Principles of Flight Complete
Principles of Flight Complete
Principles of Flight Complete
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ii
Printed in Germany
PREFACE_______________________
As the world moves toward a single standard for international pilot licensing, many nations have
adopted the syllabi and regulations of the Joint Aviation Requirements-Flight Crew Licensing"
(JAR-FCL), the licensing agency of the Joint Aviation Authorities (JAA).
Though training and licensing requirements of individual national aviation authorities are similar in
content and scope to the JAA curriculum, individuals who wish to train for JAA licences need
access to study materials which have been specifically designed to meet the requirements of the
JAA licensing system. The volumes in this series aim to cover the subject matter tested in the
JAA ATPL ground examinations as set forth in the ATPL training syllabus, contained in the JAA
publication, JAR-FCL 1 (Aeroplanes).
The JAA regulations specify that all those who wish to obtain a JAA ATPL must study with a
flying training organisation (FTO) which has been granted approval by a JAA-authorised national
aviation authority to deliver JAA ATPL training. While the formal responsibility to prepare you for
both the skill tests and the ground examinations lies with the FTO, these Jeppesen manuals will
provide a comprehensive and necessary background for your formal training.
Jeppesen is acknowledged as the world's leading supplier of flight information services, and
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experience as an acknowledged expert in the development and publication of pilot training
materials.
We at Jeppesen wish you success in your flying and training, and we are confident that your
study of these manuals will be of great value in preparing for the JAA ATPL ground examinations.
The next three pages contain a list and content description of all the volumes in the ATPL series.
iii
ATPL Series
Meteorology (JAR Ref 050)
The Atmosphere
Wind
Thermodynamics
Clouds and Fog
Precipitation
Hydraulics
Pneumatic Systems
Air Conditioning System
Pressurisation
De-Ice / Anti-Ice Systems
Fuel Systems
Engine Systems
Auxiliary Power Unit (APU)
iv
Generator / Alternator
Semiconductors
Circuits
Boundary Layer
High Speed Flight
Stability
Flying Controls
Adverse Weather Conditions
Propellers
Operating Limitations
Flight Mechanics
Meteorological Messages
Point of Equal Time
Point of Safe Return
Medium Range Jet Transport
Planning
vi
Table of Contents
CHAPTER 1
Laws and Definitions
Introduction .................................................................................................................................................. 1-1
SI Units ........................................................................................................................................................ 1-1
Derived Units ............................................................................................................................................... 1-1
Airspeeds ..................................................................................................................................................... 1-5
Newtons Laws of Motion ............................................................................................................................. 1-5
CHAPTER 2
The Flight Environment
Introduction .................................................................................................................................................. 2-1
The Atmosphere .......................................................................................................................................... 2-1
The Universal Gas Law................................................................................................................................ 2-1
The Effect of Pressure on Density ............................................................................................................... 2-1
The Effect of Temperature on Density ......................................................................................................... 2-2
The Effect of Altitude on Density.................................................................................................................. 2-2
The Effect of Humidity on Density................................................................................................................ 2-2
The International Standard Atmosphere ...................................................................................................... 2-2
CHAPTER 3
Aircraft Components and Terminology
Wing Position Terminology .......................................................................................................................... 3-1
Wing Planform Terminology......................................................................................................................... 3-2
Wing Section Terminology ........................................................................................................................... 3-6
Aerofoil Cross-sectional Shapes .................................................................................................................. 3-7
CHAPTER 4
Lift
Introduction .................................................................................................................................................. 4-1
Airflow .......................................................................................................................................................... 4-1
Equation of Continuity .................................................................................................................................. 4-3
Bernoulli's Theorem ..................................................................................................................................... 4-4
Angle of Attack............................................................................................................................................. 4-6
Two-Dimensional Airflow about an Aerofoil.................................................................................................. 4-8
Effect of Angle of Attack on the Airflow about an Aerofoil Section ............................................................... 4-9
Chordwise Pressure Distributions about an Aerofoil Section ..................................................................... 4-11
The Centre of Pressure.............................................................................................................................. 4-14
Aerodynamic Centre .................................................................................................................................. 4-16
Lift Formula ................................................................................................................................................ 4-17
Variation of Coefficient of Lift with Angle of Attack..................................................................................... 4-17
Three-Dimensional Airflow About an Aerofoil............................................................................................. 4-18
Wing Shape and its Effect on Lift ............................................................................................................... 4-21
vii
Table of Contents
CHAPTER 5
Drag
Introduction .................................................................................................................................................. 5-1
Form Drag .................................................................................................................................................... 5-2
Boundary Layer............................................................................................................................................ 5-4
Skin Friction Drag......................................................................................................................................... 5-7
Factors Affecting Skin Friction Drag............................................................................................................. 5-7
Interference Drag ......................................................................................................................................... 5-8
Induced Drag ............................................................................................................................................... 5-9
Factors Affecting Induced Drag.................................................................................................................. 5-10
Methods to Reduce Induced Drag.............................................................................................................. 5-14
Drag Formula ............................................................................................................................................. 5-15
Drag Curves ............................................................................................................................................... 5-16
Lift/Drag Ratio ............................................................................................................................................ 5-18
Drag Ploar .................................................................................................................................................. 5-21
CHAPTER 6
Flying Controls
Introduction .................................................................................................................................................. 6-1
Elevators ...................................................................................................................................................... 6-2
The Stabilator............................................................................................................................................... 6-2
The Rudder .................................................................................................................................................. 6-3
Ailerons ........................................................................................................................................................ 6-4
Adverse Aileron Yaw.................................................................................................................................... 6-5
Combined Primary Control Surfaces............................................................................................................ 6-6
Aerodynamic Balance .................................................................................................................................. 6-9
Tabs ........................................................................................................................................................... 6-12
Mass Balance............................................................................................................................................. 6-14
Powered Flying Controls ............................................................................................................................ 6-14
Powered Flying Control System ................................................................................................................. 6-16
Layout and Requirements .......................................................................................................................... 6-16
Control Input Systems................................................................................................................................ 6-16
The Power Control Unit (PCU) ................................................................................................................... 6-17
Artificial Feel Systems................................................................................................................................ 6-19
Trimming Control Systems ......................................................................................................................... 6-22
Principle of a Trim Tab ............................................................................................................................... 6-22
Trimming of Powered Flying Controls ........................................................................................................ 6-25
Spoilers ...................................................................................................................................................... 6-30
CHAPTER 7
Lift Augmentation
Basic Lift Augmentation System................................................................................................................... 7-1
Trailing Edge Flaps ...................................................................................................................................... 7-2
Types of Trailing Edge Flaps ....................................................................................................................... 7-3
Comparison of Different Types of Trailing Edge Flap................................................................................... 7-5
The Effect of Trailing Edge Flaps on the Stalling Angle ............................................................................... 7-6
The Effect of Trailing Edge Flaps on the Stall Speed................................................................................... 7-6
Operation of Trailing Edge Flaps.................................................................................................................. 7-7
Use of Trailing Edge Flaps for Take-off........................................................................................................ 7-8
The Effects of Raising the Flaps in Flight..................................................................................................... 7-9
The Use of Trailing Edge Flaps During the Approach and Landing ............................................................. 7-9
High Lift Devices on Transport Category Aircraft ....................................................................................... 7-10
Leading Edge High Lift Devices ................................................................................................................. 7-11
The Effect of Leading Edge Flaps on the Stalling Angle ............................................................................ 7-16
The Operation of High Lift Devices on Transport Category Aircraft ........................................................... 7-17
Protection of High Lift Devices on Transport Category Aircraft .................................................................. 7-19
viii
Table of Contents
CHAPTER 8
Stalling
Introduction .................................................................................................................................................. 8-1
Separated Airflow......................................................................................................................................... 8-1
The Stalling Angle of Attack ......................................................................................................................... 8-4
Definition of the JAR/FAR Stalling Speed (VS) ............................................................................................ 8-5
The Relationship between Stalling Speed and Lift....................................................................................... 8-5
Recognition of the Stall at Low Airspeeds.................................................................................................... 8-8
Stall Warning in Light Aircraft....................................................................................................................... 8-8
Recovery from a Normal Stall ...................................................................................................................... 8-9
The Effect of Wing Section on the Stall........................................................................................................ 8-9
The Effect of Wing Planform on the Stall ................................................................................................... 8-10
The Cause of Pitch-up on Sweptback Wings at the Stall ........................................................................... 8-13
Devices to Alleviate Wing Tip Stalling ........................................................................................................ 8-14
Stall Sensing in Transport Category Aircraft .............................................................................................. 8-16
The Stall Warning System on Transport Category Aircraft......................................................................... 8-17
The Stall Prevention System on Transport Category Aircraft..................................................................... 8-18
Super Stall (Deep Stall).............................................................................................................................. 8-18
Accelerated or G-Stall .............................................................................................................................. 8-19
Spinning ..................................................................................................................................................... 8-20
Recovery from a Spin................................................................................................................................. 8-24
CHAPTER 9
Forces Acting On An Aeroplane
Forces in Steady Level Flight....................................................................................................................... 9-1
Lift/Weight and Thrust/Drag Couples ........................................................................................................... 9-2
The Contribution of the Tailplane ................................................................................................................. 9-5
Straight Steady Climb .................................................................................................................................. 9-6
Forces in a Straight Steady Climb................................................................................................................ 9-7
Forces Parallel to the Flight Path ................................................................................................................. 9-7
Forces Perpendicular to the Flight Path ....................................................................................................... 9-8
Load Factor in the Climb .............................................................................................................................. 9-8
Steady Descending Flight ............................................................................................................................ 9-9
The Glide ................................................................................................................................................... 9-10
The Effect of Weight on Glide Performance............................................................................................... 9-11
Factors Affecting Glide Performance ......................................................................................................... 9-12
Steady Co-ordinated Turn.......................................................................................................................... 9-15
Vertical Forces in the Turn ......................................................................................................................... 9-15
Load Factor in the Turn.............................................................................................................................. 9-16
The Effect of Turning on Stall Speed ......................................................................................................... 9-16
Lateral Forces in the Turn .......................................................................................................................... 9-17
The Relationship between Angle of Bank, TAS and Turn Radius .............................................................. 9-18
Rate of Turn ............................................................................................................................................... 9-20
Balancing the Turn..................................................................................................................................... 9-21
Aircraft Response During a Level Banked Turn ......................................................................................... 9-23
Aircraft Response During Climbing and Descending Turns ....................................................................... 9-24
ix
Table of Contents
CHAPTER 10
Stability
Introduction to Stability............................................................................................................................... 10-1
Controllability.............................................................................................................................................. 10-1
Static Stability............................................................................................................................................. 10-2
The Degree of Stability............................................................................................................................... 10-2
Dynamic Stability........................................................................................................................................ 10-3
Static Longitudinal Stability ........................................................................................................................ 10-3
Mathematical Representation of Static Longitudinal Stability..................................................................... 10-4
Factors Affecting Static Longitudinal Stability ............................................................................................ 10-6
Graphical Representation of Static Longitudinal Stability........................................................................... 10-9
The Effect of Elevator Deflection on Pitching Moments ........................................................................... 10-11
Control Force Stability.............................................................................................................................. 10-12
Manoeuvring Stability............................................................................................................................... 10-14
Tailoring The Control Forces.................................................................................................................... 10-15
Dynamic Longitudinal Stability ................................................................................................................. 10-16
Pilot Induced Oscillations ......................................................................................................................... 10-17
Directional Static Stability......................................................................................................................... 10-17
Graphical Representation of Static Directional Stability ........................................................................... 10-18
The Factors Affecting Static Directional Stability...................................................................................... 10-18
Lateral Static Stability............................................................................................................................... 10-21
Graphical Representation of Static Lateral Stability ................................................................................. 10-25
Factors Affecting Static Lateral Stability................................................................................................... 10-26
Interaction Between Lateral and Directional Static Stability ..................................................................... 10-26
Dutch Roll ................................................................................................................................................ 10-27
Yaw Damper Systems.............................................................................................................................. 10-28
Speed Stability ......................................................................................................................................... 10-30
CHAPTER 11
Ground Effect
Introduction ................................................................................................................................................ 11-1
The Characteristics of Ground Effect ......................................................................................................... 11-1
The Influence of Ground Effect on Landing................................................................................................ 11-4
The Influence of Ground Effect on Take-Off .............................................................................................. 11-4
The Influence of Ground Effect on Trailing Edge Flaps.............................................................................. 11-4
CHAPTER 12
Propellers
Introduction ................................................................................................................................................ 12-1
Propeller Terminology ................................................................................................................................ 12-1
Factors Affecting the Blade Angle of Attack ............................................................................................... 12-3
Factors Affecting the Blade Thrust Distribution .......................................................................................... 12-6
Forces Acting on a Blade Section .............................................................................................................. 12-6
Centrifugal Turning Moment (CTM)............................................................................................................ 12-7
Aerodynamic Turning Moment (ATM) ........................................................................................................ 12-8
Centrifugal Forces...................................................................................................................................... 12-8
Thrust Bending Forces............................................................................................................................... 12-9
Torque Bending Forces.............................................................................................................................. 12-9
Propeller Efficiency .................................................................................................................................... 12-9
Forces Acting on a Windmilling Blade Section ......................................................................................... 12-11
Propeller Pitch.......................................................................................................................................... 12-13
Disadvantages of Fixed Pitch Propellers.................................................................................................. 12-15
The Variable and Constant Speed Propeller............................................................................................ 12-16
Power Absorption..................................................................................................................................... 12-17
Propeller Solidity ...................................................................................................................................... 12-17
Propeller Effects on Take-off.................................................................................................................... 12-17
Propeller Icing .......................................................................................................................................... 12-21
x
Principles Of Flight (Rev Q407)
Table of Contents
CHAPTER 13
Asymmetric Flight
Introduction ................................................................................................................................................ 13-1
Single Engine Performance ....................................................................................................................... 13-1
Yawing Moments ....................................................................................................................................... 13-3
Asymmetric Blade Effect ............................................................................................................................ 13-6
The Effect of Bank ..................................................................................................................................... 13-9
The Effect of Weight ................................................................................................................................ 13-10
Rolling Moments ...................................................................................................................................... 13-10
Minimum Airspeeds During Asymmetric Flight......................................................................................... 13-11
Turning Flight ........................................................................................................................................... 13-12
Recognition of a Failed Engine .................................................................................................................13-12
CHAPTER 14
High Speed Flight
Introduction ................................................................................................................................................ 14-1
The Speed of Sound .................................................................................................................................. 14-1
Mach Number ............................................................................................................................................ 14-2
Relationship between CAS, TAS and Mach number.................................................................................. 14-3
Pressure Waves from a Moving Source..................................................................................................... 14-4
Nature of Compressibility ........................................................................................................................... 14-5
Free Stream Mach number ........................................................................................................................ 14-6
Local Mach number ................................................................................................................................... 14-6
Critical Mach number ................................................................................................................................. 14-6
Flight Speed Classifications ....................................................................................................................... 14-7
Comparison of Subsonic and Supersonic Flow Patterns ........................................................................... 14-7
The Development of Shock Waves ............................................................................................................ 14-8
Shock Stall ............................................................................................................................................... 14-11
The Effect of Altitude on the Shock Stall .................................................................................................. 14-14
Buffet Onset Boundary Chart ................................................................................................................... 14-15
Methods of Reducing or Delaying the Transonic Drag Rise..................................................................... 14-17
Transonic Area Rule ................................................................................................................................ 14-18
Supercritical Wings .................................................................................................................................. 14-19
Control Problems in Transonic Flight ....................................................................................................... 14-19
Vortex Generators.................................................................................................................................... 14-21
The Effect of Transonic Flight on Aircraft Trim and Stability .................................................................... 14-22
Mach Trim ................................................................................................................................................ 14-23
Supersonic Flight ..................................................................................................................................... 14-23
Oblique Shock Wave................................................................................................................................ 14-24
Mach Cone............................................................................................................................................... 14-24
Expansion Wave ...................................................................................................................................... 14-25
Summary of Supersonic Wave Characteristics ........................................................................................ 14-25
xi
Table of Contents
CHAPTER 15
Flight in Adverse Weather Conditions
Introduction ................................................................................................................................................ 15-1
Ice and Frost .............................................................................................................................................. 15-1
The Effect of Ice, Frost, and Snow on the Aircrafts Performance.............................................................. 15-1
The Effects of Contamination on Maximum Wing Lift Capability ................................................................ 15-2
The Effects of Contamination on Flaps and Slats ...................................................................................... 15-4
The Effect of Contamination on Take-off Performance .............................................................................. 15-6
The Effect of Contamination on Aircraft Landing Performance .................................................................. 15-8
Tail Icing................................................................................................................................................... 15-10
Windshear ................................................................................................................................................ 15-11
Vertical Gusts........................................................................................................................................... 15-11
Horizontal Gusts....................................................................................................................................... 15-12
Downdraughts and Updraughts................................................................................................................ 15-13
Indications of a Windshear Encounter...................................................................................................... 15-13
General Recovery from a Windshear Encounter...................................................................................... 15-14
Recovery from a Windshear Encounter During the Take-off, Approach, and Landing ............................. 15-14
Microbursts .............................................................................................................................................. 15-15
The Effect of a Microburst Encounter During the Approach ..................................................................... 15-15
The Effect of a Microburst on Take-off ..................................................................................................... 15-16
Airborne Windshear Detection Systems................................................................................................... 15-17
The Effect of Heavy Rain on Aircraft Performance................................................................................... 15-17
CHAPTER 16
Operating Limitations
Introduction ................................................................................................................................................ 16-1
Structural Strength ..................................................................................................................................... 16-1
Load Factor ................................................................................................................................................ 16-1
The Flight Operating Envelope................................................................................................................... 16-2
Design Limitations...................................................................................................................................... 16-3
Operating Limitations ................................................................................................................................. 16-4
Gust Load Factor ....................................................................................................................................... 16-5
Factors Affecting Gust Load Factor............................................................................................................ 16-6
Aeroelastic Distortion (Aileron Reversal).................................................................................................... 16-9
Emergency Descents ............................................................................................................................... 16-11
xii
INTRODUCTION
Before studying aerodynamics, it is essential to have a thorough grounding in basic mechanics
and any related units of measurement. In aeronautics all measurements world-wide are based on
the International System (SI) of units, but in practice some anomalies exist. For example, altitude
is quoted in terms of feet (ft), and airspeed is quoted in nautical miles per hour (kt).
SI UNITS
The fundamental SI units are those of:
Mass
Length
Time
DERIVED UNITS
The following quantities and their related units of measurement are extensively used in
aerodynamics:
Area
Volume
Velocity
Acceleration
Momentum
Force
1-1
Chapter 1
The unit of force is the Newton (N). One Newton is the force
required to give a mass of one kilogram an acceleration of one
metre per second per second.
Weight
Work
Power
The rate of doing work; measured in units of work per unit time;
measured in Watts (W), where 1 watt = 1 J/s or 1 Nm/s.
Power = Force x Velocity
Energy
1-2
Pressure
Chapter 1
FIG 1.1
FIG 1.2
1-3
Chapter 1
Total Pressure (PT) The sum of both the static and dynamic
pressures; This is a very important term in aerodynamic
formulae, as it is used in the calculation of lift, drag, and
indicated airspeeds. (These terms are explained later.)
Total Pressure = Static Pressure + Dynamic Pressure
In aerodynamics, this is also referred to as Pitot Pressure.
Density
Temperature (T)
Viscosity
Wing Loading
The total aircraft weight supported per unit area of the wing;
measured in Newtons per square metre (N/m2).
Wing Loading = AUW/wing area
1-4
Chapter 1
AIRSPEEDS
Indicated
Airspeed (IAS)
The indicated airspeed of an aircraft as shown on its pitotstatic airspeed indicator (ASI). This provides vital airspeed
information, e.g. stalling and structural limitation airspeeds, to
the flight-crew. It is calibrated to reflect standard atmospheric
adiabatic compressible flow at sea level and is uncorrected
for airspeed system errors.
Calibrated
Airspeed (CAS)
Equivalent
Airspeed (EAS)
True
Airspeed (TAS)
Mach No.
Newtons 2nd Law. States that a body at rest or in uniform motion will, when
acted on by an external force, accelerate in the direction of
the force. The magnitude of the acceleration for any given
mass is directly proportional to the size of the force applied
(i.e. when a force of 1 N is applied to a mass of 1 kg, it will
accelerate at 1 m/s2).
Force = Mass x Acceleration
Newtons 3rd Law.
1-5
Chapter 1
1-6
INTRODUCTION
In order to study the principles of flight it is first necessary to understand the medium in which
flight takes place.
THE ATMOSPHERE
The atmosphere is a region of air surrounding the Earth up to a height of approximately 500 miles
(900 km). Air is a mixture of gases, primarily oxygen (21% by volume) and nitrogen (78% by
volume). Up to a height of 6 miles (11 km), water vapour also occurs in varying quantities. The
actual amount of water vapour, in a given mass of air, depends on the temperature and whether
the air has recently passed over a large area of water. Generally, the higher the temperature, the
greater the amount of water vapour a given mass of air can hold. Air has weight and is also
compressible. Its pressure, density, and temperature all decrease with increasing altitude. An
aircraft performs work on the air to sustain flight, and any change in pressure, density, and
temperature will affect the amount of energy that the aircraft can extract from the air.
P = constant
2-1
Chapter 2
2-2
DENSITY
3
KG/M
PRESSURE
MILLIBARS
TEMPERATURE
C
52,496
16,000
0.166
104
-56.6
45,934
14,000
0.288
142
-56.5
39,372
12,000
0.312
194
-56.5
32,810
10,000
0.414
265
-50
26,248
8,000
0.526
357
-37
19,686
6,000
0.660
472
-24
13,124
4,000
0.819
612
-11
6,562
2,000
1.007
795
1.225
1013.25
15
LOW WING
HIGH WING
MID WING
FIG. 3.1
3-1
Chapter 3
The wings may be inclined above or below the horizontal. Dihedral is the term for wing inclination
above the horizontal, and anhedral is the term for inclination below the horizontal (Fig. 3.2).
DIHEDRAL
WINGSPAN
ANHEDRAL
WINGSPAN
FIG. 3.2
Gross Wing Area (S) The plan view area of the wing including the portion of the
wing normally cut out to accommodate the fuselage (Fig. 3.3).
FIG 3.3
3-2
Chapter 3
Net Wing Area The area of the wing excluding the fuselage portion (Fig. 3.4).
FIG 3.4
Wing Span (B) The straight-line distance between wing tips (Fig. 3.5).
FIG 3.5
Average Chord (CAV) The Mean chord (Fig. 3.5). The product of the span and
average chord gives the gross wing area (i.e. B x CAV = S).
3-3
Chapter 3
Aspect Ratio (AR) The ratio of wing span to average chord. Long narrow wings
have a high aspect ratio, whilst short stubby wings have a low aspect ratio (Fig. 3.6).
FIG 3.6
Aspect Ratio =
(Wing Span) 2
Wing Span
Gross Wing Area
or
or
Gross Wing Area
Average Chord
(Average Chord) 2
Taper Ratio (TR) The ratio of tip chord (Ct) to root chord (Cr) (Fig. 3.7).
FIG 3.7
3-4
Chapter 3
The Angle of Sweepback The angle between the line of 25% chord and a
perpendicular to the root chord (Fig. 3.8).
FIG. 3.8
Mean Aerodynamic Chord (MAC) The chord drawn through the centroid (centre
of area) of the halfspan area. Note that the MAC and CAV are not the same (Fig. 3.9).
FIG. 3.9
Aspect ratio, taper ratio, and sweepback are some of the main factors that determine the
aerodynamic characteristics of a wing.
3-5
Chapter 3
FIG. 3.10
The Chord
Maximum Camber
Maximum Thickness
3-6
Chapter 3
FIG. 3.11
The above are both examples of asymmetrical aerofoils, with the upper surface more curved than
the lower surface. When the mean camber line coincides with the chord line, the wing camber is
reduced to zero and the aerofoil is symmetrical . A symmetrical aerofoil is shown below
(Fig. 3.12).
FIG. 3.12
3-7
Chapter 3
3-8
INTRODUCTION
As air flows around an aerofoil the pressure differential set up over the upper and lower surfaces
produces a force. This force acts perpendicular to the relative airflow and is known as lift. In
steady level flight, lift exactly balances the aircraft's weight. For a given airspeed, a lower weight
requires less lift.
AIRFLOW
To understand fully how the aerodynamic forces of lift and drag act on an aircraft, it is necessary
to study the effect of airflow. In principle it does not matter whether an aircraft is moving through
the air, or whether air is flowing over a stationary aircraft, since the result is the same. Airflow can
be either streamline or turbulent in nature.
Streamline flow exists when succeeding molecules follow a steady path, with the molecules
flowing in an orderly pattern along streamlines around an object (Fig. 4.1).
FIG 4.1
At any given point in the streamline, the molecules experience the same velocities and pressures
as the preceding molecules, but the values may alter from point to point along the streamline.
Widely spaced streamlines indicate a reduction in velocity, whereas a narrow spacing between
the streamlines indicates an increase in velocity. If the streamlines flow without mixing, the flow is
known as laminar. Laminar flow is desirable in most phases of flight, and produces the ideal flow
pattern around an aircraft. (Fig. 4.2).
FIG 4.2
Principles Of Flight (Rev Q407)
4-1
Chapter 4
Lift
If a sudden change in the direction of the airflow occurs, the streamline flow breaks down and
becomes turbulent flow.
Turbulent Flow occurs when the succeeding molecules can no longer follow a streamlined flow
pattern and instead travel along a path different than the preceding molecules (Fig. 4.3).
FIG. 4.3
Turbulent flow is also called unsteady or eddying flow and results in wasted energy. This is
undesirable in most phases of flight (Fig. 4.4).
FIG. 4.4
Free Stream Airflow (FSA) is airflow that is far enough away from an aircraft that the aircraft
does not disturb it.
4-2
Lift
Chapter 4
EQUATION OF CONTINUITY
The equation of continuity applies only to streamlined or steady flow. It states that, if a fluid flows
through a pipe its mass flow remains constant, since mass can neither be created nor destroyed.
If air flows through a pipe of varying cross-sectional area (venturi tube), the mass of air entering
the pipe in a given time equals the mass of air leaving the pipe in the same time (Fig. 4.5).
Station 1
Station 2
Station 3
1 A1 V1
2 A2 V
3 A3 V3
Fig 4.5
The mass airflow at any point in the pipe is the product of the density (), the cross-sectional area
(A), and the velocity (V).
Mass Airflow = AV
Mass Airflow is expressed in kg/s where:
= kg/m3
A = m
V = m/s
This equation applies equally to both subsonic and supersonic airflow, provided the flow remains
steady. At velocities less than 0.4 Mach, air is considered to be incompressible and inviscid
(ideal). Density, therefore, remains constant and can be deleted from the equation, such that:
Mass Airflow AV
4-3
Chapter 4
Lift
This shows that velocity is inversely proportional to the cross-sectional area, with any reduction in
area resulting in an increase in velocity and vice versa. This effect can be illustrated using
streamline flow patterns (stream tube), where converging streamlines indicate an increase in
velocity and vice versa (Fig. 4.6).
Speed Decreasing
Speed Increasing
V2
V3
V1
A1
A3
A2
FIG. 4.6
BERNOULLI'S THEOREM
Bernoulli's Theorem uses the principle of Conservation of Energy. It states that when a fluid flows
at a steady rate through a pipe, its total energy remains constant, since energy can neither be
created nor destroyed. At any point in a pipe, the total energy is a combination of:
Potential Energy
Pressure Energy
Kinetic Energy
When considering airflow at a given height, changes in potential energy are negligible, and can
be essentially ignored. Total energy therefore equals the sum of the pressure energy and kinetic
energy.
Pressure Energy + Kinetic Energy = Total Energy
In aerodynamics, it is the mass airflow per unit volume that is of most interest to us, so the
Conservation of Energy equation is better stated in terms of pressure. At any point in a pipe, the
total pressure is the sum of the static pressure and dynamic pressure measured in Pascals.
Static Pressure (PS) + Dynamic Pressure ( V) = Total Pressure (PT)
4-4
Lift
Chapter 4
To satisfy Bernoulli's theorem, this value must remain constant at all points along the pipe, such
that any rise in dynamic pressure is accompanied by a reduction in static pressure and vice
versa.
From the Equation of Continuity, if a steady stream of air flows through the restricted section of a
venturi, its velocity increases and vice versa. Any rise in velocity results in an increase in dynamic
pressure and a reduction in static pressure and vice versa, according to Bernoullis Theorem
(Fig. 4.7).
FIG 4.7
The airflow around an aerofoil section also resembles the flow through a venturi (Fig. 4.8).
INCREASED VELOCITY
REDUCED STATIC PRESSURE
1
1
2
2
REDUCED VELOCITY
INCREASED STATIC PRESSURE
FIG. 4.8
The flow over the upper surface is representative of a convergent section (1), whilst the flow over
the lower surface is representative of a divergent section (2). The static pressure likewise varies
and the resulting pressure differential produces lift.
4-5
Chapter 4
Lift
ANGLE OF ATTACK
The angle of attack () is the angle between the free stream relative airflow and the chord line of
an aerofoil section (Fig. 4.9).
FIG. 4.9
Changes in the angle of attack cause the velocity and pressure of the flow to vary as the air
passes over the upper and lower surfaces. This in turn affects the pressure differential that exists
and hence the amount of lift developed.
Do not confuse Angle of Attack with Angle of Incidence. The Angle of Incidence is the angle at
which the wing is fixed to the fuselage, relative to the aircrafts longitudinal axis (Fig. 4.10).
FIG. 4.10
4-6
Lift
Chapter 4
The angle of incidence is fixed, but the angle of attack changes in flight. Likewise, do not confuse
the Pitch Angle or Pitch Attitude of the aircraft with the angle of attack. For any given angle of
attack, the pitch angle can vary (Fig. 4.11).
FIG. 4.11
Similarly for any given pitch angle, the angle of attack can also vary (Fig. 4.12).
FIG. 4.12
4-7
Chapter 4
Lift
FIG. 4.13
As the dividing streamline approaches the aerofoil it slows down, and momentarily comes to rest
just below the leading edge, forming a stagnation point. A stagnation point also exists at the
rear of the aerofoil. At these points the velocity of the airflow reduces to zero, and the static
pressure reaches a maximum value (stagnation pressure), which is higher than atmospheric. At
normal angles of attack, the forward stagnation point is situated below the leading edge, allowing
the airflow passing over the upper surface to initially travel forward.
The pressure differential (negative pressure gradient) associated with the upper surface also
imparts acceleration to the flow, and helps draw the air locally upward, producing upwash
(Fig. 4.14).
FIG. 4.14
At the rear of the aerofoil, the faster moving airflow over the upper surface relative to the lower
surface tends to force the lower streamlines downward, producing downwash.
4-8
Lift
Chapter 4
FIG. 4.15
The airflow velocity above and below the aerofoil increases by an equal amount and the static
pressures reduce by an equal amount. Consequently, no pressure differential exists, and no net
lift is created.
If the same aerofoil section is placed at a positive angle of attack, the stagnation point moves
below the leading edge point (Fig. 4.16).
FIG. 4.16
Upwash occurs in front of the aerofoil section, and the airflow accelerates as it passes over the
upper surface (venturi effect), resulting in a reduction in the static pressure. Conversely, the
airflow passing over the lower surface decreases in velocity and the static pressure increases. A
pressure differential now exists, generating lift.
Principles Of Flight (Rev Q407)
4-9
Chapter 4
Lift
If an asymmetrical aerofoil section is placed in the same airstream at zero degrees angle of
attack, a stagnation point forms below the leading edge, producing upwash (Fig. 4.17).
FIG. 4.17
The velocity of the airflow increases over the more curved upper surface, whilst the static
pressure decreases. A pressure differential now exists, generating lift. With increasing angle of
attack, the air flowing over the upper surface travels a greater distance and must speed up in
order to satisfy the Equation of Continuity.
Conversely, because the air travels a shorter distance over the lower surface, it slows down. This
produces a greater pressure differential, generating more lift (Fig. 4.18).
FIG. 4.18
The angle of attack in conjunction with the actual shape of an aerofoil section is therefore one of
the factors that is instrumental to the production of lift.
4-10
Lift
Chapter 4
The actual pressure distribution over the upper and lower surfaces varies with changes in angle
of attack, as does the pressure differential and the amount of lift developed. To appreciate these
effects it is useful to display the actual pressure distribution diagrammatically (Fig. 4.19).
RELATIVE AIRFLOW
+
Fig 4.19
A series of pressure arrows drawn normal (at right angles) to the aerofoil surface and joined at
their extremities produces a pressure envelope. An arrow on each line pointing inward represents
a positive pressure (i.e. above atmospheric pressure), whilst those pointing outward represent a
negative pressure (i.e. below atmospheric pressure).
4-11
Chapter 4
Lift
-5
-2
+2
+8
+
C
+20
+1
05
+
F
FIG. 4.20
The above figure shows a series of diagrams which represents the chordwise pressure
distribution about an asymmetrical aerofoil, as the angle of attack increases from -5 to +20.
