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TABLE OF CONTENTS
Principles of Flight
CHAPTER 01 INTRODUCTION
Introduction to Principles of Flight
Introduction to Units
The SI Unit System
Imperial Units and Conversion Factors
Newtons Laws of Motion
CHAPTER 02 AIR, THE ATMOSPHERE AND AIRSPEED
The Characteristics of Air
Mass Flow and Density Variation
Characteristics of the Earths Atmosphere
The International Standard Atmosphere
The Fundamental Origin of Aerodynamic Force
Airspeed
Indicated Airspeed
Isolating and Measuring Dynamic Pressure
The Air Speed Indicator
Speeds Obtained from Dynamic Pressure
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TABLE OF CONTENTS
CHAPTER 03 DESCRIBING AND UNDERSTANDING AIR FLOW
Introduction
Streamlines, Stream Tubes and Pathlines
Patterns of Flow
Basic Assumptions
The Equation of Continuity and the Venturi
Bernoullis Theorem
Airflow Summary
CHAPTER 04 AERODYNAMIC FORCE Introduction
Pressure and Force
Two Dimensional Flow
Flow Pattern Around a Cylinder
Pressure Distribution Around a Cylinder
The Effect of Viscosity
The Aerofoil
Airflow Around an Aerofoil
The Cause of Accelerated Air flow on the Upper Surface
Pressure Around an Aerofoil
Aerodynamic Force
Summary
Appendix to Chapter 4 Circulation and Lift
Circulation Around an Aerofoil
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TABLE OF CONTENTS
CHAPTER 05 AEROFOIL PRESSURE DISTRIBUTION
Introduction
Air Flow Speed
Angle of Attack
Camber
Effect of Angle of AoA on a Cambered Aerofoil
Pressure Distribution Summary
Aerodynamic Force Coefficient
CHAPTER 06 INTRODUCTION TO LIFT Introduction
Aerodynamic Force and the Force Coefficient
Lift and the Basic Lift Equation The Lift Coefficient (C
L)
Coefficient of Lift Summary
Using the Lift Equation
IAS, Lift and CLin Level Flight
CLand AOA: Slow and High Speed Aerofoils
Numerical Calculations Using the Lift Equation
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TABLE OF CONTENTS
CHAPTER 07 INTRODUCTION TO DRAG
Introduction
Causes of Drag in 2-Dimensional Flow
Drag and the Basic Drag Equation
The Boundary Layer
Types of Boundary Layer
The Transition Point
Factors Determining Boundary Layer Type
The Separation Point
Chapter Summary
CHAPTER 08 AIRCRAFT AXES AND THE AIRCRAFT WING
Aircraft Frames of Reference
Aircraft Axes
The Aircraft Wing - Terms and Definitions
Wing Taper
Average Chord
Aspect Ratio
Sweep Angle
Mean Aerodynamic Chord
Rigging Angle and Angle of Incidence
Washout
Dihedral and Anhedral
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TABLE OF CONTENTS
CHAPTER 09 THREE DIMENSIONAL FLOW
Introduction
Factors Influencing Flow Direction
The Wingtip Vortex
Factors Affecting Vortex Intensity
Spanwise Flow
Vortices and Downwash
The Effective Airflow
Lift and Induced Drag
Refining our Definitions of Angle of Attack Change of Effective Angle of Attack with Span
CHAPTER 10 DESIGNING A WING FOR MAXIMUM EFFICIENCY
Introduction
Aspect Ratio
Elliptical Lift Distribution
Elliptical Planform
Rectangular Planform
Tapered wing
Sweepback
Washout
Camber Change
Wing Loading
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TABLE OF CONTENTS
CHAPTER 11 AIRCRAFT DRAG
Introduction
Interference Drag
Categories of Aircraft Drag
Factors Affecting Form Drag
Factors Affecting Skin Friction Drag
Factors Affecting Interference Drag
Parasite Drag
The Parasite Drag Equation
Induced Drag The Induced Drag Equation
Lift and Drag Calculations
Tip Modifications to Reduce Induced Drag
CHAPTER 12 TOTAL DRAG AND THE DRAG POLAR
Total Drag
Minimum Drag Speed - VMD
Speed Stability
Factors Affecting the Drag Curve
The Total Drag Equation
Variation of CDP
with CL
Variation of CDI
with CL
The Drag Polar The Lift Drag Ratio
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TABLE OF CONTENTS
CHAPTER 13 STALLING
Introduction
The Cause of the Stall
Effect of the Stall on Lift and Drag
The Stalling Angle of Attack
Influence of Planform on the Stalling Angle
Summary of Effects of Planform Shape
The Deep Stall
Measures to Reducing the Tip Stalling Tendency
Influence of Cross-section on the Stalling Angle Factors Affecting Stalling Speed
The Accelerated Stall
Stalling in the Turn
Stall Speed in a Pitching Manoeuvre
Stalling Summary
CHAPTER 14 SPINNING
Introduction
Autorotation
