B-8 Aerodynamics SR

7/25/2019 B-8 Aerodynamics SR

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Student Resource

Subject B-8:

Aerodynamics

Copyright 2009 Aviation Australia

All rights reserved. No part of this document may be reproduced, transferred, sold,or otherwise disposed of, without the written permission of Aviation Australia.


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Training Material Only B-8 Aerodynamics

Issue B: Jan 2008 Revision 3 Page 1 of 6

CONTENTS

Study Resources 3

Learning Outcomes 5

Physics of the Atmosphere B-8.1-1

Aerodynamics B-8.2-1

Theory of Flight B-8.3-1

Flight Stability and Dynamics B-8.4-1


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STUDY RESOURCES

Jeppesen General

Jeppesen Airframe

Aircraft Engineering Principles Dingle & Tooley.

Mechanics of Flight A. C. Kermode

B-8 Student Resource


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LEARNING OUTCOMES

The purpose of this subject is to familiarise you with basic aerodynamics and the theoryof flight. It also covers flight controls and conditions which affect the aerodynamics ofaircraft.

On completion of the following topics you will be able to:

Topic 8.1 Physics of the Atmosphere

Describe the application of the International Standard Atmosphere (ISA) toaerodynamics.

Describe the following characteristics associated with the atmosphere:

Composition,

Pressure and temperature distribution effects of altitude and

Effects of humidity, temperature and pressure on density.

Topic 8.2 Aerodynamics

Describe airflow around a body in relation to the following terms:

Boundary layer

Laminar and turbulent flow

Free stream flow

Relative airflow

Upwash and downwash

Vortices and stagnation

Describe the following terms and list their interaction with related forces:

Camber

Chord

Mean Aerodynamic Chord (MAC)

Profile (Parasite) Drag

Induced Drag

Centre of Pressure

Angle of Attack

Wash In and Wash Out

Fineness Ratio

Wing Shape and Aspect Ratio

Describe the relationship between thrust, weight and aerodynamicresultant.


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Describe how lift and drag are generated and define the followingassociated terms:

Angle of Attack

Lift Coefficient

Drag Coefficient

Polar Curve

Stall

Describe aerofoil contamination including ice, snow and frost.

Describe the relationships between:

Ground speed (GS)

True air speed (TAS) Indicated air speed (IAS)

Topic 8.3 Theory of Flight

Describe the relationship between lift, weight, thrust and drag.

Describe glide ratio.

Describe steady state flight and define performance.

Describe the theory of the turn.

Describe load factor and its influence on stalling, flight envelope andstructural limitations.

Describe methods of lift augmentation.

Topic 8.4 Flight Stability and Dynamics

Describe the following types of flight stability (active and passive):

Longitudinal

Lateral

Directional

In relation to longitudinal, lateral, and directional stability, be able to state:

The axis about which they apply

The aircraft structural features that provide stability about that axis.

Describe flight stability including:

Anhedral

Dihedral

Asymmetric power

Dynamic stability

Longitudinal dihedral

Static stability

Torque effect

Ground effect


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Training Material Only B-8.1 Physics of the Atmosphere


TOPIC 8.1: PHYSICS OF THE ATMOSPHERE

TABLE OF CONTENTS

Introduction...................................................................................................................3

Atmosphere Composition ...............................................................................................3

Air Density.....................................................................................................................9

International Standard Atmosphere (ISA) .....................................................................13


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LIST OF FIGURES

Figure 1: Gas composition graph....................................................................................3

Figure 2: Physical composition of atmosphere ................................................................4

Figure 3: Pressure of the atmosphere .............................................................................5

Figure 4: Temperature v Altitude....................................................................................5

Figure 5: Effects of altitude on temperature....................................................................6

Figure 6: Atmospheric conditions...................................................................................8

Figure 7: Effects of temperature on air density ...............................................................9

Figure 8: Molecule mass and altitude ...........................................................................10

Figure 9: Air density effect on aircraft in flight ..............................................................10

Figure 10: Water vapour ..............................................................................................11

Figure 11: Morning dew ...............................................................................................12


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INTRODUCTION

The atmosphere is the life giving substance which surrounds our planet earth. We rely

on it to provide adequate gases to sustain life and a climate which is suitable for us toperform our everyday activities. Most of the atmosphere exists within a height of 10 kmabove the earth, and it is within this region that all weather and climatic conditions aregenerated.

This topic will discuss in relation to the atmosphere:

Composition.

Pressure and temperature distribution effects of altitude.

Effect of humidity and pressure on density.

ISA standard conditions.

ATMOSPHERE COMPOSITION

The atmosphere is a complex and ever changing mixture, commonly called air. The air isa mixture of gases, but also contains quantities of foreign matter, such as pollen, dust,bacteria, soot, volcanic ash and dust from outer space.

The proportions of gases in the atmosphere are shown below. (Figure 1)

The remaining 0.003% is made up of microscopic quantities of other gases such as neon,

helium, krypton, ozone etc.

Figure 1: Gas composition graph

The nature of the atmosphere may vary considerably from day to day at any given place,and may also vary from place to place at any given time. Because of these variations andbecause aircraft move from one place to another quickly, they continually experiencechanges in the air in which they fly.

The characteristics of the atmosphere have important effects on the operation and

maintenance of aircraft.

Aircraft performance and forces such as lift, drag, and engine power are affected by

changes in densities which result from variations in atmospheric pressure, temperatureor humidity.




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Many maintenance operations are also affected by atmospheric conditions:

Ground running of engines.

Adjusting components.

Adjusting and monitoring instruments.

Applying surface finishes, i.e. paint.

The Physical Composition of the Atmosphere

The atmosphere is classified into regions based on the variation of temperature withaltitude. These regions are:

Troposphere.

Tropopause. Stratosphere.

Mesosphere.

Thermosphere (Ionosphere).

(Figure 2)

Aircraft fly only in the Troposphere and the lowest part of the Stratosphere. Civil aircraftwould rarely exceed altitudes of 45,000 ft (nearly 14 km)

Figure 2: Physical composition of atmosphere




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The Pressure of the Atmosphere

The weight of air above any surface causes pressure at that surface. The average

pressure at sea-level due to the weight of the atmosphere is about 14.7 psi (1013.25 mb[millibars]). This pressure is referred to as one atmosphere.

The higher we ascend in the atmosphere, the less will be the weight above us. Therefore,the pressure will be less.

(Figure 3)

Figure 3: Pressure of the atmosphere

Temperature Changes in the Atmosphere

As we ascend in the atmosphere, there is a gradual decrease in temperature. Thetemperature drops at a steady rate called the lapse rate.

The lapse rate at a given place varies from day to day and even during each day. Thelapse rate is about minus 6.5 deg C for each 1000m of height up to 11 000m (36,000 ft).Above 11 000m the temperature remains nearly constant until the outer regions of theatmosphere is reached.

(Figure 4)

Figure 4: Temperature v Altitude




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The atmosphere is classified into regions based on the variation of temperature withaltitude as shown in Figure 5. Air temperature undergoes considerable change asaltitude increases:

Troposphere -gradual temperature decrease.

Tropopause -temperature approx constant.

Stratosphere -gradual temperature increase.

Mesosphere - gradual temperature decrease.

Thermosphere (ionosphere) - rapid temperature increase.

Figure 5: Effects of altitude on temperature

The composition of the atmosphere (oxygen, nitrogen etc) remains almost constant fromsea level up, but its density diminishes rapidly with altitude. For example, atapproximately 30 000 ft(10 kms), it is too thin to support respiration and at 60,000 ft there is not enough oxygento support combustion.