4-12
Lift
Chapter 4
Figure 4.20A shows the aerofoil at -5 angle of attack. The pressure above the aerofoil is greater
than ambient atmospheric pressure and acceleration of the airflow beneath the aerofoil results in
a drop in static pressure to less than ambient. The lift is therefore negative or downward due to
both the higher pressure above the aerofoil and the lower pressure below the aerofoil.
Figure 4.20B shows a typical small negative angle of attack at which no net lift is produced, which
is known as the zero-lift angle of attack. The upper surface of the aerofoil has an area of higher
pressure at the front, behind which there is an area of lower pressure. Below the aerofoil the
pressure is slightly lower than ambient. It is noticeable that there will be a tendency for the nose
to pitch down (negative pitch moment).
Figures 4.20C to 4.20E show that as the angle of attack increases, the low pressure above the
aerofoil deepens and the suction peak moves forward. This results in the lift increasing and more
of the lift being generated further forward.
Also note that the higher than ambient pressure beneath the aerofoil remains relatively constant
in shape and magnitude as the angle of attack increases. This means that the increase in lift, as
angle of attack increases, is mainly due to the suction above the aerofoil and not due to the high
pressure below the aerofoil.
If the angle of attack increases further, lift increases until the stalling angle of attack is
exceeded. Figure 4.20F shows a stalled aerofoil at an angle of attack of +20. In the stalled
condition, the higher than ambient pressure below the aerofoil is the same as the unstalled
aerofoil in Figure 4.20E, but the suction peak above the aerofoil has flattened and spread,
causing lift to decrease and the centre of pressure to move aft.
For conventional low speed aerofoils the angle of attack at which an aerofoil stalls is usually
about 15 to 16. Beyond this angle the streamline flow over the upper surface separates from
the majority of the upper surface. The relationship between velocity and static pressure is no
longer applicable beyond this point, since Bernoulli's Theorem only applies to streamline flow.
4-13
Chapter 4
Lift
FIG. 4.21
At normal cruising airspeeds with a small positive angle of attack, the CP is positioned on the
chord line near the centre of an aerofoil. With increasing angle of attack, the centre of pressure
moves forward toward the leading edge. Figures 4.22a to 4.22c show this forward movement of
the centre of pressure and increase in magnitude of the total reaction.
Beyond the stalling angle of attack the low-pressure peak rapidly collapses, causing the
magnitude of the total reaction to decrease and the centre of pressure to move rapidly rearward
toward the trailing edge. This is shown in figure 4.22d.
Figure 4.22 resolves the total reaction into forces of lift and drag. Lift is the component of the total
reaction perpendicular to the relative airflow, whilst drag is the component of the total reaction
parallel to, and in the same direction as, the relative airflow.
As the angle of attack increases from +2 in figure 4.22a, to +15 in figure 4.22c, the magnitude
of the total reaction increases. Lift and drag, the components of the total reaction, also increase
but by differing amounts.
4-14
Lift
Chapter 4
TR
L
RELATIVE AIRFLOW
CP
+2
L
RELATIVE AIRFLOW
CP
+8
TR
TR
RELATIVE AIRFLOW
CP
+15
RELATIVE AIRFLOW
TR
CP
+20
d
FIG. 4.22
4-15
Chapter 4
Lift
AERODYNAMIC CENTRE
At normal angles of attack, an increase in angle of attack causes lift to increase and the centre of
pressure, the point at which the lift acts, to move forward.
Figure 4.23 considers the turning effect of the lift force around three points (A, B, and AC). First,
consider the turning moment of the lift force about point A, which is at the leading edge. The
turning moment is anti-clockwise or nose-down in direction. The size of the moment depends on
the product of the lift force and the distance between A and the centre of pressure. As the angle
of attack increases the large increase in lift multiplied by only a small reduction in the distance
between A and the centre of pressure results in the nose-down moment increasing.
Conversely, the effect of the lift force around point B at the trailing edge causes a clockwise or
tail-down moment. The tail-down moment increases as the angle of attack increases, because
both the lift force and distance between point B and the CP are increasing. However, there is a
further point on the chord line; labelled AC. Point AC is at the aerodynamic centre. The
aerodynamic centre is important when considering the moment of the lift force.
nose-down
turning
moment
A
TR
AC
tail-down
turning
moment
CP
B
Fig 4.23
Figure 4.23 shows that the size of moment around the aerodynamic centre remains the same as
the AOA changes. This is because the product of the increasing lift force and decreasing distance
between the AC and the CP remains at a constant magnitude at all normal angles of attack.
4-16
Lift
Chapter 4
LIFT FORMULA
The amount of lift generated by a wing depends on the following:
Wing Shape
Angle of Attack
Air Density ()
Free Stream Air Velocity Squared (V)
Wing Planform Surface Area (S)
The dynamic pressure possessed by a moving fluid equals half the density times the velocity
squared.
(Dynamic Pressure = V). The combination of this pressure and a wings planform surface
area (S) produces a force, which is proportional to the area on which it acts. This force is known
as Lift.
Lift = Pressure x Area
= V x S
Lift does not directly equal the product of the two terms and therefore the lifting efficiency of the
wing also needs to be taken into account. This involves the wing's shape and angle of attack. Lift
is expressed in Newtons (N) and the general lift formula is:
Lift = CL V S
4-17
Chapter 4
Lift
Each aerofoil possesses a unique lift curve. The graph below compares an asymmetrical aerofoil
against a symmetrical aerofoil (Fig. 4.24).
1.6
Asymmetrical
(Cambered)
Aerofoil
1.4
1.2
1.0
CL 0.8
Symmetrical
Aerofoil
0.6
0.4
0.2
0
- 2
10
6
8
Angle of Attack
12
14
16
FIG. 4.24
Asymmetrical aerofoils clearly produce more lift at any given angle of attack, but stall at a lower
stalling angle of attack than symmetrical aerofoils.
FIG. 4.25
4-18
Lift
Chapter 4
The lower surface of a wing is normally at a pressure above atmospheric, whilst the upper
surface is at a pressure below atmospheric. Beyond the wing tips the air is nominally at
atmospheric pressure. This causes a spanwise flow of air outward away from the fuselage on the
lower surface and an inward flow toward the fuselage on the upper surface. The air now flows in
both the chordwise and spanwise directions. At the trailing edge of the wing, where the two flows
meet, a twisting motion is imparted to the air and a series of vortices form. These are trailing edge
vortices (Fig. 4.26) shown in black, The trailing edge vortices rotate in opposite directions,
becoming progressively weaker toward the centre-line of the aircraft
FIG. 4.26
At the wing tips, a pressure gradient causes the air to flow from beneath the wing around the wing
tip up to the upper surface while the aeroplane also moves forwards. This creates two strong
wing tip vortices, shown in the above diagram (Fig 4.26)in red. By convention the right wing is
always the starboard wing (ie right as viewed from behind). The direction of the wingtip vortex
about the right wing is anticlockwise, while the wingtip vortex about the left wing is clockwise. This
is shown in the below diagram.
FIG. 4.27
Principles Of Flight (Rev Q407)
4-19
Chapter 4
Lift
FIG. 4.28
We now need to consider the effect of the wing tip and trailing edge vortices on the down wash
behind the wing. Since the downwash is much greater than upwash in front of the wing, the
airflow close to the wing, the effective air flow (EAF), is inclined to the relative air flow (RAF)
by an angle called the induced angle of attack (i). This is shown in the above diagram.
FIG. 4.29
Because the lift force acts perpendicular to the effective airflow (EAF) the lift vector is inclined
rearward through the same angle, (i). This is shown in Fig 4.29 above. The angle of attack
producing this lift force is the effective angle of attack (e), which is smaller than the original
angle of attack between the RAF and the wing chord. Not only does the effective lift decrease
(until the angle of attack is increased further), but a component of the lift force, also acts
horizontally, retarding the forward motion of the aeroplane. This component of lift is induced drag.
The induced drag increases when the induced angle of attack increases.
In order to recover the lost lift, the angle of attack must be further increased, giving an increased
effective angle of attack. This causes a corresponding increase in the drag component.
4-20
Lift
Chapter 4
Root
Semispan distance
Tip
FIG. 4.30
Fig 4.30 shows us that the local coefficient of lift (and effective angle of attack), is greatest at the
root for a rectangular wing, toward the tip for a tapered and swept wing, and constant (a
rectangular distribution) for an elliptical wing. This means that as the angle of attack increases,
the wing stalls first;
4-21
Chapter 4
4-22
Lift
INTRODUCTION
During flight, all the parts of an aircraft exposed to the airflow produce an aerodynamic force,
which opposes the forward motion of the aircraft. This force is known as drag, and is the air
resistance experienced by an aircraft as it moves through the air (Fig. 5.1).
FIG. 5.1
Drag acts parallel to and in the same direction as the relative airflow. In steady level flight (SLF),
drag is directly balanced by the thrust produced by an engine or propeller. For a given airspeed, it
follows that the lower the drag, the less thrust is required to balance it (Fig. 5.2).
5-1
Chapter 5
Drag
FIG. 5.2
Low drag is therefore beneficial, since it leads to reduced fuel consumption and lower operating
costs.
The total drag acting on an aircraft in flight is the sum of:
Profile drag
Induced drag
Interference drag
Form drag
Skin friction drag
FORM DRAG
Form drag is produced whenever the streamline airflow passing over an aircraft separates from
the surface and becomes turbulent. An example of extreme form drag is the effect of a flat plate
placed at right angles to the airflow (Fig. 5.3).
FIG. 5.3
5-2
Drag
Chapter 5
The pressure immediately in front of the plate is above atmospheric, whilst the pressure behind
the plate is below atmospheric. This results in a sucking effect behind the plate and the formation
of vortices. The more rapidly the airflow changes direction, the greater the pressure gradient, the
earlier the separation, and the higher the form drag. Changing the shape, or streamline, of a
given object reduces drag by delaying the point at which the airflow separates (Fig. 5.4).
DRAG
DRAG
5%
15%
50%
100%
FIG. 5.4
On aircraft, for example, a fairing is often fitted around a fixed undercarriage leg to reduce form
drag to an acceptable level (Fig. 5.5).
FIG. 5.5
A relationship exists between the ratio of the length (a) to the maximum thickness (b) of a body
and the resulting form drag of that body (Fig. 5.6).
b
a
FIG. 5.6
Streamline shapes that give the least form drag at subsonic speeds normally have a fineness
ratio of 4 to 1, but these values may vary considerably without increasing drag to any great
extent.
Principles Of Flight (Rev Q407)
5-3
Chapter 5
Drag
As air flows around an object, there is a point where it is unable to remain on the surface and it
separates away. This is known as the separation point (Fig. 5.7).
Separation
Point
Separation
Point
STALL
FIG. 5.7
With increasing angles of attack, the separation point moves steadily toward the leading edge.
The further forward this occurs, the greater the form drag.
BOUNDARY LAYER
Skin friction drag is a function of the layer of air closest to the surface. As air flows over a wing,
the roughness of the surface and the viscous property of the air itself slow it down. Much like
fluids, the more viscous the air, the greater its retardation. At the surface, the air particles adhere
to it and their relative velocity is reduced to zero (Fig. 5.8).
Free Stream
Velocity
V
Air at
Rest
Relative Air
Velocities
Surface
FIG. 5.8
Just above the surface, the air particles slow down due to the friction effects between the
particles, but except for the layer in contact with the surface, the particles do not completely come
to rest. The relative velocity of the air particles increases steadily with distance from the surface,
until reaching a point where the particles do not slow up at all and instead travel at the free
stream velocity.
5-4
Drag
Chapter 5
The boundary layer is the layer of air between the surface and the free stream velocity in which
local retardation takes place. Like the main airflow, the boundary layer flow can be either laminar
or turbulent in nature (Fig. 5.9).
Transition
Laminar
Turbulent
Surface
FIG. 5.9
The laminar boundary layer is a very thin layer of smooth airflow. It consists of a
series of laminations or smooth regular streamlines, in which the air particles do not
intermingle.
The turbulent boundary layer is a layer of disturbed or turbulent airflow, in which the
streamlines break up. The air particles become intermingled and move in a random,
irregular pattern. Notably, the turbulent boundary layer creates greater drag than the
laminar boundary layer.
The usual tendency is for the boundary layer to start in a laminar condition near the leading edge
of an aircraft wing, and then become turbulent. The change from laminar to turbulent flow takes
place in the transition region. In fact, the transformation from laminar to turbulent flow can be
clearly seen in the smoke rising from a fire in still air (Fig. 5.10).
Turbulent
Laminar
FIG. 5.10
5-5
Chapter 5
Drag
The boundary layer also increases in thickness as it moves rearward over an aircraft wing, with
the turbulent boundary layer being proportionally thicker than the laminar boundary layer under
the same free stream velocity conditions (Fig. 5.11).
FREE STREAM
VELOCITY OF
AIRFLOW
FREE STREAM
VELOCITY OF
AIRFLOW
THICKNESS
0.01m
THICKNESS OF
BOUNDARY
LAYER
SURFACE
OF WING
(A) LAMINAR
(B) TURBULENT
FIG. 5.11
Following the transition from laminar to turbulent boundary layer, the boundary layer thickens and
grows at a more rapid rate. The maximum thickness of the boundary layer is comparatively small
and in practice is only about 0.01 m in depth. It is also possible to compare the characteristics of
laminar and turbulent boundary layer using velocity profiles (Fig. 5.12).
Laminar
Distance
Turbulent
V
FIG. 5.12
These profiles show the variation in boundary layer velocity with distance above a surface. Note
that the turbulent boundary layer has much higher local velocities immediately adjacent to the
surface. The airflow in this region therefore possesses much higher kinetic energy than the
laminar boundary layer at the same distance above the surface. The nature of the boundary layer
is extremely important in aerodynamics, since it determines the maximum coefficient of lift and
the stalling characteristics of an aerofoil (explained later in detail).
5-6
Drag
Chapter 5
FIG. 5.13
The gradual velocity change associated with the laminar boundary layer shows that low shear
stresses exist near the surface, resulting in low skin friction drag. Conversely, the rapid velocity
change associated with the turbulent boundary layer is evidence of high skin friction drag.
If the conditions of flow were such that either a turbulent or a laminar boundary layer could exist,
laminar skin friction drag would be about one-third of the turbulent flow. Laminar boundary layers
are therefore desirable, but the natural transition into a turbulent boundary layer prevents this
occurring. This makes the point where transition takes place important when determining the
amount of skin friction drag that exists. Fig. 5.14 shows how the boundary layer develops on a
typical aerofoil.
LAMINAR
LAYER
TRANSITION
TURBULENT
LAYER
SEPARATION
POINT
WAKE
FIG. 5.14
5-7
Chapter 5
Drag
The Effect of Surface Roughness causes a premature transition from a laminar to a turbulent
boundary layer if a wing has a rough surface. For example, an accumulation of ice could cause
surface roughness (Fig. 5.15).
ICE
FIG. 5.15
This also causes a large increase in skin friction drag. The degree of skin friction drag may be
minimised by polishing and de-icing the surface. Since all of the aircraft skin is exposed to the
airstream, this type of drag affects all surfaces.
INTERFERENCE DRAG
Considering an aircraft as a whole, the total drag acting on it may be greater than the sum of the
drags of the individual components. This is a result of the airflow being greatly disturbed where
the various components join together, principally between the wing and fuselage. The disturbance
imparted to the airflow produces additional drag, known as interference drag (Fig. 5.16).
DRAG
INTERFERENCE
DRAG
DRAG
FIG. 5.16
This type of drag occurs because a large pressure gradient is set up across the junction that
causes the boundary layer to prematurely separate from the surface and form a turbulent wake.
Placing a suitably shaped fairing or fillet over the intersection encourages streamline flow and
minimises this effect, reducing interference drag. Minimising interference drag is particularly
important at high airspeeds.
Note:
5-8
Drag
Chapter 5
INDUCED DRAG
Whenever a wing produces lift, concentrated vortices form at the wing tips. The vortices are
strongest at the wing tips and become progressively weaker toward the centre-line of the aircraft
(Fig. 5.17).
LEFT-WING VORTEX
RIGHT-WING VORTEX
WING
TRAILING
EDGE
VORTEX
TRAILING EDGE
CENTRE-LINE OF AIRCRAFT
FIG. 5.17
The vortices induce downwash to the airflow behind the wing, causing the lift vector to tilt
rearward. The horizontal component of lift opposes the forward flight of the aircraft, and is known
as induced drag (Fig. 5.18).
Induced
Drag
Lift
Chord
Effective Relative
Airflow
Drag
Free Stream
Relative Airflow
Induced
Downwash
Angle of Induced
Downwash
FIG. 5.18
The larger the vortex, the greater the induced downwash, and the greater the induced drag.
5-9
Chapter 5
Drag
C 2
Induced Drag (DI) = LA V2 S
Where: CL
A
V
S
C 2
L
A
=
=
=
=
=
Coefficient Of Lift
Aspect Ratio
Density (kg/m3)
Velocity m/s
Planform Surface Area (m2)
Rectangular
12
Effective
Angle of 10
Attack
8
Elliptical
Tapered
6
4
2
10
20
30
40 50 60 70
% of Semi-span
80
90
100
FIG. 5.19
5-10
Drag
Chapter 5
Clearly, a rectangular planform wing produces a much larger vortex than the tapered section.
This is because the longer the tip chord, the greater the spillage of air from the lower surface onto
the upper surface, and the larger the wing tip vortex. In aerodynamic terms, the elliptical planform
wing is the most aerodynamically efficient because the downwash remains constant across the
complete wingspan, giving minimal induced drag (Fig. 5.20).
LIFT
CONSTANT DOWNWASH
FIG. 5.20
From a practical point of view however, the manufacturing and structural problems associated
with an elliptical planform wing preclude its use. For structural reasons, a straight tapered wing
provides a good compromise, giving low induced drag (Fig. 5.21).
PREFERRED PLANFORM FOR
PURELY STRUCTURAL
CONSIDERATIONS
FIG. 5.21
To preserve the aerodynamic efficiency, the resulting planform is usually tailored by using wing
twist and cross sectional variation, in order to obtain as near as possible the elliptical lift
distribution.
5-11
Chapter 5
Drag
The Effect of Aspect Ratio is another factor used to minimise induced drag. Making the
wingspan as long as possible relative to the chord increases the aspect ratio. This reduces the
overall size of the wing tip vortices and thus induced drag (Fig. 5.22).
36 ft Span
Span
Aspect Ratio =
Average Chord
Wing Area = 100 sq ft
Aspect Ratio = 25
2 ft
Average
Chord
50 ft Span
FIG. 5.22
5-12
Drag
Chapter 5
The Effect of Airspeed relates to the changes in induced drag with the variation of airspeed.
Induced drag is most significant at low airspeeds and high angles of attack (i.e. during take-off
and landing, when it can account for approximately three-quarters of the total drag). To maintain
steady level flight, as the airspeed decreases and the angle of attack increases, the slower
passage of air rearward over the wing increases the spanwise flow of air around the wing tip. This
results in larger wing tip vortices and greater induced drag (Fig. 5.23).
SLOW SPEED
HIGH SPEED
INDUCED
DRAG
INDUCED
DRAG
INDUCED
DRAG
INDUCED
DRAG
SLOW
HIGH
AOA
FAST
LOW
AOA
AIRSPEED
FIG. 5.23
L
L
D
D
W
FIG. 5.24
5-13
Chapter 5
Drag
FIG. 5.25
Washout means constructing the wing with a small amount of twist from root to tip, so
that the inboard wing section is at a higher angle of incidence, and hence a greater angle
of attack, compared to the wing tip (Fig. 5.26).
CROSS SECTION
AT WINGTIP
RELATIVE AIRFLOW
CROSS SECTION
AT WING ROOT
FIG. 5.26
This ensures that the inner part of the wing generates most of the lift, thus minimising the
leakage of airflow around the wing tips. This reduces the size of the wing tip vortex and
reduces the total amount of induced drag.
5-14
Drag
Chapter 5
Wing tip modifications reduce the leakage of airflow around the wing tip and limit the size of
the vortex. Some of the more typical designs appear in Fig. 5.27.
PLAIN WING
MODIFIED
WINGTIP
WINGTIP TANK
WINGLET
FIG. 5.27
DRAG FORMULA
Like lift, a drag formula can also be derived. The drag acting on an aircraft depends on the
following factors:
Shape
Angle of attack
Air density ()
Air velocity squared (free stream air velocity) (V2)
Wing planform surface area (S)
Dynamic pressure takes into account the air density and velocity, but when combined with the
wing planform surface area (S) it produces a force known as drag. Like lift, drag is not exactly
equal to the dynamic pressure times the area, but varies with shape and angle of attack. The
Coefficient of Drag (CD ) represents these factors.
The general drag formula is thus:
Drag = CD VS
5-15
Chapter 5
Drag
A graph of Coefficient of Drag against Angle of Attack illustrates how drag varies in flight
(Fig. 5.28).
0
15
Usual Flight
Angles
0.28
0.24
0.20
CD
Stalling
Angle
0.16
0.12
0.08
0.04
0
-4
8
12
16
Angle of Attack
20
FIG. 5.28
DRAG CURVES
Plotting graphs of profile or parasite drag and induced drag on the same axes shows the
relationship between them (Fig. 5.29).
ra
g
Drag
ra
lD
ta
o
T
Minimum
Drag
it
as
r
Pa
Indu
VMD
ced Drag
Speed
FIG. 5.29
Adding these two drag values together at any given velocity produces a total drag curve. It is
essential to remember that this curve only applies to an aircraft of constant weight and
configuration in level flight at any given altitude.
Total drag is at its minimum when the profile (or parasite drag) and induced drag are
equal.
5-16
Drag
Chapter 5
This is known as the minimum drag point and occurs at the minimum drag speed (VIMD). This is
the speed where the required lift is developed with the minimum amount of drag and is also the
most economical speed at which an aircraft flies.
Total Drag
Light
ra
g
Drag
He
av
y
Changes in weight affect the drag curves. If the weight of an aircraft alters, a
corresponding change in the coefficient of lift must occur to maintain level flight at a given
airspeed. It follows that since induced drag is proportional to CL (or weight), any change
in weight also alters the total drag curve (Fig. 5.30).
ra
d
Induce
l
ta
To
e
sit
ra
a
P
a
Dr
Li
gh
t
I nd
uced
D
V MD VMD
Light
rag Heavy
Speed
Heavy
FIG. 5.30
Any change in weight moves the point at which the induced drag and profile drag curves
cross. This leads to a change in the minimum drag speed (e.g. an increase in weight
increases VIMD as well as the total drag).
Dr
To
le
an
ta
l
ot
al
Dr
ag
Drag
ag
Di
rty
Cl
ea
High drag devices affect the drag curves. In flight, it is sometimes necessary to
decrease VIMD by deliberately increasing the total drag. The use of airbrakes or spoilers
causes an increase in profile drag (Fig. 5.31).
rag
ite D
Paras
ra
Pa
ty
Dir
e
sit
a
Dr
Induced Drag
V MD VMD
Dirty
Clean
Speed
FIG. 5.31
As parasite drag increases, the point at which the parasite drag and the induced drag
curves cross alters, and the minimum drag speed decreases.
5-17
Chapter 5
Drag
LIFT/DRAG RATIO
To determine the efficiency of an aircraft, consider the lift and drag curves together (Fig. 5.32).
0
1.4
1.2
CL
15
Usual
Flight
Angles
0.28
0.24
1.0
0.8
0.16
0.6
0.12
Stalling
Angle
0.4
0.08
0.2
0
Stalling
Angle
0.20
CD
15
Usual
Flight
Angles
0.04
-4
12
16
20
-4
12
16
20
Angle of Attack
Angle of Attack
FIG. 5.32
For maximum efficiency, the wings should produce maximum lift with the least possible drag. The
lift curve shows that maximum lift occurs at 15 angle of attack, whereas the drag curve shows
minimum drag occurs at -2 angle of attack. Neither of these angles is satisfactory, since the ratio
of lift to drag at both extremes is very low. In practice, maximum lift at minimum drag (i.e.
maximum lift/drag ratio, or L/D Ratio) should occur at the same angle of attack. To establish
where this occurs it is necessary to examine the Lift/Drag ratio at various angles of attack using
the lift and drag formulas. The following formula gives the Lift/Drag ratio for an aerofoil at any
selected angle of attack:
Lift = CL V2 S =
Drag
CD V S
CL
CD
Note that the same result is obtained irrespective of whether the lift and drag, or their coefficients,
are used in the calculations. The most efficient angle of attack can be found by plotting lift/drag
ratio against angle of attack.
5-18
Drag
Chapter 5
28
15
ORDINARY ANGLES
OF FLIGHT
24
LIFT/DRAG
RATIO
20
STALLING
ANGLE
MOST
EFFICIENT
ANGLE
16
12
8
4
0
-4
4
8
12
ANGLE OF ATTACK
16
20
FIG. 5.33
Fig. 5.33 shows that the lift/drag ratio increases rapidly up to about 3 or 4, at which point the lift
is nearly 24 times the drag. This value varies depending on the type of aerofoil. For transport
aircraft this value is typically 1220, and for propeller powered trainer aircraft is typically 10-15.
At higher angles of attack, the lift/drag ratio steadily reduces because, even though the
Coefficient of Lift (CL) continues to increase, the Coefficient of Drag (CD) increases at a greater
rate. In fact, at the stalling angle, lift may only be 10 to 12 times greater than drag.
The most important point on the lift/drag curve is the angle of attack that gives the best lift/drag
ratio, in this case 3 or 4. This is the most efficient (optimum) angle of attack, at which the aerofoil
gives its best all round performance (i.e. it produces the most lift for the least amount of drag). At
any other angle of attack, the same lift will be obtained at a greater cost in drag.
5-19
Chapter 5
Drag
Since thrust balances drag in steady level flight, it follows that by minimising drag, thrust can also
be minimised. This allows the use of a smaller engine, resulting in better fuel economy and lower
maintenance costs. In practice, most aircraft are not fitted with an instrument that indicates angles
of attack, so the pilot must rely on the airspeed indicator, since airspeed relates to angle of attack
in level flight (Fig. 5.34).
L
150 IAS
85
IAS
8 AOA
2 AOA
W
65
IAS
12 AOA
W
FIG. 5.34
Therefore, the minimum drag speed relates to the angle of attack that gives the best lift/drag ratio
(i.e. 3 or 4). Consequently, aircraft fly at the minimum drag speed to give best all round
performance, but remember this is only correct for a given weight and any change in weight
necessitates a change in airspeed to maintain the best lift/drag ratio. Changes in altitude do not
affect the best lift/drag ratio.
5-20
Drag
Chapter 5
Fig. 5.35
The coefficient of parasite drag is constant for a given wing cross section and does not vary with
angle of attack (CL) until very close to the stall. A thicker wing, a wing with more camber or a wing
with flaps extended will have a greater CDP. The CDP is shown on the above drag polar diagram
by the offset in CD at zero CL (when the CDI is zero). The curved shape of the drag polar is due to
the coefficient of induced drag which is proportional to the CL2 (ie increase rapidly as CL
increases).
Two important points that can be identified on the drag polar are:
CL/CD maximum, (tangent to the curve in the above drag polar graph), and
CL maximum
Note that it is not possible to read off the actual value of lift (only the CL) or the actual values of
parasite or total drag.
5-21
Chapter 5
5-22
Drag
INTRODUCTION
In flight, an aircraft can rotate about any one, or any combination of, its three axes. These axes
are at right angles to each other and all pass through the aircrafts centre of gravity (Fig. 6.1).
Lateral
Axis
Normal Axis
Longitudinal
Axis
FIG. 6.1
Movement about the lateral axis is pitch. Movement about the longitudinal axis is roll. Finally,
movement about the normal axis is yaw. This is achieved via a primary flying control system,
which in its basic form consists of moveable control surfaces linked by a series of cables and rods
to controls in the cockpit (Fig. 6.2).
RUDDER
CONTROL
WHEEL
ELEVATOR
AILERON
RUDDER
PEDALS
FIG. 6.2
The primary control surfaces are the elevators, ailerons, and rudder. These surfaces hinge at
the trailing edges of the main surfaces and manoeuvre the aircraft about its three axes, producing
both primary and secondary effects.
Principles Of Flight (Rev Q407)
6-1
Chapter 6
Flying Controls
ELEVATORS
The primary effect of elevators is to provide pitch control about the lateral axis (Fig. 6.3).
Lateral
Axis
Increased
Angle of Attack
Pitch Down
Increased
Lift
Chord Line
Relative Wind
Elevator
HORIZONTAL STABILIZER
FIG. 6.3
Pushing the control column forward causes the elevator to move downward. This produces an
aerodynamic force acting on the tailplane in an upward direction causing the aircraft to pitch
nose-down. Pulling the control column rearward has the reverse effect, and causes the aircraft to
pitch nose-up. The elevators produce no real secondary effect on an aircraft, although changes in
pitch attitude change the angle of attack and thus airspeed.
THE STABILATOR
On some aircraft, the tailplane and elevator are combined into one surface, known as a
stabilator, or an all-moving tailplane (Fig. 6.4).
AERODYNAMIC
FORCE
TAILPLANE
ELEVATOR
AERODYNAMIC
FORCE
STABILATOR
FIG. 6.4
Forward movement of the control column causes the leading edge of the stabilator to rise,
thereby generating a force that causes the tail to rise and the aircraft's nose to drop. A rearward
movement of the control column has the opposite effect.
6-2
Flying Controls
Chapter 6
THE RUDDER
The primary effect of the rudder is to provide yaw control about the normal axis (Fig. 6.5).
Normal Axis
TOP VIEW
OF VERTICAL
STABILIZER
Increased
Angle of
Attack
Relative
Wind
Chord
line
Increased
Lift
Yaw Left
Rudder
FIG. 6.5
Moving the left rudder pedal forward moves the rudder to the left. In flight, this produces an
aerodynamic force on the fin and the aircraft yaws to the left. Moving the right rudder pedal
forward reverses the action, and the aircraft yaws to the right. The secondary effect of rudder is
roll in the same direction as yaw (Fig. 6.6).
YAW
OUTER WING
MOVES FASTER
MORE LIFT
ROLL
YAW
FIG. 6.6
This occurs because the outer wing travels faster than the inner wing, thereby generating more
lift.
6-3
Chapter 6
Flying Controls
AILERONS
The primary effect of ailerons is to provide roll control about the longitudinal axis (Fig. 6.7).
Increased
Lift
Chord
Line
Aileron
Longitudinal
Axis
Relative
Wind
Increased
Angle of
Attack
RIGHT WING
Chord
Line
Decreased
Angle of
Attack
Decreased
Lift
Roll Left
Relative
Wind
Aileron
LEFT WING
FIG. 6.7
When a pilot starts a rolling manoeuvre by deflecting the ailerons, the down-going aileron
increases the camber of the up going wing, while the up-going aileron decreases the camber of
the down-going wing. This increases the lift on the wing with the downward going aileron while
reducing the lift on the wing with the upward going aileron. This is shown in Fig 6.7 above and
results in the desired roll to the left.
6-4
Flying Controls
Chapter 6
LIFT
This yaw in the opposite direction to the desired turn is known as adverse aileron yaw and is the
secondary effect of ailerons.
Adverse
Yaw
LIFT
AG
DR
G
DRA
FIG. 6.8
This adverse aileron yaw can be countered, by equalising the drag produced by the ailerons.
There are a number of methods of achieving this, include using Differential or Frise type ailerons.
Differential ailerons are designed so that the up-going aileron is deflected through a
greater angle than the down-going aileron (Fig. 6.9).
Up-going
Aileron - Large
Deflection
Down-going
Aileron - Small
Deflection
FIG. 6.9
6-5
Chapter 6
Flying Controls
Frise ailerons are designed so that the leading edge of the aileron projects beneath the
wing when the aileron is deflected upward (Fig. 6.10).
Lift
Lift
Drag
Drag
FIG. 6.10
Some aircraft combine the two methods to form Differential/Frise type ailerons (Fig. 6.11).
Lift
Lift
Drag
FIG. 6.11
PITCH
LEFT ELEVONS UP
RIGHT ELEVONS UP
ELEVON
FIG. 6.12
6-6
Flying Controls
Chapter 6
Turning the control wheel moves the elevons upward on one wing, and downward on the other,
as in the case of conventional ailerons. For example, turning the control wheel to the right raises
the elevons on the right and lowers the elevons on the left, causing the aircraft to roll to the right
(Fig. 6.13).
ROLL
LEFT ELEVONS DOWN
RIGHT ELEVONS UP
FIG. 6.13
The control systems are interconnected to allow control inputs to produce combined pitching and
rolling moments.
Aircraft with a V or butterfly tail employ ruddervators, which combine the functions of the rudder
and elevators (Fig. 6.14).
RUDDERVATORS
FIG. 6.14
6-7
Chapter 6
Flying Controls
The ruddervators operate using conventional control system inputs from the control column and
rudder pedals. When functioning as elevators, they move in the same direction by equal amounts.
