m8 b1 b2 ejamf

EASA Part-66

Lufthansa Resource

Fundamentals

Basic AerodynamicsModule 8

eJAMF

EJAMF M8 B1E / B2E

B1/B2

For Training Purposes Only

LTT 2006

Author XyZIssue: 1JAN2008

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

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ATA DOC

BASIC AERODYNAMICSPHYSICS OF AERODYN & ATMOSPHERE

FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007

M8 BASIC AERODYNAMICS

LufthansaTechnicalTraining

FORTRAININGPURPOSESONLY!

01|Fundamental/ALL

BASIC AERODYNAMICSPHYSICS OF AERODYN & ATMOSHERE

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PHYSICS OF AERODYNAMICS & ATMOSHERE

FUNDAMENTAL UNITS

In this lesson you will get a basic understanding of the laws of physics thataffect the aircraft in flight and on the ground. These laws are described usingthe international SI system. The SI system is based on the metric system andmust 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 basicquantities.The fundamental units can not be defined in other quantities.Thebasic quantities 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 7 fundamental units in physics -- mass, length, time, temperature,current, mol number and the intensity of light.

The fundamental units used in aerodynamics are mass, length, time andtemperature.



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Figure 1 International SI-System


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Fundamental Units cont.

Mass

The 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 1 kilogram is also the volume of one liter of pure water at atemperature of 4 degrees Celsius. Mass is not the same as weight. Theastronauts flying around in their space labs have no weight but their bodieshave a mass.

Length

The 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 aparticular colour of light.

Time

The 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 sameduration so the second is now defined as fraction of the unchangeable speed oflight.

Temperature

The unit of measurement for temperature is kelvin, denoted by K. Zero kelvin iscalled absolute zero because it is the lowest temperature possible.The kelvinscale starts at zero and only has positive numbers. 1 kelvin is the same size as1 degree Celsius.



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Fundamental Units cont.

We can describe all the basic quantities we need for aerodynamics by usingthe 4 fundamental units mass, length, time and temperature. These basicquantities are:

� speed

� acceleration

� force

� work

� power

� and pressure.



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02|Speed&Acc/ALL


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SPEED AND ACCELERATION

Speed is the distance that a moving object covers in a unit of time. Forexample, we can say that an aircraft has a speed of 500 kilometers per hour.

Speed is denoted by v, which comes from the Latin word velocitas. Thereforeinstead of speed you also can find the word velocity, with basically the samemeaning.

Acceleration is the change in speed divided by the time during which thechange takes place.

In this example the acceleration is 50 meters per second per 10 seconds.

This is equal to 5 meters per second per one second which is 5 meters persquare second. Acceleration is measured in meters per square second.

Acceleration is denoted by ’a’.



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Figure 4 Speed and Acceleration


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Speed and Acceleration cont.

A 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 earth’s surface but on averageit is 9.8 meters per square second. For ease of calculation 10 meters persquare second is often used.



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Figure 5 Acceleration due to Gravity


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FORCE AND WEIGHT

We begin our look at force with an experiment. You can see that our friend isstanding on a weighing scale in an elevator and is observing his weight.

What do you think happens to his weight when the elevator moves upward at aconstant velocity?

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 theweight.

The second law of Sir Isaac Newton, the great physicist, states that forceequals mass multiplied by acceleration. In our example the force is equal to themass of our friend multiplied by the acceleration of the elevator.

Force is measured in Newtons. The term deca--Newton is used in all technicalmanuals for force and for weight and corresponds to 10 Newton.

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.



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Figure 6 Force and Weight


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WORK AND POWER

Work

In this segment we look at work. Work is done when an object is moved over adistance. It is force multiplied by distance. 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 600 Newton is moved a distance of30 meters.

The work is 600 Newton multiplied by 30 meters which is 18 000 Newtonmeters.



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Figure 7 Work


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Power

Power 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 Newton is moved a distance of30 meters in 10 seconds.

The power is 600 Newton multiplied by 30 meters divided by 10 seconds whichis 1 800 watts or 1.8 kilowatts.



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Figure 8 Power


07|Pressure/All


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PRESSURE

Pressure is the force acting on a unit of area.

It is denoted by Pascal (Pa) and measured in Newtons per square meter.

Static pressure acts equally in all directions. It is denoted by a small ’p’ andmeasured in Newtons per square meter.

Static pressure is calculated as height multiplied by density multiplied bygravity.

Dynamic 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.

Dynamic pressure is calculated as half the density multiplied by the speedsquared.

The static pressure for aircraft technical systems is denoted by ’bar’ andmeasured in decaNewtons per square centimeter.

One bar is equal to 100 000 PASCAL.



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Figure 9 Pressure / Static and Dynamic Pressure


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SPEED OF SOUND

Sound 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 of the speed of sound, the number 20 is an approximation of thetotal of all the relevant constant values and ’T’ for temperature represents theonly variable value.

Note that the temperature must be expressed in Kelvin!





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Figure 10 Sound Waves




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Speed of Sound cont.

Now you know that the speed of sound depends on the temperature.

For example if the temperature on a Summer day is 15 degrees Celsius, whichis 288 degrees Kelvin then we calculate the speed of sound to be 339.4 metersper second.

If the temperature decreases in Winter to minus 50 degrees Celsius, which is223 degrees Kelvin then the speed of sound is 298.6 meters per second.

The speed of sound is less at high altitudes because the temperature is lower.





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Figure 11 Speed of Sound




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Now let’s 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 is below the speed of sound.

You can see that the pressure wave moves ahead of the aircraft and alsobehind 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.

The 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.





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Figure 12 Aircraft Speed




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Now let’s 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 meters per second.

You can see that the aircraft speed is below the speed of sound at this altitude.We assume the speed of sound is 330 meters per second.

Now the same aircraft is flying at an altitude of 10 kilometers. The aircraftcontinues to fly with a speed of 300 meters per second.

At this higher altitude the temperature is lower and the speed of sounddecreases to 300 meters per second.

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 kilometers has a Machnumber of one (M = 1). A Mach number of one indicates that the aircraft isflying at the speed of sound.





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Figure 13 Mach Number




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These graphics illustrate the 3 sound regions which are defined by the Machnumbers. In the subsonic region all speeds around the aircraft are below thespeed 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 between the critical Mach number and 1.3 Mach.

Finally we have the supersonic region.

Here all speeds around the aircraft are higher than the speed of sound. This isthe region at Mach numbers higher than 1.3.





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Figure 14 Sound Regions


13|Atmosphere/All


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ATMOSHERE

To understand aerodynamics we need to know something about theatmosphere where flying happens.

The atmosphere is the whole mass of air extending upwards from the surfaceof the earth.

The atmosphere has many layers. The troposphere is the lowest of theselayers. In the troposphere we have clouds and rain and many different weatherconditions.

The stratosphere is the layer above the troposphere.There are no rain clouds inthe stratosphere and the temperature does not change as the altitudeincreases.

The tropopause is the name given to the boundary between the troposphereand the stratosphere.

The tropopause has different heights around the earth. It is approximately 8kilometers over the north and south poles and 16 kilometers over the equator.



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Figure 15 Atmosphere


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Atmoshere cont.

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.

A standard atmosphere was introduced by the International Civil AviationOrganisation, the ICAO . This standard atmosphere is known as the ISA forICAO standard atmosphere or International Standard Atmosphere.

Now let’s 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 andpressure. Note that the standard altitude for the tropopause is 11 kilometers.

Under standard conditions temperature decreases with altitude at a rate of 6.5degrees per kilometer. This gives a standard temperature of minus 56.5degrees Celsius at the tropopause.

You can see that there is no change in temperature in the stratosphere.

You can see that the density and pressure gradually decrease with altitude.