NOTE: Aircraft altitude is still measured in feet.

Civil aircraft normally fly at altitudes up to 45,000 ft (14km). Although the atmosphere isdivided into several regions, we will only be covering the three closest to the earthssurface, these being:

Troposphere.

Tropopause.

Stratosphere.




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Troposphere

The troposphere is the layer in which we live and in which most aircraft fly. It is

characterised by large changes in temperature, humidity and by generally turbulentconditions. Nearly all cloud formations are within the troposphere and approximatelythree quarters of the total weight of the atmosphere is within it.

It extends from the surface of the earth to where the temperature ceases to decrease with

altitude (roughly 36,000 ft). In the troposphere, for every 1,000 ft increase in altitude, thetemperature drops approximately 2C(lapserate).

Tropopause

The tropopause is defined as the point in the atmosphere at which the decrease intemperature (with increasing altitude), abruptly ceases. The tropopause is located at the

top of the troposphere and the start of the stratosphere. The temperature at the

tropopause is around a chilling -57C.The tropopause is not at a constant altitude above the earth. At the poles it can be as lowas 28,000 ft, while over the equator it can be as high as 55,000 ft. These heights mayvary due to seasonal changes which cause temperature fluctuations. However, theaverage of approximately 36,000 ft is taken to be the tropopause. At this height, theatmospheric pressure is approximately

3 PSI or5

1 the sea level pressure.

The troposphere is also characterised by a rapid drop in atmospheric pressure. Thepressure drops from approximately 15 PSI at sea level to 3 PSI at 36,000 ft.

Stratosphere

The atmospheric layer extending from the tropopause up to an average altitude ofbetween 50 to 55 kilometres is termed the stratosphere. Pressure continues to drop from3 psi at the tropopause to about 0.015 psi at the top of the stratosphere.

The temperature remains almost constant at -57C,forminganisothermallayerfromthetropopauseuptoanaltitudeof20 kilometres (70,000 ft).

Between 20 kilometres and approximately 32 kilometres the temperature begins to slowlyrise. Above an altitude of 32 kilometres, the temperature starts to increase more rapidly.

The temperature rise ceases at around 0C, between the altitudes of 50 to 55 kilometres.This point is called the stratopause.

(Refer to Figure 6, next page)




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Figure 6: Atmospheric conditions




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AIR DENSITY

Density is described as mass per unit of volume of a substance. Density is of great

importance when studying aerodynamics because of its effects on an aircraft or aerofoil.

Three factors affect air density:

1. Altitude as altitude increases, density decreases due to decreased atmosphericpressure.

2.Temperature as temperature increases, density decreases due to the volume ofair expanding.

3. Humidity as humidity increases, density decreases due to a decreased molecularweight in a given volume (relatively lighter water vapour molecules displaceoxygen, nitrogen etc. molecules).

Air Density with Altitude Changes

In the troposphere, the air is warmest nearest the surface of the Earth.

As altitude increases:

Air temperature decreases.

Air density increases.

Air pressure decreases.

The decrease in air pressure has a greater effect on air density than the decrease intemperature. Therefore, the air becomes less dense with increasing altitude .

Air is under greater pressure at the earths surface. It is denser because it is compressed.It becomes less dense with increasing altitude. Aircraft and engine performance isdecreased if air density is decreased.

These effects are illustrated below in Figure 7.

Figure 7: Effects of temperature on air density




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Half of all air molecule mass is found below 5500m (18,000 feet) altitude. (Figure 8)

Figure 8: Molecule mass and altitude

Air density has a major effect on an aircraft in flight. At high altitude (less air density), agreater speed and distance can be achieved because of reduced resistance (drag).

(Figure 9)

Figure 9: Air density effect on aircraft in flight

Water Vapour

Water vapour makes up only a very small fraction of the total mass of air but it has amajor effect on flight.

Because water vapour is only 63% as heavy as air, it soon mixes with air and lowers airdensity.

This less dense air near the Earths surface rises and cools until its temperature drops towhere it can no longer hold the water as a vapour. The water condenses out to become aliquid, the liquid forms very tiny droplets small enough to be supported by the moving aircurrents. This forms clouds.




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Humidity

Humidity is caused by the condition of moisture or dampness. Water vapour is alwayspresent in the atmosphere and is one of the most important factors in human comfort.The proportion of water vapour in the atmosphere varies widely from place to place, andtime to time.

Travelling around Australia in the summer months you would come across large

fluctuations of humidity, depending on where you were. In Melbourne the temperaturemay be 30C with a humidity of 60%, while in Darwin the temperature may be 30C witha humidity of 95%. If you were to travel into the outback away from the coast thetemperature could fluctuate between 20C and 50C, with almost no humidity (the air isvery dry).

When the proportion of water vapour is small, the air is said to be dry. When the

proportion is significant, the atmosphere is described as moist, damp, wet or humid.Figure 10below shows that on a humid day air is less dense for a given volume due towater vapour displacing some of the dry air.

Figure 10: Water vapour

Humidity can be stated as:

Absolute humidity.

Relative humidity.

Absolute humidityrefers to the actual amount of water vapour in a mixture of air andwater. The amount of water the air can hold varies with air temperature. The higher theair temperature the more water vapour the air can hold.

Relative humidityis the ratio between the amount of moisture in the air to the amountthat would be present if the air were saturated. For example, a relative humidity of 75%means that the air is holding 75% of the total water vapour it is capable of holding.Relative humidity has a dramatic effect on aircraft performance because of its effect onair density. In equal volumes, water vapour weighs 62% as much as air. This means thatin high humidity conditions the density of the air is less than that of dry air.




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Dew Point

The amount of water vapour present in the air can be measured by blowing air over awet-bulb and a dry-bulb thermometer. The different in readings between the twothermometers is compared on a chart to find the relative humidity. This measurement isthe ratio of how much water vapour the air will hold at a given temperature. For practicalapplication in aviation, temperature and dew point are used more often than relativehumidity to measure the amount of water vapour in the air.

Dew point is the temperature to which the air must be lowered before the water vapourcondenses out and becomes liquid water.

Figure 11: Morning dew




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INTERNATIONAL STANDARD ATMOSPHERE (ISA)

Changing atmospheric conditions cause significant changes in the performance of

aircraft.

As the atmospheres temperature, pressure, and density vary from place to place andfrom day to day, it became necessary to develop a standard set of conditions to whichperformance of an aircraft could be measured. For this reason, an InternationalStandard Atmosphere (ISA) was adopted.

The ISA was formulated by the National Advisory Committee for Aeronautics (NACA), nowcalled National Aeronautics and Space Administration (NASA).

The International Civil Aviation Organisation (ICAO) now administers the ISA, and youmay therefore find reference to ICAO (SA) Standard Atmosphere in some publications.

Aircraft performance is measured under actual atmospheric conditions. This actualperformance can be compared to an ideal performance by recording parameters andcorrecting them to ISA conditions using graphs and charts.

ISA Standard Conditions

The set of standard conditions is known as the International Standard Atmosphere (ISA).

ISA defines precise values of:

Lapse rate.

Tropopause height.

It also defines sea-level values for:

Air pressure.

Air temperature.

Air density.

ISA values for the above are:

Lapse rate is minus 6.49 deg C / I000m.

Tropopause height is at 11 000m (36,000 ft).

Mean sea-level pressure is:

1013.25 millibars (mb).