For example, pulling the control column rearward causes both ruddervators to move up, and the
aircraft to pitch nose-up (Fig. 6.15).
FIG. 6.15
When functioning as rudders, the ruddervators move by equal amounts in opposite directions. For
example, when pushing the right rudder pedal forward the left ruddervator will move up and the
right ruddervator will move down, causing the aircraft to yaw to the right (Fig. 6.16).
FIG. 6.16
The control column and rudder pedal systems connect to the surfaces through a differential
linkage or gearing arrangement to obtain the combined pitching and yawing moments.
Some aircraft use flaperons fitted to increase lift at low airspeeds in order to operate from shorter
runways. They combine the functions of ailerons and flaps to create a full-span trailing edge flap.
When lowered, the flaperon is able to move up and down providing roll control whilst still
contributing to the wings overall lift.
6-8
Flying Controls
Chapter 6
AERODYNAMIC BALANCE
When the control surfaces deflect, the product of the aerodynamic force acting through the centre
of pressure of the surface and its distance from the hinge-line produces an opposing moment
(Fig. 6.17).
Aerodynamic
Force (F)
Hinge Line
X
Hinge
Moment
Hinge Moment = FX
Centre of
Pressure
FIG. 6.17
This is known as the hinge moment of the control surface. Its magnitude determines the amount
of effort (stick force) required by the pilot to maintain its position. Stick force also depends on how
the control column is linked to the control surface. The ratio of stick movement to control surface
deflection is known as stick-gearing (Fig. 6.18).
Stick
Movement
Control
Surface
Deflection
Control
Column
Stick
Gearing =
Stick Movement
Control Surface Deflection
FIG. 6.18
If the stick forces are high, designers incorporate some form of assistance to help move the
control surface. Likewise, if the stick forces are too light, the surface must be artificially loaded to
increase the opposing moment. To achieve the necessary stick forces, the control surfaces are
aerodynamically balanced using one or more of the following methods:
6-9
Chapter 6
Flying Controls
The inset hinge places the hinge-line inside the control surface. This reduces the length of the
moment arm and therefore the size of the hinge moment, thus reducing the overall stick force
(Fig. 6.19).
Hinge Line
Aerodynamic
Force (F)
X
Hinge Moment = FX
Hinge
Moment
Centre of
Pressure
FIG. 6.19
The amount of inset is normally limited to 20 - 25% of the chord length to ensure that the centre
of pressure does not move in front of the hinge-line at high deflection angles.
If the centre of pressure moves ahead of the hinge line. the resulting hinge moment no longer
opposes the movement of the control surface, but instead assists it (Fig. 6.20).
Assisting
Moment
Aerodynamic
Force (F)
Overbalanced Control
Moves CP ahead of Hinge
Line
X Hinge Line
Centre of
Pressure
FIG. 6.20
This is known as control surface overbalance,
increase in the progressive stick forces required
deflection angle. In this condition, the control
deflection. To stop this, the pilot must reverse
reversibility.
6-10
Flying Controls
Chapter 6
The Horn Balance method is used mainly on rudders and elevators, but may be used on other
control surfaces (Fig. 6.21).
Aerodynamic
Horn Balance
Hinge
Line
Airflow
Hinge
Line
FIG. 6.21
The control surface is designed with an area ahead of the hinge line forming a horn. As the
surface moves, the horn projects into the airflow and assists the movement ahead of the hingeline. The action of the horn balance is similar to the inset hinge, and reduces the overall stick
force.
Internal Balance is used on ailerons and elevators. It operates in conjunction with tabs to reduce
the stick force. Unlike other methods, it is totally contained within the control surface (Fig. 6.22).
Shroud
Airflow
High Pressure
Wing
Structure
Hinge Line
Decreased Vent Gap
Hinge
FIG. 6.22
A hinged balance panel divides the area ahead of the control surface into two vented
compartments. When the control surface is deflected upward, the higher pressure developed in
the upper compartment creates a downward force on the balance panel, producing a partial
balancing moment, thereby reducing the overall stick force. Downward deflection of the surface
produced the opposite action.
6-11
Chapter 6
Flying Controls
TABS
Unlike the previous methods of aerodynamic balance, tabs are small, hinged surfaces forming
part of the primary control surface. In its basic form, the pilot does not directly control the tab, but
its deflection angle changes automatically whenever the main control surface moves. These tabs
partially balance the aerodynamic load acting on a control surface, reducing the overall stick
force.
Balance Tabs are sometimes incorporated as part of the elevator on conventional tailplanes.
They are connected to the tailplane by a mechanical linkage that causes them to move in the
opposite direction to the control surface (Fig. 6.23).
F
X
Control Rod
Aerodynamic Force
for Main Surface
Area of Control
CP of Control Surface
FIG. 6.23
For example, moving the control column rearward moves the elevator upward and the balance
tab downward. The resulting aerodynamic force acting on the tab produces a balancing moment,
and reduces the overall stick force.
Anti-Balance Tabs are used when it is necessary to increase the stick force. This is because
small movements of a control surface can produce large aerodynamic loads, leading to over
control (Fig. 6.24).
Main Aerodynamic
Force
Small Aerodynamic
Force Increases
Hinge Moment
Control
Input
FIG. 6.24
These tabs operate in the same manner as balance tabs, except that they move in the same
direction as the control surface to increase the stick force (i.e. control surface down, tab down).
6-12
Flying Controls
Chapter 6
The Servo Tab is directly controlled by the pilot through a pivot point and movement of the tab
supplies the hinge moment necessary to move the main control surface (Fig. 6.25).
CONTROL
INPUT
FREE
TO PIVOT
FIG. 6.25
Movement of the tab provides an aerodynamic force that produces a hinge moment about the
hinge line of the control surface. This causes the control surface to move to a new position of
equilibrium in a direction of travel opposite to that of the tab (i.e. tab down, control surface up).
The stick forces involved are therefore determined by the hinge moments acting on the tab. In
practice, the servo tab lacks effectiveness at low airspeeds when large control deflections are
required. This is because the amount of airflow passing over the tab is too low to produce the
necessary hinge moment and hence the required deflection.
The Spring Servo Tab overcomes the low-speed problems associated with a servo tab by
including a spring box in the system (Fig. 6.26).
Control Rod
Springs
Servo Tab
Control Arm
Hinge
FIG. 6.26
The spring tension is such that the tab does not come into operation until the stick force exceeds
a predetermined value. At low airspeeds, the spring tension prevents movement of the servo tab
and any control input by the pilot moves the control surface and tab as one piece. At higher
airspeeds, the springs compress and the tab moves by way of the pivot point in the opposite
direction to the control surface, providing the necessary aerodynamic assistance.
6-13
Chapter 6
Flying Controls
MASS BALANCE
During flight, the main control surfaces can vibrate, producing a condition known as flutter. It is
caused by the combined effects of changes in the pressure distribution around the control surface
with changing angles of attack (aerodynamic forces), and the forces due to the elastic nature of
the aircraft structure itself (aeroelastic forces). If these forces become coincident and act in
phase with each other, the resultant oscillations quickly increase in amplitude, and if left
unchecked, may ultimately lead to structural failure.
To help eliminate flutter in flight, manually operated control surfaces are generally mass
balanced. Attaching weights forward of the hinge line brings the centre of gravity of the control
surface to the hinge-line, thus altering the period of vibration and the liability to flutter. These
additional weights are usually installed internally along the leading edge of the control surface,
inside the horn balance, or on an arm attached to the surface (Fig. 6.27).
BALANCE WEIGHT
HINGE-LINE
ORIGINAL C OF G
NEW C OF G
BALANCE WEIGHT
FIG. 6.27
AILERONS
(ROLL)
ELEVATOR
(PITCH)
RUDDER
(YAW)
FIG. 6.28
6-14
Flying Controls
Chapter 6
The control surfaces are hydraulically activated and are powered from the aircrafts main
hydraulic systems. Due to the importance of the flying control systems, the surfaces are also
normally powered by at least two independent hydraulic systems (Fig. 6.29).
SPOILERS
G
G
L AIL
B
G
G
B
Y
Y
G
B
R AIL
B
G
HYDRAULIC
B BLUE SYSTEM
G GREEN SYSTEM
Y YELLOW SYSTEM
Y
Y
L ELEV
B
R ELEV
RUDDER
FIG. 6.29
ELEC
MOTOR
PUMP
LEFT
ENGINE
ELEC
MOTOR
PUMP
ENGINE
DRIVEN
PUMP
RAM
AIR
TURB
ELEC
MOTOR
PUMP
RIGHT
ENGINE
ELEC
MOTOR
PUMP
ENGINE
DRIVEN
PUMP
FIG. 6.30
6-15
Chapter 6
Flying Controls
Irrespective of their design, all powered flying control systems are regulated by the Joint
Airworthiness Requirements (JARs), and must comply with the following standards:
Sense:
The aircraft must move in the direction signified by the control input,
e.g. control column back, pitch nose-up.
Rigidity:
Stability:
Sensitivity:
Safety:
Fail-Safe:
FIG. 6.31
6-16
HY DR OM ECHANIC AL
ACT UATOR
Flying Controls
Chapter 6
The Electro-Hydraulic system measures the control signals using electrical transducers,
whose output is amplified, then relayed to electrically position the servo valve (Fig. 6.32).
MOTION
SENSORS
TYPICALLY 80 WIRES
SENSOR
FLIGHT
COMPUTER
ELECTRO-HYDRAULIC
ACTUATOR
FIG. 6.32
This is commonly known as a fly-by-wire (FBW) system. In some aircraft this system
controls only certain flying control surfaces, for example, spoiler control panels in the
case of the Boeing 767 or Airbus 320.
CONTROL
COLUMN
HYDRAULIC
PRESSURE
IN
RETURN
RETURN
FLUID
FLUID OUT
OUT
PIVOT
SERVO VALVE
(NEUTRAL POSITION)
PORT
CONTROL SURFACE
AIRCRAFT
STRUCTURE
JACK RAM
PISTON
JACK BODY
FIG. 6.33
It consists of a jack ram/piston arrangement, which is fixed to the aircraft structure, hydraulic
fluid, inlet/outlet ports, and a jack body. These parts form a hydraulic actuator, which is
controlled by a servo (control) valve and is connected via a control run to the flight deck controls.
When displaced in either direction from its neutral position, the valve allows hydraulic fluid under
pressure to pass to one side of the piston, and opens a return path from the other side.
6-17
Chapter 6
Flying Controls
For example, a rearward movement of the control column causes the servo valve to move to the
left (Fig. 6.34).
CONTROL
COLUMN
HYDRAULIC
PRESSURE
IN
RETURN
RETURN
FLUID
FLUID OUT
OUT
PRESSURE FLUID
RETURN FLUID
PIVOT
SERVO VALVE
(DISPLACED FROM
NEUTRAL POSITION)
AIRCRAFT
STRUCTURE
CONTROL SURFACE
MOVEMENT OF
JACK BODY
PISTON
JACK BODY
FIG. 6.34
Since the jack is in a fixed position, the resulting pressure differential across the piston causes
the jack body to move to the left, which in turn deflects the control surface upward via a
mechanical linkage. The body continues to move until it centralises itself on the servo valve,
returning it to its neutral position (Fig. 6.35).
CONTROL
COLUMN
HYDRAULIC
PRESSURE
IN
RETURN
RETURN
FLUID
FLUID OUT
OUT
PIVOT
SERVO VALVE
(NEUTRAL POSITION)
AIRCRAFT
STRUCTURE
CONTROL SURFACE
PISTON
JACK BODY
FIG. 6.35
The hydraulic fluid trapped on either side of the jack forms a hydraulic lock, maintaining the
control surface rigidly in its selected position. The surface will remain so, irrespective of the
aerodynamic loads acting on it, until another flight deck control input repositions the servo valve.
This is alternatively known as an irreversible control system. Conversely, moving the control
column forward moves the servo valve to the right, the jack body then moves to the right, and the
control surface deflects downward. Some power control units also operate in response to
electrical inputs from the Autopilot and Autostabilisation systems when they are engaged.
6-18
Flying Controls
Chapter 6
CONTROL COLUMN
PIVOT
POWER CONTROL
UNIT
ELEVATOR
JACK
RAM
FIG. 6.36
It is designed so that any flight deck control movement is first made against spring tension, so the
larger the movement, the greater the opposing spring force. For example, moving the control
column rearward compresses the left-hand side of the spring in the feel unit in proportion to the
control column movement and subsequent deflection of the control surface. Centralising the
control column relieves the spring pressure as the flying control surface returns to its neutral
position.
Principles Of Flight (Rev Q407)
6-19
Chapter 6
Flying Controls
This type of feel unit by itself may be adequate at low airspeeds, but higher airspeeds require
greater resistance to flight deck control movement to prevent overstressing the aircraft. This is
because the amount of feel only varies in proportion to control surface deflection, and takes no
account of airspeed. On transport category aircraft this type of feel unit is normally used by itself
only in aileron control systems.
Like spring feel units, Q-feel Units are fitted in the operating linkage between the flight deck
controls and the power control units (Fig. 6.37).
PITOT
STATIC
AIRCRAFT
STRUCTURE
PIVOT
TO POWER
CONTROL UNIT
Q FEEL UNIT
FIG. 6.37
A basic Q-feel unit consists of a diaphragm with static pressure acting on one side and pitot
pressure on the other, with the difference between the two being dynamic pressure. The unit is
also arranged so that movement of the flight deck controls in either direction deflects the
diaphragm against pitot pressure (Fig. 6.38).
FIG. 6.38
If the dynamic pressure increases due to an increase in airspeed (IAS), the forces required to
move the flight deck controls would similarly increase. Conversely, an airspeed reduction causes
the load on the flight deck controls to decrease. This system therefore ensures that the stick
forces vary during flight in proportion to varying loads acting on the control surfaces. To obtain the
necessary feedback forces from dynamic pressure alone, these units tend to be very large.
Alternatively, the sensing pressures can be used to operate a piston subjected to hydraulic
pressure, thereby providing hydraulic Q-feel (Fig. 6.39).
6-20
Flying Controls
Chapter 6
FIG. 6.39
Hydraulic pressure supplies artificial feel in this system, so the unit itself can be much smaller.
Like the spring feel unit, the Q-feel unit also incorporates a self-centring mechanism that operates
when the pilot releases the flight deck controls. This type of unit is typically used in the rudder and
elevator control systems on most transport category aircraft, but is usually combined with a spring
feel unit (Fig. 6.40).
Spring Feel
Unit
FIG. 6.40
Two feel units normally act together to resist movement of the flight deck controls from their
neutral position.
6-21
Chapter 6
Flying Controls
FIG. 6.41
a
F1 a
TAB
CONTROL SURFACE
F2 b
F1
FIG. 6.42
In this condition, the control surface remains in its set position without any effort from the pilot (i.e.
the control forces are zero).
6-22
Flying Controls
Chapter 6
Moveable trim tabs are normally fitted on elevator and rudder control surfaces. In each case, the
tabs connect via a cable and gearing system to trim wheels in the cockpit. For example, consider
the operation of an elevator trim tab (Fig. 6.43).
TRIM TAB
FLAP LEVER
TRIM WHEEL
DOWN
UP
FIG. 6.43
In this system, the trim wheel is mounted to give movement about a lateral axis and rotates in the
natural sense to give the required pitch trim change. A forward movement of the trim wheel
produces a nose-down trim change and vice versa (Fig. 6.44).
TRIM TAB
MOVEMENT OF
TRIM WHEEL
MOVEMENT OF
TRIM WHEEL
ELEVATOR
NOSE-UP TRIM
NOSE-DOWN TRIM
FIG. 6.44
Notice that the trim tab moves in the opposite direction to the control surface. In practice, to trim
the aircraft in a given pitch attitude, first move the elevator to produce the desired pitch. Then
eliminate the force necessary to maintain this pitch by rotating the trim wheel. Turn it in the same
direction as the control column pressure until the stick loading reduces to zero.
Note: Trim tab deflection reduces the maximum available elevator authority.
6-23
Chapter 6
Flying Controls
Rudder trim works like elevator trim, except that the trim wheel is mounted so that it rotates about
a normal axis. For example, to provide nose right trim, the trim wheel rotates in the clockwise
direction and vice versa (Fig. 6.45).
TRIM TAB
MOVEMENT OF
RUDDER TRIM
WHEEL
MOVEMENT OF
RUDDER TRIM
WHEEL
RUDDER
NOSE RIGHT TRIM
FIG. 6.45
On some light aircraft, the trim tabs are moved electrically instead of mechanically. In this case,
the switch is normally spring-loaded to the central off position and in order to reduce the stick
forces to zero, the switch operates in a natural sense. When the switch is released it returns to
the OFF position.
Note: Irrespective of the positioning method, the tab remains in the same fixed position
relative to the control surface until it is necessary to re-trim the aircraft in a new attitude.
Fixed trim tabs operate completely independently of the pilot and can only be adjusted on the
ground (Fig. 6.46).
FIXED TAB
ADJUSTABLE
ON THE GROUND
TO CONTROL COLUMN
FIG. 6.46
Their actual setting is determined by flight tests, and when they are set to give no resultant stick
forces, the trailing position of the control surfaces is governed by the actual deflection of the tab.
On light aircraft, this type of tab is normally fitted on ailerons to make wing level flight more easily
achievable without having to maintain a constant stick force (i.e. to correct for a wing-low
tendency).
6-24
Flying Controls
Chapter 6
On some aircraft, combined trim/anti-balance tabs provide a dual function, operating either as
a trim tab or as an anti-balance tab, for example, on an all-moving tailplane (Fig. 6.47).
FIG. 6.47
When providing elevator trim, the tab is positioned using the trim wheel to achieve zero stick
force.
SPRING STRUT
TRIM ACTUATOR
TO CONTROL
SERVO VALVE
FIG. 6.48
Operating a trim actuator alters the effective length of the input lever to the servo valve, thereby
making a selection, and moving the control surface to a new neutral position. Between the trim
actuator and the control input linkage, a spring strut is used as a safety device. This normally
operates as a fixed member, but should the servo valve seize, a spring inside the unit
compresses or extends to protect the valve from further damage.
6-25
Chapter 6
Flying Controls
On most transport category aircraft, aileron and rudder trim is applied through the movement of
electrically operated trim switches. These switches are normally on the centre pedestal, and are
spring-loaded to their central Off position (Fig. 6.49).
RUDDER TRIM
INDICATOR
AILERON TRIM
6 4 2 0 2 4 6
15
10
NOSE LEFT
RUDDER TRIM
5 0
5 10 15
UNITS
NOSE RIGHT
AILERON
AILERON
TRIM
SWITCHES
LEFT
WING
DOWN
RIGHT
WING
DOWN
CONTROL
COLUMN
NOSE
LEFT
R
U
D
D
E
R
NOSE
RIGHT
FIG. 6.49
To provide aileron trim, move both switches simultaneously in the same direction to provide
system integrity. The amounts of aileron and rudder trim applied are usually displayed on
dedicated trim indicators. The rudder trim indicator is typically on the centre pedestal, while
aileron trim indicators are located on each control column.
The Variable Incidence Horizontal Stabiliser provides pitch trim on most transport category
aircraft. Varying the angle of incidence has the same effect as moving the elevator, but is
aerodynamically more efficient, particularly at high airspeeds, and can provide a considerable trim
range. An actuator near the leading edge varies the angle of incidence of the stabiliser. This
normally operates in conjunction with the elevator to produce the least trim drag (Fig. 6.50).
Tailplane
Elevator
Actuator
Control
Input
Actuator
FIG. 6.50
6-26
Flying Controls
Chapter 6
An electrically signalled hydraulic trim motor normally moves the leading edge of the stabiliser up
or down in flight. This is in response to signals primarily from the electrical trim switches on the
control column or signals from the autopilot pitch channel (Fig. 6.51).
AUTO
PILOT
AP
ENGAGED
TRIM
COMPUTER 1
TRIM
COMPUTER 2
ELECTRIC
PITCH TRIM
SERVO- M
MOTORS
VALVE
VALVE
VALVE
MOTOR
MOTOR
MOTOR
G
ELECTRICAL PITCH
TRIM
B
MANUAL
PITCH
TRIM
LEGEND
SCREWJACK
MECHANICAL LINKAGE
ELECTRICAL LINKAGE
FIG. 6.51
TRIMMABLE
HORIZONTAL
STABILISER
Like the aileron trim system, the simultaneous movement of two switches, located on each control
wheel, provides pitch trim. This provides system integrity and prevents pitch trim runaway. The
rate of trim varies and is controlled by trim control modules. The trim rate decreases with
increasing IAS.
6-27
Chapter 6
Flying Controls
In the event of a malfunction in any of these methods, pitch trim is alternatively provided by
manually positioning the hydraulic servo valves via a series of control cables and pulleys. Inputs
are normally provided by trim wheels on either side of the centre console on the flight deck,
which rotate together (Fig. 6.52).
STAB
TRIM
STAB
TRIM
A/C
NOSE
DOWN
A/C
NOSE
DOWN
10
10
15
A/C 15
NOSE
UP
A/C
NOSE UP
STABILISER TRIM
INDICATOR
M
ELECTRICAL PITCH TRIM
SERVO MOTORS
STABILISER
TRIM WHEEL
STABILISER
TRIM
MECHANISM
M
SCREW
JACK
STABILISER
FIG. 6.52
The amount of stabiliser trim is indicated by a pointer, which forms an integral part of the trim
wheel. The pointer moves up and down a fixed scale adjacent to it, and a green band indicates
the normal trim settings for take off. The wheels also move in response to electrical input, by way
of feedback through the mechanical linkage.
6-28
Flying Controls
Chapter 6
Some aircraft, such as the Boeing 757, have stabiliser trim levers on the centre console. Like
trim wheels, these pass manual pitch trim control signals to the pitch trim servo motors
(Fig. 6.53).
STABILISER TRIM
LEVERS
M
A/C NOS A/C NOS
E U
E U
P
P
M
STABILISER
TRIM
MECHANISM
SCREW
JACK
STABILISER
FIG. 6.53
To vary the amount of pitch trim, move both levers simultaneously in the same direction. This
increases the overall system integrity, and prevents the possibility of pitch trim runaway. Signals
from the trim levers override all other trim inputs in this system. Unlike trim wheels, the levers do
not move in response to electrical trim inputs. On aircraft with trim levers, all stabiliser trim
indications are displayed on two dedicated indicators, normally on the centre pedestal (Fig. 6.54).
6-29
Chapter 6
Flying Controls
STABILISER
TRIM
LEVERS
R
I
A
B
STAB TRIM
A/C
NOSE
0
DN
2
S
T
4
A
6
B
T
R
I
M
O
F
A/C F
NOSE
UP
FLAP
STAB TRIM
A/C
NOSE
0
DN
2
S
T
4
A
6
B
8
T
10
R
I
12
M O
F 14
A/C F
NOSE
UP
APL NOSE UP
APL NOSE UP
8
10
12
14
FIG. 6.54
SPOILERS
Spoilers are flap type control surfaces, normally located on the upper surface of the wing, just in
front of the trailing edge flaps (Fig. 6.55).
PANELS SHOWN
RAISED
FIG. 6.55
6-30
Flying Controls
Chapter 6
These surfaces individually hinge at their leading edges and are actuated by hydraulic power
supplied by dedicated power control units. As their name implies, the main purpose of the
surfaces is to disturb the smooth airflow over the top of the wing, thereby reducing the wings
lifting capability. When fully extended, they considerably increase aircraft drag. The spoilers are
positioned so that aircraft pitch trim is not adversely affected by their deployment, and the
surfaces are extended in various sequences depending upon the mode of flight.
Roll Spoilers operate asymmetrically in flight whenever the control wheel rotates, assisting the
ailerons in providing roll control, particularly at high airspeeds. When this occurs, the appropriate
spoiler servo valves are signalled by way of the aileron operating system and the requisite
surfaces are deflected upward in proportion to the roll input. During a roll, the spoilers on the
lowering wing deflect upward, decreasing the wings overall lifting capability and increasing the
aircrafts roll rate, whilst the spoilers on the opposite wing remain retracted (Fig. 6.56).
UP GOING WING SPOILERS
REMAIN RETRACTED
AILERON
SPOILERS RAISED
ON LOWERING WING
PROPORTIONAL TO
ROLL INPUT
4
AILERON
3
2
1
SPOILER
RETRACTED
FIG. 6.56
The innermost spoiler on the lowering wing also remains retracted to prevent tail buffet and
degraded pitch control.
6-31
Chapter 6
Flying Controls
On aircraft fitted with two sets of ailerons, (inboard and outboard), as the airspeed increases the
aerodynamic loads on the ailerons tend to twist the wing at the tips, where it is more flexible. To
overcome this tendency, some aircraft use the technique of locking the outboard ailerons in the
faired or neutral position, and use an inboard aileron/spoiler combination above flap retraction
speeds to provide the necessary roll control (Fig. 6.57).
INBOARD
AILERON
OUTBOARD AILERON
FIG. 6.57
Flight Spoilers operate symmetrically about the aircrafts longitudinal axis to slow an aircraft
down in flight (speed brakes). Their deflection angle is determined from the flight deck in
response to movements of a speedbrake lever, typically located on the centre pedestal on
transport category aircraft (Fig. 6.58).
SPEEDBRAKE
LEVER
FIG. 6.58
6-32
Flying Controls
Chapter 6
With all spoilers fully retracted the lever is held in its down (DETENT) position to prevent
inadvertent operation (Fig. 6.59).
DOWN
ARMED
FLIGHT
DETENT
UP
FIG. 6.59
Movement of the lever from this position signals the flight spoilers to rise, and they reach their
maximum attainable in-flight deflection angles with the lever in its flight detent position (Fig. 6.60).
DOWN
ARM
FLIGHT
DETENT
UP
SPEEDBRAKE
LEVER
40
10 9
20
8
7
20
5
6
SPOILERS
RETRACTED
40
3
SPOILERS
RETRACTED
FIG. 6.60
Movement of the speed brake lever for in-flight use is normally limited by a solenoid-actuated
stop.
6-33
Chapter 6
Flying Controls
In this mode, the outboard spoilers usually remain retracted to prevent the aircraft pitching noseup, whilst the innermost spoilers deflect by a lesser amount to prevent tail buffet. There are
sometimes occasions in flight when both airbrake and roll commands occur together. On these
occasions, both inputs feed into a complex box, containing a mixture of levers, bell cranks, and
quadrants, called a spoiler mixer unit (Fig. 6.61).
LEFT ROLL
INPUT
SPEEDBRAKE
LEVER
SPEED
BRAKE
DOWN
ARMED
FLIGHT
DETENT
UP
SPOILER
MIXER
UNIT
SIGNALS TO
SPOILER ACTUATORS
FIG. 6.61
This unit sums both inputs and gives a revised output, which in turn varies the movement of the
spoilers during an aileron input depending upon the amount of speedbrake selected (Fig. 6.62).
RIGHT SPOILERS
PARTIALLY RAISED
SPOILERS
RETRACTED
GREATER INPUT
TO LEFT SPOILERS
FIG. 6.62
Spoilers in this role can normally be used at any airspeed, but at increasingly higher airspeeds
they are forced down (blowback) progressively.
6-34
Flying Controls
Chapter 6
The Ground Spoilers (lift dump) mode causes the spoiler panels on both wings to automatically
rise to their full extension after touchdown, increasing an aircrafts rate of retardation when certain
conditions are fulfilled (Fig. 6.63).
12
11 10
FIG. 6.63
As the spoilers deploy the speedbrake lever automatically moves to the up position in line with
their movement (Fig. 6.64).
SPEED
BRAKE
DOWN
DOWN
ARMED
ARMED
SPEED
BRAKE
FLIGHT
DETENT
FLIGHT
DETENT
UP
UP
FIG. 6.64
6-35
Chapter 6
Flying Controls
The maximum deflection angles are greater in the ground mode than the flight mode. With the
spoilers in their fully extended position, approximately 80% of the wing/flap lift is destroyed and
the aerodynamic drag of the aircraft more than doubles. The subsequent loss of lift causes the
aircraft to fully settle on the main undercarriage and increases its potential braking force. The
flaps remain in their landing configuration because of the drag benefits on deceleration. Should
any of the thrust levers be advanced the speedbrake lever automatically moves to the down
position and the spoilers retract.
6-36
AILERON
FIG. 7.1
These surfaces, known as trailing edge flaps, are lowered in unison, primarily to increase the
wings lifting capability at any given angle of attack (Fig. 7.2). This allows the development of the
lift required to support a given weight at a lower airspeed.
Lift Curve
with Flap
Deflection
CL
Basic Lift
Curve
Increased Lift at
Constant Angle of Attack
FIG. 7.2
Principles Of Flight (Rev Q407)
7-1
Chapter 7
Lift Augmentation
Flap
Deflected
Flap
Neutral
Angle of Attack ()
FIG. 7.3
In some instances, the trailing edge flaps may also increase the wings surface area. Extending
the trailing edge flaps alters the pressure distribution around the wing.
This not only alters the pressure distribution over the rear of the wing, where the flap is situated,
but over the front of the wing as well. The majority of the additional lift is developed over the rear
of the wing, and results in the centre of pressure moving aft as the flaps are lowered (Fig. 7.5).
L
L
CoG
CoG
MOMENT ARM
FIG. 7.5
7-2
Lift Augmentation
Chapter 7
This also alters the lift/weight couple and produces a nose down pitching moment, which requires
correction whenever changing the flap setting. Any flap deflection increases the effective camber
of the wing and affects the coefficient of drag (Fig. 7.6).
CD
Small Flap Deflection
Large Flap Deflection
Clean Wing
Angle of Attack ()
FIG. 7.6
Flap
Deflected
FIG. 7.7
This flap increases the wings effective camber and alters the curvature of the wings upper
surface. The increase in curvature causes earlier separation of the boundary layer and increases
form drag.
The split flap is a plate which is hinged to, and set into the lower surface of the wing trailing edge
(Fig. 7.8).
Flap
Neutral
Flap
Deflected
FIG. 7.8
7-3
Chapter 7
Lift Augmentation
Deflecting the split flap increases the wings effective camber but the curvature of the upper
surface remains unchanged. This produces a large turbulent wake at low angles of attack and
hence drag, but provides better lift performance than the plain flap at high angles of attack. This is
because the less curved upper surface delays the separation of the boundary layer.
The slotted flap is similar to the plain flap except that when deflected, a slot forms between the
flap and main wing (Fig. 7.9).
Flap
Neutral
High Pressure
Air
Flap
Deflected
FIG. 7.9
This allows high pressure air below the wing to flow through the slot and re-energise the
boundary layer over the upper surface of the flap. The combination of variable geometry and
boundary layer control thus increases the wings lift performance beyond that of the plain flap at
all angles of attack.
The fowler flap arrangement is similar to the slotted flap, except the flap first moves aft along
rollers in a track before being deflected downward (Fig. 7.10).
Flap
Neutral
Flap
Deflected
FIG. 7.10
The rearward movement of the flap increases the wing chord and the overall effective wing area.
This enhances the wings lift capability without any flap deflection, but the resulting reduction in
the thickness-chord ratio causes the wing to stall at a lower angle of attack. The slot effect and
the wings reduced thickness-chord ratio results in a smaller increase in drag compared to the
other types of flaps.
7-4
Lift Augmentation
Chapter 7
CL
(CL/CD)MAX
Fowler Flap
Slotted Flap
Split Flap
Plain Flap
Bare
Wing
CD
FIG. 7.11
Drawing tangents to the curves makes it possible to compare the lift/drag ratio, and hence the
efficiencies of each type of flap. The maximum lift/drag ratio in each case occurs where the line
touches the curve, and this shows that the Fowler flap produces the largest amount of lift for the
least amount of drag (i.e. it has the best lift/drag ratio). The gradient of the tangents also shows
how efficient each type of flap is; the steeper the gradient, the more efficient the flap.
7-5
Chapter 7
Lift Augmentation
EFFECTIVE
CHORD LINE
MORE NOSE UP
ATTITUDE
FLATTER
ATTITUDE
A
RELATIVE AIRFLOW
HIGHER
STALLING ANGLE
LOWER
STALLING ANGLE
FIG. 7.12
This is because the chord line with the flap deflected changes relative to the wing region. This is
known as the effective chord line. In practice, however, the stalling angle is always referenced to
the chord line of the original clean wing, which acts as a datum line. Thus, the greater the flap
deflection, the steeper the effective chord line, and the lower the stalling angle of attack. The wing
actually stalls when the angle between the effective chord line and the relative airflow (i.e. the
effective angle of attack) reaches its normal stalling value of 15 or 16 in the case of light aircraft.
40
KT
50
KT
FIG. 7.13
7-6
Lift Augmentation
Chapter 7
The stalling speed depends on the amount of flap deflection. The greater the deflection, the lower
the stalling speed due to the variation in the maximum coefficient of lift (Fig. 7.14).
