General Chart Properties — Page 288, Lesson 257

I want to walk you through the core idea of what makes a chart useful for navigation. People produce charts for many reasons—farming, for example. If you're a farmer, you might want to know whether 1,000 hectares in Kansas produces more wheat than 1,000 hectares in Azerbaijan. For that, you need a map that shows area accurately. But it wouldn't matter to you whether bearings are represented accurately. For navigation, it's the opposite. From the vast range of projections available, we have to select only those which are orthomorphic, also called conformal. That's the key term: orthomorphic or conformal means the chart preserves shape and angles locally. There are two fundamental conditions that must be met to achieve orthomorphism or conformality. Condition 1: The meridians and parallels on the chart must intersect at right angles—just as they do on the Earth. Let me illustrate that with Figure 17.7. Consider a rectangle on the Earth's surface. Let's say the bearing of position X from position 0 is 056°. Now look at Figure 17.7b: the chart graticule has been distorted, and the meridian-parallel intersection is not 90°. The shape is incorrect, and the bearing from 0 to X is now 028° instead of 056°. That chart is not conformal. The graticules we've discussed so far all meet the 90° intersect rule. Condition 2: This relates to the scale at a point on the chart. Look at Figure 17.8. A square on the Earth is shown, with a line 0Y that has a bearing of 045° True. In Figure 17.8b, representing the chart, the north-south scale has changed, but the east-west scale has stayed the same. The shape has changed to a rectangle, and the bearing 0Y is now 035° True instead of the correct 045° True on the Earth. That chart is not orthomorphic or conformal. So here's the rule: on an orthomorphic chart, scale at a point should be the same in all directions. Now, that diagram might make you think a chart should have constant scale everywhere—but we know constant scale is only true on a globe. On a flat chart, scale will change. So condition 2 is modified to say: 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 that back to the simple cylindrical projection from Figure 17.3. On that projection, shapes have been distorted—stretched in the north-south direction because the north-south scale is changing at a greater rate than the east-west scale. Mercator, the Flemish cartographer, recognized this problem. He mathematically adjusted the north-south scale change to produce the conformal Mercator chart, which is the subject of the next chapter.