14.69 pounds per square inch (psi).

29.92 inches mercury (in hg).

Mean sea-level temperature is 15 deg Celsius.

Mean sea level humidity is zero (0%).

Gravity (g) is 9.809m/sec2(32.174 ft/sec2).

These values are referred to as ISA Standard Day.

The reason 15C (when the air is perfectly dry) is used is because it is the average

condition prevailing at latitude 40 North.


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Issue B: Jan 2008 Re


vision 4 Page 14 of 14

Changes in atmosphere can effect:

Lift.

Drag.

Engine performance.

Component adjustments.

Instrument adjustment and monitoring.

The application of surface finishes.

Manufacture and repair of composite structures.

Pressure Altitude

Pressure altitude is the altitude in the standard atmosphere corresponding to aparticular value of air pressure. The aircraft altimeter is essentially a sensitive barometercalibrated to indicate altitude in the standard atmosphere.

With the altimeter of an aircraft set at 1013.2 mb (29.92 inches Hg), the dial will indicatethe number of feet above or below a level where 1013.2 mb exists, not necessarily aboveor below sea level, unless standard day conditions exist. In general, the altimeter willindicate the altitude at which the existing pressure would be considered standardpressure. The symbol H is used to indicate pressure altitude.


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Training Material Only B-8.2 Aerodynamics


TOPIC 8.2: AERODYNAMICS

TABLE OF CONTENTS

Airflow...........................................................................................................................4

Aerofoils ......................................................................................................................13

Aspect Ratio.................................................................................................................17

Generation of Lift .........................................................................................................20

Drag ............................................................................................................................25

Conditions of Flight......................................................................................................29

Aircraft Speed ..............................................................................................................33

Icing Effects .................................................................................................................37


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LIST OF FIGURES

Figure 1 Airflow disturbance ..........................................................................................4

Figure 2 Air Flow Resistance ..........................................................................................5

Figure 3 Boundary Layer................................................................................................6

Figure 4 Laminar and Turbulent Airflow.........................................................................7

Figure 5 Transition Point ...............................................................................................8

Figure 6 Airflow Separation ............................................................................................9

Figure 7 Relative Airflow ..............................................................................................10

Figure 8 Coanda Effect.................................................................................................10

Figure 9 Upwash..........................................................................................................11

Figure 10 Cause of vortices ..........................................................................................12

Figure 11 Wing Tip Vortices .........................................................................................12

Figure 12 Aerofoil Nomenclature ..................................................................................13

Figure 13 Chord Line ...................................................................................................13

Figure 14 Camber ........................................................................................................13

Figure 15 Mean Camber...............................................................................................14

Figure 16 Fineness Ratio..............................................................................................14

Figure 17 Aerofoil Shapes ............................................................................................14

Figure 18 High Lift Aerofoil ..........................................................................................15

Figure 19 General Purpose Aerofoil ..............................................................................15

Figure 20 High-Speed Aerofoil ......................................................................................16

Figure 21 Aspect Ratio .................................................................................................17

Figure 22 Aspect Ratio and Maximum Lift Coefficient...................................................18

Figure 23 Aspect Ratio and Induced Drag.....................................................................18

Figure 24 Wing Planforms ............................................................................................19

Figure 25 Mean Aerodynamic Chord (MAC). .................................................................19

Figure 26 Angle of Incidence ........................................................................................20

Figure 27 Angle of Attack .............................................................................................20

Figure 28 Pressure Distribution ...................................................................................21

Figure 29 Pressure Distribution/Angles of Attack.........................................................22

Figure 30 Lift Coefficient ..............................................................................................23

Figure 31 Resultant Lift ...............................................................................................24

Figure 32 Parasite Drag ...............................................................................................25

Figure 33 Form Drag....................................................................................................25

Figure 34 Skin Friction ................................................................................................26

Figure 35 Interference Drag .........................................................................................26


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Figure 36 Induced Drag ...............................................................................................27

Figure 37 Induced Drag ...............................................................................................27

Figure 38 Lift/Drag Ratio .............................................................................................28

Figure 39 Maximum Coefficient of Lift ..........................................................................29

Figure 40 The Four Aerodynamic Forces ......................................................................29

Figure 41 Drag Curve...................................................................................................30

Figure 42 The Stall ......................................................................................................31

Figure 43 Washin and Washout ...................................................................................32

Figure 44 One nautical mile .........................................................................................33

Figure 45 Airspeed Indicator ........................................................................................34

Figure 46 Flight Computer ...........................................................................................35

Figure 47 True Speed Indicator ....................................................................................35

Figure 48 Ground speed...............................................................................................36

Figure 49 The effects of icing........................................................................................37

Figure 50 Ice build-up..................................................................................................37


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AIRFLOW

Air is a viscous fluid. As you can see in Figure 1, air behaves differently when it moves,

or when a body moves through it, at speeds below the speed of sound and at speedsabove the speed of sound. Because air is invisible, it is difficult to understand whathappens in flight.

Figure 1 Airflow disturbance




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Free Stream Airflow

The free stream airflow around a shape is the clean flow, distant enough to be unaffected

by the body passing through it, and does not change direction.Lines which show the direction of the flow are called streamlines. A body shaped toproduce the least possible resistance is called a streamline shape.

The amount of free stream air is directly relative to the resistance applied to the airflow(DRAG). Resistance creates turbulence (Figure 2). The greater the resistance, the greaterthe turbulence; therefore the further the locality of the free stream air. The amount ofdrag depends on when the airflow separates. The airflow around the ball has remainedattached for longer.

Figure 2 Air Flow Resistance

Friction

Skin friction is caused by the resistance which is set up when relative motion existsbetween the surface of a body and the air; contact between the two gives rise to a layer ofretarded air in immediate contact with the surface over which it is passing. This layer is

known as the boundary layer and the amount of drag arising from it is determined by thenature and thickness of the flow in the layer.




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Boundary Layer

The boundary layer is the layer of air adjacent to the surface of the body. The air velocity

in the boundary layer varies from zero on the surface of the aerofoil to the velocity of thefree stream at the outer edge of the boundary layer (Figure 3).

Figure 3 Boundary Layer

The boundary layer is caused by the viscosity of the air sticking to the surface of thewing and the succeeding layers of air. The thickness of the boundary layer is relative tothe velocity, and depends on the type of flow.




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Laminar Boundary Layer

The amount of drag produced depends on whether the flow in the boundary layer is

laminar or turbulent.Laminar flow is an orderly motion in which successive strata of air particles slide pasteach other in much the same way as the action of a pack of cards when thrown along aflat surface.

If we could ensure a laminar boundary layer over the whole surface of a wing the skinfriction would be reduced to about one-tenth of its value on a conventional type of wing.

As the speed increases the boundary layer becomes turbulent and the drag becomesgreater.

The usual tendency is for the boundary layer to start by being laminar over the surfacenear the leading edge of a body, but there comes a point, called the transition point,

when the layer tends to break away from the surface and become turbulent and thicker.

The boundary layer differs from the free air stream in that the particles of air are rotatingas they move rearwards. Those on the upper surface in a clockwise direction, and thosebelow anti-clockwise, in exactly the same way as ball bearings when rolled along asurface.

Refer Figure 4.

Figure 4 Laminar and Turbulent Airflow




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Transition Point:

That point on the wing at which the boundary layer changes from laminar to turbulent

flow is called the transition point. Because the increase in drag resulting from aturbulent boundary layer is considerable, care is taken to preserve laminar flow over asmuch of the wing as possible, for example in a true laminar flow wing shown in Figure 5.Skin friction is a major source of drag at high speeds and it is one of the most difficult toreduce. It can never be eliminated completely.

