PilotHandbook

these variable and others, a pilot must reference the
performance instruments.

Navigation Instruments
The navigation instruments indicate the position of the
aircraft in relation to a selected navigation facility or fix.
This group of instruments includes various types of course
indicators, range indicators, glideslope indicators, and
bearing pointers. Newer aircraft with more technologically
advanced instrumentation provide blended information,
giving the pilot more accurate positional information.

Navigation instruments are comprised of indicators that
display GPS, very high frequency (VHF) omni-directional
radio range (VOR), nondirectional beacon (NDB),
and instrument landing system (ILS) information. The
instruments indicate the position of the aircraft relative to a
selected navigation facility or fix. They also provide pilotage
information so the aircraft can be maneuvered to keep it on a
predetermined path. The pilotage information can be in either
two or three dimensions relative to the ground-based or space-
based navigation information. [Figures 2-21 and 2-22]

Figure 2-18. Analog display (top) and digital display (bottom) from Global Positioning System (GPS)
a Cessna 172.
GPS is a satellite-based navigation system composed of a
Whether an aircraft has analog or digital (“glass”) network of satellites placed into orbit by the United States
instruments, the instrumentation falls into three different Department of Defense (DOD). GPS was originally intended
categories: performance, control, and navigation. for military applications, but in the 1980s the government
made the system available for civilian use. GPS works in all
Performance Instruments weather conditions, anywhere in the world, 24 hours a day. A
The performance instruments indicate the aircraft’s actual GPS receiver must be locked onto the signal of at least three
performance. Performance is determined by reference to the satellites to calculate a two-dimensional position (latitude
altimeter, airspeed or vertical speed indicator (VSI), heading and longitude) and track movement. With four or more
indicator, and turn-and-slip indicator. The performance satellites in view, the receiver can determine the user’s three-
instruments directly reflect the performance the aircraft dimensional position (latitude, longitude, and altitude). Other
is achieving. The speed of the aircraft can be referenced satellites must also be in view to offset signal loss and signal
on the airspeed indicator. The altitude can be referenced ambiguity. The use of the GPS is discussed in more detail in
on the altimeter. The aircraft’s climb performance can be Chapter 15, Navigation. Additionally, GPS is discussed in
determined by referencing the VSI. Other performance the Aeronautical Information Manual (AIM).
instruments available are the heading indicator, angle of
attack indicator, and the slip-skid indicator. [Figure 2-19] Chapter Summary

Control Instruments This chapter provides an overview of aircraft structures.
The control instruments [Figure 2-20] display immediate A more in-depth understanding of aircraft structures and
attitude and power changes, and are calibrated to permit controls can be gained through the use of flight simulation
adjustments in precise increments. The instrument for attitude software or interactive programs available online through
display is the attitude indicator. The control instruments do aviation organizations such as the Aircraft Owners and Pilots
not indicate aircraft speed or altitude. In order to determine Association (AOPA). Pilots are also encouraged to subscribe
to or review the various aviation periodicals which contain
valuable flying information. As discussed in Chapter 1, the
National Air and Space Administration (NASA) and the FAA
also offer free information for pilots.

2-12

Airspeed indicator Altitude indicator Altimeter indicator

Turn coordinator Heading indicator Vertical speed indicator

NAV1 108.00 113.00 WPT _ _ _ _ _ _ DIS _ _ ._ NM DTK _ _S_li°pT/STkRiKd ind36ic0a°tTor 134.000 118.000 COM1
NAV2 108.00 110.60 123.800 118.000 COM2
Airspeed tape indicator
Altimeter and 44030000 2
130 Altitude trend tape 4200
120 4100 Vertical speed and
270° tape indicator
1110 60
100 1
44000000 500
9 20
1
90 3900
80 3800 270°Turn rate trend vector
70
4300 2
TAS 100KT

VOR 1 Turn rate indicator

XPDR 5537 IDNT LCL23:00:34
ALERTS

Figure 2-19. Performance instruments.

2-13

Figure 2-20. Control instruments.
2-14

2 A

The aircraft illustrated is heading 33 N
020°, but the course is to the left. 30
TO
6 2
020° W 3
36
HDG 360° CRS 340° 24
21
E

OBS S 15
12
VOR 1
30 33

2I 24 I2 I5

1 1

Present position, inbound on 30 33
160° radial.

HDG 360° 340° CRS 340° 33 N 36
30
33 N 3W 30 21 24 TO 2I 24
GS S
24
NAV 6 E 12
OBSS 2115 6
3
View is from the pilots W I2 I5
perspective, and the
movable card is reset 24 E
21
after each turn 15
OBS S 12

160°

Figure 2-21. A comparison of navigation information as depicted on both analog and digital displays.

Fly down Fly up

Glideslope needle indicates “fly Glideslope needle indicates “fly up” to intercept glideslope
down” to intercept glideslope
4200
12 15 12 15
E E 4100
TO TO 20
21 24
20 36 20 36 S 4000
I0 N I0 N
80
I0 I0 I0 I0 FR 3900
20 20 20 20

FR NAV 1
30 33
NAV 1 W
30 33 OBS
OBS W

3800

4200

4100 Glideslope

20

4000

80
3900

3800

25

Figure 2-22. Analog and digital indications for glideslope interception.

2-15

2-16

PCharpteirn3 ciples of
Flight

Introduction

This chapter examines the fundamental physical laws
governing the forces acting on an aircraft in flight, and
what effect these natural laws and forces have on the
performance characteristics of aircraft. To control an aircraft,
be it an airplane, helicopter, glider, or balloon, the pilot
must understand the principles involved and learn to use or
counteract these natural forces.

Structure of the Atmosphere

The atmosphere is an envelope of air that surrounds the
Earth and rests upon its surface. It is as much a part of the
Earth as the seas or the land, but air differs from land and
water as it is a mixture of gases. It has mass, weight, and
indefinite shape.

The atmosphere is composed of 78 percent nitrogen, 21
percent oxygen, and 1 percent other gases, such as argon
or helium. Some of these elements are heavier than others.
The heavier elements, such as oxygen, settle to the surface
of the Earth, while the lighter elements are lifted up to the
region of higher altitude. Most of the atmosphere’s oxygen
is contained below 35,000 feet altitude.

Air, like fluid, is able to flow and change shape when
subjected to even minute pressures because it lacks strong
molecular cohesion. For example, gas completely fills any
container into which it is placed, expanding or contracting
to adjust its shape to the limits of the container.

3-1

Atmospheric Pressure temperature is considered constant up to 80,000 feet. A
Although there are various kinds of pressure, pilots are standard pressure lapse rate is one in which pressure decreases
mainly concerned with atmospheric pressure. It is one of at a rate of approximately 1 "Hg per 1,000 feet of altitude gain
the basic factors in weather changes, helps to lift an aircraft, to 10,000 feet. [Figure 3-2] The International Civil Aviation
and actuates some of the important flight instruments. These Organization (ICAO) has established this as a worldwide
instruments are the altimeter, airspeed indicator, vertical standard, and it is often referred to as International Standard
speed indicator, and manifold pressure gauge. Atmosphere (ISA) or ICAO Standard Atmosphere. Any
temperature or pressure that differs from the standard lapse
Air is very light, but it has mass and is affected by the rates is considered nonstandard temperature and pressure.
attraction of gravity. Therefore, like any other substance, it
has weight, and because of its weight, it has force. Since it is Standard Atmosphere
a fluid substance, this force is exerted equally in all directions,
and its effect on bodies within the air is called pressure. Under Altitude (ft) Pressure (Hg) Temperature
standard conditions at sea level, the average pressure exerted (°C) (°F)
by the weight of the atmosphere is approximately 14.70 0
pounds per square inch (psi) of surface, or 1,013.2 millibars 1,000 29.92 15.0 59.0
(mb). Its thickness is limited; therefore, the higher the altitude, 2,000 28.86 13.0 55.4
the less air there is above. For this reason, the weight of the 3,000
atmosphere at 18,000 feet is one-half what it is at sea level. 4,000 27.82 11.0 51.9
5,000 26.82 9.1 48.3
The pressure of the atmosphere varies with time and location. 6,000
Due to the changing atmospheric pressure, a standard 7,000 25.84 7.1 44.7
reference was developed. The standard atmosphere at sea 8,000 24.89 5.1 41.2
level is a surface temperature of 59 °F or 15 °C and a surface 9,000
pressure of 29.92 inches of mercury ("Hg), or 1,013.2 mb. 10,000 23.98 3.1 37.6
[Figure 3-1] 11,000 23.09 1.1 34.0
12,000
13,000 22.22 -0.9 30.5
14,000 21.38 -2.8 26.9
15,000
16,000 20.57 -4.8 23.3
17,000 19.79 -6.8 19.8
18,000
19,000 19.02 -8.8 16.2
20,000 18.29 -10.8 12.6

17.57 -12.7 9.1
16.88 -14.7 5.5

Standard Inches of Millibars Standard 16.21 -16.7 1.9
Sea Level Mercury 1016 Sea Level 15.56 -18.7 -1.6
Pressure 30 847 Pressure
14.94 -20.7 -5.2
29.92 Hg 25 1013 mb 14.33 -22.6 -8.8

13.74 -24.6 -12.3

20 677 FigureF3i-g2u. Prero2p-e2r.tiePsroopf esrttaineds aorfdstaatnmdoasrpdhaertme.osphere.

15 508

10 339 Since aircraft performance is compared and evaluated with
respect to the standard atmosphere, all aircraft instruments
5 170 are calibrated for the standard atmosphere. In order to account
Atmospheric Pressure properly for the nonstandard atmosphere, certain related
terms must be defined.
00

Figure 3-1. StFaingduarred2s-e1a. lSetvaenl dparerdsssuerae.level pressure. Pressure Altitude
Pressure altitude is the height above a standard datum plane
A standard temperature lapse rate is one in which the (SDP), which is a theoretical level where the weight of the
temperature decreases at the rate of approximately 3.5 °F atmosphere is 29.92 "Hg (1,013.2 mb) as measured by a
or 2 °C per thousand feet up to 36,000 feet which is barometer. An altimeter is essentially a sensitive barometer
approximately -65 °F or -55 °C. Above this point, the calibrated to indicate altitude in the standard atmosphere. If
the altimeter is set for 29.92 "Hg SDP, the altitude indicated
is the pressure altitude. As atmospheric pressure changes, the
SDP may be below, at, or above sea level. Pressure altitude
is important as a basis for determining airplane performance,
as well as for assigning flight levels to airplanes operating at
or above 18,000 feet.

3-2

The pressure altitude can be determined by either of two Regardless of the actual altitude at which the aircraft is
methods: operating, it will perform as though it were operating at an
altitude equal to the existing density altitude.
1. Setting the barometric scale of the altimeter to 29.92
and reading the indicated altitude. Air density is affected by changes in altitude, temperature,
and humidity. High density altitude refers to thin air while
2. Applying a correction factor to the indicated altitude low density altitude refers to dense air. The conditions that
according to the reported altimeter setting. result in a high density altitude are high elevations, low
atmospheric pressures, high temperatures, high humidity, or
Density Altitude some combination of these factors. Lower elevations, high
SDP is a theoretical pressure altitude, but aircraft operate in a atmospheric pressure, low temperatures, and low humidity
nonstandard atmosphere and the term density altitude is used are more indicative of low density altitude.
for correlating aerodynamic performance in the nonstandard
atmosphere. Density altitude is the vertical distance above sea Effect of Pressure on Density
level in the standard atmosphere at which a given density is Since air is a gas, it can be compressed or expanded. When
to be found. The density of air has significant effects on the air is compressed, a greater amount of air can occupy a given
aircraft’s performance because as air becomes less dense, volume. Conversely, when pressure on a given volume of air
it reduces: is decreased, the air expands and occupies a greater space.
At a lower pressure, the original column of air contains
• Power because the engine takes in less air. a smaller mass of air. The density is decreased because
density is directly proportional to pressure. If the pressure is
• Thrust because a propeller is less efficient in thin doubled, the density is doubled; if the pressure is lowered, the
air. density is lowered. This statement is true only at a constant
temperature.
• Lift because the thin air exerts less force on the
airfoils. Effect of Temperature on Density
Increasing the temperature of a substance decreases its density.
Density altitude is pressure altitude corrected for nonstandard Conversely, decreasing the temperature increases the density.
temperature. As the density of the air increases (lower density Thus, the density of air varies inversely with temperature.
altitude), aircraft performance increases and conversely This statement is true only at a constant pressure.
as air density decreases (higher density altitude), aircraft
performance decreases. A decrease in air density means In the atmosphere, both temperature and pressure decrease
a high density altitude; an increase in air density means a with altitude, and have conflicting effects upon density.
lower density altitude. Density altitude is used in calculating However, the fairly rapid drop in pressure as altitude is
aircraft performance, because under standard atmospheric increased usually has the dominating effect. Hence, pilots
conditions, air at each level in the atmosphere not only has can expect the density to decrease with altitude.
a specific density, its pressure altitude and density altitude
identify the same level. Effect of Humidity (Moisture) on Density
The preceding paragraphs refer to air that is perfectly dry. In
The computation of density altitude involves consideration reality, it is never completely dry. The small amount of water
of pressure (pressure altitude) and temperature. Since aircraft vapor suspended in the atmosphere may be almost negligible
performance data at any level is based upon air density under certain conditions, but in other conditions humidity
under standard day conditions, such performance data may become an important factor in the performance of an
apply to air density levels that may not be identical with aircraft. Water vapor is lighter than air; consequently, moist
altimeter indications. Under conditions higher or lower than air is lighter than dry air. Therefore, as the water content
standard, these levels cannot be determined directly from of the air increases, the air becomes less dense, increasing
the altimeter. density altitude and decreasing performance. It is lightest or
least dense when, in a given set of conditions, it contains the
Density altitude is determined by first finding pressure maximum amount of water vapor.
altitude, and then correcting this altitude for nonstandard
temperature variations. Since density varies directly with Humidity, also called relative humidity, refers to the amount
pressure, and inversely with temperature, a given pressure of water vapor contained in the atmosphere, and is expressed
altitude may exist for a wide range of temperature by allowing
the density to vary. However, a known density occurs for any
one temperature and pressure altitude. The density of the air
has a pronounced effect on aircraft and engine performance.

3-3

as a percentage of the maximum amount of water vapor the manner open to human understanding, many philosophers,
air can hold. This amount varies with temperature. Warm air mathematicians, natural scientists, and inventors spent their
holds more water vapor, while colder air holds less. Perfectly lives unlocking the secrets of the universe. One of the best
dry air that contains no water vapor has a relative humidity known was Sir Isaac Newton, who not only formulated the
of zero percent, while saturated air, which cannot hold any law of universal gravitation, but also described the three
more water vapor, has a relative humidity of 100 percent. basic laws of motion.
Humidity alone is usually not considered an important factor
in calculating density altitude and aircraft performance, but Newton’s First Law: “Every object persists in its state of rest
it does contribute. or uniform motion in a straight line unless it is compelled to
change that state by forces impressed on it.”
As temperature increases, the air can hold greater amounts
of water vapor. When comparing two separate air masses, This means that nothing starts or stops moving until some
the first warm and moist (both qualities tending to lighten outside force causes it to do so. An aircraft at rest on the ramp
the air) and the second cold and dry (both qualities making remains at rest unless a force strong enough to overcome
it heavier), the first must be less dense than the second. its inertia is applied. Once it is moving, its inertia keeps
Pressure, temperature, and humidity have a great influence it moving, subject to the various other forces acting on it.
on aircraft performance because of their effect upon density. These forces may add to its motion, slow it down, or change
There are no rules of thumb that can be easily conveyed its direction.
but the affect of humidity can be determined using online
formulas. In the first case, the pressure is needed at the Newton’s Second Law: “Force is equal to the change in
altitude for which density altitude is being sought. Using momentum per change in time. For a constant mass, force
Figure 3-2, select the barometric pressure closest to the equals mass times acceleration.”
associated altitude. As an example, the pressure at 8,000 feet
is 22.22 "Hg. Using the National Oceanic and Atmospheric When a body is acted upon by a constant force, its resulting
Administration (NOAA) website (http://www.srh.noaa.gov/ acceleration is inversely proportional to the mass of the body
elp/wxcalc/densityaltitude.html) for density altitude, enter the and is directly proportional to the applied force. This takes
22.22 for 8,000 feet in the station pressure window. Entering into account the factors involved in overcoming Newton’s
a temperature of 80° and a dew point of 75°. The result is a First Law. It covers both changes in direction and speed,
density altitude of 11,564 feet. With no humidity, the density including starting up from rest (positive acceleration) and
altitude would be almost 500 feet lower. coming to a stop (negative acceleration or deceleration).

Another site (http://wahiduddin.net/calc/density_altitude. Newton’s Third Law: “For every action, there is an equal
htm) provides a more straight forward method of determining and opposite reaction.”
the effects of humidity on density altitude without using
additional interpretive charts. In any case, the effects of In an airplane, the propeller moves and pushes back the
humidity on density altitude include a decrease in overall air; consequently, the air pushes the propeller (and thus the
performance in high humidity conditions. airplane) in the opposite direction—forward. In a jet airplane,
the engine pushes a blast of hot gases backward; the force of
Theories in the Production of Lift equal and opposite reaction pushes against the engine and
forces the airplane forward.
Newton’s Basic Laws of Motion
The formulation of lift has historically been the adaptation Magnus Effect
over the past few centuries of basic physical laws. These In 1852, the German physicist and chemist, Heinrich Gustav
laws, although seemingly applicable to all aspects of lift, Magnus (1802–1870), made experimental studies of the
do not answer how lift is formulated. In fact, one must aerodynamic forces on spinning spheres and cylinders.
consider the many airfoils that are symmetrical, yet produce (The effect had already been mentioned by Newton in
significant lift. 1672, apparently in regard to spheres or tennis balls). These
experiments led to the discovery of the Magnus Effect, which
The fundamental physical laws governing the forces acting helps explain the theory of lift.
upon an aircraft in flight were adopted from postulated
theories developed before any human successfully flew
an aircraft. The use of these physical laws grew out of the
Scientific Revolution, which began in Europe in the 1600s.
Driven by the belief the universe operated in a predictable

3-4

Flow of Air Against a Nonrotating Cylinder cylinder have a certain roughness, albeit at a microscopic
level, causing resistance for a fluid to flow. This reduction
If air flows against a cylinder that is not rotating, the flow of in velocity of the airflow about a surface is caused by skin
air above and below the cylinder is identical and the forces friction or drag.
are the same. [Figure 3-3A]

A Rotating Cylinder in a Motionless Fluid When passing over a surface, molecules actually adhere
In Figure 3-3B, the cylinder is rotated clockwise and observed (stick, cling) to the surface, illustrated by the rotating cylinder
from the side while immersed in a fluid. The rotation of the in a fluid that is not moving. Thus,
cylinder affects the fluid surrounding the cylinder. The flow
around the rotating cylinder differs from the flow around a 1. In the case of the rotating cylinder, air particles near
stationary cylinder due to resistance caused by two factors: the surface that resist motion have a relative velocity
viscosity and friction. near zero. The roughness of the surface impedes their
motion.
Viscosity
Viscosity is the property of a fluid or semifluid that causes it 2. Due to the viscosity of the fluid, the molecules on the
to resist flowing. This resistance to flow is measurable due surface entrain, or pull, the surrounding flow above it
to the molecular tendency of fluids to adhere to each other to in the direction of rotation due to the adhesion of the
some extent. High-viscosity fluids resist flow; low-viscosity fluid to itself.
fluids flow easily.
There is also a difference in flow around the rotating cylinder
Similar amounts of oil and water poured down two identical and in flow around a nonrotating cylinder. The molecules at
ramps demonstrate the difference in viscosity. The water seems the surface of the rotating cylinder are not in motion relative
to flow freely while the oil flows much more slowly. (An to the cylinder; they are moving clockwise with the cylinder.
excellent website to demonstrate types of viscosity is found at Due to viscosity, these molecules entrain others above
the Cornell University website on viscosity, located at http:// them resulting in an increase in fluid flow in the clockwise
atlas.geo.cornell.edu/education/student/viscosity.html.) direction. Substituting air for other fluids results in a higher
velocity of air movement above the cylinder simply because
more molecules are moving in a clockwise direction.

