Great Circles, Rhumb Lines & Directions on the Earth — Page 37, Lesson 41

I want to walk you through the next part of our navigation work. We've been looking at the shape of the Earth and how latitude is defined, and now we're moving into the practical business of measuring distances along the Earth's surface — specifically along great circles. First, let me clarify something about the nautical mile itself, because it isn't a fixed length everywhere. The excerpt tells us that a nautical mile is longer at the Poles, measuring about 6108 feet there. Why? Because the Earth is not a perfect sphere — it's an oblate spheroid, flattened at the poles. The amount of curvature of the Earth's surface is greatest at the Equator, meaning the radius of curvature is smaller there. Since a nautical mile is defined as the length of arc that subtends an angle of one minute at the centre of curvature, a smaller radius of curvature means a shorter arc length. So the nautical mile is shortest at the Equator, measuring about 6048 feet. The average value of these varying lengths is 6076.1 feet, and that is known as the International Nautical Mile. It is approximately 1852 metres. However — and this is important for your course — for all navigation calculations in this syllabus, we use the Standard Nautical Mile, also called the Admiralty Nautical Mile, which is 6080 feet. So when you do distance calculations, you will work in nautical miles of 6080 feet each. Now, let me give you two conversion factors that tie nautical miles to kilometres. From the Equator to either pole, the distance is 5400 nautical miles, and that equals 10,000 kilometres. The full circumference of the Earth is 21,600 nautical miles, which equals 40,000 kilometres. Keep those in mind. Moving on to great circle distances. The general equation for calculating the great circle distance between any two points on the Earth involves spherical geometry, but the excerpt tells us that is not part of the EASA syllabus. So for ATPL problems, we are limited to cases where the two points lie on special great circles. Those special great circles are: the same meridian, a meridian and its anti-meridian, or the Equator. There are five general cases, and we are going to work through the first one now. Example 1: Same meridian, same hemisphere. We have point A, London, at 51 degrees 37 minutes north, 000 degrees 12 minutes west. And point B, Accra, at 06 degrees 48 minutes north, 000 degrees 12 minutes west. Notice that both positions are on the same meridian — 000 degrees 12 minutes west. So they lie on the same great circle, which is that meridian and its anti-meridian at 179 degrees 48 minutes east, though we don't need the anti-meridian for this example. Let me describe what you would draw. You have a simple sectional diagram of the Earth showing the great circle formed by that meridian. Point B is 06 degrees 48 minutes north of the Equator, measured at the centre of the Earth. Point A is 51 degrees 37 minutes north of the Equator. Both are on the same meridian. The angular distance between them is the change in latitude, abbreviated as ch.lat. That is 51 degrees 37 minutes minus 06 degrees 48 minutes, which gives us 44 degrees 49 minutes. And because we are going from A, which is further north, to B, which is further south, that change is southward — so we say 44 degrees 49 minutes south from A to B. Now, to convert that angular distance into a linear distance — the great circle distance — we multiply the degrees by 60 and add the extra minutes. Why 60? Because one minute of latitude corresponds to one nautical mile along a meridian. So 44 degrees is 44 times 60, which is 2640 minutes, plus the 49 minutes gives us 2689 minutes of latitude. And that equals 2689 nautical miles. That is the shortest, great circle distance from London to Accra along that meridian. Be prepared to convert that answer into kilometres or statute miles if the exam question asks for it. The basic calculation is done in nautical miles, but the examiner may want the answer in different units, so always read the question carefully.