Figure 5 Transition Point

As the speed increases the transition point tends to come further forward, so more of theboundary layer becomes turbulent and the skin friction becomes greater.

If this much is understood it will be obvious that the main purpose of research work hasbeen to discover why the transition point moves forward, and how its movement can becontrolled so as to maintain laminar flow over as much of the surface as possible.

On examining the flow in the boundary layer closely, it will be seen that it differs fromthe free air stream in that the particles of air are rotating as they move rearwards, thoseon the upper surface in a clockwise direction, and those below anti-clockwise, in exactlythe same way as ball bearings when rolled along a surface.




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Stagnation point

The stagnation point, as shown below in Figure 6is that point at which the air is brought

to rest by the leading edge and the point from which the boundary layer originates. Thestagnation point is also the first point of contact of relative airflow, or, the point on theleading edge of an aerofoil where the airflow divides. Some airflow goes over the wing andsome goes under the wing.

Separation Points

The separation points are the points on the wing at which the boundary layers breakaway from the surface.

Wake

The wake consists of the unsteady rotational flow, resulting from separation of theboundary layers from the wing, and which tends to be dragged behind the trailing edge.

For a chord of seven feet the wake is about four to five inches in depth during flight atsmall angles of attack.

Refer Figure 6

Figure 6 Airflow Separation




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Relative Airflow

Relative Airflow (US Relative wind) is the direction of the airflow with respect to the wing.

If a wing moves forward horizontally, the relative airflow moves backward horizontally.Relative airflow is parallel to and opposite the flight path of the aeroplane. (Figure 7)

Figure 7 Relative Airflow

Coanda Effect

Viscosity is defined as a fluids resistance to flow. One of the consequences of this is thetendency of a viscous fluid to follow a reasonable curvature of, for example, the back of a

spoon, or the top surface of a wing. (Figure 8)

Figure 8 Coanda Effect




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Upwash

Figure 9shows that, in advance of the wing, the streamlines of air curve upwards

towards the top surface. Upwash, as this is called, is an inherent feature of any surfacewhich is giving lift and exists because air always tends to flow towards an area of lowpressure. The deeper the low-pressure region, the greater the amount of upwash.

Figure 9 Upwash

Downwash

Hydrodynamics is similar to aerodynamics except for the fluid used. When a personwater-skis, the towing boat must have enough speed through the water that the ski willcontinually force down enough water to equal the weight of the skier. When the rope isreleased, the skier slows down sinks into the water.

An aeroplane generates its lift in the same way as the water ski. The aeroplane ispropelled through the air by its powerplant, and as the air passes over the lift-producingsurfaces, called the airfoils, it is deflected downward. This downward deflection ordownwashing of the air has an opposing effect, that of pushing upward on the aeroplane.

There is nothing mysterious about this downwashing action. In fact, any inclined plane

will force air downward, but, the shape of the aeroplane wing makes this downwashingaction more efficient.

This downwash should not be confused with the downwards flow caused be wing tipvortices




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Vortices

When the airflow over the top surface of a wing meets with the airflow over the lower

surfaces at the trailing edge they are flowing at different angles to each other. Thiscauses eddies or vortices rotating clockwise (viewed from the rear) from the left wing, andcounter-clockwise from the right wing. (Figure 10)

All the vortices on one side tend to join up and form one large vortex at each wing tip.

These are called Wing-tip Vortices.

Vortices occur continuously while an aeroplane is flying.

The central core of the vortex is made visible by the condensation of moisture caused bythe decrease of pressure and temperature, in the vortex. These visible (and sometimesaudible!) trails from the wing tips should not be confused with the vapour trails caused

by condensation trails left by hot exhaust gases at high altitudes.

This downward flow must not be confused with the ordinary downwash.

Figure 10 Cause of vortices

Wing Tip Vortices

Wingtip vortices are caused by the higher pressure air beneath the wing leaking aroundthe wingtip and mixing with the low pressure air above the wing. (Figure 11)

This causes a spiral or vortex that trails behind each wingtip whenever lift is being

produced. The influence vortices have on flow extends well beyond their central core,modifying the whole flow pattern. The trailing vortices have a strong influence on lift,drag and handling properties of the aircraft. Wake turbulence is mainly due to these

wingtip vortices.



Figure 11 Wing Tip Vortices


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AEROFOILS

Figure 12 shows the names assigned to parts of an aerofoil.

Figure 12 Aerofoil Nomenclature

Chord Line

The chord of the aerofoil is the straight line joining the leading edge to the trailing edge.(Figure 13) It is used as an arbitrary reference line when measuring the angular positionof the wing in relation to the airflow.

Figure 13 Chord Line

Camber

Camber is defined as the curvature of an aerofoil surface or an aerofoil section from theleading edge to the trailing edge. (Figure 14) The degree or amount of camber isexpressed as the ratio of the maximum departure of the curve from the chord to the

chord length. An aerofoil having a double convex curvature means that it has camberabove and below the chord line.

Upper camber refers to the curve on the upper surface of an aerofoil, and lower camberrefers to the curve of the lower surface.

Mean camber is the curvature of the mean line of an aerofoil profile from the chord.Camber is positive, when the departure from the straight line is upward and negativewhen it is downward. When the upper and lower cambers of an aerofoil are the same, theaerofoil is said to be symmetrical.

Figure 14 Camber


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profile from the chord.

(Figure 15) Camber is positive, when the departure from the straight line is upward andnegative when it is downward. When the upper and lower cambers of an aerofoil are thesame, the aerofoil is said to be symmetrical.

Figure 15 Mean Camber

Fineness Ratio

The fineness ratio is a measure of the thickness of the aerofoil.

There is also a thickness rati

Mean Camber

Mean camber is the curvature of the mean line of an aerofoil

o ofc

t where t is breadth and c is the length. (Figure 16)

Figure 16 Fineness Ratio

Aerofoil Shapes

The performance of an aerofoil is governed by its contour. Generally, aerofoils can bedivided into three classes:

High lift.

General purpose.

High speed.

Refer Figure 17

Figure 17 Aerofoil Shapes


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ilsHigh Lift Aerofo

There sections employ a highc

t ratio (15%), a pronounced camber, and a well-rounded

leading edge (Figure 18). Their maximum thickness is at about 25 per cent to 30 per centof the chord aft of the leading edge.

The greater the camber, i.e. the amount of curvature of the mean camber line, thegreater the shift of centre of pressure for a given change in the angle of attack. The rangeof movement of the Centre of Pressure (CP) is therefore large on a high-lift section. Thismovement can be greatly decreased by reflexing upwards the trailing edge of the wing,but some lift is lost as a result.

Sections of this type are used ma her aircraft where a highCoefficient of Lift (CL) all important and spe sideration.

Figure 18 High Lift Aerofoil

General Purpose Aerofoils

These sections employ a lower

inly on sailplanes and oted a secondary con

c

t

he

ratio (10%), less camber and a sharper leading edge

than those of a high-lift type (Figure 19), but their maximum thickness is still at about

25 per cent to 30 per cent of t ge. The lowerchord aft of the leading edc

t ratio results

lower CLthan those of a high-lift aerofoil.

y.