Since molecular resistance to motion underlies viscosity, A Rotating Cylinder in a Moving Fluid
grease is very viscous because its molecules resist flow. When the cylinder rotates in a fluid that is also moving,
Hot lava is another example of a viscous fluid. All fluids are the result is a higher circulatory flow in the direction of the
viscous and have a resistance to flow whether this resistance rotating cylinder. [Figure 3-3C] By adding fluid motion, the
is observed or not. Air is an example of a fluid whose magnitude of the flow increases.
viscosity can not be observed.
The highest differences of velocity are 90° from the relative
Since air has viscosity properties, it will resist flow to some motion between the cylinder and the airflow. Additionally,
extent. In the case of the rotating cylinder within an immersed and as shown in Figure 3-4, at point “A,” a stagnation point
fluid (oil, water, or air), the fluid (no matter what it is) resists exists where the air stream impacts (impinges) on the front
flowing over the cylinder’s surface. of the airfoil’s surface and splits; some air goes over and
some under. Another stagnation point exists at “B,” where
Friction the two airstreams rejoin and resume at identical velocities.
Friction is the second factor at work when a fluid flows When viewed from the side, an upwash is created ahead of
around a rotating cylinder. Friction is the resistance one the airfoil and downwash at the rear.
surface or object encounters when moving over another and
exists between a fluid and the surface over which it flows. In the case of Figure 3-4, the highest velocity is at the top of
the airfoil with the lowest velocity at the bottom. Because
If identical fluids are poured down the ramp, they flow in the these velocities are associated with an object (in this case,
same manner and at the same speed. If one ramp’s surface an airfoil) they are called local velocities as they do not exist
is coated with small pebbles, the flow down the two ramps outside the lift-producing system, in this case an airfoil. This
differs significantly. The rough surface ramp impedes the concept can be readily applied to a wing or other lifting
flow of the fluid due to resistance from the surface (friction). surface. Because there is a difference of velocity above and
It is important to remember that all surfaces, no matter below the wing, the result is a a higher pressure at the bottom
how smooth they appear, are not smooth and impede the of the wing and a lower pressure on the top of the wing.
flow of a fluid. Both the surface of a wing and the rotating

3-5

A. Flow of air against a nonrotating cylinder AB
B. Rotating cylinder in a fluid

AB Leading edge
C. Rotating cylinder in a moving fluid D. Leading edge of wing

E. Leading edge of wing under 1,500x magnification

Figure 3-3. A illustrates uniform circulation. B illustrates the increased airflow over the top of a rotating cylinder. The airflow speed is
further increased when the rotating cylinder is in a moving stream of air (C). The air molecules near the surface of an object are slowed
and almost stationary. D is an example of typical aircraft grade aluminum used in aircraft construction to include wings and leading
edges of wings as shown in E (left). When magnified at 1,500x (E, right), polished aluminum is visibly rough. This demonstrates why
airflow is affected by molecular irregularities of the surface.

3-6

A practical application of Bernoulli’s Principle is the venturi

Leading edge stagnation point tube. The venturi tube has an air inlet that narrows to a throat

(constricted point) and an outlet section that increases in

diameter toward the rear. The diameter of the outlet is the

same as that of the inlet. At the throat, the airflow speeds up

and the pressure decreases; at the outlet, the airflow slows
A and the pressure increases. [Figure 3-5]

B Since air is recognized as a body and it is accepted that it must
follow the above laws, one can begin to see how and why an
Trailing edge stagnation point airplane wing develops lift. As the wing moves through the
air, the flow of air across the curved top surface increases in
Figure 3-4. Air cirFciugluatrieon2-a3r.oAunirdcairncualiartfiooinl .occurs when the front velocity creating a low-pressure area.
stagnation point is below the leading edge and the aft stagnation
point is beyond the trailing edge. Although Newton, Magnus, Bernoulli, and hundreds of other
early scientists who studied the physical laws of the universe
This low-pressure area produces an upward force known as did not have the sophisticated laboratories available today,
the Magnus Effect, the physical phenomenon whereby an they provided great insight to the contemporary viewpoint
object’s rotation affects its path through a fluid, to include of how lift is created.
air. Two early aerodynamicists, Martin Kutta and Nicolai
Joukowski, eventually measured and calculated the forces for Airfoil Design
the lift equation on a rotating cylinder (the Kutta-Joukowski
theorem). An airfoil is a structure designed to obtain reaction upon its
surface from the air through which it moves or that moves
To summarize the Magnus effect, an airfoil with a positive past such a structure. Air acts in various ways when submitted
AOA develops air circulation about the upper surface of the to different pressures and velocities; but this discussion
wing. Its sharp trailing edge forces the rear stagnation point is confined to the parts of an aircraft that a pilot is most
to be aft of the trailing edge, while the front stagnation point concerned with in flight—namely, the airfoils designed to
falls below the leading edge. [Figure 3-4] produce lift. By looking at a typical airfoil profile, such as
the cross section of a wing, one can see several obvious
Bernoulli’s Principle of Differential Pressure characteristics of design. [Figure 3-6] Notice that there is
A half-century after Newton formulated his laws, Daniel a difference in the curvatures (called cambers) of the upper
Bernoulli, a Swiss mathematician, explained how the pressure and lower surfaces of the airfoil. The camber of the upper
of a moving fluid (liquid or gas) varies with its speed of surface is more pronounced than that of the lower surface,
motion. Bernoulli’s Principle states that as the velocity of a which is usually somewhat flat.
moving fluid (liquid or gas) increases, the pressure within
the fluid decreases. This principle explains what happens to NOTE: The two extremities of the airfoil profile also differ in
air passing over the curved top of the airplane wing. appearance. The end, which faces forward in flight, is called

46 46 46 46 46 46
VELOCITY PRESSURE VELOCITY PRESSURE VELOCITY PRESSURE
28 28 28 28 28 28

0 I0 0 I0 0 I0 0 I0 0 I0 0 I0

Figure 3-5. Air pressure decreases in a ventuFrigi tuurbee.2-4. Air pressure decreases in a venturi.

3-7

Mean camber line Trailing edge Different airfoils have different flight characteristics. Many
Camber of upper surface thousands of airfoils have been tested in wind tunnels and in
actual flight, but no one airfoil has been found that satisfies
Camber of lower surface every flight requirement. The weight, speed, and purpose
of each aircraft dictate the shape of its airfoil. The most
Leading edge Chord line efficient airfoil for producing the greatest lift is one that has
a concave, or “scooped out” lower surface. As a fixed design,
Figure 3-6. Typical airfoil section. this type of airfoil sacrifices too much speed while producing
lift and is not suitable for high-speed flight. Advancements
the leading edge, and is rounded; the other end, the trailing in engineering have made it possible for today’s high-speed
edge, is quite narrow and tapered. jets to take advantage of the concave airfoil’s high lift
characteristics. Leading edge (Kreuger) flaps and trailing
A reference line often used in discussing the airfoil is the chord edge (Fowler) flaps, when extended from the basic wing
line, a straight line drawn through the profile connecting the structure, literally change the airfoil shape into the classic
extremities of the leading and trailing edges. The distance concave form, thereby generating much greater lift during
from this chord line to the upper and lower surfaces of the slow flight conditions.
wing denotes the magnitude of the upper and lower camber at
any point. Another reference line, drawn from the leading edge On the other hand, an airfoil that is perfectly streamlined
to the trailing edge, is the mean camber line. This mean line is and offers little wind resistance sometimes does not have
equidistant at all points from the upper and lower surfaces. enough lifting power to take the airplane off the ground.
Thus, modern airplanes have airfoils that strike a medium
An airfoil is constructed in such a way that its shape takes between extremes in design. The shape varies according to
advantage of the air’s response to certain physical laws. the needs of the airplane for which it is designed. Figure 3-7
This develops two actions from the air mass: a positive shows some of the more common airfoil sections.
pressure lifting action from the air mass below the wing,
and a negative pressure lifting action from lowered pressure Early airfoil
above the wing.
Later airfoil

As the air stream strikes the relatively flat lower surface of Clark 'Y' airfoil
a wing or rotor blade when inclined at a small angle to its (Subsonic)
direction of motion, the air is forced to rebound downward,
causing an upward reaction in positive lift. At the same time, Laminar flow airfoil
the air stream striking the upper curved section of the leading (Subsonic)
edge is deflected upward. An airfoil is shaped to cause an
action on the air, and forces air downward, which provides Circular arc airfoil
an equal reaction from the air, forcing the airfoil upward. If (Supersonic)
a wing is constructed in such form that it causes a lift force
greater than the weight of the aircraft, the aircraft will fly. Double wedge airfoil
(Supersonic)
If all the lift required were obtained merely from the
deflection of air by the lower surface of the wing, an aircraft Figure 3-7. AirfoilFdiegsuigrnes2. -6. Airfoil designs.
would only need a flat wing like a kite. However, the balance
of the lift needed to support the aircraft comes from the flow Low Pressure Above
of air above the wing. Herein lies the key to flight. In a wind tunnel or in flight, an airfoil is simply a streamlined
object inserted into a moving stream of air. If the airfoil profile
It is neither accurate nor useful to assign specific values to were in the shape of a teardrop, the speed and the pressure
the percentage of lift generated by the upper surface of an changes of the air passing over the top and bottom would be
airfoil versus that generated by the lower surface. These are the same on both sides. But if the teardrop shaped airfoil were
not constant values and vary, not only with flight conditions, cut in half lengthwise, a form resembling the basic airfoil
but also with different wing designs.

3-8

(wing) section would result. If the airfoil were then inclined so Low angle of attack
the airflow strikes it at an angle (angle of attack (AOA)), the CP
air moving over the upper surface would be forced to move
faster than the air moving along the bottom of the airfoil. This Angle
increased velocity reduces the pressure above the airfoil. attofack

Applying Bernoulli’s Principle of Pressure, the increase in -8°
the speed of the air across the top of an airfoil produces a
drop in pressure. This lowered pressure is a component of
total lift. The pressure difference between the upper and
lower surface of a wing alone does not account for the total
lift force produced.

The downward backward flow from the top surface of an Normal angle of attack
airfoil creates a downwash. This downwash meets the flow
from the bottom of the airfoil at the trailing edge. Applying
Newton’s third law, the reaction of this downward backward
flow results in an upward forward force on the airfoil.

High Pressure Below Angle CP
A certain amount of lift is generated by pressure conditions attoafck
underneath the airfoil. Because of the manner in which air +4° High angle of attack
flows underneath the airfoil, a positive pressure results, CP
particularly at higher angles of attack. But there is another
aspect to this airflow that must be considered. At a point Aanttglaeckof
close to the leading edge, the airflow is virtually stopped +10°
(stagnation point) and then gradually increases speed. At
some point near the trailing edge, it again reaches a velocity
equal to that on the upper surface. In conformance with
Bernoulli’s principle, where the airflow was slowed beneath
the airfoil, a positive upward pressure was created i.e., as the
fluid speed decreases, the pressure must increase. Since the
pressure differential between the upper and lower surface
of the airfoil increases, total lift increases. Both Bernoulli’s
Principle and Newton’s Laws are in operation whenever lift
is being generated by an airfoil.

Pressure Distribution FFigiguurere32-8-8. .PrPersessusurereddiissttrriibbuuttiioonn oonn aann aaiirrfofoilil&aCnPdchCaPngchesanges
From experiments conducted on wind tunnel models and on wwitihthAaOnAa.ngle of attack.
full size airplanes, it has been determined that as air flows
along the surface of a wing at different angles of attack, there travel is very important, since it affects the position of the
are regions along the surface where the pressure is negative, air loads imposed on the wing structure in both low and high
or less than atmospheric, and regions where the pressure is AOA conditions. An airplane’s aerodynamic balance and
positive, or greater than atmospheric. This negative pressure controllability are governed by changes in the CP.
on the upper surface creates a relatively larger force on the
wing than is caused by the positive pressure resulting from
the air striking the lower wing surface. Figure 3-8 shows the
pressure distribution along an airfoil at three different angles
of attack. The average of the pressure variation for any given
angle of attack is referred to as the center of pressure (CP).
Aerodynamic force acts through this CP. At high angles of
attack, the CP moves forward, while at low angles of attack
the CP moves aft. In the design of wing structures, this CP

3-9

Airfoil Behavior trailing edge of the airfoil. This downwash results in an overall
Although specific examples can be cited in which each of reduction in lift for the affected portion of the airfoil.
the principles predict and contribute to the formation of lift,
lift is a complex subject. The production of lift is much more Manufacturers have developed different methods to
complex than a simple differential pressure between upper counteract this action. Winglets can be added to the tip of
and lower airfoil surfaces. In fact, many lifting airfoils do an airfoil to reduce this flow. The winglets act as a dam
not have an upper surface longer than the bottom, as in the preventing the vortex from forming. Winglets can be on the
case of symmetrical airfoils. These are seen in high-speed top or bottom of the airfoil. Another method of countering
aircraft having symmetrical wings, or on symmetrical rotor the flow is to taper the airfoil tip, reducing the pressure
blades for many helicopters whose upper and lower surfaces differential and smoothing the airflow around the tip.
are identical. In both examples, the relationship of the airfoil
with the oncoming airstream (angle) is all that is different. A Chapter Summary
paper airplane, which is simply a flat plate, has a bottom and
top exactly the same shape and length. Yet these airfoils do Modern general aviation aircraft have what may be considered
produce lift, and “flow turning” is partly (or fully) responsible high performance characteristics. Therefore, it is increasingly
for creating lift. necessary that pilots appreciate and understand the principles
upon which the art of flying is based. For additional
As an airfoil moves through air, the airfoil is inclined information on the principles discussed in this chapter, visit
against the airflow, producing a different flow caused by the the National Aeronautics and Space Administration (NASA)
airfoil’s relationship to the oncoming air. Think of a hand Beginner’s Guide to Aerodynamics at http://www.grc.nasa.
being placed outside the car window at a high speed. If the gov/WWW/K-12/airplane/index.html.
hand is inclined in one direction or another, the hand will
move upward or downward. This is caused by deflection,
which in turn causes the air to turn about the object within
the air stream. As a result of this change, the velocity about
the object changes in both magnitude and direction, in turn
resulting in a measurable velocity force and direction.

A Third Dimension

To this point the discussion has centered on the flow across
the upper and lower surfaces of an airfoil. While most of the
lift is produced by these two dimensions, a third dimension,
the tip of the airfoil also has an aerodynamic effect. The high-
pressure area on the bottom of an airfoil pushes around the tip
to the low-pressure area on the top. [Figure 3-9] This action
creates a rotating flow called a tip vortex. The vortex flows
behind the airfoil creating a downwash that extends back to the

Tip vortex

Figure 3-9. Tip vortex.
3-10

AChaepterr4odynamics
of Flight

Forces Acting on the Aircraft

Thrust, drag, lift, and weight are forces that act upon all
aircraft in flight. Understanding how these forces work and
knowing how to control them with the use of power and
flight controls are essential to flight. This chapter discusses
the aerodynamics of flight—how design, weight, load factors,
and gravity affect an aircraft during flight maneuvers.
The four forces acting on an aircraft in straight-and-level,
unaccelerated flight are thrust, drag, lift, and weight. They
are defined as follows:

• Thrust—the forward force produced by the powerplant/
propeller or rotor. It opposes or overcomes the force
of drag. As a general rule, it acts parallel to the
longitudinal axis. However, this is not always the case,
as explained later.

4-1

• Drag—a rearward, retarding force caused by This refinement of the old “thrust equals drag; lift equals

disruption of airflow by the wing, rotor, fuselage, and weight” formula explains that a portion of thrust is directed

other protruding objects. Drag opposes thrust, and acts upward in climbs and acts as if it were lift while a portion

rearward parallel to the relative wind. of weight is directed backward and acts as if it were drag.

• Weight—the combined load of the aircraft itself, the [Figure 4-2F]orce vectors during a stabilized climb
crew, the fuel, and the cargo or baggage. Weight pulls

the aircraft downward because of the force of gravity. Flightpath CG
It opposes lift, and acts vertically downward through Relative wind
the aircraft’s center of gravity (CG).
Thrust
• Lift—opposes the downward force of weight, is
produced by the dynamic effect of the air acting on

the airfoil, and acts perpendicular to the flightpath

through the center of lift.