This 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 documentation.



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Figure 16 ICAO Standard Atmosphere (ISA)


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BASIC AERODYNAMICSAERODYNAMICS

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BASIC AERODYNAMICS

CONTINUITY EQUATION

In the subsonic region the speed is so slow that a flying body does notcompress the air. We say that the air is incompressible in the subsonic region.

Now let’ have a closer look at the behaviour of the air streamlines.

The streamlines are parallel to each other if there is no disturbance.

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.



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Figure 17 Flow Pattern in a Tube


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Continuity Equation cont.

Here we isolate the stream tube and identify two cross--sections, A1 and A2.

Assume that the area of the cross--section at point A one is 20 squarecentimeters and the speed of the airflow at this point is 10 meters per second.

The continuity equation states that the speed of the airflow is inverselyproportional to the area of the cross section of the tube as long as thedensity remains constant.

For example if the area of the cross section is halved then the speed of theairflow is doubled or if the area is four times smaller then the speed is fourtimes greater.



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Continuity Equation

V V21 1 2A A=. .Density is Constant

� �=1 2LufthansaTechnicalTraining

Figure 18 Continuity Equation


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Continuity Equation cont.

We use the term diffuser outlet when the diameter increases and the speeddecreases and the term jet outlet when the diameter decreases and the speedincreases.



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Figure 19 Defuser & Jet Outlet


04|Bernoulli/All


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BERNOULLI’S PRINCIPLE

In this segment we look at another important equation used in aerodynamics,Bernoulli’s equation.

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 Closed

The fluid inside the tube has a static pressure. The static pressure isrepresented by the blue arrows in the tube and by the blue line on the graph atthe bottom of the picture.

The static pressure acts in all directions.

The total pressure is represented by the green circle in the tube and by thegreen line on 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.

Valve Open

When the valve is moved to the quarter open position the fluid begins to flow.You can see that the static pressure decreases and a new pressure, thedynamic pressure, is introduced. You should remeber that the dynamicpressure only acts in the direction of the flow. The dynamic pressure isrepresented by the red arrows in the tube and the red line on the graph. Thegraph shows the amount of static pressure, dynamic pressure and totalpressure in the quarter open position.

The static pressure decreases every time the valve is opened more and thedynamic pressure increases as the valve opens.

This is the physical law known as Bernoulli’s 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.



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1/4 OPEN POSITIONVALVE CLOSED


Figure 20 Valve positions


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Bernoulli’s principle cont.

Now let’s 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 speed 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.L

ufthansaTechnicalTraining


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Figure 21 Point of Stagnation


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Bernoulli’s principle cont.

At the graphic below you can see how we measure the static and dynamicpressure when we have a speed.

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 speed.

If the density is constant, the dynamic pressure increases sixteen times if thespeed increases four times.

The dynamic pressure is indicated to the pilot as the indicated air speed or IASin short.



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Figure 22 Pressure Measuring


07|Lift Prod/All


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LIFT PRODUCTION

In 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 speed of the airflow increases until it reaches the narrowest point in thetube.

You know that as the speed increases the static pressure decreases and thedynamic pressure increases.

The speed 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 dynamicpressure decreases.

The speed of the airflow in the Venturi tube is like the speed of a ball rollingalong a surface like this one.

As the ball rolls downhill some of the potential energy, that is the staticpressure, is exchanged for kinetic energy, that is dynamic pressure.

As the ball rolls past the lowest point the speed decreases and the staticpressure increases again.



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INLET OUTLET


Figure 23 Venturi Tube


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Lift production cont.

Now let’s replace the upper surface of the Venturi tube with a straight line andsee what happens to the airflow.

As you can see this doesn’t change things very much. The streamlines are stillcloser to each other in the center and the static pressure decreases in thisarea.

If we remove the upper surface we find that the streamlines themselvesprovide 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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Figure 24 Lift


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You can see that the paper lifts when we blow above it.

The dynamic pressure above the paper increases and the static pressuredecreases.

The static pressure below the paper remains unchanged.

The difference in static pressure above and below the paper lifts it up.LufthansaTechnicalTraining


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Figure 25 Lift


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You see that some of the streamlines approaching the profile in a low positionslope upwards in front of the wing and pass the aerofoil on the upper surface.

This is called an up--wash.

Looking at the trailing edge you see that some of the streamlines of the uppersurface flow downwards when leaving the profile.

This is called the down--wash.



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Figure 26 Up-wash / Down-wash


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Here 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 we have no differential pressure we have no lift.

Let’s see what happens if we rotate the cylinder.

When the cylinder rotates the circulatory flow causes an increase in localspeed on the upper surface of the cylinder and a decrease in local speed onthe lower 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--washimmediately in front of the cylinder and a down--wash immediately behind thecylinder.

You can also see that the fore and aft neutral streamlines are lowered.



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Figure 27 Magnus Effect


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

But where does the circulation around the profile come from as the wing profiledoesn‘t rotate as the cylinder does when creating the Magnus effect?

As you see the air near the trailing edge tends to flow upwards to the uppersurface of the wing where the static pressure is low due to the higher speed.So the air forms a vortex which is soon washed away by the airflow.

There is a rule that says that vortices always form in pairs, rotatingcounterclockwise. The matching vortex to that at the trailing edge is thecirculating vortex, that reinforces the airflow on the top of the aerofoil, making itfaster.



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Figure 28 Circulation


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BASIC AERODYNAMICSPROFILE AND WING GEOMETRY

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PROFILE AND WING GEOMETRY

PROFILE GEOMETRY

In this lesson we look at the geometry of a wing and a profile. This is importantfor our understanding of lift and drag.

We begin with the geometry of a profile.

As you can see a profile is a cross section of a wing.

The aircraft wing is sometimes called an airfoil and the profile is then an airfoilsection.



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Figure 29 Geometry of a Profile


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Profile Geometry cont.

The profile has a leading edge and a trailing edge.

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

The mean camber line is a line drawn halfway between the upper and the lowersurfaces of the profile.

The shape of the mean camber line is very important in determining theaerodynamic characteristics of a profile.

The end points of the mean camber line are the same as the end points of thechord line.

The camber of the profile is the displacement of the mean camber line from thechord line.

The maximum camber and the location or the maximum camber help to definethe shape of the mean camber line.

These quantities are expressed as a fraction or a percentage of the basicchord dimension.

A typical low speed profile might have a maximum camber of 5 % located 45 %aft of the leading edge.



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Figure 30 Camber of a profile


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Profile Geometry cont.

The maximum thickness of a profile is defined as a fraction or a percentage ofthe chord.

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 thechord.

For example a typical low speed profile might have a maximum thickness of18% located 30% aft of the leading edge.



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Figure 31 Thickness of a Profile


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Relative Wind

The 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 pathvelocity.

The relative wind depends on the flight path and is therefore not alwayshorizontal.



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Figure 32 Relative Wind


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Angle of Attack

The angle of attack is the angle between the chord line of the profile and therelative wind.

It is denoted by α (alpha).

The angle of incidence is the angle between the chord line of the profile andthe longitudinal axis of the aircraft.

It is denoted by gamma.



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Figure 33 Angle of Attack / Angle of Incidence


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WING GEOMETRY

In this segment we look at wing geometry. The wing area is the projection ofthe outline on the plane of the chord.

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 bythe chord of the wing, c.



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Figure 34 Wing Area S


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Wing Geometry

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

The taper ratio λ (lambda), is the ratio of the tip chord to the root chord.

λ = Ct/Cr

The wing area S is the average chord multiplied by the wing span.

The average chord, c, is the geometric average of all the chords and the wingspan, b, is measured from tip to tip.



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Figure 35 Taper Ratio λ


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Aspect Ratio

The aspect ratio is the wing span, b, divided by the average chord, c.

