We are starting a new chapter: Great Circles, Rhumb Lines & Directions on… — Page 20, Lesson 32

We are starting a new chapter: Great Circles, Rhumb Lines & Directions on the Earth. This is a core topic in general navigation, and I want to walk you through what this chapter covers. First, let me give you the structure. The chapter begins with a reminder about great circles, then moves to the rhumb line, then looks at lines that are both great circles and rhumb lines. After that, we cover great circle direction, distance on the Earth, variations in the length of a nautical mile, conversion factors, great circle distances, and mean latitude. Finally, there are questions and answers at the end. Let me define the two key terms you need right from the start. A great circle is any circle on the surface of a sphere whose plane passes through the centre of the sphere. On the Earth, the equator and every meridian of longitude is a great circle. The shortest path between any two points on the Earth's surface follows a great circle — that's why aircraft fly great circle routes. A rhumb line is a line on the Earth's surface that crosses all meridians at the same angle. That means if you follow a constant true heading, you are following a rhumb line. It is not the shortest path, but it is very easy to navigate because your heading stays constant. Now, there are some lines that are both great circles and rhumb lines. The equator is one example — it is a great circle, and it also crosses all meridians at a constant angle of 90 degrees. Similarly, any meridian of longitude is a great circle, and it also crosses all other meridians at a constant angle — in fact, it crosses them at 0 degrees, because it is itself a meridian. So meridians and the equator are special cases. Next, we look at great circle direction. Because a great circle constantly changes its angle relative to the meridians it crosses, the direction along a great circle is not constant. If you want to fly a great circle route, you must continuously adjust your heading. That is a key difference from a rhumb line. Then we move to distance on the Earth. The standard unit of distance in aviation is the nautical mile. One nautical mile is defined as one minute of latitude along a meridian. That is a fixed relationship: 1 nautical mile = 1 minute of latitude. But there is a subtlety: variations in the length of a nautical mile. Because the Earth is not a perfect sphere — it is an oblate spheroid, slightly flattened at the poles — the length of one minute of latitude varies slightly depending on your latitude. At the equator, one minute of latitude is slightly shorter than at the poles. For practical navigation, we use a standard value: 1 nautical mile = 1,852 metres exactly. That is the internationally agreed definition. We also have conversion factors between nautical miles, statute miles, and kilometres. You will need to know these for calculations: 1 nautical mile = 1.15078 statute miles, and 1 nautical mile = 1.852 kilometres. Then we get into great circle distances. To calculate the great circle distance between two points on the Earth, you use spherical trigonometry. The formula involves the latitudes and longitudes of the two points and the Earth's radius. The result is the angular distance, which you then convert to nautical miles by multiplying by 60 — because 1 degree of great circle arc equals 60 nautical miles. Finally, we have mean latitude. When you are calculating distances along a parallel of latitude — that is, east-west along a line of constant latitude — you cannot simply use the difference in longitude. Because the meridians converge as you go towards the poles, the distance represented by one degree of longitude decreases. The mean latitude is the average of the two latitudes involved, and you use it to find the correct conversion factor for that parallel. That is the overview of what this chapter covers. We will go through each section in detail as we proceed.