Large Flap
Deflection
Coefficient
of Lift
Small Flap
Deflection
Clean Wing
Angle of
Attack
FIG. 7.14
FLAP LEVER
FIG. 7.15
7-7
Chapter 7
Lift Augmentation
The flap lever raises or lowers the flaps, operating in a similar manner to the handbrake on a car
(Fig. 7.16).
FLAP
LEVER
RIGHT
WING FLAP
FLAP LEVER
LEFT
WING FLAP
FLAP SETTING
FIG.7.16
To extend the flaps, pull the lever upward through a series of ratchet settings, each setting
relating to a fixed angular deflection, for example, 10, 25, and 40. The first two settings are
normally referred to as take-off settings, and the latter as the landing setting, which is clearly
indicated on the housing. To retract the flaps, push in the button on the end of the lever and move
the lever downward. In the case of an electrically operated flap system, the flap setting is
determined by the position of a flap selector switch, normally positioned on the instrument panel.
Moving the switch to the desired flap setting operates an electric motor until the pre-selected flap
position is reached, and a micro-switch then cuts off the current supply to the motor. The actual
flap position is usually displayed on an indicator positioned beside the switch.
FLAPLESS TAKE-OFF
FLAPPED TAKE-OFF
FIG. 7.17
Larger amounts of flap cause a significant increase in drag, which greatly reduces the
acceleration and increases the take-off run. The reduced stalling angle of attack and increased
drag associated with flaps also reduces the rate and angle of climb.
7-8
Lift Augmentation
Chapter 7
O O
N I
N G
FIG. 7.18
This effect is only short-lived because the subsequent increase in drag associated with the flap
deflection quickly slows the aircraft down and the excess lift reduces. To prevent ballooning,
lower the aircraft's nose when the flaps are deflected. Once the aircraft has returned to its former
equilibrium state, the aircraft naturally settles in a nose-down pitch attitude due to the rearward
movement of the centre of pressure. This ultimately provides improved visibility, which is
especially important during the approach and landing phases of flight (Fig. 7.19).
ASI
ASI
KT
KT
65
85
FIG. 7.19
7-9
Chapter 7
Lift Augmentation
In the landing configuration, the flaps are normally fully extended to achieve the greatest increase
in the coefficient of lift at any given angle of attack. This results in a significant reduction in the
stall speed, and hence landing speed. The landing speed in this configuration must, however, be
at least 1.3 times the stalling speed (1.3 VS0) to provide adequate controllability. In large
aeroplanes, which use a stall reference speed (VSR), the landing speed must be 1.23 VSR0 It is
also important that the flaps not be lowered at an airspeed greater than the maximum flaps
extended speed (VFE). If the flaps extend at different rates, flap asymmetry occurs, setting up a
rolling moment.
The increase in drag associated with flap deflection also requires an increased power setting in
order to maintain a given airspeed and attitude, or a steady rate of descent. The reduction in the
lift-drag ratio with flaps lowered also affects an aircraft's glide performance.
FLAPS RETRACTED
AIRFLOW
LEADING EDGE
FLAPS
TRAILING EDGE
FLAPS
FORWARD
FIG. 7.20
All aircraft are fitted with trailing edge flaps, but most transport category aircraft with sweptback
planform wings are additionally equipped with leading edge high lift devices to further enhance
the wings lifting capability at low airspeeds. The devices most commonly used are flaps, slats,
and slots. For example, the Boeing 757 has trailing edge flaps and leading edge slats (Fig. 7.21).
7-10
Lift Augmentation
Chapter 7
LEADING EDGE
HIGH LIFT DEVICES
TRAILING EDGE
FLAPS
FIG. 7.21
Other types of aircraft are alternatively fitted with leading edge flaps, while others employ a
combination of leading edge flaps and leading edge slats. The manufacturer determines the
actual configuration. Trailing edge flaps normally fitted at inboard and outboard positions along
the wing. These are normally slotted fowler flaps, configured during the landing and take-off
phases of flight to provide the requisite lift/drag characteristics (Fig. 7.22).
SLOTS
LANDING POSITION
FIG. 7.22
For take-off purposes, the trailing edge flaps are normally set to provide the best lift/drag ratio
other than that associated with a clean wing, by increasing only the wings surface area. When
the flaps are set to the landing configuration, they not only increase the maximum coefficient of
lift, but also increase drag and help to retard the aircraft.
7-11
Chapter 7
Lift Augmentation
Leading Edge Slats are movable control surfaces attached to the leading edges of the wing
along the complete span (Fig. 7.23).
FIXED LEADING EDGE
PANELS & FAIRINGS
LEADING
EDGE SLATS
FIG. 7.23
When the slat is closed (retracted) it forms the leading edge of the wing, but in the open position
(extended) a slot is created between the slat and the upper surface of the wings leading edge
(Fig. 7.24).
SLAT EXTENDED
SLOT
AIR THROUGH
SLOT RE-ENERGIZES
BOUNDARY LAYER
FIG. 7.24
This allows air to pass through the slot from the high pressure region below the wing into the lowpressure region above the wing, thereby accelerating the flow by the venturi effect and reenergising the boundary layer. This delays its separation from the upper surface, substantially
increasing the wings overall lifting capability (CL) by delaying the stall until a higher angle of
attack (Fig. 7.25).
7-12
Lift Augmentation
Chapter 7
2.0
Coefficient of Lift
(CL)
Wing plus
Slats
1.5
Plain
Wing
1.0
0.5
10 15 20 25
Angle of Attack
30
FIG. 7.25
The subsequent increase in the maximum coefficient of lift, like other high lift devices, lowers the
aircrafts stalling speed. The deployment of slats may increase the maximum coefficient of lift by
more than 70%, and the stalling angle of attack from 15 to 22. When operating at high angles of
attack, the slat has no significant effect on the wings camber, but affects the pressure distribution
over the upper surface of the wing (Fig. 7.26).
NO SLAT
WITH SLAT
FIG. 7.26
7-13
Chapter 7
Lift Augmentation
This produces a more gradual pressure gradient, and even at moderate angles of attack, enables
the boundary layer to penetrate almost the full chord of the wing before separation takes place.
This results in a stronger pressure distribution than that obtainable from a wing without slats. The
deployment of the slats also affects the airflow around the wing (Fig. 7.27).
FIG. 7.27
The slats are normally arranged in sections along the leading edge, so the combined effect of the
airflow through each slot reduces the overall spanwise flow of the boundary layer and helps
alleviate the tendency for wing-tip stalling on sweptback planform wings.
The deployment of slats is normally manually controlled from the flight deck in conjunction with
the trailing edge flaps. On some aircraft, the slats move from the take-off position to the landing
position automatically whenever the stall warning system activates. The slats then return to their
former set position when the warning cancels.
Leading Edge Flaps improve the wings lifting capability at low airspeeds in a similar manner to
that of trailing edge flaps by principally increasing the wings camber. These devices are
comparable to slats in that they produce approximately the same increase in the maximum
coefficient of lift, although this occurs at a slightly lower stalling angle of attack (Fig. 7.28).
7-14
Lift Augmentation
Chapter 7
With Leading
Edge Flap
Coefficient of Lift
(CL)
Clean Wing
Angle of Attack
FIG. 7.28
The lift curve differs slightly from that associated with slats due to the additional camber effect.
These devices are particularly beneficial on wings of high speed section (thin with little camber) to
improve their otherwise poor low-speed handling characteristics. This is because the sharp
leading edge associated with this type of wing is difficult for the air to negotiate, and stall
consequently occurs at moderate angles of attack. The main types are:
Drooped Leading Edge Flaps (Droop Snoot) normally cover the complete span, being drooped
at high angles of attack, and retracted at low angles of attack. This provides the required leading
edge profile (Fig. 7.29).
Retracted
Extended
Leading Edge
Flap
FIG. 7.29
They extend via a jackscrew arrangement and pivot about a hinge on the lower wing surface
(Fig. 7.30).
HINGE
FIG. 7.30
7-15
Chapter 7
Lift Augmentation
Krueger Flaps fitted on the inboard leading edge section and are similar to drooped leading edge
flaps, except that when they are retracted they form part of the under surface of the wing. When
extended they hinge downward and forward (Fig. 7.31).
KRUEGER FLAP
FIG. 7.31
They are extended by a screwjack arrangement to produce a well-rounded leading edge (Fig.
7.32).
FIG. 7.32
7-16
Lift Augmentation
Chapter 7
MORE NOSE-UP
PITCH ATTITUDE
EFFECTIVE
CHORDLINE
+
UNFLAPPED STALLING
ANGLE OF ATTACK
RELATIVE AIRFLOW
INCREASE IN ACTUAL
STALLING ANGLE
OF ATTACK
FIG. 7.33
Since the angle of attack, by definition, references the original chord line of an aircraft wing, when
the leading edge flaps deflect, the aircraft stalls with a more nose-up pitch attitude and thus a
higher stalling angle of attack.
FLAP
UP
FLAP LEVER
FLAP
FLAP
15
20
25
30
FLAP
DOWN
FIG. 7.34
7-17
Chapter 7
Lift Augmentation
In operation, the flap lever moves in a flap quadrant in which a series of detents mark the various
flap settings. Altering the flap setting requires physically lifting the control lever to move it to its
next designated detent. The flap lever then forwards a signal to the trailing edge power drive
unit (PDU), which hydro-mechanically alters the position of the flaps (Fig. 7.35).
FLAP LEVER
ALTERNATE
FLAP CONTROLS
DETENT
FROM
HYDRAULIC
SYSTEM
LE POWER
DRIVE UNIT
TE POWER
DRIVE UNIT
BYPASS
VALVE
FIG. 7.35
An alternative electrical system allows operation of the high lift devices using electric motors
should the hydraulic system fail. As the flaps move toward their selected position, a signal goes to
a separate power drive unit, which hydro-mechanically drives the leading edge high lift devices to
their selected position. On some aircraft, the leading edge high lift devices are driven
pneumatically rather than hydraulically to their selected position in normal operation.
7-18
Lift Augmentation
Chapter 7
The leading edge high lift devices normally have only two extended settings (take-off and
landing). They extend first and retract last, whereas the trailing edge flaps have various take-off
settings, but normally only one landing setting (fully extended). The aircraft can land with any flap
setting, but it is important to remember that the flap position also determines the landing speed
and distance. The flap quadrant is additionally fitted with gates (baulks) at specified flap settings
(Fig. 7.36).
FLAP
UP
FLAP LEVER
FLAP
5
GATES
15
20
25
30
FLAP
DOWN
FIG. 7.36
These gates are designed to prevent inadvertent rearward movement of the flap lever if specified
flight and aircraft conditions do not exist. The first gate is normally set at a point which allows the
airspeed to build up sufficiently before the leading edge high lift devices are fully retracted,
whereas the second gate normally marks the flap setting required for go-around with all engines
operating.
7-19
Chapter 7
Lift Augmentation
Flap Load Relief is an automatic function incorporated in most systems to partially retract the
flaps if they are fully lowered at high airspeeds, as serious structural damage may occur. If the
airspeed subsequently reduces, the flaps automatically return to their former set position,
commonly called blow back. The maximum flap extension speeds appear on the flight deck
placard (Fig. 7.37).
FIG. 7.37
7-20
INTRODUCTION
As the air flows around the aerofoil, both the velocity and static pressure vary with distance from
the leading edge. The pressure distribution over the upper surface greatly affects the flow
characteristics of the boundary layer, eventually causing it to break away or separate from the
surface. When the upper surface of an aerofoil is predominantly covered in separated airflow the
aerofoil is stalled. This occurs upon reaching the stalling angle of attack. At this point, the wing
can no longer produce sufficient lift to support the weight of the aircraft, and the separated airflow
results in a dramatic rise in form drag. It is desirable for any wing to stall at the root first, but this is
not always possible, and principally depends on a wing's cross-section and planform area.
SEPARATED AIRFLOW
The static pressure varies over the upper surface of a typical aerofoil section. Close to the leading
edge the airflow comes to rest and the static pressure reaches a maximum value. This is the
stagnation point and is where the boundary layer first forms (Fig. 8.1).
AIRFLOW ACCELERATING
AIRFLOW DECELERATING
PRESSURE DECREASING
LAMINAR
BOUNDARY
LAYER
TRANSITION POINT
TURBULENT
BOUNDARY
LAYER
PRESSURE INCREASING
SEPARATION POINT
WAKE
STAGNATION POINT
FIG. 8.1
8-1
Chapter 8
Stalling
Proceeding rearward from this point, the static pressure decreases forming a positive pressure
gradient (i.e. positive to negative). This continues until the air reaches its point of minimum
pressure. Beyond this point, the pressure increases, forming an adverse pressure gradient (i.e.
negative to positive) (Fig. 8.2).
Positive Pressure
Gradient
Adverse Pressure
Gradient
FIG. 8.2
The pressure gradient opposes the flow of the boundary layer and impedes its progress rearward.
A reduction in the velocity of flow near the surface also occurs in this region and is highlighted
using velocity profiles (Fig. 8.3).
Airflow
Reversed
Flow
Separation
Point
FIG. 8.3
In the presence of a strong adverse gradient, the boundary layer eventually separates from the
surface (separation point). The airflow behind this point is turbulent in nature and effectively
destroys the lift capability of the aerofoil in this region, as the energy possessed by the boundary
layer is too low to overcome the adverse pressure gradient (Fig. 8.4).
Separation Point
Airflow
Wake
Stagnation Point
FIG. 8.4
8-2
Stalling
Chapter 8
The absence of the boundary layer behind the separation point allows some air to flow forward
toward the leading edge, termed reverse flow. With increasing angles of attack, the adverse
pressure gradient increases in magnitude and the separation point moves closer to the
leading edge. This causes a large turbulent wake to form behind the wing, resulting in a
reduction in lift and an increase in drag.
When the separation point occurs so far forward that the majority of the aerofoil is covered in
turbulent airflow, the wing is stalled. There is a drastic reduction in the lift generated by the
aerofoil and it is no longer possible to maintain steady level flight (Fig. 8.5).
STALLING ANGLE
OF ATTACK
L
CL
CL
CL
CL
-4
ANGLE OF ATTACK
LEVEL FLIGHT
NOT POSSIBLE
IN THIS AREA
10
STALLED
15
FAST
SLOW
ANGLES EXAGGERATED
FOR ILLUSTRATION
FIG. 8.5
8-3
Chapter 8
Stalling
CL MAX
15
Usual
Flight
Angles
CL
Usual
Flight
Angles
16
CD
Stalling
Angle
Stalling
Angle
16
Angle of Attack
16
Angle of Attack
FIG. 8.6
Most light aircraft tend to stall when the wing reaches an angle of attack of approximately 15 - 16
in any phase of flight, regardless of the airspeed, provided that the aircraft configuration is not
altered (Fig. 8.7).
IAS
50
KT
DESCENDING
IAS
50
KT
IAS
80
KT
IAS
50
KT
16AoA
16 AoA
CLIMBING
IAS
70
KT
60 BANK
STEEP TURN
16
FIG. 8.7
8-4
Stalling
Chapter 8
CL
V
S
= coefficient of lift
= air density (kg/m3)
= airspeed (m/s)
= wing planform area (m2 )
If the air density and wing planform area remain constant at a given altitude, then the lift formula
can be simplified as follows:
Lift is a function of CL x (IAS)2
At the stalling angle of attack, the coefficient of lift reaches a maximum value so that:
Lift is a function of CL MAX x (IAS STALL)2
Since CL MAX is a constant value for a given aerofoil section, the amount of lift produced at the stall
is directly proportional to the indicated stalling speed squared, so that:
Lift is proportional to (IAS STALL)2
The stalling speed depends on the amount of lift a wing needs to generate, as determined by the
following factors:
Weight
To maintain steady level flight requires sufficient lift to support the total weight of the
aircraft. A heavier aircraft requires greater lift and has an increased stalling speed
(Fig. 8.8).
L
L
IAS
70
KT
IAS
65
KT
16 AoA
16 AoA
GREATER
WEIGHT
W
W
FIG. 8.8
8-5
Chapter 8
Stalling
This relationship is true for any given angle of attack, provided that the maximum
coefficient of lift is not affected by airspeed. If the aircraft weight reduces by 10% the
stalling speed changes as follows:
New Weight
Original Weight
Flap
Deflected
Flap
Neutral
Angle of Attack ()
FIG 8.9
This alters the shape of a wing and increases its maximum coefficient of lift. Flaps
enhance the wing's overall lifting capability at any given angle of attack, and enable it to
support the same weight at a lower airspeed, reducing the stalling speed. Stalling with
flaps may also be accompanied by a wing drop. Pick up the wing by using the rudder, not
ailerons. Trying to raise a dropped wing using opposite aileron may have a reverse effect
when operating near the stall and the wing will drop more quickly.
8-6
Stalling
Chapter 8
Power
Until now, the assumption has been that the wings completely support the weight of an
aircraft. This remains the case when a piston engine is throttled back, but when power is
applied the resultant slipstream behind the propeller provides additional kinetic energy to
the airflow (Fig. 8.10).
SLIPSTREAM
FIG. 8.10
This delays the separation of the boundary layer from the upper surface of a wing and
results in the aircraft stalling at a lower indicated airspeed. Approaching the stalling angle
with power on, a component of thrust partially supports the weight of the aircraft. The
wings become slightly off-loaded, and produce less lift.
Approaching the power-on stall, the airflow increases over the tail section, increasing the
effectiveness of the rudder and elevator. The slipstream also generates greater lift from
the inner sections of the wing, but the outer sections may stall first. The ailerons become
ineffective and one wing may stall earlier, causing the wing to drop.
Manoeuvres
For an aircraft to carry out a manoeuvre the wings must generate more lift, causing the
stalling speed to increase (e.g. during a turn).
Wing Loading
This is a measure of the total aircraft weight supported per unit area of the wing. If two
aircraft are identical, except for their weights, then the heavier aircraft (i.e. higher wing
loading) has an increased stalling speed.
Wing Contamination
Any ice or snow on the wing causes the total aircraft weight to increase, and thus the
stalling speed.
8-7
Chapter 8
Stalling
FIG. 8.11
Known as pre-stall buffet, this normally takes place a few degrees before the stall. This buffeting
is usually felt through the control column and rudder pedals and provides adequate warning of an
impending stall. The reduction in lift at the stall also results in an aircraft sinking or losing altitude
at any given airspeed.
When the stalling angle of attack is reached, the pressure envelope over the upper surface of the
wing collapses and the centre of pressure moves rapidly rearward. This alters the wings pitching
moment, and in conjunction with the change in downwash acting on the tailplane, most aircraft
experience a nose-down pitching moment at the stall.
MOVING VANE
FIG. 8.12
8-8
Stalling
Chapter 8
Airflow holds down the vane at normal operating angles of attack, but just before the wing stalls,
movement of the stagnation point around the leading edge lifts the vane (Fig. 8.13).
AIR FLOW
LEADING
EDGE OF
WING
STAGNATION POINT
AIRFLOW
REVERSES
VANE POSITION
STAGNATION
POINT
NORMAL FLIGHT
AT THE STALL
FIG. 8.13
This closes a micro-switch and sounds a buzzer in the cockpit, giving warning of an impending
stall. On some light aircraft, a flashing red light on the instrument panel replaces the aural
warning. On aircraft cleared to operate in icing conditions, the sensing device is electrically
heated. Stall warning normally activates 5 to 10 kt above the stalling speed.
8-9
Chapter 8
Stalling
CL
CL
FIG 8.14
Fig. 8.14 shows typical lift curves for two different wing sections. A lift curve with a sharp peak
and a rapid drop after the stall indicates bad stalling characteristics, whereas a flatter peaked
curve depicts a more gentle approach to the stall. A predetermined stall pattern can be achieved
by carefully altering the wing section across the complete span. The designs that affect stall
behaviour are:
Thickness-chord ratio
Camber
Chordwise location of maximum thickness
Leading edge radius of curvature
The sharper the leading edge, the thinner the wing, or the further aft the positions of maximum
camber and thickness, the more sudden the stall.
1.5
TAPERED
C1
1.0
CL
0.5
ELLIPTICAL
RECTANGULAR
ROOT
SEMI-SPAN DISTANCE
TIP
FIG. 8.15
8-10
Stalling
Chapter 8
Fig. 8.15 shows how this ratio varies from the root to the tip and where the stall first commences.
On elliptical wings, the stall occurs simultaneously over the complete span. On rectangular wings,
it occurs at the wing root, and on tapered wings, it occurs at the wing tips. The stalling
characteristics of a wing vary depending on their planform as follows:
Elliptical Wing
On an elliptical wing, the local coefficients of lift remain constant over the complete semispan, so that all sections reach the stall at approximately the same angle of attack.
Therefore the stall progresses uniformly along the span (Fig. 8.16).
FIG. 8.16
An elliptical wing is capable of reaching high coefficients of lift prior to the stall, but there
is little advance warning of the complete stall. The ailerons may also lack effectiveness
when the wing is operating near the stall, leading to poor lateral control.
Rectangular Wing
On a rectangular wing, the stall commences at the wing root, where the highest local
coefficient of lift exists, spreading progressively outward toward the outboard regions
(Fig. 8.17).
FIG. 8.17
This produces a strong root stall tendency and gives adequate stall-warning buffet as the
separated air passes over the tail section of the aircraft. The loss of lift associated with
the stall is initially felt near the rolling axis of the aircraft, so even if one wing stalls before
the other, which is often the case, there is little tendency for the aircraft to roll.
Ailerons remain effective up to the stall, and the natural tendency of this type of wing
automatically places the aircraft in a nose-down pitch attitude as the centre of pressure
moves rapidly rearward. This is the most desirable response to the stall, but the wings
structural inefficiency limits its application to low cost, low speed, light aircraft.
8-11
Chapter 8
Stalling
Tapered Wing
On a highly tapered wing, the stall commences near the tips, before spreading inward
toward the inboard sections (Fig. 8.18).
Aileron
Stall
Progression
FIG. 8.18
This is an extremely undesirable stalling characteristic because the loss of lift at one wing
tip before the other may set up a considerable rolling moment, and may lead to
autorotation unless recovery action is taken promptly. Tip stalling also results in a loss of
lateral control since the ailerons are located in this region.
Sweptback Wing
On a sweptback wing, the stalling pattern resembles that of a tapered wing with the
maximum section coefficient of lift existing near the wing tips (Fig. 8.19).
Tip Stall Tendency of UnModified Wing
Section Coefficient
of Lift
Wing Coefficient of 10
Lift
0
Root
Tip
FIG 8.19
8-12
Stalling
Chapter 8
The stall begins at the tips, and then spreads inward toward the inboard sections
(Fig. 8.20).
FIG. 8.20
Like the tapered wing, this stalling pattern may also lead to large rolling moments and a
loss of lateral control. Since the wing tips are well aft of an aircraft's centre of gravity a
loss of lift in these regions also results in a severe nose-up pitching moment, known as
pitch-up. This further increases the angle of attack, rather than reducing it.
The normal recovery procedure from the stall is to reduce the angle of attack, since the
aircraft otherwise continues to move in the wrong direction. This may lead to an
extremely dangerous situation, especially if it occurs near the ground, during landing or
take-off, when the aircraft is operating at high angles of attack. Even well away from the
ground, this pitch-up generally results in an overall loss of pitch control, and can prove
extremely difficult to recover from, particularly at high airspeeds.
FIG. 8.21
8-13
Chapter 8
Stalling
At the same time, the downwash from the inner wing sections becomes concentrated on the
tailplane, giving a more severe nose-up pitch effect. The shift in the centre of pressure combined
with the increase in downwash acting on the tailplane produces an overall nose-up pitching
moment, pitch-up (Fig. 8.22).
FIG. 8.22
FIG. 8.23
This delays stalling at the wing tip, allowing the wing root to stall first. The amount of
washout is limited, because too much may result in the wing tip angle of attack becoming
less than the zero lift angle of attack when operating at high airspeeds. This causes the tip
to carry a download, reducing the wings overall efficiency.
8-14
Stalling
Chapter 8
FIG. 8.24
Vortex Generators
These are small upright aerofoils, normally fitted on the upper surface of the wing in front
of the ailerons (Fig. 8.25).
FIG. 8.25
Vortex generators re-energise the low-energy boundary layer at the wing tips by making it
more turbulent, thus alleviating tip stall.
8-15
Chapter 8
Stalling
FIG. 8.26
Fixing
Link
Airfoil
Pivot
FIG 8.27
8-16
Stalling
Chapter 8
The sensor measures the angle of attack as the aerofoil varies its position relative to the airflow.
When it exceeds a predetermined limit, an electrical signal operates the stall warning system.
This limit is usually 12 - 14 angle of attack, depending on the aircraft design. On some aircraft,
these sensors compute the rate of change of angle of attack, providing much earlier warning of
an impending stall. These devices are heated so that they remain operational throughout the
flight.
CONTROL
COLUMN
ECCENTRIC
WEIGHT
STICKSHAKER
MOTOR
FIG. 8.28
The devices are designed to activate at no less than VS (1.05 VS) and vibrate the control column
whenever the motor operates. Since the control columns are joined together, the activation of
either stick shaker causes both columns to shake. It is usual, however, for both stick shakers to
operate simultaneously, via stall warning computers whenever the aircraft angle of attack,
configuration, and airspeed are such that a stall condition is imminent. The system is energised in
flight at all times, but is deactivated on the ground via a weight on undercarriage safety sensor.
8-17
Chapter 8
Stalling
FIG. 8.29
Jet transport category aircraft with sweptback wings, a high T-tail configuration, and rear fuselage
mounted engines do not behave in this manner. They possess no pre-stall buffet warning,
because the separated airflow from the wing does not pass over the tail surface, and the
progressive stalling of the wing-tips causes the aircraft to pitch nose-up, thus intensifying the stall.
The whole of the tailplane is covered in disturbed air, compromising the pitching capability
required for recovery (Fig. 8.30).
8-18
Stalling
Chapter 8
FIG. 8.30
The resulting loss of lift and rapid increase in drag also intensify the aircraft's rate of sink. In this
condition, the aircraft is considered to be super-stalled. Since recovery is impossible, a stick
pusher is mandatory.
ACCELERATED OR G-STALL
Another possible type of stall is the accelerated or g-stall. This can occur during a manoeuvre
(e.g. turning) when the aircraft's wings are subject to high load factors (g). It occurs when either
wing reaches the stalling angle of attack, and like a conventional stall can occur at any airspeed.
Over tightening the turn (i.e. increasing load factor) may cause either wing to stall without prior
warning, causing the aircraft to flick in or out of the turn. On sweptback, planform wings, this may
also be accompanied by pitch-up. To recover from this condition, move the control column
forward to decrease the angle of attack.
8-19
Chapter 8
Stalling
SPINNING
Spinning is a condition of stalled flight in which an aircraft describes a downward spiral path, and
is normally the by-product of wing drop when operating near the stall (Fig. 8.31).
FIG. 8.31
The spin manoeuvre can be divided into the following three distinct phases:
The Incipient Spin (Autorotation)
If the wing drops at the stall, the resulting rolling action alters the direction of the relative
airflow on to the wing. It increases the angle of attack of the down-going wing and
reduces the angle of attack of the up-going wing (Fig. 8.32).
RAF
ROLL
COMPONENT
ROLL
COMPONENT ROLL
RAF
TAS
DECREASED STALL
ON RISING WING
RAF
TAS
ROLL
RAF
STALL
INCREASED
ON DOWN-GOING WING
FIG. 8.32
8-20
Stalling
Chapter 8
This alters each wings coefficient of lift and drag. The down-going wing becomes more
stalled, leading to a reduction in the coefficient of lift and an increase in the coefficient of
drag. Conversely, the up-going wing becomes less stalled, leading to an increase in the
coefficient of lift and a reduction in the coefficient of drag. The difference in lift between the
wings produces a rolling moment and the aircraft rolls in the direction of the down-going
wing. The yawing moment resulting from the large difference in drag between the downgoing and up-going wings further aids this (Fig. 8.33).
Stall
Roll to Downgoing Wing
CL
CL and CD
Up-going
Wing
CD
L R
Angle of Attack
FIG 8.33
These moments lead to autorotation; the aircraft continues to roll, a side-slip develops,
and the nose drops. Without corrective action, the rate of rotation steadily increases,
resulting in a fully developed spin. To recover from the incipient spin:
8-21
Chapter 8
Stalling
CENTRIFUGAL
FORCE
LIFT
SPIN
AXIS
WEIGHT
RELATIVE
AIRFLOW
FIG. 8.34
In a steady, stable spin, the forces are in equilibrium. Weight acts vertically downward
through the centre of gravity and is balanced by the aircraft drag; whilst lift acts at 90 to
the relative airflow toward the centre of the spin (centripetal force) and is balanced by
the centrifugal forces arising from the distribution of the aircraft's masses or inertias. The
moments about the centre of gravity determine the aircraft's state of equilibrium, as well
as the recovery characteristics. The main forces affecting this are the resultant of the
aerodynamic forces, lift and drag, and the centrifugal forces resulting from the
distribution of masses in the nose and tail of the aircraft (Fig. 8.35).
SPIN
AXIS
TOTAL RESULTANT
OF THE
AERODYNAMIC FORCES
CENTRIFUGAL
FORCE DUE
TO MASSES
IN TAIL
CENTRIFUGAL
FORCE DUE
TO MASSES
IN NOSE
COUPLE DUE
TO CENTRIFUGAL
FORCES
C of G
FIG. 8.35
8-22
Stalling
Chapter 8
The centrifugal forces produce a moment that tends to flatten the spin, whilst the
resultant aerodynamic force produces a moment that tends to steepen the spin. The
position of the centre of gravity consequently determines the final attitude of the aircraft
and its spinning characteristics. The position of the centre of gravity, even if it remains
within its permitted safety limits, affects the spin as follows:
Forward Centre of Gravity
This results in a steeper spin and a faster rate of sink. This makes the recovery
easier because the spin is less stable. If the centre of gravity is forward of its
permitted limits, it significantly reduces the likelihood of a spin occurring, and
instead results in an unusually steep spiral descent, during which the indicated
airspeed increases.
Aft Centre of Gravity
This results in a flatter spin and a lower rate of sink. This makes the recovery
more difficult, because the spin is more stable. If the centre of gravity is aft of its
permitted limits, it significantly reduces the likelihood of recovery from a settled
spin condition.
When an aircraft is in a steep spin rotation it is primarily in roll, whereas in a flat spin it is
primarily in yaw (Fig. 8.36).
STEEP SPIN
FLAT SPIN
YAW
ROLL
FIG. 8.36
8-23
Chapter 8
Stalling
Note: When pulling out of the ensuing dive, be careful to prevent an accelerated or g-stall, and
subsequent entry into another spin.
8-24
FIG. 9.1
Lift acts through the centre of pressure and weight acts through the centre of
gravity.
Thrust and drag act in opposite senses, parallel to the direction of flight, through
points which vary with aircraft attitude and design.
In steady level flight:
Lift = Weight and Thrust = Drag
9-1
Chapter 9
DRAG
THRUST
CENTRE OF GRAVITY
WEIGHT
FIG. 9.2
During flight, the forces alter their points of action, and are normally arranged so that the
lift/weight and thrust/drag forces are as follows:
Lift/Weight Couple
Lift acting behind weight causes a nose-down pitch moment and lift acting in front of
weight causes a nose-up pitch moment (Fig. 9.3).
LIFT
LIFT
NOSE
UP
NOSE
DOWN
CoG
CoP
CoP
CoG
WEIGHT
WEIGHT
FIG. 9.3
Thrust/Drag Couple
Thrust acting below drag causes a nose-up pitch moment and thrust acting above drag
causes a nose-down pitch moment (Fig. 9.4).
NOSE
UP
THRUST
DRAG
THRUST
NOSE
DOWN
DRAG
FIG. 9.4
9-2
Chapter 9
To prevent the aircraft from rotating the forces can be distributed as shown in Fig. 9.5.
Lift
Lift
Thrust
Drag
Thrust
Drag
Weight
Weight
B
A
FIG. 9.5
Most aircraft have the forces arranged so that if the thrust is removed (i.e. in the event of engine
failure) the remaining lift/weight couple pitches the aircraft nose-down (without any action by the
pilot), so that it assumes a gliding attitude. Conversely, when power is added, thrust increases
and the aircraft tends to pitch nose-up toward a level flight attitude (Fig. 9.6).
LIFT
(NOSE-UP
MOMENT)
T.D
COUPLE
L.W
COUPLE
(NOSE-DOWN
MOMENT)
DRAG
(REDUCED
NOSE-UP
MOMENT)
D
CoG
THRUST
L.W
COUPLE
(NOSE-DOWN
MOMENT)
WEIGHT
FIG. 9.6
9-3
Chapter 9
The forces are normally arranged so that lift acts behind weight and thrust acts below drag. There
is usually a considerable difference in magnitude between the two pairs of forces, with lift and
weight being greater. In an effort to balance the pitching moments, the spacing between the
thrust and drag forces is normally greater than the spacing between the lift and weight forces.
Ideally, the pitching moments should cancel each other out, but in practice this is not always
possible and a secondary method of balancing must be used. The tailplane normally provides this
balancing force (Fig. 9.7).
