Dead reckoning is navigation solely by means of computations based on time, airspeed, distance, and direction. The products derived from these variables, when adjusted by wind speed and velocity, are heading and GS. The predicted heading takes the aircraft along the intended path and the GS establishes the time to arrive at each checkpoint and the destination. Except for flights over water, dead reckoning is usually used with pilotage for cross-country flying. The heading and GS as calculated is constantly monitored and corrected by pilotage as observed from checkpoints.

15.6.1 The Wind Triangle or Vector Analysis #

If there is no wind, the aircraft’s ground track is the same as the heading and the GS is the same as the true airspeed. This condition rarely exists. A wind triangle, the pilot’s version of vector analysis, is the basis of dead reckoning.

The wind triangle is a graphic explanation of the effect of wind upon flight. GS, heading, and time for any flight can be determined by using the wind triangle. It can be applied to the simplest kind of cross-country flight as well as the most complicated instrument flight. The experienced pilot becomes so familiar with the fundamental principles that estimates can be made which are adequate for visual flight without actually drawing the diagrams. The beginning student, however, needs to develop skill in constructing these diagrams as an aid to the complete understanding of wind effect.

If flight is to be made on a course to the east, with a wind blowing from the northeast, the aircraft must be headed somewhat to the north of east to counteract drift. This can be represented by a diagram as shown in Figure 15-19. Each line represents direction and speed. The long line shows the direction the aircraft is heading, and its length represents the distance traveled at airspeed for 1 hour. The short arrow at the right shows the wind direction, and its length represents the wind velocity for 1 hour. The solid line shows the direction of the track, or the path of the aircraft as measured over the earth, and its length represents the distance traveled in 1 hour, or the GS. [Figure 15-18]

In actual practice, the triangle illustrated in Figure 15-19 is not drawn; instead, construct a similar triangle as shown in Figure 15-20.

Suppose a flight is to be flown from E to P. Draw a line on the aeronautical chart connecting these two points; measure its direction with a protractor, or plotter, in reference to a meridian. This is the true course, which in this example is assumed to be 090° (east). From the NWS, it is learned that the wind at the altitude of the intended flight is 40 knots from the northeast (045°). The true airspeed of the aircraft is 120 knots.

On a plain sheet of paper draw a vertical line representing north to south. [Figure 15-21]

Place the protractor with the base resting on the vertical line and the curved edge facing east. At the center point of the base, make a dot labeled “E” (point of departure), and at the curved edge, make a dot at 90° (indicating the direction of the true course) and another at 45° (indicating wind direction).

With the ruler, draw the true course line from E, extending it somewhat beyond the dot at 90°, and labeling it “TC.”

Next, align the ruler with E and the dot at 45°, and draw the wind arrow from E, not toward 045°, but downwind in the direction the wind is blowing, making it 40 units long to correspond with the wind velocity of 40 knots. Identify this line as the wind line by placing the letter “W” at the end.

Finally, measure 120 units on the ruler to represent the airspeed, making a dot at this point. Place the ruler so that the end is on the arrowhead (W) and the 120-knot dot intercepts the true course line. Draw the line and label it “AS 120.” The point “P” placed at the intersection represents the position of the aircraft at the end of 1 hour.

The distance flown in 1 hour (GS) is measured as the number of units on the true course line (88 knots). The true heading necessary to offset drift is indicated by the direction of the airspeed line, which can be determined in one of two ways: by placing the straight side of the protractor along the north-south line, with its center point at the intersection of the airspeed line and north-south line, and reading the true heading directly in degrees (076°) [Figure 15-22]; or by placing the straight side of the protractor along the true course line, with its center at P, and reading the angle between the true course and the airspeed line (the WCA). If the wind blows from the right of true course, the angle is added; if from the left, it is subtracted. In the example given, the WCA is 14° and the wind is from the left; therefore, subtract 14° from the true course of 090°, making the true heading 076°. [Figure 15-23]

After obtaining the true heading, apply the correction for magnetic variation to obtain magnetic heading, and the correction for compass deviation to obtain a compass heading. The compass heading can be used to fly to the destination by dead reckoning.

To determine the time and fuel required for the flight, first find the distance to destination by measuring the length of the course line drawn on the aeronautical chart. If the distance measures 220 NM, divide by the GS of 88 knots, which gives 2.5 hours, or 2:30, as the time required. If fuel consumption is 8 gallons an hour, 8 × 2.5, or about 20 gallons, is used. Briefly summarized, the steps in obtaining flight information are:

TC—direction of the line connecting two desired points, measured clockwise in degrees from true north;

WCA—determined from the wind triangle (added to TC if wind is from the right, subtracted if from the left); TH—direction in which the nose should point to make good the desired course;

Variation—obtained from the isogonic line on the chart (added to TH if west, subtracted if east); MH—obtained by applying variation to true heading;

Deviation—obtained from the deviation card on the aircraft; Compass heading—obtained by applying deviation to MH;

Total distance—obtained by measuring the length of the TC line on the chart; GS—obtained from the wind triangle; estimated time en route (ETE)—total distance divided by GS; and fuel rate—predetermined gallons per hour used at cruising speed. NOTE: Additional fuel for adequate reserve should be added as a safety measure.