Basic Aerodynamics module 4

7/23/2019 Basic Aerodynamics module 4

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Contents

1. ATMOSPHERE.................................................................................................1

1.1 nature.......................................................................................................... 11.2 properties....................................................................................................1

2. AERODYNAMICS............................................................................................1

2.1 mass flow.................................................................................................... 12.2 energy.........................................................................................................1

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

3.1 aerodynamic forces.....................................................................................13.2 definitions....................................................................................................23.3 aerodynamic resultants...............................................................................23.4 lift & drag.....................................................................................................33.5 factors affecting forces................................................................................ 3

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

3.6 centre of pressure....................................................................................... 6

3.6.1 Pitching moment coefficient..................................................................73.7 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 drag......................................................................................... 64.11 total drag...................................................................................................8

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

5. FORCES IN FLIGHT........................................................................................1

5.1 four forces................................................................................................... 15.2 straight & level.............................................................................................15.3 forces in climb ............................................................................................25.4 forces in glide & descent............................................................................35.5 rate of climb (performance).........................................................................3

5.5.1 Power curves........................................................................................45.5.2 Effect of altitude....................................................................................5

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

6.1 centripetal force...........................................................................................16.2 looping.........................................................................................................16.3 load factor....................................................................................................2

6.4 level turns....................................................................................................26.5 stalling ........................................................................................................3

6.5.1 Stalling speed.......................................................................................3

Basic Aerodynamics by COBC - Issue 1 - 28 May 2013 Page 1



6.5.2 Effect of weight / load factor..................................................................36.5.3 Aerofoil Contamination..........................................................................3

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............................................................................................2

7.5 design features............................................................................................37.6 control.........................................................................................................77.7 control about 3 axes....................................................................................87.8 aerodynamic balancing................................................................................97.9 balance of tabs..........................................................................................107.10 fixed & trim tabs......................................................................................117.11 balance tabs............................................................................................127.12 lift augmentation......................................................................................137.13 use of high lift devices.............................................................................147.14 flaps, slots & slats....................................................................................157.15 Drag devices..........................................................................................17

8. HIGH SPEED FLIGHT......................................................................................18.1 high speed airflow....................................................................................... 18.2 shock waves................................................................................................1

8.2.1 Mach angle & Mach cone......................................................................28.3 growth of a shockwave system....................................................................38.4 speed of sound............................................................................................38.5 mach number..............................................................................................48.6 effects of a shockwave................................................................................68.7 shock induced separation............................................................................88.8 shock induced drag.....................................................................................8

8.8.1 Buffet.................................................................................................... 88.8.2 High speed / low incidence stall ( shock stall).......................................9

8.9 centre of pressure changes.........................................................................98.10 controlled separation - conical vortex lift................................................108.11 transonic flight.........................................................................................108.12 Critical mach (mcrit).................................................................................11

8.12.1 Transonic wing planform...................................................................118.13 sweep back............................................................................................. 118.14 instability..................................................................................................138.15 the super critical wing..............................................................................148.16 shock-free compression..........................................................................158.17 the transonic area rule ............................................................................168.18 buffet boundary....................................................................................... 17

8.19 airflow through an oblique shockwave.....................................................188.20 supersonic aerofoil sections....................................................................188.20.1 Flat plate aerofoil..............................................................................198.20.2 Generation of lift................................................................................198.20.3 Double wedge aerofoil section..........................................................208.20.4 Bi-convex aerofoil section.................................................................218.20.5 Pressure distribution.........................................................................21

8.21 supersonic wing planforms......................................................................228.21.1 The unswept supersonic wing...........................................................228.21.2 The swept supersonic wing...............................................................238.21.3 Subsonic & supersonic trailing edges...............................................248.21.4 Supersonic engine intakes................................................................25

9. HELICOPTER AERODYNAMICS.....................................................................1

9.1 cyclic & collective controls...........................................................................3




9.2 Anti-torque control.......................................................................................49.3 effect of the tail rotor....................................................................................59.4 main rotor head configuration & movement.................................................5




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1. ATMOSPHERE

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

1.1 NATURE

The atmosphere is composed of 78% Nitrogen, 21% Oxygen and 1% of other

gases (e.g. Carbon Dioxide, Hydrogen, Neon etc). These percentages arevolumetric.

