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Contents 1. ATMOSPHERE............................................. 3 1.2 nature................................................3 1.3 properties............................................3 2. AERODYNAMICS........................................... 4 2.1 mass flow.............................................4 2.2 energy................................................4 3. AEROFOILS.............................................. 1 3.1 aerodynamic forces....................................1 3.2 definitions...........................................2 3.3 aerodynamic resultants................................3 3.4 lift & drag...........................................3 3.5 factors affecting forces..............................4 3.5.1............................Lift & drag coefficient 4 3.5.2....................................Angle of attack 5 3.6 centre of pressure....................................6 3.6.1........................Pitching moment coefficient 7 3.7 aerodynamic centre....................................8 3.8 downwash..............................................8 4. DRAG................................................... 1 4.1 drag equation.........................................1 4.2 drag coefficient......................................1 4.3 drag components.......................................1 4.4 flow characteristics..................................1 4.5 form drag.............................................1 4.6 boundary layers.......................................2 4.7 skin friction.........................................3 4.7.1...................................Transition point 3 4.7.2....................................Reynolds number 4 4.7.3..........................Adverse pressure gradient 4 4.8 separation............................................4 4.9 interference drag.....................................5 4.10 induced drag........................................5 4.10.1 Vortex diagram...................................6 4.11 total drag..........................................8 Mod 8 Basic Aerodynamics by COBC 1

Mod 8 Basic Aeromod 2

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Contents

1. ATMOSPHERE...............................................................................................3

1.2 nature..........................................................................................................31.3 properties.....................................................................................................3

2. AERODYNAMICS...........................................................................................4

2.1 mass flow.....................................................................................................42.2 energy..........................................................................................................4

3. AEROFOILS...................................................................................................1

3.1 aerodynamic forces.....................................................................................13.2 definitions....................................................................................................23.3 aerodynamic resultants...............................................................................33.4 lift & drag.....................................................................................................33.5 factors affecting forces................................................................................4

3.5.1 Lift & drag coefficient............................................................................43.5.2 Angle of attack......................................................................................5

3.6 centre of pressure........................................................................................63.6.1 Pitching moment coefficient.................................................................7

3.7 aerodynamic centre.....................................................................................83.8 downwash....................................................................................................8

4. DRAG..............................................................................................................1

4.1 drag equation...............................................................................................14.2 drag coefficient............................................................................................14.3 drag components.........................................................................................14.4 flow characteristics......................................................................................14.5 form drag.....................................................................................................14.6 boundary layers...........................................................................................24.7 skin friction...................................................................................................3

4.7.1 Transition point.....................................................................................34.7.2 Reynolds number.................................................................................44.7.3 Adverse pressure gradient...................................................................4

4.8 separation....................................................................................................44.9 interference drag.........................................................................................54.10 induced drag............................................................................................5

4.10.1 Vortex diagram.................................................................................64.11 total drag..................................................................................................8

4.11.1 Drag polar.........................................................................................8

5. FORCES IN FLIGHT.......................................................................................9

5.1 four forces....................................................................................................95.2 straight & level.............................................................................................95.3 forces in climb............................................................................................105.4 forces in glide & descent..........................................................................115.5 rate of climb (performance).......................................................................11

5.5.1 Power curves......................................................................................135.5.2 Effect of altitude..................................................................................14

6. FORCES & MANOEUVRE.............................................................................1

6.1 centripetal force...........................................................................................16.2 looping.........................................................................................................1

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6.3 load factor....................................................................................................26.4 level turns....................................................................................................26.5 stalling.........................................................................................................3

6.5.1 Stalling speed.......................................................................................36.5.2 Effect of weight / load factor.................................................................36.5.3 Aerofoil Contamination.........................................................................4

6.6 flight envelopes............................................................................................4

7. STABILITY......................................................................................................1

7.1 basic concept & definition............................................................................17.2 static stability...............................................................................................17.3 dynamic stability..........................................................................................27.4 aircraft stability.............................................................................................37.5 design features............................................................................................37.6 control..........................................................................................................77.7 control about 3 axes....................................................................................87.8 lift augmentation.......................................................................................87.9 use of high lift devices............................................................................107.10 flaps, slots & slats..................................................................................117.11 Drag devices............................................Error! Bookmark not defined.

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1.1 1.ATMOSPHERE

Most civil aircraft operate between Sea Level (SL) and 45,000 feet. Our studies of the atmosphere concentrate on this region.

1.2 NATURE

The atmosphere is composed of 78% Nitrogen, 21% Oxygen and 1% of other gases (e.g. Carbon Dioxide, Hydrogen, Neon etc). These percentages are volumetric.

1.3 PROPERTIES

Any gas will have the physical properties such as pressure, density and temperature, which can vary (as in an air-breathing engine). Study of the previous diagrams will show how these properties vary within the atmosphere. Because of these variations, the performance of an aircraft will vary. If meaningful comparisons between measured performance are to be made, some standard or datum conditions must be established. This standard is termed as the International Standard Atmosphere (ISA).

An ISA is based on the following SL criteria.

SL Pressure 1013.2 millibars / hecto pascals

SL Density 1.225 kg/m3

SL Temperature 15ºC / 288 K

SL Lapse rate 1.98ºC / 1000 feet (6.5k/km)

Study of the diagram will highlight a particular characteristic of the lapse rate. It is initially 1.98C/1000 feet and virtually constant up to approximately 36,000 feet, and then the lapse rate is zero. This feature is used in order to establish different regions. The lowest region is the Troposphere and the next region is the Stratosphere. The boundary between the two is known as the Tropopause. (The upper regions need not be seriously considered for our purposes).

Air also contains varying amounts of water vapour. This presence is known as humidity. It is a fact that air is most dense when it is perfectly dry, and vice versa.

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2.AERODYNAMICS

Aerodynamics is the study of air in motion, which includes changes in the physical characteristics, such as pressure and density. (Thermodynamics is similar but is likely to involve significant temperature changes). Because the air is in motion, changes in velocity and mass flow-rates are also important.

Aerodynamics also involves the study of forces being generated (e.g. the "lift" force on a wing), and so a brief mention must be made of some basic principles.

2.1 MASS FLOW

Volumetric flow-rate is given by Av (m3/s) where A = cross-sectional area

Mass-flow rate is given by AV (kg/s) v = velocity

= density

In a converging / diverging duct, the mass flow rate must be constant (what goes in must come out) and if density is unchanged, volumetric flow rate will also remain constant. (This is shown by A1 V1 = A2V2). If the cross-sectional area changes then the velocity will change. (Area reduces, then velocity increases).

