Pilot's Handbook of Aeronautical Knowledge (Federal Aviation Administration)
Page 67
Figure 16-14. Aircraft flight path resulting from its airspeed and direction and the wind speed and direction.
Figure 16-15. Effects of wind drift on maintaining desired course.
Figure 16-16. Relationship between true, magnetic, and compass headings for a particular instance.
To summarize:
• Course—intended path of an aircraft over the ground or the direction of a line drawn on a chart representing the intended aircraft path, expressed as the angle measured from a specific reference datum clockwise from 0° through 360° to the line.
• Heading—direction in which the nose of the aircraft points during flight.
• Track—actual path made over the ground in flight. (If proper correction has been made for the wind, track and course are identical.)
• Drift angle—angle between heading and track.
• WCA—correction applied to the course to establish a heading so that track coincides with course.
• Airspeed—rate of the aircraft’s progress through the air.
• GS—rate of the aircraft’s inflight progress over the ground.
Figure 16-17. Establishing a wind correction angle that counteracts wind drift and maintains the desired course.
Basic Calculations
Before a cross-country flight, a pilot should make common calculations for time, speed, and distance, and the amount of fuel required.
Converting Minutes to Equivalent Hours
Frequently, it is necessary to convert minutes into equivalent hours when solving speed, time, and distance problems. To convert minutes to hours, divide by 60 (60 minutes = 1 hour). Thus, 30 minutes is 30/60 = 0.5 hour. To convert hours to minutes, multiply by 60. Thus, 0.75 hour equals 0.75 × 60 = 45 minutes.
Time T = D/GS
To find the time (T) in flight, divide the distance (D) by the GS. The time to fly 210 NM at a GS of 140 knots is 210 ÷ 140 or 1.5 hours. (The 0.5 hour multiplied by 60 minutes equals 30 minutes.) Answer: 1:30.
Distance D = GS X T
To find the distance flown in a given time, multiply GS by time. The distance flown in 1 hour 45 minutes at a GS of 120 knots is 120 × 1.75 or 210 NM.
GS GS = D/T
To find the GS, divide the distance flown by the time required. If an aircraft flies 270 NM in 3 hours, the GS is 270 ÷ 3 = 90 knots.
Converting Knots to Miles Per Hour
Another conversion is that of changing knots to miles per hour (mph). The aviation industry is using knots more frequently than mph, but is important to understand the conversion for those that use mph when working with speed problems. The NWS reports both surface winds and winds aloft in knots. However, airspeed indicators in some aircraft are calibrated in mph (although many are now calibrated in both mph and knots). Pilots, therefore, should learn to convert wind speeds that are reported in knots to mph.
A knot is 1 nautical mile per hour (NMPH). Because there are 6,076.1 feet in 1 NM and 5,280 feet in 1 SM, the conversion factor is 1.15. To convert knots to mph, multiply speed in knots by 1.15. For example: a wind speed of 20 knots is equivalent to 23 mph.
Most flight computers or electronic calculators have a means of making this conversion. Another quick method of conversion is to use the scales of NM and SM at the bottom of aeronautical charts.
Fuel Consumption
To ensure that sufficient fuel is available for your intended flight, you must be able to accurately compute aircraft fuel consumption during preflight planning. Typically, fuel consumption in gasoline-fueled aircraft is measured in gallons per hour. Since turbine engines consume much more fuel than reciprocating engines, turbine-powered aircraft require much more fuel, and thus much larger fuel tanks. When determining these large fuel quantities, using a volume measurement such as gallons presents a problem because the volume of fuel varies greatly in relation to temperature. In contrast, density (weight) is less affected by temperature and therefore, provides a more uniform and repeatable measurement. For this reason, jet fuel is generally quantified by its density and volume.
This standard industry convention yields a pounds-of-fuel-per-hour value which, when divided into the nautical miles (NM) per hour of travel (TAS ± winds) value, results in a specific range value. The typical label for specific range is NM per pound of fuel, or often NM per 1,000 pounds of fuel. Preflight planning should be supported by proper monitoring of past fuel consumption as well as use of specified fuel management and mixture adjustment procedures in flight.
