The Polar Stereographic Chart — Page 367, Lesson 327

Let’s pick this up right where the numbers matter most. We’ve just worked out that at 70°N, over a 90° change of longitude, the straight line on the chart and the Great Circle track differ by only 2.7°. That’s the key result that lets us make a practical rule for the Polar Stereographic chart. Here’s the reasoning again, because it’s the heart of the whole idea. At 70°N, the angle between a straight line and a Rhumb Line over a 90° change of longitude is 45°. The angle between the Great Circle and the Rhumb Line is what we call the conversion angle, and that’s calculated as half the change of longitude times the sine of the mean latitude. So we have ½ × 90 × 0.9397, which gives us 42.3°. The sine of 70° is 0.9397, and that’s where that number comes from. So the difference between the straight line and the Great Circle is 45° minus 42.3°, which is 2.7°. Now, why does this matter? Because it tells us that even in the worst case—a full 90° change of longitude—the straight line on the chart is within less than 3° of the true Great Circle. And with any smaller change of longitude, the difference gets even smaller, and it falls to zero for a track that goes directly over the Pole. So the general rule we can state is this: on a Polar Stereographic chart, at latitudes greater than 70°, a straight line may be taken to be a Great Circle. That’s the practical takeaway—you can treat the straight line as the Great Circle for navigation purposes in those high latitudes. Now let’s talk about the uses of the Polar Stereographic chart. It’s used mainly for plotting in Polar regions. And here’s an important operational point: grid and gyro steering technique is usually used as well, not only because of the projection itself, but also because of the proximity to the North Magnetic Pole. That’s a real-world consideration—when you’re that close to the magnetic pole, magnetic compasses become unreliable, so you steer by grid and gyro instead. The chart is also used for some meteorological charts, either on this projection or on a modified polar stereographic. And finally, it’s used for planning purposes, because it shows the Pole and, if desired, the Equator. So to tie it all together: the Polar Stereographic chart is your tool for high-latitude work, and the reason you can trust a straight line on it as a Great Circle is exactly that 2.7° worst-case difference we calculated. That’s the whole point of the projection for navigation.