2.2 ENERGY

This change in velocity implies a corresponding change in kinetic energy (KE = ½ mv2). The principle known as Conservation of Energy suggests that unless extra energy is introduced into a moving airstream (such as fuel) the overall energy content must remain unchanged from one point to another. Hence, if KE increases some other energy form decreases.

Bernoulli's equation highlights the relationship between pressure energy and kinetic energy.

P + ½v2 = Constantpressure kinetic total(static) (dynamic) ("Pitot")

This can be expressed as p1 + ½v21 = p2 + ½v2. This implies that if v2 is

greater than v1 (as in the throat of a venturi, then p2 is less than p1, i.e. there is a drop in pressure).

This is of particular interest to students of aeronautics because the flow through a venturi has similar characteristics to the flow over an aerofoil. )The aerofoils cambered shaped is virtually the shape of a venturi). Bernoulli's equation showing the relationship between changes of pressure and velocity is used to explain the "lifting" effect of aerofoil (see diagram on the following page).

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3. AEROFOILS

There are several theories used to describe how a lifting force is generated by the action of air in motion past an aerofoil. Whatever the theory, the lift force results from a difference between the pressures acting in the upper and lower surfaces.

3.1 AERODYNAMIC FORCES

The diagrams shows a typical pressure distribution around an aerofoil. This can be determined by the wind - tunnel experiment, where the pressures acting at several points on the aerofoil can be measured using manometers. The manometer will indicate the difference in the static pressure (p) acting at a particular point and the free - stream static (po). This difference (p - po) at each point is plotted to give the distribution shown. The length of the arrows represent the pressure difference; the direction of the arrows represent the sense; towards the surface indicates pressure greater than static, away from the surface indicates less than static (i.e. a "suction"). Different distributions will result from different angles of attack.

Aerodynamic forces result from the action of these aerodynamic pressures acting on the areas of the aerofoil surfaces. It is possibly clearer to understand the effect of these pressures by studying the diagram below. On this, the pressures have been plotted, using the chord line as a datum. Note that negative (suction) pressure has been plotted upwards. The difference (or area enclosed) between the two curves is proportional to the overall lifting - effect of the aerofoil.

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3.2 DEFINITIONS

Aerofoil is the term used to describe the characteristic shape of the cross-section of an aircraft wing, and whose purpose is to generate lift. Discussion of aerofoil performance is the main purpose of this module, and so some descriptions and definitions of this shape will be essential. (Note that the aerofoil section is considered with its plane parallel to the relative airflow).

Relative AirFlow (RAF) is the movement of the air relative to the aircraft (or aerofoil). (In practice, it is the aircraft which moves relative to the air, but in aerodynamic theory and wind - tunnel experiment, it is the air which is considered to be in motion).

Leading Edge is the foremost point on the aerofoil.

Trailing Edge is the rear-most point on the aerofoil.

Chord Line is the straight line joining leading and trailing edges.

Chord Length (C) is the length of the chord line.

Camber Line is the line drawn through points equidistant from the upper and lower surfaces. (The camber line is usually a curved line; the greater the curvature, the greater will be the aerodynamic forces generated).

Camber is the curvature of the aerofoil above and below the chord line.

Thickness of an aerofoil is the greatest distance between the upper and lower surfaces. (It is generally between and way back along the chord line).

Thickness / chord ratio = thickness chord, normally expressed as a percentage.

Angle of Attack () - the angle formed between the chord-line and relative airflow.

Span (b) is the distance from tip to tip, measured perpendicular to the chord line.

Aspect Ratio (AR) is Span chord .

If the wing is tapered, i.e. it has a varying chord, then the AR may be expressed as span2 wing area = .

Wing Area (S) is the area projected onto a plane perpendicular to the normal axis.

Stagnation Point is a point on the surface of the aerofoil where the RAF has been brought to rest.

Wash out is the reduction in the angle of incidence spanwise

from root to tip

Wash in is the increase in the angle of incidence spanwise

from root to tip.

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3.3 AERODYNAMIC RESULTANTS

Whether the student studies pressures or forces depends largely on the depth of his studies. It is simpler to consider forces and this will be sufficient for much of this module.

It has been stated that pressure acting on area produces a force. The force (F) resulting from air in motion, is termed 'an aerodynamic force'. The pressure distribution is then replaced by an arrow representing this force in terms of magnitude and direction.

The line of action of the force determines the centre of pressure; i.e. that point (CP) on the chord line through which the aerodynamic force can be considered to act.

3.4 LIFT & DRAG

It is of greater benefit to resolve the force F into 2 components which are defined as:

Lift - the component of aerodynamic force resolved perpendicular to the RAF.

Drag - the component of force resolved parallel to the RAF.

This is so that variation of lift and drag (associated with variation in angle of attack and camber) can be studied individually. It will be appreciated that the purpose of the aerofoil is to generate lift so as to overcome the effect of weight - the drag should be seen as an unavoidable obstacle to motion

.

3.5 FACTORS AFFECTING FORCES

What factors affect the magnitude of these aerodynamic forces? Clearly, the greater the area and the greater the pressure involved.

What effects the pressure force? The greater the suction, the greater the lift. The suction (p-po) will be greatest when the static pressure (p) is least and this will occur when the velocity (v) is greatest.

Summarising, it can be stated that (following on from Bernoulli).

Aerodynamic force is proportional to

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fluid density × (fluid velocity)2 × (area of body surface)

F proportional to ½v2S

(similarly, Lift and Drag are proportional to ½v2S)

So density, velocity and area are all factors that affect Lift and Drag. (There are a number of other factors but only two more will be considered at this stage.)

Note that we have made a statement of proportionality;

It is not an equation just yet. This will be derived by wind-tunnel the experiment.

3.5.1LIFT & DRAG COEFFICIENT

If an aerofoil is placed in a wind tunnel, tests may be conducted to establish pressure distributions, or to measure forces. Suppose the aerofoil (area S) is placed in the tunnel and air (density ) is drawn across the aerofoil at a constant velocity (v). Then Lift and Drag forces will be generated. These forces may be measured on a force - balance rig. Because it has been stated that forces change as angle of attack () changes, will be measured as well.

Remember that L proportional to ½v2S.

An equation may be formed L = C½v2S by including some number (or coefficient) c.