The Fully Developed Spin
The Causes of Roll and Yaw
The Effect of CG Position
The Effect of Mass Distribution on Spin Characteristics Recognising and Avoiding the Spin
Spin Phases and Generic Recovery Actions
Spin Recovery Drill for Your Aircraft
Spin Avoidance
Spin Versus Spiral Dive
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TABLE OF CONTENTS
CHAPTER 15 STALL WARNING, STALL RECOVERY AND ASSOCIATED
Introduction
Aerodynamic Stall Warning Straight Wings
Stall Warning and Characteristics - Swept Wings
Stall Warning and Characteristics - Forward Swept Wings
Stall Warning and Characteristics Canard Designs
Artificial Stall Warning Systems
Angle of Attack Sensing
Warning Indications
Stall Recovery EASA Regulations
CHAPTER 16 LIFT AUGMENTATION
Introduction
Trailing and Leading Edge Flap Changing the Camber
The Fowler Flap - Increasing the Surface Area
Slats, Slots and Slotted Flaps Increasing the Circulation
Summary of Aerodynamic Effects
The Effect of Flap on the Tailplane
The Effect of Flap on Tip Vortices
Vortex Generators
Operation of Flaps and Slats
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TABLE OF CONTENTS
CHAPTER 17 GROUND EFFECTS
Introduction
The Cause of Ground Effect
Influence of Ground Effect on Lift and the Stalling Angle
Change in Pitching Moment
Influence of Ground Effect on IAS
Summary
CHAPTER 18 CONTROL
Introduction Aircraft Axes and Controls
Principle of Operation
Hinge Moments
Aerodynamic Balances
Mass Balancing
Powered Controls
Artificial Feel
The Effect of Aircraft Controls on Angle of Attack
Pitch Control
Other Tailplane Considerations
The Effect of Downwash
Control in Yaw
Fin Stall Rudder Travel Limiter
Control in Roll Light and Medium Sized Aircraft
Aerodynamic Damping
Adverse Aileron Yaw
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TABLE OF CONTENTS
CHAPTER 21 TURNING
Introduction
Load Factor
Forces in a Turn
Forces in a Level Turn
Turn Calculations
Drag and Thrust in the Turn
Rate of Turn
The Turn and Slip Indicator
Rate of Turn Calculations TAS and Bank Angle in a Rate 1 Turn
CHAPTER 22 INTRODUCTION TO STABILITY AND CONTROL
Introduction
Stability and Control
Equilibrium
Stability Concepts
Static Stability
Trim, Controllability and Static Stability
Dynamic Stability
Types of Dynamic Stability
Summary of Types of Stability
Axes of Control and Stability The Aerodynamic Centre
Moment Coefficients
Key Design Influences on Stability
Stick Free or Stick Fixed
Simplifying Stability Problems
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TABLE OF CONTENTS
CHAPTER 23 LONGITUDINAL STABILITY & CONTROL
Introduction
CG Location
The Absolute Angle of Attack
The Pitching Moment Coefficient
Graphical Representation of Static Longitudinal Stability
Negative and Neutral Static Longitudinal Stability
Variation in Static Longitudinal Stability
Design Influences on Static Longitudinal Stability
Whole Aircraft Stability The Effect of CG on Longitudinal Stability
The CM/Alpha Graph
Longitudinal Control
Trimming for Changes in IAS
Effect of Elevator or Stabiliser Deflection and Trim
Effect of CG Position
Manoeuvre Stability Stick Force Per G
Factors Affecting Manoeuvre Stability
Longitudinal Dynamic Stability
The Effect of Altitude and CG on Dynamic Stability
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TABLE OF CONTENTS
CHAPTER 24 DIRECTIONAL AND LATERAL STABILITY
Introduction
Static Directional Stability
Definitions
Factors Affecting Static Directional Stability
Static Lateral Stability
The Cl/ Graph
Factors Affecting Static Lateral Stability
Lateral and Directional Dynamic Stability
Spiral Instability Dutch Roll
Effect of Pressure Altitude on Dynamic Stability
CHAPTER 25 PROPELLERS
Introduction
Propeller Definitions
Types of Propeller
Aerodynamic Forces
The Aerodynamics of the Fixed Pitch Propeller
Blade Twist
The Aerodynamics of Variable Pitch Propellers
Engine Failure
The Effects of Engine Failure Reverse Thrust
Propeller Efficiency
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TABLE OF CONTENTS
CHAPTER 26 PROPELLER DESIGN AND PROPELLER EFFECTS
Introduction
Power Absorption
Propeller Solidity
Propeller Effects
Torque Reaction Effect
Slipstream Effect
Asymmetric Blade Effect - P Factor
Gyroscopic Effect
Summary
CHAPTER 27 ASYMMETRIC FLIGHT
