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

We're starting a fresh topic now: Great Circles, Rhumb Lines, and Directions on the Earth. I want to walk you through the core ideas here, and we'll begin with the nautical mile, because everything we do in navigation distance calculations hangs off that unit. Let me set the scene. The Earth is not a perfect sphere — it's an oblate spheroid, slightly flattened at the Poles and bulging at the Equator. That shape matters because a nautical mile is defined as the length of arc that subtends an angle of one minute at the centre of curvature. Now, because the Earth's curvature is greatest at the Equator — meaning the radius of curvature is decreased there — the arc length needed to generate that one-minute angle is shorter. So the nautical mile is shortest at the Equator, measuring about 6048 feet. At the Poles, where the curvature is less, the nautical mile is longer, at about 6108 feet. The average of these values is 6076.1 feet, and that's known as the International Nautical Mile, which is approximately 1852 metres. But here's the critical point for this course: for all navigation calculations, we use the Standard, or Admiralty, Nautical Mile of 6080 feet. So when you see a distance in nautical miles in an ATPL problem, you're working with 6080 feet per mile unless the question explicitly says otherwise. Now, let's look at some conversion factors that tie this into the metric system. From the Equator to either Pole is 5400 nautical miles, which equals 10,000 kilometres. And the full circumference of the Earth is 21,600 nautical miles, which equals 40,000 kilometres. These are handy benchmarks — if you ever need to convert a distance from nautical miles to kilometres, you can scale from these. Next, let's talk about Great Circle distances. The Great Circle distance between any two points on the Earth can be calculated using a general equation involving spherical geometry, but that's not part of the EASA syllabus. So for ATPL problems, we're limited to cases where the two points lie on special Great Circles — that is, on the same meridian, on a meridian and its anti-meridian, or on the Equator. There are five general cases, and we'll work through them with examples. In all of them, pay attention to the direction flown — there may be some surprises. Let's start with Example 1: same meridian, same hemisphere. We have London at 51°37'N, 000°12'W, and Accra at 06°48'N, 000°12'W. Both are on the same meridian, 000°12'W. So we draw a simple sectional diagram of the Earth using the Great Circle formed by that meridian and its anti-meridian, 179°48'E — though the anti-meridian isn't needed for this particular example. The angular distance between these two points is the Change in Latitude, abbreviated as ch.lat. London is 51°37' north of the Equator, and Accra is 06°48' north of the Equator. So the ch.lat is 51°37' minus 06°48', which gives us 44°49' — and the direction is South, because we're going from London down to Accra. To convert that angular distance into a linear distance, we multiply the degrees by 60 and add the extra minutes. So 44°49' becomes (44 × 60) + 49, which is 2689 minutes of latitude, and that equals 2689 nautical miles. That's the Great Circle distance from London to Accra. One important note: be prepared to convert this answer to kilometres or statute miles as the question requires. The basic calculation is done in nautical miles, but the examiner may want the answer in different units, so always read the question carefully. Now, let me show you the geometry with a diagram. That figure shows the positions of B, which is Accra at 06°48' north of the Equator measured at the centre of the Earth, and A, which is London at 51°37' north. Both are on the 000°12'W meridian, and you can see the angular distance between them is the ch.lat we calculated. So the key takeaway from this example: when two points share a meridian, the Great Circle distance is simply the difference in latitude, converted to minutes, and each minute of latitude equals one nautical mile. That's the fundamental relationship we'll build on.