In steady flight, the sum of these opposing forces is always Drag
zero. There can be no unbalanced forces in steady, straight
flight based upon Newton’s Third Law, which states that for Component of weight
every action or force there is an equal, but opposite, reaction opposed to lift
or force. This is true whether flying level or when climbing
or descending. Rearward component of weight

It does not mean the four forces are equal. It means the Figure 4-2. Force vectors during a stabilized climb.
opposing forces are equal to, and thereby cancel, the effects
of each other. In Figure 4-1 the force vectors of thrust, In glides, a portion of the weight vector is directed forward,
drag, lift, and weight appear to be equal in value. The usual and, therefore, acts as thrust. In other words, any time
explanation states (without stipulating that thrust and drag the flightpath of the aircraft is not horizontal, lift, weight,
do not equal weight and lift) that thrust equals drag and lift thrust, and drag vectors must each be broken down into two
equals weight. Although basically true, this statement can components.
be misleading. It should be understood that in straight, level,
unaccelerated flight, it is true that the opposing lift/weight Discussions of the preceding concepts are frequently omitted
forces are equal. They are also greater than the opposing in aeronautical texts/handbooks/manuals. The reason is not
forces of thrust/drag that are equal only to each other. that they are inconsequential, but because the main ideas
Therefore, in steady flight: with respect to the aerodynamic forces acting upon an
airplane in flight can be presented in their most essential
• The sum of all upward forces (not just lift) equals the elements without being involved in the technicalities of the
sum of all downward forces (not just weight). aerodynamicist. In point of fact, considering only level flight,
and normal climbs and glides in a steady state, it is still true
• The sum of all forward forces (not just thrust) equals that lift provided by the wing or rotor is the primary upward
Ctohrerescutmreolaftiaolnl sbhaicpkowf afordrcfeosrcaecstin(ngootnjuasnt adirrapgla).ne force, and weight is the primary downward force.

Lift Weight By using the aerodynamic forces of thrust, drag, lift, and
weight, pilots can fly a controlled, safe flight. A more detailed
discussion of these forces follows.

Thrust Drag Thrust
For an aircraft to move, thrust must be exerted and be greater
Figure 4-1. Relationship of forces acting on an airplane. than drag. The aircraft will continue to move and gain
speed until thrust and drag are equal. In order to maintain a
constant airspeed, thrust and drag must remain equal, just as
lift and weight must be equal to maintain a constant altitude.
If in level flight, the engine power is reduced, the thrust is
lessened, and the aircraft slows down. As long as the thrust

4-2

Level high speed Level cruise speed Level low speed

3°
6°
12°

Flightpath Flightpath Flightpath
Relative wind Relative wind Relative wind

Figure 4-3. Angle of attack at various speeds. because with the aircraft in a nose-high attitude, there is a
vertical component of thrust that helps support it. For one thing,
is less than the drag, the aircraft continues to decelerate until wing loading tends to be less than would be expected. Most
its airspeed is insufficient to support it in the air. pilots are aware that an airplane will stall, other conditions
being equal, at a slower speed with the power on than with the
Likewise, if the engine power is increased, thrust becomes power off. (Induced airflow over the wings from the propeller
greater than drag and the airspeed increases. As long as also contributes to this.) However, if analysis is restricted to
the thrust continues to be greater than the drag, the aircraft the four forces as they are usually defined during slow-speed
continues to accelerate. When drag equals thrust, the aircraft flight the thrust is equal to drag, and lift is equal to weight.
flies at a constant airspeed.
During straight-and-level flight when thrust is increased and
Straight-and-level flight may be sustained at a wide range the airspeed increases, the AOA must be decreased. That is,
of speeds. The pilot coordinates angle of attack (AOA)—the if changes have been coordinated, the aircraft will remain in
acute angle between the chord line of the airfoil and the level flight, but at a higher speed when the proper relationship
direction of the relative wind—and thrust in all speed regimes between thrust and AOA is established.
if the aircraft is to be held in level flight. Roughly, these
regimes can be grouped in three categories: low-speed flight, If the AOA were not coordinated (decreased) with an
cruising flight, and high-speed flight. increase of thrust, the aircraft would climb. But decreasing
the AOA modifies the lift, keeping it equal to the weight,
When the airspeed is low, the AOA must be relatively high and the aircraft remains in level flight. Level flight at even
if the balance between lift and weight is to be maintained. slightly negative AOA is possible at very high speed. It is
[Figure 4-3] If thrust decreases and airspeed decreases, lift evident then, that level flight can be performed with any
becomes less than weight and the aircraft starts to descend. AOA between stalling angle and the relatively small negative
To maintain level flight, the pilot can increase the AOA angles found at high speed.
an amount which will generate a lift force again equal to
the weight of the aircraft. While the aircraft will be flying Some aircraft have the ability to change the direction of the
more slowly, it will still maintain level flight if the pilot has thrust rather than changing the AOA. This is accomplished
properly coordinated thrust and AOA. either by pivoting the engines or by vectoring the exhaust
gases. [Figure 4-4]
Straight-and-level flight in the slow-speed regime provides
some interesting conditions relative to the equilibrium of forces

Figure 4-4. Some aircraft have the ability to change the direction of thrust.

4-3

Drag Interference Drag
Drag is the force that resists movement of an aircraft through
the air. There are two basic types: parasite drag and induced Interference drag comes from the intersection of airstreams
drag. The first is called parasite because it in no way functions that creates eddy currents, turbulence, or restricts smooth
to aid flight, while the second, induced drag, is a result of an airflow. For example, the intersection of the wing and the
airfoil developing lift. fuselage at the wing root has significant interference drag.
Air flowing around the fuselage collides with air flowing
Parasite Drag over the wing, merging into a current of air different from
Parasite drag is comprised of all the forces that work to slow the two original currents. The most interference drag is
an aircraft’s movement. As the term parasite implies, it is observed when two surfaces meet at perpendicular angles.
the drag that is not associated with the production of lift. Fairings are used to reduce this tendency. If a jet fighter
This includes the displacement of the air by the aircraft, carries two identical wing tanks, the overall drag is greater
turbulence generated in the airstream, or a hindrance of air than the sum of the individual tanks because both of these
moving over the surface of the aircraft and airfoil. There are create and generate interference drag. Fairings and distance
three types of parasite drag: form drag, interference drag, between lifting surfaces and external components (such as
and skin friction. radar antennas hung from wings) reduce interference drag.
[Figure 4-6]

Form Drag

Form drag is the portion of parasite drag generated by the

aircraft due to its shape and airflow around it. Examples
include the engine cowlings, antennas, and the aerodynamic
shape of other components. When the air has to separate
to move around a moving aircraft and its components, it
eventually rejoins after passing the body. How quickly
and smoothly it rejoins is representative of the resistance
that it creates which requires additional force to overcome.

[Figure 4-5]

Form drag

FLAT PLATE

Figure 4-6. A wing root can cause interference drag.

SPHERE Skin Friction Drag

SPHERE WITH Skin friction drag is the aerodynamic resistance due to the
A FAIRING contact of moving air with the surface of an aircraft. Every
surface, no matter how apparently smooth, has a rough,
SPHERE INSIDE ragged surface when viewed under a microscope. The air
A HOUSING molecules, which come in direct contact with the surface of
the wing, are virtually motionless. Each layer of molecules
Figure 4-5. Form drag. above the surface moves slightly faster until the molecules
Notice how the flat plate in Figure 4-5 causes the air to swirl are moving at the velocity of the air moving around the
around the edges until it eventually rejoins downstream. Form aircraft. This speed is called the free-stream velocity. The
drag is the easiest to reduce when designing an aircraft. The area between the wing and the free-stream velocity level is
solution is to streamline as many of the parts as possible. about as wide as a playing card and is called the boundary
layer. At the top of the boundary layer, the molecules increase
velocity and move at the same speed as the molecules
outside the boundary layer. The actual speed at which the
molecules move depends upon the shape of the wing, the
viscosity (stickiness) of the air through which the wing or
airfoil is moving, and its compressibility (how much it can
be compacted).

4-4

The airflow outside of the boundary layer reacts to the behind the wing’s trailing edge. This induced downwash has
shape of the edge of the boundary layer just as it would nothing in common with the downwash that is necessary to
to the physical surface of an object. The boundary layer produce lift. It is, in fact, the source of induced drag. The
gives any object an “effective” shape that is usually slightly greater the size and strength of the vortices and consequent
different from the physical shape. The boundary layer may downwash component on the net airflow over the airfoil, the
also separate from the body, thus creating an effective shape greater the induced drag effect becomes. This downwash over
much different from the physical shape of the object. This the top of the airfoil at the tip has the same effect as bending
change in the physical shape of the boundary layer causes a the lift vector rearward; therefore, the lift is slightly aft of
dramatic decrease in lift and an increase in drag. When this perpendicular to the relative wind, creating a rearward lift
happens, the airfoil has stalled. component. This is induced drag.

In order to reduce the effect of skin friction drag, aircraft
designers utilize flush mount rivets and remove any
irregularities which may protrude above the wing surface.
In addition, a smooth and glossy finish aids in transition of
air across the surface of the wing. Since dirt on an aircraft
disrupts the free flow of air and increases drag, keep the
surfaces of an aircraft clean and waxed.

Induced Drag Figure 4-7. Wingtip vortex from a crop duster.

The second basic type of drag is induced drag. It is an
established physical fact that no system that does work in the
mechanical sense can be 100 percent efficient. This means
that whatever the nature of the system, the required work
is obtained at the expense of certain additional work that is
dissipated or lost in the system. The more efficient the system,
the smaller this loss.

In level flight the aerodynamic properties of a wing or rotor In order to create a greater negative pressure on the top of an
produce a required lift, but this can be obtained only at the airfoil, the airfoil can be inclined to a higher AOA. If the AOA
expense of a certain penalty. The name given to this penalty of a symmetrical airfoil were zero, there would be no pressure
is induced drag. Induced drag is inherent whenever an airfoil differential, and consequently, no downwash component and
is producing lift and, in fact, this type of drag is inseparable no induced drag. In any case, as AOA increases, induced
from the production of lift. Consequently, it is always present drag increases proportionally. To state this another way—the
if lift is produced. lower the airspeed the greater the AOA required to produce
lift equal to the aircraft’s weight and, therefore, the greater
An airfoil (wing or rotor blade) produces the lift force by induced drag. The amount of induced drag varies inversely
making use of the energy of the free airstream. Whenever with the square of the airspeed.
an airfoil is producing lift, the pressure on the lower surface
of it is greater than that on the upper surface (Bernoulli’s Conversely, parasite drag increases as the square of the
Principle). As a result, the air tends to flow from the high airspeed. Thus, as airspeed decreases to near the stalling
pressure area below the tip upward to the low pressure area speed, the total drag becomes greater, due mainly to the sharp
on the upper surface. In the vicinity of the tips, there is a rise in induced drag. Similarly, as the airspeed reaches the
tendency for these pressures to equalize, resulting in a lateral terminal velocity of the aircraft, the total drag again increases
flow outward from the underside to the upper surface. This rapidly, due to the sharp increase of parasite drag. As seen
lateral flow imparts a rotational velocity to the air at the tips, in Figure 4-8, at some given airspeed, total drag is at its
creating vortices, which trail behind the airfoil. minimum amount. In figuring the maximum endurance and
range of aircraft, the power required to overcome drag is at
When the aircraft is viewed from the tail, these vortices a minimum if drag is at a minimum.
circulate counterclockwise about the right tip and clockwise
about the left tip. [Figure 4-7] Bearing in mind the direction
of rotation of these vortices, it can be seen that they induce
an upward flow of air beyond the tip, and a downwash flow

4-5

Total Drag CD= Ratio of drag pressure to dynamic pressure. Typically
Form Drag at low angles of attack, the drag coefficient is low and small
changes in angle of attack create only slight changes in the
drag coefficient. At high angles of attack, small changes in
the angle of attack cause significant changes in drag.

Total Drag L = CL . ρ . V2 . S
2
Minimum Induced Drag
Drag Airspeed D = CD . ρ . V2 . S
2

Figure 4-8. Drag versus speed. The above formulas represent the coefficient of lift (CL)
and the coefficient of drag (CD) respectively. The shape of
Lift/Drag Ratio an airfoil and other life producing devices (i.e., flaps) effect
Drag is the price paid to obtain lift. The lift to drag ratio (L/D) the production of lift and alter with changes in the AOA. The
is the amount of lift generated by a wing or airfoil compared lift/drag ratio is used to express the relation between lift and
to its drag. A ratio of L/D indicates airfoil efficiency. Aircraft drag and is determined by dividing the lift coefficient by the
with higher L/D ratios are more efficient than those with drag coefficient, CL/CD.
lower L/D ratios. In unaccelerated flight with the lift and drag
data steady, the proportions of the CL and coefficient of drag Notice in Figure 4-9 that the lift curve (red) reaches its
(CD) can be calculated for specific AOA. [Figure 4-9] maximum for this particular wing section at 20° AOA, and
then rapidly decreases. 15° AOA is therefore the stalling
The L/D ratio is determined by dividing the CL by the CD, angle. The drag curve (yellow) increases very rapidly from
which is the same as dividing the lift equation by the drag 14° AOA and completely overcomes the lift curve at 21°
equation. All terms except coefficients cancel out. AOA. The lift/drag ratio (green) reaches its maximum at 6°
L = Lift in pounds AOA, meaning that at this angle, the most lift is obtained for
D = Drag the least amount of drag.

Where L is the lift force in pounds, CL is the lift coefficient, Note that the maximum lift/drag ratio (L/DMAX) occurs at
ρ is density expressed in slugs per cubic feet, V is velocity one specific CL and AOA. If the aircraft is operated in steady
in feet per second, q is dynamic pressure per square feet, and flight at L/DMAX, the total drag is at a minimum. Any AOA
S is the wing area in square feet. lower or higher than that for L/DMAX reduces the L/D and

.2000 CL

.1800 CLMAX 1.8 18
.1600 1.6 16
Coefficient of drag (CD).1400 L/DMAX 1.4 14
Lift/drag12
.1200 1.2 10
.1000 CL 1.0 8
6
.0800 L/D 0.8 4
2
.0600 0.6 0

.0400 0.4
.0200 Stall
CD 0.2

00
0° 2° 4° 6° 8° 10° 12° 14° 16° 18° 20° 22°

Critical Angle of attack

Figure 4-9. Lift coefficients at various angles of attack.

4-6

consequently increases the total drag for a given aircraft’s velocity. For example, an airplane traveling at 200 knots has
lift. Figure 4-8 depicts the L/DMAX by the lowest portion of four times the lift as the same airplane traveling at 100 knots,
the orange line labeled “total drag.” The configuration of an if the AOA and other factors remain constant.
aircraft has a great effect on the L/D.
Actually, an aircraft could not continue to travel in level
Weight flight at a constant altitude and maintain the same AOA if
Gravity is the pulling force that tends to draw all bodies to the velocity is increased. The lift would increase and the
the center of the earth. The CG may be considered as a point aircraft would climb as a result of the increased lift force.
at which all the weight of the aircraft is concentrated. If the Therefore, to maintain the lift and weight forces in balance,
aircraft were supported at its exact CG, it would balance in any and to keep the aircraft straight and level (not accelerating
attitude. It will be noted that CG is of major importance in an upward) in a state of equilibrium, as velocity is increased,
aircraft, for its position has a great bearing upon stability. lift must be decreased. This is normally accomplished by
reducing the AOA by lowering the nose. Conversely, as the
The location of the CG is determined by the general design aircraft is slowed, the decreasing velocity requires increasing
of each particular aircraft. The designers determine how far the AOA to maintain lift sufficient to maintain flight. There
the center of pressure (CP) will travel. They then fix the CG is, of course, a limit to how far the AOA can be increased, if
forward of the center of pressure for the corresponding flight a stall is to be avoided.
speed in order to provide an adequate restoring moment to
retain flight equilibrium. All other factors being constant, for every AOA there is a
corresponding airspeed required to maintain altitude in steady,
Weight has a definite relationship to lift. This relationship unaccelerated flight (true only if maintaining “level flight”).
is simple, but important in understanding the aerodynamics Since an airfoil always stalls at the same AOA, if increasing
of flying. Lift is the upward force on the wing acting weight, lift must also be increased. The only method of
perpendicular to the relative wind. Lift is required to increasing lift is by increasing velocity if the AOA is held
counteract the aircraft’s weight (which is caused by the force constant just short of the “critical,” or stalling, AOA.
of gravity acting on the mass of the aircraft). This weight
(gravity) force acts downward through the airplane’s CG. Lift and drag also vary directly with the density of the air.
In stabilized level flight, when the lift force is equal to the Density is affected by several factors: pressure, temperature,
weight force, the aircraft is in a state of equilibrium and and humidity. At an altitude of 18,000 feet, the density of
neither gains nor loses altitude. If lift becomes less than the air has one-half the density of air at sea level. In order to
weight, the aircraft loses altitude. When lift is greater than maintain its lift at a higher altitude, an aircraft must fly at a
weight, the aircraft gains altitude. greater true airspeed for any given AOA.

