Direction, Latitude and Longitude 1 — Page 20, Lesson 29

Right, let's pick this up. We've just been looking at how we write positions to different levels of accuracy, and I want to make sure you've got that table firmly in your head, because it's a really practical piece of navigation. We saw that a position written as 5321N is only accurate to the nearest nautical mile, which is 6080 feet. That's fine for en route navigation. But if we write it as 5321.3N, we're suddenly accurate to 600 feet, or 185 metres, which is what you'd see on an INS, IRS, FMS, or GPS display. Then we go to degrees, minutes and seconds — 53°21'17"N — and that gets us to 100 feet, or 30 metres, which is the sort of accuracy you need for an airfield diagram chart. Go one decimal further, 53°21'17.3"N, and we're at 10 feet, or 3 metres — that's the location of a precision navaid, like an ILS. And finally, 53°21'17.32"N gives us 1 foot, or 30 centimetres, which is what you'd need for calibrating that precision navaid. So you can see the whole system scales beautifully from a rough en route fix right down to sub-metre calibration work. Now, I want to move on to something a bit more conceptual — the vertices of a Great Circle. This is a classic exam area, so listen carefully. The northern vertex of a Great Circle is simply the most northerly point on that Great Circle. And by the same logic, the southern vertex is the most southerly point on the Great Circle. Now here's the key relationship: the two vertices are antipodal — that means they're diametrically opposite each other on the Earth. And the Great Circle distance between them is 10,800 nautical miles. That's a fixed figure, so remember it. Now, because they're antipodal, the vertices lie on a meridian and its anti-meridian. And their latitude values are of equal value but of opposite sign. Let me give you the example from the book: if the southern vertex of a Great Circle is 63S 170W, then its northern vertex will be 63N 010E. Notice the latitude is the same number, 63, but one is South and one is North. And the longitudes are 180 degrees apart — 170W and 010E are on the same meridian and anti-meridian. Here's another important fact: at either of its vertices, the direction of the Great Circle will be exactly East, 090°(T), or exactly West, 270°(T). So at the very top or bottom of its curve, the track is running purely east-west. Now, if you know the co-ordinates of either vertex, you can calculate where and at what angle the Great Circle crosses the Equator. And the rule is this: a Great Circle will cross the Equator at two points whose longitude is 90° of change of longitude from either of its vertices. So in our example, with the vertex at 170W, the Great Circle would cross the Equator at 080°W and 100°E. Let's check that: 170W plus 90 degrees of longitude going east gives you 80W. And 170W minus 90 degrees going west gives you 100E. So those are your two crossing points. Now, the track angle at which the Great Circle crosses the Equator is based on the latitude of each vertex. And the track angle depends on which direction the Great Circle is travelling from the vertex — whether it's going East or West. So in our example, the vertex latitude is 63 degrees. If we're travelling Eastbound, the track angle at the Equator would be 90° plus 63°, which gives us 153°. Then, having passed the Southern Vertex, still travelling East, the track angle at the second crossing of the Equator would be 90° minus 63°, which gives us 027°. But if the original direction had been West from the Northern Vertex, the track angles crossing the Equator would be the reciprocals — that is, 207° and 333°. So you see, the direction of travel from the vertex dictates whether you add or subtract the vertex latitude from 90 degrees, and whether you use the reciprocal. Let me just recap the whole picture. The vertices are the extreme north and south points of the Great Circle, they're antipodal, 10,800 NM apart, and they sit on a meridian and anti-meridian with equal but opposite latitudes. At the vertex, the track is due east or due west. The Equator crossings are 90 degrees of longitude away from the vertices, and the crossing angle is 90 degrees plus or minus the vertex latitude, depending on your direction of travel. That's the whole vertex story in one go.