Typical aspects ratios vary from 35 for a high performance sail--plane to 3.5 fora jet fighter plane.

You can see in the formula that the aspect ratio can also be expressed as thewing span squared divided by the wing area.

Λ =bC

Λ =b2

S



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Figure 36 Aspect Ratio


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Sweep Angle

The sweep angle is the angle between the line of 25 percent chords and a lineperpendicular to the root chord.

Positive sweep = Backwards !

Negative sweep = Forewards !

Dihedral

The dihedral of the wing is the angle formed between the wing and thehorizontal 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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Figure 37 Sweep Angle / Dihedral


01|Intro/All

BASIC AERODYNAMICSLIFT AND DRAG

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LIFT AND DRAG

INTRODUCTION

You 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.

In this lesson you will see that the design of the profile is very important.

Here you see the distribution of static pressure on a profile. The red area infront of the leading edge is where the static pressure is higher than the ambientstatic 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 of stagnation where the air comes toa stop.

In the blue areas above and below the profile the static pressure is lower thanthe ambient static pressure.

This is because the air speeds up again as it passes above and below theprofile so that the local air velocity is greater than the 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 red area at the trailing edge the static pressure is higher than theambient static pressure.

This is caused by low velocity turbulent air in this area.



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Figure 38 Distribution of Static Pressure


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AERODYNAMIC FORCES

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 the relative wind and

� drag which is parallel to the relative wind.

Here the center of pressure is identified. This is the point on which allpressures and all forces act.

This point is located where the cord of a profile intersects with the resultant ofthe aerodynamic forces lift and drag.

The aerodynamic forces of lift and drag depend on the combined effect ofmany variables:

� The dynamic pressure,

� the surface area of the profile,

� the shape of the profile and

� the angle of attack.



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Figure 39 Aerodynamic Force


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Aerodynamic Forces cont.

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 it’s not as easy as you might think. In reality a profile has differentpressures because of different angles of attack.

First let’s look at the simple calculation of theoretical lift.

The theoretical lift is the dynamic pressure multiplied by the surface area.

You already know that the dynamic pressure is half the air density multiplied bythe velocity squared.

Theoretical Lift = ½ x ρ x V2 x AIn this example we assume that the air density is 1.225 kilograms per cubicmeter and the air velocity is 28 meters per second and the surface area of theprofile is 0.05 square meters.

This gives a theoretical lift of 24 Newton.



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Figure 40 Theoretical Lift


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Aerodynamic Forces cont.

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 2 scales attached to the support arm

� a horizontal scale to measure the drag and

� a vertical scale to measure the lift.

Now let’s see what happens when we switch on the wind tunnel.



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Figure 41 Wind Tunnel


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CL AND CD

You can see that the measured lift is only 8.4 Newton.

This is much less than the theoretical lift of 24 Newton.

The theoretical lift must therefore be adjusted.

A coefficient of lift, CL, is introduced to the lift equation to account for thedifference between the measured lift and the theoretical lift.

The coefficient of lift is the measured lift divided by the theoretical lift.

In our example it is 0.34.

The lift equation is now the coefficient of lift multiplied by the dynamic pressuremultiplied by the surface area.



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Figure 42 Lift Equation


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CL and Cd cont.

For the same reasons a coefficient of drag, CD, is introduced to the dragequation to account for the difference between measured drag and theoreticaldrag.

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.



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Figure 43 Drag Equation


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EFFECT OF ANGLE OF ATTACK

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 below.

Now observe the coefficient of lift on the scale and the relationship between theangle of attack and the coefficient of lift on the graph.

You can see on the graph that the coefficient of lift increases up to themaximum coefficient of lift, CL max, and then decreases again.

The maximum coefficient of lift corresponds to the maximum angle of attack,alpha max.

If the angle of attack increases above α max the airflow cannot follow the uppersurface of the profile and an airflow separation known as stall occurs.



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Figure 44 Angle of Attack (AOA)


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EFFECT OF PROFILE SHAPE

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.

Here you see a cross section of the profile we used in the wind tunnelexperiment and the graph showing the associated coefficient of lift curve.

Now let’s 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 attackincreases above approximately ten degrees.

You can see also that the thicker profile has a higher maximum coefficient of liftand a higher alpha max.



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Figure 45 Change of the Profile Thickness


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Effect of Profile Shape

Now let’s 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 highercoefficient of lift at the zero angle of attack.

You can also see that this profile has a higher maximum coefficient of lift but alower alpha max than the basic profile.



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Figure 46 Change of the Profile Chamber


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Effect of Profile Shape

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 featuresdesired in a profile.



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Figure 47 Profile


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EFFECT OF ICE ON SURFACE

Upper surface frost and especially leading edge ice formation reduce themaximum coefficient of lift and the maximum angle of attack.

This is quite dangerous for low speed flights and the reason we have anti--icingor deicing systems.L

ufthansaTechnicalTraining


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Figure 48 Effect of Ice on Surface


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FACTORS AFFECTING DRAG

Next we look at the factors affecting the coefficient of drag.

The drag equation is similar to the lift equation except that we use thecoefficient 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.



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Figure 49 Coefficient of Drag


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Factors affecting drag cont.

We 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 below.

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.



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Figure 50 Factors affecting Drag II


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POLAR DIAGRAM

Here you can see how the lift and drag coefficients can be combined to give usinformation about the performance of profiles.

Now we’re going to look at the polar diagram. This shows the coefficient of liftplotted against the coefficient of drag for each angle of attack.

This method of evaluating windtunnel tests was invented by Otto Lilienthal thefirst researcher and pioneer in the field of aerodynamics and flying at the end ofthe nineteenth century.

He used this diagram to find out the angle of attack that brings the best glideratio.

You find the angle for the best glide ratio by drawing a tangent from theintersection of the axis to the graph.

The point where this tangent contacts the graph represents the angle of thebest glide ratio. No higher lift to drag ratio is possible by this profile.



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Figure 51 Polar Diagram


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LILIENTHAL DIAGRAM

The glide ratio represents not only the aerodynamic efficiency of a profile butcan tell you about the layout of a complete aircraft if you draw the diagram withthe coefficients of the aircraft.

A higher glide ratio means a lower drag at a given lift. This results in a lowerinstalled engine thrust to overcome the drag and this means lower weight,lower fuel consumption, higher payload or longer range.



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Figure 52 Lilienthal Diagram


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Lilienthal Diagram

This picture shows the relationship between the polar diagram and thebehaviour of a real aircraft.

You see 4 forces acting on the aircraft while it is gliding with zero engine thrust.

The potential energy of the lost height substitutes the thrust of the engines andcompensates the drag.

The weight of the aircraft acts vertical to the ground and the drag parallel to theglide path.

The third force is the lift perpendicular to the glidepath and finally the resultantof lift and drag.

The angle ϕ between the lift vector and the resultant is the same as the angleof the glide path to the horizon.

The smaller this angle, the smaller the dragvector, the smaller the necessarythrust, the higher the efficiency of the aircraft.

This triangle can also be identified in the polar diagram, because CD isproportional to the drag and CL to the lift.

Therefore the polar diagram can tell us a lot about the performance of the realaircraft.

You see: the smaller the drag, the smaller the glide angle.

When the aircraft should fly horizontally, the engine thrust has to compensatethe drag. So an aircraft with a small glide angle needs less thrust.



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Figure 53 Relationship between Polar Diagram and Behaviour of an Aircraft


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LIFT TO DRAG RATIO

A variation of the polar diagram is the lift drag ratio diagram.

Here the ratio of the lift to the drag is plotted against the angle of attack.

As you can see the ratio of the lift to the drag is the same as the ratio of the liftcoefficient to the drag coefficient.

