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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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





The Aerofoil

Airow Around an Aerofoil

The Cause of Accelerated Airow on the Upper Surface


Aerodynamic Force

Summary

Circulation and Lift


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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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Principles of Flight Aerodynamic Forc

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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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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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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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.


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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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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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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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

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