Aerodynamics

JAR-66

Book No: JAMF AERODYNAMICS

Lufthansa

Lufthansa Base Hamburg

Issue: July 2000For Training Purposes OnlyLufthansa 1995

Technical Training GmbH

Training Manual

Jet

AERODYNAMICS

Fundamentals

AircraftMaintenance

BeijingAmecoAviation College

For training purposes and internal use only.

Copyright by Lufthansa Technical Training GmbH.

All rights reserved. No parts of this trainingmanual may be sold or reproduced in any formwithout permission of:

Lufthansa Technical Training GmbH

Lufthansa Base Frankfurt

D-60546 Frankfurt/Main

Tel. +49 69 / 696 41 78

Fax +49 69 / 696 63 84

Lufthansa Base Hamburg

Weg beim Jger 193

D-22335 Hamburg

Tel. +49 40 / 5070 24 13

Fax +49 40 / 5070 47 46

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1

ATA AERODYNAMICS


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AERODYNAMICSPHYSICS FOR AERODYNAMICS

FUNDAMENTALS

Aerodynamics Lesson 1

2HAM US/F ro/ka March 1998

1. Physics for AerodynamicsThe laws of physics that affect the aircraft in flight and on the ground are de-scribed using the international SI system.The SI system is based on the metricsystem and must be used by law throughout the world.You need to use conversion tables for the English or American systems. Youcan find conversion tables in the appendix of most technical documentation.The laws of physics are described by fundamental units and basic quanti-ties.The fundamental units can not be defined in other quantities.The basicquantities are defined in fundamental units.Speed, for example, is a basic quantity. It is defined by the fundamental unitsdistance and time.Speed, denoted by V is distance, denoted by m over time, denoted by s.There are seven fundamental units in physics -- mass, length, time, tempera-ture, current, mol number and the intensity of light.The fundamental units used in aerodynamics are mass, length, time and tem-perature.

1.1. Fundamental units

1.1.1. MassThe unit of measurement for mass is kilograms, denoted by kg. The mass ofone kilogram is defined by a piece of platinum alloy at the office of weights andmeasurements in Paris.The mass of one kilogram is also the volume of one liter of pure water at atemperature of four degrees Celsius.Mass is not the same as weight. The astronauts flying around in their spacelabs have no weight but their bodies have a mass.

1.1.2. LengthThe unit of measurement for length is meters, denoted by m.The meter was established as a standard unit of length by a commission set upby the French government in 1790.A meter is more precisely defined as a certain number of wavelengths of a par-ticular colour of light.

1.1.3. TimeThe unit of measurement for time is seconds, denoted by s. Originally this wasbased on the length of a day. However not all days are exactly the same dura-tion so the second is now defined as the time it takes for a certain number ofenergy changes to occur in the caesium atom.

1.1.4. TemperatureThe unit of measurement for temperature is kelvin, denoted by K. Zero kelvin iscalled absolute zero because it is the lowest temperature possible.The kelvin scale starts at zero and only has positive numbers.One kelvin is the same size as one degree Celsius.


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FUNDAMENTALS




Page 3Figure 1

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FUNDAMENTALS



1.2. Speed and acceleration

1.2.1. Speed and velocitySpeed is the distance that a moving object covers in a unit of time. For exam-ple, we can say that an aircraft has a speed of 500 kilometers per hour.Speed is denoted by V.Velocity is the distance that a moving object covers in a given direction in a unitof time. We can say that an aircraft has a velocity of 500 kilometers per hournorthward.Velocity is also denoted by V.

1.2.2. AccelerationAcceleration is the change in velocity divided by the time during which thechange takes place.You can see that the velocity changes from 100 m/s to 150 m/s during this tensecond period.In this example the acceleration is 50 m/s per ten seconds. This is equal to fivemeters per second per one second which is 5 m/s2. Acceleration is measuredin meters per square second ( m/s2 ).

Acceleration is denoted by a.


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FUNDAMENTALS




Page 5Figure 2

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FUNDAMENTALS



1.2.3. Acceleration due to gravityA special form of acceleration is acceleration due to gravity. An object, such asthis ball, which falls freely under the force of gravity has uniform acceleration ifthere is no air resistance.Acceleration which is due to gravity is denoted by g.The value of this acceleration varies across the earths surface but on averageit is nine point eight meters per square second. For ease of calculation ten me-ters per square second is often used.

1.3. Force and weightWe begin our look at force with an experiment. You can see that our friend isstanding on a weighing scale in an elevator and observing his weight ( Fig. be-low, left ).There is no change in weight if a body stays at rest or if it moves with uniformvelocity.But what happens to the weight if the elevator accelerates as it moves upward?As the elevator accelerates there is an additional force which increases theweightForce is measured in Newtons. The term deca--Newton is used in all technicalmanuals for force and for weight.Weight is one kind of force. It is mass multiplied by the acceleration due togravity. You know that gravity is the attraction exerted on any material towardsthe center of the earth.Weight is also measured in Newtons ( Fig. below, right ).


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FUNDAMENTALS




Page 7Figure 3

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FUNDAMENTALS



1.4. Work and Power

1.4.1. WorkWork is done when an object is moved over a distance. It is force multiplied bydistance. Work = N x m.Work is denoted by joule and is measured in Newton meters.You can see that the object with a force of six hundred Newton is moved a dis-tance of thirty meters.The work is six hundred Newton multiplied by thirty meters which is eighteenthousand Newton meters.


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FUNDAMENTALS



1.4.2. PowerPower is work over time or more specifically force multiplied by distance overtime.Power is measured in Watts which is Newton meters per second.You probably know the term horse power. When steam engines were first usedtheir power was compared to the power of horses because they were used forwork which was previously done by horses. Now the international SI systemuses watts and kilowatts instead of horsepower.You can see that the object with a force of 600 N is moved a distance of 30 min 10 seconds.The power is six hundred Newton multiplied by thirty meters divided by ten se-conds which is 1800 watts or 1.8 kilowats.