The lift drag ratio diagram shows the maximum lift drag ratio.

This point which is the same as the best glide ratio in the polar diagramrepresents the most efficient operation of the profile. It is the point where weget the most lift for the least drag.



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Figure 54 Lift - Drag Ratio


01|Intro/All

BASIC AERODYNAMICSCATEGORIES OF DRAG

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CATEGORIES OF DRAG

INTRODUCTION

You know that drag is the aerodynamic force which is parallel to the relativewind.

It is the opposite force to thrust.

The total aircraft drag is the sum of the:

� Induced Drag

� Parasite Drag

� Compressible Drag

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 dragcaused by the distribution of pressure or friction drag which is drag caused byskin friction or interference drag which is drag caused by aerodynamicinterference.

Compressible drag is caused by the shock waves on an aircraft approachingthe speed of sound.



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Figure 55 Categories of Drag


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INDUCED DRAG

If an aircraft wing had an infinite span the air would flow directly from theleading edge to the trailing edge.

The blue lines represent the airflow over the wing and the red lines representthe airflow under the wing.

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 tipvortices.

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.

On the graphic below you can see that on a wing with an infinite span the liftdistribution is always the same and on a wing with a finite span we get a loss oflift near the wing tips.

The induced drag is lower if the finite wing has an elliptical lift distribution suchas the one you see here.



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Figure 56 Induced Drag


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EFFECT OF UP/ DOWN WASH

You know from an earlier lesson 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.

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.

The design of the gutter above the entry doors on this Aircraft 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 anddownwards to reflect the downwash aft of the wing.



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Figure 57 Effects of Up/Down Wash


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EFFECT OF ASPECT RATIO

The 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.

The wing tips can be designed to reduce the induced drag.

On smaller aircraft we have a special wing tip form and on larger aircraft wehave wing tip fences such as on this Airbus 310 or winglets such as on thisBoeing 747.



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Airbus 310

Boeing 747


Figure 58 Induced Drag Affection by the Aspect Ratio and the Wing Tip Design


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Effect of Aspect Ratio cont.

These designs reduced the energy of the wing tip vortices.

You can see 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. This bird doesn’t needwinglets because the pressure difference is very low at the wing tips.



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Figure 59 Wing Tips in Nature


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Effect of Aspect Ratio cont.

During 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 and the upper surface ofthe wing and this creates small wing tip vortices and therefore low induceddrag.



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Figure 60 Induced Drag Affection by the Aircraft Speed


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FORM DRAG

You know that form drag is a parasite drag and that it is caused by thepressure distribution on a body.

Take a look at the cylinder in an airstream. There is no friction in the airstreamand we have a perfectly symmetrical flow pattern.

You can see on the graphic that the pressure in front of the cylinder is thesame as the pressure aft of the cylinder.

In this situation there is no drag.

On the bottom of the graphic we have an airflow with friction. You can see thatwe don’t have a symmetrical flow pattern any more and that the pressure infront of the cylinder is not the same as the pressure behind the cylinder.

This difference in pressure causes form drag.

Form drag depends on the frontal area of a body and also on the speed of theairflow.



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AIRFLOW WITHOUT FRICTION


Figure 61 Airflow with and without Friction


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Form Drag

Now let’s compare the form drag of three different bodies with the same frontalarea:

� a disc,

� a disc with a bullet shaped nose and

� 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 20% and if we then add astreamline tail the drag goes down to less than 10%.

Form drag is reduced by streamlining.

One obvious way of streamlining an aircraft is to have retractable landing gear.

Sometimes form drag on the wing is distinguished from form drag on otherparts of the aircraft.

Form drag on the wing is called wing drag or profile drag.



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Figure 62 Ways to reduce Form Drag


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FRICTION DRAG

Now let’s have a look at friction drag: Here you see 10 different profiles. Youcan see that they all have the same height or diameter, D, and different length,L.

The length to diameter ratio is shown on the left side of the profiles. This ratioranges from 1 at the top to 10 at the bottom.

The profile with the highest length to diameter ratio has the lowest form dragand the profile with the length to diameter ratio of one has the highest formdrag.

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 of2, 3 and 4 produce the lowest combination of form and friction drag.



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Figure 63 Form Drag


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Friction Drag

Now let’s 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 immediately above the surface is retarded.

The retarded layer of air at the surface slows down the layer immediatelyabove it and this layer in turn slows down the next layer and so on until thefreestream velocity is restored.

The retarded air is called the boundary layer.



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Figure 64 Boundary Layer


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BOUNDARY LAYER

There a 2 basic types of boundary layer -- the turbulent boundary and thelaminar 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 3 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.



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Figure 65 Laminar and Turbulent Boundary Layer


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Boundary Layer cont.

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 highpressure area to a low pressure area and then back to a high pressure areaagain.

The area where the ball enters the valley corresponds to the high pressurearea where the air particle meets the leading edge of the profile and 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 ofmaximum 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 see that the ball decelerates as it rolls up the other side of the valleyand 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.



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Figure 66 Air Particle in a Boundary Layer


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Now you can give the ball some additional energy with this billiard cue.

The additional energy from the billard cue takes the ball back to the elevation itstarted from.

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 stationary air particle the energy it needs to moveto the high pressure area at the trailing edge.

The slot prevents a flow separation.



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Figure 67 Slot in the Profile


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Take a look at the 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 chordof the lower profile compared to 30% of the chord of the upper profile.

The lower profile is known as a laminar profile.



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Figure 68 Laminar Profile


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INTERFERENCE DRAG

In this segment we use an example to illustrate interference drag. You can seethat we have three separate aircraft components:

� a wing which creates a drag of 700 daN

� a strut which creates a drag of 50 daN

� an engine which creates a drag of one 150 daN

The sum of the drag on each of these separate components is 900 daN.

The total drag on the wing with the strut and the engine attached is greaterthan the 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 different types of parasite drag.



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Figure 69 Interference Drag


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COMPRESSIBLE DRAG

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 weencounter shock waves.

You can learn more about shock waves in Module 11 in the lessons on highspeed flight. For now we concentrate on how shock waves create drag.



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Figure 70 Compressible Drag I


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Compressible Drag cont.

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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Figure 71 Compressible Drag II


18|Total/B1/B2


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TOTAL DRAG

In this segment we look at how induced drag and parasite drag combine to givetotal drag.

The red curve represents the induced drag. It shows that the induced drag ishigh at low speeds and decreases as the speed increases.

The blue curve represents the parasite drag. The parasite drag increases withincreases in speed.

The green curve represents the total drag. It is the sum of the induced dragand the 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.



18|Total/B1/B2


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Figure 72 Total Drag


01|Intro/All

BASIC AERODYNAMICSLIFT DISTRIBUTION

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LIFT DISTRIBUTION

INTRODUCTION

In this lesson we look at the lift distribution.

Here you see 4 different wing shapes with their lift distribution.

� an elliptical wing

� a rectangular wing

� a tapered wing

� a swept wing



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Figure 73 Wing Shape and Lift Distribution


02|Up--Down/B1/B2


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EFFECT OF UP/DOWN WASH

Wing Design

While the wing with elliptical lift distribution stalls all over the wingspan at thesame time, the rectangular wing begins to stall at the root and tapered wingsand swept wings stall at the tip section first.

The reason for the different stall characteristics of each of these wing shapesis, that the downwash behind the wing changes the local angle of attack.

A high downwash produces a low local angle of attack and an low downwashproduces a high local angle of attack.

Elliptical Wing

The elliptical wing has a constant downwash behind the wing.

This 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.

Rectangular Wing

The 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 therectangular wing.

This means that the tip sections are the last to stall.

