Direction, Latitude and Longitude — Page 20, Lesson 26

I want to walk you through how we convert latitude and longitude into actual distance on the Earth’s surface — a fundamental skill for any professional pilot. Let’s start with the nautical mile. The definition of a nautical mile was deliberately chosen to relate angular arc on a Great Circle to distance. The mean radius of the Earth is approximately 20.9 million feet. Because of that, on a Great Circle, one minute of arc corresponds to a distance on the Earth’s surface of 6080 feet. That distance — 6080 feet — can be defined as one nautical mile. However, the official ICAO definition of a nautical mile is 1852 metres. So you have two equivalent definitions: 6080 feet, or 1852 metres. Now, here’s the key relationship: you can relate angle along a Great Circle arc directly to distance on the Earth. All meridians — lines of longitude — are Great Circles. So the distance going north or south along a meridian, which is a change of latitude, follows this exact relationship. For example, take two positions: 5000N 00100W and 5005N 00100W. The difference in latitude between them is exactly 5 minutes. Because one minute of arc on a Great Circle equals one nautical mile, they are exactly 5 nautical miles apart. But this relationship for longitude only holds true at the Equator. Why? Because the Equator is the only parallel of latitude that is also a Great Circle. Every other parallel of latitude — like 50°N — is a small circle, not a Great Circle. So the distance represented by one minute of longitude shrinks as you move away from the Equator. Now let’s talk about resolution accuracy when quoting positions. Suppose a position is given as 51°49’N, 001°19’W, or written in shorthand as 5149N 00119W. By writing 5149, you are declaring the accuracy of the resolution you’re interested in. You are saying that the position is nearer to 5149 than it is to 5148 or 5150. That means you are quoting to the nearest one minute of latitude — which gives you an accuracy of about one nautical mile. For longitude, if you write 00119W, you are also quoting to the nearest minute. But here’s the complication: at latitude 50°N, the meridians are closer together than they are at the Equator. So one minute of longitude at 50°N corresponds to about 0.6 nautical miles, not one full nautical mile. The excerpt notes that we’ll avoid this complication for now, but it’s important to be aware that longitude resolution in nautical miles varies with latitude. To help visualise this, let me bring up a diagram that shows the relationship between the Greenwich Meridian and how eastern and western longitudes are defined. And here’s another diagram that shows how the vertices of a Great Circle lie on a meridian and its anti-meridian, with latitude values of equal magnitude but opposite sign. So to summarise what we’ve covered: one nautical mile equals one minute of arc on a Great Circle, which is 6080 feet or 1852 metres. This works perfectly for latitude changes along any meridian, but for longitude it only works at the Equator. When quoting positions to the nearest minute, latitude gives you about one nautical mile accuracy, while longitude accuracy in nautical miles depends on your latitude.