Introduction
Yawing Moments
Factors Affecting the Size of the Yawing Moment
Failure to Stop The Yaw
Achieving Equilibrium - Wings Level Method
Achieving Equilibrium - Banking Method
Engine Failure and Angle of Climb
The Critical Engine
Minimum Control Speeds
Influence of Air Density on Minimum Control Speeds
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TABLE OF CONTENTS
CHAPTER 28 INTRODUCTION TO HIGH SPEED FLIGHT
Introduction
The Speed of Sound
Mach Effects and Mach Number
Local and Free Stream Mach Numbers
Categorisation of High Speed Flows
Wave Characteristics
Normal Shock Waves
Oblique Shock Waves
Mach Waves Expansion Waves
Wave Summary
The Relationship Between CAS, TAS and Mach Number
Further Effects of Altitude Change
CHAPTER 29 EFFECTS OF HIGH SPEED FLIGHT
Introduction
The Critical Mach Number
Surface Pressure and Shock Waves in the Transonic Region
The Effects of Shock Waves in the Transonic Region
The Drag Divergence Mach Number
Drag
Centre of Pressure Effects Speed Envelope Considerations
Factors Affecting the Stalling Speeds
The Buffet Onset Boundary Chart
Reducing the Effect of Shock Waves
Thin Aerofoils
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TABLE OF CONTENTS
The Supercritical Aerofoil Section
Sweepback
Advantages and Disadvantages of Sweepback
Vortex Generators
Area Ruling
CHAPTER 30 AIRFRAME CONTAMINATION AND DEFORMATION
Introduction
Ice, Frost and Snow
Aerodynamic Effects of Frost, Ice and Snow Tailplane Icing
Considerations by Flight Phase
Heavy Rain
Airframe Deformation and Damage
CHAPTER 31 LIMITATIONS
Introduction
Structural Strength
The Manoeuvre Envelope
Design Speeds
Operating Speeds
Gust Loads
Gust Load Factor
Gust Load Factor Envelope
Aeroelasticity
Flutter and Resonance
Control Surface Flutter
Aileron Reversal
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CHAPTER 4: AERODYNAMIC FORCE
Introduction
Pressure and Force
Two Dimensional Flow
Flow Pattern Around a Cylinder
Pressure Distribution Around a Cylinder
The Effect of Viscosity
The Aerofoil
Airow Around an Aerofoil
The Cause of Accelerated Airow on the Upper Surface
Pressure Around an Aerofoil
Aerodynamic Force
Summary
Circulation and Lift
Circulation Around an Aerofoil
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Aerodynamic Force
Introduction
Earlier we stated that to become, or remain, airborne an aircraft mustcreate an aerodynamic force which opposes the force of gravity. While
there is no simple andcorrect explanation for aerodynamic force we
will use our understandingBernoullis theorem combined with the
effects of viscosity to explain how aerodynamic forces are generated.
We will start by applying the Bernoulli explanation, initially to an ideal
uid owing across a cylinder, and then to a viscous uid owing across
a cylinder and across an innitely long aerofoil. Well end the chapter by
looking at the air ow around an aerofoil. With this in mind we need to
draw a precise distinction between ideal ow and air ow:
J Ideal ow means the ow of an ideal gas.
J Air ow means the ow of air (the characteristic mixture of
molecules that makes up our atmosphere).
04
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Pressure and Force
Before we look at objects in an ideal ow and in air ow, we need
to establish the relationship between pressure and force. A pressure
acting on a surface provides a force. The force will be greater when the
surface pressure is larger and when the surface area that the pressure
is acting over is bigger. This relationship is shown in the equation;
Force = pressure x area
However if the surface pressure acting on both sides of an object is
the same, the forces created will be equal and opposite. The object
will experience no net (unbalanced force) force will thus remain either
stationary or will continue to move at its original velocity.If, however, there is asymmetry in the pressures acting on an object,
then the forces created on either side will not be equal and opposite
and a net (unbalanced force) will exist. It only takes a small pressure
difference acting over a large area to produce an appreciable net force.
Think of how the slight pressure difference created in your home on a
windy day can produce a force large enough to slam a door.