Tapered Wing

On the tapered wing the downwash increases towards the root and the tipstalls before the root.

Swept Wing

A swept wing also tends to stall at the tip section first.

Swept wings are used on most aircraft.

A tendency to stall at the tip section first has dangerous implications for thelateral control and stability of the aircraft.



02|Up--Down/B1/B2


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Figure 74 Wing Design


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WING DESIGN

The wing can be designed so that the root stalls before the tip and the aircraftremains controllable.

This is achieved by geometrically twisting or ’washing out’ the wing or byaerodynamically twisting the wing.

Geometrically Twisted Wing

On 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 chord lines are not parallel.

When the aircraft approaches the stall angle there is a flow separation on theroot before the tip.

Aerodynamically Twisted Wing

On 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 chordlines 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.



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Figure 75 Wing Twist


04|Stall/All


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STALL CONDITIONS

The total wing lift is the resultant of the lift distribution. It is represented by thelarge blue arrows on the lower graphic.

The total wing lift acts on the center of lift.

The chord line through the center of lift is known as the mean aerodynamicchord, 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.



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Figure 76 Mean Aerodynamic Chord


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Stall Conditions cont.

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 thecenter of gravity we have a nose up reaction and when the position of thecenter of lift moves aft of the position of the center of gravity we have a nosedown reaction.



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Figure 77 Center of Lift Conditions


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Wing Root Stall

Here we have a stall at the root of the wing.

You can see the loss of lift that results from the flow separation in the area ofthe root.

When we have a flow separation at the root of the wing the center of lift movestowards the tip and also behind the center of gravity.

The aircraft rotates to the nose down position.

The aircraft loses altitude rapidly, the airspeed increases and the angle ofattack decreases.

The aircraft recovers from the stall without pilot input.



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Figure 78 Wing Root Stall


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Wing Tip Stall Prevention

A flow separation at the tip of the wing is much more dangerous. The center oflift moves towards the root and also forward of the center of gravity.

The aircraft rotates to the nose up position.

The angle of attack increases and the stall condition gets worse. Pilot input isrequired to keep the aircraft under control.

A stall strip is a knife edge like device which is used on smaller aircraft toprevent the wing tip from stalling first.

Here the stall strip is mounted at the leading edge of the wing root.

The disadvantage of this device is that it disturbs the lift.



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Figure 79 Wing Tip Stall Effects


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Wing Tip Stall Prevention cont.

Slats are used to prevent wing tip stall on some larger aircraft.

On aircraft such as the Boeing 737 or the MD11 the slats extend automaticallyif the angle of attack is too high.

The slats are located at the leading edge of the wing tips.

When the slat is extended a slot opens and the boundary layer receives moreenergy. As you know this prevents a flow separation at the wing tip.



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Figure 80 Wing Tip Stall Prevention


09|BoundLay/All


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BOUNDARY LAYER CONTROL

As air particles flow over this swept wing they are split in 2 directions.

One is at right angles to the leading edge and the other follows the leadingedge.

This produces a spanwise flow.

The spanwise flow has the effect of thickening the boundary layer towards thewing tip -- especially during low speed flight with a high angle of attack.

This increases the possibility of a flow separation.

Wing fences reduce the effects of the spanwise flow.

The wing fences are placed at several locations on the wing.

They tend to keep the air particles going in a straight line direction.

Wing fences are also called boundary layer fences.

A saw tooth leading edge has the same effect as wing fences.



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Figure 81 Saw Tooth Leading Edge and Wing Fences


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Vortex Generator

A vortex generator is another device which is used to improve boundary layercontrol.

It is a small, low aspect ratio wing which is placed vertically on the surface of alarge wing.

The vortex generator produces lift and has an associated tip vortex which iscomparable to induced drag.

The vortex is large relative to the generator because the aspect ratio is small.

The vortex generator takes relatively high energy air from outside the boundarylayer and mixes it with low energy air in the boundary layer.

The generator must be the right size and in the right location to go through theboundary layer.

The number of vortex generators and their location depends on flight testinvestigation.



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Figure 82 Vortex Generator


01|Forces/All

BASIC AERODYNAMICSTHEORY OF FLIGHT

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THEORY OF FLIGHT

FORCES ACTING ON AN AIRCRAFT

You know that the 4 forces acting on an aircraft are:

� Lift

� Weight

� Thrust

� Drag

Thrust is the force which moves the aircraft forward through the air.

Thrust is provided by jet engines or by a propeller.

Drag is the aerodynamic force which is parallel to the flight path.

You can see that drag acts towards the rear of the aircraft.

Lift is the aerodynamic force which is ninety degrees to the flight path.

You can see that lift acts toward the top of the aircraft.

Weight is the force of gravity.

It always acts towards the center of the earth.



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Figure 83 Forces acting on an Aircraft


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forces acting on an aircraft cont.

In theory lift, thrust, weight and drag all act through the aircraft’s center ofgravity.

The center of gravity can be thought of as a center of balance.

An equilibrium exists when the aircraft is in steady, level flight.

The aircraft is trimmed so that the lift is equal to the weight, or in other wordsthe sum of the vertical forces is 0 and the power plant is set so that the thrustis equal to the drag, or in other words the sum of the horizontal forces is equalto 0.

A third condition for equilibrium is that the clockwise rotation of the aircraft isequal to the anti clockwise rotation or in other words the sum of the moments isequal to 0.

Moments are caused by forces on a lever that do not act through the point ofrotation.

The value of a moment is equal to the force multiplied by the moment arm.

The moment arm is the shortest distance between the point of rotation and theline of action of the force.

Earlier we assumed that all forces acted through the center of gravity. In realityhowever, it is a requirement for stable flight that the center of lift is aft of thecenter of gravity.

The distance between the center of gravity and the center of lift creates therotating effect known as a moment.



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Figure 84 Center of Lift / Center of Gravity


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forces acting on an aircraft cont.

The lift force acts with the moment arm L 1 to produce an anti clockwiserotation and a downward force on the aircraft nose.

This must be balanced with a clockwise rotation which gives an upward forceon the aircraft nose.

The stabilizer force acts with the moment arm L 2 to produce the clockwiserotation and an upward force on the aircraft nose.

The lift on the wing now has to carry the weight of the aircraft and thedownward acting stabilizer force.

But what about the thrust and the drag?

In reality the thrust line is below the drag line.

The thrust force acts with the moment arm L 3 to produce a clockwise rotationand an upward force on the aircraft nose and the drag force acts with themoment arm L 4 also to produce a clockwise rotation and an upward force onthe aircraft nose.

The sum of the moments is 0.

The anti clockwise rotation is equal to the clockwise rotation or the lift forcemultiplied by the moment arm L 1, is equal to the sum of the thrust forcemultiplied by the moment arm L 3, the drag force multiplied by the moment armL4 and the stabilizer force multiplied by the moment arm L 2.Here all conditions for steady flight are satisfied.

The sum of the horizontal forces is 0, the sum of the vertical forces is 0 and thesum of the moments is 0.



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Figure 85 Steady Flight Conditions


04|Turn/All


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THEORY OF TURN

In this segment we look at the theory of turn.

When an aircraft is in constant altitude, wings level flight you know that the liftis equal to the weight of the aircraft.

To produce a turn, an additional force is necessary.

This force is called centrifugal force and acts on an aircraft during a steady,co--ordinated turn.

You can see that the centrifugal force acts horizontally.

If the aircraft is to maintain altitude during a turn the lift in the turn must beequal to the resultant of the centrifugal force and the weight.

When this happens you can see that the vertical lift and the vertical weightremain the same as in level flight.

The load factor is the resultant force divided by the weight.

The load factor ” n ” is also called the g--load.

In the example with a bank angle ” β ” of 45� the load factor is 1.41.