For simple aircraft with reciprocating engines, the Aircraft Flight Manual/Pilot’s Operating Handbook (AFM/POH) supplied by the aircraft manufacturer provides gallons-per-hour values to assist with preflight planning.
When planning a flight, you must determine how much fuel is needed to reach your destination by calculating the distance the aircraft can travel (with winds considered) at a known rate of fuel consumption (gal/hr or lbs/hr) for the expected groundspeed (GS) and ensure this amount, plus an adequate reserve, is available on board. GS determines the time the flight will take. The amount of fuel needed for a given flight can be calculated by multiplying the estimated flight time by the rate of consumption. For example, a flight of 400 NM at 100 knots GS takes 4 hours to complete. If an aircraft consumes 5 gallons of fuel per hour, the total fuel consumption is 20 gallons (4 hours times 5 gallons). In this example, there is no wind; therefore, true airspeed (TAS) is also 100 knots, the same as GS. Since the rate of fuel consumption remains relatively constant at a given TAS, you must use GS to calculate fuel consumption when wind is present. Specific range (NM/lb or NM/gal) is also useful in calculating fuel consumption when wind is a factor.
You should always plan to be on the surface before any of the following occur:
• Your flight time exceeds the amount of flight time you calculated for the consumption of your preflight fuel amount
• Your fuel gauge indicates low fuel level
The rate of fuel consumption depends on many factors: condition of the engine, propeller/rotor pitch, propeller/rotor revolutions per minute (rpm), richness of the mixture, and the percentage of horsepower used for flight at cruising speed. The pilot should know the approximate consumption rate from cruise performance charts or from experience. In addition to the amount of fuel required for the flight, there should be sufficient fuel for reserve. When estimating consumption you must plan for cruise flight as well as startup and taxi, and higher fuel burn during climb. Remember that ground speed during climb is less than during cruise flight at the same airspeed. Additional fuel for adequate reserve should also be added as a safety measure.
Flight Computers
Up to this point, only mathematical formulas have been used to determine such items as time, distance, speed, and fuel consumption. In reality, most pilots use a mechanical flight computer called an E6B or electronic flight calculator. These devices can compute numerous problems associated with flight planning and navigation. The mechanical or electronic computer has an instruction book that probably includes sample problems so the pilot can become familiar with its functions and operation. [Figure 16-18]
Plotter
Another aid in flight planning is a plotter, which is a protractor and ruler. The pilot can use this when determining TC and measuring distance. Most plotters have a ruler that measures in both NM and SM and has a scale for a sectional chart on one side and a world aeronautical chart on the other. [Figure 16-18]
Pilotage
Pilotage is navigation by reference to landmarks or checkpoints. It is a method of navigation that can be used on any course that has adequate checkpoints, but it is more commonly used in conjunction with dead reckoning and VFR radio navigation.
The checkpoints selected should be prominent features common to the area of the flight. Choose checkpoints that can be readily identified by other features, such as roads, rivers, railroad tracks, lakes, and power lines. If possible, select features that make useful boundaries or brackets on each side of the course, such as highw
ays, rivers, railroads, and mountains. A pilot can keep from drifting too far off course by referring to and not crossing the selected brackets. Never place complete reliance on any single checkpoint. Choose ample checkpoints. If one is missed, look for the next one while maintaining the heading. When determining position from checkpoints, remember that the scale of a sectional chart is 1 inch = 8 SM or 6.86 NM. For example, if a checkpoint selected was approximately one-half inch from the course line on the chart, it is 4 SM or 3.43 NM from the course on the ground. In the more congested areas, some of the smaller features are not included on the chart. If confused, hold the heading. If a turn is made away from the heading, it is easy to become lost.
Roads shown on the chart are primarily the well-traveled roads or those most apparent when viewed from the air. New roads and structures are constantly being built and may not be shown on the chart until the next chart is issued. Some structures, such as antennas, may be difficult to see. Sometimes TV antennas are grouped together in an area near a town. They are supported by almost invisible guy wires. Never approach an area of antennas less than 500 feet above the tallest one. Most of the taller structures are marked with strobe lights to make them more visible to pilots. However, some weather conditions or background lighting may make them difficult to see. Aeronautical charts display the best information available at the time of printing, but a pilot should be cautious for new structures or changes that have occurred since the chart was printed.
