The Polar Stereographic Chart — Page 367, Lesson 327

I want to walk you through the Polar Stereographic Chart, and I want to start with the key practical question every navigator asks: when can I treat a straight line drawn on the chart as a Great Circle? That's the heart of this whole section. Let me set the scene with the numbers. We're looking at a case at a certain latitude, over a 90° change of longitude. The straight line on the chart makes an angle of 45° with the meridian. The Great Circle, however, makes an angle of 34½°. So the difference between the straight line and the Great Circle is 45° minus 34½°, which gives you 10½°. That is a large initial difference. And because it's that big, you simply cannot approximate a straight line to a Great Circle at that latitude over that change of longitude. The tracks diverge too much right from the start. But now here's the crucial contrast. If you were flying directly over the Pole, both the straight line track and the Great Circle track would initially be 000°, then 180°, and there would be no difference at all. So you can see immediately that the amount of change of longitude makes a difference. The geometry changes depending on how far around the world you're turning. Now let's move up to 70°N. At 70°N, over a 90° change of longitude, the angle between a straight line and a Rhumb Line is also 45°. The angle between the Great Circle and the Rhumb Line is what we call the conversion angle. And the conversion angle is ½ ch.long × sin mean latitude. Let me unpack that. "ch.long" is change of longitude, so ½ of 90 is 45. "sin mean latitude" — the sine of the mean latitude — at 70°N that's 0.9397. So 45 × 0.9397 gives you 42.3°. That's the conversion angle. So now the difference between the straight line and the Great Circle at 70°N is 45° minus 42.3°, which is just 2.7°. That's the worst case, a full 90° change of longitude, and you're still under 3° of difference. That tells you something fundamental: the difference between a straight line and a Great Circle becomes smaller as the latitude increases. The higher you go, the closer the straight line hugs the true Great Circle. And with any other change of longitude at 70°N, the difference will be even smaller, falling all the way to zero for a track directly over the Pole. So the rule you need to remember is this: a straight line may be taken to be a Great Circle on a Polar Stereographic chart at latitudes greater than 70°. That's the operational takeaway — above 70°N, you can trust the straight line as a Great Circle. Now, what is this chart actually used for? It's used mainly for plotting in Polar regions. And here's an important practical point: grid and gyro steering technique is usually used as well. That's not just because of the projection itself, but also because of the proximity to the North Magnetic Pole. The compass behaves oddly up there, so you steer by grid and gyro instead. Beyond that, some meteorological charts are on this projection, or on a modified polar stereographic. And the chart is also used for planning purposes, because it shows the Pole and, if desired, the Equator. So you get the whole hemisphere on one sheet for route planning. Let me just tie the geometry together once more, because this is the part that matters for your exam and for real flying. The straight line on the chart, the Great Circle, and the Rhumb Line are three different things. The Rhumb Line crosses every meridian at the same angle. The Great Circle is the shortest path between two points on the sphere. And the straight line on the Polar Stereographic chart sits between them. At low latitudes the straight line is far from the Great Circle — that 10½° case. At high latitudes, above 70°, the straight line and the Great Circle practically coincide, within 3° even in the worst case. That's why the chart is trusted for polar navigation. So when you're up in the polar regions, you can draw your straight line, treat it as a Great Circle, and plan your route with confidence — as long as you're north of 70° and you remember to steer by grid and gyro, not by magnetic compass.