Now from the experiment, L is measured, , v, S are known (measured) and so C = .

The coefficient used to form the equation has been deduced from the results of the experiment (it is worth noting that the term ½v2 is often replaced by q; therefore C = ).

The same can be done for the drag case.

C = but we must clearly differentiate between the different cases and values of C.

= CL (the lift coefficient).

= CD (the drag coefficient).

The two other factors, which affect the aerodynamic forces, can now be included. It will be found by experiment that CL and CD will vary (or change) when either angle of attack () or aerofoil camber (shape) is changed.

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3.5.2ANGLE OF ATTACK

The factors affecting Lift and Drag have just been outlined. All can be determined by experiment but changes in the force are generally deduced from the relationship between CL (or CD) and . These relationships are best shown graphically. (The general shape of these graphs must be memorised by any aeronautical student!).

Note how CL increases steadily (and linearly) as increases, up to a maximum, after which it decreases rapidly.

Note how CD is a curve that increases steadily, but that the rate of increase becomes greater.

If the experiment were repeated with aerofoil of different camber or shape, the general shape of the graphs would be similar, but the curves would be displaced vertically and/or horizontally.

A final but important point to consider is this section is the Lift to Drag ratio.

= =

Lift is what is required - it should be maximised.

Drag is not required - It should be minimised.

So for maximum aerodynamic efficiency, the ratio should be as great as possible.

This ratio cannot be deduced directly by experiment, but CL and CD can be derives as stated, and the ratio derived by division (CL CD). This ratio is then plotted against .

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This graph clearly indicates that the best (maximum) ratio generally occurs at a relatively small angle of attack (typically 3º - 5º). Designers and operators endeavour to operate any aerofoil at an angle of attack in this range as much as possible.

Finally, a word is introduced that is of great significance - the Stall.

Looking at the diagrams, there is an angle of attack beyond which CL has reduced substantially, CD has increased markedly and has reduced.

This means that there has been a sudden loss of lift and a rapid increase in drag. The aerofoil (wing) is said to have stalled, and is a potentially dangerous scenario if it occurs in flight

Wash out is one method of alleviating sudden loss of lift due to aerofoil stall.

.

3.6 CENTRE OF PRESSURE

The two components, Lift and Drag, have been shown to vary as Angle of Attack varies. But not only does the magnitude of the force vary, but the line of action (and hence the centre of pressure) changes.

As the angle of attack increases, the pressure distribution changes shape, with proportionately greater suction generated towards the forward portion of the wing. This causes a forward movement of the Cp. This forward movement continues until the CL values start to reduce. At this point the Cp now reverses its movement (it moves backwards), as the stall condition is approached.

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So now it can be understood that both force and Cp vary as varies.

3.6.1PITCHING MOMENT COEFFICIENT

Consider the diagram, which shows an aerofoil which can be considered to be pivoted at either A or B. The lift L would cause rotation about the pivot; anticlockwise or nose down about A and clockwise or nose up about B.

Rotation is caused by application of a moment M which itself is dependent on lift L magnitude, multiplied by the distance of the CP from the pivot.

From this, it can be deduced that the strength and sense of the rotation depends on angle of attack and position of the pivot.

Again, we rely on this to be illustrated graphically. Nose-up is considered a positive pitching moment, nose-down is negative.

Just as before, coefficients were introduced to create the Lift and Drag equations, so a pitching moment coefficient CM is introduced.

M = qSc CM

Pitching moment where c = chord length CM = moment coefficient

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As with CL and CD, it is usual to draw graphs using CM rather than M (see diagram below).

3.7 AERODYNAMIC CENTRE

Another interesting feature emerges. There must be some point lying between A and B, such that if the aerofoil was pivoted at that point, the pitching moment (coefficient) would be constant regardless of the angle of attack.

This point is known as the Aerodynamic centre;

i.e. the point on the chord-line about which the pitching moment is constant.

3.8 DOWNWASH

The flow of air around the aerofoil causes variation in speeds and pressures that result in the creation of lift. Lift is the resultant force applied to the airframe, considered perpendicular to the RAF. From Newton’s 3rd Law, there must be an opposite force applied to the air. This ‘reaction’ causes deflection of the airflow as it leaves the trailing-edge, termed ‘downwash’. (There may well be an ‘upwash’ effect ahead of the leading-edge).

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4. DRAG

4.1 DRAG EQUATION

The drag equation so far has been written as:

D = v2S CD (qSCD)

4.2 DRAG COEFFICIENT

It is now appropriate to analyse the drag coefficient CD in order to more fully understand the factors affecting total drag, so that designer and maintenance engineers alike can take whatever steps to minimise drag, which ultimately will allow operation at higher speeds or reduce fuel consumption. Both of these are significant to the economic success of air transport.

4.3 DRAG COMPONENTS

The total drag is considered as the sum of the zero-lift drag and the lift dependent drag. (This means that some drag is always present, even though lift may not be generated, and some drag will be proportional to the lift generated).

4.4 FLOW CHARACTERISTICS

Before considering drag, reconsider streamline flow. So far, the streamlines have been shown as a series of parallel or converging / diverging lines showing the direction of flow at any point. Because of the "layered" appearance, such flow is termed laminar flow and a characteristic is that unless a change is deliberately introduced, it will be unchanged from one instant to another. It is therefore considered as steady flow.

Although streamlines are in concept imaginary, they can be artificially created (e.g. using smoke) and then the observer will notice an extremely important feature. At some point, the laminar flow will cease and be replaced by a mixture of both translational and rotational pattern of flow, whose pattern changes continuously. This unsteady pattern is termed turbulent flow.

The fact that the fluid (air) is now being caused to rotate (stirred) and that this is continuously changing implies that forces are present. This in turn means that energy is expended in creating turbulence. But the only source of energy present must ultimately be the chemical energy in the fuel. So, we can deduce that fuel is used when turbulence is created. The student must appreciate that the creation of turbulence results in the creation of drag.

4.5 FORM DRAG

The change from laminar to turbulent flow is basically a function of the viscosity of the fluid. (Theoretically, a fluid with no viscosity would result in zero drag). How much turbulence occurs is usually dependent on the shape or form of the body being considered. Some shapes produce considerable turbulence; others minimise it. These shapes are obviously to be preferred and are often described as "streamlined". Some recognisable shapes are shown below, and a comparison made of the resulting turbulence. To allow comparison, it is assumed that the shapes present an identical cross-section to the airflow i.e. circular.