Figure 19 General Purpose Aerofoil

in less drag and a

Sections of this type are used on aircraft whose duties require speeds which, althoughhigher than those previously mentioned, are not high enough to subject the aerofoil tothe effects of compressibilit


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sHigh-Speed Aerofoil

These sections employ a very lowc

t ratio (7%), no camber, and a sharp leading edge

(Figure 20). Their maximum thickness is at about the 50 per cent chord point.

Most of these sections lie in the 5 per cent to 10 per cent tic ratio band, but even thinner

rcs of a circle placed symmetrically about the chord line.

Figure 20 High-Speed Aerofoil

sections have been used on research aircraft. The reason for this is the overridingrequirement for low drag; naturally the thinner sections have low maximum-liftcoefficients.

High-speed aerofoils are symmetrical about the chord fine; some sections are wedge-shaped whilst others consist of a


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ASPECT RATIO



i

h

atio iswing with the same span but with an area of 150 square feet would have an

d

tio of 10. From the foregoing, it can be concluded that the smaller the mean chord inn to the span the higher the aspect ratio.

The dimensions of the wing-Hp vortices and therefore the amount of induced drag can bereduced considerably by increasing the aspect ratio. Figure 21 shows three wings of thesame area but with different asp her aspect ratio formssmaller wing-tip vortices than roportion of the total area isinvolved in the process of spilling air from the lower to the upper surface. Consequently,the rate of spilling or circulation around the tips of high aspect ratio wings is less.

The high aspect ratio wing can be said to be more efficient, from the point of view of lowinduced drag. Since the total drag of a wing is the sum of the profile and induced drags,and the induced drag changes with aspect ratio, the total drag also changes with aspectratio. The graph shows the effect of aspect ratio on the total drag of two wings of differentaspect ratios over the working range of angles of attack.

Figure 21 Aspect Ratio

Any plan form can be described br efly, but well enough to give a rough idea of its

performance, by its aspect ratio. T e aspect ratio of a wing is found by dividing thesquare of the wing span by the area of the wing i.e.

Thus, if a wing has an area of 250 square feet and a span of 30 feet, the aspect r3.6. Another

aspect ratio of 6. Aspect ratio can also be found by dividing the span by the mean chorof the wing. For example, a span of 50 feet with a mean chord of 5 feet gives an aspect

ect ratios. The wing with the higthe others because a smaller p

rarelatio


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Maximum Lift Coefficient

on is

ost noticeable at very low aspectratios of about 2 to 3 (Figure 22). Therefore, stalling speeds for a given wing loading arenot very seriously affected by a reduction in the aspect ratio.

Aspect Ratio and Induced DragThe relationship for the induced drag coefficient emphasises the need for a high aspect

ratio for aircraft which are continually operated at high lift coefficients. On the otherhand, long thin wings increase structural weight and eventually a compromise has to bereached.

Aircraft developed for very high speed flight operate at relatively low lift coefficients andrequire great aerodynamic cleanliness. These aircraft, in consequence, usually have lowaspect ratio planforms.

The limiting factor in the use of high aspect ratio is the difficulty of providing sufficientstrength for the wings without the excessive weight which neutralises the advantage

gained. Broadly, it can be said that the lower the cruising speed of the aircraft the higherthe aspect ratio that can be usefully employed. ReFigure 23 Aspect Ratio and InducedDragfer

Figure 23 Aspect Ratio and Induced Drag

Aspect Ratio and

The maximum lift coefficient (CL) obtained from a given wing area and aerofoil secti

almost unaffected by aspect ratio. However, there is a tendency for the CLmax todecrease as the aspect ratio is reduced, becoming m

Figure 22 Aspect Ratio and Maximum Lift Coefficient


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Wing Planforms

Planform refers to the shape of the aeroplanes wing when viewed from above or below:

Rectangular is the cheapest to build.

Elliptical is most efficient.

Tapered is a compromise.



Sweepback is for high speed.

Refer Figure 24

Figure 24 Wing Planforms

Mean Aerodynamic Chord (MAC).

Certain aerodynamic and weight-and-balance characteristics are referenced as a percent

of the wing chord. However, when a wing is tapered, the chord is not uniform across theentire wing span. F a percent of themean aerodynamic chord (MAC).

chord drawn through the centre of the area of the)

hord but a MAC equal to two-thirds of the root chord.

Figure 25 Mean Aerodynamic Chord (MAC).

or this reason these characteristics are referenced as

The mean aerodynamic chord is theaerofoil; that is, equal amounts of wing area will lie on both sides of the MAC. (Figure 25Often, the MAC is confused with the average chord.

As an example, the pointed-tip delta wing would have an average chord equal to one-halfthe root c


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LIFT

he wing chord makes with thethe wing is attached to fuselage. (Figure 26)

T does not change.

Figure 26 Angle of Incidence

Angle of Attack

The angle of inclination between the aerofoil chord and the relative airflow is of greatimportance. This angle is called the Angle of Attack (A of A; Figure 27).

For most aerofoils, lift increases s from zero, at a slightlyout 15 degrees.

Figure 27 Angle of Attack

Centre of Pressure CP

The centre of pressure is a point along the wing chord line where lift is considered to beconcentrated. For this reason, the centre of pressure is often referred to as the centre oflift.

During flight, this point different flightattitudes. It moves forward as the angle of attack increases and aft as the angle of attackdecreases. As a result, pitching tendencies created by the position of the centre of lift inrelation to the Centre of Gravity (CG) vary.

For example, with a high angle of attack and the centre of lift in a forward position(closer to the CG) the nose-down pitching tendency is decreased. The position of the

centre of gravity in relation to the centre of lift is a critical factor in longitudinal stability.

GENERATION OF

Angle of Incidence

The angle of incidence is the acute angle which tlongitudinal axis of the aircraft, when

his angle is fixed in manufacture and

as angle of attack increasenegative angle, to maximum lift at ab

Above about 15 degrees angle of attack lift will very rapidly drop to zero again, where theaerofoil is said to have stalled.This applies to wings, propeller blades, helicopter rotorblades and jet engine fan, compressor and turbine blades.

along the chord line changes position with


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Pressure Distribution



trates the pressure distribution over an aerofoil at an angle of attack

han thed and

, by means of its lower pressure

which provides the greater part of the lift at some angles of attack as much as 80%.

ill move depends upon theshape of the aerofoil section and the angle of attack.

The centre of pressure (CP) is the point at which the resultant force intersects the chordof an aerofoil. Lift acts from the centre of pressure, or, stated another way, the centre ofpressure is the centre of lift.

The location and direction in which the resultant will point depends upon the shape ofthe aerofoil section and the angle at which it is set to the airstream. Throughout most ofthe flight range, that is, at the usual angles of attack, the CPmoves forward as the angleof attack increases and backward as the angle of attack decreases.

Figure 28 below illus

of 4 deg. It shows that the decrease in pressure on the upper surface is greater tincrease in pressure on the lower surface, also the pressure is not evenly distributeboth pressures are greater on the forward portion of the aerofoil.

Although both surfaces contribute, it is the upper surface

Figure 28 Pressure Distribution

The location and direction in which the centre of pressure w


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9 the resultant intersects the chord line or centre of pressure at

ately the 25% chord position for

Generally, at subsonic speeds at a given angle of attack, the greater the amount of liftobtained from a given wing; conversely, the flatter the camber and the thinner the wingthe less the lift.

This difference is due to the greater accelerating effect on the air stream of pronouncedcamber, resulting in a larger reduction in pressure.

The measure of the lifting effectiveness, or power of wing under a given set of conditions,is its lift coefficient or CL.

