Direction, Latitude and Longitude — Page 20, Lesson 26

Let’s pick up right where the idea of latitude and longitude as angular measures becomes something you can actually fly with — converting those angles into distance on the Earth’s surface. The whole trick rests on the nautical mile. Its definition was deliberately chosen so that it relates to angular arc on a Great Circle. Here’s the chain of reasoning. The mean radius of the Earth is approximately 20.9 million feet. Because of that, on a Great Circle, 1 minute of arc corresponds to a distance on the Earth’s surface of 6080 feet. And that 6080 feet is defined as 1 nautical mile. Now, the ICAO definition of a nautical mile is 1852 metres — so keep both numbers in mind: 6080 feet, or 1852 metres, for one nautical mile. So the key relationship is: angle along a Great Circle arc converts directly to distance on the Earth. Since all meridians — that is, all lines of longitude — are Great Circles, the distance up or down a meridian, which is a change of latitude, follows this exact relationship. Let me give you a concrete example. Take two positions: 5000N 00100W and 5005N 00100W. The difference in latitude between them is exactly 5 minutes, so they are exactly 5 nautical miles apart. Simple, clean, one-to-one. But here’s the crucial limitation: this same relationship holds for differences in longitude only at the Equator. Why? Because the Equator is the only parallel of latitude that is also a Great Circle. Every other parallel — every other line of latitude — is a small circle, so the meridians converge as you move away from the Equator, and the distance per minute of longitude shrinks. Now let’s talk about resolution accuracy using latitude and longitude. Suppose a position is quoted as 51°49’N, 001°19’W, or written in the shorthand form 5149N 00119W. By writing 5149, you are making a declaration of the accuracy of the resolution you are interested in. You are saying that the position is nearer to 5149 than it is to 5148 or 5150. In other words, you are quoting to the nearest 1 minute of latitude, which is an accuracy to the nearest one nautical mile. Now for longitude. If you write 00119W, you are also quoting to the nearest minute. But here’s the catch — because at latitude 50N the meridians are closer together than they are at the Equator, you are quoting to about the nearest 0.6 of a nautical mile, not a full nautical mile. So the same one-minute resolution means different physical distances depending on whether you’re talking latitude or longitude, and depending on your latitude. That’s the complication we’re setting up to deal with. Let me make sure the core idea is crystal clear. The nautical mile is defined so that one minute of arc on a Great Circle equals one nautical mile. Meridians are Great Circles, so latitude changes map directly to nautical miles. Longitude changes only map directly at the Equator, because that’s the only parallel that’s a Great Circle. And when you quote a position to the nearest minute, you’re declaring a resolution — one nautical mile in latitude, but less than that in longitude away from the Equator.