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FUNDAMENTALS



1.5. Pressure

1.5.1. Static pressurePressure is the force acting on a unit of area.It is denoted by Pascal ( Pa ) and measured in Newtons per square meter( N/m2 ).Static pressure acts equally in all directions. It is denoted by a small p andmeasured in Newtons per square meter ( N/m2 ).Static pressure is calculated as height multiplied by density multiplied by grav-ity. Pstat. = h x x g.

1.5.2. Dynamic pressureDynamic pressure acts only in the direction of the flow.It is denoted by a small q and sometimes called q pressure and, like staticpressure, measured in Newtons per square meter ( N/m2 ).Dynamic pressure is calculated as half the density multiplied by the velocitysquared. q = x x v2 .The static pressure for aircraft technical systems is denoted by bar and mea-sured in decaNewtons per square centimeter ( daN/cm2 ).One bar is equal to one hundred thousand PASCAL.

The STATIC PRESSURE for technical systems e. g. for AIR-CRAFT HYDRAULIC SYSTEMS is denotet by

bar

and has the unit

daNcm2

1 bar= 1 daN1 cm2

1 bar = 100 000 Pa


Page 10

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FUNDAMENTALS



p = h x x g q = x x v2


Page 11Figure 4

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FUNDAMENTALS



1.6. Sound wavesSound waves are the same as pressure waves.The speed of sound is the speed of the small pressure waves which occurwhen you ring the bell.The speed of sound is denoted by a.In the formula for the speed of sound, the number twenty is an approximationof the total of all the relevant constant values and T for temperature repre-sents the only variable value.Note that the temperature must be expressed in Kelvin!

Now you know that the speed of sound depends on the temperature. For ex-ample if the temperature on a Summer day is 15E C, which is 288 K, then wecalculate the speed of sound to be 339.4 m/s.If the temperature decreases in Winter to - 50E C, which is 223 K, then thespeed of sound is 298.6 m/s.The speed of sound is less at high altitudes because the temperature is lower.


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FUNDAMENTALS



a= 20 223 = 298.6 ms


Page 13Figure 5

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FUNDAMENTALS



1.6.1. Speed of soundNow lets see what happens if the source of the sound moves, for example ifwe have an aircraft flying. First we see an aircraft flying at a speed which isbelow the speed of sound.You can see that the pressure wave moves ahead of the aircraft and also be-hind it.Next we see an aircraft flying at the same speed as the speed of sound.The pressure wave cannot escape at the front of the aircraft and we get a bigpressure wave forming. This pressure wave is known as a shock wave.Finally we see an aircraft flying at a speed which is above the speed of sound.In this case the pressure waves increase behind the aircraft and shock wavesform outside the periphery of the pressure waves.Now you know that different aircraft speeds affect the sound waves.

Below the speed of sound At the speed of sound Above the speed of sound

V< 1 M V>1 MV =1 M


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FUNDAMENTALS



1.6.2. Mach numberThe pilot must know the relationship between the speed of the aircraft and thespeed of sound.On most aircraft the pilot must make sure that the speed of the aircraft is lessthan the speed of sound.Now lets see what happens when an aircraft flies at a constant speed but indifferent temperatures. In this example the aircraft is flying at a low altitude witha speed of 300 m/s.You can see that the aircraft speed is below the speed of sound at this altitude.We assume the speed of sound is 330 m/s.Now the same aircraft is flying at an altitude of 10 km. The aircraft continues tofly with a speed of 300 m/s.

At this higher altitude the temperature is lower and the speed of sound de-creases to 300 m/s.Now the aircraft is flying at the speed of sound and you can see that shockwaves are produced.A special indication known as the Mach number, M is used to keep the pilotinformed of the relationship between the speed of the aircraft and the speed ofsound.The Mach number is the speed of the aircraft divided by the speed of sound.In our example the aircraft flying at an altitude of 10 km has a Mach number ofone ( M = 1 ). A Mach number of one indicates that the aircraft is flying at thespeed of sound.

300 MS


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FUNDAMENTALS



1.6.3. Sound regionsThese graphics illustrate the three sound regions which are defined by theMach numbers. In the subsonic region all speeds around the aircraft are belowthe speed of sound. This is the region up to the critical Mach number.In the transonic region some speeds around the aircraft are below the speed ofsound and some are higher than the speed of sound. This is the region be-tween the critical Mach number and 1.3 Mach.Finally we have the supersonic region. Here all speeds around the aircraft arehigher than the speed of sound. This is the region at Mach numbers higherthan 1.3 Mach.Thats all we have to say about the speed of sound in this segment. You willsee more on this subject in the chapter for high speed flight.


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FUNDAMENTALS



Subsonic Transonic Supersonic

V< Mcrit Mcrit < V< 1.3 M V> 1.3 M


Page 17Figure 6

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FUNDAMENTALS



1.7. AtmosphereTo understand aerodynamics we need to know something about the atmo-sphere where flying happens.The atmosphere is the whole mass of air extending upwards from the surfaceof the earth.Air is a mixture of several gases. Pure, dry air has approximately 78% nitrogen,21% oxygen and one percent other gases such as argon and carbon dioxide.For practical purposes it is sufficient to say that air is a mixture of four fifthsnitrogen and one fifth oxygen.The atmosphere has many layers.The troposphere is the lowest of these layers. In the troposphere we haveclouds and rain and many different weather conditions.There are no rain clouds in the stratosphere and the temperature does notchange as the altitude increases.The tropopause is the name given to the boundary between the troposphereand the stratosphere. The tropopause has different heights around the earth. Itis approximately eight kilometers over the north and south poles and sixteenkilometers over the equator.