LIFT
LIFT
UPLOAD
DRAG
THRUST
LIFT
DOWNLOAD
WEIGHT
FIG. 9.7
On some aircraft, canards or foreplanes provide the secondary balancing required. Canard-type
aircraft do not use a conventional tailplane. In this configuration, horizontal surfaces mounted in
front of the main wing replace the horizontal tailplane. The rearward location of the main wing
allows more of the fuselage to be used as cabin space than if the wing were mounted at the midfuselage position (Fig. 9.8).
FIG. 9.8
Unlike aircraft with conventional tailplanes, both the canard surface and the wing of the aircraft
create an upward lifting force under all normal conditions of flight, thus sharing the weight of the
aircraft over both surfaces. This allows for a lighter wing loading, and therefore, a lighter
structure.
One of the effects of mounting a small wing forward of the main wing is that the lift from the
canard counters the negative pitching moment of the wing.
Canards are mounted with a slightly larger angle of incidence than that of the main wing, with the
result that canards have a greater angle of attack than the main wings (Fig. 9.8). Creation of a
positive pitching moment by the wing lifts the nose of the aircraft, further increasing the angle of
attack of the canard. If the pitching continues, the canard stalls before the wing stalls.
9-4
Chapter 9
DOWNLOAD
MOMENT ARM
WEIGHT
FIG. 9.9
For this reason, the area of the tailplane and subsequent lift force required need only be small,
compared to the lift force produced by the mainplane. If the overall pitching moment is normally
nose-down, the tailplane provides a downward aerodynamic force (down-load) and vice versa.
During some phases of flight, the correcting moment provided by the tailplane may be insufficient
to counteract the existing out of balance moments. In this case, the lifting capability of the
tailplane needs to be increased. This is achieved by altering the position of the elevator to provide
an upward or downward force. On other aircraft, the actual tailplane position is adjustable to
maintain level flight. In producing this force at any given airspeed, an aircraft experiences an
increase in drag, known as Trim Drag (Fig. 9.10).
LIFT
TRIM
DRAG
DOWNLOAD
WEIGHT
FORWARD
CoG
FIG. 9.10
9-5
Chapter 9
ALTITUDE GAINED IN
A GIVEN TIME
MAX RATE
OF CLIMB VY
MAX ANGLE
OF CLIMB VX
BEST
GRADIENT
BEST VERTICAL SPEED
START
OF
CLIMB
FIG. 9.11
9-6
Chapter 9
In the above diagram the forces parallel to the climb path are in red. The only force pulling
forward up the climb path is thrust. If the aeroplane is to remain at the same velocity, a force
and/or components of forces pulling backward must balance the thrust. These forces are drag
plus the component of weight parallel to the climb path, which is shown by the dashed red line
and equal to W sin
The following relationship therefore exists:
Thrust = Drag + component of weight opposing flight, or
T = D + W sin
9-7
Chapter 9
In the above diagram, the forces perpendicular to the climb path are in blue. If the aeroplane is
not to diverge from a straight climbing climb path, the forces perpendicular to the climb path must
also be in balance. This means that lift must be equal and opposite to the part of weight at right
angles to the climb path, W cos (shown by the blue dashed line).
Therefore,
L = W cos
To summarise, in a steady climb:
L = W cos , and
T = D + W sin
This means that in a steady climb:
(i)
(ii)
Note: The first of these two statements, that weight exceeds lift, often upsets students. It may
help to think of the forces acting vertically. Now weight is balanced by lift plus a part of thrust
(W = L + sin T). Hence, weight must be greater than lift.
9-8
Chapter 9
The above diagram shows the forces in the descent. Again look at the forces parallel and
perpendicular to the descent path. To descend at a constant angle, lift must equal the component
of weight, W cos (shown in blue).
From practical flying experience, you know that when lowering the aeroplanes nose to descend,
thrust must be reduced, otherwise the aeroplane accelerates. The above diagram shows that this
is because a component of weight (W sin ) is now acting in the same direction as thrust. For
these two forces to be balanced by drag, which is the only force pulling backward up the descent
path, thrust must be smaller than in straight-and-level flight.
In the above diagram the forces parallel to the descent path are shown in red. The forces
perpendicular to the descent path are shown in blue.
Therefore,
D = T + W sin , and
L = W cos
This means that weight is greater than lift (W > L) and drag is greater than thrust (D >T).
The terms descent and descending flight normally mean a powered descent. If the engines are
producing no thrust, such as when they have failed, this is called a glide.
9-9
Chapter 9
THE GLIDE
As the term glide always means a descent with no thrust, there are only three forces acting on the
aeroplane in a glide; namely lift, weight, and drag.
Looking at the above diagram, the balancing forces are now simplified with:
D = W sin , and
L = W cos
However, it is the fact that the two components of weight, parallel and perpendicular to the glide
path, are equal to lift and drag that is most significant. This is shown in the diagram above.
There is a special relationship between the glide angle of descent (), lift, and drag.
Tan =
D
L
Tan is therefore minimum and the glide path gradient shallowest when the ratio of drag to lift is
minimum (D/L min).
Tan
minimum
D
L
minimum
L
D
maximum
This is the same as saying the ratio of lift to drag is maximum (L/D max). Since the minimum glide
path gradient will also result in maximum range, maximum glide range will also occur when the
L/D ratio is maximum.
The L/D maximum always occurs at the speed VMD; the speed where drag is minimum.
For a typical training aeroplane, the L/D ratio is maximum at about 4 degrees angle of attack.
9-10
Chapter 9
The above diagram shows that if the angle of attack stays at 4 degrees (which is VMD), a heavier
aeroplane will increase its lift and drag in the same proportion. This will result in the lift to drag
ratio remaining the same and aeroplane gliding the same distance. The heavier aeroplane,
therefore, has the same glide path and angle of descent as the lighter aeroplane. However
because the heavier aeroplane will be flying faster to remain at VMD, its rate of descent will be
greater and its glide endurance reduced. This is a commonly misunderstood concept and is often
examined in the JAA exam.
In summary:
To glide for minimum glide angle (maximum glide range);
The lift/drag ratio must be maximum,
The glide speed is VMD ,
The angle of attack is 4 degrees.
Weight has no effect on the glide angle and range provided the aeroplane remains at VMD
9-11
Chapter 9
TOO SLOW
55 KT
70 KT
TOO FAST
80 KT
FIG. 9.19
The reduction in the lift/drag ratio at airspeeds above and below the minimum drag speed is due
to high induced drag at slow airspeeds and high parasite drag at high airspeeds. If the aircraft is
gliding at the recommended airspeed for maximum glide distance and looks like it will not reach
its designated landing point, do not raise the nose (know as stretching the glide) as this will
reduce the glide distance, instead reselect a closer landing area.
9-12
Chapter 9
Extending flaps
The above drag polar (CL against CD) displays that the maximum lift to drag ratio occurs at the
tangent to the drag polar (shown by the red lines). The diagram shows two configurations, flaps
retracted and flaps extended. It can be seen that flaps reduce the lift/drag ratio, which increases
the glide path angle and reduces the glide range.
Note that the JAA question will often use the term a higher flap setting to mean more flap (higher
in the sense of degrees of flap).
No Flaps
Flaps Extended
Steeper Glidepath
Flaps Extended
Original Glidepath
No Flaps
Be particularly aware of the effect of flaps when practising forced landings in light aeroplanes. Do
not extend flaps until a landing well into the chosen landing area is assured. This is because
extending the flaps steepens the glide path, which brings the aiming point back toward you.
Flaps decrease the L/D ratio, which increases the glide angle and reduces the range.
9-13
Chapter 9
ALTITUDE
TAILWIND
HEADWIND
NIL
WIND
GROUND
FIG. 9.20
A tailwind increases an aircraft's gliding distance over the ground (i.e. reduces the angle of glide)
whilst a headwind reduces the distance over the ground (i.e. increases the angle of glide). The
time taken to reach the ground from a given start altitude in either case remains the same (i.e.
glide endurance is unaffected by wind).
9-14
Chapter 9
The above diagram shows an aeroplane in a level turn to the left. In the diagram (PHI) is the
angle of bank. Since the only forces acting on the aeroplane in the vertical plane are, lift and
weight, weight must equal the vertical component of lift. This means that lift must be greater than
weight.
Looking at the right angle triangle a,b,c this means that,
Cos = W/L
And, since load factor is L/W,
Load factor = 1/cos
9-15
Chapter 9
Load Factor,
( 1/cos)
1.00
15
1.04
30
1.15
45
1.41
60
2.00
The above table shows the load factor at a number of different angles of bank. Remember to read
a question carefully to discover if it is asking for the total or increase in lift or load factor. For
example the total load factor in a 60 angle of bank turn is 2, but the increase in load factor is 1.
Similarly the % lift in a 30 angle of bank turn is 115%, while the increase in lift is 15%.
The increase in lift is achieved by increasing the back pressure on the control column, which
increases the angle of attack. The increase in the coefficient of lift (due to the angle of attack
increasing) causes the induced drag to increase. This has implications for the level turn.
In a level turn at constant speed, the increase in drag, which now exceeds the thrust, would
cause the aeroplane to slow down. To keep the airspeed constant in the turn, the thrust must be
increased to equal the new greater drag.
Load Factor,
( 1/cos)
Stall Speed
(load factor)
1.00
1.00
15
1.04
1.02
30
1.15
1.07
45
1.41
1.19
60
2.00
1.41
If the straight and level stall speed was 85kts the stall speed in a 45 angle of bank turn will be
85kts x 1.19 = 101kts.
Again using the table the increase in stall speed in a 60 angle of bank turn will be 41%. If the
straight and level stall speed was 60 kt, the stalling speed in the turn is:
60kt x 2 = 60kt x 1.41 = 85 kt
9-16
Chapter 9
The previous example showed that for an aeroplane with a straight and level stall speed of 60
knots in a 60 degree angle of bank the turning stall speed was 85 knots. This means that the
stalling speed has increased by 25 knots, which effectively reduces the safety margin (i.e. the
margin above the stalling speed). Therefore avoid steep turns at low airspeeds.
240
220
40
AIRSPEED60
200
80
STALL SPEED
INCREASES
IN A TURN
KNOTS
180
100
160
140
120
REDUCED SAFETY
MARGIN
AIRSPEED
DECREASES IN A TURN
FIG. 9.35
In a steady level turn the centripetal force required to make the aeroplane turn, is produced by the
lateral component of lift, shown in the above diagram.
The centripetal force = Mass x V2
r
where, V is the velocity (TAS) in metres per second, around the circumference of a circle
of radius r metres.
9-17
Chapter 9
Looking in the above diagram at triangle a, b, c and using tan = opposite side/adjacent side, it
is now possible to see that,
Tan = ab = mV2 x
bc
r
1
W
and, as W = m x g
Tan = mV2 x
1
r
mxg
Tan = V2 (cancelling m, the mass)
rg
This equation shows that the angle of bank is only influenced by the TAS and radius of turn, and
is not affected by aeroplane weight. Therefore two aeroplanes (identical, except one is twice the
weight of the other) which have the same TAS and angle of bank, will have the same turn radius.
Similarly, if two aeroplanes are turning at the same angle of bank, but aeroplane B is flying twice
as fast as aeroplane A, aeroplane B will have four times the turn radius.
Tan = V2
rg
This is because for Tan to remain constant, the effect of doubling V is that V2 will increase by
22= 4, so the radius must also increase by 4
9-18
Chapter 9
Example;
Using the previous equation quantitatively, find the turn radius at 300kts TAS, in a 45 angle of
bank turn, given acceleration due to gravity is 10 m/s2.
We already know that:
Tan = V
rg
Rearranging to find the turn radius, r;
r=
V
g Tan
There is a issue of units that must now be considered. The questions normally work in SI units,
hence, TAS needs to be converted into meters per second, the acceleration due to gravity has
already been given in m/s2 and the radius will be in metres. The JAA expect the candidate to
know and use, the approximate conversion, that knots are approximately double the m/s. Hence
in the above question a TAS of 300kts is approximately 150m/s.
r=
V
= 150 = 22500
g Tan
10 x 1*
10
= 2250m
(note *, Tan 45 = 1)
It is interesting to note that for a given angle of bank, the aeroplane's radius of turn is determined
solely by its airspeed. The minimum turn radius will therefore be achieved on the stall buffet,
provided there is sufficient thrust to equal the drag. The turn radius will therefore be smallest with
flaps extended (if they are not limited by load factor, and there is sufficient thrust), and at low
altitude where the TAS is less for a given IAS.
9-19
Chapter 9
RATE OF TURN
This is measurement of how long it takes for an aircraft to turn, measured in degrees per second.
This is particularly important during instrument flying where rate 1 turns require a turn of 3 per
second. This means that the aircraft turns through 180 in 1 minute, or 360 in 2 minutes. A
steeper angle of bank would be required to carry out a rate 1 turn at higher airspeeds.
Rate of turn =
V
r
where V is the TAS in m/s, r is the turn radius and rate of turn is in radians per second.
Note that the rate of turn is in radians per second. There are 2 radians in 360 degrees, therefore
there are 57.3 degrees in one radian.
There are two types of exam questions on rate of turn. The first simply asks for what happens to
the rate of turn.
Remember from page 9-17, that if the TAS doubles at a constant angle of bank, the radius is 4
times greater. Now consider the effect of this on the rate of turn. Since rate of turn = V/ r, and the
V has doubled while the radius has increased by a factor of 4, the rate of turn will be halved.
The second type of question is rare, but requires an actual rate of turn to be determined.
For example is an aeroplane is turning at 240kts TAS, with a turn radius of 3000m, what is the
rate of turn? First remember that 240kts TAS, is approximately 120m/s, so using
Rate of turn =
9-20
Chapter 9
TURN INDICATOR
BALANCE
INDICATOR
2 MIN TURN
FIG.9.28
When the ball is in the centre, it indicates that the turn is balanced. Any displacement of the ball
indicates that the turn is unbalanced (Fig. 9.29).
RIGHT RUDDER
REQUIRED
UNBALANCED TURN
BALANCED TURN
FIG. 9.29
If the ball is only partially displaced from its centre position, it is possible to balance the turn using
only the rudder (i.e. ball to the right, apply right rudder). If the ball is at the extremities of the
indicator, the use of rudder alone produces a highly inefficient turn. In this case, use the ailerons
initially to help balance the turn.
9-21
Chapter 9
Slipping turn
A slipping turn occurs if the angle of bank is too large for a given rate of turn (i.e. the aircraft is
over-banked). This is indicated by the ball moving toward the lower side of the balance indicator
and a sensation of falling in toward the centre of the turn (Fig. 9.30). To correct for a slip either
decrease the angle of bank using ailerons, or use rudder to reduce the turn radius.
SLIPPING TURN
L
R
FIG. 9.30
Skidding turn
A skidding turn occurs if the angle of bank is too small for the rate of turn (i.e. the aircraft is underbanked). This is indicated by the ball moving toward the upper side of the balance indicator and
the sensation of being thrown out of the turn (Fig. 9.31). To correct for a skid either increase the
angle of bank using ailerons, or use rudder to increase the turn radius.
SKIDDING TURN
L
R
FIG. 9.31
9-22
Chapter 9
Balanced turn
During a balanced turn the ball remains in the centre of the balance indicator and the pilot
remains upright in the seat relative to the aeroplane, with no feeling of falling in, or being thrown
out (Fig. 9.32).
BALANCED TURN
L
R
FIG. 9.32
Any deviation from a balanced turn is corrected by applying rudder according to the position of
the ball. By maintaining the ball in the centre the pilot will maintain a balanced turn.
FIG. 9.36
9-23
Chapter 9
GAIN IN
HEIGHT
FLIGHT PATH OF
OUTER WING
INNER WING
LARGER AoA
FIG. 9.37
The faster moving outer wing is subject to a smaller reduction in angle of attack. This makes the
net coefficient of lift higher than on the inner wing, thereby producing greater lift. Its increased
velocity further enhances the lifting capability of the outer wing. An aircraft in a climbing turn
therefore tends to overbank more than in a steady level turn. If necessary, utilise the ailerons to
maintain the desired angle of bank.
9-24
Chapter 9
Descending Turns
During descending turns, an aircraft describes a downward spiral path. The airflow comes upward
to meet the wings, thus increasing their angles of attack and hence their coefficients of lift
(Fig. 9.38).
INNER WING
LOSS IN
HEIGHT
LARGER AoA
FIG. 9.38
The increase in angle of attack of the outer wing is less than that of the inner wing, as is its lifting
capability. The faster outer wing may compensate for the variation in lift due to the difference in
angle of attack, although the aircraft may still tend to underbank. If this occurs, maintain the desired
angle of bank by using the ailerons.
9-25
Chapter 9
9-26
INTRODUCTION TO STABILITY
Stability is the natural tendency of an aircraft to return to its former equilibrium or trimmed position
(i.e. straight and level flight) following a disturbance without any pilot assistance. The stability of
an aircraft is static and dynamic in nature. The actual stability characteristics of an aircraft are not
only governed by its design, but are also dependent on crew workload. Thus, a close relationship
exists between stability and controllability.
CONTROLLABILITY
This is the ability of the pilot to alter the position or attitude of an aircraft using the flying control
surfaces. Adequate controllability does not necessarily exist with adequate stability. In fact, high
stability makes an aircraft resistant to change and reduces its controllability (i.e. good stability
makes it harder for the pilot to control and manoeuvre an aircraft). Thus, the upper limits of
stability are determined by the lower limits of controllability. No aircraft is completely stable, but all
must possess desirable stability and handling characteristics. Stability naturally occurs whenever
an aircraft is rotated about any one, or a combination of its axes (Fig.10.1).
YAW
LONGITUDINAL
AXIS
LATERAL AXIS
ROLL
NORMAL AXIS
CENTRE OF
GRAVITY
PITCH
FIG. 10.1
10-1
Chapter 10
Stability
These axes act at right angles to each other and all pass through the aircraft's centre of gravity.
Stability about the lateral axis (pitch) is known as longitudinal stability. Stability about the
longitudinal axis (roll) is known as lateral stability. Directional stability is the term for stability
about the normal axis (yaw). Lateral and directional stability are not entirely independent of each
other, and tend to act together to produce certain undesirable motions. In fact, an aircraft can be
unstable about two of its axes, but stable about the third or vice versa.
The degree of stability also differs between types of aircraft, with transport category aircraft being
generally more stable than light aircraft. Equilibrium of an aircraft in flight is more commonly
referred to as the trimmed condition and occurs when no net moments act to displace it from this
condition (i.e. its moments in pitch, roll, and yaw are zero). Trimming of an aircraft is normally
attributed to trimming devices such as tabs, but in terms of stability simply means that no net
moments exist. Stability falls into two main categories; static stability and dynamic stability.
Furthermore, displacing an aircraft from its normal trimmed position causes the air loads acting
on it to oppose and damp out the subsequent motion. This is known as aerodynamic damping,
and it greatly affects an aircraft's degree of dynamic stability.
STATIC STABILITY
Static stability is the initial tendency that an aircraft displays after being displaced from a given
equilibrium position. If an aircraft tends to return to its former position, it is said to be statically
stable. A statically unstable aircraft continues to move in the direction of the displacement.
Finally, if an aircraft tends to remain in the disturbed position it has neutral static stability. This
type of stability can be demonstrated using ball bearings and a curved container (Fig. 10.2).
TENDENCY TO CONTINUE
IN THE DIRECTION OF DISPLACMENT
TENDENCY TO RETURN
TO EQULIBRIUM
EQUILIBRIUM ENCOUNTERED
AT ANY POINT OF DISPLACEMENT
EQUILIBRIUM
EQUILIBRIUM
STATICALLY
STABLE
STATICALLY
NEUTRAL
STATICALLY
UNSTABLE
FIG. 10.2
THE DEGREE OF STABILITY
The different degrees of stability are categorised by how quickly an aircraft tends to return to its
trimmed position following a disturbance. To analyse this, consider the analogy of a ball in a
curved container (Fig. 10.3).
Static
Stability
Increased
Static
Stability
FIG. 10.3
10-2
Stability
Chapter 10
In this case, the steeper the container the greater the static stability, but as stability increases,
controllability decreases. The upper limits of stability are therefore set by the lower limits of
controllability.
DYNAMIC STABILITY
Dynamic stability is the movement of an aircraft with respect to time in response to its static
stability following a displacement from a given equilibrium position. For example, consider a
statically stable aircraft, which, following a disturbance, overshoots its equilibrium position. Its
inbuilt stability attempts to correct for this and an oscillatory motion occurs (Fig. 10.4).
Displacement
Displacement
Un-Damped
Oscillation
Damped
Oscillation
Time
Time
Dynamically
Stable
Dynamically
Neutral
Displacement
Divergent
Oscillation
Time
Dynamically
Unstable
FIG. 10.4
The time taken for the motion to subside is a measure of the aircraft's dynamic stability. If the
oscillations damp out with time, the aircraft is dynamically stable. If the oscillations increase in
magnitude, the aircraft is dynamically unstable. Finally, if the oscillations persist without either
increasing or decreasing in magnitude the aircraft has neutral dynamic stability. Overall, it is
desirable for an aircraft to be both statically and dynamically stable.
STATIC LONGITUDINAL STABILITY
This is the aircraft's natural or inbuilt tendency when disturbed in pitch, to return to its former
trimmed angle of attack without pilot input, and is desirable throughout the aircraft's complete
speed range. Conversely, if the aircraft continues to diverge away from its trimmed angle of
attack following a disturbance, it is said to be statically longitudinally unstable. If it remains at
whatever angle of attack the disturbance causes, it is longitudinally neutrally statically stable. This
type of stability is mainly provided by the tailplane.
For example, consider the effect of a gust that causes an aircraft to pitch nose-up. Due to its
inertia, the aircraft momentarily continues to follow its original flight path and present itself to the
relative airflow at an increased angle of attack. The subsequent increase in the angle of attack of
the tailplane produces a small aerodynamic force.
Principles Of Flight (Rev Q406)
10-3
Chapter 10
Stability
This force, multiplied by the distance from the centre of gravity, produces a strong restoring
pitching moment and pitches the aircraft back to its former equilibrium position (Fig. 10.5). The
pitching moment is defined in a coefficient form (Cm).
Cm =
Where
M
qS(MAC)
CG
GUST
LIFT
FIG. 10.5
FIG. 10.6
10-4
Stability
Chapter 10
For this to occur, the angle of incidence of the tailplane is usually less than that of the mainplane
(Fig. 10.7).
LONGITUDINAL DIHEDRAL ANGLE (+2)
MAIN PLANE
TAIL PLANE
+4
+2
FIG. 10.7
The angle between the chord line of the tailplane and the chord line of the mainplane is known as
the longitudinal dihedral angle, and is a practical aspect in most types of aircraft. The actual
degree of longitudinal stability is determined by the interaction between an aircraft's centre of
gravity, its centre of pressure, and the position of its tailplane. For example, consider an aircraft in
steady level flight where the angle of attack of the mainplane and tailplane are +6 and -4
respectively (Fig. 10.8).
FIG. 5.1
In this case, wing lift (LW) of 8 units of force acts through the centre of pressure (CP), 4 units from
the CG, producing a nose down moment of 8 x 4 = 32 units. A download (LT) of 4 units acts on
the tailplane, 8 units distance from the CG. This produces a tail down moment of 4 x 8 = 32 units.
The aircraft is in a trimmed condition, with no resulting moment.
LW x 4 (nose down moment) = LT x 8 (nose up moment)
i.e. 8 x 4 units nose down = 4 x 8 units tail down
10-5
Chapter 10
Stability
If an aircraft is suddenly subjected to an upward gust its nose rises, but at the same time due to
its inertia, it momentarily continues to travel along its original flight path and presents itself to the
airflow at an increased angle of attack. In the diagram below, the effective pitch change is 2
degrees up and is shown by the grey area. (Fig. 10.9).
FIG. 10.9
This results in the wing lift increasing, to for example 10 units, and a reduction in the download
acting on the tailplane, to example 2 units, so that the aircraft is no longer in a trimmed condition.
For ease of explanation, it has also been assumed that even though the angle of attack increases
(by 2 degrees), the points of action do not significantly move with respect to the aircraft's centre
of gravity and the moment arms therefore remain unaltered, so that:
LW x 4 (nose down moment) > LT x 8 (nose up moment)
i.e. 10 x 4 units nose down > 2 x 8 units tail down
These figures show that the pitching moment due to the wing increases by 20%, whilst the
pitching moment due to the tailplane decreases by 50%, so the aircraft is no longer in a trimmed
condition. The combined effect of these changes in pitch moment, is to rotate the aircraft back to
its former trimmed position, with a nose down moment of 40 16 = 24 units.
FACTORS AFFECTING STATIC LONGITUDINAL STABILITY
The degree of longitudinal static stability normally varies depending on the:
Position of the Centre of Gravity
Variations in the position of the centre of gravity greatly affect the static longitudinal
stability of an aircraft. Generally, the further forward the centre of gravity the greater the
stability (Fig. 10.10).
10-6
Stability
Chapter 10
AFT CG
FORWARD CG
LIFT
LIFT
STABLE
LESS STABLE
A B
B
FIG. 10.10
Its forward position is limited by the fact that high stability results in poor controllability.
This is because stability tends to resist movement away from the aircraft's trimmed
attitude, which is reflected in the amount of stick force necessary to displace an aircraft
from this position. It follows that the further forward the centre of gravity, the greater the
stick force and the greater the effort required to manoeuvre the aircraft. Positioning the
centre of gravity too far forward results in excessive stick forces, making the aircraft
extremely tiring to fly.
The forward position of the centre of gravity is also limited because if it is too far forward,
the aircraft becomes uncontrollably nose heavy at low airspeeds. This is particularly
important in the landing phase when elevator deflection may be insufficient to allow the
pilot to flare the aircraft on landing, unless the airspeed is increased to give greater
elevator authority.
Conversely, moving the centre of gravity progressively aft steadily decreases the degree
of stability, as well as the stick forces, and the aircraft returns less quickly to trimmed
flight. Eventually, a position is reached where the aircraft has no tendency to return to a
trimmed condition following a disturbance and instead remains in its disturbed position.
This is the aircraft's neutral point, and is the centre of gravity position giving statically
neutral stability (Fig. 10.11).
FIG. 10.11
10-7
Chapter 10
Stability
Any movement aft of this point makes an aircraft statically longitudinally unstable. Most aircraft are
designed to be statically longitudinally stable, so the centre of gravity is normally positioned ahead of
the neutral point. The distance between the centre of gravity and the neutral point is called the static
margin (Fig. 10.12).
FIG. 10.12
C OF G
PITCH UP
C OF P
DIST URBANCE
RELATIVE
AIR FLOW
WEIGHT
RESTORING (PITCH DOWN) M OM ENT
FIG. 10.13
Conversely, if the centre of pressure moves ahead of the centre of gravity, a nose-up
moment is applied to an aircraft in response to a pitch-up disturbance, and has a
destabilising effect (Fig. 10.14).
10-8
Stability
Chapter 10
UNSTABLE
(PITCH UP)
M OM ENT
LIFT
INCREASED LIFT
C OF G
RELATIVE
AIR FLOW
C OF P
W EIGHT
PITCH UP DISTURBANCE
FIG. 10.14
Design of the Tailplane
The overall function of the tailplane is to provide a force to counteract any residual, outof-balance couples existing between the four main forces. The degree of longitudinal
stability is determined by the interaction between the aircraft's centre of gravity, tailplane
area, and tailplane position. The tailplanes position relative to the centre of gravity is of
most importance, since it has the greatest stabilising effect on the aircraft. This is
because the greater the moment arm, the greater the stability. If downwash from the wing
acts on the tailplane, it also affects the aircraft's degree of stability, by affecting its angle
of attack. Furthermore, the tailplane is usually of symmetrical section and the position of
its centre of pressure does not vary much in flight.
Wing Downwash
Any disturbance in pitch alters the wings angle of attack and thus the amount of
downwash from the wing. This also alters the angle of attack of the tailplane (e.g. if the
aircraft pitches nose-up, the downwash angle increases and the effective angle of attack
of the tailplane decreases). The aerodynamic force produced by the tailplane thus
decreases, as does the restoring moment. To compensate for this, the CG is moved
forward to increase the moment arm.
NOSE-UP
(+)
TRIM
COEFFICIENT OF LIFT (CL )
0
NOSE-DOWN
PITCHING MOMENT Cm
ANGLE OF ATTACK (
(-)
FIG. 10.15
Principles Of Flight (Rev Q406)
10-9
Chapter 10
Stability
The graph shows that if the angle of attack increases (e.g. due to a disturbance) a nose-down (-)
pitching moment is created, tending to rotate the aircraft back to its original trimmed position.
Conversely, decreasing the angle of attack creates a nose-up (+) pitching moment. Thus for an
aircraft to be statically longitudinally stable, the pitching moment must decrease with increasing
angle of attack (i.e. have a negative slope). It is the steepness of the slope, which actually
determines the aircraft's degree of stability (Fig. 10.16).
Unstable
+
D
Pitching
Moment
Cm
Neutral
Stable
FIG. 10.16
Fig. 10.16 shows the static longitudinal stability characteristics of four different aircraft. Aircraft A
and B both have negative slopes, and are thus longitudinally stable, although aircraft A is most
stable because it has a more negative slope. Conversely, aircraft C is longitudinally unstable
because the pitching moment increases with increasing angle of attack and has a positive slope.
Aircraft D is different than the other aircraft because the pitching moment remains constant
regardless of changes in angle of attack, and the aircraft has no tendency to return its former
trimmed position following a disturbance. Aircraft D therefore exhibits static neutral stability, and
alternatively takes up a new trimmed position. Any aft movement of the CG reduces the degree of
static longitudinal stability and produces a less negative slope. The following conditions also
influence the slope of the graph:
Stick-Fixed Static Longitudinal Stability
This involves the response of an aircraft to a disturbance in pitch if the flying control
surfaces are held in set position. When the disturbance takes place, the aircraft has a
natural tendency to return its former equilibrium or trimmed position. The amount of
control deflection required to maintain any new equilibrium position is a measure of the
aircrafts stick-fixed static longitudinal stability.
Stick-Free Static Longitudinal Stability
This involves the response of an aircraft to a disturbance in pitch when the control
surfaces are free to find their own position depending on the aerodynamic forces acting
on them (i.e. with manual flying controls the stick forces have been reduced to zero by
way of the trim tab system prior to the disturbance). This only applies to manual flying
controls because in power-operated flying control systems, the surfaces are not free to
float and there is no difference between stick-fixed and stick-free static longitudinal
stability.
10-10
Stability
Chapter 10
NOSE-UP
(+)
ELEVATOR DEFLECTION
TRIM POSITION (STICK FIXED)
COEFFICIENT OF LIFT (C )
0
NOSE-DOWN
PITCHING MOMENT Cm
20UP
10UP
(-)
0
10DOWN
20DOWN
FIG. 10.17
This is because the angle of attack of the mainplane has increased and the tailplane produces a
greater nose-up moment due to the change in effective camber. If the aircraft is trimmed to
maintain the new pitch attitude (i.e. zero stick forces) and the elevators are allowed to float free,
any change in the aircrafts angle of attack causes the control surfaces to move away from their
trimmed position in the direction of the relative airflow. For example, an increase in angle of
attack causes the elevators to float upward, thus reducing the lift force (upload) acting on the
tailplane and reducing the aircrafts static longitudinal stability compared to the stick fixed
condition (Fig. 10.18).
Unstable
+
D
Pitching
Moment
Cm
Neutral
Stable
FIG. 10.18
10-11
Chapter 10
Stability
Column Aft
Unstable
Up
Elevator
Position
EAS
El
t
Down
Stable
Column
Forward
FIG. 10.19
An aircraft that demonstrates stick position stability requires moving the control column forward to
reduce the angle of attack and trim at a higher airspeed, and vice versa (i.e. with increasing
forward airspeed, an increasing forward stick force must be applied to maintain steady straight
and level flight). Conversely, an aircraft exhibiting stick position instability requires moving the
control column aft to trim at a higher airspeed and vice versa.
In a manually controlled aircraft the control stick forces are dependent on:
With increasing EAS less and less nose-up tab is required and if the aircraft is correctly trimmed,
(i.e. if positive stick force stability exists) a push force will be required to maintain a new attitude
with increasing airspeed and vice-versa (Fig. 10.20).
10-12
Stability
Chapter 10
If the position of the CG is varied whilst maintaining the same trim airspeed, its actual position
affects stick force stability. For example, an aft movement of the CG reduces the negative slope
of the graph, and thus the degree of stick force stability as illustrated in Fig. 10.21.
FIG. 10.21
This also means that smaller stick forces are required to displace the aircraft from its original
trimmed airspeed. In accordance with JAR 25.173 a minimum gradient for stick force is required
for an aircraft to be certified, with the following rules being applicable:
A pull force must be present to obtain and maintain airspeeds below the specified
trim speed, and a push force must be present to obtain and maintain airspeeds
above the specified trim speed.