Figure 16-18. A plotter (A), the computational and wind side of a mechanical flight computer (E6B) (B), and an electronic flight computer (C).
Dead Reckoning
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.
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 that 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. Either consciously or unconsciously, every good pilot thinks of the flight in terms of wind triangle.
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 16-19. Each line represents direction and speed. The long blue and white hashed line shows the direction the aircraft is heading, and its length represents the distance traveled at the indicated airspeed for 1 hour. The short blue arrow at the right shows the wind direction, and its length represents the wind velocity for 1 hour. The solid yellow 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.
In actual practice, the triangle illustrated in Figure 16-19 is not drawn; instead, construct a similar triangle as shown by the blue, yellow, and black lines in Figure 16-20, which is explained in the following example.
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 TC, 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°). Since the NWS reports the wind speed in knots, if the true airspeed of the aircraft is 120 knots, there is no need to convert speeds from knots to mph or vice versa.
Now, on a plain sheet of paper draw a vertical line representing north to south. (The various steps are shown in Figure 16-21.)
Step 1
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).
Figure 16-19. Principle of the wind triangle.
Figure 16-20. The wind triangle as is drawn in navigation practice.
Figure 16-21. Steps in drawing the wind triangle.
Step 2
With the ruler, draw the true course line from E, extending it somewhat beyond the dot by 90°, and labeling it “TC 090°.”
Step 3
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 to show the wind direction.
Step 4
Finally, measure 120 units on the ruler to represent the airspeed, making a dot on the ruler at this point. The units used may be of any convenient scale or value (such as ¼ inch = 10 knots), but once selected, the same scale must be used for each of the linear movements involved. Then place the ruler so that the end is on the arrowhead (W) and the 120-knot dot intercepts the TC 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 diagram is now complete.
The distance flown in 1 hour (GS) is measured as the numbers of units on the TC line (88 NMPH or 88 knots). The TH 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, read the TH directly in degrees (076°). [Figure 16-22]
• By placing the straight side of the protractor along the TC line, with its center at P, read the angle between the TC and the airspeed line. This is the WCA, which must be applied to the TC to obtain the TH. If the wind blows from the right of TC, 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 TC of 090°, making the TH 076°. [Figure 16-23]
After obtaining the TH, 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 your destination by measuring the length of the course line drawn on the aeronautical chart (using the appropriate scale at the bottom of the 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.
Figure 16-22. Finding true heading by the wind correction angle.
Figure 16-23. Finding true heading by direct measurement.
Briefly summarized, the steps in obtaining flight information are as follows:
• TC—direction of the line connecting two desired points, drawn on the chart and measured clockwise in degrees from TN on
the mid-meridian
• WCA—determined from the wind triangle. (Added to TC if the wind is from the right; subtracted if wind is from the left)
• TH—direction measured in degrees clockwise from TN, in which the nose of the plane should point to remain on the desired course
• Variation—obtained from the isogonic line on the chart (added to TH if west; subtracted if east)
• MH—an intermediate step in the conversion (obtained by applying variation to TH)
• Deviation—obtained from the deviation card on the aircraft (added to or subtracted from MH, as indicated)
• Compass heading—reading on the compass (found by applying deviation to MH) that is followed to remain on the desired course
• Total distance—obtained by measuring the length of the TC line on the chart (using the scale at the bottom of the chart)
• GS—obtained by measuring the length of the TC line on the wind triangle (using the scale employed for drawing the diagram)
• Estimated time en route (ETE)—total distance divided by GS
• Fuel rate—predetermined gallons per hour used at cruising speed
NOTE: Additional fuel for adequate reserve should be added as a safety measure.
Flight Planning
Title 14 of the Code of Federal Regulations (14 CFR) part 91 states, in part, that before beginning a flight, the pilot in command (PIC) of an aircraft shall become familiar with all available information concerning that flight. For flights not in the vicinity of an airport, this must include information on available current weather reports and forecasts, fuel requirements, alternatives available if the planned flight cannot be completed, and any known traffic delays of which the PIC has been advised by ATC.