Likewise when an object is placed in a ow, an aerodynamic force willbe generated if different pressures act on its opposite sides to produce
a net force. The size of the force depends on:
J The size of the pressure difference between the two sides and
J The size of the surface area over which the pressure difference
occurs.
The overall net force acting on an object in an airow, is called the totareaction.
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Two Dimensional Flow
The term two dimensional owsimply means that the ow can only
move in two directions. In our diagrams this means left and right (along
the main ow direction) and up or down.
The left and right movement is, of course, initially provided by the
relative speed of the ow itself. Up and down movements start to occur
when an object is placed into the ow. If the object has ends to it, for
example a wing complete with wing tip, then the ow can move in the
third dimension as well. This is a complication we can do without for
the moment, which is why we begin by considering any object placed
in the ow to be of innite length. In this way we can restrict our
considerations of ow to just two dimensions.
In case you are thinking that this is unfeasibly abstract, innitely long
wings are in fact modelled in wind tunnels. The engineers simply build a
model where the wings extend all the way to the walls of the tunnel.
For the remainder of this chapter bear in mind that we will be talking
only about two-dimensional ows.
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Flow Pattern Around a Cylinder
We start by looking at the ow pattern around a very simple object a
cylinder because the perfectly spherical cross-section of a cylinder is
just about the simplest shape we can consider.
Figure 4.1 shows the streamline pattern of an ideal ow around a
cylinder. As the ow approaches the cylinder the streamlines separate,
moving either up or down to ow around the cylinder. Notice that the
distance between the streamlines changes. In front of and behind the
cylinder the streamlines are further apart; above and below the cylinde
they are closer together.
Speed and dynamic
pressure increase,
static pressure reduces
AV A V
q Ps
A V
Stagnation points)
V=0, q=0
Figure 4.1
Ideal flow speed and pressures around a cylinder
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From what we have learned so far we can deduce a number of
important facts about the inuence of the cylinder on the ideal ow.
J To preserve a constant mass ow, the speed of the ow must have
increased in the areas where streamlines are closer together. It
must have slowed down where the streamlines are further apart.
J Where the ow is faster the static pressure must have reduced
(because the dynamic pressure has increased).
J Where the ow is slower in front of, and behind, the cylinder the
static pressure must have increased.
We can also see from gure 4.1 that at one precise point on the front
of the cylinder a streamline impacts the object head on. This brings theow to an abrupt and complete stop. All dynamic pressure is converted
into static pressure. This is known as a stagnation point.
There is a second stagnation point at the rear of the cylinder caused by
the meeting of the separated ows. At the point nearest the cylinders
surface the two ows meet head on and thus convert all their dynamic
pressure to static pressure.
Pressure at the Stagnation Points
The stagnation points are the points on the objects surface at which
the ow is brought completely to rest. At these points the dynamic
pressure is zero, which means that the static pressure is at its
maximum value total pressure. For this reason is it also known as the
stagnationpressure. At the stagnation point the static pressure exceeds
the atmospheric or free stream pressure by the value of the dynamic
pressure. If the ow rate across the cylinder increases, so too will the
stagnation pressure.
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Pressure Distribution Around a Cylinder
The next diagram shows thepressuredistribution around the cylinder
caused by the ow. We use the following conventions:
J Higher than ambient (free stream) pressure is denoted by redarrows.
J Lower than ambient (free stream) pressure is denoted by blue
arrows.
J The length of the arrow indicates the approximate magnitude of the
pressure differential relative to the free steam pressure.
J The arrow heads indicate the direction in which the resulting forceacts.
Its important to understand that the areas bounded by dotted lines
do notrepresent the boundaries of volumes of low and high pressure
around the cylinder. They are simply pressure contours indicating the
magnitude of surfacepressure force at any point on the cylinder.
Static pressure on
surface less than
atmospheric
Stagnation points(V=0)
Static pressure on
surface greater
than atmospheric
Figure 4.2
Cylinder surface pressure in an ideal air flow.
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The surface pressure is lowest where the streamlines are closest
together at the top and bottom of the cylinder. It is highest at the
stagnation points and higher than ambient in the areas where the
streamlines are spaced further apart.
Looking at gure 4.2 we can see that the pressure distribution around
the cylinder is completely symmetrical. This means that there is no
net force and thus no total reaction. Not even rearwards. Which rather
strangely means that this cylinder provides no resistance to the ow.
In fact it produces no aerodynamic forces at all! This phenomenon
is known as the Paradox of dAlembert and isexplained entirely by
the fact that we are considering an ideal ow which has no friction or
viscosity.