The airspeed must return to within 10% of the original trim speed during the climb,
approach, and landing conditions, and must return to within 7.5% of the original trim
speed during the cruise.
The average gradient of the stable slope of the stick force versus speed curve may
not be less than 1 lb for each 6 kt.
The degree of static longitudinal stability must also be such that a stable slope exists between
85% and 115% of the airspeed at which the aircraft is trimmed, with:
Flaps retracted
Undercarriage retracted
Maximum take-off weight
75% of maximum continuous power (piston), or maximum power or thrust (jet)
10-13
Chapter 10
Stability
MANOEUVRING STABILITY
Whenever an aircraft is manoeuvring, acceleration forces act on it (e.g. if the aircraft is pulling out
of a dive, its flight path will be curved and the resultant pitching velocity provides aerodynamic
damping in pitch due to the downward movement of the tailplane). This acts with the inbuilt static
longitudinal stability of the aircraft and tends to resist this motion. The tailplane provides the
largest contribution toward damping in pitch, although other aircraft components such as the
wings do assist. A graph of stick force versus load factor illustrates the manoeuvring stability of
an aircraft (Fig. 10.22).
30
C of G MOVING AFT & STICK FORCE
GRADIENT REDUCING
20
STICK FORCE GRADIENT
or STICK FORCE / g
10
FIG. 10.22
6
LOAD FACTOR or g
The gradient of the graph should be positive (i.e. with increasing load factor the stick force must
also increase). This gradient must not be excessively high or the aircraft would be difficult and
tiring to manoeuvre. Conversely, it should not be too low or the stick forces would be too light and
the aircraft could be over-stressed.
The manoeuvring stick force gradient, or stick force per g for a transport category aircraft is
approximately 9 lb/g. Aircraft with high static longitudinal stability possess high manoeuvre
stability (i.e. low controllability) and also have a high stick force gradient. Any aft movement of the
CG reduces the stick force gradient and the longitudinal static stability of the aircraft. With
increasing altitude, the manoeuvre stick force stability decreases. This is because as the density
of the air decreases, the TAS increases, and the amount of pitch damping decreases (10.23).
10
20
30
STICK FORCE
STICK FORCE
CG Position
% MAC
Low
Altitude
High
Altitude
40
LOAD FACTOR
LOAD FACTOR
FIG. 10.23
10-14
Stability
Chapter 10
DOWN SPRING
FIG. 10.24
This contributes to an increment of pull force that is independent of airspeed or control
deflection. When the aircraft is retrimmed for its original airspeed, the airspeed stick force
gradient increases resulting in a stronger feel for airspeed. The force increment due to
the down spring is not affected by stick position or normal acceleration, whilst
manoeuvring stick force stability is unchanged.
The bob-weight is designed to improve the stick force stability. It consists of an eccentric
mass attached to the flying control system and, in unaccelerated flight, acts like the down
spring. In accelerated flight during a manoeuvre, the bob-weight experiences the same
forces as the aircraft and provides an increment of stick force in direct proportion to the
magnitude of the manoeuvring acceleration, thus increasing the manoeuvring stick force
stability (Fig. 10.25).
BOBWEIGHT
FIG. 10.25
10-15
Chapter 10
Stability
DRAG
AIRSPEED
FIG. 10.26
If the aircraft is statically stable and is operating at an airspeed in excess of VIMD, any
increase in airspeed not only increases the drag, but also increases the lift and the
aircraft momentarily gains height. Some of the aircrafts kinetic energy is subsequently
converted into potential energy and the aircraft slows down.
As the airspeed drops below its original value, the aircraft momentum reduces and the
aircraft descends. An oscillatory motion takes place as the aircraft successively gains and
loses altitude. If this motion damps out, the aircraft is dynamically longitudinally stable,
although in some instances the aircraft may be slightly unstable. In either case, the pilot
needs to take some form of corrective action, but since the period of oscillation is usually
long, any necessary action is easily applied.
Short Period Oscillation
This involves very short periods of oscillation, typically 1-2 sec, when an aircraft is
subjected to a vertical gust. The disturbance causes the aircraft to rotate about its lateral
axis, and varies its angle of attack, whilst the airspeed remains virtually constant. The
change in angle of attack also varies the lift, resulting in a pitching moment. If the aircraft
is statically longitudinally stable, any disturbance in pitch sets up an oscillatory motion
about the aircrafts lateral axis, where oscillation is dynamically stable or unstable.
Unlike the phugoid oscillation, the frequency of this oscillation is normally high and the
pilot cannot correct for it. This form of oscillation must be quickly damped by an automatic
stabiliser, which must be included in the aircrafts flying control system. It follows that an
aircraft operating at airspeeds less than the minimum drag speed will show speed
instability. When a jet transport category aircraft flies at an airspeed less than the
minimum drag speed, for instance on landing, speed instability can prove extremely
serious.
10-16
Stability
Chapter 10
LIFT
LIFT
AIRCRAFT CENTRE-LINE
FIG. 10.27
10-17
Chapter 10
Stability
Where
N
qSb
+ Cn
YAWING
MOMENT
COEFFICIENT
STABLE
SIDESLIP ANGLE
- Cn
UNSTABLE
FIG. 10.28
The slope of the graph is a measure of the aircrafts static directional stability. If the aircraft
experiences a positive sideslip angle and a positive yawing moment coefficient exists, static
directional stability is present. For example, relative airflow coming from the right (+) creates a
yawing moment to the right (+Cn) and tends to weathercock the aircraft into wind. A positive
slope shows that the aircraft is directionally stable, with a steeper slope indicating a greater
degree of stability. Conversely, if the slope is negative it shows that the aircraft is directionally
unstable and that it tends to diverge or move away from the direction of the airflow.
THE FACTORS AFFECTING STATIC DIRECTIONAL STABILITY
The vertical fin is the primary source of static directional stability and is highly stabilising up to the
stall. By incorporating fin sweepback, directional stability can be improved by reducing the aspect
ratio and increasing the stalling angle. Also the centre of pressure moves rearward thereby
increasing the tail yawing moment.
The addition of a dorsal fin, as a forward extension of the fin, helps to delay the stall by
increasing the surface area that is located aft of the CG and by reducing the fins effective aspect
ratio, therefore increasing the stalling angle of attack (Fig.10.29).
10-18
Stability
Chapter 10
Unlike dorsal fins, ventral fins are located on the underside of the tail. They have no effect on
static longitudinal stability. They have a negative effect on static lateral stability and a positive
effect on static directional stability (Fig.10.29).
FIG. 10.29
At high angles of attack, the fuselage may cause an overall decrease in static directional stability.
This is due to an increase in the fuselage boundary layer at the vertical tail location and is most
significant for low aspect ratio aircraft with sweepback. The fitting of strakes improves directional
stability by re-energising the fuselage boundary layer and stopping cross flow around the
fuselage at high angles of attack that may stall the fin due to the resulting disturbed airflow
(Fig.10.30).
FIG. 10.30
10-19
Chapter 10
Stability
Aeroplane with
Dorsal Fin Added
Tail
Alone
Cn
+
Complete
Aeroplane
+
-
Fuselage Alone
FIG. 10.31
10-20
Stability
Chapter 10
RESULTANT FORCE
PRODUCING SIDESLIP
SIDE-SLIP COMPONENT
OF RELATIVE AIRFLOW
WEIGHT
FIG. 10.32
In this attitude, the lift force is tilted so that it no longer directly opposes weight. The resultant of
these two forces causes the aircraft to sideslip in the direction of the dropped wing. Due to inertia,
the aircraft also continues in a forward direction. The sideslip subjects the aircraft to a sideways
component of relative airflow. As in the case of directional stability, the aircrafts inbuilt design
features produce a rolling moment that restores the aircraft to its original wings-level attitude. This
is defined as the rolling coefficient (CL) in the following formula:
CL =
Where
L
qSb
10-21
Chapter 10
Stability
To provide the necessary stability characteristics, one or a combination of the following design
features may be utilised:
Wing Dihedral
As the aircraft sideslips, the dihedral of the wing places the lower wing at an increased
angle of attack, whilst the upper wing has a reduced angle of attack (Fig. 10.33).
LIFT
UNWANTED ROLL
LIFT
DIHEDRAL EFFECT
FIG. 10.33
The lower wing produces greater lift than the upper wing, and the difference in lift
between the two wings thus produces a rolling moment, which returns the aircraft to its
former equilibrium position. The fuselage may also partially shield the upper wing, further
reducing the amount of lift it develops.
10-22
Stability
Chapter 10
Wing Sweepback
As the aircraft sideslips, the lower wing presents more of its span (known as effective
span) to the airflow than the upper wing, as shown in Fig. 10.34.
The effective chord of the lower wing also decreases, whilst that of the upper wing
increases. The aspect ratio of the lower wing thus becomes greater than that of the upper
wing and it produces greater lift. The increased lift produces a rolling moment and the
aircraft rolls back to its former equilibrium position.
EFFECTIVE
SPAN
EFFECTIVE
SPAN
FIG. 10.34
10-23
Chapter 10
Stability
RELATIVE AIR
FLOW DIRECTION
(SIDE COMPONENT)
WEIGHT
FIG. 10.35
The position of the lift force produces a rolling moment about the aircraft's centre of
gravity and rolls the aircraft back to its former wings-level condition. Thus, the lower the
centre of gravity, the greater the lateral stability characteristics. On some high-winged
aircraft, the amount of stability is so large that low dihedral, or even anhedral wings are
fitted (i.e. to de-stabilise the aircraft). This form of recovery is also known as the
pendulous effect.
10-24
Stability
Chapter 10
SIDE-SLIP
CG
FIG. 10.36
The lower the centre of gravity, the greater the degree of lateral stability.
GRAPHICAL REPRESENTATION OF STATIC LATERAL STABILITY
Static lateral stability is shown graphically by plotting a graph of rolling moment coefficient (Cl)
against sideslip angle () (Fig. 10.37).
+ Cl
SIDESLIP ANGLE
- Cl
STABLE
FIG. 10.37
If the aircraft is subject to a positive sideslip angle, it is laterally stable if a negative rolling moment
is applied. For example, relative airflow coming momentarily from the right (+) creates a
negative rolling moment (-Cl) and the aircraft rolls to the left, returning it to its former equilibrium
position. Static lateral stability only exists if a negative gradient exists.
Principles Of Flight (Rev Q406)
10-25
Chapter 10
Stability
10-26
Stability
Chapter 10
Depending on the design of the aircraft, both of these conditions may result. The
oscillation may not damp out without some form of assistance. The resulting motion can
be simply unpleasant, but in some cases may lead to the total loss of the aircraft,
particularly when flying under instrument conditions. The main factors determining the
degree of oscillatory instability are the:
Amount of dihedral
Amount of sweepback
Keel surface area (including the fin and rudder)
In transport category aircraft, the most common form of oscillatory instability is Dutch roll.
DUTCH ROLL
Consider an aircraft with sweepback where the directional stability is less than its lateral stability.
If the aircraft is yawed to the right, the left wing advances (sideslip) and generates more lift, whilst
the right wing slows down and produces less lift. The result of the imbalance in lift is to roll the
aircraft in the direction of the initial yaw. The lift generated by the left wing will be further
increased by becoming less sweptback, as it offers a greater span to the airflow. The right wing
becomes more sweptback, decreasing the effective span exposed to the airflow. This effect is
similar to that of dihedral. The advancing wing also produces greater drag due to the larger areas
exposed to the airflow, which causes the aircraft to yaw in the opposite direction (i.e. to the left).
This results in the right wing producing more lift than the left wing, reversing the direction of the
roll. The final result is an undulating, or corkscrew motion, where the rolling and yawing
oscillations have the same frequency, but are out of phase with each other (Fig. 10.38).
FIG. 10.38
Principles Of Flight (Rev Q406)
10-27
Chapter 10
Stability
This unstable motion continues until the pilot applies corrective action or the motion naturally
damps out. This motion is primarily due to excessive lateral stability. One method of curing this
problem is to reduce the amount of wing dihedral, or to set the wings at a slight anhedral. If the
aircraft has anhedral wings, the angle of attack of the advancing wing decreases, whilst that of
the retreating wing increases. This effectively reduces the aircraft's lateral stability, and thus its
tendency to Dutch roll, but does tend to increase an aircraft's spiral instability. The Dutch roll
tendency may also be reduced by increasing the size of the fin/rudder, but this adversely affects
handling characteristics. This is because the pilot must first fight the weather-cocking tendency of
the fin before the aircraft can be turned (i.e. it increases an aircraft's spiral instability). Conversely,
if the fin/rudder is too small, the aircraft becomes oscillatory unstable (i.e. lateral stability exceeds
directional stability, and the amplitude of the oscillatory motions in Dutch roll quickly increase).
Therefore, aircraft are usually designed with a small degree of spiral instability, in order to help
alleviate the less pleasant Dutch roll tendency.
Aircraft with straight wings are less susceptible to Dutch roll because any movements in yaw
quickly damp out. Aircraft with sweptback wings have more problems with Dutch roll because
sweepback tends to worsen the aircraft's roll and sideslip tendencies. All transport category
aircraft are generally prone to Dutch roll and require artificial damping in the form of a yaw
damper system. This is because the magnitude of the oscillatory motion is normally
comparatively small and is therefore extremely difficult for a pilot to co-ordinate reactions in phase
with the Dutch roll. Any manual input may result in over-correction, intensifying the resulting
oscillatory motion.
LEFT
M AX
DIS PLAC EM ENT
RIGHT
M AX RATE
OF DIS PLAC EM ENT
FIG. 10.39
10-28
Stability
Chapter 10
By using this method, it is possible to stop the Dutch roll before the effects are felt. Most transport
category aircraft have at least two yaw damper systems, which operate continually, and in their
basic operation act independently of the autopilot system. On some aircraft, however, the yaw
dampers additionally co-ordinate turns made by the pilot or autopilot from information sensed in
the aileron control circuit as shown in fig. 10.40.
ON
IN OP
IN OP
RAT E G YRO
RAT E G YRO
Y AW D AM PER
CONTR OLLERS
AILERON
POSIT ION
AILERON
POSIT ION
R
U
D
D
E
R
RUDDER
ACT UAT OR
FIG. 10.40
Each system has its own yaw damper controller, which provides signals to operate a yaw damper
actuator, which in turn generates rudder control inputs. The inputs normally operate in series with
the pilot input and do not result in rudder pedal movement.
10-29
Chapter 10
Stability
SPEED STABILITY
THE BACK OF THE DRAG CURVE AND SPEED STABILITY
The above diagram shows the total drag curve or thrust required curve. The speeds slower than
VMD are known as on the back of the drag curve or the back of the thrust required curve.
The problem with flying at speeds slower than VMD is that the aeroplane is speed-unstable.
Refer to the diagram above and consider an aeroplane flying straight and level at 150 kt. The
aeroplane now flies through wind shear, which results in the CAS suddenly reducing to 125 kt. At
this slower speed, there is even more drag than at 150 kt. To maintain level flight at the same
speed of 125 kt, thrust must equal drag. However, drag now exceeds thrust and the aeroplane
slows further and stalls if the pilot does not react and quickly apply power.
Flying slower than VMD, on the back of the drag curve, means that the aeroplane is speedunstable. If the aeroplane suddenly flies faster, it continues to accelerate, and if slower, it
continues to slow down. When the aeroplane is speed unstable, such as on the approach to land,
the pilot must react quickly in changes to CAS by adjusting the power.
10-30
Stability
Chapter 10
Consider flying straight and level at 230 kt and then entering wind shear, which results in the CAS
reducing to 210 kt. The total drag has now decreased. There is more thrust than drag, so the
aeroplane accelerates back to its original speed of 230 kt without the pilot changing the power
setting.
As speed increases above VMD, the gradient or steepness of the curve increases which increases
the speed stability.
In the graph above, consider the aeroplane flying at 270 kt. The gradient or slope of the drag
curve at this speed is much steeper than at slower speeds. This means that after flying through
wind shear resulting in the same 20 kt drop in CAS, there is a much bigger reduction in drag. The
aeroplane now accelerates back to its original speed of 270 kt much more quickly.
10-31
Chapter 10
Stability
In summary, the faster the airspeed is above VMD, the greater the speed stability. Conversely, the
slower the airspeed is below VMD, the greater the speed instability.
Consequently, an aircraft operating at airspeeds less than the minimum drag speed exhibit speed
instability. If a jet transport category aircraft is flying at an airspeed less than the minimum drag
speed (e.g. on landing) speed instability can prove extremely serious because:
The response to throttle movement is much slower than for a piston-engine aircraft
There is no slipstream effect.
The high momentum of large aircraft requires a long time, and a lot of thrust, to
increase speed. It similarly takes time to reduce speed.
Care must be taken during the approach to avoid situations where the maximum thrust cannot be
obtained before the minimum airspeed is reached (i.e. where the time to reach the minimum
airspeed from the minimum drag speed may be less than the time taken for the engines to
accelerate to maximum thrust).
By comparison, piston-engine aircraft are less susceptible to speed instability because the:
Deploying the flaps and lowering the undercarriage (landing configuration) help to delay the onset of
speed instability by increasing profile drag, thus reducing the minimum drag speed (Fig. 10.47).
DRAG
MINIMUM DRAG
IN LANDING
CONFIGURATION
DRAG CURVE IN
LANDING CONFIGURATION
M INIM UM DRAG
FOR CLEAN
AIRCRAFT B
SPEED INSTABILITY
FOR CLEAN
AIRCRAFT
AIRSPEED (IAS)
FIG. 10.47
10-32
INTRODUCTION
When an aircraft flies close to a surface (e.g. ground or water) the lift, drag, and stability
characteristics change significantly. The changes are collectively known as ground effect.
Ground Effect occurs whenever an aircraft is one wingspan or less above the surface and is
considered noticeable when at or below wingspan of the surface. The closer to the surface, the
more pronounced the effect.
FIG. 11.1
This results in a reduction in the amount of induced downwash behind the wing and increases the
wings effective angle of attack (Fig. 11.2).
INCREASED LIFT
INCREASED EFFECTIVE
ANGLE OF ATTACK
FIG. 11.2
Principles Of Flight (Rev Q407)
11-1
Chapter 11
Ground Effect
It also alters the pressure distribution around the wing and the amount of lift developed. This
occurs because the change in effective angle of attack increases the wings coefficient of lift (CL)
and thus its lifting capability at any given angle of attack. The aircraft also stalls at a lower angle
of attack when flying in ground effect. (Fig. 11.3).
Thrust
Available
Drag or
Thrust
Required
Speed
Instability
Stalling Speed
VIMD
Airspeed
FIG. 11.3
The magnitude of the wing tip vortices, and thus downwash, also determine the amount of
induced drag produced by the wing. The closer the aircraft is to the surface, the greater the
reduction in induced drag at any given angle of attack (Fig. 11.4).
60
50
PERCENTAGE 40
REDUCTION
IN
INDUCED DRAG 30
20
10
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
RATIO OF WING HEIGHT TO SPAN,
FIG. 11.4
The reduction in induced drag is approximately 1% at a height of one wingspan above the
surface, decreasing to 50% at a height of one tenth of the wingspan. This effect is therefore
significant, very close to the runway on take off and landing.
11-2
Ground Effect
Thrust Required
(N)
Chapter 11
Aircraft In Ground
Effect
Velocity (Knots)
FIG. 11.5
The second characteristic associated with ground effect is the change in aircraft trim and stability.
This occurs because the surface deflects the downwash acting behind the wing, thus altering the
angle at which the airflow meets the tailplane (Fig. 11.6).
REDUCED
DOWN
LOAD
DOWN
LOAD
DOWNWASH
DOWNWASH
DOWNWASH PATH OUT
OF GROUND EFFECT
DOWNWASH PATH IN
GROUND EFFECT
FIG. 11.6
This places the tailplane at a less negative, or increased angle of attack, and reduces the
download acting on the tailplane. In this condition, the aircraft experiences a nose-down pitching
moment, although high T tailed aircraft do not respond in this manner, since the tailplane is
outside the influence of the downwash.
11-3
Chapter 11
Ground Effect
FIG. 11.7
This significantly reduces the maximum lift capability of the wing, compared to that obtained
outside ground effect. This is one of the main reasons why STOL aircraft are manufactured with a
high wing configuration
11-4
INTRODUCTION
The purpose of the propeller is to convert the power output from the engine into thrust. The power
developed (BHP) is transmitted to the propeller shaft as engine torque and rotates the propeller.
As the propeller rotates, it accelerates a large mass of air rearward at a relatively low velocity.
The reaction to this is a force known as thrust, which propels an aircraft along its flight path.
Propellers are classified as either left-handed or right-handed, depending on the direction in
which they rotate. If viewed from the cockpit, a left-handed propeller rotates anti-clockwise and a
right-handed propeller rotates clockwise. The propellers on most modern single engine aircraft
are right-handed (Fig. 12.1).
CLOCKWISE
FIG. 12.1
PROPELLER TERMINOLOGY
Fixed pitch propellers are usually manufactured in one piece and are normally used on low power
single-engine aircraft. They usually consist of two or more blades attached to a central hub. Most
are attached directly to the end of the engine crankshaft (Fig. 12.2).
HUB
CRANKSHAFT
FIG. 12.2
Principles Of Flight (Rev Q407)
12-1
Chapter 12
Propellers
The propellers are mainly manufactured from aluminium-alloy forgings and are anodised or
painted to provide the necessary protection. Like a wing, each blade has an aerofoil section,
leading edge, trailing edge, and tip (Fig. 12.3).
TRAILING EDGE
LEADING EDGE
TIP
SHANK
FIG. 12.3
The part of the blade nearest the hub is called the shank. It has greater cross-section than the
rest of the blade, because this is where the greatest stresses occur in normal operation. The
blades are also twisted along their length and have a decreasing chord and depth of section from
root to tip (Fig. 12.4).
BLADE ANGLE
PLANE OF ROTATION
FIG. 12.4
The blades twist more at the root than the tip to maintain a constant angle of attack along the
complete blade. The angle at which the chord line of each section is inclined to the plane of
rotation (i.e. the plane in which the propeller rotates, 90 to the crankshaft centre-line) is the
blade angle (Fig. 12.5).
12-2
Propellers
Chapter 12
PLANE OF
ROTATION
BLADE
BACK
BLADE
ANGLE
DIRECTION
OF FLIGHT
SPINNER
CHORDLINE
BLADE
FACE
FIG. 12.5
Fine pitch is a setting that produces less resistance to rotation and is a low blade angle. Coarse
pitch is a setting that increases the resistance to rotation and is a high blade angle.
The flat side of a propeller blade is called the blade face, pressure face, or thrust face (the side
facing the pilot) and the curved face is called the blade back. The propeller hub is also
streamlined via an aerodynamically shaped structural cover, called a spinner.
Resultant
Velocity
Direction of
Flight
Rotational Velocity
(rpm)
Forward Velocity
(TAS)
FIG. 12.6
12-3
Chapter 12
Propellers
For any given blade section, the forward velocity remains constant but the rotational velocity
increases with distance from the blade hub (i.e. the closer to the tip the greater the rotational
velocity) (Fig. 12.7).
DISTRIBUTION OF
ROTATION VELOCITY
COMPONENT
FIG. 12.7
As the blade rotates, the air opposes its movement and each blade section experiences a
different relative airflow (Fig. 12.8).
Chord
Relative Airflow
Airflow due to
Rotation
Plane of
Rotation
Airflow due to
Forward Movement
FIG. 12.8
The angle between the relative airflow and the blade section chord line is the angle of attack.
This angle consequently varies if either the rotational velocity or the forward airspeed changes
(Fig. 12.9).
12-4
Propellers
Chapter 12
SAME AIRSPEED
DIFF. AIRSPEED
DIFF. RPM
SAME RPM
AT HIGH RPM
HIGH AoA
LOW AoA
LOW RPM
FIG. 12.9
The propeller blades twist from the hub to the tip (i.e. the blade angle reduces toward the tip) so
that all blade sections along the entire length operate at the same angle of attack (Fig. 12.10).
HOW BLADE SECTION
IS SET AT TIP
RELATIVE AIRFLOW
FOR TIP SECTION
FORWARD
VELOCITY
IN HALF A
REVOLUTION
FIG. 12.10
12-5
Chapter 12
Propellers
TIP VORTEX
FIG. 12.11
At positive angles of attack, the greatest useful thrust is produced at 75% of the tip radius. By
convention, the blade angle at this radius is the reference pitch for the whole propeller blade.
Chord
Relative Airflow
Airflow due to
Rotation
Plane of
Rotation
Airflow due to
Forward Movement
FIG. 12.12
12-6
Propellers
Chapter 12
Thrust acts parallel to the direction of flight, whilst propeller torque (the resistance to the motion in
the plane of rotation) acts perpendicular to the direction of flight. The propeller torque must thus
be overcome or balanced by engine torque for a propeller section to provide thrust. As with a
wing, the relative size of the components depends on the angle of attack, with the greatest ratio
of thrust to propeller torque occurring at an angle of attack of 3 or 4 degrees. As the angle of
attack decreases, the thrust similarly decreases.
There are five operational forces acting on a propeller. They are:
FIG. 12.13
12-7
Chapter 12
Propellers
FIG. 12.14
CENTRIFUGAL FORCES
Due to the centrifugal action, high stress is felt on the propeller as the blades are thrown out of
the hub (Fig. 12.15).
FIG. 12.15
12-8
Propellers
Chapter 12
FIG. 12.16
FIG. 12.17
PROPELLER EFFICIENCY
Propeller efficiency is defined as the ratio of thrust horsepower delivered compared to the engine
power required to drive a propeller at a given rpm (brake horsepower), so that:
Propeller Efficiency =
Thrust Horsepower
Brake Horsepower
12-9
Chapter 12
Propellers
It is alternatively defined as the ratio of useful work done by the propeller in moving an aircraft,
compared to the work supplied by the engine. The work done by the propeller is the product of
the thrust and forward airspeed (TAS), whilst the work supplied by the engine is the torque
required to turn the propeller at a given rotational velocity (rpm), so that:
Propeller Efficiency =
Thrust x TAS
Propeller Torque x RPM
The efficiency is therefore zero when either the thrust or forward airspeed is zero. If the airspeed
is zero, no work is being done in moving the aircraft, so none of the power being delivered by the
propeller is being used.
Likewise, if the thrust is zero, no work is being done in moving the aircraft. Furthermore, since the
brake horsepower delivered by the engine is proportional to the propeller torque, the efficiency of
the propeller depends on the ratio of the thrust force to propeller torque, which depends on the
blade angle of attack.
PROPELLER
EFFICIENCY
BLADE
ANGLE OF ATTACK
3/4
FIG. 12.18
Fig. 12.18 shows how propeller efficiency varies with blade angle of attack. Like a wing, the
propeller is most efficient when the blade section angle of attack is 3 to 4 degrees. For a fixed
pitch propeller, the angle of attack at any given rpm also depends directly on the aircraft's forward
airspeed which also determines a propeller's efficiency (Fig. 12.19).
100
90
80
70
60
50
FIXED PITCH
40
30
AVERAGE
PITCH ANGLE
20
10
0
FIG.12.19
12-10
Propellers
Chapter 12
Maximum efficiency occurs at one airspeed and one particular blade angle of attack. The highest
efficiency obtained by a propeller is 85% to 88%. The blade angle is usually set so that the speed
for maximum efficiency is close to the cruising speed. At any other airspeed, the efficiency is
relatively low and only a small proportion of the power being delivered by the engine is used to
propel the aircraft. Consider a fixed pitch propeller travelling at different forward airspeeds at a
constant rpm (Fig. 12.20).
RELATIVE AIRFLOW
RELATIVE AIRFLOW
HIGH
SPEED
OPTIMUM
SPEED
FORWARD AIRSPEED (TAS)
RELATIVE AIRFLOW
LOW
SPEED
FIG. 12.20
At low airspeeds, the thrust increases with the angle of attack, but because the speed is low,
propeller efficiency is low. For example, no useful work is being done when holding the aircraft
against the brakes, with the angle of attack the same as the blade angle. At high airspeeds, the
angle of attack is minimal and the propeller efficiency is low.
RELATIVE
AIRFLOW
NEGATIVE
ANGLE OF
ATTACK
POSITIVE
ANGLE OF
ATTACK
RELATIVE
AIRFLOW
VARYING
ROTATIONAL
VELOCITY
CONSTANT
FORWARD AIRSPEED (TAS)
FIG. 12.21
Principles Of Flight (Rev Q407)
12-11
Chapter 12
Propellers
When this occurs, the total reaction acts in a rearward direction and its components alter their
orientation (Fig. 12.22).
PLANE OF
ROTATION
ANGLE OF
ATTACK
DIRECTION
DRAG
OF FLIGHT
PROPELLER
TORQUE
FORCE
RELATIVE
AIRFLOW
TOTAL
REACTION
FIG. 12.22
The components of the total reaction are drag and propeller torque. The torque force no longer
opposes the blade rotation, but instead acts in the direction of rotation and assists with rotation,
thus driving the engine. At the same time, the airflow impinging on the blade back produces a
drag force, opposing the forward flight of the aircraft. The drag force caused by a windmilling
propeller can be extremely high, causing a decelerating effect on the aircraft.
On aeroplanes where it is possible to feather the propeller following an engine failure, this
should be done to reduce the drag. When a propeller is feathered the blade angle is increased to
approximately 90 so that it is almost inline with the relative airflow and produces no torque.
12-12
Propellers
Chapter 12
PROPELLER PITCH
Due to the interaction between forward velocity and rotational velocity, each propeller blade
section follows a corkscrew, or helical path through the air. For example, consider the helix traced
by the blade tip in one revolution (Fig. 12.23).
HELIX TRACED BY BLADE
TIP IN ONE REVOLUTION
ACTUAL
PATH OF
BLADE
SLIP
EFFECTIVE
PITCH
THEORETICAL DISTANCE MOVED
PER REVOLUTION GEOMETRIC PITCH
FIG. 12.23
The theoretical distance moved forward in each complete revolution is the geometric pitch. This
does not take into account any losses due to inefficiency. The actual distance moved forward in
each revolution is the effective pitch. The difference between the two is known as slip, so that:
Slip = Geometric Pitch - Effective Pitch
12-13
Chapter 12
Propellers
The effective pitch is not a fixed quantity, and it varies with forward airspeed, as does the amount
of slip for a given rpm.
Direction of
Rotation
Chord
Blade Angle
Direction of
Flight
Relative
Airflow
Slip
Sli
Helix Angle
Plane of
Rotation
Effective
Pitch
Geometric
Pitch
FIG. 12.24
Fig. 12.24 shows that slip is directly related to angle of attack, whilst the effective pitch is
governed by the helix angle (angle of advance). These two angles together constitute the blade
angle, so that:
Blade Angle = Angle of Attack + Helix Angle
The effective pitch varies with changes in angle of attack.
12-14
Propellers
Chapter 12
They are only efficient at one particular combination of airspeed and rotational
velocity (rpm).
During take-off, the angle of attack is large because the airspeed is low and the
rotational velocity is high (Fig. 12.25).
BLADE
ROTATIONAL VELOCITY
HIGH
ANGLE
OF ATTACK
ANGLE
LOW
SPEED
FIG. 12.25
During cruise conditions, the angle of attack is small and so forward airspeeds are
limited to prevent engine overspeed (Fig. 20.26).
ROTATIONAL VELOCITY
LOW ANGLE
OF ATTACK
BLADE
ANGLE
FIG. 12.26
Good take-off performance is achieved at the expense of cruise performance and vice versa.
More complex single and multi-engine light aircraft use variable pitch or constant speed
propellers, where the blade angle varies in flight.
12-15
Chapter 12
Propellers
FIG. 12.27
12-16
Propellers
Chapter 12
POWER ABSORPTION
For maximum efficiency, the propeller must be capable of fully absorbing the engines maximum
power output during its normal operating range as it accelerates air rearward. If the engine power
exceeds the propeller torque, the propeller overspeeds, causing both the engine and propeller to
become inefficient.
A propellers capacity for absorbing power depends on the following design features:
Installing an engine of greater power output allows any of these quantities to be increased,
although each has its own limitations. A compromise is normally necessary in the final propeller
design. The load on the engine created by the propeller also limits the engine speed.
The blade diameter is an important factor since the greater the diameter the greater the tip
speeds at a lower rpm, therefore allowing the tips to reach sonic velocity earlier. At sonic velocity,
the compressibility effects reduce thrust and increase drag, therefore reducing the propeller
efficiency. This effect also results in unacceptably high noise levels. One solution to reduce
propeller noise is to obtain lower tip velocities by decreasing the diameter and increasing the
number of blades.
PROPELLER SOLIDITY
Solidity is the usual method of increasing the power absorption capability of the propeller and is a
ratio between the solid part of the propeller disc and the circumference at a specified radius.
Normally 70% tip radius is used, since this is the most efficient region of a propeller blade.
There are two ways to increase solidity: increase the number of blades or the blade chord. It can
be expressed by the following formula:
Solidity = Number of Blades x Chord at 70% Tip Radius
Circumference at 70% Tip Radius
There is obviously a limit to the size and number of blades that can be fitted, but newer methods
are constantly being developed, like the swept sabre sword shape that increases the solidity
whilst safeguarding tip speed.