21% Oxygen

78% Nitrogen

TROPOSPHERE


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FUNDAMENTALS



1.7.1. ICAO Standard Atmosphere ( ISA )You know from watching the weather forecast that temperature, pressure anddensity vary quite a lot in the troposphere.These variations must be reduced to a standard so that we have a basis forcomparing aircraft performance in different parts of the world and under varyingatmospheric conditions.In order to have a reference for all aerodynamic computations, the InternationalCivil Aviation Organisation ( ICAO ) has agreed upon a standard atmospherecalled ISA ( ICAO standard atmosphere). The pressure, temperature and den-sity in the standard atmosphere serve as a reference only. When all aerody-namic computations are related to this standard, a meaningful comparison offlight test data between aircraft can be madeNow lets take a look at the temperature, pressure and density of the ISA atsea level and at high altitudes.You can see the standard sea level values for temperature, density and pres-sure. Note that the standard altitude for the tropopause is eleven kilometers.Under standard conditions temperature decreases with altitude at a rate of6,5E C per 1000m, or 2E C ( 3.5E F ) per 1000 foot.This gives a standard temperature of -56,5E C at the tropopause.There is no change in temperature in the stratosphere.The density and pressure decrease gradually with altitude.The graph shows the basic tendencies for temperature, pressure and density.You can find more precise information in the standard atmosphere tables whichyou can usually find in the appendix of technical documentations.

These are the ISA conditions for sea level:

Temperature T : 288 K = 15E CDensity : 1,225 kg/m3Pressure P : 1013,25 hPa


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AERODYNAMICSBASIC AERODYNAMICS

FUNDAMENTALS


20HAM US/F ro/ka MARCH 1998

2. Basic AerodynamicsIn this chapter we look at some of the basic principles of aerodynamics in thesubsonic region.In the subsonic region the speed is so slow that a flying body does not com-press the air. We say that the air is incompressible in the subsonic region.

2.1. Continuity equationNow lets have a closer look at the behaviour of the air streamlines.You can see that the streamlines are parallel to each other if there is no distur-bance.The airflow between the streamlines is similar to the flow in a closed tube. Youwill see later that we use the term stream tube.Here you see the flow pattern in a tube with different diameters.

You can see that as the diameter gets smaller the streamlines move closer toeach other.At the lower picture we isolate the stream tube and identify two cross--sections,A1 and A2. Assume that the area of the cross--section at point A1 is twentysquare centimeters and the velocity of the airflow at this point is 10 m/s.

The area of the cross--section at point A2 is five square centimeters and thevelocity of the airflow at this point is 40 m/s.The continuity equation states that the velocity of the airflow is inverselyproportional to the area of the cross section of the tube as long as den-sity remains constant !For example if the area of the cross section is halved then the velocity of theairflow is doubled or if the area is four times smaller then the velocity is fourtimes greater.We use the term defuser outlet when the diameter increases and the velocitydecreases and the term jet outlet when the diameter decreases and the veloc-ity increases.


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FUNDAMENTALS



DENSITY IS CONSTANT ! 1 = 2

A2 = 5 cm2


Page 21Figure 7

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FUNDAMENTALS



2.2. Bernoulli s principleIn this segment we look at another important equation used in aerodynamics,Bernoullis equation. Here we will see, how speed effects pressure.We will describe this equation using a tube with a valve.You can see that the valve is closed and that the tube is filled with fluid on theleft side of the valve.

Valve closedThe fluid inside the tube has a static pressure. The static pressure is repre-sented by the arrows in the tube and by a line on the graph at the bottom of thepicture.This static pressure acts in all directions.The total pressure is represented by the circle in the tube and by another lineon the graph at the bottom of the picture.You can see on the graph that the total pressure is equal to the static pressurewhen the valve is closed.At the next steps, the valve will be opened slightly.

Valve half openWhen the valve is moved to the half open position the fluid begins to flow.You can see that the static pressure decreases and a new pressure, the dy-namic pressure, is introduced. Remember that the dynamic pressure only actsin the direction of the flow.The dynamic pressure is represented by the horizontal arrows in the tube and aline on the graph. The graph shows the amount of static pressure, dynamicpressure and total pressure in the half open position.

Valve full openFinally the valve is moved to the fully open position.Did you notice that the total pressure remained constant in all valve positions?The static pressure decreased every time the valve was opened more and thedynamic pressure increased as the valve opened.What you have seen is the physical law known as Bernoullis principle.

The Bernoulli equation states that total pressure is always the sum ofstatic pressure and dynamic pressure or in short hand notation: P totequals p plus q !The total pressure remains constant.

Ptot = p + q = const.p = pstat; q = V2

VALVE CLOSED


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FUNDAMENTALS



VALVE HALF OPEN VALVE FULL OPEN


Page 23Figure 8

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FUNDAMENTALS



2.2.1. Pressure measuringNow lets see how pressure is measured. You know that the airflow around thesurface of this object has static pressure and dynamic pressure.At the point of stagnation the velocity of the airflow falls to zero and the staticpressure equals the total pressure. You know that there is no dynamic pressureif there is no flow.At the picture below you can see how we measure the static and dynamic pres-sure when there is a velocity.The actual static pressure is sensed directly at the static port.The static pressure line and the total pressure line are attached to a differentialpressure gauge.The net pressure indicated on the gauge is the dynamic pressure. As you knowthe dynamic pressure is the total pressure minus the static pressure.The dynamic pressure varies directly with changes in density and with thesquare of the change in velocity.If the density is constant, the dynamic pressure increases sixteen times if thevelocity increases four times.The dynamic pressure is the indicated air speed.


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q = V2


Page 25Figure 9

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2.3. Lift productionIn this segment we see how lift is produced. We begin by looking at a specialdesign of tube known as a venturi tube.You can see that the inlet and the outlet of the venturi tube are the same size.