The CLis not constant but varies with the angle of attack. Furthermore, various

aerodynamic aids can be used to increase the CLand thus raise the lifting effectivenessof a wing.

As illustrated in Figure 2

progressively forward locations as the angle of attack is increased.

Figure 29 Pressure Distribution/Angles of Attack

The centre of pressure is generally located at approximmost aerofoils. On an aerofoil with a 60 inch chord, this would locate the centre ofpressure at 15 inches aft from the leading edge.

Lift Coefficient

When several wings of the same geometrical shape and area, but with different aerofoilsections, are compared at a given angle of attack and air speed, the lift obtained fromeach wing varies the exact amount of lift depending on the aerofoil section used.


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is:

The graph (Figure 30) shows that as angle of attack increases, so does coefficient in liftup to a maximum of about 15 degrees.

Figure 30 Lift Coefficient

Since the expression amic forces, it is,

foil combination is placed in an air stream at a given angle of attack,this stream is then progressively increased, the lift increases in

s this is called, brings with it a reduction in the CLand hence a falling

city only affects the lift force of the aerofoil not the coefficient of lift.

Note2: Rho (Greek letter ) - air density at standard day (0.02378 slugs per cubic foot).

All else being equal, the higher the CLthe lower is the minimum speed at which a givenwing can produce a required lift. The formula for calculating the lift

V2S (GreekletterRho)applies to all aerodynsufficient, when considering increases or decreases of lift under a given set of conditionsto refer to the increase or decrease of the lift coefficient alone. Thus an increased CLimplies an increased lift, and vice versa.

When a wing aeroand the speed ofproportion to the square of the speed as shown by the lift formula.

At higher subsonic speeds the rate at which the lift has been increasing, in accordancewith the V2law, begins to fall appreciably.

This effect is caused by the compressible nature of the air which, although negligible atlower subsonic speeds, begins to play an important part at the higher subsonic speeds.

Compressibility, aoff in the rate of increase of lift, owing to fundamental changes in the nature of theairflow.

Summarising: The two math factors affecting co-efficient of lift are:

Aerofoil shape.

Angle of attack.

Note1: Velo


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icular to the

relative airflow.

Refer Figure 31

Figure 31 Resultant Lift

Resultant Lift

The resultant lift produced by an aerofoil is the net force produced perpend

The resultant drag incurred by an aerofoil is the net force produced parallel to therelative airflow.

TOTAL AERODYNAMIC

REACTION

DRAG

LIFT


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DRAG



lane. A highly cambered, large surface area wing creates more drag (and

irspeed, or angle of attack, you increase drag (and lift).

osition to the direction of flight, opposes the forward-acting force ofthrust, and limits the forward speed of the aeroplane.

Drag is broadly classified as either parasite or induce

Parasite Drag

Parasite drag (Figure 32) includes all drag created by the aeroplane, except that dragdirectly associated with the production of lift. It is created by the disruption of the flow of

air around the aeroplanes surfaces.

Parasite drag normally is divided into three types:

Form drag.

Skin friction drag.

Interference drag.

Each type of parasite drag varies with the speed of the aeroplane. The combined effect ofall parasite drag varies proportionately to the square of the airspeed. In other words, ifairspeed is doubled, parasite drag increases by a factor of four.

Figure 32 Parasite Drag

Form Drag

Form drag is created by any structure which protrudes into the relative airflow. (Figure

33) The amount of drag created is related to both the size and shape of the structure. Forexample, a square strut creates substantially more drag than a smooth or rounded strut.Streamlining reduces form drag.

Figure 33 Form Drag

Drag is caused by any aircraft surface that deflects or interferes with the smooth airflow

around the aeroplift) than a small, moderately cambered wing.

If you increase a

Drag acts in opp

d.


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iction

which

Figure 34 Skin Friction

t.of drag is the mixing of

the air where the wing and fuselage join. (Figure 35)

Each type of parasite drag varies with the speed of the aeroplane.

ure 35 Interference Drag

Skin Fr

Skin friction drag is caused by the roughness of the aeroplanes surfaces. Even though

these surfaces may appear smooth, under a microscope they may be quite rough. (Figure34)

A thin layer of air clings to these rough surfaces and creates small eddiescontribute to drag.

Interference Drag

Interference drag occurs when varied currents of air over an aeroplane meet and interacThis interaction creates additional drag. One example of this type

Fig


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Induced Drag



e the wing usually is at a low angle of attack at high speed, and a high angle of.

nd Figure 37 below.

Induced drag is the main by-product of the production of lift. It is directly related to the

angle of attack of the wing. The greater the angle, the greater the induced drag.Sincattack at low speed, the relationship of induced drag to speed also can be plotted

Refer to Figure 36 a

Figure 36 Induced Drag

Figure 37 Induced Drag


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Polar Curve

teadily.

At the stall the L/D is about 6.

Refer Figure 38.

Lift/Drag - The

The polar curve is a name given to mathematical representation of data involving

lift/drag/speed/angle of attack.The lift/drag ratio increases rapidly up to an angle of attack of about 4. Lift may bebetween 12 to 20 times the drag, the exact figure depending on the aerofoil used.

At larger angles the L/D ratio decreases s

Figure 38 Lift/Drag Ratio


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CONDITIONS OF FLIGHT



aight and level flight, the amount of lift is dependant on

of

t at the maximum coefficient of lift, any further increasewill cause a stall, and with that, rapid decrease in coefficient of lift.

Figure 39 Maximum Coefficient of Lift

Aerodynamic Forces

ircraft flight is controlled by adjusting the relationship between the four aerodynamicrces (Figure 40):

Lift is the component of the aerodynamic reaction perpendicular to the relativeairflow.

Drag is the component of the aerodynamic reaction parallel to the relativeairflow.

Weight is due to gravity.

Thrust is produced by the power plant.

Figure 40 The Four Aerodynamic Forces

Straight and Level Flight

For an aeroplane to remain in strairspeed and the angle of attack.

At low airspeed the aircraft has a large angle of attack. At high airspeed the angleattack can be reduced.

The graph (Figure 39) shows thain angle of attack

Afo


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t and level flight:

.

t be added to change the equilibrium. To descend,

At high speeds, parasite drag dominates. Total drag starts high, decreases to aminimum, and then increases towards the aircrafts maximum speed.

For constant speed, straigh

Lift equals Weight

Thrust equals Drag.

To accelerate or climb, thrust musthrust is reduced.

Drag Curves

In Figure 41, at low speeds, induced drag is high due to the large vortices created at highangle of attack.

Figure 41 Drag Curve


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The Stall



tion of airflow from the wings upper surface. (Figure 42)

in lift. For a given aeroplane, a stall always occurs at theof air speed, flight attitude, or weight. This is the stallingny

ht attitude, or at any weight.

erofoil, the stall always occurs at the same angle of attack but can occur

f attack (about 15 degrees):

Aircraft loses height

Figure 42 The Stall

A stall is caused by the separa

This results in a rapid decreasesame angle of attack, regardlessor critical angle of attack. It is important to remember that an aeroplane can stall at aairspeed, in any flig

For a specific aat any speed.

At critical angle o

Airflow separates

Wing stalls


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d Washout

f the aircraft to fall off on one wing.

right and left wings of an aircraft is usedorque causes the aircraft to roll in a

propeller rotation. To compensate for this, the right wing isa smaller angle of incidence at the tip than that of the left wing.washed out more than the left.