Lift Warm air is less dense than cool air, and moist air is less dense
The pilot can control the lift. Any time the control yoke than dry air. Thus, on a hot humid day, an aircraft must be
or stick is moved fore or aft, the AOA is changed. As the flown at a greater true airspeed for any given AOA than on
AOA increases, lift increases (all other factors being equal). a cool, dry day.
When the aircraft reaches the maximum AOA, lift begins
to diminish rapidly. This is the stalling AOA, known as If the density factor is decreased and the total lift must equal
CL-MAX critical AOA. Examine Figure 4-9, noting how the the total weight to remain in flight, it follows that one of the
CL increases until the critical AOA is reached, then decreases other factors must be increased. The factor usually increased
rapidly with any further increase in the AOA. is the airspeed or the AOA, because these are controlled
directly by the pilot.
Before proceeding further with the topic of lift and how it
can be controlled, velocity must be interjected. The shape Lift varies directly with the wing area, provided there is no
of the wing or rotor cannot be effective unless it continually change in the wing’s planform. If the wings have the same
keeps “attacking” new air. If an aircraft is to keep flying, the proportion and airfoil sections, a wing with a planform area
lift-producing airfoil must keep moving. In a helicopter or of 200 square feet lifts twice as much at the same AOA as a
gyro-plane this is accomplished by the rotation of the rotor wing with an area of 100 square feet.
blades. For other types of aircraft such as airplanes, weight-
shift control, or gliders, air must be moving across the lifting Two major aerodynamic factors from the pilot’s viewpoint
surface. This is accomplished by the forward speed of the are lift and velocity because they can be controlled readily
aircraft. Lift is proportional to the square of the aircraft’s and accurately. Of course, the pilot can also control density

4-7

by adjusting the altitude and can control wing area if the As the air curls upward around the tip, it combines with the
aircraft happens to have flaps of the type that enlarge wing wash to form a fast-spinning trailing vortex. These vortices
area. However, for most situations, the pilot controls lift and increase drag because of energy spent in producing the
velocity to maneuver an aircraft. For instance, in straight-and- turbulence. Whenever an airfoil is producing lift, induced
level flight, cruising along at a constant altitude, altitude is drag occurs, and wingtip vortices are created.
maintained by adjusting lift to match the aircraft’s velocity
or cruise airspeed, while maintaining a state of equilibrium Just as lift increases with an increase in AOA, induced
in which lift equals weight. In an approach to landing, when drag also increases. This occurs because as the AOA is
the pilot wishes to land as slowly as practical, it is necessary increased, there is a greater pressure difference between the
to increase lift to near maximum to maintain lift equal to the top and bottom of the airfoil, and a greater lateral flow of air;
weight of the aircraft. consequently, this causes more violent vortices to be set up,
resulting in more turbulence and more induced drag.
Wingtip Vortices
In Figure 4-10, it is easy to see the formation of wingtip
Formation of Vortices vortices. The intensity or strength of the vortices is directly
The action of the airfoil that gives an aircraft lift also causes proportional to the weight of the aircraft and inversely
induced drag. When an airfoil is flown at a positive AOA, proportional to the wingspan and speed of the aircraft. The
a pressure differential exists between the upper and lower heavier and slower the aircraft, the greater the AOA and the
surfaces of the airfoil. The pressure above the wing is less stronger the wingtip vortices. Thus, an aircraft will create
than atmospheric pressure and the pressure below the wing wingtip vortices with maximum strength occurring during
is equal to or greater than atmospheric pressure. Since air the takeoff, climb, and landing phases of flight. These
always moves from high pressure toward low pressure, vortices lead to a particularly dangerous hazard to flight,
and the path of least resistance is toward the airfoil’s tips, wake turbulence.
there is a spanwise movement of air from the bottom of the
airfoil outward from the fuselage around the tips. This flow Avoiding Wake Turbulence
of air results in “spillage” over the tips, thereby setting up a Wingtip vortices are greatest when the generating aircraft is
whirlpool of air called a “vortex.” [Figure 4-10] “heavy, clean, and slow.” This condition is most commonly
encountered during approaches or departures because an
Vortex aircraft’s AOA is at the highest to produce the lift necessary
to land or take off. To minimize the chances of flying through
an aircraft’s wake turbulence:

• Avoid flying through another aircraft’s flightpath.

• Rotate prior to the point at which the preceding aircraft
rotated, when taking off behind another aircraft.

• Avoid following another aircraft on a similar flightpath
at an altitude within 1,000 feet. [Figure 4-11]

• Approach the runway above a preceding aircraft’s
path when landing behind another aircraft, and touch
down after the point at which the other aircraft wheels
contacted the runway. [Figure 4-12]

Figure 4-10. Wingtip vortices. A hovering helicopter generates a down wash from its main
rotor(s) similar to the vortices of an airplane. Pilots of small
At the same time, the air on the upper surface has a tendency aircraft should avoid a hovering helicopter by at least three
to flow in toward the fuselage and off the trailing edge. This rotor disc diameters to avoid the effects of this down wash.
air current forms a similar vortex at the inboard portion of the In forward flight this energy is transformed into a pair of
trailing edge of the airfoil, but because the fuselage limits the strong, high-speed trailing vortices similar to wing-tip
inward flow, the vortex is insignificant. Consequently, the vortices of larger fixed-wing aircraft. Helicopter vortices
deviation in flow direction is greatest at the outer tips where should be avoided because helicopter forward flight airspeeds
the unrestricted lateral flow is the strongest. are often very slow and can generate exceptionally strong
wake turbulence.

4-8

Nominally
500–1,000 ft

AVOID

Sink rate
several hundred ft/min

Figure 4-11. Avoid following another aircraft at an altitude within 1,000 feet.

Wake ends

Wake begins Touchdown 25

Rotation 14

Figure 4-12. Avoid turbulence from another aircraft.

Wind is an important factor in avoiding wake turbulence Figure 4-13. Ground effect changes airflow.
because wingtip vortices drift with the wind at the speed of
the wind. For example, a wind speed of 10 knots causes the due to the interference of the ground (or water) surface with
vortices to drift at about 1,000 feet in a minute in the wind the airflow patterns about the aircraft in flight.
direction. When following another aircraft, a pilot should
consider wind speed and direction when selecting an intended While the aerodynamic characteristics of the tail surfaces
takeoff or landing point. If a pilot is unsure of the other and the fuselage are altered by ground effect, the principal
aircraft’s takeoff or landing point, approximately 3 minutes effects due to proximity of the ground are the changes in
provides a margin of safety that allows wake turbulence the aerodynamic characteristics of the wing. As the wing
dissipation. For more information on wake turbulence, see encounters ground effect and is maintained at a constant
Advisory Circular 90-23. lift coefficient, there is consequent reduction in the upwash,
downwash, and wingtip vortices.
Ground Effect
Induced drag is a result of the airfoil’s work of sustaining
It is possible to fly an aircraft just clear of the ground (or the aircraft, and a wing or rotor lifts the aircraft simply by
water) at a slightly slower airspeed than that required to accelerating a mass of air downward. It is true that reduced
sustain level flight at higher altitudes. This is the result of a pressure on top of an airfoil is essential to lift, but that is
phenomenon better known of than understood even by some
experienced pilots.

When an aircraft in flight comes within several feet of the
surface, ground or water, a change occurs in the three-
dimensional flow pattern around the aircraft because the
vertical component of the airflow around the wing is restricted
by the surface. This alters the wing’s upwash, downwash,
and wingtip vortices. [Figure 4-13] Ground effect, then, is

4-9

only one of the things contributing to the overall effect of drag is 23.5 percent and, when the wing is at a height equal
pushing an air mass downward. The more downwash there to one-tenth its span, the reduction in induced drag is 47.6
is, the harder the wing pushes the mass of air down. At high percent. Thus, a large reduction in induced drag will take
angles of attack, the amount of induced drag is high; since place only when the wing is very close to the ground. Because
this corresponds to lower airspeeds in actual flight, it can be of this variation, ground effect is most usually recognized
said that induced drag predominates at low speed. during the liftoff for takeoff or just prior to touchdown when
landing.
However, the reduction of the wingtip vortices due to ground
effect alters the spanwise lift distribution and reduces the During the takeoff phase of flight, ground effect produces
induced AOA and induced drag. Therefore, the wing will some important relationships. An aircraft leaving ground
require a lower AOA in ground effect to produce the same effect after takeoff encounters just the reverse of an aircraft
CL. If a constant AOA is maintained, an increase in CL results. entering ground effect during landing; i.e., the aircraft leaving
[Figure 4-14] ground effect will:

Ground effect also alters the thrust required versus velocity. • Require an increase in AOA to maintain the same
Since induced drag predominates at low speeds, the reduction CL.
of induced drag due to ground effect will cause the most
significant reduction of thrust required (parasite plus induced • Experience an increase in induced drag and thrust
drag) at low speeds. required.

The reduction in induced flow due to ground effect causes • Experience a decrease in stability and a nose-up
a significant reduction in induced drag but causes no direct change in moment.
effect on parasite drag. As a result of the reduction in induced
drag, the thrust required at low speeds will be reduced. Due • Experience a reduction in static source pressure and
to the change in upwash, downwash, and wingtip vortices, increase in indicated airspeed.
there may be a change in position (installation) error of
the airspeed system, associated with ground effect. In the Ground effect must be considered during takeoffs and
majority of cases, ground effect will cause an increase in landings. For example, if a pilot fails to understand the
the local pressure at the static source and produce a lower relationship between the aircraft and ground effect during
indication of airspeed and altitude. Thus, an aircraft may takeoff, a hazardous situation is possible because the
be airborne at an indicated airspeed less than that normally recommended takeoff speed may not be achieved. Due to
required. the reduced drag in ground effect, the aircraft may seem
capable of takeoff well below the recommended speed. As
In order for ground effect to be of significant magnitude, the the aircraft rises out of ground effect with a deficiency of
wing must be quite close to the ground. One of the direct speed, the greater induced drag may result in marginal initial
results of ground effect is the variation of induced drag with climb performance. In extreme conditions, such as high
wing height above the ground at a constant CL. When the gross weight, high density altitude, and high temperature, a
wing is at a height equal to its span, the reduction in induced deficiency of airspeed during takeoff may permit the aircraft
drag is only 1.4 percent. However, when the wing is at a to become airborne but be incapable of sustaining flight
height equal to one-fourth its span, the reduction in induced out of ground effect. In this case, the aircraft may become
airborne initially with a deficiency of speed, and then settle
back to the runway.

In ground effect

Thrust required
Lift coefficient CL
Out of ground effect

In ground effect Out of ground effect
Velocity Angle of attack

Figure 4-14. Ground effect changes drag and lift.
4-10

A pilot should not attempt to force an aircraft to become aeronautical terminology due to the similarity of motion of
airborne with a deficiency of speed. The manufacturer’s aircraft and seagoing ships. The motion about the aircraft’s
recommended takeoff speed is necessary to provide adequate longitudinal axis is “roll,” the motion about its lateral axis is
initial climb performance. It is also important that a definite “pitch,” and the motion about its vertical axis is “yaw.” Yaw
climb be established before a pilot retracts the landing gear is the horizontal (left and right) movement of the aircraft’s
or flaps. Never retract the landing gear or flaps prior to nose.
establishing a positive rate of climb, and only after achieving
a safe altitude. The three motions of the conventional airplane (roll, pitch,
and yaw) are controlled by three control surfaces. Roll is
If, during the landing phase of flight, the aircraft is brought into controlled by the ailerons; pitch is controlled by the elevators;
ground effect with a constant AOA, the aircraft experiences yaw is controlled by the rudder. The use of these controls
an increase in CL and a reduction in the thrust required, and a is explained in Chapter 5, Flight Controls. Other types of
“floating” effect may occur. Because of the reduced drag and aircraft may utilize different methods of controlling the
power-off deceleration in ground effect, any excess speed at movements about the various axes.
the point of flare may incur a considerable “float” distance.
As the aircraft nears the point of touchdown, ground effect is For example, weight-shift control aircraft control two axes,
most realized at altitudes less than the wingspan. During the roll and pitch, using an “A” frame suspended from the
final phases of the approach as the aircraft nears the ground, flexible wing attached to a three-wheeled carriage. These
a reduced power setting is necessary or the reduced thrust aircraft are controlled by moving a horizontal bar (called a
required would allow the aircraft to climb above the desired control bar) in roughly the same way hang glider pilots fly.
glidepath (GP). [Figure 4-16] They are termed weight-shift control aircraft

Axes of an Aircraft

The axes of an aircraft are three imaginary lines that pass
through an aircraft’s CG. The axes can be considered as
imaginary axles around which the aircraft turns. The three axes
pass through the CG at 90° angles to each other. The axis from
nose to tail is the longitudinal axis, the axis that passes from
wingtip to wingtip is the lateral axis, and the axis that passes
vertically through the CG is the vertical axis. Whenever an
aircraft changes its flight attitude or position in flight, it rotates
about one or more of the three axes. [Figure 4-15]

The aircraft’s motion about its longitudinal axis resembles Figure 4-16. A weight-shift control aircraft.
the roll of a ship from side to side. In fact, the names
used to describe the motion about an aircraft’s three axes
were originally nautical terms. They have been adapted to

Pitching Rolling Yawing

Lateral axis Longitudinal axis Vertical axis
Figure 4-15. Axes of an airplane.

4-11

because the pilot controls the aircraft by shifting the CG. or power-off condition of flight. Although designers have
For more information on weight-shift control aircraft, see some control over the location of the drag forces, they are not
the Federal Aviation Administration (FAA) Weight-Shift always able to make the resultant drag forces pass through the
Control Flying Handbook, FAA-H-8083-5. In the case of CG of the aircraft. However, the one item over which they
powered parachutes, aircraft control is accomplished by have the greatest control is the size and location of the tail.
altering the airfoil via steering lines. The objective is to make the moments (due to thrust, drag, and
lift) as small as possible and, by proper location of the tail,
A powered parachute wing is a parachute that has a cambered to provide the means of balancing an aircraft longitudinally
upper surface and a flatter under surface. The two surfaces are for any condition of flight.
separated by ribs that act as cells, which open to the airflow
at the leading edge and have internal ports to allow lateral The pilot has no direct control over the location of forces
airflow. The principle at work holds that the cell pressure is acting on the aircraft in flight, except for controlling the
greater than the outside pressure, thereby forming a wing that center of lift by changing the AOA. Such a change, however,
maintains its airfoil shape in flight. The pilot and passenger immediately involves changes in other forces. Therefore,
sit in tandem in front of the engine which is located at the the pilot cannot independently change the location of one
rear of a vehicle. The airframe is attached to the parachute force without changing the effect of others. For example,
via two attachment points and lines. Control is accomplished a change in airspeed involves a change in lift, as well as a
by both power and the changing of the airfoil via the control change in drag and a change in the up or down force on the
lines. [Figure 4-17] tail. As forces such as turbulence and gusts act to displace
the aircraft, the pilot reacts by providing opposing control
forces to counteract this displacement.

Some aircraft are subject to changes in the location of the
CG with variations of load. Trimming devices are used to
counteract the forces set up by fuel burnoff, and loading or
off-loading of passengers or cargo. Elevator trim tabs and
adjustable horizontal stabilizers comprise the most common
devices provided to the pilot for trimming for load variations.
Over the wide ranges of balance during flight in large aircraft,
the force which the pilot has to exert on the controls would
become excessive and fatiguing if means of trimming were
not provided.

Figure 4-17. A powered parachute. Aircraft Design Characteristics

Moment and Moment Arm Each aircraft handles somewhat differently because each
resists or responds to control pressures in its own way. For
A study of physics shows that a body that is free to rotate example, a training aircraft is quick to respond to control
will always turn about its CG. In aerodynamic terms, the applications, while a transport aircraft feels heavy on the
mathematical measure of an aircraft’s tendency to rotate controls and responds to control pressures more slowly.
about its CG is called a “moment.” A moment is said to be These features can be designed into an aircraft to facilitate
equal to the product of the force applied and the distance at the particular purpose of the aircraft by considering certain
which the force is applied. (A moment arm is the distance stability and maneuvering requirements. The following
from a datum [reference point or line] to the applied force.) discussion summarizes the more important aspects of an
For aircraft weight and balance computations, “moments” aircraft’s stability, maneuverability and controllability
are expressed in terms of the distance of the arm times the qualities; how they are analyzed; and their relationship to
aircraft’s weight, or simply, inch-pounds. various flight conditions.

Aircraft designers locate the fore and aft position of the Stability
aircraft’s CG as nearly as possible to the 20 percent point Stability is the inherent quality of an aircraft to correct for
of the mean aerodynamic chord (MAC). If the thrust line conditions that may disturb its equilibrium, and to return to
is designed to pass horizontally through the CG, it will not or to continue on the original flightpath. It is primarily an
cause the aircraft to pitch when power is changed, and there aircraft design characteristic. The flightpaths and attitudes an
will be no difference in moment due to thrust for a power-on aircraft flies are limited by the aerodynamic characteristics of

4-12

the aircraft, its propulsion system, and its structural strength. Dynamic stability refers to the aircraft response over time
These limitations indicate the maximum performance and when disturbed from a given AOA, slip, or bank. This type
maneuverability of the aircraft. If the aircraft is to provide of stability also has three subtypes: [Figure 4-19]
maximum utility, it must be safely controllable to the full
extent of these limits without exceeding the pilot’s strength • Positive dynamic stability—over time, the motion
or requiring exceptional flying ability. If an aircraft is to fly of the displaced object decreases in amplitude and,
straight and steady along any arbitrary flightpath, the forces because it is positive, the object displaced returns
acting on it must be in static equilibrium. The reaction of toward the equilibrium state.
any body when its equilibrium is disturbed is referred to as
stability. The two types of stability are static and dynamic. • Neutral dynamic stability—once displaced, the
displaced object neither decreases nor increases in
Static Stability amplitude. A worn automobile shock absorber exhibits
Static stability refers to the initial tendency, or direction of this tendency.
movement, back to equilibrium. In aviation, it refers to the
aircraft’s initial response when disturbed from a given AOA, • Negative dynamic stability—over time, the motion
slip, or bank. of the displaced object increases and becomes more
divergent.
• Positive static stability—the initial tendency of the
aircraft to return to the original state of equilibrium Stability in an aircraft affects two areas significantly:
after being disturbed [Figure 4-18]
• Maneuverability—the quality of an aircraft that
• Neutral static stability—the initial tendency of permits it to be maneuvered easily and to withstand
the aircraft to remain in a new condition after its the stresses imposed by maneuvers. It is governed by
equilibrium has been disturbed [Figure 4-18] the aircraft’s weight, inertia, size and location of flight
controls, structural strength, and powerplant. It too is
• Negative static stability—the initial tendency of the an aircraft design characteristic.
aircraft to continue away from the original state of
equilibrium after being disturbed [Figure 4-18] • Controllability—the capability of an aircraft to
respond to the pilot’s control, especially with regard to
Dynamic Stability flightpath and attitude. It is the quality of the aircraft’s
Static stability has been defined as the initial tendency to response to the pilot’s control application when
return to equilibrium that the aircraft displays after being maneuvering the aircraft, regardless of its stability
disturbed from its trimmed condition. Occasionally, the characteristics.
initial tendency is different or opposite from the overall
tendency, so a distinction must be made between the two.

Positive static stability Neutral static stability Negative static stability

Applied Applied Applied
Force Force Force

CG
CG
CG
CG

Figure 4-18. Types of static stability.

4-13

Positive static Damped oscillation
(positive dynamic) Undamped oscillation
Divergent oscillation
Displacement
Time

Positive static Positive Static
(neutral dynamic) (negative dynamic)

Figure 4-19. Damped versus undamped stability.