The velocity of the airflow increases until it reaches the narrowest point in thetube.You know that as the velocity increases the static pressure decreases and thedynamic pressure increases.The velocity decreases again after the narrowest point and returns to the inletlevel by the time the airflow reaches the outlet.During this phase the static pressure increases again and the dynamic pres-sure decreases.

Now lets replace the upper surface of the venturi tube with a straight line andsee what happens to the airflow.As you can see this doesnt change things very much. The streamlines are stillcloser to each other in the center and the static pressure decreases in this area


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If we remove the upper surface we find that the streamlines themselves pro-vide the upper boundary.

The next step is to change the lower surface of the venturi tube into a profileand to add some streamlines below it.Now we have a surface with an area of low static pressure above it and area ofunchanged static pressure below it.This difference in static pressure acts on the surface to create the force whichwe call lift.


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2.4. Magnus Effect and CirculationHere you see the side view of a cylinder in an airstream.The static pressure on the upper surface of the cylinder is the same as thestatic pressure on the lower surface.

If there is no differential pressure, there is no lift !Lets see what happens if we rotate the cylinder.

When the cylinder rotates the circulatory flow causes an increase in local veloc-ity on the upper surface of the cylinder and a decrease in local velocity on thelower surface.This generates lift.

This mechanically induced circulation is called the Magnus effect.You can see that the circulatory flow produces what we call an up--wash im-mediately in front of the cylinder and a down--wash immediately behind the cyl-inder.You can also see that the fore and aft neutral streamlines are lowered.


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Circulation around a profileIf the cylinder in the flow will be replaced by a profile, we will get the same ef-fect as for the cylinder with circulation.A velocity difference between the upper and lower profile surface will be ob-tained and lift will be created.This lift will be normal to the direction of flow, as for the Cylinder.

This profile also generates a circulation which produces an up--wash and adown--wash.

There is no lift without circulation !


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AERODYNAMICSPROFILE AND WING GEOMETRY

FUNDAMENTALS



3. Profile and wing geometryIn this chapter we look at the geometry of a wing and a profile. This is impor-tant for our understanding of lift and drag.In the first segment we look at profile geometry and in the second segment welook at wing geometry.

3.1. Geometry of a profileAs you can see a profile is a cross section of a wing.It is sometimes called an airfoil.

Cord line, Leading edge, Trailing edgeThe profile has a leading edge and a trailing edge.

The cord line is a straight line connecting the leading edge and the trailingedge.


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Camber of a ProfileThe mean camber line is a line drawn half way between the upper and thelower surfaces of the profile.The shape of the mean camber line is very important in determining the aero-dynamic characteristics of a profile.The end points of the mean camber line are the same as the end points of thecord line.

0% 100%

Camber

The camber of the profile is the displacement of the mean camber line from thecord line.The maximum camber and the location of the maximum camber help to definethe shape of the mean camber line.These quantities are expressed as a fraction or a percentage of the basic corddimension.A typical low speed profile might have a maximum camber of 5 % located 45 %aft of the leading edge.

Thickness of a ProfileThe maximum thickness of a profile is defined as a fraction or a percentage ofthe cord.The maximum thickness as a fraction is also known as the fineness ratio.The location of the maximum thickness is also defined as a percentage of thecord.For example a typical low speed profile might have a maximum thickness of18 % located 30 % aft of the leading edge.

Thickness

0% 100%


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Relative windThe flight path velocity is the speed of the aircraft in a certain direction throughthe air.The relative wind is the speed and direction of the air acting on the aircraftwhich is passing through it.You can see that the relative wind is opposite in direction to the flight path ve-locity.The relative wind depends on the flight path and is therefore not always hori-zontal.

Angle of attack The angle of attack is the angle between the cord line of the profile and the rel-ative wind. It is denoted by the greec letter ( alpha ).

Angle of incidenceThe angle of incidence is the angle between the cord line of the profile and thelongitudinal axis of the aircraft. It is denoted by the greec letter gamma.


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3.2. Wing geometryWing area SIn this segment we look at wing geometry. The wing area is the plan surfacearea of the wings.It includes the area of the fuselage which is between the wings.On this simplified graphic the wing area S, is the wing span b, multiplied by thecord of the wing c.

On this more realistic tapered wing we have different wing cords. You can seethat the root cord Cr, is the cord at the wing centerline and the tip cord Ct, is thecord at the wing tip.

C

Taper ratio The taper ratio ( lambda ), is the ratio of the tip cord to the root cord.

= Ct/CrThe wing area is the average cord multiplied by the wing span.The average cord C, is the geometric average of all the cords and the wingspan b, is measured from tip to tip.


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Aspect ratio The aspect ratio is the wing span b, divided by the average cord C.Typical aspects ratios vary from 35 for a high performance sail--plane, to 3.5 fora jet fighter plane.You can see, that the aspect ratio can also be expressed as the wing spansquared divided by the wing area.

= bC

= b2S


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Sweep angleThe sweep angle is the angle between the quarter cord, or the 25 % line andthe pitch axis.

Positive sweep = Backwards !Negative sweep = Forewards !

DihedralThe dihedral of the wing is the angle formed between the wing and the horizon-tal plane passing through the root of the wing.We have a positive dihedral when the tip of the wing is above the horizontalplane and a negative dihedral when the tip of the wing is below the horizontalplane.


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AERODYNAMICSLIFT AND DRAG

FUNDAMENTALS



4. Lift and dragIn this Chapter we look in more detail at the factors affecting the lift -- first theangle of attack and then the shape of the profile.After that we will have a look at the factors affecting the drag.At the end we will see how lift and drag are represented in the polar diagramYou know that the main function of a profile is to provide lift so that the aircraftcan overcome the force of gravity and rise into the air.You will see that the design of the profile is very important.