Figure 43 Wash

Washin an

Many aeroplanes are designed with a greater angle of incidence at the root of the wing

than at the tip; this characteristic of a wing is called washout. The purpose of washout isto improve the stability of the aircraft as it approaches a stall condition. The section ofthe wing near the fuselage will stall before the outer section, thus enabling the pilot tomaintain good control and reducing the tendency oIf a wing is designed so that the angle of incidence is greater at the tip than at the root,the characteristic is called washin. (Figure 43)

A difference in the washout and washin of theto compensate for propeller torque. Propeller tdirection opposite that of therigged or designed with

Thus, the right wing is

in and Washout


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AIRCRAFT SPEED



ional Bureau of Weights and Measures

ile were based on the length of

one minute of arc (

Knot

A knot is a measure of speed, and equates to one nautical mile per hour.

The international nautical mile was defined by the First International ExtraordinaryHydrographic Conference, Monaco (1929) as exactly 1852 metres. This is the onlydefinition in widespread current use, and is the only one accepted by the InternationalHydrographic Organisation and by the Internat(BIPM).

Before 1929, different countries had different definitions, and the Soviet Union, theUnited Kingdom and the United States did not immediately accept the internationalvalue.

Both the Imperial and U.S. definitions of the nautical m

6

degree) along a great circle of a hypothetical sphere (Figure 44).

The United States nautical mile was defined as 1853.248 metres: It was abandoned infavour of the international nautical mile in 1954.

The Imperial (UK) nautical mile, also known as the Admiralty mile, was defined in termsof the knot such that one nautical mile was exactly 6080 feet (1853.184m). It wasabandoned in 1970.

The nautical mile has now been standardised as 1853 metres exactly

Figure 44 One nautical mile

A knot is also a measure of subsonic airspeed.

Multiply knots by 1.15 to find statute miles per hour

Multiply knots by 1.85 to find kilometres per hour

Divide miles per hour by 0.87 to find knots

Divide kilometres per hour by 0.54 to find knots

For example, to find the approximate speed in kilometres/hour of an aircraft flying at250 knots:

250 knots X 1.85 = 462.5km/hr


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namic pressure of the relative airflow is the most commonly used measure of

nsity,

dmust also fall off with altitude.

Indicated Air Speed (IAS).

read the true airspeed at only one

an aircraft drops below its true airspeed. At 40 000 feet the

Indicated airspeed is important to the pilot because it is a gauge of the lift and otheraerodynamic forces acting on the aircraft. This is because the indicated airspeed isaerodynamic pressure.

Thus, an aeroplane stalls at the same indicated airspeed close to sea level, or at 40 000feet, even though at the higher altitude the true airspeed is twice the indicated airspeed.If an aeroplane stalls at an indicated airspeed of 70 knots, the true airspeed at which itstalls varies from 70 knots at sea level up to 140 knots at 40 000 feet.

Figure 45 Airspeed Indicator

Airspeed Indication

The dy

aircraft airspeed.This pressure is used to position the pointer of an airspeed indicator.

As with any other fluid, the dynamic pressure of airflow is V2, where is air deand V is velocity.

Since air density () decreases with altitude, then for a constant velocity (V) the indicateairspeed

There are several ways of recording aircraft speed. Three common indications are:

Ground Speed (GS).

True Air speed (TAS).

Indicated Airspeed

Airspeed indicators (Figure 45) can be calibrated to

value of air density. It is universal that they are calibrated to read true airspeed instandard density air at sea level (ISA). It follows that with increase in altitude, theindicated airspeed ofindicated airspeed is only half the true airspeed.


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True Airspeed



poses. In many aircraft pilots have a simple computer (

peed, altitude, and

pilot cannot readily determine.

tomatically compute and display the

Figure 47 True Speed Indicator

A thorough understanding of true airspeed is absolutely critical for navigational

pur

Figure 46) that calculates true airspeed when they input indicated airsambient temperature. Altitude and ambient temperature give a close approximation ofdensity, which the

Figure 46 Flight Computer

A few aircraft have true airspeed indicators that autrue airspeed.


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True

head indof 50 knots, the

Figure 48 Ground speed

Ground speed

airspeed may not be an aircrafts actual speed over the ground. If there is a

wind of 50 knots, the ground speed is true airspeed minus 50 knots. With a tailwground speed is true airspeed plus 50 knots. (Figure 48)


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in

Increases drag and reduces lift.

s.

nced or frozen.

e slots jammed.

Figure 49 The effects of icing

Contamination caused by ice, snow and frost can alter the aerofoil shape. Ice build-upcan change the effective chord line. It can also alter the upper and lower camber of theaerofoil. (Figure 50)

Figure 50 Ice build-up

ICING EFFECTS

Rain, snow, and ice can have a detrimental effect on flight (Figure 49). Under certa

atmospheric conditions, ice can build rapidly on airfoils and engine air inlets.Ice on an aircraft affects its performance and efficiency in many ways:

Causes destructive vibration.

Hampers true instrument reading

Control surfaces become unbala

Fixed slots are filled and movabl

Radio reception is hampered.

Engine performance is affected.

Stalling speed increases.


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Page Intentionally Left Blank


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Training Material Only B-8.3 Theory of Flight


TOPIC 8.3: THEORY OF FLIGHT

TABLE OF CONTENTS

Aerodynamic Forces ....................................................................................................................3

Aerodynamic Forces ....................................................................................................................3

Straight and Level Flight ............................................................................................................. 6

Forces in a Glide .........................................................................................................................8

Theory of the Turn ......................................................................................................................9

Wing Loading ............................................................................................................................12

Lift Augmentation......................................................................................................................14


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LIST OF FIGURES

Figure 1 Centre of Gravity (CG) and Centre of Pressure (CP) ...........................................3

Figure 2 Adverse Forward CG.........................................................................................4

Figure 3 Adverse Aft CG.................................................................................................5

Figure 4 CG Limits.........................................................................................................5

Figure 5 Four Forces......................................................................................................6

Figure 6 Increasing thrust to climb ................................................................................7

Figure 7 Decreasing thrust to descend ...........................................................................7

Figure 8 Forces in a Glide ..............................................................................................8

Figure 9 Glide L/D Ratio................................................................................................8

Figure 10 Glide Angle.....................................................................................................9

Figure 11 Centrifugal Force and Centripetal Force..........................................................9

Figure 12 Turning Flight ..............................................................................................10

Figure 13 Sideslip ........................................................................................................10

Figure 14 Skidding.......................................................................................................11

Figure 15 Balanced Turn .............................................................................................11

Figure 16 Wing loading ................................................................................................12

Figure 17 Resultant Lift in a Turn................................................................................13

Figure 18 High g turn ................................................................................................13

Figure 19 Changing shape of aerofoil............................................................................14

Figure 20 Full flaps approach ......................................................................................14

Figure 21 Slot ..............................................................................................................15

Figure 22 Slat ..............................................................................................................15

Figure 23 The affects of flaps and slats on CL ...............................................................16


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AERODYNAMIC FORCES

Weight

Weight has a definite relationship with lift, and thrust with drag. This relationship isquite simple, but very important in understanding the aerodynamics of flying. As statedpreviously, lift is the upward force on the wing acting perpendicular to the relativeairflow.

Lift is required to counteract the aircrafts weight, caused by the force of gravity acting onthe mass of the aircraft. This weight force acts downward through a point called thecentre of gravity (Figure 1) which is the point at which all the weight of the aircraft isconsidered to be concentrated.