Longitudinal Stability (Pitching) The CL in most asymmetrical airfoils has a tendency to
In designing an aircraft, a great deal of effort is spent in change its fore and aft positions with a change in the AOA.
developing the desired degree of stability around all three The CL tends to move forward with an increase in AOA and
axes. But longitudinal stability about the lateral axis is to move aft with a decrease in AOA. This means that when the
considered to be the most affected by certain variables in AOA of an airfoil is increased, the CL, by moving forward,
various flight conditions. tends to lift the leading edge of the wing still more. This
tendency gives the wing an inherent quality of instability.
Longitudinal stability is the quality that makes an aircraft (NOTE: CL is also known as the center of pressure (CP).)
stable about its lateral axis. It involves the pitching motion
as the aircraft’s nose moves up and down in flight. A Figure 4-20 shows an aircraft in straight-and-level flight. The
longitudinally unstable aircraft has a tendency to dive or line CG-CL-T represents the aircraft’s longitudinal axis from
climb progressively into a very steep dive or climb, or even the CG to a poRiendt uTceodn pthoewherorailzloownstapl isttcahbdiloizwenr.
a stall. Thus, an aircraft with longitudinal instability becomes
difficult and sometimes dangerous to fly. CL CL

Static longitudinal stability or instability in an aircraft, is CG CG
dependent upon three factors:

1. Location of the wing with respect to the CG

2. Location of the horizontal tail surfaces with respect
to the CG

3. Area or size of the tail surfaces

In analyzing stability, it should be recalled that a body free Figure 4-20. Longitudinal stability.
to rotate always turns about its CG.
Most aircraft are designed so that the wing’s CL is to the rear
To obtain static longitudinal stability, the relation of the of the CG. This makes the aircraft “nose heavy” and requires
wing and tail moments must be such that, if the moments that there be a slight downward force on the horizontal
are initially balanced and the aircraft is suddenly nose up, stabilizer in order to balance the aircraft and keep the nose
the wing moments and tail moments change so that the sum from continually pitching downward. Compensation for this
of their forces provides an unbalanced but restoring moment nose heaviness is provided by setting the horizontal stabilizer
which, in turn, brings the nose down again. Similarly, if the at a slight negative AOA. The downward force thus produced
aircraft is nose down, the resulting change in moments brings holds the tail down, counterbalancing the “heavy” nose. It
the nose back up.

4-14

Reduced power allows pitch down

is as if the line CG-CL-T were a lever with an upward force Thrust CG Lift
at CL and two downward forces balancing each other, one Weight
a strong force at the CG point and the other, a much lesser
force, at point T (downward air pressure on the stabilizer). Normal downwash
To better visualize this physics principle: If an iron bar were
suspended at point CL, with a heavy weight hanging on it at
the CG, it would take downward pressure at point T to keep
the “lever” in balance.

Even though the horizontal stabilizer may be level when the Thrust CG Lift
aircraft is in level flight, there is a downwash of air from the Weight
wings. This downwash strikes the top of the stabilizer and
produces a downward pressure, which at a certain speed is Reduced downwash
just enough to balance the “lever.” The faster the aircraft
is flying, the greater this downwash and the greater the Figure 4-22. Reduced power allows pitch down.
downward force on the horizontal stabilizer (except T-tails).
[Figure 4-21] In aircraft with fixed-position horizontal the downward force on the horizontal stabilizer is once again
stabilizers, the aircraft manufacturer sets the stabilizer at an increased. Consequently, the tail is again pushed downward
angle that provides the best stability (or balance) during flight and the nose rises into a climbing attitude.
at the design cruising speed and power setting.

Reduced power allows pitch down

CG As this climb continues, the airspeed again decreases, causing
Balanced tail load the downward force on the tail to decrease until the nose
lowers once more. Because the aircraft is dynamically stable,
Cruise speed the nose does not lower as far this time as it did before. The
aircraft acquires enough speed in this more gradual dive to
CG start it into another climb, but the climb is not as steep as
the preceding one.
Lesser downward tail load
Low speed After several of these diminishing oscillations, in which
the nose alternately rises and lowers, the aircraft finally
CG settles down to a speed at which the downward force on the
Greater downward tail load tail exactly counteracts the tendency of the aircraft to dive.
When this condition is attained, the aircraft is once again in
High speed balanced flight and continues in stabilized flight as long as
this attitude and airspeed are not changed.
Figure 4-21. Effect of speed on downwash.
A similar effect is noted upon closing the throttle. The
If the aircraft’s speed decreases, the speed of the airflow downwash of the wings is reduced and the force at T in
over the wing is decreased. As a result of this decreased Figure 4-20 is not enough to hold the horizontal stabilizer
flow of air over the wing, the downwash is reduced, causing down. It seems as if the force at T on the lever were allowing
a lesser downward force on the horizontal stabilizer. In turn, the force of gravity to pull the nose down. This is a desirable
the characteristic nose heaviness is accentuated, causing the characteristic because the aircraft is inherently trying to
aircraft’s nose to pitch down more. [Figure 4-22] This places regain airspeed and reestablish the proper balance.
the aircraft in a nose-low attitude, lessening the wing’s AOA
and drag and allowing the airspeed to increase. As the aircraft Power or thrust can also have a destabilizing effect in that
continues in the nose-low attitude and its speed increases, an increase of power may tend to make the nose rise. The
aircraft designer can offset this by establishing a “high
thrust line” wherein the line of thrust passes above the CG.
[Figures 4-23 and 4-24] In this case, as power or thrust is
increased a moment is produced to counteract the down

4-15

Thrust line affect longitudinal stability

Thrust CG Conclusion: with CG forward of the CL and with an
aerodynamic tail-down force, the aircraft usually tries to
Below center of gravity return to a safe flying attitude.

Thrust CG The following is a simple demonstration of longitudinal
stability. Trim the aircraft for “hands off” control in level
Through center of gravity flight. Then, momentarily give the controls a slight push to
nose the aircraft down. If, within a brief period, the nose rises
Thrust CG to the original position and then stops, the aircraft is statically
stable. Ordinarily, the nose passes the original position (that
Above center of gravity of level flight) and a series of slow pitching oscillations
Figure 4-23. Thrust line affects longitudinal stability. follows. If the oscillations gradually cease, the aircraft has
positive stability; if they continue unevenly, the aircraft has
Power changes affect longitudinal stability neutral stability; if they increase, the aircraft is unstable.

Thrust CGLift Lift Lift Lateral Stability (Rolling)
Stability about the aircraft’s longitudinal axis, which extends
Cruise power from the nose of the aircraft to its tail, is called lateral
stability. This helps to stabilize the lateral or “rolling effect”
when one wing gets lower than the wing on the opposite side
of the aircraft. There are four main design factors that make
an aircraft laterally stable: dihedral, sweepback, keel effect,
and weight distribution.

Dihedral

The most common procedure for producing lateral stability
is to build the wings with an angle of one to three degrees
above perpendicular to the longitudinal axis. The wings on
either side of the aircraft join the fuselage to form a slight V or
angle called “dihedral.” The amount of dihedral is measured
by the angle made by each wing above a line parallel to the
lateral axis.

Thrust CG Dihedral involves a balance of lift created by the wings’ AOA
on each side of the aircraft’s longitudinal axis. If a momentary
Idle power gust of wind forces one wing to rise and the other to lower, the
aircraft banks. When the aircraft is banked without turning,
Thrust CG the tendency to sideslip or slide downward toward the lowered
wing occurs. [Figure 4-25] Since the wings have dihedral,
Full power the air strikes the lower wing at a much greater AOA than the
higher wing. The increased AOA on the lower wing creates
Figure 4-24. Power changes affect longitudinal stability. more lift than the higher wing. Increased lift causes the lower
wing to begin to rise upward. As the wings approach the
load on the tail. On the other hand, a very “low thrust line” level position, the AOA on both wings once again are equal,
would tend to add to the nose-up effect of the horizontal tail causing the rolling tendency to subside. The effect of dihedral
surface. is to produce a rolling tendency to return the aircraft to a
laterally balanced flight condition when a sideslip occurs.

The restoring force may move the low wing up too far, so
that the opposite wing now goes down. If so, the process
is repeated, decreasing with each lateral oscillation until a
balance for wings-level flight is finally reached.

4-16

Normal angle of attack Laterally stable aircraft are constructed so that the greater

portion of the keel area is above and behind the CG.

[Figure 4-26] Thus, when the aircraft slips to one side, the

combination of the aircraft’s weight and the pressure of the

airflow against the upper portion of the keel area (both acting

about the CG) tends to roll the aircraft back to wings-level

flight. Keel area for lateral stability

Dihedral lateral stability

CG centerline CG
CG
Lesser angle Greater angle
of attack of attack

Figure 4-25. Dihedral for lateral stability. Figure 4-26. Keel area for lateral stability.

Conversely, excessive dihedral has an adverse effect on Vertical Stability (Yawing)
lateral maneuvering qualities. The aircraft may be so stable Stability about the aircraft’s vertical axis (the sideways
laterally that it resists an intentional rolling motion. For this moment) is called yawing or directional stability. Yawing or
reason, aircraft that require fast roll or banking characteristics directional stability is the most easily achieved stability in
usually have less dihedral than those designed for less aircraft design. The area of the vertical fin and the sides of
maneuverability. the fuselage aft of the CG are the prime contributors which
make the aircraft act like the well known weather vane or
Sweepback arrow, pointing its nose into the relative wind.
Sweepback is an addition to the dihedral that increases the
lift created when a wing drops from the level position. A In examining a weather vane, it can be seen that if exactly the
sweptback wing is one in which the leading edge slopes same amount of surface were exposed to the wind in front
backward. When a disturbance causes an aircraft with of the pivot point as behind it, the forces fore and aft would
sweepback to slip or drop a wing, the low wing presents its be in balance and little or no directional movement would
leading edge at an angle that is perpendicular to the relative result. Consequently, it is necessary to have a greater surface
airflow. As a result, the low wing acquires more lift, rises, aft of the pivot point than forward of it.
and the aircraft is restored to its original flight attitude.

Sweepback also contributes to directional stability. When Similarly, the aircraft designer must ensure positive
turbulence or rudder application causes the aircraft to yaw directional stability by making the side surface greater aft
to one side, the right wing presents a longer leading edge than ahead of the CG. [Figure 4-27] To provide additional
perpendicular to the relative airflow. The airspeed of the right positive stability to that provided by the fuselage, a vertical
wing increases and it acquires more drag than the left wing. fin is added. The fin acts similar to the feather on an arrow
The additional drag on the right wing pulls it back, turning in maintaining straight flight. Like the weather vane and the
the aircraft back to its original path. arrow, the farther aft this fin is placed and the larger its size,
the greater the aircraft’s directional stability.
Keel Effect and Weight Distribution
If an aircraft is flying in a straight line, and a sideward gust
An aircraft always has the tendency to turn the longitudinal of air gives the aircraft a slight rotation about its vertical
axis of the aircraft into the relative wind. This “weather vane” axis (i.e., the right), the motion is retarded and stopped by
tendency is similar to the keel of a ship and exerts a steadying the fin because while the aircraft is rotating to the right, the
influence on the aircraft laterally about the longitudinal air is striking the left side of the fin at an angle. This causes
axis. When the aircraft is disturbed and one wing dips, the pressure on the left side of the fin, which resists the turning
fuselage weight acts like a pendulum returning the airplane motion and slows down the aircraft’s yaw. In doing so, it
to its original attitude.

4-17

Fuselage and fin for vertical stability Because of structural reasons, aircraft designers sometimes
CG cannot attach the wings to the fuselage at the exact desired
point. If they had to mount the wings too far forward, and at
foArrweaard Area after center of gravity (CG) right angles to the fuselage, the center of pressure would not
of CG be far enough to the rear to result in the desired amount of
longitudinal stability. By building sweepback into the wings,
however, the designers can move the center of pressure
toward the rear. The amount of sweepback and the position
of the wings then place the center of pressure in the correct
location.

CGyaw The contribution of the wing to static directional stability is
usually small. The swept wing provides a stable contribution
Relative wind yaw depending on the amount of sweepback, but the contribution
is relatively small when compared with other components.
Figure 4-27. Fuselage and fin for vertical stability.
acts somewhat like the weather vane by turning the aircraft Free Directional Oscillations (Dutch Roll)
into the relative wind. The initial change in direction of the Dutch roll is a coupled lateral/directional oscillation that is
aircraft’s flightpath is generally slightly behind its change usually dynamically stable but is unsafe in an aircraft because
of heading. Therefore, after a slight yawing of the aircraft of the oscillatory nature. The damping of the oscillatory mode
to the right, there is a brief moment when the aircraft is still may be weak or strong depending on the properties of the
moving along its original path, but its longitudinal axis is particular aircraft.
pointed slightly to the right.
If the aircraft has a right wing pushed down, the positive
sideslip angle corrects the wing laterally before the nose is
realigned with the relative wind. As the wing corrects the
position, a lateral directional oscillation can occur resulting
in the nose of the aircraft making a figure eight on the
horizon as a result of two oscillations (roll and yaw), which,
although of about the same magnitude, are out of phase with
each other.

The aircraft is then momentarily skidding sideways, and In most modern aircraft, except high-speed swept wing
during that moment (since it is assumed that although the designs, these free directional oscillations usually die out
yawing motion has stopped, the excess pressure on the left automatically in very few cycles unless the air continues to
side of the fin still persists) there is necessarily a tendency be gusty or turbulent. Those aircraft with continuing Dutch
for the aircraft to be turned partially back to the left. That is, roll tendencies are usually equipped with gyro-stabilized yaw
there is a momentary restoring tendency caused by the fin. dampers. Manufacturers try to reach a midpoint between too
much and too little directional stability. Because it is more
This restoring tendency is relatively slow in developing and desirable for the aircraft to have “spiral instability” than
ceases when the aircraft stops skidding. When it ceases, the Dutch roll tendencies, most aircraft are designed with that
aircraft is flying in a direction slightly different from the characteristic.
original direction. In other words, it will not return of its own
accord to the original heading; the pilot must reestablish the Spiral Instability
initial heading. Spiral instability exists when the static directional stability
of the aircraft is very strong as compared to the effect of its
A minor improvement of directional stability may be obtained dihedral in maintaining lateral equilibrium. When the lateral
through sweepback. Sweepback is incorporated in the design equilibrium of the aircraft is disturbed by a gust of air and a
of the wing primarily to delay the onset of compressibility sideslip is introduced, the strong directional stability tends
during high-speed flight. In lighter and slower aircraft, to yaw the nose into the resultant relative wind while the
sweepback aids in locating the center of pressure in the comparatively weak dihedral lags in restoring the lateral
correct relationship with the CG. A longitudinally stable balance. Due to this yaw, the wing on the outside of the
aircraft is built with the center of pressure aft of the CG.

4-18

turning moment travels forward faster than the inside wing could be seen, lift and weight would be apparent: two forces.
and, as a consequence, its lift becomes greater. This produces If the aircraft were in a bank it would be apparent that lift
an overbanking tendency which, if not corrected by the pilot, did not act directly opposite to the weight, rather it now acts
results in the bank angle becoming steeper and steeper. At in the direction of the bank. A basic truth about turns: when
the same time, the strong directional stability that yaws the the aircraft banks, lift acts inward toward the center of the
aircraft into the relative wind is actually forcing the nose turn, as well as upward.
to a lower pitch attitude. A slow downward spiral begins
which, if not counteracted by the pilot, gradually increases Newton’s First Law of Motion, the Law of Inertia, states
into a steep spiral dive. Usually the rate of divergence in the that an object at rest or moving in a straight line remains
spiral motion is so gradual the pilot can control the tendency at rest or continues to move in a straight line until acted on
without any difficulty. by some other force. An aircraft, like any moving object,
requires a sideward force to make it turn. In a normal turn,
All aircraft are affected to some degree by this characteristic, this force is supplied by banking the aircraft so that lift is
although they may be inherently stable in all other normal exerted inward, as well as upward. The force of lift during a
parameters. This tendency explains why an aircraft cannot turn is separated into two components at right angles to each
be flown “hands off” indefinitely. other. One component, which acts vertically and opposite
to the weight (gravity), is called the “vertical component of
Much research has gone into the development of control lift.” The other, which acts horizontally toward the center
devices (wing leveler) to correct or eliminate this instability. of the turn, is called the “horizontal component of lift,” or
The pilot must be careful in application of recovery controls centripetal force. The horizontal component of lift is the force
during advanced stages of this spiral condition or excessive that pulls the aircraft from a straight flightpath to make it
loads may be imposed on the structure. Improper recovery turn. Centrifugal force is the “equal and opposite reaction”
from spiral instability leading to inflight structural failures of the aircraft to the change in direction and acts equal and
has probably contributed to more fatalities in general aviation opposite to the horizontal component of lift. This explains
aircraft than any other factor. Since the airspeed in the spiral why, in a correctly executed turn, the force that turns the
condition builds up rapidly, the application of back elevator aircraft is not supplied by the rudder. The rudder is used to
force to reduce this speed and to pull the nose up only correct any deviation between the straight track of the nose
“tightens the turn,” increasing the load factor. The results and tail of the aircraft. A good turn is one in which the nose
of the prolonged uncontrolled spiral are inflight structural and tail of the aircraft track along the same path. If no rudder
failure or crashing into the ground, or both. The most common is used in a turn, the nose of the aircraft yaws to the outside
recorded causes for pilots who get into this situation are: of the turn. The rudder is used to bring the nose back in line
loss of horizon reference, inability to control the aircraft by with the relative wind.
reference to instruments, or a combination of both.
An aircraft is not steered like a boat or an automobile. In
Aerodynamic Forces in Flight Maneuvers order for an aircraft to turn, it must be banked. If it is not
banked, there is no force available to cause it to deviate from
Forces in Turns a straight flightpath. Conversely, when an aircraft is banked,
If an aircraft were viewed in straight-and-level flight from it turns, provided it is not slipping to the inside of the turn.
the front [Figure 4-28], and if the forces acting on the aircraft

Level flight Medium banked turn Steeply banked turn

Lift Weight Vertical Total lift Vertical
component component

Total lift

Horizontal Centrifugal Centrifugal
component force force

Resultant load Horizontal Resultant load
Weight component Weight

Figure 4-28. Forces during normal coordinated turn.