1.2 PROPERTIES

Any gas will have the physical properties such as pressure, density andtemperature, which can vary (as in an air-breathing engine). Study of the abovediagram will show how these properties vary within the atmosphere. Because of these variations, the performance of an aircraft will vary. If meaningfulcomparisons between measured performance are to be made, some standard or datum conditions must be established. This standard is termed as theInternational 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 1.98°C/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 differentregions. The lowest region is the Troposphere and the next region is theStratosphere. 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 ashumidity. It is a fact that air is most dense when it is perfectly dry, and viceversa.




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2. AERODYNAMICS

Aerodynamics is the study of air in motion, which includes changes in thephysical characteristics, such as pressure and density. (Thermodynamics issimilar 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 ρ AV (kg/s) v = velocity

ρ = density

In a converging / diverging duct, the mass flow rate must be constant (what goesin must come out) and if density is unchanged, volumetric flow rate will alsoremain constant. (This is shown by A1 V1 = A2V2). If the cross-sectional areachanges 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 thatunless extra energy is introduced into a moving airstream (such as fuel) theoverall 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 andkinetic energy.

P + ½ρv2 = Constant

pressure kinetic total(static) (dynamic) ("Pitot")

This can be expressed as p1 + ½ρv

2

1 = p2 + ½ρv. This implies that if v2 isgreater than v1 (as in the throat of a venturi, then p2 is less than p1, i.e. there isa drop in pressure).

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







3. AEROFOILS

There are several theories used to describe how a lifting force is generated bythe action of air in motion past an aerofoil. Whatever the theory, the lift forceresults 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 canbe determined by the wind - tunnel experiment, where the pressures acting atseveral points on the aerofoil can be measured using manometers. Themanometer will indicate the difference in the static pressure (p) acting at aparticular point and the free - stream static (po). This difference (p - po) at eachpoint is plotted to give the distribution shown. The length of the arrows representthe pressure difference; the direction of the arrows represent the sense; towardsthe surface indicates pressure greater than static, away from the surfaceindicates less than static (i.e. a "suction"). Different distributions will result fromdifferent angles of attack.

Aerodynamic forces result from the action of these aerodynamic pressures actingon the areas of the aerofoil surfaces. It is possibly clearer to understand theeffect 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) betweenthe two curves is proportional to the overall lifting - effect of the aerofoil.




3.2 DEFINITIONS

Aerofoil is the term used to describe the characteristic shape of the cross-sectionof an aircraft wing, and whose purpose is to generate lift. Discussion of aerofoilperformance is the main purpose of this module, and so some descriptions anddefinitions of this shape will be essential. (Note that the aerofoil section isconsidered 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 inaerodynamic 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 thecurvature, the greater will be the aerodynamic forces generated).

• Thickness of an aerofoil is the greatest distance between the upper andlower 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 (α) - 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 beexpressed 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.

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 pressuredistribution 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 toact.

3.4 LIFT & DRAG

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

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

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 thepurpose 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, thegreater 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 thiswill occur when the velocity (v) is greatest.




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

Aerodynamic force is proportional tofluid density × (fluid velocity)2 × (area of body surface)

F proportional to ½ρv2S

(similarly, Lift and Drag are proportional to ½ρv2S)

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 theexperiment.

3.5.1LIFT & DRAG COEFFICIENT

If an aerofoil is placed in a wind tunnel, tests may be conducted to establishpressure distributions, or to measure forces. Suppose the aerofoil (area S) is

placed in the tunnel and air (density ρ) 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 forceschange as angle of attack (α) changes, α will be measured as well.

Remember that L proportional to ½ρv2S.

An equation may be formed L = C½ρv2S by including some number (or

coefficient) c.

Now from the experiment, L is measured, ρ, 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 ½ρv2 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 beincluded. It will be found by experiment that CL and CD will vary (or change) when

either angle of attack (α) or aerofoil camber (shape) is changed.




3.5.2ANGLE OF ATTACK

The factors affecting Lift and Drag have just been outlined. All can be determinedby experiment but changes in the force are generally deduced from the

relationship between CL (or CD) and α. These relationships are best shown

graphically. (The general shape of these graphs must be memorised by anyaeronautical student!).

