Figure 16-11. Magnetized portions of the airplane cause the
compass to deviate from its normal indications.
N33
30
W
24
21
S 15
12
E
6
3
N33
30
W
24
21
S 15
12
E
6
3
N33
30
W
24
21
S 15
12
E
6
3
Magnetic North
Magnetic North Magnetic North
Magnetized engine
Figure 16-12. Compass deviation card.
For (Magnetic)
Steer (Compass)
For (Magnetic
Steer (Compass)
E
86
W
274
60
57
240
243
N
0
S
180
30
28
210
212
120
117
300
303
150
148
330
332
Remember, if variation is west, add; if east, subtract. One
method for remembering whether to add or subtract variation
is the phrase “east is least (subtract) and west is best (add).”
Deviation
Determining the magnetic heading is an intermediate step
necessary to obtain the correct compass heading for the flight.
To determine compass heading, a correction for deviation
must be made. Because of magnetic influences within an
aircraft, such as electrical circuits, radio, lights, tools, engine,
and magnetized metal parts, the compass needle is frequently
deflected from its normal reading. This deflection is called
deviation. The deviation is different for each aircraft, and
it also may vary for different headings in the same aircraft.
For instance, if magnetism in the engine attracts the north
end of the compass, there would be no effect when the plane
is on a heading of MN. On easterly or westerly headings,
however, the compass indications would be in error, as shown
in Figure 16-11. Magnetic attraction can come from many
other parts of the aircraft; the assumption of attraction in the
engine is merely used for the purpose of illustration.
Some adjustment of the compass, referred to as compensation,
can be made to reduce this error, but the remaining correction
must be applied by the pilot.
Proper compensation of the compass is best performed by
a competent technician. Since the magnetic forces within
the aircraft change because of landing shocks, vibration,
mechanical work, or changes in equipment, the pilot should
occasionally have the deviation of the compass checked. The
procedure used to check the deviation is called “swinging the
compass” and is briefly outlined as follows.
The aircraft is placed on a magnetic compass rose, the engine
started, and electrical devices normally used (such as radio)
are turned on. Tailwheel-type aircraft should be jacked up into
flying position. The aircraft is aligned with MN indicated on
the compass rose and the reading shown on the compass is
recorded on a deviation card. The aircraft is then aligned at
30° intervals and each reading is recorded. If the aircraft is to
be flown at night, the lights are turned on and any significant
changes in the readings are noted. If so, additional entries
are made for use at night. The accuracy of the compass can
also be checked by comparing the compass reading with the
known runway headings.
A deviation card, similar to Figure 16-12, is mounted near
the compass showing the addition or subtraction required to
correct for deviation on various headings, usually at intervals
of 30°. For intermediate readings, the pilot should be able to
interpolate mentally with sufficient accuracy. For example,
if the pilot needed the correction for 195° and noted the
correction for 180° to be 0° and for 210° to be +2°, it could
be assumed that the correction for 195° would be +1°. The
magnetic heading, when corrected for deviation, is known
as compass heading.
Effect of Wind
The preceding discussion explained how to measure a TC
on the aeronautical chart and how to make corrections for
variation and deviation, but one important factor has not
been considered—wind. As discussed in the study of the
atmosphere, wind is a mass of air moving over the surface of
the Earth in a definite direction. When the wind is blowing
from the north at 25 knots, it simply means that air is moving
southward over the Earth’s surface at the rate of 25 NM in
1 hour.
Under these conditions, any inert object free from contact
with the Earth is carried 25 NM southward in 1 hour. This
effect becomes apparent when such things as clouds, dust,
and toy balloons are observed being blown along by the wind.
Obviously, an aircraft flying within the moving mass of air
is similarly affected. Even though the aircraft does not float
freely with the wind, it moves through the air at the same
time the air is moving over the ground, and thus is affected
by wind. Consequently, at the end of 1 hour of flight, the
aircraft is in a position that results from a combination of
the following two motions:
Figure 16-13. Motion of the air affects the speed with which aircraft
move over the Earth’s surface. Airspeed, the rate at which an
aircraft moves through the air, is not affected by air motion.
090°
Groundspeed 120 knots
WINDS ARE CALM
090°
Groundspeed 140 knots
WINDS 270° AT 20 KNOTS
090°
Groundspeed 100 knots
WINDS 090° AT 20 KNOTS
• Movement of the air mass in reference to the ground
• Forward movement of the aircraft through the air mass
Actually, these two motions are independent. It makes no
difference whether the mass of air through which the aircraft
is flying is moving or is stationary. A pilot flying in a 70-
knot gale would be totally unaware of any wind (except for
possible turbulence) unless the ground were observed. In
reference to the ground, however, the aircraft would appear
to fly faster with a tailwind or slower with a headwind, or to
drift right or left with a crosswind.