A higher bank angle gives a higher load factor.

On the turn with a 45� bank angle the resultant force is 1.41 times the weightso the load factor n is 1.41.

On a the turn with a 60� bank angle the resultant force is twice the weight sothe load factor n is 2.

The structural strength of the aircraft and consideration for passenger comfortlimit the maximum load factor and therefore the maximum bank angle during aturn.

For example the load factor on military or acrobatic aircraft is much higher thanon passenger aircraft.



04|Turn/All


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Figure 86 Theory of Turn


05|LiComp/B1/B2


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LIFT COMPENSATION DURING TURN

You know that we need additional lift during the turn to compensate for theextra weight brought about by the resultant of the centrifugal force and theweight.

You can see from the lift equation that the extra lift can be generated byincreasing the coefficient of lift or by increasing the speed.

First let’s see what happens when the aircraft is in cruise flight.

You can see that the coefficient of lift is much less than the maximumcoefficient of lift.

The pilot can increase the coefficient of lift up to the maximum during a turn.

When the aircraft is in low speed flight the coefficient of lift is at, or close to, themaximum.

The pilot must increase the speed to create the additional lift required for theturn.

The stall speed during a turn divided by the stall speed during level flight isequal to the square root of the load factor.



05|LiComp/B1/B2


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Figure 87 Lift Compensation during Turn


01|StaticStab/All

BASIC AERODYNAMICSFLIGHT STABILITY AND DYNAMICS

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FLIGHT STABILITY AND DYNAMICS

STATIC STABILITY

When we talk about stability we refer to how the aircraft is able to follow aplanned straight and level course without pilot action.

There are two types of stability

� static stability and

� dynamic stability.

First we look at static stability.

Here you see a ball on a concave surface. This is an example of static stability.

When the ball is displaced from the center it returns to its original position ofequilibrium.

Now you see a ball on a convex surface. Again you can move the ball to theleft or the right.

This is an example of negative static stability.

When the ball is displaced from the center it moves away from its originalposition of equilibrium.

Finally you see a ball on a flat surface. Again you can move the ball to the leftor the right.

This is an example of neutral static stability.

When the ball is displaced from the center it shows no tendency to roll back oraway from its original position of equilibrium.



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Figure 88 Static Stability


02|DynamicStab/All


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DYNAMIC STABILITY

Dynamic stability refers to how the continuous motion of a body varies overtime.

Dynamic stability only applies if we have positive static stability.

Here you see an example of neutral dynamic stability.

We assume that there are no friction forces acting between the ball and thesurface. The ball theoretically oscillates forever after the initial displacement.

This is called an undamped oscillation.



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Figure 89 Undamped Oscilliation


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dynamic stability cont.

This is an example of positive dynamic stability.

We assume that there is friction between the ball and the surface. The motionof the ball tends to ’damp out’ after the initial displacement.

When we have damped oscillation the ball is dynamically stable.LufthansaTechnicalTraining


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Figure 90 Damped Oscillation


04|DynamicStab/All


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dynamic stability cont.

Here you see an example of negative dynamic stability.

We assume that there is another force acting on the ball which is stronger thanthe friction -- for example a wind which blows the ball in the direction of themotion.

The ball departs further and further from its equilibrium position. When we havedivergent oscillation like this the ball is dynamically unstable.



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Figure 91 Divergent Oscillation


05|StatDynamic/All


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STATIC AND DYNAMIC STABILITY

Here you see another example to illustrate stability. The center of gravity of thisruler is located at hole number 4.

If the pivot point and the center of gravity are in the same place then we have aneutral static stability. There is no tendency to move back to the originalposition from the displaced position.

If the ruler is tilted to the left it stays in this position and if it is tilted to the right itstays in this position.



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Figure 92 Neutral Static Stability


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static and dynamic stability cont.

If the pivot point is below the center of gravity we have a negative staticstability.

When we have a displacement out of the vertical position the weight and themoment arm L1 move the ruler away from the original equilibrium position.

If the pivot point is above the center of gravity we have a positive staticstability.

When we have a displacement out of the vertical position the weight and themoment arm L2 bring the ruler back to the original equilibrium position.



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NEGATIVE STATIC STABILITY POSITIVE STATIC STABILITY


Figure 93 Negative and Positive Static Stability


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static and dynamic stability cont.

The distance between the pivot point and the center of gravity influences thestability.

The longer the distance the greater the stability.

If the pivot point is in hole 1 the large moment arm L1 gives a high tendencyfor the ruler to return to the equilibrium position after displacement.

If the pivot point is in hole 3, the relatively small moment arm L3 gives a lowertendency for the ruler to return to the equilibrium position after displacement.

You will see how this is relevant to aircraft stability in the segment onlongitudinal stability.



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Figure 94 Influences on Stability


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FLIGHT STABILITY INTRODUCTION

Here you see 3 aircraft encountering a disturbance.

The aircraft on the right of the graphic has positive dynamic stability after thedisturbance.

Positive dynamic stability is usually required in aircraft design. It preventscontinuous oscillations of the aircraft around its axes.



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Figure 95 Flight Stability


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flight stability introduction cont.

Aircraft Axes

The 3 aircraft axes are:

� the longitudinal axis,

� the vertical axis

� and the lateral axis.

These axes are perpendicular to each other and intersect at the center ofgravity.

Lateral stability refers to the roll movement around the longitudinal axis.

Directional stability refers to the yaw movement around the vertical axis andlongitudinal stability refers to the pitch movement around the lateral axis.

The aircraft has positive static stability when the sum of all the forces and allthe moments is equal to 0.



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Figure 96 Aircraft Axes


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DIRECTIONAL STABILITY

The directional or ’weathercock’ stability of an aircraft is the stability around thevertical axis.

The directional stability depends on the fin of the aircraft which is also calledthe vertical stabilizer and on the ’sweepback’ of the wing. First we look at theeffect of the fin.

Here you see an aircraft which has been deflected from its flight path.

This results in a pressure along the surface of one side of the aircraft, in thisexample the right side.

If the turning moment behind the center of gravity is greater than the turningmoment in front of the center of gravity the aircraft turns back to its originalflight path.

The aircraft is directionally stable.



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Figure 97 Directional Stability


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directional stability cont.

Some aircraft increase the surface area behind the center of gravity to improvethe directional stability.

One method of doing this is with a dorsal fin and another, used on somemilitary aircraft and on the old Boeing 707, is a keel surface. Both of thesefeatures increase the side forces to produce positive directional stability.

The sweepback of a wing also improves directional stability.

When the aircraft is deflected from its original flight path the forward going wingpresents a larger frontal area to the airflow than the other wing.

The drag on the forward going wing is therefore greater than on the other wingand this produces a yawing moment which returns the aircraft to its originalflight path.

You will realise that the forward going wing also produces higher lift.



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Figure 98 Directional Stability II


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LATERAL STABILITY INTRODUCTION

Lateral stability is the stability of the aircraft around the longitudinal axis.

It is mainly determined by the wing or more specifically by the angle of attack,the dihedral angle and the sweepback angle.

First we look at the effect of the angle of attack.

You know that during level flight the lift is equal to the weight.



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Figure 99 Lateral Stability I


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LATERAL STABILITY

Now let’s see what happens when we have a gust of wind under the right wing.

The gust moves the right wing upward and the left wing downward and theaircraft rotates around the longitudinal axis.

While the left wing is going down, it meets the relative wind coming from theopposite direction. This wind stops the movement of the wing but cannot turn itback.

You know that the angle of attack is the angle between the flight velocity andthe chord line.

Now let’s take a closer look at what happens to the down going wing.

When the gust forces the aircraft to rotate we have an additional velocity -- thedown going wing velocity.