Figure 1 Centre of Gravity (CG) and Centre of Pressure (CP)

When the lift force is in equilibrium with the weight force, the aircraft neither gains norloses altitude and can be considered to be in straight and level flight at a constantairspeed. The lift will act through the centre of pressure, which will depend on theposition of the wings; so the designer must be careful to place the wings in the correctposition along the fuselage. But the problem is complicated by the fact that a change inthe angle of attack means a movement of the lift, and usually in the unstable direction. Ifthe angle of attack is increased the pitching moment about the centre of gravity willbecome more nose-up, and tend to increase the angle even further.

Centre of Gravity

Centre of gravity is of major importance in an aircraft for its position has a great bearingupon stability.

The centre of gravity is determined by the general design of the aircraft. The designerestimates how far the centre of pressure will travel and will fix the centre of gravity infront of the centre of pressure for the corresponding flight speed in order to provide anadequate restoring moment for flight equilibrium. (Figure 1)




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Adverse Forward Centre of Gravity

When too much weight is toward the forward part of the aeroplane, the centre of gravity

(CG) is shifted forward (Figure 2) and any one of the following conditions may exist orthey may occur in combinations at the same time:

Increased fuel consumption.

Increased power for any given speed.

Increased tendency to dive, especially with power off.

Increased difficulty in raising the nose of the aeroplane when landing.

Increased oscillation tendency.

Increased stresses on the nose wheel.

Increased danger during flap operation.

Development of dangerous spin characteristics.

Figure 2 Adverse Forward CG




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Adverse Aft Centre of Gravity

When too much weight is toward the tail of the aeroplane (Figure 3), any one of the

following conditions may exist or they may occur in combination: Decreased flying speed.

Decreased range.

Increased strain on the pilot during instrument flight.

Increased danger of stall.

Dangerous spin characteristics.

Reduction of long range optimum speed.

Poor stability.

Increased danger if tail assembly is damaged.

Poor landing characteristics.

A study of the above listed conditions will reveal that most of them could lead to anaccident with a resulting loss of life and destruction of the aeroplane.

Figure 3 Adverse Aft CG

Centre of Gravity Limits

Each aeroplane type has its own centre of gravity limits, typically from about 15 per centto 40 per cent of the wing chord (Figure 4). These will have been established by designand from the aircrafts flight handling characteristics. The actual centre of gravity of aloaded aeroplane varies in flight as fuel is used or as people move along the cabin. The

centre of pressure and the centre of gravity will rarely coincide, resulting in either a noseup or a nose down pitching moment.

Figure 4 CG Limits




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STRAIGHT AND LEVEL FLIGHT

Lift and drag are components of the total aerodynamic force acting upon the wing. This

total force is called the resultant. Each tiny portion of the wing in flight has a small forceacting upon it. The force acting on one small portion of the wing is different in magnitudeand direction from all the other small forces acting upon all the other portions of thewing. By considering the magnitude, direction, and location of each of these small forces,it is possible to add them all together into one resultant force. This resultant force hasmagnitude, direction, and location with respect to the wing.

The resultant force on an aerofoil flying at a specified speed and angle of attack can beshown as a single entity possessing both magnitude and direction. It is also possible tobreak the resultant down into two major components (lift and drag), with magnitudes intwo directions. In aerodynamics these forces are discussed as having directionsperpendicular and parallel to the relative airflow. The component of the resultant force

which acts perpendicular to the relative airflow is lift. The component of the resultantforce which acts parallel to the relative airflow is called drag. The resultant forces arebroken down into separate component forces. (Figure 5)

Recall that in straight and level flight at a constant air speed, Lift = Weight and Thrust =Drag.

To accelerate or climb, thrust must be added to change the equilibrium.

To descend, thrust is reduced.

Figure 5 Four Forces




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Forces in a Climb

In a steady climb, thrust must balance the drag plus a portion of the weight.

Lift is less than weight.

Thrust is greater than drag.

To operate at the maximum angle of climb possible we need the biggest possible value ofthrust minus drag. If the thrust minus the drag is equal to the weight we have verticalclimb. If thrust minus drag is greater than the weight then the aircraft will be in anaccelerating rather than steady climb.

As the climbing angle increases, lift proportionally decreases (w cos ), therefore morethrust is required. (Figure 6)

Figure 6 Increasing thrust to climb

Forces in a Descent

In a powered descent, thrust may be reduced as gravity supplies some of the energy.

Lift is less than weight.

Drag is balanced by the reduced thrust and a part of the weight.

As the aeroplane descends, weight is once again greater than lift and thrust is reduced toallow gravity to pull the aircraft towards the Earth. (Figure 7)

Figure 7 Decreasing thrust to descend




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FORCES IN A GLIDE

In a glide there is no thrust, and the pilot adopts the descent angle that gives the best lift

to drag ratio (L/D) and the lowest rate of descent. This occurs at the minimum dragspeed. (Figure 8)

Glide Ratio = L/D.

Gravity provides all of the energy to remain flying. Lift is less than weight.

Figure 8 Forces in a Glide

The Glide

In a glide, thrust is removed from the four forces. In a steady glide the aeroplane must bekept is a state of equilibrium by lift, drag and weight.

Lift and drag must be exactly opposite to the weight.

Lift is at right angles to the glide path.

Drag acts rearwards, parallel to the glide path.

If an aeroplane is to glide as far as possible, the Angle of Attack (AoA) during the glidemust produce the maximum lift/drag ratio (L/D). If the pilot attempts to glide at an AoAgreater or less than the best L/D ratio the glide path will be steeper. The pilot has tomaintain the best L/D ratio. There is no way that the pilot can extend the glide beyondthe best L/D ratio. (Figure 9)

Figure 9 Glide L/D Ratio




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Glide Angle

If a glider is in a steady (constant velocity and no acceleration) descent, it loses altitude

as it travels. The glider's flight path is a simple straight line, shown as the inclined line inthe figure. The flight path intersects the ground at an angle a, called the glide angle. Ifwe know the distance flown and the altitude change, we can calculate the glide angleusing trigonometry.

The tangent tan of the glide angle a is equal to the change in height h divided by thedistance flown d:

tan(a) = h / d

Figure 10 Glide Angle

THEORY OF THE TURN

Centrifugal Force and Centripetal Force

Everyone is familiar with the fact that a weight attached to the end of a cord and twirledaround (Figure 11) will produce a force tending to cause the weight to fly outward fromthe centre of the circle. This outward pull is called centrifugal force. There is an equal

and opposite force pulling the weight inward and preventing it from flying outward; thisis called centripetal force.

From Newtons first law of motion we know that a body in motion tends to continue inmotion in a straight line. Hence, when we cause a body to move in a circular path, acontinuous force must be applied to keep the body in the circular path. This iscentripetal force.

Figure 11 Centrifugal Force and Centripetal Force




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Turning Flight

Before an aeroplane turns it must overcome inertia; the tendency to continue in a

straight line.The necessary turning force is created by banking the aeroplane so that the direction oflift is inclined. Now, one component of lift still acts vertically to oppose weight, just as itdid in straight-and-level flight, while another acts horizontally.

To maintain altitude, lift must be increased by increasing back pressure and, therefore,the angle of attack, until the vertical component of lift equals weight.

The horizontal component of lift, called centripetal force, is directed inward, toward thecentre of rotation. It is this centre-seeking force which causes the aeroplane to turn.Centripetal force is opposed by centrifugal force, which acts outward from the centre ofrotation. When the opposing forces are bala

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B-8 Aerodynamics SR