4.1. IntroductionHere you see the distribution of static pressure on a profile. The dark area infront of the leading edge, is where the static pressure is higher than the ambi-ent static pressure.This is because the velocity of the air approaching the leading edge, slows toless than the flight path velocity. The static pressure is highest at the point ofstagnation where the air comes to a stop.

In the lighter areas above and below the profile, the static pressure is lowerthan the ambient static pressure. This is because the air speeds up again as itpasses above and below the profile so that the local air velocity is greater thanthe flight path velocity.We have maximum air velocity and minimum static pressure at a point near themaximum thickness of the profile.

The air velocity decreases and the static pressure increases after this point.In the dark area at the trailing edge the static pressure is higher than the ambi-ent static pressure.This is caused by low velocity turbulent air in this area.

The aerodynamic force is the resultant of all forces on a profile in an airflowacting on the center of pressure.The aerodynamic force has two components -- lift which is perpendicular to therelative wind and drag which is parallel to the relative wind. Here the center ofpressure is identified. This is the point on which all pressures and all forces act.This point is located where the cord of a profile intersects with the resultant ofthe aerodynamic forces lift and drag.

Aerodynamic Force


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The aerodynamic forces of lift and drag depend on the combined effect ofmany variables -- the dynamic pressure the surface area of the profile theshape of the profile and the angle of attack.

Aerodynamic Force

Now we look at how to calculate the lift. You might think that this is simple -- allwe need to know about is the surface and the pressure.However its not as easy as you might think. In reality a profile has differentpressures because of different angles of attack.First lets look at the simple calculation of theoretical lift.The theoretical lift is the dynamic pressure multiplied by the surface area. Youknow from an earlier lesson that the dynamic pressure is half the air densitymultiplied by the velocity squared.

Theoretical Lift = x x V2 x A

In this example we assume that the air density is 1,225 kg/m3 and the air ve-locity is 28 m/s and the surface area of the profile is 0,05 m2 and we get atheoretical lift of 24 N.

= 1,225 kg/m3

V = 28 m/sA = 0,05 m2

Theoretical Lift = x 1,225 x 282 x 0,05 = 24 N


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It is not possible to calculate the actual lift. We have to measure it using a windtunnel.You can see that a universal joint provides the bearing for this construction.There are two scales attached to the support arm -- a horizontal scale to mea-sure the drag and a vertical scale to measure the lift.

Now lets see what happens when we switch on the wind tunnel.


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4.1.1. Lift EquationYou can see that the measured lift is only 8,4 N. This is much less than thetheoretical lift of 24 N.The theoretical lift must therefore be adjusted.A coefficient of lift CL, is introduced to the lift equation to account for the differ-ence between the measured lift and the theoretical lift.The coefficient of lift is the measured lift divided by the theoretical lift. In ourexample it is 0,34.The lift equation is now the coefficient of lift multiplied by the dynamic pressuremultiplied by the surface area.

Coefficient of Lift = Measured LiftTheoretical Lift

Lift = Cl12 V2 S

Dynamic Pressure q

V

4.1.2. Drag EquationFor the same reasons a coefficient of drag CD, is introduced to the drag equa-tion to account for the difference between measured drag and theoretical drag.The coefficient of drag is the measured drag divided by the theoretical drag.The drag equation becomes the coefficient of drag multiplied by the dynamicpressure multiplied by the surface area.

Drag = Cd12 V2 S

Dynamic Pressure q

Coefficient of Drag = Measured DragTheoretical Drag

V


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4.2. Factors Affecting Lift

4.2.1. Angle of Attack ( AOA ) You know that the coefficient of lift is the ratio of the measured lift to thetheoretical lift.The coefficient of lift is a function of the angle of attack and of the shape of theprofile.We look at the effect of the angle of attack in this segment.In this wind tunnel experiment you will see that each angle of attack produces adifferent measured lift and therefore a different coefficient of lift.The vertical scale will show the coefficient of lift as the angle of attack changes.The relationship between the angle of attack and the coefficient of lift will beplotted on the graph.Now you can see what will hapen, when the angle of attack varies between8E to 20E .Remember to observe the coefficient of lift on the scale and the relationshipbetween the angle of attack and the coefficient of lift on the graph.You can see on the graph that the coefficient of lift increases up to the maxi-mum coefficient of lift, CL max, and then decreases again.The maximum coefficient of lift corresponds to the maximum angle of attack, max.If the angle of attack increases above max, the airflow cannot follow the uppersurface of the profile and an airflow separation, known as stall occurs.

= 8E

= 0E


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= 8E

= 16E

= 20E


Page 41

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4.2.2. Shape of a ProfileNext we look at the other main influence on the coefficient of lift.The shape of the profile is the second influence on the coefficient of lift.A profile can have different thickness and different camber and its shape maybe influenced by disturbances such as ice on the leading edge.The cross section of the profile is the same, we used in the wind tunnel experi-ment and the graph showing the associated coefficient of lift curve.

Change of the Profile ThicknessNow lets see the coefficient of lift curve for a profile with the same camber butwith greater thickness.You can see that the thicker profile has the same coefficient of lift at lowerangles of attack but a higher coefficient of lift when the angle of attack in-creases above approximately ten degrees.The thicker profile has a higher maximum coefficient of lift and a higher max.

Change of the Profile CamberNow lets see the coefficient of lift curve for a profile with the same thickness asthe basic profile but with a higher camber.You can see that the profile with the higher camber has a much higher coeffi-cient of lift at the zero angle of attack.This profile has a higher maximum coefficient of lift but a lower alpha max thanthe basic profile.

An advantage of a high maximum lift coefficient is that the aircraft can flyslowly.The disadvantages are that the thickness and camber necessary for profileswith a high maximum lift coefficient may produce high drag and low criticalMach number.In other words, a high maximum lift coefficient is just one of many features de-sired in a profile. Next we look at the factors affecting the coefficient of drag.