The resultant of the flight velocity and the down going wing velocity is used todetermine the angle of attack.

The effective angle of attack is now the angle between the resultant velocityand the chord line.

You can see that this new angle of attack is higher than the previous angle ofattack and produces more lift.

As you can imagine there is a similar but opposite effect on the up going wing.

This wing gets an decrease in lift.

The increase in lift on the down going wing and the decrease in lift on the upgoing wing stops the roll motion but does not bring the aircraft back to the levelflight position.



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Figure 100 Lateral Stability II


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EFFECT OF DIHEDRAL

Now let’s see how the dihedral angles help to restore level flight.

The lift is always at right angles to the lateral axis. In level flight the lift isvertically straight up but as you can see here in disturbed flight the lift isinclined in the direction of the lower wing.

In this situation the lift and the weight create a resultant force.

The resultant force causes a sideslip which means that the aircraft glides toone side without changing flight direction.

The sideslip causes a flow of air in the opposite direction to the relative wind.

Because of the dihedral angle the relative wind strikes the down going wing ata greater angle than the up going wing.

This increases the lift on the down going wing and decreases the lift on the upgoing wing.

This difference in lift turns the aircraft back to its original flight position and thesideslip motion is stopped.

The relative wind also strikes the vertical stabilizer and this also assists the turnback motion.

Lateral stability affects directional stability and vice versa.



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Figure 101 Effect of Dihedral


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effect of dihedral cont.

The sideslip angle is the angle between the aircraft centerline and the sideslipdirection.

You know that the relative wind is opposite to the sideslip direction.

The wing in the sideslip direction, the right wing, produces more lift than theother wing.

This wing has a longer effective leading edge and a thicker effective profilethan the left wing.

The difference in lift on the wings brings the aircraft back to level flight.



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Figure 102 Sideslip


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LATERAL DIRECTIONAL INTERACTIONS

In the previous segments we separated the lateral and the directional effects ofthe swept wing during a disturbance.

You saw that the lateral response and the directional response both produce asideslip because of different effective lift on the wings.

In reality when an aircraft in free flight is placed in a sideslip the lateralresponse and the directional response happen together and the sideslipproduces a rolling moment and a yawing moment.

The complex interaction of the rolling moment and the yawing momentproduces two main types of aircraft reaction, the spiral dive and the dutch rolleffect.



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Figure 103 Lateral Directional Interactions


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SPIRAL DIVE

The tendency for spiral dive exists when there is a greater effect on thedirectional stability than on the lateral stability.

When this aircraft with a large vertical stabilizer is disturbed from level flight itbegins a slow spiral which gradually increases to a spiral dive.

When we have a sideslip the strong directional stability effect tends to turn thenose of the aircraft into the wind and the relatively weak dihedral effect cannotrestore the aircraft laterally.

The rate of divergence in the spiral motion is usually so gradual that the pilotcan control the tendency without difficulty.



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Figure 104 Spiral Dive


18|Dutch/All


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DUTCH ROLL

Dutch roll is a lateral -- directional oscillation.

The tendency for dutch roll exists when there is a greater effect on the lateralstability than on the directional stability.

When the aircraft is disturbed from its directional equilibrium the forward wingproduces more lift and more drag than the other wing.

When the effect of the lift is greater than the effect of the drag we get a sideslipin the opposite direction and the dutch roll cycle is repeated.

This yaw and roll motion of the aircraft is like the motion of someone ’waltzing’on skates. In fact the term ’dutch roll’ comes from ice skating.

The dutch roll problem is found on all aircraft with swept wings.

It can be partially overcome by reducing the sweep angle of the wings and byimproving the directional stability.

The directional stability can be improved by increasing the size of the verticalstabilizer but this has weight and drag disadvantages.

Most aircraft use a yaw damping system to improve directional stability. This isan automatic system which deflects the control surface on the verticalstabilizer, called the rudder, to give the necessary directional stability.



18|Dutch/All


FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007


Figure 105 Dutch Roll


19|LongStab/All


FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007

LONGITUDINAL STABILITY

Longitudinal stability is the stability of the aircraft around the lateral axis.

It is positive if the aircraft tends to return to its equilibrium, or the trim angle ofattack, after it is displaced by a gust.

The longitudinal stability depends on the angle of attack and the pitchingmoment effects of the horizontal stabilizer and the wing.

The horizontal stabilizer produces a downward force during level flight.

This force acts with a long moment arm around the center of gravity.

The wing produces upward lift forces during level flight which act with a shortmoment arm around the center of gravity.

As long as both forces are balanced there will be no change of the attitude.

When a gust hits the lower front part of the aircraft we get a nose up rotation.

This changes the angle of attack of the horizontal stabilizer which decreasesthe stabilizer force.

The nose up rotation also produces additional lift on the wing because of theincreasing angle of attack.

The moment of the additional lift and the lever arm L1 and the reduceddownward force on the stabilizer with the moment arm L2 bring the aircraftback to equilibrium.

When a gust hits the upper front part of the aircraft we get a nose downrotation.

This changes the angle of attack of the horizontal stabilizer which increases thedown going stabilizer force.

The nose down rotation also reduces the lift on the wing.

The moment of the reduced lift and the lever arm L1 and the increasingdownward force on the stabilizer with the moment arm L2 return the aircraft tothe previous position.



19|LongStab/All


FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007


Figure 106 Longitudinal Stability


20|LongStab/All


FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007

Longitudinal stability cont.

In general positive longitudinal stability is achieved when the center of gravityas the resultant of all aircraft weights is forward of the aerodynamic center, alsocalled the neutral point, which is the center of all lift forces.

If the distance between the center of gravity and the aerodynamic center isgreat then the longitudinal stability is high and if this distance is small then thelongitudinal stability is low.



20|LongStab/All


FUNDAMENTALS

HAM US/F-4 KaJ 01.12.2007


Figure 107 Quality of Longitudinal Stability

TABLE OF CONTENTS

EJAMF M08 B1 E

Page i

M8 BASIC AERODYNAMICS 1. . . . . . . . . . . . . . . .

PHYSICS OF AERODYNAMICS & ATMOSHERE 2. . . . . . . . . . . . . . . .

FUNDAMENTAL UNITS 2. . . . . . . . . . . . . . . . . . . . . . . . . . .

SPEED AND ACCELERATION 8. . . . . . . . . . . . . . . . . . . . .FORCE AND WEIGHT 12. . . . . . . . . . . . . . . . . . . . . . . . . . . .WORK AND POWER 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

PRESSURE 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .SPEED OF SOUND 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ATMOSHERE 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BASIC AERODYNAMICS 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CONTINUITY EQUATION 34. . . . . . . . . . . . . . . . . . . . . . . . . .BERNOULLI’S PRINCIPLE 40. . . . . . . . . . . . . . . . . . . . . . . . .LIFT PRODUCTION 46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

PROFILE AND WING GEOMETRY 58. . . . . . . . . . . . . . . . . . . . . . . . . . . .

PROFILE GEOMETRY 58. . . . . . . . . . . . . . . . . . . . . . . . . . . .WING GEOMETRY 68. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIFT AND DRAG 76. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION 76. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .AERODYNAMIC FORCES 78. . . . . . . . . . . . . . . . . . . . . . . . .CL AND CD 84. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

EFFECT OF ANGLE OF ATTACK 88. . . . . . . . . . . . . . . . . . .EFFECT OF PROFILE SHAPE 90. . . . . . . . . . . . . . . . . . . . .EFFECT OF ICE ON SURFACE 96. . . . . . . . . . . . . . . . . . . .