In real life objects in a ow always provide some resistance. Resistance
to ow is known as drag. To explain drag and many other aspects
of aerodynamic force we must take account of the airs viscosity.
Consequently from now on throughout this book we will be referring to
air owrather than ideal ow.
The Effect of Viscosity
At the molecular level no object no matter how well polished it is
has a perfectly smooth surface. When air ows around it, molecules of
gas impact the surface imperfections, lose kinetic energy to the object,
and thus slow down. In an ideal gas this effect is inconsequential
because it only affects the few molecules which are in direct contact
with the objects surface. Immediately above this layer in an ideal ow
with no viscositythe next layer of molecules slide past with no energylost.
But in real life air is viscous. The airs viscosity means that the next
layer of molecules up from the surface are indeed slowed down by the
slower molecules at the surface. And the layer above that and above
that. Each layer is slightly slowed by the layer below it but eventually,
after many layers, the inuence of the lowest layer becomes negligible.
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But up to this level there is a volume of air around the surface which
ows at signicantly lower speed than the free stream velocity. This is
known as the boundary layerand will be discussed in detail later. Its
presence explains many important aerodynamic phenomenon.
One of the effects of the air ows viscosity is the production of two
types of drag.
J Skin Friction Drag. Skin friction drag is caused directly from
friction within the boundary layer.
J Form Drag. Form drag is produced by the effect that viscosity has
on the pattern of pressure distribution around the object.
Because of skin friction a small proportion of pressure energy is lost inan actual air ow. This means that Bernoullis Theorem (total pressure
= dynamic pressure + static pressure) is almost, but not quite, true.
Nevertheless it is still an entirely valid explanation of how a pressure
differential is created around an object in an airow.
Because air has viscosity the streamline ow on the rear of an object in
an airow breaks away from the surface and a wake of turbulent air is
produced. In this turbulent wake the air tumbles and mixes to form aturbulent ow.
q PsV
Wake
Figure 4.3
Turbulent wake behind the cylinder
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The dynamic pressure therefore doesnt reduce by nearly as much as
it does in an ideal ow. Consequently the high pressure area which we
saw behind the object in an ideal gas ow is, in reality, much weaker in
an air ow. In fact it may even become an area of low pressure. Figure
4.4 shows the effect this has on the surface pressure distribution.
Surface static pressure
less than atmospheric
Surface static pressure
greater than atmospheric
Force
Figure 4.4
Surface pressure distribution in a non ideal airflow
The pattern of pressure distribution around the cylinder is no longer
symmetrical. There is now a pressure differential acting on the cylinder
in the direction of the airow. The size of this net (unbalanced) force is
determined by the pressure difference between the forward and rear
halves of the cylinder. The net force produced acts rearwards and is the
cause of form drag.
Unless we do something to alter the shape of this cylinder no amount
of air ow will ever produce a total reaction which acts upwards only
rearwards. Force acting upwards is what we will soon come to know as
lift and, unlike drag, lift is desirable.
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The simplest way to produce an unbalanced force acting upwards would
be to remove the cause of the symmetrical pressure distribution on the
upper and lower halves of the cylinder. If we cut off the lower half we
mightget a streamline ow and pressure distribution as shown in gure
4.5
Speed and dynamic
pressure increase,
static pressure reduces
AV A V
q Ps
A V
Figure 4.5
Streamline flow and pressure distribution across a half cylinder.
Now we are getting somewhere. Although we still have an unbalanced
force acting rearwards (form drag) we also have an unbalanced force
acting upwards. If we add the two together we get a total reaction
which, although inclined rearwards, comprises upwards and rearward
acting forces.
In reality there are two problems to this apparently simple approachwhich prevent it from being a practical solution.
Firstly, a half cylinder would not in practice generate any signicant
upward force unless it was able to induce a circulatory owaround
itself more of which later. Secondly a half cylinder in the shape shown
above would be an extremely inefcient way of creating an upwards
force. Which is why you will never see a wing shaped like this.
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Principles of Flight Aerodynamic Forc
Through a long process of trial, error and experiment early pioneers
developed the aerofoil sectionwhich, in its most simple form, you could
imagine to be a very stretched half cylinder.
Before we look at how air ow behaves around an aerofoil section we
need to become familiar with its shape, design and terminology.
The Aerofoil
An aerofoil, is a shaped structure designed to produce a signicant
amount of force when a stream of air moves across it. The term is most
commonly used to describe the shape seen in the cross-section of a
wing, propeller or helicopter rotor blade, although we can describe any
object which has an aerofoil section as an aerofoil.
Figure 4.6 shows a cross section through a propeller blade which shows
the characteristic shape of an aerofoil. This could just as easily be the
cross section of a wing.