Slipstream effect
Torque reaction
Gyroscopic effect
Asymmetric blade effect
12-17
Chapter 12
Propellers
To analyse these effects, consider a right-handed propeller, which rotates clockwise as viewed
from the cockpit.
Slipstream Effect
As the propeller rotates clockwise, it imparts a rotational flow to the air and produces a
slipstream, which passes around the fuselage and strikes the left side of the fin (Fig.
12.28).
Propeller Rotation
Tail Moves
Right
Left Yaw
Slipstream
Normal Axis
FIG. 12.28
This causes the aircraft to yaw to the left. The actual amount of rotation imparted to the
air is dependent on the power setting. Applying right rudder counteracts this effect, but on
some aircraft, the fin is alternatively offset (Fig. 12.29).
SLIPSTREAM
RELATIVE AIRFLOW
OFFSET FIN
FIG. 12.29
Torque Reaction
This occurs because the air resists the motion of the propeller. In so doing, it tends to
twist the engine and airframe in the opposite direction to the propeller (i.e. counterclockwise) (Fig. 12.30).
12-18
Propellers
Chapter 12
Direction of
Prop Rotation
Longitudinal
Axis
Torque
Reaction
FIG. 12.30
This causes the aircraft to roll to the left and, whilst on the ground, places more weight on
the left wheel than the right wheel. This effectively increases the rolling resistance (i.e.
drag) of the left wheel, thus slowing the aircraft down and causing it to yaw to the left.
Gyroscopic Effect
With a tail-dragger type aircraft, the tail is lifted off the ground as soon as possible during
the take-off run in order to minimise drag and place the aircraft in a flying attitude (Fig.
12.31).
Tail is Raised
Applied Force
90
Resultant Force
Aircraft Pitches
About Lateral Axis
FIG. 12.31
As the tailwheel leaves the ground, a forward force is applied to the top of the rotating
propeller disc, tending to alter its plane of rotation in the nose-down sense. Since the
propeller disc constitutes a large rotating mass, it behaves like a basic gyroscope and
tends to resist any attempt to change its plane of rotation. As a result, the propeller disc is
subject to gyroscopic precession and a similar force is applied 90 later in the direction
of the propeller rotation (Fig. 12.32).
Principles Of Flight (Rev Q407)
12-19
Chapter 12
Propellers
AIRCRAFT YAWS
TO THE LEFT
FIG. 12.32
This causes a forward force to act on the right-hand side of the propeller disc and the
aircraft yaws to the left. Conversely, an aircraft purposely yawed to the right in flight
experiences a nose down pitching moment due to the gyroscopic effect of the rotating
propeller. The effects on the aircraft are reversed if the propeller rotates in a counterclockwise direction when viewed from the cockpit (i.e. a left-handed propeller yaws the
aircraft to the right on take-off).
Asymmetric Blade Effect
This effect occurs when the axis of rotation of the propeller is inclined to the direction of
flight. For example, when the tail wheel on a tail-dragger type aircraft is in contact with
the ground, its longitudinal axis inclines above the horizontal (Fig. 12.33).
LARGE
AOA
RELATIVE AIRFLOW
TO UPGOING BLADE
RELATIVE AIRFLOW
TO DOWNGOING
BLADE
SMALL
AOA
FIG. 12.33
12-20
Propellers
Chapter 12
This causes the down-going blade to have a greater effective angle of attack than the up-going
blade, thus developing greater thrust (Fig. 12.34).
The thrust asymmetry between the two blades causes the aircraft to yaw to the left on
take-off. Conversely, if an aircraft is flying yawed, then the asymmetry of the thrust
causes a pitching moment.
These effects all act together during take-off to yaw the aircraft in the same direction. Some
aircraft compensate for some of these effects (e.g. undercarriage design and biased trim). For
example, an aircraft fitted with a tricycle type undercarriage is virtually unaffected by asymmetric
blade effect and gyroscope effect, because it remains in a level flight attitude during the complete
take-off run.
PROPELLER ICING
Ice contamination on the propeller has the same effect as ice on the wings, in that both reduce
the efficiency of the aerofoils. Leading edge ice on the propeller reduces the generated thrust in
the same way the lift of the wing is reduced; by creating turbulent air flow.
In the same way, as the drag of an ice contaminated aeroplane increases, the resisting force on
the propeller increases for a given rpm and blade angle. Ice separating from the propeller blades,
as well as vibration due to propeller imbalance, may cause damage to the aeroplane structure.
Since ice on the propeller blades reduces the available thrust, extra power may be required from
the engine to overcome the increased drag.
12-21
Chapter 12
12-22
Propellers
INTRODUCTION
If one engine on a conventional twin-engine aircraft fails in flight, it adversely affects its
performance and controllability (Fig. 13.1).
THRUST
FIG. 13.1
This is because the subsequent reduction in thrust drastically reduces the aircrafts overall climb
capability. If the airspeed is too low, the yawing moments due to the failed engine may even
make the aircraft uncontrollable.
13-1
Chapter 13
Asymmetric Flight
THP Available
Both Engines
Operating
300
Excess THP
Available
150
THP
HP Required
50
100
150
200
TAS
FIG. 13.2
The THP available in this example is well in excess of that required to maintain level flight and the
aircraft exhibits a good rate of climb. If one engine fails, however, the total power available
immediately decreases by 50% to 150 THP (Fig. 13.3).
300
THP AVAILABLE
BOTH ENGINES OPERATING
ONE
ENGINE
INOPERATIVE
THP
THP AVAILABLE
150
HP REQUIRED
EXCESS THRUST
HORSE POWER
AVAILABLE
50
100
TAS
150
200
FIG. 13.3
Even with the propeller of the inoperative engine feathered, and the aircraft in a clean
configuration, additional drag exists. This leads to a significant reduction in the amount of excess
power available. In some aircraft, the loss can be as high as 80% or more of the original value.
The aircrafts rate of climb decreases substantially during asymmetric power conditions. In some
cases, depending on the aircraft type, gross weight, configuration, and air temperature, a
situation may occur where it is impossible even to maintain level flight. For example, consider an
aircraft in its take-off configuration (i.e. with its undercarriage and flaps lowered) where any
associated increase in drag results in a power requirement that exceeds the amount of power
available, thereby preventing an aircraft from being able to maintain a given altitude (Fig. 13.4).
13-2
Asymmetric Flight
Chapter 13
300
THP Available
One Engine
Inoperative
150
THP
HP Required
Excess THP
Available
0
50
100
150
200
TAS
FIG. 13.4
YAWING MOMENTS
With both engines operating at the same power setting on a twin-engine aircraft, the amount of
thrust produced by each engine is identical and their lines of action are symmetrically displaced
about the aircraft's normal axis (Fig. 13.5).
THRUST
THRUST
FIG. 13.5
13-3
Chapter 13
Asymmetric Flight
If one engine fails in flight, the remaining thrust forces are asymmetrically displaced and the
aircraft yaws in the direction of the failed engine (Fig. 13.6).
MAX THRUST
NO THRUST
MOMENT ARM
FIG. 13.6
The resulting yawing moment is a product of the thrust force and its perpendicular distance from
the aircraft's centre of gravity. Thus, at any given airspeed the moment is greatest when the
operating engine is producing maximum thrust. The distance of the engine from the aircraft's
centre line also determines the strength of the yawing moment (i.e. the further away the engine is,
the greater the yawing moment.
Therefore, aircraft engines are normally located as close to the fuselage as possible to minimise
the yawing tendency if an engine fails. On propeller driven aircraft, the significant rise in drag
resulting from the windmilling propeller on the failed engine further intensifies the yawing moment
(Fig. 13.7).
13-4
Asymmetric Flight
Chapter 13
THRUST
NORMAL
DRAG
NORMAL DRAG
ADDITIONAL DRAG
FROM WINDMILLING
PROPELLER
FIG. 13.7
The thrust and drag forces produce a couple which acts about the aircraft's centre of gravity and
further increases the yawing tendency toward the failed engine. Using the rudder can counteract
this yawing tendency (e.g. if the left engine fails, the rudder should be deflected to the right or in
the same direction as the operating engine) (Fig. 13.8).
YAWING MOMENT
THRUST
DRAG
RUDDER
FORCE
CORRECTING MOMENT
FIG. 13.8
13-5
Chapter 13
Asymmetric Flight
If the yawing moment produced by the thrust/drag couple is balanced by the rudder force
multiplied by its distance from the centre of gravity, the aircraft continues along its original flight
path. The further aft the centre of gravity (X), the greater the rudder force needed for a given set
of conditions (Fig. 13.9).
THRUST
THRUST
FORWARD C G
SHORT MOMENT
ARM
LONG MOMENT
ARM
RUDDER FORCE
AFT C G
FIG. 13.9
The rudder must therefore be sufficiently effective to be able to overcome the yawing moment
produced by the thrust/drag couple. The amount of force being applied by the rudder depends on
the aircraft's airspeed (IAS), so the lower the airspeed the greater the rudder deflection required
to produce the same force.
ASCENDING
BLADE
INCLINATION OF
PROPELLER SHAFT
LINE OF FLIGHT
DESCENDING
BLADE
HIGHER ANGLE
OF ATTACK
FIG. 13.10
13-6
Asymmetric Flight
Chapter 13
The amount of thrust developed by the descending blade is further augmented by the fact that it
moves a greater distance forward than the ascending blade in a given time. As a result, it travels
faster relative to the air (Fig. 13.11).
DESCENDING BLADE
ASCENDING BLADE
FIG. 13.11
These two effects combine to create a thrust line that is slightly offset from the centre line of the
engine. For example, if the propeller rotates in a clockwise direction (viewed from the cockpit), the
thrust line offsets to the right, intensifying the yawing moment on the right engine (Fig. 13.12).
THRUST
NO THRUST
FIG. 13.12
13-7
Chapter 13
Asymmetric Flight
Conversely, if both propellers rotate clockwise, failure of the right engine results in a smaller
yawing moment, because the thrust line of the left engine is closer to the aircraft's centre line
(Fig. 13.13).
CRITICAL ENGINE
FIG. 13.13
In this case, the left engine is considered to be the critical engine (i.e. the engine whose failure
would most adversely affect the performance or handling characteristics of the aircraft). If the
propellers were left-handed, the right engine would be the critical engine. To overcome this
problem, some aircraft have the engines arranged so that the propeller on the left engine rotates
clockwise, whilst the propeller on the right engine rotates counter-clockwise (e.g. Piper Seneca)
(Fig. 13.14).
FIG. 13-14
13-8
Asymmetric Flight
Chapter 13
This ensures that the thrust lines act the same distance from the aircrafts centre of gravity, so
that no critical engine exists and the strength of the yawing moment toward the failed engine is
identical if either engine should fail.
RELATIVE
AIRFLOW
RELATIVE
AIRFLOW
FIG. 13.15
This is because the fin and rudder are presented to the airflow at an increased angle of attack.
The angle of bank should be strictly limited, since excessive bank results in a large reduction in
the lift force directly opposing the aircrafts weight (Fig. 13.16).
REDUCTION
IN LIFT
TILTED
LIFT LINE
WEIGHT
FIG. 13.16
13-9
Chapter 13
Asymmetric Flight
In order to recover the lost lift it is necessary to increase either the angle of attack or the airspeed.
These actions result in increased drag, consequently requiring more thrust to maintain a given
altitude, thus worsening the asymmetric effect. The angle of bank available to counter the effect
of engine failure is therefore limited to 5.
RELATIVE
AIRFLOW
3000LBS
5000LBS
5000LBS
WEIGHT
3000LBS THRUST
FIG. 13.17
Thus, the greater the weight, the greater the induced side slip and the greater the rudder
effectiveness. This benefit is insignificant compared to the penalties associated with any
additional weight.
ROLLING MOMENTS
A secondary effect of engine failure is a rolling moment toward the failed engine due to the
variation in the wing lift distributions (Fig. 13.18).
FIG. 13.18
This is primarily due to the absence of propeller slipstream behind the failed engine and the
disturbance of the airflow behind the windmilling propeller.
13-10
Asymmetric Flight
Chapter 13
The aircraft initially continues to travel along its original flight path due to its inertia and, as it yaws
toward the failed engine, the outer wing travels faster than the inner wing and produces more lift.
This intensifies the roll toward the failed engine. Due to side slip, the fuselage also shields part of
the wing on the side of the failed engine, thus weakening its lift distribution and intensifying the
rolling moment toward the failed engine (Fig. 13.19).
AREA OF
REDUCED
LIFT
FIG. 13.19
13-11
Chapter 13
Asymmetric Flight
If one engine fails when the aircraft is operating close to VMCA, it is vital to reduce the drag as
soon as possible by feathering the propeller on the failed engine.
If the critical engine fails during the take-off phase, maintain the airspeed above VMCG, which is
the minimum control speed with the wheels still on the ground. The definition of VMCG is the
minimum control speed on the ground during the take-off run when it is still possible to maintain
directional control using the rudder only. VMCG must be established with the:
If the critical engine fails during the approach and landing phase of flight, maintain the airspeed
above VMCL, which is the minimum control speed during the approach and landing. The definition
of VMCL is the minimum control speed at which it is possible to maintain directional control in the
landing configuration with an angle of bank of not more than 5. VMCL must be established with
the:
Aircraft in its most critical landing configuration and all engines operating
Centre of gravity as far aft as possible and the aircraft at its maximum landing weight
Propeller on the failed engine (propeller aircraft only) in the position it achieves
without pilot action, whilst maintaining a 3 glide slope
Go-around power/thrust setting on the operating engine
It is also a requirement that when VMCL is demonstrated, the aeroplane must be able to be rolled
through 20 degrees in either direction in not more than 5 seconds.
Remember that all minimum control speeds (except VMCL when limited by minimum required roll
rate rather than directional control) increase as air density increases. This is because the yaw is
caused by the engine thrust of the working engine, and there will be more thrust and therefore
yaw when the air is dense. Dense air occurs when the air is cold and at low pressure altitude.
TURNING FLIGHT
The main factors which affect an aircraft turning under asymmetric power conditions are airspeed
and the direction of the turn relative to the failed engine. For example, consider an aircraft where
the left engine has failed and the yawing and rolling moments have been stabilised using right
rudder. To initiate and hold a balanced left turn, the amount of right rudder needed to counteract
the yaw has to be reduced, whilst a balanced right turn requires additional right rudder under the
same conditions. If the airspeed is too low, turning toward the operating engine may reduce the
control forces to a critical level. At low indicated airspeeds, it is therefore necessary to limit turns
to only small angles of bank, since rudder deflection may become insufficient to maintain a
balanced turn.
INTRODUCTION
During high-speed flight, significant changes occur in the flow and pressure distributions around
the aeroplane, which result in a loss of lift and an increase in drag. This is caused by the
formation of shock waves, which adversely affect the stability and control characteristics of the
aeroplane. Aeroplane designed to fly at high Mach numbers therefore incorporate features
designed to minimise these effects.
40
30
20
10
0
-10
-20
-30
-40
-50
-60
570
590
610
630
650
KNOTS
670
690
700
FIG. 14.1
Alternately the speed of sound can be calculated using the equation
a = 38.95 temperature in Kelvin. (in knots)
14-1
Chapter 14
High-Speed Flight
The speed of sound is therefore solely dependent on the ambient air temperature and varies with
altitude as illustrated in the following table:
ALTITUDE (ft)
TEMPERATURE (C)
Sea Level
5000
10 000
15 000
20 000
25 000
30 000
35 000
40 000
50 000
60 000
15.0
5.1
-4.8
-14.7
-24.6
-34.5
-44.4
-54.3
-56.5
-56.5
-56.5
661.7
650.3
638.6
626.7
614.6
602.2
598.6
576.6
573.8
573.8
573.8
The speed of sound at sea level is approximately 660 kt and steadily reduces up to the base of
the Tropopause, where after it remains constant.
Fully subsonic aeroplane can be heard approaching because they send out pressure
disturbances, or waves in all directions, which travel at the speed of sound. This enables an
approaching aeroplane to be heard, and for the air to start moving ahead of the aeroplane to
allow its passage. Conversely, aeroplanes travelling at supersonic speeds cannot be heard until
the aeroplane has passed because the aeroplane is travelling faster that the pressure sound
waves that it produces.
MACH NUMBER
Mach number is named after Ernst Mach, an Austrian physicist, and is the ratio of the actual
speed of a body or flow to the speed of sound in the surrounding atmosphere, so that:
V
The TAS of a body or flow
=
The Local Speed of Sound
a
This means that if the TAS is 450knots and the local speed of sound 600knots, the mach number
is 0.75M.
14-2
High-Speed Flight
Chapter 14
The left hand graph shows what would happen to the CAS and TAS, if the aeroplane were to
climb or descend at a constant mach number, which is the normal operational situation at higher
altitudes. Climbing the CAS and TAS would both decrease (although the CAS would decrease at
a faster rate than the TAS) and descending the CAS and TAS would both increase.
The centre graph shows the unpractical situation of an aeroplane climbing or descending at a
constant TAS. Climbing at a constant TAS the CAS would decrease and the mach number
increase. In the descent at a constant TAS, the CAS would increase and the mach number would
decrease.
The right hand graph shows the normal operational situation at lower altitudes, where an
aeroplane climbs and descends at a constant CAS. In a climb at a constant CAS, the TAS and
mach number both increase. In a descent at a constant CAS the TAS and mach number both
decrease.
14-3
Chapter 14
High-Speed Flight
FIG. 14.2
The waves maintain their separation and have no tendency to bunch up. As long as the pressure
waves continue to travel faster than the source, a disturbance occurs ahead of the object as a
normal wave under subsonic flow conditions. If the source moves at the speed of sound, the
waves no longer move ahead of the source and bunch up to form a normal Mach wave, which
acts at right angles to the direction of movement (Fig. 14.3).
1
2
3
-A
2 1
FIG. 14.3
If the source travels faster than the wave progression (i.e. at a speed greater than the speed of
sound), a supersonic flow condition exists and the waves pile up on each other to form a
boundary beyond which no wave passes as it is the pressure waves cannot propagates faster
than the local speed of sound . This boundary is an oblique shockwave, and the angle it makes
with the flight path is called the Mach angle (Fig. 14.4) which is designated by the greek letter
MU ().
14-4
High-Speed Flight
Chapter 14
As this shockwave is inclined backwards in all directions from the aeroplane, it will form the
surface of a cone, called the Mach cone.
In the above diagram triangle ABC has side AB equal to the local speed of sound, and side BC is
the TAS.
Since is the angle ACB, sin = LSS/TAS = 1/Machnumber.
Hence as the machnumber of an aeroplane increases, the Mach cone angle (), decreases.
Numerically, at Mach 2 sin = , and the Mach cone angle, , is 30 degrees .
NATURE OF COMPRESSIBILITY
Air is termed incompressible whenever it undergoes changes in pressure without apparent
changes in density, (i.e. air is analogous to the flow of water, hydraulic fluid, or any other
incompressible fluid). If air was fully incompressible, the speed at which pressure disturbances
travelled would be infinite. The disturbance created by an aeroplane would thus be felt
everywhere instantaneously, regardless of the aeroplane speed. Air is compressible, however,
and changes in density and temperature accompany a change in pressure. The speed of
propagation of the pressure waves therefore has a finite value, which is directly related to the
speed of sound. The principle difference between low subsonic and supersonic airflow is that
supersonic airflow is compressible. Any change in the velocity or pressure of the supersonic
airflow results in a change in density. The following table identifies the main differences between
subsonic and supersonic airflow in a stream-tube:
SUBSONIC FLOW
SUPERSONIC FLOW
CONVERGING
CHANNEL
decreasing velocity,
increasing static pressure,
increasing density
DIVERGING CHANNEL
increasing velocity,
decreasing static
pressure, reducing density
MFS =
Principles Of Flight (Rev Q407)
TAS
Aircraft' s True Airspeed
=
Local speed of Sound
LSS
14-5
Chapter 14
High-Speed Flight
.74
.78
.82
.78
.74
M = .70
M = .70
FIG. 14.5
For a given aerofoil section and free stream Mach number, the local Mach number also varies
directly with changes in the angle of attack.
.95
1.00
.95
.90
M = .85
M = .85
(CRIT ICAL M ACH
NUM BER)
FIG . 14.6
14-6
High-Speed Flight
Chapter 14
In subsonic flight, the total airflow around an aeroplane is travelling at a speed less
than the speed of sound. This includes speeds of approximately Mach 0.75 or less.
Transonic flight occurs at speeds approximately Mach 0.75 and Mach 1.2, where
the airflow around an aeroplane is partly subsonic, and partly supersonic.
Supersonic flight occurs at speeds between approximately Mach 1.2 and Mach 5.0,
where the total airflow around an aeroplane is travelling at a speed greater than the
speed of sound.
FIG . 14.7
In supersonic flow, where the object is travelling at speeds in excess of the speed of sound, the
pressures acting upon it will not influence the flow ahead of the object. It will only be influenced
when the air particles are suddenly forced out of the way by a concentrated pressure wave set up
by the object (Fig. 14.8).
FIG. 14.8
Principles Of Flight (Rev Q407)
14-7
Chapter 14
High-Speed Flight
FIG. 14.9
At low subsonic airspeeds (e.g. Mach 0.6), the disturbances travel forward faster than the
oncoming flow, thus warning the air ahead of the aeroplanes approach. As the air flows over the
wing, it accelerates, but remains fully subsonic, and no shock wave forms (Fig. 14.10).
S U B S O N IC F L O W
S U B S O N IC
S E P A R A T IO N
P O IN T
M = 0 .6
FLOW
S U B S O N IC F L O W
F IG . 1 4.1 0
With increasing Mach number, the flow over the wing continues to accelerate and eventually
reaches a sonic value at a particular point on the wing, normally the point of maximum thickness
(Fig. 14.11).
AIRFLOW REACHES
SONIC VALUE
SUBSONIC
SUBSONIC
FLOW
SUBSONIC
FLOW
FLOW
M = 0.75
(CRITICAL M ACH
NUM BER)
SUBSONIC FLOW
FIG. 14.11
14-8
High-Speed Flight
Chapter 14
The aeroplane is now travelling at its critical Mach number, with the airflow to either side of this
point remaining subsonic. With increasing Mach number, this point grows into an area of
supersonic flow, so the air moving over the upper surface will now be moving rearward faster
than the pressure disturbances can move forward. These disturbances consequently pile up on
each other and form a shock wave (Fig. 14.12).
SUPERSONIC
FLOW
SUBSONIC FLOW
SUBSONIC
FLOW
M = 0.77
SUBSONIC FLOW
M = 0.77
FIG. 14.12
The shock wave acts perpendicular, or normal, to the surface, and is more commonly referred to
as a normal shock wave. Notably, this occurs where the flow changes from supersonic back to
subsonic. With increasing Mach number, the shock wave grows in intensity and moves rearward
with a greater portion of the upper surface being covered by supersonic flow. The overall direction
of the airflow remains the same, but as it passes through the shock wave, the following changes
take place:
At Mach 0.82, a weak shock wave also forms on the lower surface of the wing (Fig. 14.13).
SUPERSONIC
FLOW
SUBSONIC
FLOW
SUBSONIC FLOW
NORMAL SHOCK
SEPARATION
M = 0.82
NORMAL SHOCK
SUBSONIC FLOW
FIG. 14.13
14-9
Chapter 14
High-Speed Flight
As the free stream Mach number approaches the speed of sound, the areas of supersonic flow
continue to grow as both shock waves increase in intensity and move rearward (Fig. 14.14).
SUBSONIC FLOW
SUPERSONIC
FLOW
NORM AL SHOCK
SUBSONIC
FLOW
M = 0.95
M = 0.95
NORM AL SHOCK
SUBSONIC FLOW
FIG. 14.14
At speeds just above the speed of sound (M 1.05), another shock wave appears ahead of the
wing, known as a bow wave, and the original shock waves move to the trailing edge (Fig. 14.15).
SUPERSONIC
SUPERSONIC
FLOW
M = 1.05
SUBSONIC
M = 1.05
SUBSONIC
AIRFLOW
"BOW WAVE"
SUPERSONIC
FLOW
SUPERSONIC
FIG. 14.15
14-10
High-Speed Flight
Chapter 14
Behind this shock wave a small region of subsonic flow exists, but everywhere else the flow is
supersonic. Finally, when the flow is fully supersonic (M 2.0), fully developed bow and tail waves
firmly attach themselves at the leading and trailing edges respectively (Fig. 14.16).
SUPERSONIC
SUPERSONIC
FLOW
SUPERSONIC
M = 2.0
SUPERSONIC
SUPERSONIC
FULLY DEVELOPED
BOW WAVE
FULLY DEVELOPED
TAIL WAVE
FIG. 14.16
The Mach number when this occurs is called the shock attachment Mach number (MSA).
PR E S S UR E
DE C R E AS ING
E F FE C T O F S H O C K W A V E
S U D D E N INC R E AS E
IN PR E S S UR E
M = 1
M C R IT
LO C A L
S P E E D O F F LO W
DR O P S T O M C R IT
M = 0
T .E .
L.E .
S U B S O NIC
M = 2
S U P E R S O NIC
SUCTION ON UPPER
SURFACE OF WING
SHOCK STALL
At airspeeds above the critical Mach number, the formation of a shock wave and its associated
pressure gradient results in a significant increase in drag and a reduction in lift (Fig. 14.17).
S U B S O NIC
FL O W
FIG . 1 4.1 7
14-11
Chapter 14
High-Speed Flight
This results from the sudden increase in pressure across the shock wave, which causes localised
heating of the air and the eventual separation of the boundary layer behind the shock wave. At
airspeeds just above the critical Mach number, the increase in drag is mainly due to the loss of
kinetic energy used in heating the air, which needs to be continuously supplied by the engines.
With increasing Mach number the strength of the shock wave steadily increases, as does
the size of the adverse pressure gradient and this determines the point at which the boundary
layer separates from the surface. Both upper and lower surface shock waves can cause
separation of the airflow and, as in the case of a conventional low-speed stall, the larger the
adverse pressure gradient, the larger the associated turbulent wake (Fig. 14.18).
FIG. 14.18
0.75 0.8
1.0
(DRAG DIVERGENCE
SPEED)
COEFFICIENT OF DRAG
COEFFICIENT OF LIFT
When separation first occurs, the coefficient of lift begins to fall and the coefficient of drag begins
to rise rapidly (Fig. 14.19).
0.75 0.8
1.0
FIG. 14.19
This is called the shock stall. It differs from a conventional low-speed stall because it normally
occurs at low angles of attack, although with increasing angles of attack the stall will occur at a
lower Mach number.
14-12
High-Speed Flight
Chapter 14
The combined effect of the energy loss across the shock wave, and the turbulent wake behind
the shock wave, is called wave drag (Fig. 14.20).
DRAG
BOUNDARY
LAYER
SEPARATION
WAVE DRAG
ENERGY
DRAG
FIG. 14.20
The drag varies significantly from the standard drag curve at the drag divergence speed, and the
associated increase in drag is known as the transonic drag rise. This is similar to a conventional
low-airspeed stall, since the separation of the boundary layer during the shock stall also results in
buffeting of the aeroplane and a reduction in control effectiveness.
As the upper layer surface shock wave moves rearward with increasing Mach number, the region
of shock induced separation reduces. Once the lower surface shock is established at the trailing
edge some measure of recovery may occur. A common characteristic of shock wave induced
separation is the increasing severity of buffet intensity with increasing Mach number. In fact, it is
possible that the maximum angle of attack may not be achievable due to this severe buffet
intensity. The aeroplanes manoeuvring capability (load factor) is also reduced.
14-13
Chapter 14
High-Speed Flight
100
50
10
150
200
250
300
350
80
60
POSSIBLE SPEED
RANGE OF FLIGHT
BETWEEN LOW
SPEED & HIGH
SPEED SHOCK
STALL
TROPOPAUSE
40
20
SHOCK
STALL
SPEED
HIGH
A of A
STALL
SPEED
SEA LEVEL
100
SEA LEVEL
200
300
400
500
600
700
FIG.14.21
Stalling can occur conventionally at low airspeeds and high angles of attack, or at high airspeeds
due to shock stall. A specified range of flight speeds is attainable between the two limits at a
given altitude.
The margin between the two types of stall, however, narrows with increasing altitude. Notably the
true airspeed of the low-speed stall increases with increasing altitude for a given indicated
airspeed, whilst the true airspeed of the shock stall reduces up to the base of the tropopause,
above which it remains constant. During manoeuvres, the two stalls will occur at considerably
lower altitudes, because the high angle of attack stalling speed increases, whilst the shock
stalling speed decreases.
The point at which the two stalls coincide is often referred to as the coffin corner. The altitude at
which an aeroplane can fly at one airspeed in a 1g manoeuvre is called the aerodynamic
ceiling. Since this condition has no safety margin, aeroplane must be operated within a buffet
margin of 0.3g. Therefore it is normal to draw a buffet onset boundary chart for 1.3g.
14-14
High-Speed Flight
Chapter 14
14-15
Chapter 14
High-Speed Flight
FIG. 14.22
14-16
High-Speed Flight
Chapter 14
Wing planform has the most significant effect on MCRIT. Careful design not only delays the shock
stall, but also significantly reduces the severity when it occurs. If a wing has sweepback, the
effective chord (parallel to the aeroplanes longitudinal axis) is lengthened, but the wing's
thickness remains unchanged (Fig. 14.23).
ANGLE OF SWEEPBACK
FREE STREAM
AIRFLOW
NORMAL
CHORD
EFFECTIVE
CHORD
FIG. 14.23
This reduces the thickness/chord ratio of the wing, which results in a higher value of MCRIT, and
delays the transonic drag rise (Fig. 14.24).
14-17
Chapter 14
High-Speed Flight
UNSWEPT WING
D
MODERATE SWEEPBACK
HIGH SWEEPBACK
DELAYED
TRANSONIC
DRAG RISE
1.0
FIG. 14.24
Thus, the greater the sweepback, the higher the value of MCRIT and the greater the reduction in
drag under all transonic speeds. Although sweepback is a great asset in increasing the critical
Mach number, it does have a number of disadvantages, which are:
The tailplane behaves similarly to the wing, where shock associated drag is reduced by utilising
thin sections and sweepback. The tailplane is also designed to have a higher critical Mach
number than the wing, so that shock stall can be avoided and full elevator efficiency maintained.
AREA
Regardless of the aeroplanes configuration, there is always additional drag due to interference
between the various components. Interference drag can reach extremely large values at
transonic airspeeds. Thus, to minimise it, the cross-sectional area along its complete length must
follow a smooth pattern, with the area gradually increasing to a maximum, and then decreasing
again giving the optimum area distribution (Fig. 14.25).
WING
FUSELAGE
TAIL
FIG. 14.25
14-18
High-Speed Flight
Chapter 14
SUPERCRITICAL WINGS
To reduce the severity of the shock stall and allow aeroplane to travel faster, some modern jet
transport category aeroplane have supercritical wings. The point of maximum thickness is
positioned close to the trailing edge and the upper surface has a very slight curvature. This
ensures that the localised Mach number remains just above the critical Mach number and results
in a flattish pressure distribution over the majority of the upper surface (Fig. 14.26).
MACH NUMBER
SUPERCRITICAL
FLOW STARTS TO
BE SUPERSONIC
1.0
50
PERCENTAGE OF CHORD
100
FIG. 14.26
This ensures that the flow gradually decelerates near the trailing edge, to a subsonic speed, to
discourage the formation of shock waves. The wings are thicker at the root than conventional
wings and more fuel can be stored in them. The increased thickness at the root also allows the
wings to be of lighter construction. These wings also have less sweepback, giving them a higher
aspect ratio and thus better lift characteristics at a given angle of attack.
SHOCK INDUCED
SEPARATION
FIG. 14.27
The disturbed airflow over the control surfaces may cause uncommanded erratic movements,
although this will not directly affect the air ahead of the shock wave, because the resulting
Principles Of Flight (Rev Q407)
14-19
Chapter 14
High-Speed Flight
pressure disturbances are prevented from travelling forward. The pressure distribution over the
front of the wing is, however, altered; which varies the position of the wings centre of pressure
and its overall pitching moment. This alters the wings angle of attack and results in rapid
backward and forward movements of the shock waves. A kind of instability is set up, and the
rapid changes in the pressure distribution result in vibration of the whole aeroplane. This is
primarily due to the distributed airflow behind the shock wave hitting the tailplane. If shock waves
form on the control surfaces, it will also affect the stick forces by altering their hinge moments
(Fig. 14.28).
F
SHOCK WAVE
CENTRE OF PRESSURE
HINGE
HINGE LINE
FIG. 14 28
Since the hinge moment, which opposes the movement of the control surfaces, is the product of
the force acting through its centre of pressure multiplied by its distance from the hinge line, it
fluctuates, accompanied by the stick force, in phase with any shock wave movement. Thus, any
rearward movement of the shock wave acting on the control surface results in increasing stick
forces. This reaches a maximum value when the shock wave is at the trailing edge (Fig. 14.29).