FACTORS AFFECTING DRAG 98. . . . . . . . . . . . . . . . . . . . .POLAR DIAGRAM 102. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .LILIENTHAL DIAGRAM 104. . . . . . . . . . . . . . . . . . . . . . . . . . . .LIFT TO DRAG RATIO 108. . . . . . . . . . . . . . . . . . . . . . . . . . . .

CATEGORIES OF DRAG 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION 110. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .INDUCED DRAG 112. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

EFFECT OF UP/ DOWN WASH 114. . . . . . . . . . . . . . . . . . . .EFFECT OF ASPECT RATIO 116. . . . . . . . . . . . . . . . . . . . . .FORM DRAG 122. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FRICTION DRAG 126. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .BOUNDARY LAYER 130. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .INTERFERENCE DRAG 138. . . . . . . . . . . . . . . . . . . . . . . . . . .

COMPRESSIBLE DRAG 140. . . . . . . . . . . . . . . . . . . . . . . . . . .TOTAL DRAG 144. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIFT DISTRIBUTION 146. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

INTRODUCTION 146. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

EFFECT OF UP/DOWN WASH 148. . . . . . . . . . . . . . . . . . . . .WING DESIGN 150. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .STALL CONDITIONS 152. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BOUNDARY LAYER CONTROL 162. . . . . . . . . . . . . . . . . . . .

THEORY OF FLIGHT 166. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FORCES ACTING ON AN AIRCRAFT 166. . . . . . . . . . . . . . .THEORY OF TURN 172. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIFT COMPENSATION DURING TURN 174. . . . . . . . . . . . .

FLIGHT STABILITY AND DYNAMICS 176. . . . . . . . . . . . . . . . . . . . . . . . . .

STATIC STABILITY 176. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

DYNAMIC STABILITY 178. . . . . . . . . . . . . . . . . . . . . . . . . . . . .STATIC AND DYNAMIC STABILITY 184. . . . . . . . . . . . . . . . .FLIGHT STABILITY INTRODUCTION 190. . . . . . . . . . . . . . .

DIRECTIONAL STABILITY 194. . . . . . . . . . . . . . . . . . . . . . . . .LATERAL STABILITY INTRODUCTION 198. . . . . . . . . . . . . .LATERAL STABILITY 200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .EFFECT OF DIHEDRAL 202. . . . . . . . . . . . . . . . . . . . . . . . . . .

LATERAL DIRECTIONAL INTERACTIONS 206. . . . . . . . . . .SPIRAL DIVE 208. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .DUTCH ROLL 210. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LONGITUDINAL STABILITY 212. . . . . . . . . . . . . . . . . . . . . . . .

TABLE OF FIGURES

EJAMF M08 CAT B1 E

Page ii

Figure 1 International SI-System 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 2 International SI-System 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 3 International SI-System 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 Speed and Acceleration 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 5 Acceleration due to Gravity 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 6 Force and Weight 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 7 Work 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 8 Power 17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 9 Pressure / Static and Dynamic Pressure 19. . . . . . . . . . . . . . . . . .

Figure 10 Sound Waves 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 11 Speed of Sound 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 12 Aircraft Speed 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 13 Mach Number 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 14 Sound Regions 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 15 Atmosphere 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 16 ICAO Standard Atmosphere (ISA) 33. . . . . . . . . . . . . . . . . . . . . .

Figure 17 Flow Pattern in a Tube 35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 18 Continuity Equation 37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 19 Defuser & Jet Outlet 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 20 Valve positions 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 21 Point of Stagnation 43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 22 Pressure Measuring 45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 23 Venturi Tube 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 24 Lift 49. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 25 Lift 51. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 26 Up-wash / Down-wash 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 27 Magnus Effect 55. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 28 Circulation 57. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 29 Geometry of a Profile 59. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 30 Camber of a profile 61. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 31 Thickness of a Profile 63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 32 Relative Wind 65. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 33 Angle of Attack / Angle of Incidence 67. . . . . . . . . . . . . . . . . . . . .Figure 34 Wing Area S 69. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 35 Taper Ratio l 71. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 36 Aspect Ratio 73. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 37 Sweep Angle / Dihedral 75. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 38 Distribution of Static Pressure 77. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 39 Aerodynamic Force 79. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 40 Theoretical Lift 81. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 41 Wind Tunnel 83. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 42 Lift Equation 85. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 43 Drag Equation 87. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 44 Angle of Attack (AOA) 89. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 45 Change of the Profile Thickness 91. . . . . . . . . . . . . . . . . . . . . . . .Figure 46 Change of the Profile Chamber 93. . . . . . . . . . . . . . . . . . . . . . . . .Figure 47 Profile 95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 48 Effect of Ice on Surface 97. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 49 Coefficient of Drag 99. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 50 Factors affecting Drag II 101. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 51 Polar Diagram 103. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 52 Lilienthal Diagram 105. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 53 Relationship between Polar Diagram and Behaviour of an

Aircraft 107. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 54 Lift - Drag Ratio 109. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 55 Categories of Drag 111. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 56 Induced Drag 113. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 57 Effects of Up/Down Wash 115. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 58 Induced Drag Affection by the Aspect Ratio and the Wing

Tip Design 117. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 59 Wing Tips in Nature 119. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 60 Induced Drag Affection by the Aircraft Speed 121. . . . . . . . . . . . .

Figure 61 Airflow with and without Friction 123. . . . . . . . . . . . . . . . . . . . . . . .Figure 62 Ways to reduce Form Drag 125. . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 63 Form Drag 127. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 64 Boundary Layer 129. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 65 Laminar and Turbulent Boundary Layer 131. . . . . . . . . . . . . . . . . .Figure 66 Air Particle in a Boundary Layer 133. . . . . . . . . . . . . . . . . . . . . . . .

Figure 67 Slot in the Profile 135. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 68 Laminar Profile 137. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

TABLE OF FIGURES

EJAMF M08 CAT B1 E

Page iii

Figure 69 Interference Drag 139. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 70 Compressible Drag I 141. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 71 Compressible Drag II 143. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 72 Total Drag 145. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 73 Wing Shape and Lift Distribution 147. . . . . . . . . . . . . . . . . . . . . . . .Figure 74 Wing Design 149. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 75 Wing Twist 151. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 76 Mean Aerodynamic Chord 153. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 77 Center of Lift Conditions 155. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 78 Wing Root Stall 157. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 79 Wing Tip Stall Effects 159. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 80 Wing Tip Stall Prevention 161. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 81 Saw Tooth Leading Edge and Wing Fences 163. . . . . . . . . . . . . .

Figure 82 Vortex Generator 165. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 83 Forces acting on an Aircraft 167. . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 84 Center of Lift / Center of Gravity 169. . . . . . . . . . . . . . . . . . . . . . . .

Figure 85 Steady Flight Conditions 171. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 86 Theory of Turn 173. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 87 Lift Compensation during Turn 175. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 88 Static Stability 177. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 89 Undamped Oscilliation 179. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 90 Damped Oscillation 181. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 91 Divergent Oscillation 183. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 92 Neutral Static Stability 185. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 93 Negative and Positive Static Stability 187. . . . . . . . . . . . . . . . . . . .

Figure 94 Influences on Stability 189. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 95 Flight Stability 191. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 96 Aircraft Axes 193. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 97 Directional Stability 195. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 98 Directional Stability II 197. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 99 Lateral Stability I 199. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 100 Lateral Stability II 201. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 101 Effect of Dihedral 203. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 102 Sideslip 205. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 103 Lateral Directional Interactions 207. . . . . . . . . . . . . . . . . . . . . . . .

Figure 104 Spiral Dive 209. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 105 Dutch Roll 211. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Figure 106 Longitudinal Stability 213. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 107 Quality of Longitudinal Stability 215. . . . . . . . . . . . . . . . . . . . . . . .

m8 b1 b2 ejamf

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