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Note also the approximate value of the form drag associated with each shape, assuming the flat plate (disc) as representing 100%.

4.6 BOUNDARY LAYERS

Laminar, turbulent and viscosity have just entered our vocabulary. The region of flow where these have greatest significance is the boundary layer, so - called because it is the layer between the body and the free-stream. (It is called free - stream because it is considered virtually free from the effects of viscosity).

The boundary layer, however, exists because of viscosity. To assist our understanding, imagine a river flowing between two banks. To an observer, the flow rate (velocity) will be greater in the centre of the river. At the bank, the water is very slow - moving, maybe virtually stationary and maybe forming eddies. Between the centre and banks, the flow - velocity reduces. This is comparable to the situation that exists between the free-stream and the body surface.

On the diagram, the length of the arrows indicates the flow velocity at that point. The (parabolic) pattern is termed the velocity distribution or profile.

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4.7 SKIN FRICTION

What is significant about this profile? It implies that each layer of fluid molecules is moving at a different velocity relative to its neighbours. In turn, this means that a frictional force is generated in such a direction to oppose this relative motion. (This is what viscosity creates; it is a resistance to flow). So throughout the boundary layer, there is a frictional force, and this layer exists because of the presence of the (stationary) body and the interaction between its surface (skin) and the fluid. Hence, the introduction of the term skin - friction and its inclusion as a type of drag.

Skin - friction drag depends on :

The surface area.

The viscosity

The rate of change of the velocity (shown by the profile).

The diagram conveys some idea of the layer thickness (it is fairly thin!) The layer is considered to be the region where the velocity relative to the surface (skin) varies from zero to 99% of the free-stream.

4.7.1TRANSITION POINT

Note that the flow is initially laminar, but changes to turbulence at the transition point. Comparing the velocity profiles reveals that the turbulent layer has a greater rate of change of velocity near the surface. This will cause greater friction, which introduces a random (unsteady) element into the flow resulting in a greater degree of mixing with the free-stream. This thickens the turbulent layer and introduces greater kinetic energy. Note the laminar sub-layer whose presence is important, but detailed study is beyond the scope of this module.

The transition point depends on:

Surface condition

Speed of flow

Size of object

Adverse pressure gradient

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4.7.2REYNOLDS NUMBER

The effect of surface condition, speed of flow and size of object basically affect a phenomena termed Reynolds Number (named after the physicist). Reynolds number is very significant in the study of fluid dynamics, particularly when attempting to 'model' full-size situations, but again, a more detailed study is beyond our requirements. It might, however be useful to express Reynolds Number as:

Re =

= density, v = velocity, d = size, = viscosity.

As Reynolds Number becomes greater, the earlier will be the transition point.

4.7.3ADVERSE PRESSURE GRADIENT

The adverse pressure gradient (APG) refers to the point in the flow where the static pressure begins to increase. In nature, fluid flows from high to low pressure; it does not flow from low to high. So if the static pressure now increases (due to shape of the body), a pressure gradient now exists to impede flow. It is not assisting flow - it is an adverse gradient. The student can visualise that this will occur beyond the point of least pressure, i.e. the point on the body where thickness is greatest.

4.8 SEPARATION

The overall effect of friction is to reduce the velocity and energy of the air-flow within the boundary layer. This reduction is further exacerbated by introducing an APG, as with a curved or cambered body. This effect can be shown at several successive points within the boundary-layer. As shown on the following diagram, the boundary-layer is brought to rest and separates, forming a turbulent wake. Beyond the separation point, flow reversal may occur.

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When the boundary layer separates and forms a turbulent wake, much energy has been lost in creating rotational flow and consequently the static pressure within this flow is reduced (this will be restated when vortex flow is considered). This means that there is less static pressure acting on the rear of the body, compared to the front. In turn, this means that a net (pressure) force acts rearwards (= drag). Hence, separated, turbulent flow should be avoided / delayed whenever possible. This is achieved by streamlining and maintaining as smooth a surface as possible.

4.9 INTERFERENCE DRAG

Another element of drag that can be mentioned is Interference drag. Experiments shows that the total drag of the aircraft exceeds the sum of the drags resulting from the component parts. The increase in drag is caused by the individual flow patterns interacting or "interfering" with their neighbours. This is generally reduced by the addition of fairings at the functions of the aircraft components.

In summary, zero-lift drag is a combination of form and skin-friction drag, with the probable addition of interference drag. It is related to the separation of the airflow into a turbulent wake. This will be linked to the separation point, itself a function of Reynolds Number. Increased velocity leads to increased Reynolds Number and earlier separation. In fact, zero-lift drag is directly proportional to speed2.

4.10 INDUCED DRAG

Lift dependent drag is commonly referred to a (lift) Induced drag, although another term, Vortex drag might be more descriptive. Consider the diagram below.

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4.10.1 VORTEX DRAG

The presence of regions of different pressure (as happens when lift is generated) will cause a flow to develop from high to low pressure. This results in a spanwise component forming in addition to the chordwise component. It will be, root to tip on lower surfaces and vice-versa on the upper surface.

At the tip, the flow will rotate as shown. The greater the pressure differences, the greater will be the rotation. Now flow rotations are sometimes weak (eddies) or sometimes form extremely strong vortices (as in hurricanes) and a feature is the high kinetic energy (or rotation), but a low (static) core pressure. At the trailing-edge the chordwise plus spanwise components on the upper and lower surfaces meet to create a series of vortices, termed a vortex sheet. These also drift towards and combine at the tip.

The net effect of these vortices is to induce a downwash additional to that resulting from lift generation. The creation of the vortices, the creation of a downwash component, must imply an expenditure of energy; an increase in (induced) drag. Vortex drag arises from introducing wings of finite span.

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The factors affecting induced drag are:

Lift (weight)

Aspect ratio

Wing planform

Speed

Obviously the greater the weight, the more lift must be created which is the result of greater pressure difference. Greater pressure differences create more downwash / stronger vortices.

A high aspect ratio means that the strength of the spanwise flow component is reduced. Hence, the vortex strengths are reduced.

The vortices tend to combine towards the wing-tip and so an ideal wing-planform will create a lift distribution that minimises these vortices. This ideal is the so-called elliptical distribution or loading, which was attempted on the Spitfire by using an elliptical wing. In practice, the ideal is impossible to achieve totally.

The factors all influence the equation for induced drag coefficient.

CDI =

k = a coefficient introduced to take account of the deviation from the ideal elliptical lift distribution.