Figure 4.6
This propeller cross section is a perfect example of the aerofoil section
There is nothing particularly magical about aerofoils. Almost any object
placed in a stream of owing air will produce an aerodynamic force; you
only have to stick your hand out of a car window to realise that. The
special characteristic of an aerofoil is that it is very efcient at creating
a relatively large force to lift (or drive) an aircraft whilst minimising its
resistance to the ow.
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Aerofoil Design
Aerofoils, such as the one shown above, have a very characteristic
shape. The edge meeting the airow is called the leading edge which
for most general purpose aerofoils tends to be quite rounded. The rear
edge is known as the trailing edgeand is alwayssharp. The uppersurface of the aerofoil is curved. The lower surface could be at but is
usually curved.
Point of
maximum thickness
Point of maximum camber
ChamberLeading edge
radius
Leading edge
Meancamberline
Chord
Chordline
Trailing edg
Figure 4.7
Aerofoil definitions
The leading edge is dened by the leading edge radius. On a generalpurpose aerofoil the leading edge radius tends to be quite large.
However, as we shall see in later chapters the leading edge radius of a
high speed aerofoil is much smaller, resulting in a sharp leading edge.
There are a number of other key characteristics of the aerofoil, and
dened terms, that you need to learn and remember.
Chord Line
The chord lineis an imaginary straight line drawn between the centre
of the leading edge and the trailing edge. The chord line is used as a
reference line for angles.
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Chord
The chordis the distance from the leading to trailing edge measured
along the chord line.
Angle of Attack
The angle of attackis the angle between the aerofoils chord line and
the direction of the air ow. Angle of attack is often abbreviated to
alphaor its Greek symbol a. The direction of the airow is known as
the relative air owto emphasise that it describes the direction of ow
relativeto the aerofoil and not the Earth.
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Point of Maximum Thickness
Point of Maximum CamberLeading Edge Radius
Leading Edge
TrailingEdge
Aerofoil Naming Conventions
Aerofoil Shapes
Aerofoils and Airf low
Positively Cambered
SymmetricalBi-Convex
The Relative AirflowAngle of Attack
ChordLine
MeanCamberLine
Negatively Cambered
Chord
Chord Line
Figure 4.8
The relationship between the aerofoil and the airflow
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Mean Camber Line
The mean camber lineis an imaginary line half way (equidistant)
between the upper and lower surfaces of the aerofoil. It is also known
as the camber line.
Camber
Camber describes the distance between the mean camber line and the
chord line. A highly cambered aerofoil has a greater maximum distance
between the mean camber line and the chord line.
Aerofoils can have identically curved upper and lower surfaces, in which
case they are known as symmetric aerofoils, or they can have different
curves on the upper and lower surfaces in which case they are knownas asymmetric or cambered aerofoils.
Note that a symmetrical aerofoil has no camber because the mean
camber line coincides with the chord line. The n and rudder often use
symmetrical aerofoil sections.
Positively Cambered
Symmetrical
Chord line
Camber line
Chordline
Camberline
Camberline
Chordline
Negatively Cambered
Figure 4.9Aerofoil shapes are often categorised by their camber
On apositively camberedaerofoil the mean camber line is above the
chord line. Most wings are positively cambered.A negatively cambered
aerofoil is one in which the mean camber line is below the chord line.
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Thickness Chord Ratio
The thickness chord ratio(also known as thefneness ratio), is the ratio
of the aerofoils maximum thickness to the length of its chord. When
expressed as a percentage it is known as the thickness to chord or
T/C. The aerofoil section of a low speed wing tends to have a greaterthickness chord ratio.
Figure 4.10
Comparison of aerofoil thickness ratios high and low speed designs
Bearing these denitions in mind. Lets move on to see how air ows
around an aerofoil.
Airow Around an Aerofoil
Figure 4.11 shows the behaviour of air owing round a positivelycambered aerofoil. You can see from the curves in the streamlines
that a large volume of air is affected by the aerofoil. The air which
remains beyond the inuence of the aerofoil is called the free stream
owwhich ows at the free stream velocityand is at free stream
(atmospheric) pressure.
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a b c
ed f
Figure 4.11Air flow around an aerofoil
Figure 4.11 is divided into six successive time frames. A short pulse
of smoke (shown in blue) has been introduced at Frame a and with
time moves back over the aerofoil.
Compare the streamline spacing to the speed at which the smoke
pulse travels over and under the aerofoil. From what we have learned
so far it should be no surprise to see that the air ows faster over theupper surface where the streamlines are closer together.
Furthermore, because the air over the upper surface has greater
dynamic pressure we can quickly deduce that the pressure above the
upper surface of the aerofoil is lower than the pressure below the
lower surface.