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4.3. Factors affecting DragThere are three different types of drag:- induced drag- parasite drag and- compressible dragYou will learn more about these different kinds of drag in the next chapters.Earlier in this chapter you saw that the drag equation is similar to the lift equa-tion except that we use the coefficient of drag instead of the coefficient of lift.You know that the coefficient of drag is the ratio of the measured drag to thetheoretical drag.The coefficient of drag is a function of the angle of attack and of the shape ofthe profile.

Drag = Cd12 V2 S

Dynamic Pressure q

Coefficient of Drag = Measured DragTheoretical Drag


Page 43

Michael Erd LTT

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4.3.1. Relation between and the Drag Coefficient CDWe use the wind tunnel experiment again to show that each angle of attackproduces a different measured drag and therefore a different coefficient ofdrag.The horizontal scale will show the coefficient of drag as the angle of attackchanges.The relationship between the angle of attack and the coefficient of drag will beplotted on the graph.You can see the coefficient of drag at angles of attack from 8E to 20E .You can see on the graph that at lower angles of attack the coefficient of dragis low and small changes in the angle of attack produce only slight changes inthe coefficient of drag.At higher angles of attack the coefficient of drag is much greater and smallchanges in the angle of attack produce significant changes in the coefficient ofdrag.You can see that a stall produces a large increase in drag.

=8E

= 0E


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= 20E = > 20E


Page 45Figure 10

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4.4. Polar DiagramIn this segment we see how the lift and drag coefficients can be combined togive us information about the performance of profiles.Now were going to plot the polar diagram. This shows the coefficient of liftplotted against the coefficient of drag for each angle of attack.The lift drag ratio diagram is a variation of the polar diagram.The ratio of the lift to the drag is plotted against the angle of attack.You can see that the ratio of the lift to the drag is the same as the ratio of thelift coefficient to the drag coefficient.The lift drag ratio diagram shows the maximum lift drag ratio.This point represents the most efficient operation of the profile. It is the pointwhere we get the most lift for the least drag.It is not possible to calculate aerodynamic forces without wind tunnel experi-ments.Thousands of tests are performed to get information on the most efficient pro-files under various flight conditions.The results of these tests are collected by a U.S. government agency, the Na-tional Advisory Committee for Aeronautics or NACA and given an identification.These profiles are called NACA profiles.You can find more detailed informations about all these profiles in special pro-file catalogs.


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Polar Diagram LiftDrag

=Cl q SCd q S

LiftDrag

=ClCd

q = Dynamic PressureS = surface area

Lift/Drag Diagram


Page 47Figure 11

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AERODYNAMICSCATEGORIES OF DRAG

FUNDAMENTALS



5. Categories of Drag5.1. IntroductionDrag is caused by any aircraft surface that deflects or interferes with thesmooth airflow around the airplane.In this Chapter we look in more detail at the 5 different types of drag:1. Induced Drag2. Form Drag3. Friction Drag4. Interference Drag5. Compressible DragWe will see how the different types of drag are combined to give the total drag.The total aircraft drag is the sum of the induced drag, the parasite drag and thecompressible drag.Drag is the aerodynamic force which acts in opposition to the direction of flight,opposes the foreward - acting force of thrust, and limits the forward speed ofthe airplane.The induced drag is the drag on the wing which is caused by the lift.The parasite drag is not related to the lift.It can be form drag which is drag caused by the distribution of pressure, or fric-tion drag which is drag caused by skin friction, or interference drag which isdrag caused by aerodynamic interference.Compressible drag is caused by the shock waves on an aircraft approachingthe speed of sound. Sometimes the compressible drag is called Wave Drag .


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5.2. Induced DragIf an aircraft wing had an infinite span the air would flow directly from the lead-ing edge to the trailing edge.In reality, of course, an aircraft wing has a finite span -- it has ends which arecalled wing tips.The air with higher pressure under the wing spills over the wing tips into theair with lower pressure above the wing.This turbulence at the wing tips causes the streamlines to form wing tip vor-tices.The streamlines below the wing bend towards the wing tips and the streamlinesabove the wing bend towards the center.The turbulence absorbs energy and increases the drag. This type of drag iscalled induced drag.

Wing Tip Vortices

Here you can see that on a wing with an infinite span, the lift distribution is al-ways the same and on a wing with a finite span we get a loss of lift near thewing tips.The induced drag is lower if the finite wing has an elliptical lift distribution suchas the one you see here.You will learn more about the lift distribution over the wing in the next chapter.

Lift Distribution


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You know from an earlier chapter, that there is a circulation around the profile.If the wing span is infinite the circulation around the profile causes an upwashon the leading edge and a downwash on the trailing edge.This circulation is called the bound vortex.

Infinite Wing

On a finite wing span we have the bound vortex and we also have the wing tipvortices.The graph shows that the total of the bound vortex and the wing tip vorticescreates the upwash and the downwash on the wing.

Finite Wing

The design of the gutter above the entry doors on the Boeing 747 reflects theupwash and the downwash caused by the vortices.You can see that the gutters are in line with the flow pattern of the airstreamaround the wing.They are sloped upwards to reflect the upwash forward of the wing and down-wards to reflect the downwash aft of the wing.


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Induced Drag Affection by the Aspect RatioThe induced drag is affected by the aspect ratio, the wing tip design and theaircraft speed.You can see that the wing tip vortex and therefore the induced drag is less onthe aircraft with the high aspect ratio.

Induced Drag Affection by the Wing Tip DesignThe wing tips can be designed to reduce the induced drag.On smaller aircraft we have a special wing tip form.On larger aircraft we have wing tip fences such as on this Airbus 310, or wing-lets such as on this Boeing 747.These designs reduce the energy of the wing tip vortices.There are many examples of different wing tip designs from nature.A heavy bird spreads its feathers like winglets to reduce the drag and a fastflying bird has a high aspect ratio and sharp wing tips.

