The way we solve this problem is by constructing a vector triangle of… — Page 130, Lesson 122

Let’s pick up where we left off. We were talking about the whole air mass moving over the ground, at least 60 nautical miles by 60 nautical miles in size, like a river. Your aircraft is supported by this broad mass of air, just like a boat or a twig is supported by the river, and it travels in it just as the twig travels in the river. Now, because the air is moving, we have to account for that movement when we navigate. The way we solve this problem is by constructing a vector triangle of velocities. The components are always the same. First, we have the Air Vector. The Air Vector consists of Heading and True Airspeed, which we abbreviate as TAS. TAS is the true speed of the aircraft through the air — not the indicated speed, but the actual speed relative to the air mass. It is the speed the aircraft would travel over the ground if there were no wind. The Air Vector is always drawn with one direction arrow. Second, we have the Wind Vector. The Wind Vector consists of Wind Direction and Wind Speed. Wind direction is always given in terms of the direction the wind has come from, not where it is blowing to. So if you see a wind vector like the one in Figure 7.3, it indicates a wind direction of 330° true, not 150° true. This matches how we normally talk about wind in everyday speech — a south wind is warm because it has blown up from Morocco, a west wind is warm and wet because it has blown across the Atlantic and over Ireland, and so on. The Wind Vector is always drawn with three direction arrows. Third, we have the Ground Vector. The Ground Vector is drawn by joining up the Air Vector and the Wind Vector. The resultant vector gives you Track and Ground Speed. The Ground Vector is always drawn with two direction arrows. Figure 7.4 is a diagram of the Triangle of Velocities. In practice, pilots do not normally draw it out to scale on graph paper. Instead, we solve it using an analogue navigation computer. But the Navigation Computer is really just a device for quickly producing a scale drawing — it is actually drawing the Triangle of Velocities for you. Let’s work through a practical example. Imagine you are in a Warrior PA 28. Your True Airspeed is 100 knots. Your Heading is 000° true. The forecast wind velocity, abbreviated W/V, is 240/30 — that means wind direction 240° true, wind speed 30 knots. The question is: what will be your track and ground speed? Start by drawing out your Triangle of Velocities. On a piece of paper — graph paper is ideal — draw in the Air Vector. It will have a direction of 000° true and a vector length equivalent to 100 knots. For convenience, you could use 100 millimetres to represent 100 knots. Now draw in the Wind Vector. It was 240/30. Remember, wind direction is given as the direction the wind comes from, so it is from 240°. That means the wind vector will actually point in the direction 060° true — the opposite direction. Whatever units you used for the Air Vector — say 100 millimetres for 100 knots — draw the length of the Wind Vector in the same units, so 30 millimetres for 30 knots. Now join the start of the Air Vector to the end of the Wind Vector to establish the resultant — that is the Ground Vector. That gives you your track and ground speed.