The Navigation Computer - Triangle of Velocities — Page 136, Lesson 127

We've just worked through the scale-drawing method of the triangle of velocities, and now I want to show you how the navigation computer does the exact same job, but as an analogue model. That's the key phrase here — an analogue model. Instead of drawing lines on paper and measuring them with a ruler and protractor, the computer physically represents the vectors with its moving parts, and you read the answers straight off the scales. Let's pick up the example we've been using. You've set your heading of 000° on the computer, and you've plotted the wind vector downwind yourself. Now look where the wind mark is positioned on the face of the computer. In this case, it sits about 12 degrees to the right of the centre line. That means you have 12 degrees of starboard drift. Your heading is 000°, so your track is 012°. Remember, drift is the angular difference between heading and track, and starboard means the track is to the right of the heading. Then you read the ground speed off against the radial arcs — those are the curved lines that radiate outward from the centre. In this example, the ground speed comes out at 118 knots. And here's the important point: these are the same answers we got by scale drawing. The navigation computer hasn't done any new mathematics; it has simply produced an analogue model of our scale drawing. The physical positions of the parts represent the vectors, and the scales give you the magnitudes and directions directly. Now let me walk you through the geometry on the face of the computer, because this is the heart of the triangle of velocities. The centre line of the computer is the Air Vector. It points along 000°, and its length represents your true airspeed of 100 knots. That's the vector that represents your motion through the air, in the direction you're heading. Joined to the end of that Air Vector is the Wind Vector, which you have plotted downwind yourself. That's the vector that represents the movement of the air mass over the ground. You place it by hand, using the wind speed and direction you've been given. Now, the resultant vector — the one that connects the start of the Air Vector to the end of the Wind Vector — is the Ground Vector. This is the vector that represents your actual path over the ground. It tracks up the 12° starboard drift line, and that gives you two things at once: the Track direction, which is 012°, and the ground speed, which is the length of that vector, 118 knots. So you see, the triangle of velocities is always the same three vectors: Air Vector, Wind Vector, and Ground Vector. The Air Vector plus the Wind Vector equals the Ground Vector. The computer just arranges them physically so you can read the result without drawing. Now, the excerpt gives us a set of practice examples with answers, and these are the book's practice questions — let's try them one at a time.