4-19

Good directional control is based on the fact that the aircraft applied to prevent a reduction in airspeed in level turns. The
attempts to turn whenever it is banked. Pilots should keep required amount of additional thrust is proportional to the
this fact in mind when attempting to hold the aircraft in angle of bank.
straight-and-level flight.
To compensate for added lift, which would result if the
Merely banking the aircraft into a turn produces no change airspeed were increased during a turn, the AOA must be
in the total amount of lift developed. Since the lift during the decreased, or the angle of bank increased, if a constant altitude
bank is divided into vertical and horizontal components, the is to be maintained. If the angle of bank is held constant and
amount of lift opposing gravity and supporting the aircraft’s the AOA decreased, the ROT decreases. In order to maintain
weight is reduced. Consequently, the aircraft loses altitude a constant-ROT as the airspeed is increased, the AOA must
unless additional lift is created. This is done by increasing remain constant and the angle of bank increased.
the AOA until the vertical component of lift is again equal
to the weight. Since the vertical component of lift decreases An increase in airspeed results in an increase of the turn
as the bank angle increases, the AOA must be progressively radius, and centrifugal force is directly proportional to the
increased to produce sufficient vertical lift to support the radius of the turn. In a correctly executed turn, the horizontal
aircraft’s weight. An important fact for pilots to remember component of lift must be exactly equal and opposite to the
when making constant altitude turns is that the vertical centrifugal force. As the airspeed is increased in a constant-
component of lift must be equal to the weight to maintain rate level turn, the radius of the turn increases. This increase
altitude. in the radius of turn causes an increase in the centrifugal
force, which must be balanced by an increase in the horizontal
At a given airspeed, the rate at which an aircraft turns depends component of lift, which can only be increased by increasing
upon the magnitude of the horizontal component of lift. It is the angle of bank.
found that the horizontal component of lift is proportional
to the angle of bank—that is, it increases or decreases In a slipping turn, the aircraft is not turning at the rate
respectively as the angle of bank increases or decreases. As appropriate to the bank being used, since the aircraft is
the angle of bank is increased, the horizontal component of yawed toward the outside of the turning flightpath. The
lift increases, thereby increasing the ROT. Consequently, at aircraft is banked too much for the ROT, so the horizontal lift
any given airspeed, the ROT can be controlled by adjusting component is greater than the centrifugal force. [Figure 4-29]
the angle of bank. Equilibrium between the horizontal lift component and
centrifugal force is reestablished by either decreasing the
To provide a vertical component of lift sufficient to hold bank, increasing the ROT, or a combination of the two
altitude in a level turn, an increase in the AOA is required. changes.
Since the drag of the airfoil is directly proportional to its
AOA, induced drag increases as the lift is increased. This, A skidding turn results from an excess of centrifugal force
in turn, causes a loss of airspeed in proportion to the angle over the horizontal lift component, pulling the aircraft
of bank. A small angle of bank results in a small reduction toward the outside of the turn. The ROT is too great for the
in airspeed while a large angle of bank results in a large angle of bank. Correction of a skidding turn thus involves a
reduction in airspeed. Additional thrust (power) must be

Normal turn Slipping turn Skidding turn

Vertical lift Vertical lift Vertical lift
Lift Lift Lift

Centrifugal Centrifugal Centrifugal force
force force Load

Horizontal Horizontal Horizontal
lift lift lift

Centrifugal Load Centrifugal Load Centrifugal force Weight
force equals Weight force less than Weight greater than
horizontal lift horizontal lift
horizontal lift

Figure 4-29. Normal, slipping, and skidding turns.

4-20

reduction in the ROT, an increase in bank, or a combination drag (including the component of weight acting in the same
of the two changes. direction) equals the thrust. [Figure 4-31] Due to momentum,
the change in airspeed is gradual, varying considerably with
To maintain a given ROT, the angle of bank must be varied differences in aircraft size, weight, total drag, and other
with the airspeed. This becomes particularly important in factors. Consequently, the total drag is greater than the thrust,
high-speed aircraft. For instance, at 400 miles per hour (mph), and the airspeed decreases.
an aircraft must be banked approximately 44° to execute a
standard-rate turn (3° per second). At this angle of bank, T Level flight
only about 79 percent of the lift of the aircraft comprises the forces balanced
vertical component of the lift. This causes a loss of altitude D constant speed
unless the AOA is increased sufficiently to compensate for T
the loss of vertical lift. WL
WL
Forces in Climbs WL
For all practical purposes, the wing’s lift in a steady state D D
normal climb is the same as it is in a steady level flight at T
the same airspeed. Although the aircraft’s flightpath changed Steady climb
when the climb was established, the AOA of the wing with forces balanced Climb entry drag
respect to the inclined flightpath reverts to practically the constant speed greater than thrust
same values, as does the lift. There is an initial momentary
change as shown in Figure 4-30. During the transition from speed slowing
straight-and-level flight to a climb, a change in lift occurs
when back elevator pressure is first applied. Raising the Figure 4-31. Changes in speed during climb entry.
aircraft’s nose increases the AOA and momentarily increases
the lift. Lift at this moment is now greater than weight and Generally, the forces of thrust and drag, and lift and weight,
starts the aircraft climbing. After the flightpath is stabilized again become balanced when the airspeed stabilizes but at
on the upward incline, the AOA and lift again revert to about a value lower than in straight-and-level flight at the same
the level flight values. power setting. Since the aircraft’s weight is acting not only
downward but rearward with drag while in a climb, additional
power is required to maintain the same airspeed as in level
flight. The amount of power depends on the angle of climb.
When the climb is established steep enough that there is
insufficient power available, a slower speed results.

L The thrust required for a stabilized climb equals drag plus a
L percentage of weight dependent on the angle of climb. For
L example, a 10° climb would require thrust to equal drag plus
L 17 percent of weight. To climb straight up would require
thrust to equal all of weight and drag. Therefore, the angle
Steady climb Climb entry Level flight of climb for climb performance is dependent on the amount
normal lift increased lift normal lift of excess power available to overcome a portion of weight.
Note that aircraft are able to sustain a climb due to excess
Figure 4-30. Changes in lift during climb entry. thrust. When the excess thrust is gone, the aircraft is no
longer able to climb. At this point, the aircraft has reached
its “absolute ceiling.”

If the climb is entered with no change in power setting, the Forces in Descents
airspeed gradually diminishes because the thrust required As in climbs, the forces which act on the aircraft go through
to maintain a given airspeed in level flight is insufficient to definite changes when a descent is entered from straight-
maintain the same airspeed in a climb. When the flightpath and-level flight. For the following example, the aircraft is
is inclined upward, a component of the aircraft’s weight descending at the same power as used in straight-and-level
acts in the same direction as, and parallel to, the total drag flight.
of the aircraft, thereby increasing the total effective drag.
Consequently, the total drag is greater than the power, and As forward pressure is applied to the control yoke to initiate
the airspeed decreases. The reduction in airspeed gradually the descent, the AOA is decreased momentarily. Initially,
results in a corresponding decrease in drag until the total the momentum of the aircraft causes the aircraft to briefly

4-21

continue along the same flightpath. For this instant, the AOA be operated outside of the CG, the pilot may have difficulty
decreases causing the total lift to decrease. With weight now recovering from a stall. The most critical CG violation would
being greater than lift, the aircraft begins to descend. At the occur when operating with a CG which exceeds the rear limit.
same time, the flightpath goes from level to a descending In this situation, a pilot may not be able to generate sufficient
flightpath. Do not confuse a reduction in lift with the force with the elevator to counteract the excess weight aft of
inability to generate sufficient lift to maintain level flight. the CG. Without the ability to decrease the AOA, the aircraft
The flightpath is being manipulated with available thrust in continues in a stalled condition until it contacts the ground.
reserve and with the elevator.
The stalling speed of a particular aircraft is not a fixed value
To descend at the same airspeed as used in straight-and- for all flight situations, but a given aircraft always stalls at
level flight, the power must be reduced as the descent is the same AOA regardless of airspeed, weight, load factor,
entered. The component of weight acting forward along the or density altitude. Each aircraft has a particular AOA where
flightpath increases as the angle of rate of descent increases the airflow separates from the upper surface of the wing and
and, conversely, decreases as the angle of rate of descent the stall occurs. This critical AOA varies from 16° to 20°
decreases. The component of weight acting forward along the depending on the aircraft’s design. But each aircraft has only
flightpath increases as the angle of rate of descent increases one specific AOA where the stall occurs.
and, conversely, decreases as the angle of rate of descent
decreases. There are three flight situations in which the critical AOA
can be exceeded: low speed, high speed, and turning.
Stalls
The aircraft can be stalled in straight-and-level flight by flying
An aircraft stall results from a rapid decrease in lift caused by too slowly. As the airspeed decreases, the AOA must be
the separation of airflow from the wing’s surface brought on increased to retain the lift required for maintaining altitude.
by exceeding the critical AOA. A stall can occur at any pitch The lower the airspeed becomes, the more the AOA must
attitude or airspeed. Stalls are one of the most misunderstood be increased. Eventually, an AOA is reached which results
areas of aerodynamics because pilots often believe an airfoil in the wing not producing enough lift to support the aircraft
stops producing lift when it stalls. In a stall, the wing does which starts settling. If the airspeed is reduced further, the
not totally stop producing lift. Rather, it can not generate aircraft stalls, since the AOA has exceeded the critical angle
adequate lift to sustain level flight. and the airflow over the wing is disrupted.

Since the CL increases with an increase in AOA, at some Low speed is not necessary to produce a stall. The wing can
point the CL peaks and then begins to drop off. This peak is be brought into an excessive AOA at any speed. For example,
called the CL-MAX. The amount of lift the wing produces drops an aircraft is in a dive with an airspeed of 100 knots when the
dramatically after exceeding the CL-MAX or critical AOA, but pilot pulls back sharply on the elevator control. [Figure 4-32]
as stated above, it does not completely stop producing lift. Gravity and centrifugal force prevent an immediate alteration

In most straight-wing aircraft, the wing is designed to stall L
the wing root first. The wing root reaches its critical AOA CF
first making the stall progress outward toward the wingtip.
By having the wing root stall first, aileron effectiveness is L
maintained at the wingtips, maintaining controllability of
the aircraft. Various design methods are used to achieve CF
the stalling of the wing root first. In one design, the wing is W
“twisted” to a higher AOA at the wing root. Installing stall W
strips on the first 20–25 percent of the wing’s leading edge L W CF
is another method to introduce a stall prematurely.

The wing never completely stops producing lift in a stalled CF
condition. If it did, the aircraft would fall to the Earth. Most
training aircraft are designed for the nose of the aircraft to Figure 4-32. Forces exerted when pulling out of a dive.
drop during a stall, reducing the AOA and “unstalling” the
wing. The “nose-down” tendency is due to the CL being aft
of the CG. The CG range is very important when it comes
to stall recovery characteristics. If an aircraft is allowed to

4-22

of the flightpath, but the aircraft’s AOA changes abruptly expected aircraft performance. If ice is allowed to accumulate
from quite low to very high. Since the flightpath of the aircraft on the aircraft during flight [Figure 4-34], the weight of
in relation to the oncoming air determines the direction of the the aircraft is increased while the ability to generate lift is
relative wind, the AOA is suddenly increased, and the aircraft decreased. As little as 0.8 millimeter of ice on the upper
would reach the stalling angle at a speed much greater than wing surface increases drag and reduces aircraft lift by 25
the normal stall speed. percent.

The stalling speed of an aircraft is also higher in a level turn Figure 4-34. Inflight ice formation.
than in straight-and-level flight. [Figure 4-33] Centrifugal
force is added to the aircraft’s weight and the wing must Pilots can encounter icing in any season, anywhere in the
produce sufficient additional lift to counterbalance the load country, at altitudes of up to 18,000 feet and sometimes
imposed by the combination of centrifugal force and weight. higher. Small aircraft, including commuter planes, are most
In a turn, the necessary additional lift is acquired by applying vulnerable because they fly at lower altitudes where ice is
back pressure to the elevator control. This increases the wing’s more prevalent. They also lack mechanisms common on jet
AOA, and results in increased lift. The AOA must increase aircraft that prevent ice buildup by heating the front edges
as the bank angle increases to counteract the increasing load of wings.
caused by centrifugal force. If at any time during a turn the
AOA becomes excessive, the aircraft stalls. Icing can occur in clouds any time the temperature drops
below freezing and super-cooled droplets build up on an
Percent increase in stall speed 100 increase 13 Load factor or “G” aircraft and freeze. (Super-cooled droplets are still liquid
90 12 even though the temperature is below 32 °Fahrenheit (F),
80 Stall speed 11 or 0 °Celsius (C).
60 factor 10
40 9 Basic Propeller Principles
20 Load 8
7 The aircraft propeller consists of two or more blades and a
00° 10° 20° 30° 40° 50° 60° 70° 6 central hub to which the blades are attached. Each blade of
Bank Angle 5 an aircraft propeller is essentially a rotating wing. As a result
4 of their construction, the propeller blades are like airfoils
3 and produce forces that create the thrust to pull, or push,
2 the aircraft through the air. The engine furnishes the power
1 needed to rotate the propeller blades through the air at high
80° 90° speeds, and the propeller transforms the rotary power of the
engine into forward thrust.
Figure 4-33. Increase in stall speed and load factor.
A cross-section of a typical propeller blade is shown in
At this point, the action of the aircraft during a stall should Figure 4-35. This section or blade element is an airfoil
be examined. To balance the aircraft aerodynamically, the CL comparable to a cross-section of an aircraft wing. One
is normally located aft of the CG. Although this makes the surface of the blade is cambered or curved, similar to the
aircraft inherently nose-heavy, downwash on the horizontal upper surface of an aircraft wing, while the other surface is
stabilizer counteracts this condition. At the point of stall, when flat like the bottom surface of a wing. The chord line is an
the upward force of the wing’s lift and the downward tail imaginary line drawn through the blade from its leading edge
force cease, an unbalanced condition exists. This allows the to its trailing edge. As in a wing, the leading edge is the thick
aircraft to pitch down abruptly, rotating about its CG. During edge of the blade that meets the air as the propeller rotates.
this nose-down attitude, the AOA decreases and the airspeed
again increases. The smooth flow of air over the wing begins
again, lift returns, and the aircraft is again flying. Considerable
altitude may be lost before this cycle is complete.

Airfoil shape and degradation of that shape must also be
considered in a discussion of stalls. For example, if ice,
snow, and frost are allowed to accumulate on the surface of
an aircraft, the smooth airflow over the wing is disrupted.
This causes the boundary layer to separate at an AOA lower
than that of the critical angle. Lift is greatly reduced, altering

4-23

Airfoil sections of propeller blade

restrained from advancing with sufficient speed to permit
its fixed-pitch blades to reach their full efficiency. In this
situation, each propeller blade is turning through the air at
an AOA that produces relatively little thrust for the amount
of power required to turn it.

Figure 4-35. Airfoil sections of propeller blade. Rotational velocity To understand the action of a propeller, consider first its
motion, which is both rotational and forward. As shown by
Blade angle, usually measured in degrees, is the angle the vectors of propeller forces in Figure 4-36, each section of
between the chord of the blade and the plane of rotation a propeller blade moves downward and forward. The angle
and is measured at a specific point along the length of the at which this air (relative wind) strikes the propeller blade is
blade. [Figure 4-36] Because most propellers have a flat its AOA. The air deflection produced by this angle causes the
blade “face,” the chord line is often drawn along the face dynamic pressure at the engine side of the propeller blade to
of the propeller blade. Pitch is not blade angle, but because be greater than atmospheric pressure, thus creating thrust.
pitch is largely determined by blade angle, the two terms are
often used interchangeably. An increase or decrease in one is The shape of the blade also creates thrust because it is
usually associated wPitrhopaenllienrcbrelaadsee aonrgdleecrease in the other. cambered like the airfoil shape of a wing. As the air flows
past the propeller, the pressure on one side is less than that
Thrust on the other. As in a wing, a reaction force is produced in the
direction of the lesser pressure. The airflow over the wing
has less pressure, and the force (lift) is upward. In the case
of the propeller, which is mounted in a vertical instead of a
horizontal plane, the area of decreased pressure is in front of
the propeller, and the force (thrust) is in a forward direction.
Aerodynamically, thrust is the result of the propeller shape
and the AOA of the blade.

of aAtntagclek bladPeitcahngolre Thrust can be considered also in terms of the mass of air
handled by the propeller. In these terms, thrust equals mass
Chord line of air handled multiplied by slipstream velocity minus
velocity of the aircraft. The power expended in producing
Relative wind Forward velocity thrust depends on the rate of air mass movement. On average,
thrust constitutes approximately 80 percent of the torque
Figure 4-36. Propeller blade angle. (total horsepower absorbed by the propeller). The other
20 percent is lost in friction and slippage. For any speed of
The pitch of a propeller may be designated in inches. A rotation, the horsepower absorbed by the propeller balances
propeller designated as a “74-48” would be 74 inches in the horsepower delivered by the engine. For any single
length and have an effective pitch of 48 inches. The pitch revolution of the propeller, the amount of air handled depends
is the distance in inches, which the propeller would screw on the blade angle, which determines how big a “bite” of
through the air in one revolution if there were no slippage. air the propeller takes. Thus, the blade angle is an excellent
means of adjusting the load on the propeller to control the
When specifying a fixed-pitch propeller for a new type of engine rpm.
aircraft, the manufacturer usually selects one with a pitch
that operates efficiently at the expected cruising speed of the The blade angle is also an excellent method of adjusting the
aircraft. Every fixed-pitch propeller must be a compromise AOA of the propeller. On constant-speed propellers, the blade
because it can be efficient at only a given combination of angle must be adjusted to provide the most efficient AOA at
airspeed and revolutions per minute (rpm). Pilots cannot all engine and aircraft speeds. Lift versus drag curves, which
change this combination in flight. are drawn for propellers, as well as wings, indicate that the
most efficient AOA is small, varying from +2° to +4°. The
When the aircraft is at rest on the ground with the engine actual blade angle necessary to maintain this small AOA
operating, or moving slowly at the beginning of takeoff, varies with the forward speed of the aircraft.
the propeller efficiency is very low because the propeller is

4-24

Fixed-pitch and ground-adjustable propellers are designed Mode Propeller travels faster at the tipsots
for best efficiency at one rotation and forward speed. They Short tra 259 knots
are designed for a given aircraft and engine combination. A Greater travel distance—very high speed—389 kn
propeller may be used that provides the maximum efficiency rate travel distance—moderate speed—speed
for takeoff, climb, cruise, or high-speed flight. Any change in
these conditions results in lowering the efficiency of both the vel distance—slownots—129 k
propeller and the engine. Since the efficiency of any machine
is the ratio of the useful power output to the actual power 20 in.
input, propeller efficiency is the ratio of thrust horsepower to 2,500 rpm
brake horsepower. Propeller efficiency varies from 50 to 87
percent, depending on how much the propeller “slips.” 40 in.
2,500 rpm
Propeller slip is the difference between the geometric pitch of
the propeller and its effective pitch. [Figure 4-37] Geometric 60 in.
pitch is the theoretical distance a propeller should advance
in one revolution; effective pitch is the distance it actually 2,500 rpm
advances. Thus, geometric or theoretical pitch is based on
no slippage, but actual or effective pitch includes propeller Figure 4-38. Propeller tips travel faster than the hub.
slippage in the air.
A constant-speed propeller automatically keeps the blade
Propeller tips travel faster than hubs angle adjusted for maximum efficiency for most conditions
encountered in flight. During takeoff, when maximum power
Slip and thrust are required, the constant-speed propeller is at
a low propeller blade angle or pitch. The low blade angle
Effective Pitch keeps the AOA small and efficient with respect to the relative
Geometric Pitch wind. At the same time, it allows the propeller to handle a
smaller mass of air per revolution. This light load allows
Figure 4-37. Propeller slippage. the engine to turn at high rpm and to convert the maximum
amount of fuel into heat energy in a given time. The high rpm
The reason a propeller is “twisted” is that the outer parts of the also creates maximum thrust because, although the mass of
propeller blades, like all things that turn about a central point, air handled per revolution is small, the rpm and slipstream
travel faster than the portions near the hub. [Figure 4-38] If velocity are high, and with the low aircraft speed, there is
the blades had the same geometric pitch throughout their maximum thrust.
lengths, portions near the hub could have negative AOAs
while the propeller tips would be stalled at cruise speed. After liftoff, as the speed of the aircraft increases, the constant-
Twisting or variations in the geometric pitch of the blades speed propeller automatically changes to a higher angle (or
permits the propeller to operate with a relatively constant pitch). Again, the higher blade angle keeps the AOA small
AOA along its length when in cruising flight. Propeller and efficient with respect to the relative wind. The higher
blades are twisted to change the blade angle in proportion blade angle increases the mass of air handled per revolution.
to the differences in speed of rotation along the length of This decreases the engine rpm, reducing fuel consumption
the propeller, keeping thrust more nearly equalized along and engine wear, and keeps thrust at a maximum.
this length.
After the takeoff climb is established in an aircraft having
Usually 1° to 4° provides the most efficient lift/drag ratio, a controllable-pitch propeller, the pilot reduces the power
but in flight the propeller AOA of a fixed-pitch propeller output of the engine to climb power by first decreasing the
varies—normally from 0° to 15°. This variation is caused manifold pressure and then increasing the blade angle to
by changes in the relative airstream, which in turn results lower the rpm.
from changes in aircraft speed. Thus, propeller AOA is the
product of two motions: propeller rotation about its axis and
its forward motion.

