Great Circles, Rhumb Lines & Directions on the Earth — Page 28, Lesson 38

Let’s pick this up right where the great-circle track direction left off, because the next thing I want you to hold onto is that little memory aid, DIID. That stands for decreasing, increasing, increasing, decreasing, and it describes how the great-circle track direction changes as you fly. The diagram spells it out with North and South as the hemispheres, and left and right telling you whether the track is Westerly or Easterly. So if you’re in the Northern Hemisphere and heading east, the track direction is decreasing; if you’re heading west, it’s increasing. Flip to the Southern Hemisphere and it reverses — east becomes increasing, west becomes decreasing. That’s the DIID pattern. And here’s the key takeaway that ties it all together: in every one of those cases, the great-circle direction always changes towards the Equator. Always. That’s the single rule you can lean on when the diagram isn’t in front of you. Now let’s shift gears entirely and talk about distance on the Earth, because this is where we start mixing metric and Imperial measures, and in aviation you genuinely need both. Many students haven’t used the smaller Imperial units, so I want you to memorise these conversions cold. Start with the metre: 1 metre equals 100 centimetres, and it also equals 1000 millimetres. Then 1 centimetre equals 10 millimetres. Now the Imperial side: 1 metre equals 3.28 feet. 1 foot equals 12 inches — and note the book writes inches with either a single quote or a double quote, so ‘in’ or “. 1 inch equals 2.54 centimetres. And 1 yard equals 3 feet. So you’ve got the chain: yard to feet, feet to inches, inches to centimetres, and metres to feet. The book makes a very practical point here: the Navigation Computer is accurate enough for any conversion you need for aviation purposes. So you don’t have to do these longhand — the computer handles it, but you still need to know the relationships. Now let’s define the kilometre properly, because it’s not just an arbitrary length. The kilometre is defined as 1/10,000th of the average distance on the Earth between the Equator and either Pole. Think about what that means: if one kilometre is one ten-thousandth of that distance, then there are exactly 10,000 kilometres between the Equator and either Pole. And since the full circumference of the Earth goes from the Equator to the North Pole, back down through the Equator to the South Pole, and back up — that’s four of those quarter-distances — the circumference of the Earth works out to 40,000 kilometres. That’s the elegant logic behind the kilometre: it’s literally derived from the size of the Earth. Finally, for conversions between kilometres and Imperial units, the book gives you this: 1 kilometre equals 3280 feet. And 1 metre — well, you already have that one from earlier, 3.28 feet. So notice the pattern: a kilometre is 1000 metres, and 3.28 feet times 1000 gives you 3280 feet. That’s your bridge between the metric distance on the Earth and the Imperial feet you’ll see on charts and in some procedures. So to pull it together: you’ve got the DIID rule for great-circle track direction, always bending towards the Equator, and you’ve got your distance conversions — the metre-to-centimetre-to-millimetre chain, the yard-foot-inch chain, the 2.54 centimetres per inch, the 3.28 feet per metre, the 3280 feet per kilometre, and the definition of the kilometre as one ten-thousandth of the Equator-to-Pole distance, giving you 10,000 kilometres to the Pole and 40,000 kilometres around the whole Earth. That’s the foundation you’ll build every distance calculation on from here.