Smaller Aircraft

A - 310

B - 747 - 400

Induced Drag Affection by the Aircraft SpeedDuring low speed flight the aircraft has a high angle of attack and therefore ahigh lift coefficient.There is a high pressure difference between the lower and the upper surface ofthe wing and this creates large wing tip vortices and therefore high induceddrag.During high speed flight the aircraft has a low angle of attack and therefore alow lift coefficient. There is a low pressure difference between the lower andthe upper surface of the wing and this creates small wing tip vortices and there-fore low induced drag.


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5.3. Parasite Drag

5.3.1. Form DragYou know that form drag is a parasite drag and that it is caused by the pres-sure distribution on a body.Take a look at this cylinder in an airstream. There is no friction in the airstreamand we have a perfectly symmetrical flow pattern.You can see on the right that the pressure in front of the cylinder is the sameas the pressure aft of the cylinder.In this situation there is no drag.

Ideal Situation Without Friction

AIRFLOW

PRESSUREDISTRIBUTION

On the next graphic we see a real airflow around the cylinder with friction.You can see that we dont have a symmetrical flow pattern any more and thatthe pressure in front of the cylinder is not the same as the pressure behind thecylinder.This difference in pressure causes form drag.Form drag depends on the frontal area of a body and also on the speed of theairflow.

Real Situation With Friction

AIRFLOW

PRESSUREDISTRIBUTION

Flow Separation


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Ways to Reduce Form DragHere you see three different bodies -- a disc, a disc with a bullet shaped noseand a disc with a bullet shaped nose and a streamline tail.The disc has very high form drag.If we add a bullet shaped nose the drag decreases to twenty percent and if wethen add a streamline tail the drag goes down to less than ten percent.Form drag is reduced by streamlining.One obvious way of streamlining an aircraft is to have retractable landing gear.Before we move on to the next segment you should note that sometimes formdrag on the wing is distinguished from form drag on other parts of the aircraft.Form drag on the wing is called wing drag or profile drag.


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5.3.2. Friction DragHere you see ten different profiles. You can see that they all have the sameheight or diameter D, and different length L.The length to diameter ratio is shown on the left side of the profiles. This ratioranges from one at the top to ten at the bottom.The profile with the length to diameter ratio of one has the highest form drag.There is a relationship between form drag and friction drag.A profile with a low form drag has a high friction drag and a profile with a highform drag has a low friction drag.You can see on the graph that the profiles with the length to diameter ratios oftwo, three and four produce the lowest combination of form and friction drag.


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Boundary LayerNow lets see what causes friction drag. First we assume that the surface ofthe aircraft is perfectly smooth.You can see that the airflow immediately above the surface is the same as thefreestream velocity. This is indicated by the length of the arrows.

In reality the surface of the aircraft is quite rough and the velocity of sometrapped air particles is reduced to zero. This means that the airflow immedi-ately above the surface is retarded. The retarded layer of air at the surfaceslows down the layer immediately above it and this layer in turn slows down thenext layer and so on until the freestream velocity is restored.The retarded air is called the boundary layer.

Surface of Aircraft

FreestreamVelocity

Boundary Layer

There a two basic types of boundary layer -- the turbulent boundary layer andthe laminar boundary layer.The laminar boundary layer is immediately downstream of the leading edge.The air particles in the laminar boundary layer do not move from one layer toanother. This is known as laminar flow.

The turbulent boundary layer is downstream of the laminar boundary layer.The laminar flow breaks down and we get turbulent flow.The air particles in the turbulent boundary layer travel from one layer to anotherand this produces an energy exchange.The turbulent boundary layer is much thicker than the laminar boundary layerand produces about three times more friction drag.The turbulent boundary layer also produces higher kinetic energy next to thesurface and this reduces the tendency for a flow separation.Small disturbances inside the laminar boundary layer bring it into the turbulentboundary layer or produce a flow separation.Because of this it is important that the area of the profile corresponding to thelaminar boundary layer is kept clean and smooth.

Turbulent Boundary Layer


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The behaviour of an air particle around a profile is similar to the behaviour of aball rolling into a valley.You already know that an air particle around a profile moves from a high pres-sure area to a low pressure area and then back to a high pressure area again.The area where the ball enters the valley corresponds to the high pressurearea where the air particle meets the leading edge of the profile. The lowestpoint of the valley corresponds to the lowest pressure point along the profile.You know that this is the point of maximum thickness.

The laminar boundary layer is between the leading edge and the point of maxi-mum thickness which is also the point of lowest static pressure.An air particle moves smoothly and with acceleration in the laminar boundarylayer just like the ball as it accelerates from the top of the hill to the bottom ofthe valley.You can imagine that the ball decelerates as it rolls up the other side of thevalley and stops before it reaches its former elevation.In the same way the air particle loses energy due to the friction it encounters asit enters the turbulent boundary layer after the point of maximum thickness.The air particle is unable to reach the area of high static pressure at the trailingedge and we get a flow separation where the air particle stops moving.

Flow Separation


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Now you can give the ball some additional energy with this billiard cue.A slot in the profile assists the air particle to reach the high pressure area at thetrailing edge in the same way that the billiard cue assists the ball to reach itsformer elevation.The slot transfers air with high energy from the lower side to the upper side ofthe profile and this gives the stationery air particle the energy it needs to moveto the high pressure area at the trailing edge.The slot prevents a flow separation.You will see more about boundary layer control in the chapters on flaps andslats.

Take a look at these two profiles with the same thickness.The lower profile has lower friction drag than the upper profile.This is because the low drag laminar region is greater on the lower profile thanon the upper profile.The transition to the turbulent boundary layer takes place at 45% of the cord ofthe lower profile, compared to 30% of the cord of the upper profile.The lower profile is known as a laminar profile.