It can be deduced that induced drag is directly proportional to weight2, and inversely proportional to the speed2.

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4.11 TOTAL DRAG

The effect of speed on zero-lift and induced drag can be shown on a single graph, and clearly the total drag is the sum of the two.

The total drag, is a minimum at the point at which the two curves intersect. Here, ZLD = ID and this point gives the minimum - drag speed.

4.11.1 DRAG POLAR

The overall or total drag coefficient CD = CDO + CDI,

Total drag coefficient CD = CDO +

The CD Total can be plotted against CL to give a curve known as the Drag Polar.

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The second diagram compares two different aerofoils, curve (a) is a conventional section, curve (b) is a low-drag section. Note that this aerofoil has a significant reduction in profile-drag between the CL range of CL1, and CL2. This shape is commonly termed the drag ‘bucket’ and is a characteristic of an aerofoil designed to maintain laminar flow. For efficient cruise performance, such a section must obviously be operated within these parameters.

5. FORCES IN FLIGHT

The Lift and Drag forces resulting from the passage of air past a body have now been studied in isolation. It is now appropriate to consider them acting on an aircraft in flight.

5.1 FOUR FORCES

The first (and most common) case of an aircraft in flight is when the aircraft is considered to be straight and level (i.e. no change in heading or altitude), and at constant speed. Immediately it can be stated to be in an unaccelerated condition and hence any forces present must be in equilibrium.

From the diagram, we can deduce that L = W, T = D.

(This is simplified here as much as possible - all four forces pass through the same point and no other forces are considered e.g. tail plane forces).

If the equilibrium of the forces is upset, e.g. Thrust (T) is increased; the aircraft will accelerate (until the increase in drag balances the increases in thrust). If the Lift is increased, the aircraft will change direction or altitude.

5.2 STRAIGHT & LEVEL

In reality, of course, the lift and weight do not act through the same point. The CP moves as the angle of attack changes, and the CG depends on the weight distribution. This means that although L = W, their different lines of action means that they create a couple. The different thrust and drag lines are also likely to create a couple. Ideally, the two couples should cancel each other.

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What is desirable is that a reduction in the thrust / drag couple should lead to a nose-down pitching tendency - this requires that the CG should be forward of the CP. (This arrangement will also improve longitudinal stability).

Given that the two couples are most likely unequal, a further moment must be created to restore equilibrium. This is provided by the tailplane. Because the distance from the CG is comparatively large, the size (area) of the tailplane can be small. With a conventional tailplane, it is usual to find that it produces a downward force.

5.3 FORCES IN CLIMB

When analysing forces in the climb, it is first necessary to draw the forces according to the previous definitions (see diagram below).

Again, it is assumed that the forces are in equilibrium. The analysis then begins by resolving the weight force into two components, perpendicular and parallel to the flight path. The forces in these directions can now be equated.

L = W cos

T = W sin + D

Two interesting and important facts emerge. If the aircraft is climbing, O and cos 1

therefore Lift is less than Weight.

Similarly, sin O and Thrust is greater than Drag.

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We can therefore deduce that aircraft climb because of increased thrust, and not increased lift. (Theoretically, this makes sense, because the aircraft gains height and therefore potential energy. The energy input is through the increase in thrust, itself resulting from the 'burning' or expenditure of fuel (chemical energy).

5.4 FORCES IN GLIDE & DESCENT

The arrangement of forces in the descent (or glide) is similar but not identical to the climb. The diagram below clarifies the situation. The weight has again been resolved into two components.

The equations becomes:

L = W cos

T + W sin = D (the W sin component has changed in direction)

In the glide, T is assumed to be zero, and W sin = D. The weight component now balances drag 'gap' - potential energy is now traded in order to maintain kinetic energy or flying speed.

In both climb and descent, the greatest angle of climb, or minimum angle of glide (giving greatest gliding range) is when the aircraft is flown at minimum drag speed, coincident with best L/D ratio.

5.5 RATE OF CLIMB (PERFORMANCE)

Climb performance, or rate of climb (ROC), is theoretically a little more complicated. In the previous discussion, climb performance was considered in terms of angle of climb and by equating forces. Rates of climb (usually expressed in feet per minute) involve lifting the aircraft (weight) at a certain rate (speed). Hence, rate of climb implies lifting a weight (force); i.e. doing work. But rate of doing work is power, power is force x speed.

We have seen that when work is done, energy is expended (or converted). When climbing, extra fuel (energy) is expended, potential energy is gained. But the fuel energy is expended in two areas; in maintaining speed whilst overcoming drag, and in increasing altitude. But how much is used in each area?

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The left-hand diagram shows that sin =

The right-hand diagram restates that sin =

Combining these two equations, ROC = =

But, TV = Power Available (from engine), and

DV = Power Required (by airframe)

TV - DV therefore equals the excess of power available to increase the altitude.

It should be noted that the kinematics of bodies in motion requires that True Air Speed (TAS) is employed.

5.5.1POWER CURVES

Another graph becomes of fundamental importance to analysis of climb performance; the plot of power required and power available, against TAS.

Clearly, the excess of power available for climbing is equal to the vertical

distance (difference) between the power available and power required curves. Study of the diagram shows that this difference is dependent on the aircraft speed. So to achieve the best rate of climb, a particular speed must be selected, i.e. the best climb speed.

To the maintenance engineer, Rate of Climb represents a useful measure of aircraft performance (and therefore of aircraft condition). Reduced thrust or increased drag will both have the effect of reducing the vertical distance which represents excess power. If an aircraft on test fails to achieve the scheduled ROC, then an investigation as to the possible cause should be made. Note the importance of operating at the best climb speed.

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5.5.2EFFECT OF ALTITUDE

Of interest, but of less importance, to the maintenance engineer is the effect of altitude on ROC.

The curves move to the upward and to the right, but the net effect is to offer a reduced ROC.

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6. FORCES & MANOEUVRE

6.1 CENTRIPETAL FORCE

The word "manoeuvre" is introduced here so as to imply a change of direction or flight path. (The speed may also change but this will not be considered here. A change in direction must imply a change in velocity (velocity is a vector quantity) and by definition, an acceleration must be present. If an acceleration is present, a resultant force must exist to cause it. (The forces present are not in equilibrium). Change of direction therefore requires a resultant force, termed the centripetal force (CPF); the force that must be present in order for a body to change its direction of motion.