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The Cause of Accelerated Airow on the Upper Surface
Air owing around an aerofoil has to obey the laws of conservation.
This means that a given volume of air which encounters an aerofoil will
suffer an effective reduction in the cross-sectional area available to it.
Therefore it must ow faster.
Because of the sharp trailing edge the two ows, upper and lower, are
effectively separated because air cant ow round the trailing edge.
The curvature of the upper surface therefore cause a bigger reduction
in cross sectional area available to the upper ow and to conserve its
mass ow the upper ow must ow faster.
Figure 4.12
Conservation of mass flow causes a greater flow speed over the upper surface.
If you look again at Figure 4.11 youll notice that the two ows dont
rejoin in the same relative position. The mass of air which has owed
over the upper surface is permanently ahead of the mass of air which
owed under the lower surface because its average speed over the
aerofoil was faster.
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Pressure Around an Aerofoil
Figure 4.13 shows the pressure distribution around a positively
cambered aerofoil. Note the large volume of air affected by the aerofoil
Blue denotes air at below free stream pressure. Red denotes air that is
above free stream pressure.
The area of lowest pressure occurs where the airow is at its fastest. In
other words it coincides with the area where the streamlines are closest
together. The patterns of low pressure above and below the wing show
that the lowest pressure occurs in the rst quarter of the chord.
Area of Reduced Pressure
Area of Increased Pressure
Incre
asedV
elocity-ReducedPressure
ReducedV
elocity-IncreasedPressure
Figure 4.13
The pattern of air pressure around an aerofoil
Most of the time you dont need to think about the pattern of pressure
distribution around an aerofoil. The thing that matters most is the
plot ofpressure differentialsbecause it is the differencein pressures
at various points on the aerofoil that provides the unbalanced
force. However we will occasionally show you the actually pressure
distributions so that you can better understand the huge volume of air
affected by an aerofoil.
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The component which is parallel to the free stream ow, but acting
in the opposite direction is known as drag the force which resists
forward movement.
The component which is perpendicular to the free stream ow is known
as lift. We will explore both lift and drag in much further depth later.
Aerodynamic
total reaction
Lift
Drag
Figure 4.15
The total reaction can be resolved into its two components lift and drag.
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Summary
Unlike an ideal gas, air has viscosity and consequently its ow is
affected by friction. Viscosity and friction are the ultimate cause of two
forms of drag: skin friction drag and form drag.
When an aerofoil shape is placed in a free owing stream of air:
J The air divides to ow above and below the aerofoil. The stagnation
line is the dividing point between the two ows.
J A very small proportion of the air ow is brought to a complete
standstill near the leading edge at the stagnation point.
J Relative to the free stream ow, the air ows much faster over theupper surface than under the lower surface. The static pressure
acting on the upper surface is therefore much less than the static
pressure acting on the aerofoils lower surface. This creates a
pressure differential across the aerofoil.
J There is upwash ahead of the aerofoil and downwash behind it.
J All the forces acting on the aerofoil can be summed into a single
vector representing the total reaction which originates at the centre
of pressure.
J Lift is the component of the total reaction which is perpendicular to
the free stream ow.
J Drag is the component of the total reaction which is parallel to the
free stream ow.
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APPENDIX
Understanding the cause of circulation is beyond the scope of the EASA
ATPL syllabus. So there is no requirement for you to read this appendix
For those of you who would like to gain a basic understanding please
read on. Well start by going back to our most simple shape, the
cylinder.
Circulation and Lift
A stationary cylinder placed in an air ow produces no lift because the
decrease in static pressure above and below the cylinder is equal and
opposite. We can change this situation by spinning the cylinder.
Consider a spinning cylinder in a stationary ow. The minute
imperfections on the surface of the cylinder cause surface roughness
which catches air molecules and drags them along. The viscosity of the
air means that these molecules start to drag along other molecules nex
to them even though they are not in direct contact with the surface.
These in turn drag other molecules above them which are even further
away from the surface. The net effect is that a rotating cylinder in stillair causes the air around it to rotate.
Increased speed
q Ps
PsStagnation point
Upwash Downwash
Decreased
local speed
Figure 4.16
A rotating cylinder will induce rotation in the air surrounding it.
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If you now introduce an air ow across the cylinder the vortex caused
by the cylinders rotation will addto the velocity of the ow above the
cylinder and subtractfrom the velocity of the ow beneath the cylinder.
Notice also that the circulatory ow has induced upwash ahead of the
cylinder and downwash behind it.
