Vector Diagrams and Wind Triangles
A vector illustration showing the effect of the wind on the flight of an aircraft is called a wind triangle. Draw a line to show the direction and speed of the aircraft through airmass (TH and TAS); this vector is called the air vector. Using the same scale, connect the tail of the wind vector to the head of the air vector. Draw a line to show the direction and speed of the wind (W/V); this is the wind vector. A line connecting the tail of the air vector with the head of the wind vector is the resultant of these two component vectors; it shows the direction and speed of the aircraft over the earth (track and GS). It is called the ground vector.
To distinguish one from another, it is necessary to mark each vector. Accomplish this by placing one arrowhead at midpoint on the air vector pointing in the direction of TH. The ground vector has two arrowheads at midpoint in the direction of track. The wind vector is labeled with three arrowheads in the direction the wind is blowing. The completed wind triangle is shown in Figure 4-30.
Remember that WD and WS compose the wind vector. TAS and TH form the air vector and GS and track compose the ground vector. The ground vector is the resultant of the other two; hence, the air vector and the wind vector are always drawn head to tail. An easy way to remember this is that the wind always blows the aircraft from TH to track.
Consider just what the wind triangle shows. In Figure 4-31, the aircraft departs from point A on the TH of 360° at a TAS of 150 knots. In 1 hour, if there is no wind, it reaches point B at a distance of 150 NM.
In actuality, the wind is blowing from 270° at 30 knots. At the end of 1 hour, the aircraft is at point C 30 NM downwind. Therefore, the length BC represents the speed of the wind drawn to the same scale as the TAS. The length of BC represents the wind and is the wind vector.
Line AC shows the distance and direction the aircraft travels over the ground in 1 hour. The length of AC represents the GS drawn to the same scale as the TAS and windspeed. The line AC, which is the resultant of AB and BC, represents the motion of the aircraft over the ground and is the ground vector.
Measuring the length of AC determines that the GS is 153 knots. Measuring the drift angle, BAC, and applying it to the TH of 360°, result in the track of 011°.
If two vectors in a wind triangle are known, the third one can be found by drawing a diagram and measuring the parts. Actually, the wind triangle includes six quantities; three speeds and three directions. Problems involving these six quantities make up a large part of DR navigation. If four of these quantities are known, the other two can be found. This is called solving the wind triangle and is an important part of navigation.
The wind triangle may be solved by trigonometric tables; however, this is unnecessary since the accuracy of this method far exceeds the accuracy of the data available and the results needed. In flight, the wind triangle is solved graphically, either on the chart or on the vector or wind face of the computer.
The two graphic solutions of the wind triangle (chart solution and computer solution) perhaps appear dissimilar at first glance. However, they work on exactly the same principles. Plotting the wind triangle on paper has been discussed; now, the same triangle is plotted on the wind face of the computer.
Wind Triangles on DR Computer
The wind face of the computer has three parts: a frame, a transparent circular plate that rotates in the frame, and a slide or card that can be moved up and down in the frame under the circular plate. [Figure 4-32]
The frame has a reference mark called the true index. A drift scale is graduated 45° to the left and 45° to the right of the true index; to the left this is marked drift left, and to the right, drift right.
The circular plate has around its edge a compass rose graduated in units of 1 degree. The position of the plate may be read on the compass rose opposite the true index. Except for the edge, the circular plate is transparent so that the slide can be seen through it. Pencil marks can be made on the transparent surface. The centerline is cut at intervals of two units by arcs of concentric circles called speed circles; these are numbered at intervals of 10 units.
On each side of the centerline are track lines that radiate from a point of origin off the slide. [Figure 4-33] Thus, the 14° track line on each side of the centerline makes an angle of 14° with the centerline at the origin.
In solving a wind triangle on the computer, plot part of the triangle on the transparent surface of the circular plate. For the other parts of the triangle, use the lines that are already drawn on the slide. Actually, there is not room for the whole triangle on the computer, for the origin of the centerline is one vertex of the triangle. When learning to use the wind face of the computer, it may help to draw in as much as possible of each triangle.
The centerline from its origin to the grommet always represents the air vector. If the TAS is 150k, move the slide so that 150 is under the grommet; then the length of the vector from the origin to the grommet is 150 units. [Figure 4-34A]
The ground vector is represented by one of the track lines, with its tail at the origin and its head at the appropriate speed circle. If the track is 15° to the right of the TH, and the GS is 180 knots, use the track line 15° to the right of the centerline and consider the intersection of this line with the 180 speed circle as the head of the vector. [Figure 4-34B]
The tail of the wind vector is at the grommet and its head is at the head of the ground vector. [Figure 4-34C]
Thus far, nothing has been said about the direction of the vectors. Since the true index is over the centerline beyond the head of the air vector, this vector always points toward the index. Therefore, TH is read on the compass rose opposite the true index.
Since track is TH with the drift angle applied, the value of track can be found on the scale of the circular plate opposite the drift correction on the drift scale. The wind vector is drawn with its tail at the grommet. [Figure 4-35] Since WD is the direction from which the wind blows, it is indicated on the compass rose by the rearward extension of the wind vector. Therefore, the most convenient way to draw the wind vector is to set WD under the true index and draw the vector down the centerline from the grommet; the scale on the centerline can then be used to determine the length of the vector.
Conversely, to read a wind already determined, place the head of the wind vector on the centerline below the grommet and read WD below the true index.