But the only forces available to act on an aircraft are aerodynamic forces, (thrust vectoring - forces will not be considered here), and changes to these forces are dependent on changes in CL (itself dependent on and shape changes). Fundamentally, therefore, manoeuvre will depend on the changes in CL applied to the main aerofoil (wing). Manoeuvres can be accomplished in the vertical (looping) plane or in the horizontal (banking) plane, (the combination of both forms is often present, but not considered here for reasons of clarity and simplicity).

6.2 LOOPING

Consider an aircraft diving towards the ground. At some point, the pilot wishes to stop the descent and position the aircraft to climb away from the ground.

At A, he pulls back on the control column, which raises the elevator so as to increase the download on the tailplane. The resulting moment pitches the aircraft so as to increase the angle of attack of the mainplane , this increases CL. The effect is to increase the mainplane Lift, perhaps considerably. The excess of lift, over and above that required to overcome weight, provides a CPF in the looping plane and the aircraft now follows a curved flight path towards B. At B, the aircraft is now in the desired attitude, back pressure on the column is reduced, mainplane and CL regain their original values and the flight path again follows a straight line.

Throughout that portion of the flight-path AB, the increased lift puts additional force or stress on the airframe and occupants. They experience the reaction to the CPF, the centrifugal force (CFF). The excess of force is often termed the 'g' force.

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6.3 LOAD FACTOR

The 'g' force can be considered as a comparison between the lift generated and the weight of the aircraft.

g = , this is often termed the Load Factor.

Note that if the flight path is as shown, the lift force (and CPF) is considered as negative and hence the Load Factor is also negative.

Because of the increased stresses, aircraft are designed with 'g' limits. Because violent manoeuvres could result in over-stressing, aircraft are operated within 'g' limits, both positive and negative. Combat aircraft are designed to be more manoeuvrable and therefore have higher 'g' limits than transport aircraft. Similarly, pilots are provided with 'g' suits to increase their personal 'g' thresholds.

6.4 LEVEL TURNS

A similar situation is found in the horizontal plane when the aircraft changes heading. The pilot must bank the aircraft so that the horizontal component of lift provides a CPF. But to maintain the vertical component equal and opposite to weight, he must apply back-pressure on the control column in order to increase lift. Hence, the load factor increases beyond 1 in a horizontal turn as well.

It is worth recalling that CPF is equal to:

CPF =

where v = speed, r = radius of turn and w = weight.

Also, it can be proved that tan = where = angle of bank.

So increased weight, high speed and "tight" radius of turn all impose high load factors on aircraft.

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It should also be appreciated that increased angle of attack leads to increased drag coefficient and increased drag. Therefore, manoeuvres involving high 'g' forces require considerable increase in thrust.

6.5 STALLING

Recalling the graphs showing variation of CL and CD which accompany changes in , it was stated that the wing stalled beyond a certain . This is known as the stalling angle.

If an aircraft is flown straight and level and the thrust is reduced, the aircraft will reduce speed (drag is exceeding thrust). The pilot can maintain lift, by raising the nose to achieve a higher CL. At some point (speed), however, the aircraft will reach the stalling angle, the CL reduces and the aircraft stalls, suddenly losing altitude.

L (=W) = ½v2S CL

To maintain equality, as v2 decreases, CL must increase. When CL reaches its maximum value, v reaches its minimum value of flying speed - the basic stall speed.

The stall has occurred because the separation point has now moved so far forward that the bulk of the airflow over the upper surface has separated or become detached. (On many of the relevant graphs, a dotted line indicates theoretical behaviour of an airflow, a full line shows actual behaviour because of separation).

A pilot is introduced to the stall and stalling speed, at an early stage of his training. He learns to recognise and recover from it, and is encouraged to avoid it!

6.5.1STALLING SPEED

But it is important to appreciate that the stall is primarily dependent on angle of attack (), not speed (v). An aircraft can in fact stall at any speed, if the critical stalling angle is exceeded. This may happen during a manoeuvre when the maximum CL is exceeded. The new (higher) stalling speed can be deduced from;

Manoeuvre stall speed = basic stall speed

6.5.2EFFECT OF WEIGHT / LOAD FACTOR

Increase in weight will require increase in lift, and so affect in turn the basic stall speed.

Stall speed = basic stall speed

The stall speeds at higher load factors, the positive and negative 'g' limits and the maximum (diving) speed form the boundaries of the aircraft's flight envelope.

6.5.3AEROFOIL CONTAMINATION

Aerofoil performance is fundamentally influenced by shape and surface characteristics, which determine flow-pattern and degree of separation. Any surface irregularity can cause a marked change, which may include changes in stall behaviour. Such irregularities may result from contamination by ice and snow accretion. Several accidents have been the result, and for this reason, careful inspection and rectification is essential before aircraft operation in adverse weather conditions.

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6.6 FLIGHT ENVELOPES

The so-called flight envelope encloses an area in which the aircraft may operate, without either stalling, exceeding 'g' limits, or exceeding speed limits.

An example is shown below.

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7. STABILITY

1.4 BASIC CONCEPT & DEFINITION

The aircraft has now been considered in both the steady flight path condition and during changes of direction (manoeuvre). It is now necessary to investigate how the designer includes features in order to maintain or encourage either condition.

For example, it will be presumed that a steady flight path is to be maintained. If the aircraft deviates from this flight path, the aircraft should be able to regain it, without control input from the pilot.

In any dynamic system, the ability of the system to regain the desired (set) condition is termed stability.

A pendulum is a classic example. It (the weight) normally hangs vertically. If it is displaced and released, it immediately moves back towards the original position. (In fact, of course, it swings past that position - the restoring force of gravity reverses its effect and it swings back again. It will swing to and fro (oscillate) many times before the oscillations (displacements) die away). Such a system is a stable system.

But a system can be unstable. Consider the 'bowl and ball' analogy.

1.5 STATIC STABILITY

If the ball is displaced and released, its initial reaction will describe its stability.

In the first diagram, it will move back towards the initial position, it has positive stability.

In the second diagram, it will not move, it remains in the new position and is described as having neutral stability.

In the third diagram, it will move further away from the initial position, it has negative stability, or is unstable.

Note that the above is the initial part of considering stability, the immediate reaction or tendency to movement following initial displacement is used to determine the static stability of the system.

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1.6 DYNAMIC STABILITY

So, following initial displacements the system may oscillate about the neutral position if the system is statically stable. The manner of the oscillations (meaning the change in amplitude) is used to describe the system dynamic stability.