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5.3.3. Interference DragIn this segment we use an example to illustrate interference drag. You can seethat we have three separate aircraft components:1. A wing which creates a drag of 700 daN.2. A strut which creates a drag of 50 daN.3. An engine which creates a drag of 150 daN.The sum of the drag on each of these separate components is 900 daN.But do you know what happens to the total drag when these components arefitted together?The total drag of the wing with the strut and the engine attached is greater thanthe sum of the drag on the individual components.This difference is the interference drag !Interference drag is the turbulence in the airflow caused by the sharp cornerswhich result when components are joined together or placed in close proximity.Interference drag can be reduced by fairings.Now you know something about each of the three different types of parasitedrag.


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Interference Drag


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5.4. Compressible DragThe compressible drag only occurs in transonic and supersonic flight.It is caused by the shock waves on an aircraft approaching the speed of sound.Sometimes it is called wave drag.In subsonic flight the local velocities on a profile are greater than the freestream velocity but, by definition, less than the speed of sound.In transonic flight we get a mix of subsonic and supersonic airflow and we en-counter shock waves.You will learn more about shock waves in the chapter on high speed flight. Fornow we concentrate on how the shock waves create drag.

Here you can see a close up view of the boundary layer in front of, and behindthe shock wave.You can see that the boundary layer thickens as it passes through the shockwave.A flow separation is caused by the thickening of the boundary layer and theexistence of an adverse pressure gradient across the shock wave.This flow separation causes additional drag which is called compressible drag.


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5.5. Total DragIn this segment we look at how induced drag and parasite drag combine to givethe total drag.The curve of the induced drag shows that the induced drag is high at lowspeeds and decreases as the speed increases.The parasite drag increases with increases in speed.The third curve represents the total drag. It is the sum of the induced drag andthe parasite drag.You can see that the total drag is very high at low speeds because of the highinduced drag.It then decreases to a minimum at an intermediate speed and then increasesagain because of the increasing parasite drag.

DRAG

SPEEDDRAG VERSUS SPEED

Total Drag

Induced Drag Parasite Drag


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AERODYNAMICSLIFT DISTRIBUTION

FUNDAMENTALS



6. Lift Distribution6.1. IntroductionIn this Chapter we look at the lift distribution.We will see how different wing designs affect the lift distribution and how thewash out helps to prevent a stall on the wing tip.Then we look at stall conditions and boundary layer control.Now take a look at these three lift distributions.You allready know that an elliptical lift distribution produces the lowest drag.

6.2. Wing DesignNext we look at how different shapes of wing produce different lift distributions.You see four different shapes of wing.Before we look at the lift distribution and stall characteristics of each of thesewing shapes, you should know that the downwash behind the wing changes thelocal angle of attack.A high downwash produces a low local angle of attack and a low downwashproduces a high local angle of attack.Now lets see the lift distribution, the downwash and the stall characteristics ofthe four wings.

6.2.1. Elliptical WingThe elliptical wing produces an elliptical lift distribution and has a constantdownwash behind the wing.

The constant downwash gives a constant local angle of attack and therefore aconstant flow separation across the span of the wing.The entire wing stalls at the same time.

6.2.2. Rectangular WingThe rectangular wing has a large tip vortex and therefore a larger downwash atthe tip than at the root.We have a higher downwash and a lower angle of attack at the tip of the rect-angular wing.This means that the tip sections are the last to stall.

6.2.3. Tapered WingOn the tapered wing the downwash increases towards the root and the tipstalls before the root.

6.2.4. Swept WingA swept wing also tends to stall at the tip section first.Swept wings are used on most aircraft.

High Down Wash Low Local Angle of AttackLow Down Wash High Local Angle of Attack


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6.3. Wing Twist, Washing Out A tendency to stall at the tip section first has dangerous implications for thelateral control and stability of the aircraft.Next we look at how the wing can be designed to prevent or delay these stal-ling characteristics.The wing can be designed so that the root stalls before the tip and the aircraftremains controllable.This is achieved by geometrically twisting the wing, or by aerodynamicallytwisting the wing.

6.3.1. Geometrically Twisted WingOn a geometrically twisted wing the camber of the profile is constant across thespan of the wing but the angle of incidence is greater at the root than at the tip.You can see that the cord lines are not parallel.When the aircraft approaches the stall angle there is a flow separation on theroot before the tip.

Wing Root ( High Angle of Incidence )

Wing Tip ( Small Angle of Incidence )

6.3.2. Aerodynamically Twisted WingOn an aerodynamically twisted wing, the camber of the profile at the root isgreater than the camber at the tip and the angle of incidence is constant acrossthe wing span. You can see that the cordlines are parallel.When the aircraft approaches the stall angle there is a flow separation at theroot before the tip.In reality most aircraft wings are tapered and swept and use a combination ofgeometric wash out and aerodynamic wash out.

Wing Tip ( Small Camber )

Wing Root ( Big Camber )


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6.4. Stall ConditionsThe total wing lift is the resultant of the lift distribution. It is represented by thetwo large arrows on the lower graphic.The total wing lift acts on the center of lift.The cord line through the center of lift is known as the mean aerodynamic cord,or MAC for short.The position of the center of lift can be described in percentage terms.The leading edge corresponds to 0 % and the trailing edge to 100 % so in thisexample we can say that the center of lift is located at approximately 30 %MAC.

0 %

100 %

The total weight of the aircraft acts on the center of gravity.The aircraft rotates around its center of gravity.When the position of the center of lift is the same as the position of the centerof gravity we have no aircraft rotation. The aircraft is in level flight.When the position of the center of lift moves forward of the position of the cen-ter of gravity we have a nose up reaction and when the position of the center oflift moves aft of the position of the center of gravity we have a nose down reac-tion.


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Aerodynamics