HINGE LINE
SHOCK WAVE
CENTRE OF PRESSURE
FIG. 14.29
14-20
High-Speed Flight
Chapter 14
If the centre of pressure moves ahead of the hinge-line, transitory overbalance occurs and control
surface reversibility takes place (Fig. 14.30).
F
SHOCK WAVE
FIG. 14.30
Since the shock waves move quickly with changes in control surface deflection, the effects are
felt on the flight deck as snatching or buffeting, depending on the position of the control surface.
The disturbed air resulting from shock induced separation also precludes the use of aerodynamic
balance methods, particularly tabs, so power operated controls are normally used in preference
to manually operated controls. Other methods used to overcome these control problems are:
VORTEX GENERATORS
These are small wing-like surfaces, which are fitted in front of the control surface and project
vertically upward into the airstream (Fig. 14.31). They operate by forcing high-energy air into the
boundary layer, enabling it to overcome the adverse pressure gradient caused by the shock
wave, and delaying its separation.
FIG. 14.31
14-21
Chapter 14
High-Speed Flight
DOWNWASH
TAIL
MOMENT
CG
TAILPLANE
CP
WING
MOMENT
WEIGHT
FIG. 14.32
This results in a nose-down pitching moment, which must be counteracted by placing a small
download on the tailplane. If the shock stall occurs, any lift aft of the shock wave is destroyed and
the tailplane becomes covered in disturbed airflow (Fig. 14.33).
LIFT
SHOCK WAVE
TOTAL
PITCHING
MOMENT
CG
CP
WING
MOMENT
TAIL
MOMENT
DOWNWASH
ELIMINATED
CHANGE IN RELATIVE
AIRFLOW OVER THE
TAILPLANE
WEIGHT
FIG. 14.33
14-22
High-Speed Flight
Chapter 14
The downwash acting on the tailplane is consequently eliminated causing a smooth and radical
change in its angle of attack. The angle of attack becomes more positive and the download acting
on the tailplane becomes an upload which, in conjunction with the wing pitching moment, causes
a violent nose-down pitching moment, known as tuck-under. The exact nature and strength of the
changes in trim and stability depend on the design of the aeroplane.
Lateral stability includes disturbances about the longitudinal axis, which are often encountered
in transonic flight. They are characterised as a wing heavy tendency as the critical Mach number
is exceeded. This occurs because shock waves do not always form simultaneously, nor at
identical places on opposite wings. Design features that normally provide lateral stability may
consequently reverse the effect and aggravate a dropping wing. This occurs because the downgoing wing sideslips and causes the airflow to accelerate. This will intensify the shock wave
causing the wing to drop further.
Directional stability is affected by the variation in wing shock wave formations, which result in
different drag characteristics. For example, if a shock wave first forms on the left wing, the
associated increase in drag causes the aeroplane to yaw in the same direction. Whilst yawing to
the left, the airflow accelerates over the right wing, so intensifying the shock wave and increasing
the drag. This process is thus self-perpetuating and results in snaking or Dutch roll, depending on
the lateral and directional characteristics of the aeroplane.
MACH TRIM
To guard against nose tuck under, frequent pitch trim changes are required. This is carried out by
a variable incidence tailplane, which is automatically positioned by a Mach trim system. This
system is designed to aid aeroplane longitudinal stability and ensures that the forward stick forces
increase proportionally with increasing Mach number. It is operational at high Mach numbers in
the transonic speed range.
SUPERSONIC FLIGHT
The supersonic flight range starts at about Mach 1.2 to 1.3, depending on the individual
aeroplane design. The airflow above a surface varies immensely from that of transonic flight and
forms a series of oblique shock waves and expansion waves.
14-23
Chapter 14
High-Speed Flight
V1 > V2
P1 < P2
T1 < T2
OBLIQUE
SHOCK WAVE
1 < 2
WAVE ANGLE
V1 P1 T1 1
SUPERSONIC FLOW
V2 P2 T2 2
WEDGE
FIG. 14.34
The wave angle depends on the Mach number of the approaching flow and the angle of the
wedge. This type of shock wave is weaker than the normal shock wave, but the energy loss still
has to be overcome by the aeroplane engines. As the air passes through an oblique shock wave
its pressure, temperature and density all increase.
MACH CONE
Only the region behind the oblique shock wave is affected by disturbances and is sometimes
referred to as the zone of action. The region ahead of the oblique shock wave is not affected by
the disturbances and is called the zone of silence. In three dimensions, the disturbances
emanating from the moving body expand outward as spheres and not circles. When the speed is
above Mach 1, these spheres are enclosed within a cone, called the Mach cone and it is within
the Mach cone that disturbances are felt.
If the source of the disturbance is a wing, the Mach lines generate two oblique plane waves
forming a wedge.
14-24
High-Speed Flight
Chapter 14
EXPANSION WAVE
Expansion waves are the opposite of shock waves (compression waves) and form where the
airstream turns around a convex corner (Fig.14.35).
V1 < V2
P1 > P2
EXPANSION WAVE
T1 > T2
1 > 2
V1
SUPERSONIC
FLOW
P1
T1
1
V2
P2
T2
2
FIG. 14.35
Pressure, temperature and density all decrease as the air flows through an expansion wave. The
velocity of the air also increases to a higher supersonic value as it passes through the wave, but
no energy is lost and lift is produced as the static pressure decreases. This is the main reason for
using double wedge aerofoils for supersonic flight, although the subsonic characteristics will be
very poor. To avoid these subsonic problems, circular arc or bi-convex aerofoil sections are used,
which use two arcs of circles to define their shape.
Oblique Shock
Wave
(Compression)
Expansion Wave
(No Shock)
Change of Direction
of Flow
No Change
Around a Corner
where it turns away
from the preceding
airflow
Effect on Velocity
and Mach No
Decreases to
Subsonic Speed
Decreases but
remains Supersonic
Increases to a Higher
Supersonic Speed
Effect on Static
Pressure
Large Increase
Increases
Decreases
Effect on Density
Large Increase
Increases
Decreases
Effect on
Temperature
Large Increase
Increases
Decreases
Effect on Total
Pressure
Large Decrease
Decreases
No Change since
there is no Shock
14-25
Chapter 14
14-26
High-Speed Flight
INTRODUCTION
When considering flight in adverse weather conditions, it is vital to know how windshear and any
accumulation of ice or frost on the aircraft affect its flight performance. Either condition seriously
affects the aircraft's climb capability and may even prove fatal if ignored.
ENGINES
PITOT-STATIC SYSTEM
FIG. 15.1
15-1
Chapter 15
The most important areas are the wings and tailplane, where the lift capability depends on the
section shape and camber. For example, a clean modern wing produces approximately twice the
amount of lift developed by a flat plate at the same angle of attack. If the aerofoil is contaminated
with frost, snow, or ice its maximum lift capability steadily deteriorates and under severe
contamination may decrease to that achievable from a flat plate (Fig. 15.2).
COEFFICIENT
OF LIFT
CLEAN
ICE
FLAT PLATE
FROST
ANGLE OF ATTACK
FIG. 15.2
Any surface contamination reduces the aircraft's stalling angle of attack and its overall climb
performance. Pitch and roll pre-stall flight characteristics may also occur before the stick shaker
activates during a normal take-off.
POTENTIAL DROP
COEFFICIENT
OF LIFT
CLEAN
ICE
CONTAMINATED HIGH LIFT SHAPE
ANGLE OF ATTACK
FIG. 15.3
15-2
Chapter 15
The formation of ice additionally increases the aircraft's gross weight, and may even increase the
stalling speed by up to 30%. Ice on the surfaces also causes a large increase in drag, which
requires additional thrust for the aircraft to be able to maintain steady level flight (Fig. 15.4).
INCREASE IN STALLING SPEED
INCREASE IN DRAG
CLEAN WING
CONTAMINATED WING
SPEED
FIG. 15.4
By comparison, a coating of hard frost does not significantly alter a wings aerodynamic contour,
but does produce a surface of considerable roughness (Fig. 15.5).
LIFT
LIFT
HIGH LIFT
DROP IN LIFT
CLEAN
ROUGH
- INCREASING SURFACE ROUGHNESS +
FIG. 15.5
The roughness of frost is similar to that of sandpaper and produces a proportionately large
increase in skin friction, which results in a substantial reduction in boundary layer energy. A wing
contaminated with frost stalls at a lower angle of attack compared to a clean wing and also has a
reduced maximum coefficient of lift (Fig. 15.6).
15-3
Chapter 15
POTENTIAL DROP
COEFFICIENT
OF LIFT
CLEAN WING
FROST ON WING
ICE ON WING
ANGLE OF ATTACK
FIG. 15.6
The overall reduction in these values is normally not as great as those associated with an icecontaminated wing.
LOW ENERGY
BOUNDARY LAYER
RE-ENERGISED
BOUNDARY LAYER
ACCELERATION
OF THE AIRFLOW
STAGNATION
POINT
SEPARATION
FROM THE FLAP
FIG. 15.7
15-4
Chapter 15
Air passing through the slot from the lower surface increases the flap lift capability, reduces the
thickness of the separation wake behind the flap and gives an overall reduction in profile drag.
Any upper surface contamination reduces the energy possessed by the boundary layer and
results in earlier separation of the airflow. This leads to a reduction in the flap lift capability and
increases the form drag (Fig. 15.8).
INCRE AS E D
FORM DRAG
FROS T OR S LUS H
ON LOW E R S URFACE
ICE IN S LOT S
FIG . 15.8
A coating of frost or frozen slush on the lower surface of the wing also acts to decelerate the flow
and further reduces the energy possessed by the upper surface boundary layer. This results in
earlier separation of the airflow. If ice forms in the slot, the condition becomes worse. Slats
operate in the same way as slotted flaps by venting high-velocity air into the upper surface
boundary layer (Fig. 15.9).
ACCELERATED FLOW
STAGNATION POINT
FIG. 15.9
15-5
Chapter 15
This produces a 20-50% increase in the maximum coefficient of lift, but if ice forms on the leading
edge of the slats, this may decrease to only 5-10%. Contamination of the slats also creates
boundary layer disturbances, which tends to downgrade the efficiency of the slotted trailing edge
flaps and reduces the wing's stalling angle of attack (Fig. 15.10).
RE DUCE S
ST ALL
ANG LE
FIG. 15.10
INCREASED
T/O DISTANCE
DUE TO INCREASED T/O SPEED
FIG. 15.11
15-6
Chapter 15
Any increase in the stall speed may also dangerously reduce the margin to stall on take-off, and
may even reach a critical level, especially when operating in turbulent conditions (Fig. 15.12).
INCREASED DRAG
THRUST AVAILABLE
THRUST
OR
DRAG
REDUCED THRUST
FOR CLIMB
CLEAN
CONTAMINATED
SPEED
V
R
REDUCED MARGIN TO STALL
FIG. 15.12
The resulting increase in aircraft drag also reduces the amount of excess thrust available at a
given climb speed, thus decreasing the aircraft's angle of climb. The aircraft's rate of climb is
similarly reduced. With severely contaminated wings, the pitch and roll pre-stall buffet
characteristics (compared to a clean wing), may occur before the stick shaker activates
(Fig. 15.13).
V2 + 15
STICK SHAKER
ACTUATES
V2
STALL
12
CONTAMINATED
AIRCRAFT
V2 + 15
STALL ONSET
STICK SHAKER
WING
ANGLE OF 14
ATTACK
16
18
20
STALL ONSET
V2
STALL
FIG. 15 13
This occurs because the stick shaker normally activates at a specific angle of attack, and a
contaminated wing normally stalls before this angle is reached. As a result, the stick shaker may
not provide adequate stall warning, although pre-stall warnings in the form of buffet should
normally be sufficient to warn of an impending stall. A contaminated aircraft may even stall at an
angle of attack lower than that associated with normal rotation.
15-7
Chapter 15
Any wing and tailplane contamination can also upset the trim characteristics of an aircraft and
may lead to a nose-up out of trim condition during the rotation (Fig. 15.14).
40
CLEAN AIRCRAFT
PULL
STICK
FORCE
LBS
CONTAMINATED AIRCRAFT
WING AND TAIL
SECONDS
PUSH
-40
12
20
28
TRIM CHANGE DUE
TO CONTAMINATION
FIG. 15.14
Surface contamination may also cause a decrease in stick force, and in conjunction with the out
of trim condition, results in higher rotation rates for the same stick-force input and requires a push
force to counter these effects. On twin-engine aircraft with both engines operating, any wing
contamination results in a reduction in the climb capability. With one engine inoperative, the
reduction in climb capability is much more pronounced and may even produce a rate of sink. It is
therefore important to ensure that all the lifting surfaces are free of ice, frost, and snow before
commencing a take-off.
15-8
Chapter 15
INCREASED.
STALLING SPEED
THRUST
OR
DRAG
INCREASED DRAG
THRUST AVAILABLE
REDUCED THRUST
FOR CLIMB
CLEAN AIRCRAFT
CONTAMINATED AIRCRAFT
SPEED
FIG. 15.15
If the margin to stall is not increased, then high sink rates result due to increased drag,and may
even cause an uncontrollable loss of altitude, particularly during windshear conditions. If the
landing is subsequently aborted, it must be remembered that the reduction in excess thrust due to
contamination reduces the aircraft's overall climb capability, particularly at large flap angles, to a
marginal level. The formation of ice along the leading edges of the wing and tailplane during flight
must be prevented. Using aircraft anti-icing systems, such as hot engine bleed air or pneumatic
boots, achieves this.
15-9
Chapter 15
TAIL ICING
As the trailing edge flaps extend on an aircraft, the wing centre of pressure moves steadily
rearward, producing a large nose-down moment which tends to rotate the aircraft nose-down
(Fig. 15.16).
LIFT FORCE MOVES AFT
THEORETICAL
CHORD
TAIL
A of A
INCREASED
DOWNLOAD ON
TAILPLANE
WING
RELATIVE
AIRFLOW
DOWNWASH
FIG. 15.16
To compensate for this, the down load acting on the tailplane naturally increases due to the
change in downwash and direction of the airflow behind the wing. With increasing forward
airspeed, the nose-down moment steadily increases and requires a further increase in the
download acting on the tailplane. On aircraft with highly efficient flaps, the download on the
tailplane becomes excessively large and the tailplane may even stall if the flaps are extended at
too high a speed. Any accumulation of ice along the leading edge of the tailplane seriously affects
its maximum lift capability, and it may even stall at the normal approach airspeed (Fig. 15.17).
REDUCED STALLING
ANGLE OF ATTACK
THEORETICAL
CHORD
AOA
WING
AOA
RELATIVE
AIRFLOW
TAIL
LOSS OF
DOWNLOAD
ON TAILPANE
DOWNWASH
AIRCRAFT PITCHES
UNCONTROLLABLY
NOSE DOWN
FIG. 15.17
If the tailplane stalls, the download is suddenly removed, the aircraft pitches nose-down, and
goes into an uncontrollable dive. Take care when increasing an aircraft's forward airspeed to
compensate for ice on the wings, since every knot of airspeed added to prevent wing stall brings
the aircraft a knot closer to tailplane stall. Consequently, it is vital that the tailplane, like the wing,
is free from contamination. This type of stall does not usually occur, but if it does, recovery is
normally impossible.
15-10
Chapter 15
WINDSHEAR
Windshear is one of the leading causes of weather related aviation accidents and can occur at
any altitude, but is particularly serious below 1500 ft. This is low level windshear (LLWS) and
occurs when the aircraft is configured for the take-off, approach, or landing phase of flight.
Windshear by definition is a variation in wind velocity and/or direction over a short period of time
or distance. It alters the direction of the relative airflow, thereby greatly affecting the aerodynamic
forces and moments acting on the aircraft. This alters the response of the aircraft to control inputs
and recovery may require substantial control action.
The following types of windshear exist:
VERTICAL GUSTS
Vertical gusts acting on the aircraft principally alter its angle of attack. An up-gust increases the
angle of attack, whilst a down-gust decreases the angle of attack. The interaction between the
vertical gust velocity and the aircraft's forward air velocity determines the variation in angle of
attack (Fig. 15.18).
INCREASING LIFT
NORMAL
RELATIVE
AIRFLOW
UP-GUST
RELATIVE
AIRFLOW
UP-GUST
INCREASING ANGLE
OF ATTACK
FIG. 15.18
Any change in angle of attack alters the total amount of lift developed by the wing, and a strong
up-gust at high airspeed may even cause structural damage to the aircraft. Conversely, if vertical
gusts are encountered at low airspeeds (e.g. during the approach landing, or take-off phases of
flight) the changes in angle of attack leads to incipient stalling or sinking, rather than overstress.
The wing shape that is least affected by turbulence is the swept wing, since it is a low aspect
ratio, low lift wing.
Principles Of Flight (Rev Q407)
15-11
Chapter 15
HORIZONTAL GUSTS
Horizontal gusts differ from vertical gusts because they result in a change in airspeed, rather than
a change in angle of attack, initially without any change in pitch attitude. For example, consider
an aircraft trimmed for straight and level flight whose airspeed decreases by 20% to 80% of its
original value when acted on by a sharp horizontal gust. This results in the aerodynamic forces of
lift and drag at the same angle of attack falling to 64% of their original values. Due to the inertia of
the aircraft, it momentarily continues to fly along the same flight path, but the subsequent
reductions in airspeed and lift cause it to sink and lose altitude until reaching a new equilibrium
condition (Fig. 15.19).
LIFT
REDUCED LIFT
THRUST
THRUST
DRAG
DRAG
WEIGHT
WEIGHT
FIG. 15.19
Conversely, if a sharp windshear increases the airspeed, the aircraft tends to float and gain
altitude before reaching equilibrium again (Fig. 15.20).
INCREASED LIFT
LIFT
DRAG
THRUST
WEIGHT
WEIGHT
FIG. 15.20
15-12
Chapter 15
SHEAR LINE
If the aircraft enters a vertical updraught or downdraught from a horizontal airflow, its momentum
temporarily maintains its original flight path relative to the new direction of the airflow. In either
case, the airspeed decreases and the aircraft's angle of attack either increases or decreases in
magnitude. For example, consider the effect of a downdraught acting on the aircraft (Fig. 15.21).
REDUCTION
IN LIFT
DOWNDRAUGHT
RELATIVE
AIRFLOW
DOWNDRAUGHT
NORMAL
DECREASING
RELATIVE
AIRFLOW ANGLE OF ATTACK
FIG. 15.21
The resulting reduction in airspeed initially causes an energy loss and a subsequent reduction in
aircraft performance. The reduction in the angle of attack leads to a reduction in lift, causing the
aircraft to pitch nose-down. Conversely, if the aircraft is subject to an updraught it causes the
angle of attack to increase, thus increasing the aircraft's lift capability. Any small increase in the
angle of attack poses no significant problems in the controllability of the aircraft, but if operating at
high angles of attack, which are normally associated with the approach and landing phases of
flight, the wing may stall. Neither condition is desirable, especially when operating close to the
ground.
These indications are displayed on the airspeed indicator, vertical speed indicator and attitude
indicator respectively.
15-13
Chapter 15
Disengage the auto-throttle and aggressively advance the thrust levers to ensure
maximum rated thrust is attained.
Disengage the auto-pilot and smoothly increase the aircraft pitch attitude using the
stick shaker as an upper limit if necessary in order to check the descent.
Except where a windshear escape guidance mode is incorporated, use the attitude director
indicator as the primary reference for pitch attitude during the recovery from a windshear
encounter and generally ignore flight director guidance. The aircraft configuration (e.g.
undercarriage and flaps) should remain the same until the vertical flight path is under control. Any
attempt to regain lost airspeed should also be disregarded until ground contact is no longer a
factor.
Note: During the recovery, refer to the vertical speed indicator and altimeter when coordinating power and pitch attitude until the rate of sink decreases to zero, or a positive
rate of climb is achieved. Conversely, if a windshear encounter occurs near the normal
point of rotation, indicated by a sudden rise in IAS and quickly followed by a decrease in
airspeed, the subsequent loss of lift may totally preclude a successful take-off. If there is
insufficient runway to stop at this stage, then either increasing the airspeed and/or
increasing the pitch attitude can alternatively obtain the required lift. Additional thrust also
helps to accelerate the aircraft, but if the remaining runway is insufficient to reach the
normal take-off speed, even at maximum thrust, the pitch attitude should be increased to
make use of the available airspeed in order to generate enough lift, thus trading airspeed
for altitude.
15-14
Chapter 15
MICROBURSTS
These are the most lethal forms of windshear. They normally occur in the vicinity of
thunderstorms and are mainly associated with cumulonimbus clouds (Fig. 15.22).
Cumulonimbus Cloud
Storm Motion
Thunderstorm
Shelf Cloud
Updraft
Outflow
Gust Front
Downdraughfts
FIG. 15.22
Increasing headwinds, causing the IAS to rise (temporary energy gain) and the
aircraft to climb above the glidepath. A reduction in thrust to increase the rate of
descent and/or a change in pitch attitude may counter this.
A downdraught that increases the rate of descent and decreases the IAS, thereby
causing the aircraft to drop further below the glidepath. The situation worsens if the
nose is still high and the thrust setting low. To counter this, power is re-applied, but
with transport-category aircraft, the thrust does not increase instantaneously because
the engines take time to speed up and the IAS continues to fall.
15-15
Chapter 15
On leaving the downdraught, increasing tail winds cause a further reduction in IAS
(Temporary Energy Loss). The rate of descent may lessen due to increased thrust
availability. To counter this, apply full power whilst maintaining pitch attitude to check
the descent and abandon the approach.
A
ENERGY GAIN - INCREASING HEADWIND
AIRSPEED INCREASING
RATE OF DESCENT REDUCING
TENDENCY TO GO HIGH ON GLIDEPATH
C
ENERGY LOSS - INCREASING TAILWIND
AIRSPEED STILL REDUCING
RATE OF DESCENT CHECKED BY MISSED
APPROACH. SUCCESS DEPENDS ON POWER,
HEIGHT AND SPEED RESERVES AVAILABLE
B
ENERGY LOSS - REDUCING HEADWIND
AND DOWNDRAUGHT
AIRSPEED REDUCING
RATE OF DESCENT INCREASED
TENDENCY TO GO LOW ON GLIDEPATH
A
B
C
FIG. 15.23
A successful recovery from a microburst encounter depends on the altitude, thrust, and speed
reserves available. In addition to these effects, severe wind, turbulence, heavy rain, and blinding
flashes of lightning often accompany microbursts.
15-16
Chapter 15
RED MASTER
WARNING LIGHT
RED OR AMBER
WINDSHEAR
MESSAGE
RED
WINDSHEAR
LIGHT
Collins
20
10
5
1 76
10
WINDSHEAR
20
FIG. 15.24
Some aircraft also have visual cues (e.g. the word Windshear appears in red across the lower
portion of the electronic attitude director indicator (EADI)).
15-17
Chapter 15
15-18
INTRODUCTION
All structural components of an aeroplane are made up of members manufactured from various
materials, and are designed to safely distribute the forces or stresses acting on the aircraft.
However, some components do not carry any structural stresses, and are designed purely to
provide a streamlined shape (e.g. engine cowlings and wing fairings). The various structures
must also be capable of dissipating additional stresses that exist during the manoeuvring phases
of flight (e.g. banking and turning) when an aircraft is subject to increased load factor. All
aeroplanes are built to safely accommodate the highest stress level anticipated during normal
operations (i.e. the maximum load the structure must withstand without sustaining permanent
damage). All aircraft also have a specific range of g forces and speeds at which they can be
safely operated. During the normal working life of the aircraft, the structure is also constantly
subjected to varying stresses due to:
Flight manoeuvres
Atmospheric turbulence
Ground loads
Cabin pressurisation and depressurisation
Thermal effects
Vibrations
STRUCTURAL STRENGTH
The strength of the aeroplane structure is its ability to withstand a load. The limit load, is the
maximum load to be expected in service. The ultimate load is the failing load of the structure. The
factor of safety is the ratio of the ultimate load to the limit load. Most structures, such as buildings
and bridges, have very large factors of safety. Aeroplanes however have a small factor of safety,
due to the extreme need to keep the aeroplane structure as light as possible. For aeroplane
structures the factor of safety is 1.5, ie the overload is only 50% of the limit load.
LOAD FACTOR
Load factor is the ratio of lift/weight. In straight and level flight, lift equals weight, and therefore the
load factor is 1. When an aeroplane turns, or flies in turbulent conditions, the load factor will
exceed 1. The load limit is normally displayed as a load factor, but as it is actually a force, a
problem of aeroplane weight occurs. An aeroplane with the same load factor, of for example 2,
will have twice the lift as its weight, the lift force will therefore be greater when the aeroplane is
heavier. To ensure that the actual limit load is not exceeded, the load factor is calculated for the
maximum all up mass of the aeroplane.
16-1
Chapter 16
Operating Limitations
FIG. 16.1
The above graph illustrates the limit load factors and limit speeds that, if exceeded, may result in
permanent structural damage. The limit load factors vary depending on aircraft type, but for
transport category aircraft these are generally +2.5g (+2 with flaps extended) and -1g. Aeroplanes
in the utility category are +4.4 to -1.76 and +6 to -3 for aeroplanes in the aerobatic category.
Since the safety margin is1.5 times the limit load, the ultimate load factor limits are 3.75g to -1.5g
for transport category aeroplanes and +9 to -4.5 for aerobatic aeroplanes. These load limits and
ultimate load factor values are the minimum required by the JAR regulations, and some
aeroplanes are produced with greater limits.
The above V-n diagram shows the V speeds; Vs, VA, VC and VD. All except Vs are design speed
limitations.
16-2
Operating Limitations
Chapter 16
DESIGN LIMITATIONS
The Design limitations are shown on the below V-n diagram.
FIG. 16.2
= 190kt
However VA is the only design speed which varies. VA varies with the square root of the
aeroplane weight, so
VA new = VA old Weight new.
Weight old
At an aeroplane mass of 55 000kg VA is 180kts, what is VA at 45 000kg?
VA new = 180 45 000 = 163kt
55 000
VA also increases at high altitude due to compressibility effects.
16-3
Chapter 16
Operating Limitations
OPERATING LIMITATIONS
The operating speed limitations, which are used by pilots, are based on the design limitations with
safety factors in some cases.
VMO, the maximum operating speed (EAS), must not be greater than VC. At high altitudes
however, VMO is unlikely to be limiting, due to the low air density. The operating maximum speed
will now be MMO, the maximum operating mach number.
VNE , the never exceed speed (for small aeroplanes). VNE is set at 0.9 or 90% of VD. VNE is
displayed on the airspeed indicator by a red radial line at the fast end of the yellow coloured arc.
VNO , the maximum structural cruise speed (for small aeroplanes). VNO is the normal operating
cruise speed and must not be greater than the lesser of VC and 0.89 VNE. VNO is at the slow end
of the yellow arc and at the fast end of the green arc on the airspeed indicator.
VLE, Maximum landing gear extended speed The maximum speed at which the aeroplane can
be flown with the undercarriage down and locked.
VLO - Maximum landing gear operating speed. Although this may be the same as VLE, it is
often a slower limiting speed than VLE , due to the undercarriage and undercarriage doors not
being as strong when travelling and unlocked.
VFE - Maximum Flap Extension Speed The maximum speed at which the aeroplane can be
flown with the flaps extended.
16-4
Operating Limitations
Chapter 16
16-5
Chapter 16
Operating Limitations
Looking at the above diagram, the same speed vertical gust will have the greatest increase in
angle of attack at a slower TAS. A slower aeroplane will therefore have a higher gust load factor
than a faster aeroplane.
ALTITUDE
For the same CAS, the TAS increases as altitude increases. Therefore for the same speed
vertical gust, an aeroplane at low altitude which will have a slower TAS, will have the greatest
increase in angle of attack and gust load factor.
16-6
Operating Limitations
Chapter 16
ASPECT RATIO
The above graph shows the effect of the same increase in angle of attack for an aeroplane with
high and low aspect ratio. Because the gradient is steeper for the high aspect ratio aeroplane, the
increase in the coefficient of lift, and gust load factor, is greater for the high aspect ratio
aeroplane.
In the above diagram the same 2 increase in angle of attack causes the CL to increase by 0.03,
for the low aspect ratio aeroplane, and 0.16 for the high aspect ratio aeroplane. Since the load
factor is proportional to the CL the load factor will change from 1 to 1.23 ( 0.18/0.21) for the low
aspect ratio aeroplane, and from 1 to 1.40 ( 0.56/0.4) for the high aspect ratio aeroplane. The
high aspect ratio aeroplane therefore has a greater gust load factor
SWEEPBACK
16-7
Chapter 16
Operating Limitations
The above graph shows the effect of the same increase in angle of attack for an aeroplane with
straight wings and sweepback. The gradient is steeper for the straight wing aeroplane and
therefore it will have the greatest increase in CL and gust load factor.
In the above diagram the same 2 increase in angle of attack causes the CL to increase by 0.08
for the low aspect ratio aeroplane, and 0.33 for the high aspect ratio aeroplane. Since the load
factor is proportional to the CL the load factor will change from 1 to 1.35 ( 0.27/0.21) for the swept
wing aeroplane, and from 1 to 1.51 ( 0.98/0.65) for the straight wing aeroplane. The straight wing
aeroplane therefore has a greater gust load factor than the swept wing aeroplane.
AEROPLANE WEIGHT
Because a heavier aeroplane will have a higher original angle of attack and CL than the lighter
one, the same increase in the CL, will have a bigger percentage increase for the lighter aeroplane
than the heavier aeroplane. The graph shows that the same increase in angle of attack eg 3
produces the same 0.15 increase in CL for both the heavy and light aeroplanes. The load factor
for the lighter airplane increased by 27% (0.15/0.55 x 100). However since the heavier aeroplane
was already at a higher CL of 0.95 the percentage increase in load factor is less at 16%,
(0.15/0.95 x 100).
The lighter aeroplane therefore has the greater gust load factor.
16-8
Operating Limitations
Chapter 16
This is because the wing is flexible and the ailerons are near the wingtips, where the wings are
less rigid. The actual torsional rigidity of a wing depends on its structure, but is normally strong
enough to prevent any distortion at low airspeeds. Aileron power, however, increases as the
square of forward airspeed, whereas the torsional stiffness of a wing remains constant with
speed.
At high airspeeds, a twisting moment due to aileron deflection eventually overcomes the torsional
rigidity of the wing and alters its angle of attack, thereby reducing the rate of roll. The rising wing
will twist nose-down, reducing its effective angle of attack and thus its coefficient of lift (below
diagram).
16-9
Chapter 16
Operating Limitations
Conversely, the lowering wing will twist nose-up, thus increasing its effective angle of attack and
its coefficient of lift.
At some airspeed, the incremental change in the coefficients of lift due to aileron deflection is
completely nullified by the wing twisting in the opposite sense. At this speed, the lift produced by
each wing is the same irrespective of aileron deflection (i.e. the ailerons become totally
ineffective). Above this speed, a downward deflection of the aileron results in a reduction in lift,
whilst an upward deflection of the aileron results in an increase in lift and the aircraft rolls in the
opposite direction to the control input. This is known as aileron reversal, and the speed at which it
occurs is known as the aileron reversal speed. This airspeed normally occurs outside the
aircraft's flight envelope, but at any airspeed below this point there will be an apparent reduction
in roll rate for a given aileron deflection.
16-10
Operating Limitations
Chapter 16
EMERGENCY DESCENTS
An emergency descent is made if a sudden and complete failure of the cabin pressurisation
system occurs. At 43 000 ft, the average person will become unconscious within 15 seconds, but
the crews capability declines sooner. If depressurisation occurs, the emergency descent
procedure should be initiated immediately, but the structural integrity of the aircraft should not be
compromised. The procedure varies between aircraft types, but all involve retarding the throttles
to their flight idle position, operating the speedbrakes, and placing the aircraft in a steep descent.
FIG. 16.7
295
FLIGHT LEVEL
285
275
290
265
255
MMO
245
340
VMO
0.76 0.77 0.78 0.79 0.80 0.81 0.82 MACH No
This should be initially carried out at a target speed of MMO, where the aircraft is Mach limited,
and VMO, where the aircraft is speed limited at lower altitudes. To assist the pilot, some aircraft
have never exceed speed needles on the airspeed indicator, which is correlated to MMO at high
altitude, and VMO at lower altitudes. Whether the aircraft is cruising at MMO or not, the effect of
reducing the thrust setting and operating the speedbrakes, initially reduces the airspeed, requiring
a fairly steep descent to return to MMO. Care must be taken not to overshoot MMO during the
descent. When the aircraft reaches the altitude where MMO = VMO, at approximately 24 500 ft, the
dive angle must be reduced to prevent the aircraft exceeding VMO. At about 15 000 ft, the cabin
pressure is acceptable and the aircraft should be slowly returned to level flight. Pulling out of the
dive too quickly may overstress the aircraft.
16-11
Chapter 16
16-12
Operating Limitations