The diagram considers the oscillation of an aircraft in the pitching plane, above and below the desired horizontal flight path. The oscillation resembles a sinusoidal function. (This is characteristic of many oscillations or vibrations). In theory, such oscillations continue indefinitely. In practice, the oscillations steadily reduce and die away.

The first diagram is unusual and represents 'dead-beat' stability.

If the amplitude decreases, the aircraft is dynamically stable, if it increases it is dynamically unstable.

When the amplitude remains constant, it is neutrally stable in the dynamic sense.

Most systems are designed to be statically and dynamically stable.

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1.7 AIRCRAFT STABILITY

Considering the stability of an aircraft, we might ask two questions. Can it oscillate, and if so, what are the neutral or zero displacement positions?

The first answer is 'yes', where the oscillations are related to angular displacements about any of the three axes. The zero displacements are considered to be those associated with straight and level flight.

Rotation about the lateral axis is termed pitch;

Rotation about the longitudinal axis is termed roll;

Rotation about the normal axis is termed yaw.

A stable aircraft will dampen oscillations that may occur about any axis, following some initial (probably random) displacement.

1.8 DESIGN FEATURES

If an aircraft is to be stable, it is obvious from the previous paragraphs that if the aircraft has been momentarily displaced relative to its flight path, there must be a restoring force or moment to return it to its original altitude. Recalling that a moment is the product of force and distance, we then deduce that an aerodynamic force must be generated at some distance from the aircraft's centre of gravity (about which the aircraft has been displaced / rotated).

Displacements about all three axes must be considered.

The easiest one to consider is displacement (yaw) about the normal axis. The diagram shows that this will cause an angle of attack to be created between the fin (vertical stabiliser) and the relative airflow, such that an aerodynamic force / moment will be created that restores the aircraft towards its original heading / direction. (As the displacement reduces, the moment reduces and the aircraft will

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again 'heads' towards the relative airflow - just like a weathercock heads into wind).

The fin gives an aircraft directional stability (about the normal axis).

The manner in which the tailplane (horizontal stabiliser) acts is similar in principle but somewhat more complicated in detail. The diagram below shows the aircraft displaced in the pitching plane. Now two aerofoils are involved, the mainplane and tailplane.

The mainplane angle of attack increases, and as drawn, this creates more lift and a forward movement of the centre of pressure. This creates an upsetting moment tending to destabilise the aircraft. (A tail-less aircraft is therefore inherently unstable).

The tailplane also generates lift so as to create a restoring moment. For the aircraft to be statically stable, clearly the restoring moment must be greater than the upsetting moment. By comparing these moments, it becomes clear how important the position of the centre of gravity becomes.

As the centre of gravity moves aft, the aircraft becomes less stable, due to the changing distances and the effect on the moments.

As the centre of gravity moves forward, the aircraft becomes more stable.

The tailplane gives an aircraft longitudinal stability (about the lateral axis).

Lateral stability considers aircraft movement / displacement in the rolling plane.

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If an aircraft has 'dropped' a wing, it should be obvious from the preceding paragraphs that a moment to raise that wing is required. But how is this to be achieved? Consider the first diagram. An aircraft that has 'dropped' a wing will side-slip towards that wing because of the imbalance of the two forces which has resulted. It is the change in aerodynamic forces resulting from this side-slipping motion which will create a restoring moment.

The most common design feature employed to promote lateral stability is the introduction of dihedral. The diagram indicates the angle concerned. Dihedral results in the 'dropped' wing meeting the revised relative airflow (due to side-slip) at a greater angle of attack than the upper wing. The net effect is therefore to create a restoring moment which is tending to roll the aircraft back towards straight and level (at which point the side-slip stops and the restoring moment becomes zero).

The next diagram shows the effect of the 'keel' area above the centre of gravity. This will also 'right' the aircraft (similar to a yacht-keel). Note that if the keel-area is mostly aft of the centre of gravity, then an additional effect is to yaw the aircraft towards the dropped-wing.

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In later studies, it will be appreciated that designers employ swept-wings to allow flight at high speeds. But an added bonus is that swept-wings encourage lateral stability. Consider the diagrams. In the first, the aircraft is flying straight and level.

The relative airflow meets both left and right leading edges at the same angle. (The RAF is then shown as two components - one normal and one parallel to the leading edges).

In the second diagram, the aircraft has dropped the left wing and is side-slipping. Due to the angle of sweep-back, the RAF now meets the leading-edges at different angles, and now has different components in respect of each wing. It will be recalled that it is the chordwise (or normal) component that creates lift and reference to the diagram shows that greater chordwise component occurring over the dropped-wing will therefore generate more lift, so as to create a rolling moment that restores the aircraft to (straight) and level flight.

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Another feature which results in enhanced lateral stability is that of a high-(mounted) wing. The designer has probably employed a high-wing because of the intended role for the aircraft but with the centre of pressure above the centre of gravity, there is an inherent 'righting' effect, in the manner of a pendulum.

Several design features have been considered which result in lateral stability. But an aircraft that is very stable will be unresponsive to control movements. Stability requirements have to complement control requirements. An aircraft that has excessive stability is as undesirable as one that lacks stability. The right 'balance' between stability and control is often dictated by the intended role of the aircraft. An aircraft that possessed all the features described would probably be too stable. So a swept-wing, high-wing aircraft might incorporate anhedral (the opposite to dihedral) in order to reduce the degree of stability.

The above paragraphs have analysed features which create a moment so as to restore the aircraft towards its undisturbed or original position. They contribute static stability. Dynamic stability in the manner in which the aircraft moves or oscillates towards / about that position. This will depend on the variation of the forces in respect of displacement / time and is too complex for this module.

1.9 CONTROL

The previous section has considered stability, where design features have been included in order to maintain or regain a desired flight path.

If the aircraft is to be manoeuvred, (i.e. the flight path is to be changed) it will be necessary to de-stabilise the aircraft. So it appears that stability and manoeuvrability are conflicting requirements - increasing one characteristic decreases the other.

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To de-stabilise the aircraft, aerodynamic forces must be created for as long as is necessary to cause a rotation about one or more of the axes. These forces are created simply by modifying the shape and angle of attack of the appropriate aerofoil. This is done generally by hinging the trailing-edge, thus allowing it to respond to control inputs from the pilot or autopilot.

Elevators are hinged to the tailplane and cause the aircraft to pitch, up or down. (It should be clear that the control surface movement will create a force in the opposite direction).

