The Navigation Computer - Triangle of Velocities — Page 130, Lesson 120

Let's start with the very heart of this chapter: the effect of wind. I want you to understand this from the ground up, because it's the foundation of everything we do in navigation. Aircraft do not always travel in the direction in which they are pointed. That's the single most important sentence in this whole topic. If there is any crosswind, the track will be different from the heading. Let me define those two terms right now, because they're going to come up constantly. Heading is the direction the aircraft's nose is pointing. Track is the actual path the aircraft makes good over the ground. They are not the same thing when wind is blowing. To make this crystal clear, the book uses a brilliant analogy: a boat crossing a river. Let's set it up. Imagine a river that is 10 NM wide. That's ten nautical miles across. It has a current of 5 knots. Now, stand at Point A on one bank and throw a stick into the water. After one hour, that stick will have been carried 5 NM downstream. That's the current doing its work — pure drift, no propulsion. Now, let's change the scene. Imagine the river has been dammed, and it's become a lake. No current, still water. You're at Point A with a boat that has an outboard motor, and it does 10 knots through the water. If you point the boat directly across to the opposite bank and set off, one hour later you'll be at Point B, exactly opposite where you started. That's your heading working perfectly, because there's no wind to disturb it. Now combine the two ideas. Remove the dam, bring back the 5-knot current. You set off from Point A, heading straight towards Point B. But the current takes you downstream as before. After one hour, you finish up at Point C — 10 miles across the river, and 5 miles downstream. Notice what happened: you pointed the boat, your heading, towards B, but you actually travelled, your track, to C. So if you want to finish up at Point B, you need to aim off to the left, towards Point D. You have to crab into the current to compensate for it. This is a continuous process, not something that only happens after a full hour. If you head towards Point B, after 12 minutes — that's one-fifth of an hour — you'll be 2 miles across the river and 1 mile displaced to the right. After 24 minutes, you'll be 4 miles across and 2 miles downstream. The boat tracks along the vector AC. That word vector is important — it's a quantity that has both magnitude and direction. The boat's motion is a combination of its own speed through the water and the current's speed downstream. Now, exactly the same process happens with aircraft travelling through the air. On a day when the air is completely calm — analogous to the lake — the aircraft tracks where it is pointed. We get completely calm days about 6 times a year. But we still have to be able to navigate on the other 359 days, so we need to take account of wind, or moving air, which is analogous to the river. Now, I know what you might be thinking. Wind seems transient, unsubstantial. How can something so light push around a dense, massive aircraft like a Boeing 747, or a fast-moving Tornado? That's exactly why this chapter uses the river analogy. It's easy to imagine a boat or a twig being carried downstream by a 10-mile expanse of river moving at 5 knots. But here's the key insight: wind is not simply little puffy, transient eddies of air. Wind is the continuous movement of an air mass. And an air mass is a large, homogenous body of air travelling over the ground. We normally don't regard it as an air mass unless it's at least, say, 60 NM by 60 NM in size. That's a huge body of air, sixty nautical miles by sixty nautical miles. This whole air mass travels over the ground, just like the river. Your aircraft is supported by that air mass, and it moves with it. So when we talk about wind affecting your aircraft, we're talking about the entire air mass carrying you along, just like the river carried the boat. That's the fundamental concept. Your aircraft moves through the air at its own speed and heading, but the air mass itself is moving over the ground, and that combination gives you your actual track over the ground. Let me just make sure you've got the key terms locked in: heading is where the nose points, track is where you actually go, wind is the movement of the air mass, and vector is a quantity with both magnitude and direction. The triangle of velocities — which we'll build on next — is how we put all these together mathematically. But for now, understand the physical picture: the boat and the aircraft are both carried by the medium they travel through, and that's why track differs from heading.