4-25

At cruising altitude, when the aircraft is in level flight and Generally, the compensating factors are permanently set
less power is required than is used in takeoff or climb, the so that they compensate for this force at cruising speed,
pilot again reduces engine power by reducing the manifold since most of the aircraft’s operating lift is at that speed.
pressure and then increasing the blade angle to decrease the However, aileron trim tabs permit further adjustment for
rpm. Again, this provides a torque requirement to match the other speeds.
reduced engine power. Although the mass of air handled per
revolution is greater, it is more than offset by a decrease in When the aircraft’s wheels are on the ground during the
slipstream velocity and an increase in airspeed. The AOA is takeoff roll, an additional turning moment around the vertical
still small because the blade angle has been increased with axis is induced by torque reaction. As the left side of the
an increase in airspeed. aircraft is being forced down by torque reaction, more weight
is being placed on the left main landing gear. This results in
Torque and P-Factor more ground friction, or drag, on the left tire than on the right,
To the pilot, “torque” (the left turning tendency of the causing a further turning moment to the left. The magnitude
airplane) is made up of four elements which cause or produce of this moment is dependent on many variables. Some of
a twisting or rotating motion around at least one of the these variables are:
airplane’s three axes. These four elements are:
1. Size and horsepower of engine,
1. Torque reaction from engine and propeller,
2. Size of propeller and the rpm,
2. Corkscrewing effect of the slipstream,
3. Size of the aircraft, and
3. Gyroscopic action of the propeller, and
4. Condition of the ground surface.
4. Asymmetric loading of the propeller (P-factor).
This yawing moment on the takeoff roll is corrected by the
Torque Reaction pilot’s proper use of the rudder or rudder trim.

Torque reaction involves Newton’s Third Law of Physics— Corkscrew Effect
The high-speed rotation of an aircraft propeller gives a
for every action, there is an equal and opposite reaction. As corkscrew or spiraling rotation to the slipstream. At high
propeller speeds and low forward speed (as in the takeoffs
applied to the aircraft, this means that as the internal engine and approaches to power-on stalls), this spiraling rotation
is very compact and exerts a strong sideward force on the
parts and propeller are revolving in one direction, an equal aircraft’s vertical tail surface. [Figure 4-40]

force is trying to rotate the aircraft in the opposite direction.

[Figure 4-39] Torque reaction

Reactio

n

Yaw slipstream

Action force

Figure 4-39. Torque reaction.

When the aircraft is airborne, this force is acting around Figure 4-40. Corkscrewing slipstream.
the longitudinal axis, tending to make the aircraft roll. To
compensate for roll tendency, some of the older aircraft are When this spiraling slipstream strikes the vertical fin it causes
rigged in a manner to create more lift on the wing that is being a turning moment about the aircraft’s vertical axis. The more
forced downward. The more modern aircraft are designed compact the spiral, the more prominent this force is. As the
with the engine offset to counteract this effect of torque. forward speed increases, however, the spiral elongates and
becomes less effective.The corkscrew flow of the slipstream
NOTE: Most United States built aircraft engines rotate the also causes a rolling moment around the longitudinal axis.
propeller clockwise, as viewed from the pilot’s seat. The
discussion here is with reference to those engines.

4-26

Note that this rolling moment caused by the corkscrew flow resultant force will still be 90° from the point of application
of the slipstream is to the right, while the rolling moment in the direction of rotation. Depending on where the force is
caused by torque reaction is to the left—in effect one may applied, the airplane is caused to yaw left or right, to pitch
be counteracting the other. However, these forces vary up or down, or a combination of pitching and yawing.
greatly and it is the pilot’s responsibility to apply proper
corrective action by use of the flight controls at all times. Yaw Efffoerccteive Applied force
These forces must be counteracted regardless of which is Refsourclteant
the most prominent at the time.
Figure 4-42. Raising tail produces gyroscopic precession.
Gyroscopic Action
Before the gyroscopic effects of the propeller can be
understood, it is necessary to understand the basic principle
of a gyroscope. All practical applications of the gyroscope
are based upon two fundamental properties of gyroscopic
action: rigidity in space and precession. The one of interest
for this discussion is precession.

Precession is the resultant action, or deflection, of a spinning It can be said that, as a result of gyroscopic action, any yawing
rotor when a deflecting force is applied to its rim. As can be around the vertical axis results in a pitching moment, and any
seen in Figure 4-41, when a force is applied, the resulting pitching around the lateral axis results in a yawing moment.
force takes effect 90° ahead of and in the direction of To correct for the effect of gyroscopic action, it is necessary
rotation. for the pilot to properly use elevator and rudder to prevent
undesired pitching and yawing.
Effective Resultant force 90°
force Asymmetric Loading (P-Factor)
When an aircraft is flying with a high AOA, the “bite” of
Yaw the downward moving blade is greater than the “bite” of the
upward moving blade. This moves the center of thrust to the
Applied force right of the prop disc area, causing a yawing moment toward
the left around the vertical axis. To prove this explanation is
Figure 4-41. Gyroscopic precession. complex because it would be necessary to work wind vector
problems on each blade while considering both the AOA of
The rotating propeller of an airplane makes a very good the aircraft and the AOA of each blade.
gyroscope and thus has similar properties. Any time a force
is applied to deflect the propeller out of its plane of rotation, This asymmetric loading is caused by the resultant velocity,
the resulting force is 90° ahead of and in the direction of which is generated by the combination of the velocity of the
rotation and in the direction of application, causing a pitching propeller blade in its plane of rotation and the velocity of the
moment, a yawing moment, or a combination of the two air passing horizontally through the propeller disc. With the
depending upon the point at which the force was applied. aircraft being flown at positive AOAs, the right (viewed from
the rear) or downswinging blade, is passing through an area of
This element of torque effect has always been associated with resultant velocity which is greater than that affecting the left
and considered more prominent in tailwheel-type aircraft, or upswinging blade. Since the propeller blade is an airfoil,
and most often occurs when the tail is being raised during increased velocity means increased lift. The downswinging
the takeoff roll. [Figure 4-42] This change in pitch attitude blade has more lift and tends to pull (yaw) the aircraft’s nose
has the same effect as applying a force to the top of the to the left.
propeller’s plane of rotation. The resultant force acting 90°
ahead causes a yawing moment to the left around the vertical When the aircraft is flying at a high AOA, the downward
axis. The magnitude of this moment depends on several moving blade has a higher resultant velocity, creating more
variables, one of which is the abruptness with which the tail lift than the upward moving blade. [Figure 4-43] This might
is raised (amount of force applied). However, precession, be easier to visualize if the propeller shaft was mounted
or gyroscopic action, occurs when a force is applied to any perpendicular to the ground (like a helicopter). If there
point on the rim of the propeller’s plane of rotation; the were no air movement at all, except that generated by the

4-27

Load on Load on For example, a load factor of 3 means the total load on an
upward moving upward moving aircraft’s structure is three times its gross weight. Since load
propeller blade propeller blade factors are expressed in terms of Gs, a load factor of 3 may
be spoken of as 3 Gs, or a load factor of 4 as 4 Gs.

Load on Load on If an aircraft is pulled up from a dive, subjecting the pilot to
downward moving downward moving 3 Gs, he or she would be pressed down into the seat with a
force equal to three times his or her weight. Since modern
propeller blade propeller blade aircraft operate at significantly higher speeds than older
Low angle of attack High angle of attack aircraft, increasing the magnitude of the load factor, this
effect has become a primary consideration in the design of
the structure of all aircraft.

Figure 4-43. Asymmetrical loading of propeller (P-factor). With the structural design of aircraft planned to withstand
only a certain amount of overload, a knowledge of load
propeller itself, identical sections of each blade would have factors has become essential for all pilots. Load factors are
the same airspeed. With air moving horizontally across this important for two reasons:
vertically mounted propeller, the blade proceeding forward
into the flow of air has a higher airspeed than the blade 1. It is possible for a pilot to impose a dangerous overload
retreating with the airflow. Thus, the blade proceeding into on the aircraft structures.
the horizontal airflow is creating more lift, or thrust, moving
the center of thrust toward that blade. Visualize rotating the 2. An increased load factor increases the stalling speed
vertically mounted propeller shaft to shallower angles relative and makes stalls possible at seemingly safe flight
to the moving air (as on an aircraft). This unbalanced thrust speeds.
then becomes proportionately smaller and continues getting
smaller until it reaches the value of zero when the propeller Load Factors in Aircraft Design
shaft is exactly horizontal in relation to the moving air. The answer to the question “How strong should an aircraft
be?” is determined largely by the use to which the aircraft is
The effects of each of these four elements of torque vary in subjected. This is a difficult problem because the maximum
value with changes in flight situations. In one phase of flight, possible loads are much too high for use in efficient design.
one of these elements may be more prominent than another. It is true that any pilot can make a very hard landing or an
In another phase of flight, another element may be more extremely sharp pull up from a dive, which would result in
prominent. The relationship of these values to each other abnormal loads. However, such extremely abnormal loads
varies with different aircraft—depending on the airframe, must be dismissed somewhat if aircraft are built that take off
engine, and propeller combinations, as well as other design quickly, land slowly, and carry worthwhile payloads.
features. To maintain positive control of the aircraft in all
flight conditions, the pilot must apply the flight controls as The problem of load factors in aircraft design becomes how
necessary to compensate for these varying values. to determine the highest load factors that can be expected in
normal operation under various operational situations. These
Load Factors load factors are called “limit load factors.” For reasons of
safety, it is required that the aircraft be designed to withstand
In aerodynamics, load factor is the ratio of the maximum load these load factors without any structural damage. Although
an aircraft can sustain to the gross weight of the aircraft. The the Code of Federal Regulations (CFR) requires the aircraft
load factor is measured in Gs (acceleration of gravity), a unit structure be capable of supporting one and one-half times
of force equal to the force exerted by gravity on a body at rest these limit load factors without failure, it is accepted that
and indicates the force to which a body is subjected when it parts of the aircraft may bend or twist under these loads and
is accelerated. Any force applied to an aircraft to deflect its that some structural damage may occur.
flight from a straight line produces a stress on its structure,
and the amount of this force is the load factor. While a course This 1.5 load limit factor is called the “factor of safety” and
in aerodynamics is not a prerequisite for obtaining a pilot’s provides, to some extent, for loads higher than those expected
license, the competent pilot should have a solid understanding under normal and reasonable operation. This strength reserve
of the forces that act on the aircraft, the advantageous use is not something which pilots should willfully abuse; rather,
of these forces, and the operating limitations of the aircraft it is there for protection when encountering unexpected
being flown. conditions.

4-28

The above considerations apply to all loading conditions, aircraft designed under the category system, and they should
whether they be due to gusts, maneuvers, or landings. The be operated accordingly.
gust load factor requirements now in effect are substantially
the same as those that have been in existence for years. Load Factors in Steep Turns
Hundreds of thousands of operational hours have proven In a constant altitude, coordinated turn in any aircraft, the
them adequate for safety. Since the pilot has little control over load factor is the result of two forces: centrifugal force and
gust load factors (except to reduce the aircraft’s speed when gravity. [Figure 4-44] For any given bank angle, the ROT
rough air is encountered), the gust loading requirements are varies with the airspeed—the higher the speed, the slower the
substantially the same for most general aviation type aircraft ROT. This compensates for added centrifugal force, allowing
regardless of their operational use. Generally, the gust load the load factor to remain the same.
factors control the design of aircraft which are intended for
strictly nonacrobatic usage. Two forces cause load factor during turns

An entirely different situation exists in aircraft design with 60° 50°40° 30° 20° 10°
maneuvering load factors. It is necessary to discuss this matter
separately with respect to: (1) aircraft designed in accordance CentrifugalGravity = 1G
with the category system (i.e., normal, utility, acrobatic); and force = 1.73 Gs
(2) older designs built according to requirements which did
not provide for operational categories. Load factor = 2 Gs

Aircraft designed under the category system are readily Figure 4-44. Two forces cause load factor during turns.
identified by a placard in the flight deck, which states the
operational category (or categories) in which the aircraft Figure 4-45 reveals an important fact about turns—the load
is certificated. The maximum safe load factors (limit load factor increases at a terrific rate after a bank has reached
factors) specified for aircraft in the various categories are: 45° or 50°. The load factor for any aircraft in a 60° bank is
2 Gs. The load factor in an 80° bank is 5.76 Gs. The wing
CATEGORY LIMIT LOAD FACTOR must produce lift equal to these load factors if altitude is to
be maintained.
Normal1 3.8 to –1.52
7
Utility (mild acrobatics, including spins) 4.4 to –1.76 6

Acrobatic 6.0 to –3.00 5

1 For aircraft with gross weight of more than 4,000 pounds, 4
the limit load factor is reduced. To the limit loads given above,
a safety factor of 50 percent is added. 3

There is an upward graduation in load factor with the 2Load factor (G units)
increasing severity of maneuvers. The category system
provides for maximum utility of an aircraft. If normal 1
operation alone is intended, the required load factor (and 00° 10° 20° 30° 40° 50° 60° 70° 80° 90°
consequently the weight of the aircraft) is less than if the
aircraft is to be employed in training or acrobatic maneuvers Bank angle
as they result in higher maneuvering loads.
Figure 4-45. Angle of bank changes load factor.
Aircraft that do not have the category placard are designs that
were constructed under earlier engineering requirements in It should be noted how rapidly the line denoting load factor
which no operational restrictions were specifically given to rises as it approaches the 90° bank line, which it never quite
the pilots. For aircraft of this type (up to weights of about reaches because a 90° banked, constant altitude turn is not
4,000 pounds), the required strength is comparable to present-
day utility category aircraft, and the same types of operation
are permissible. For aircraft of this type over 4,000 pounds,
the load factors decrease with weight. These aircraft should
be regarded as being comparable to the normal category

4-29

mathematically possible. An aircraft may be banked to 90°, Figures 4-45 and 4-46 show that banking an aircraft greater
but not in a coordinated turn. An aircraft which can be held in than 72° in a steep turn produces a load factor of 3, and the
a 90° banked slipping turn is capable of straight knife-edged stalling speed is increased significantly. If this turn is made
flight. At slightly more than 80°, the load factor exceeds the in an aircraft with a normal unaccelerated stalling speed of
limit of 6 Gs, the limit load factor of an acrobatic aircraft. 45 knots, the airspeed must be kept greater than 75 knots to
prevent inducing a stall. A similar effect is experienced in a
For a coordinated, constant altitude turn, the approximate quick pull up, or any maneuver producing load factors above
maximum bank for the average general aviation aircraft is 60°. 1 G. This sudden, unexpected loss of control, particularly in
This bank and its resultant necessary power setting reach the a steep turn or abrupt application of the back elevator control
limit of this type of aircraft. An additional 10° bank increases near the ground, has caused many accidents.
the load factor by approximately 1 G, bringing it close to the
yield point established for these aircraft. [Figure 4-46] Since the load factor is squared as the stalling speed doubles,
tremendous loads may be imposed on structures by stalling
Load Factors and Stalling Speeds an aircraft at relatively high airspeeds.
Any aircraft, within the limits of its structure, may be stalled
at any airspeed. When a sufficiently high AOA is imposed, The maximum speed at which an aircraft may be stalled safely
the smooth flow of air over an airfoil breaks up and separates, is now determined for all new designs. This speed is called
producing an abrupt change of flight characteristics and a the “design maneuvering speed” (VA) and must be entered in
sudden loss of lift, which results in a stall. the FAA-approved Airplane Flight Manual/Pilot’s Operating
Handbook (AFM/POH) of all recently designed aircraft. For
A study of this effect has revealed that the aircraft’s older general aviation aircraft, this speed is approximately 1.7
stalling speed increases in proportion to the square root of times the normal stalling speed. Thus, an older aircraft which
the load factor. This means that an aircraft with a normal normally stalls at 60 knots must never be stalled at above 102
unaccelerated stalling speed of 50 knots can be stalled at 100 knots (60 knots x 1.7 = 102 knots). An aircraft with a normal
knots by inducing a load factor of 4 Gs. If it were possible stalling speed of 60 knots stalled at 102 knots undergoes a load
for this aircraft to withstand a load factor of nine, it could be factor equal to the square of the increase in speed, or 2.89 Gs
stalled at a speed of 150 knots. A pilot should be aware: (1.7 x 1.7 = 2.89 Gs). (The above figures are approximations
to be considered as a guide, and are not the exact answers to
• Of the danger of inadvertently stalling the aircraft by any set of problems. The design maneuvering speed should be
increasing the load factor, as in a steep turn or spiral; determined from the particular aircraft’s operating limitations
provided by the manufacturer.)
• When intentionally stalling an aircraft above its
design maneuvering speed, a tremendous load factor
is imposed.

