the E-W scale. That violates condition 2. Mercator, the Flemish cartographer, recognized this problem and mathematically adjusted the N-S scale change to produce the conformal Mercator chart — and that's the subject of the next chapter. So, to summarize what we've got: orthomorphic means shape- and angle-preserving. Condition 1 requires meridians and parallels to intersect at right angles. Condition 2 requires scale at a point to be the same in all directions, or to change at the same rate in all directions. Both conditions must hold for a chart to be truly conformal.