Increased speed
q Ps
Stagnation point
Upwash Downwash
Smaller increase
(or possible decrease) , in speed
Figure 4.17
Changes in flow velocity caused by cylinder rotation
The air owing above the cylinder is owing faster than the air owing
below the cylinder. Consequently the static pressure above the cylinder
is lower than the static pressure below the cylinder. This results in an
unbalanced force giving a net upwards aerodynamic force.
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Circulation Around an Aerofoil
Weve covered one explanation for the faster ow on the upper
surface. An alternative explanation which is useful because it can be
mathematically modelled is the concept of circulation.
Air ows more quickly over the upper surface of an aerofoil because
the aerofoil has a sharp trailing edge. The sharp trailing edge sets up
a circulating ow around the aerofoil which adds to the velocity of the
free stream ow above the aerofoil and subtracts from the free stream
velocity below the aerofoil.
So why is this pattern of circulation not immediately visible to us in
gure 4.11? To answer this we need to switch our frame of reference.Streamlines are a very good way of thinking about air ow from the
perspective of a pilot sitting in an aircraft or an observer watching an
aerofoil in a wind tunnel. Relative to both, the aerofoil is stationary
and the air is owing past it. But they dont help us to understand
circulation.
Rather than thinking in terms of stationary aerofoil moving airwe
need to look at what actually happens when an aerofoil is in ight. Thatis to say moving aerofoil stationary air. In this real world situation
the air remains stationary until it is about to be impacted by the rapidly
moving aerofoil.
If we stood on the surface of the Earth, and our eyesight was ultra
sharp, we would see that the air molecules are moved, up, right, down
and left by the passage of the aerofoil.
In this frame of reference you would see that some of the air inuenced
by the lower surface of the aerofoil is accelerated forwards (not slowed
down as we previously described). You would also see that the air
inuenced by the upper surface really is accelerated backwards and
downward. Figure 4.19 shows what happens.
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Figure 4.19
Circulation around an aerofoil: stationary air moving aerofoil
For the mathematically minded, these arrows are nothing more than
the result of subtracting out the velocity of the air stream.
Circulation starts to occur almost (but not immediately) at the point
when the aerofoil starts to move.
At the precise moment that air starts to ow over an aerofoil, the rearstagnation point sits on the upper surface of the trailing edge and no
circulation exists.
Because the rear stagnation point is on the upper surface, air from
the lower surface attempts to ow around the sharptrailing edge and
towards the stagnation point. If the trailing edge were innitely sharp,
the air would have to make a turn of innitely small radius so the ow
would be innitely fast! Of course, the trailing edge is not innitelysharp but it is very sharp. In fact, the sharper the trailing edge the
faster the ow around it. Consequently the initial ow around the sharp
trailing edge of an aerofoil is very fast.
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In making its very sharp turn around the trailing edge the air creates
a vortex, the starting vortex, which initially, and very briey, sits just
above the trailing edge, Figure 4.20.
Stagnation Line
Stagnation
Line
Figure 4.20
The starting vortex
But the starting vortex cannot exist in isolation. If it did, the motion itwould produce on the air would offend the principle of conservation of
momentum. So to ensure that the sum total of momentum remains the
same, an equal and opposite vortex must be generated. This is effected
by the bound vortex- the name given to the general circulation of air
around the aerofoil.
Starting Vortex
Bound Vortex
Figure 4.21
The momentum of the starting and bound vortices are exactly equal and opposite
The bound vortex is larger than the starting vortex, but its rate of
circulation is slower. The result is that the momentum of the bound and
starting vortices are exactly equal and opposite.
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As airspeed increases, so too does the intensity of the starting vortex.
This is matched by an increase in the speed of the bound vortex. The
increased circulation effectively pushes the starting vortex off the
trailing edge of the aerofoil and a stable state is quickly reached in
which the rear stagnation point sits on the sharp trailing edge.
Stagnation Line
Bound Vortex
StagnationLine Shed Vortex
Figure 4.22
The Kutta Condition
Further increases in speed or angle of attack will result in the airow
again attempting to form a vortex around the trailing edge. But this is
again very quickly overcome by an increase in the speed of circulation
of the bound vortex. In this way the stagnation point is always held at
the trailing edge and the only visible effect of an increase in speed orangle of attack is an increase in circulation.
This stable state, in which the rear stagnation point remains attached
to the trailing edge, is known as the Kutta Condition. Put another way,
the Kutta condition is a rule which states that:
A body with a sharp trailing edge which is moving through a uid will
create about itself a circulation of sufcient strength to hold the rear
stagnation point at the trailing edge.
Circulation is caused by the effect of the sharp trailing edge which is
why, despite the structural and engineering difculties this creates, an