40
5

50

4 60
70

3 80

100
2 120

150
Ratio of acceleration Vs to unaccelerated Vs
Unaccelerated stall speed1

00 1 2 3 4 5 6 7 8 20 40 60 80 100 120 140 160 180 200 220 240 260
“G” Load Accelerated stall speed

Figure 4-46. Load factor changes stall speed.

4-30

Since the leverage in the control system varies with different inadvertently during excessive diving (and consequently high
aircraft (some types employ “balanced” control surfaces while airspeed) and abrupt pull ups to level flight. One usually leads
others do not), the pressure exerted by the pilot on the controls to the other, thus increasing the load factor. Abrupt pull ups
cannot be accepted as an index of the load factors produced at high diving speeds may impose critical loads on aircraft
in different aircraft. In most cases, load factors can be judged structures and may produce recurrent or secondary stalls by
by the experienced pilot from the feel of seat pressure. Load increasing the AOA to that of stalling.
factors can also be measured by an instrument called an
“accelerometer,” but this instrument is not common in general As a generalization, a recovery from a stall made by diving
aviation training aircraft. The development of the ability to only to cruising or design maneuvering airspeed, with a
judge load factors from the feel of their effect on the body is gradual pull up as soon as the airspeed is safely above stalling,
important. A knowledge of these principles is essential to the can be effected with a load factor not to exceed 2 or 2.5 Gs. A
development of the ability to estimate load factors. higher load factor should never be necessary unless recovery
has been effected with the aircraft’s nose near or beyond the
A thorough knowledge of load factors induced by varying vertical attitude, or at extremely low altitudes to avoid diving
degrees of bank and the VA aids in the prevention of two of into the ground.
the most serious types of accidents:
Spins
1. Stalls from steep turns or excessive maneuvering near A stabilized spin is not different from a stall in any element
the ground other than rotation and the same load factor considerations
apply to spin recovery as apply to stall recovery. Since spin
2. Structural failures during acrobatics or other violent recoveries are usually effected with the nose much lower
maneuvers resulting from loss of control than is common in stall recoveries, higher airspeeds and
consequently higher load factors are to be expected. The
Load Factors and Flight Maneuvers load factor in a proper spin recovery usually is found to be
Critical load factors apply to all flight maneuvers except about 2.5 Gs.
unaccelerated straight flight where a load factor of 1 G is
always present. Certain maneuvers considered in this section The load factor during a spin varies with the spin characteristics
are known to involve relatively high load factors. of each aircraft, but is usually found to be slightly above the
1 G of level flight. There are two reasons for this:
Turns
Increased load factors are a characteristic of all banked 1. Airspeed in a spin is very low, usually within 2 knots
turns. As noted in the section on load factors in steep turns, of the unaccelerated stalling speeds.
load factors become significant to both flight performance
and load on wing structure as the bank increases beyond 2. Aircraft pivots, rather than turns, while it is in a
approximately 45°. spin.

The yield factor of the average light plane is reached High Speed Stalls
at a bank of approximately 70° to 75°, and the stalling The average light plane is not built to withstand the repeated
speed is increased by approximately one-half at a bank of application of load factors common to high speed stalls.
approximately 63°. The load factor necessary for these maneuvers produces a
stress on the wings and tail structure, which does not leave
Stalls a reasonable margin of safety in most light aircraft.
The normal stall entered from straight-and-level flight, or an
unaccelerated straight climb, does not produce added load The only way this stall can be induced at an airspeed above
factors beyond the 1 G of straight-and-level flight. As the stall normal stalling involves the imposition of an added load
occurs, however, this load factor may be reduced toward zero, factor, which may be accomplished by a severe pull on the
the factor at which nothing seems to have weight. The pilot elevator control. A speed of 1.7 times stalling speed (about
experiences a sensation of “floating free in space.” If recovery 102 knots in a light aircraft with a stalling speed of 60 knots)
is effected by snapping the elevator control forward, negative produces a load factor of 3 Gs. Only a very narrow margin
load factors (or those that impose a down load on the wings for error can be allowed for acrobatics in light aircraft. To
and raise the pilot from the seat) may be produced. illustrate how rapidly the load factor increases with airspeed,
a high-speed stall at 112 knots in the same aircraft would
During the pull up following stall recovery, significant load produce a load factor of 4 Gs.
factors are sometimes induced. These may be further increased

4-31

Chandelles and Lazy Eights Speeds up to but not exceeding the maneuvering speed allows
A chandelle is a maximum performance climbing turn an aircraft to stall prior to experiencing an increase in load
beginning from approximately straight-and-level flight, factor that would exceed the limit load of the aircraft.
and ending at the completion of a precise 180° of turn in a
wings-level, nose-high attitude at the minimum controllable Most AFM/POH now include turbulent air penetration
airspeed. In this flight maneuver, the aircraft is in a steep information, which help today’s pilots safely fly aircraft
climbing turn and almost stalls to gain altitude while changing capable of a wide range of speeds and altitudes. It is important
direction. A lazy eight derives its name from the manner in for the pilot to remember that the maximum “never-exceed”
which the extended longitudinal axis of the aircraft is made placard dive speeds are determined for smooth air only. High
to trace a flight pattern in the form of a figure “8” lying on speed dives or acrobatics involving speed above the known
its side. It would be difficult to make a definite statement maneuvering speed should never be practiced in rough or
concerning load factors in these maneuvers as both involve turbulent air.
smooth, shallow dives and pull ups. The load factors incurred
depend directly on the speed of the dives and the abruptness Vg Diagram
of the pull ups during these maneuvers. The flight operating strength of an aircraft is presented
on a graph whose vertical scale is based on load factor.
Generally, the better the maneuver is performed, the less [Figure 4-47] The diagram is called a Vg diagram—velocity
extreme the load factor induced. A chandelle or lazy eight in versus G loads or load factor. Each aircraft has its own Vg
which the pull-up produces a load factor greater than 2 Gs will diagram which is valid at a certain weight and altitude.
not result in as great a gain in altitude, and in low-powered
aircraft it may result in a net loss of altitude. The lines of maximum lift capability (curved lines) are the
first items of importance on the Vg diagram. The aircraft in
The smoothest pull up possible, with a moderate load factor, the Figure 4-47 is capable of developing no more than +1 G
delivers the greatest gain in altitude in a chandelle and results at 62 mph, the wing level stall speed of the aircraft. Since the
in a better overall performance in both chandelles and lazy maximum load factor varies with the square of the airspeed,
eights. The recommended entry speed for these maneuvers the maximum positive lift capability of this aircraft is 2 G at
is generally near the manufacturer’s design maneuvering 92 mph, 3 G at 112 mph, 4.4 G at 137 mph, and so forth. Any
speed which allows maximum development of load factors load factor above this line is unavailable aerodynamically
without exceeding the load limits. (i.e., the aircraft cannot fly above the line of maximum lift
capability because it stalls). The same situation exists for
Rough Air negative lift flight with the exception that the speed necessary
All standard certificated aircraft are designed to withstand to produce a given negative load factor is higher than that to
loads imposed by gusts of considerable intensity. Gust load produce the same positive load factor.
factors increase with increasing airspeed, and the strength
used for design purposes usually corresponds to the highest If the aircraft is flown at a positive load factor greater than
level flight speed. In extremely rough air, as in thunderstorms the positive limit load factor of 4.4, structural damage
or frontal conditions, it is wise to reduce the speed to the is possible. When the aircraft is operated in this region,
design maneuvering speed. Regardless of the speed held, objectionable permanent deformation of the primary structure
there may be gusts that can produce loads which exceed the may take place and a high rate of fatigue damage is incurred.
load limits. Operation above the limit load factor must be avoided in
normal operation.
Each specific aircraft is designed with a specific G loading
that can be imposed on the aircraft without causing structural There are two other points of importance on the Vg diagram.
damage. There are two types of load factors factored into One point is the intersection of the positive limit load factor
aircraft design, limit load and ultimate load. The limit load and the line of maximum positive lift capability. The airspeed
is a force applied to an aircraft that causes a bending of the at this point is the minimum airspeed at which the limit load
aircraft structure that does not return to the original shape. can be developed aerodynamically. Any airspeed greater than
The ultimate load is the load factor applied to the aircraft this provides a positive lift capability sufficient to damage
beyond the limit load and at which point the aircraft material the aircraft. Conversely, any airspeed less than this does not
experiences structural failure (breakage). Load factors lower provide positive lift capability sufficient to cause damage
than the limit load can be sustained without compromising from excessive flight loads. The usual term given to this speed
the integrity of the aircraft structure. is “maneuvering speed,” since consideration of subsonic

4-32

7 Structural damage
6
5 Maneuvering speed
4
Load factor 3 Accelerated stall operating range Caution range Never exceed speed
2 Normal Structural failure

Normal stall speed Level flight at 1 G
1
0 Structural Damage
–1
–2
–3

20 40 60 80 100 120 140 160 180 200 220 240
Indicated airspeed (mph)

Figure 4-47. Typical Vg diagram. maximum lift capability. The aircraft must be operated
within this “envelope” to prevent structural damage and
aerodynamics would predict minimum usable turn radius or ensure the anticipated service lift of the aircraft is obtained.
maneuverability to occur at this condition. The maneuver The pilot must appreciate the Vg diagram as describing the
speed is a valuable reference point, since an aircraft operating allowable combination of airspeeds and load factors for
below this point cannot produce a damaging positive flight safe operation. Any maneuver, gust, or gust plus maneuver
load. Any combination of maneuver and gust cannot create outside the structural envelope can cause structural damage
damage due to excess airload when the aircraft is below the and effectively shorten the service life of the aircraft.
maneuver speed.
Rate of Turn
The other point of importance on the Vg diagram is the The rate of turn (ROT) is the number of degrees (expressed in
intersection of the negative limit load factor and line of degrees per second) of heading change that an aircraft makes.
maximum negative lift capability. Any airspeed greater than The ROT can be determined by taking the constant of 1,091,
this provides a negative lift capability sufficient to damage multiplying it by the tangent of any bank angle and dividing
the aircraft; any airspeed less than this does not provide that product by a given airspeed in knots as illustrated in
negative lift capability sufficient to damage the aircraft from Figure 4-48. If the airspeed is increased and the ROT desired
excessive flight loads. is to be constant, the angle of bank must be increased,
otherwise, the ROT decreases. Likewise, if the airspeed is
The limit airspeed (or redline speed) is a design reference held constant, an aircraft’s ROT increases if the bank angle
point for the aircraft—this aircraft is limited to 225 mph. is increased. The formula in Figures 4-48 through 4-50
If flight is attempted beyond the limit airspeed, structural depicts the relationship between bank angle and airspeed as
damage or structural failure may result from a variety of they affect the ROT.
phenomena.
NOTE: All airspeed discussed in this section is true airspeed
The aircraft in flight is limited to a regime of airspeeds (TAS).
and Gs which do not exceed the limit (or redline) speed,
do not exceed the limit load factor, and cannot exceed the

4-33

Rate of turn for a given airspeed (knots, TAS)
and bank angle

ROT = 1,091 x tangent of the bank angle conclusions can be made. Knowing the ROT is a given
airspeed (in knots) number of degrees of change per second, the number of
seconds it takes to travel 360° (a circle) can be determined
Example The rate of turn for an aircraft in a by simple division. For example, if moving at 120 knots with
coordinated turn of 30° and traveling at a 30° bank angle, the ROT is 5.25° per second and it takes
120 knots would have a ROT as follows. 68.6 seconds (360° divided by 5.25 = 68.6 seconds) to make
a complete circle. Likewise, if flying at 240 knots TAS and
ROT = 1,091 x tangent of 30° using a 30° angle of bank, the ROT is only about 2.63° per
120 knots second and it takes about 137 seconds to complete a 360°
circle. Looking at the formula, any increase in airspeed is
ROT = 1,091 x 0.5773 (tangent of 30°) directly proportional to the time the aircraft takes to travel
120 knots an arc.

ROT = 5.25 degrees per second

Figure 4-48. Rate of turn for a given airspeed (knots, TAS) and So why is this important to understand? Once the ROT is
understood, a pilot can determine the distance required to make
bank angle. Increase in the speed that particular turn which is explained in radius of turn.

Example Suppose we were to increase the speed to 240 Radius of Turn
knots, what is the rate of turn? Using the same The radius of turn is directly linked to the ROT, which
formula from above we see that: explained earlier is a function of both bank angle and
airspeed. If the bank angle is held constant and the airspeed
ROT = 1,091 x tangent of 30° is increased, the radius of the turn changes (increases). A
240 knots higher airspeed causes the aircraft to travel through a longer
arc due to a greater speed. An aircraft traveling at 120 knots
ROT = 2.62 degrees per second is able to turn a 360° circle in a tighter radius than an aircraft
traveling at 240 knots. In order to compensate for the increase
An increase in speed causes a decrease in in airspeed, the bank angle would need to be increased.
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Example Suppose we wanted to know what bank angle The radius of turn (R) can be computed using a simple
would give us a rate of turn of 5.25° per second
at 240 knots. A slight rearrangement of the formula formula. The radius of turn is equal to the velocity squared
would indicate it will take a 49° angle of bank to (V2) divided by 11.26 times the tangent of the bank angle.
achieve the same ROT used at the lower airspeed
of 120 knots. R= V2
11.26 x tangent of bank angle
1,091 x tangent of X
ROT (5.25) = 240 knots Using the examples provided in Figures 4-48 through 4-50, the
turn radius for each of the two speeds can be computed.
240 x 5.25 = 1,091 x tangent of X Note that if the speed is doubled, the radius is squared.
[Figures 4-51 and 4-52]
240 x 5.25 = tangent of X
1,091

1.1549 = tangent of X

49° = X R = V2
11.26 x tangent of bank angle
Figure 4-50. To achieve the same rate of turn of an aircraft traveling 120 knots
at 120 knots, an increase of bank angle is required.
R = 11.26 x 1202 of 30°
Airspeed significantly effects an aircraft’s ROT. If airspeed is tangent
increased, the ROT is reduced if using the same angle of bank
used at the lower speed. Therefore, if airspeed is increased R = 14,400
as illustrated in Figure 4-49, it can be inferred that the angle 11.26 x 0.5773
of bank must be increased in order to achieve the same ROT
achieved in Figure 4-50. R = 2,215 feet

The radius of a turn required by an aircraft traveling at 120 knots
and using a bank angle of 30° is 2,215 feet.

Figure 4-51. Radius at 120 knots with bank angle of 30°.

What does this mean on a practicable side? If a given
airspeed and bank angle produces a specific ROT, additional

4-34

240 knots R = V2 thumb” such as: “If I have three passengers, I can load only
11.26 x tangent of bank angle 100 gallons of fuel; four passengers, 70 gallons.”

R = 11.26 x 2402 of 30° Weight and balance computations should be part of every
tangent preflight briefing. Never assume three passengers are always
of equal weight. Instead, do a full computation of all items
R = 57,600 to be loaded on the aircraft, including baggage, as well as
11.26 x 0.57735 the pilot and passenger. It is recommended that all bags be
weighed to make a precise computation of how the aircraft
R = 8,861 feet CG is positioned.
(four times the radius at 120 knots)
The importance of the CG was stressed in the discussion
The radius of a turn required by an aircraft traveling at 240 knots of stability, controllability, and performance. Unequal load
using the same bank angle in Figure 4-51 is 8,861 feet. Speed is a distribution causes accidents. A competent pilot understands
major factor in a turn. and respects the effects of CG on an aircraft.

Figure 4-52. Radius at 240 knots. Weight and balance are critical components in the utilization
of an aircraft to its fullest potential. The pilot must know
Another way to determine the radius of turn is speed in how much fuel can be loaded onto the aircraft without
using feet per second (fps), π (3.1415) and the ROT. Using violating CG limits, as well as weight limits to conduct
the example on page 4-34 in the upper right column, it long or short flights with or without a full complement of
was determined that an aircraft with a ROT of 5.25 degrees allowable passengers. For example, an aircraft has four seats
per second required 68.6 seconds to make a complete and can carry 60 gallons of fuel. How many passengers can
circle. An aircraft’s speed (in knots) can be converted to fps the aircraft safely carry? Can all those seats be occupied at
by multiplying it by a constant of 1.69. Therefore, an aircraft all times with the varying fuel loads? Four people who each
traveling at 120 knots (TAS) travels at 202.8 fps. Knowing the weigh 150 pounds leads to a different weight and balance
speed in fps (202.8) multiplied by the time an aircraft takes computation than four people who each weigh 200 pounds.
to complete a circle (68.6 seconds) can determine the size of The second scenario loads an additional 200 pounds onto the
the circle; 202.8 times 68.6 equals 13,912 feet. Dividing by aircraft and is equal to about 30 gallons of fuel.
π yields a diameter of 4,428 feet, which when divided by 2
equals a radius of 2,214 feet [Figure 4-53], a foot within that The additional weight may or may not place the CG outside
determined through use of the formula in Figure 4-51. of the CG envelope, but the maximum gross weight could
be exceeded. The excess weight can overstress the aircraft
r = speed (fps) x 360 and degrade the performance.
ROT
Aircraft are certificated for weight and balance for two
Pi (π) principal reasons:
2
1. The effect of the weight on the aircraft’s primary
202.8 x 68.6 structure and its performance characteristics

r= π 2. The effect of the location of this weight on flight
2 characteristics, particularly in stall and spin recovery
and stability
13,912
Aircraft, such as balloons and weight-shift control, do not
r= π require weight and balance computations because the load
2 is suspended below the lifting mechanism. The CG range
in these types of aircraft is such that it is difficult to exceed
r= 4,428 = 2,214 feet loading limits. For example, the rear seat position and fuel
2 of a weight-shift control aircraft are as close as possible to
the hang point with the aircraft in a suspended attitude. Thus,
Figure 4-53. Another formula that can be used for radius. load variations have little effect on the CG. This also holds
true for the balloon basket or gondola. While it is difficult
In Figure 4-54, the pilot enters a canyon and decides to turn
180° to exit. The pilot uses a 30° bank angle in his turn.

Weight and Balance

The aircraft’s weight and balance data is important
information for a pilot that must be frequently reevaluated.
Although the aircraft was weighed during the certification
process, this data is not valid indefinitely. Equipment changes
or modifications affect the weight and balance data. Too often
pilots reduce the aircraft weight and balance into a “rule of

4-35