# Wind Triangle and Its Solution (Part Three)

Juggle Method [Figure 4-42]

1. Set WD (270°) under the true index.
2. Draw the wind vector down the center from the grommet, making its length along the speed scale correspond to the windspeed (50 knots).
3. Set the TAS (220 knots) under the grommet.
4. Set the TC (230°) under the true index. [Figure 4-42] The wind triangle is set up incorrectly, for TC rather than TH is set under the true index. However, since the TH is not known, the TC is used as a first approximation of the TH. This gives a first approximation of the drift angle, which can be applied to the TC to get a more accurate idea of the TH.
5. Determine the drift angle (10° left) on the approximate heading (230°) to obtain a second approximation of the TH (240°). If the drift angle is right, the drift correction is minus; if it is left, the drift correction is plus.
6. Set the second approximate heading (240°) under the true index. Read the drift angle for this heading (8° left). To correct the wind triangle, the drift angle which is read at the head of the wind vector must equal the difference between the TC and the TH, which is set under the true index. As it stands, the drift angle is 8° left, while the difference between TC and the indicated TH is 10° left.
7. Juggle the compass rose until the drift angle equals the difference between TC and TH. In this example, the correct drift angle is 8° left. Now the wind triangle is set up correctly.
8. Read the TH (238°) under the true index.
9. Read the GS (179 knots) on the speed circle passing through the head of the wind vector.

Figure 4-42. Solving for TH and GS using the juggle method. [click image to enlarge]

Average Wind Affecting Aircraft

An average wind is an imaginary wind that would produce the same wind effect during a given period as two or more actual winds that affect the aircraft during that period. Sometimes an average wind can be applied once instead of applying each individual wind separately.

Authentically Averaging WDs

If the WDs are fairly close together, a satisfactory average wind can be determined by arithmetically averaging the WDs and windspeeds. However, the greater the variation in WD, the less accurate the result. It is generally accepted that winds should not be averaged arithmetically if the difference in directions exceeds 090° and/or the speed of less than 15 knots. In this case, there are other methods that may be used to obtain a more accurate average wind. A chart solution is shown in Figure 4-43.

Figure 4-43. Solving for average wind using chart. [click image to enlarge]

Computer Solution

Winds can be averaged by vectoring them on the wind face of the DR computer, using the square grid portion of the slide and the rotatable compass rose. Average the following three winds by this method: 030°/l5 knots, 080°/20 knots, and 150°/35 knots:

Place the slide in the computer so that the top line of the square grid portion is directly under the grommet and the compass rose is oriented so that the direction of the first wind (030°) is under the true index. The speed of the wind (15 knots) is drawn down from the grommet. [Figure 4-44A]

Figure 4-44. Solving for average wind using computer. [click image to enlarge]

Turn the compass rose until the direction of the second wind (080°) is under the true index, and then reposition the slide so that the head of the first wind vector is resting on the top line of the square grid section of the slide. Draw the speed of the second wind (20 knots) straight down (parallel to the vertical grid lines) from the head of the first wind arrow. [Figure 4-44B]

Figure 4-44. Solving for average wind using computer (continued). [click image to enlarge]

Turn the compass rose so that the direction of the third wind (150°) is under the true index, and reposition the slide so that the head of the second wind vector is resting on the top line of the square grid section of this slide. Draw the speed of the third wind (35 knots) straight down from the head of the second wind arrow. [Figure 4-44C]

Figure 4-44. Solving for average wind using computer (continued). [click image to enlarge]

Turn the compass rose so the head of the third wind arrow is on centerline below the grommet. Reposition the slide to place the grommet on the top line of the square grid section. The resultant or average wind direction is read directly beneath the true index (108°). Measuring the length of the resultant wind vector (46) on the square grid section and divide it by the number of winds used (3) to determine the windspeed. This gives a WS of about 151/2 knots. The average wind then is 108°/15 1/2 knots. [Figure 4-44D]

Figure 4-44. Solving for average wind using computer (continued). [click image to enlarge]

With a large number of winds to be averaged or high windspeeds, it may not possible to draw all the wind vectors on the computer unless the windspeeds are cut by 1/2 or 1/3. If one windspeed is cut, all windspeeds must be cut. In determining the resultant windspeed, the length of the total vector must be multiplied by 2 or 3, depending on how the windspeed was cut, and then divided by the total number of winds used. In cutting the speeds, the direction is not affected and the WD is read under the true index.

Wind effect is proportional to time. [Figure 4-45] To sum up two or more winds that have affected the aircraft for different lengths of time, weigh them in proportion to the times. If one wind has acted twice as long as another, its vector should be drawn in twice as shown. In determining the average windspeed, this wind must be counted twice.

Figure 4-45. Weigh winds in proportion to time. [click image to enlarge]

Resolution of Rectangular Coordinates

Data for radar equipment is often given in terms of rectangular coordinates; therefore, it is important that the navigator be familiar with the handling of these coordinates. The DR computer provides a ready and easy method of interconversion.

Figure 4-46. Convert wind to rectangular coordinates. [click image to enlarge]

Figure 4-46. Convert wind to rectangular coordinates (continued). [click image to enlarge]

Given:
A wind of 340°/25 knots to be converted to rectangular coordinates. [Figure 4-46]

1. Plot the wind on the computer in the normal manner. Use the square grid side of the computer slide for the distance.
2. Rotate the compass rose until north, the nearest cardinal heading, is under the true index.
3. Read down the vertical scale to the line upon which the head of the wind vector is now located. The component value (23) is from the north under the true index.
4. Read across the horizontal scale from the center line to the head of the wind vector. The component value (9) is from the west. The wind is stated rectangularly as N-23, W-9.

Given:
Coordinates, S-30, E-36, to convert to a wind.

1. Use the square grid side of the computer.
2. Place south cardinal heading under the true index and the grommet on zero of the square grid.
3. Read down from the grommet along the centerline for the value (30) of the cardinal direction under the true index.
4. Place east cardinal heading, read horizontally along the value located in Step 3 from the centerline of the value of the second cardinal direction and mark the point.
5. Rotate the compass rose until the marked point is over the centerline of the computer.
6. Read the WD (130) under the true index and velocity (47 knots) from the grommet to the point marked.