As shown in Figure 16-13, an aircraft flying eastward at
an airspeed of 120 knots in still air has a groundspeed (GS)
exactly the same—120 knots. If the mass of air is moving
eastward at 20 knots, the airspeed of the aircraft is not
affected, but the progress of the aircraft over the ground is
120 plus 20 or a GS of 140 knots. On the other hand, if the
mass of air is moving westward at 20 knots, the airspeed of
the aircraft remains the same, but GS becomes 120 minus
20 or 100 knots.
Assuming no correction is made for wind effect, if an aircraft
is heading eastward at 120 knots and the air mass moving
southward at 20 knots, the aircraft at the end of 1 hour is
almost 120 miles east of its point of departure because of its
progress through the air. It is 20 miles south because of the
motion of the air. Under these circumstances, the airspeed
remains 120 knots, but the GS is determined by combining
the movement of the aircraft with that of the air mass. GS can
be measured as the distance from the point of departure to
the position of the aircraft at the end of 1 hour. The GS can
be computed by the time required to fly between two points a
known distance apart. It also can be determined before flight
by constructing a wind triangle, which is explained later in
this chapter. [Figure 16-14]
The direction in which the aircraft is pointing as it flies is
called heading. Its actual path over the ground, which is a
combination of the motion of the aircraft and the motion of
the air, is called track. The angle between the heading and
the track is called drift angle. If the aircraft heading coincides
with the TC and the wind is blowing from the left, the track
does not coincide with the TC. The wind causes the aircraft
to drift to the right, so the track falls to the right of the desired
course or TC. [Figure 16-15]
The following method is used by many pilots to determine
compass heading: after the TC is measured, and wind
correction applied resulting in a TH, the sequence TH ±
variation (V) = magnetic heading (MH) ± deviation (D)
= compass heading (CH) is followed to arrive at compass
heading. [Figure 16-16]
By determining the amount of drift, the pilot can counteract
the effect of the wind and make the track of the aircraft
coincide with the desired course. If the mass of air is moving
across the course from the left, the aircraft drifts to the
right, and a correction must be made by heading the aircraft
sufficiently to the left to offset this drift. In other words, if
the wind is from the left, the correction is made by pointing
the aircraft to the left a certain number of degrees, therefore
correcting for wind drift. This is the wind correction angle
(WCA) and is expressed in terms of degrees right or left of
the TC. [Figure 16-17]
Figure 16-15. Effects of wind drift on maintaining desired course.
Heading
Wind
Track
Drift angle
Desired course
Figure 16-16. Relationship between true, magnetic, and compass
headings for a particular instance.
Heading
TN MN CN
TH-088°
MH-078°
CH-074°
VAR 10° E
DEV 4°
Figure 16-14. Aircraft flight path resulting from its airspeed and direction and the wind speed and direction.
Airspeed effect (1 hour)
20 knots
Distance covered over ground (1 hour)
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.
Heading
Wind
Track
Wind
correction
angle
Desired course
090°
075°
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 highways, 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.
INSTRUCTIONS FOR USE
1. Place hole over intersection of true course and true north line.
2. Without changing position rotate plotter until edge is over true course line.
3. From hole follow true north line to curved scale with arrow pointing in direction of flight.
4. Read true course in degrees, on proper scale, over true north line. read scales counter-clockwise.
SECTIONAL CHART SIDE - 1:500,000 NAVIGATIONAL FLIGHT PLOTTER
0
180
270
90
10
190
280
100
20
200
290
110
30
210
330
150
340
160
350
170
300
120
310
130
320
140
330
150
340
160
350 170
190 10
200
20
210
30
220
40 230
50 240
60
250
70
260
80
NAUTICAL 5 MILES 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 NAUTICAL 85 MILES
0 STATUTE 5 MILES 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 9585 100 90
DEGREES
Mode ClrOn/Off
Dist Vol Wt Wx ÷
: 7 8 9 x
Sto 4 5 6 −
Rcl 1 2 3 +
Bksp 0 . +/- =
C
M
P
TSD Alt: As Wind Wt. Bal Timer
Conv: Dist Vol Wt Wx
A Plotter
B Mechanical flight computer
C Electronic flight computer
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
Heading and airspeed
Course and groundspeed
N33
3
0
W
24
21
S 15
1
2
E
6
3
P
W
E
Wind direction and velocity
N
S
Figure 16-20. The wind triangle as is drawn in navigation practice.
080° heading and 120 knots airspeed
090° course and 110 knots groundspeed
N33
30
W
24
21
S 15
12
E
6
3
Wind at 20°
direction and
35 knots velocity
N
S
10° Drift Angle
8° left correction
Figure 16-19. Principle of the wind triangle.
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).