Let’s pick this up right where the numbers left off — Page 367, Lesson 324

Let’s pick this up right where the numbers left off. We’ve just established that on the polar stereographic chart, the scale stays remarkably constant. Between latitudes 90° and 78°, the scale is within 1% of the scale at the Pole — so for all practical purposes, we can treat that whole zone as a constant-scale chart. And if we push out to latitude 70°, the scale is still within 3% of the scale at the Pole. So the summary is: 90° to 78° is within 1%, and 78° to 70° is between 1% and 3%. That constancy of scale is exactly what makes the polar stereographic projection almost ideal for flying in polar regions. Now, why does that matter operationally? Historically, polar routes were avoided — political rivalries kept aircraft away, and aircraft lacked the range and endurance. But with the breakdown of those former political rivalries, the advent of long-range, long-endurance aircraft, ETOPS procedures, and inertial navigation systems, polar routes have become common. And they’re often shorter — some go very close to the Pole indeed. So let’s put a real-world number on that 1% zone. Take the co-latitude of 78°. Co-latitude is simply 90° minus the latitude, so 90 minus 78 gives us 12°. The distance from the Pole to latitude 78° is therefore 60 nautical miles times 12, which is 720 nautical miles. If an aircraft enters the 1% zone on one side and leaves more or less on the opposite side of the circle, the total distance inside that zone is around 1400 nautical miles. At typical jet-liner speeds of around 450 knots true airspeed, that’s approximately 3 hours of flying time. So a chart that can be considered constant scale, allowing distance measurement with a simple ruler for over 3 hours of flying, is a very useful projection indeed. Now let’s look at the projection’s properties. First, orthomorphism. On this chart, meridians are straight lines originating from the pole. Parallels of latitude are arcs of circles centred at the pole. The expansion — the scale expansion — is at the same rate in any direction from any point. That uniformity of expansion in all directions is precisely what makes the projection orthomorphic. Orthomorphic means the shape of small features is preserved — angles are correct locally. Next, the graticule. This is just the network of meridians and parallels. Again, meridians are straight lines radiating from the pole, and parallels are arcs of circles centred at the pole. Now, shapes. Because of that scale expansion, shapes and areas will be distorted away from the pole. So while small shapes are preserved locally due to orthomorphism, larger shapes and areas get distorted as you move away from the pole. Finally, chart convergence. This is a critical one for navigation. The meridians converge at the pole at exactly the same rate as they do on the Earth’s surface. Therefore, on the projection, the convergency remains the same — whereas on Earth, convergency decreases away from the Pole. This gives the polar stereographic chart a convergency factor, or ‘n’, of 1. That means the chart convergence is always exactly equal to the change of longitude between two points, whatever the latitude. Chart convergence is constant all over the chart. But — and this is the key distinction — chart convergence is ‘correct’, meaning the same as the Earth, only at the Pole itself. So the convergence value on the chart is constant and equals the longitude change, but it only matches the true Earth convergence at the Pole. That’s the property you’ll use when you’re working with convergency and grid navigation on this chart.