The Rudder is hinged to the fin and causes the aircraft to yaw, left or right.

Ailerons are hinged to the out-board trailing edge of the mainplanes. They must move so as to create a difference in the forces on the left and right wings. In so doing, they cause the aircraft to Roll. They must, therefore, move in opposite directions, one goes up, the other goes down.

A problem that arises with the operation of the ailerons is that of adverse yaw. What is this? It will be assumed that a pilot wishes to make a change of heading (direction), and that he must first bank or roll the aircraft towards the "inside" of the turn. The aircraft will then follow a curved path, yawing as it does so in the same direction as the turn. However, the rising (upward) wing in generating more lift also generates more (induced) drag than the descending wing. This unbalance in the drag forces results in a moment which causes a rotation (yaw) in the opposite direction to that first intended, hence, it is termed adverse yaw.

It can be alleviated by the use of rudder, but subtle aerodynamic features can produce the same effect.

1.10 CONTROL ABOUT 3 AXES

To the maintenance engineer, the effect of the controls is very simple - as movement of the control column produces a control-surface movement which creates a force which causes a rotation about one of the three axes. In practice, and from the pilots viewpoint, it is less simple as there is usually some cross-coupling response. This is sometimes termed as the secondary effect of control, meaning that movement of the control-column produces the desired primary effect, but may be accompanied by a secondary effect, involving rotation about another axis.

Active Stability. This is when the equilibrium of an aircraft is disturbed, the flight controls are activated so as to develop forces or moments tending to restore the original condition.

1.11 LIFT AUGMENTATION

One of the greatest attractions of air transport is its relatively high speed and consequent ability to travel great distances in minimum time. This is important to operator and passenger alike. This has resulted in the development of aerofoils which have low drag but also low lift coefficient. (This means that the lift is derived largely as a result of the V2 term, rather than CL).

In turn, this means that as the aircraft slows down, the pilot tries to compensate for the reducing V2 term, by increasing the CL term towards a maximum. But there is a limit to this CL maximum (i.e. the stalling speed angle) and so the stalling speed will be relatively high for a modern aerofoil. This has a profound disadvantage as far as airfield performance is concerned, as it means that take-off and landing distances are lengthened considerably.

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What is needed is the ability to change the shape of the aerofoil (giving higher CL values) and/or the ability to delay separation (giving higher stalling angles, and consequent higher CL values). These are the features of Lift Augmentation.

The devices which are commonly incorporated in order to increase CL are flaps (generally on the trailing-edge, but increasingly common on the leading-edge as well), slats and slots (typically on the leading-edge), and systems which allow some control of the boundary-layer behaviour.

Flaps are used change the shape of the wing. They generally consist of a hinged trailing-edge to the mainplane, extending from just inboard of the ailerons, to the wing-root. They range from the simple plain flap to the multi-section Fowler flap, which moves rearwards at the same time as hinging downwards. (Hence, the area increases as well as the CL value). The different types and their individual characteristics are shown in a later diagram.

In order to delay separation which is a feature of high angles of attack, it is usual to modify the leading-edge in order to present the wing at a more favourable angle. This can be achieved by leading-edge flaps or by slats (and maybe slots). The airflow does not encounter such a strong adverse pressure gradient, and so separation is delayed. The addition of a slot allows air from beneath the aerofoil to accelerate into the airflow above the aerofoil thus adding to its energy, so delaying separation. Again, characteristics are shown in the diagram. Boundary Layer Control in where high-energy air is bled from a source (e.g. the engine) and added to the boundary layer.

The above characteristics of these devices are shown on the diagram on the following page, with CL plotted against . The graphs confirm the information given on the diagram listing the devices in detail.

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1.12 USE OF HIGH LIFT DEVICES

A modern airliner may have several different flap-settings (often designated by a setting in degrees e.g. 10º, 22º, 27º and 30º) which will be selected at different stages during the flight. These setting are essentially related to particular aircraft types, and it is more appropriate to consider the settings as simply Up (for the Cruise), Intermediate (for Take-off and climb) and Full (for Landing). This is because use of the flaps increases lift and drag, but in varying amounts, as shown in the table.

Effect on:-

Flap Setting Lift Coefficient Drag Coefficient Lift / drag

Up (cruise) - - Maximum

Intermediate (t/o) (e.g. 10 and 22)

Large Increase Small Increase Decrease

Full (landing)(e.g. 27 and 30)

Small Increase Large Increase Large Decrease

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1.13 FLAPS, SLOTS & SLATS

High-Lift Devices

Increase of

maximum lift

Angle of basic aerofoil

at max. lift

Remarks

Basic Aerofoil

-- 15Effects of all high-lift devices depend on shape of basic aerofoil.

Plain or Camber Flap

50% 12

Increase camber. Much drag when fully lowered. Nose-down pitching moment.

Split Flap

60% 14

Increase camber. Even more drag than plain flap. Nose-down pitching moment.

Zap Flap

90% 13

Increase camber and wing area. Much drag. Nose-down pitching moment.

Slotted Flap

65% 16

Control of boundary layer. Increase camber. Stalling delayed. Not so much drag.

Double-slotted Flap

70% 18

Same as single-slotted flap only more so. Treble slots sometimes used.

Fowler Flap

90% 15

Increase camber and wing area. Best flaps for lift. Complicated mechanism. Nose-down pitching moment.

Double-Slotted Flower Flap

100% 20

Same as Fowler flap only more so. Treble slots sometimes used.

table continued....

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table continued….

High-Lift Devices

Increase of

maximum lift

Angle of basic aerofoil

at max. lift

Remarks

Krueger Flap

50% 20

Nose-flap hinging about leading edge. Reduces lift at small deflections. Nose-up pitching moment.

Slotted Wing

40% 20Controls boundary layer. Slight extra drag at high speeds.

Fixed Slat

50% 20

Controls boundary layer. Increases camber and area. Nose-up pitching moment.

Movable Slat

60% 22

Controls boundary layer. Increases camber and area. Greater angles of attack. Nose-up pitching moment.

Slat and Slotted Flap

75% 25

More control of boundary layer. Increased camber and area. Pitching moment can be neutralised.

Slat and Double-Slotted Fowler Flap

120% 28

Complicated mechanisms. The best combination for lift; treble slots may be used. Pitching moment can be neutralised.

Blown Flap

80% 16Effect depends very much on details of arrangement.

Jet Flap

60% ?Depends even more on angle and velocity of jet.

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