Note how CL increases steadily (and linearly) as α 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, thegeneral shape of the graphs would be similar, but the curves would be displacedvertically 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 α.




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

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 hasreduced 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 dangerousscenario if it occurs in flight.

3.6 CENTRE OF PRESSURE

The two components, Lift and Drag, have been shown to vary as Angle of Attackvaries. 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, withproportionately greater suction generated towards the forward portion of thewing. 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 itsmovement (it moves backwards), as the stall condition is approached.




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

3.6.1PITCHING MOMENT COEFFICIENTConsider the diagram, which shows an aerofoil which can be considered to bepivoted 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 liftL 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 dependson angle of attack and position of the pivot.

Again, we rely on this to be illustrated graphically. Nose-up is considered apositive 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 lengthCM = moment coefficient




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

3.7 AERODYNAMIC CENTRE

Another interesting feature emerges. There must be some point lying between Aand 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 thatresult 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 anopposite force applied to the air. This ‘reaction’ causes deflection of the airflowas it leaves the trailing-edge, termed ‘downwash’. (There may well be an‘upwash’ effect ahead of the leading-edge).




4. DRAG

4.1 DRAG EQUATION

The drag equation so far has been written as:

D = ρv2S CD (qSCD)

4.2 DRAG COEFFICIENT

It is now appropriate to analyse the drag coefficient CD in order to more fullyunderstand the factors affecting total drag, so that designer and maintenanceengineers alike can take whatever steps to minimise drag, which ultimately willallow operation at higher speeds or reduce fuel consumption. Both of these aresignificant 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 dependentdrag. (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 havebeen shown as a series of parallel or converging / diverging lines showing thedirection of flow at any point. Because of the "layered" appearance, such flow istermed laminar flow and a characteristic is that unless a change is deliberatelyintroduced, it will be unchanged from one instant to another. It is thereforeconsidered 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 mixtureof both translational and rotational pattern of flow, whose pattern changescontinuously. This unsteady pattern is termed turbulent flow.

The fact that the fluid (air) is now being caused to rotate (stirred) and that this iscontinuously changing implies that forces are present. This in turn means thatenergy is expended in creating turbulence. But the only source of energy present must ultimately be the chemical energy in the fuel. So, we can deducethat fuel is used when turbulence is created. The student must appreciate thatthe 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 thebody being considered. Some shapes produce considerable turbulence; othersminimise it. These shapes are obviously to be preferred and are often describedas "streamlined". Some recognisable shapes are shown below, and acomparison made of the resulting turbulence. To allow comparison, it isassumed that the shapes present an identical cross-section to the airflow i.e.circular .




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 - calledbecause 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, theflow 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 tothe 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.




4.7 SKIN FRICTION

What is significant about this profile? It implies that each layer of fluid moleculesis moving at a different velocity relative to its neighbours. In turn, this means thata 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 theboundary layer, there is a frictional force, and this layer exists because of thepresence 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 agreater rate of change of velocity near the surface. This will cause greater friction, which introduces a random (unsteady) element into the flow resulting in agreater degree of mixing with the free-stream. This thickens the turbulent layer and introduces greater kinetic energy. Note the laminar sub-layer whosepresence 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




4.7.2REYNOLDS NUMBER

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

Re =

ρ = density, v = velocity, d = size, µ = 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 thestatic 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 nowincreases (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 visualisethat 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-flowwithin 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 severalsuccessive 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.




When the boundary layer separates and forms a turbulent wake, much energyhas been lost in creating rotational flow and consequently the static pressurewithin 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 actsrearwards (= drag). Hence, separated, turbulent flow should be avoided /delayed whenever possible. This is achieved by streamlining and maintaining assmooth 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 thedrags resulting from the component parts. The increase in drag is caused by theindividual flow patterns interacting or "interfering" with their neighbours. This isgenerally reduced by the addition of fairings at the functions of the aircraftcomponents.

In summary, zero-lift drag is a combination of form and skin-friction drag, with theprobable addition of interference drag. It is related to the separation of the airflowinto a turbulent wake. This will be linked to the separation point, itself a functionof 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, althoughanother term, Vortex drag might be more descriptive. Consider the diagrambelow.




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 aspanwise component forming in addition to the chordwise component. It willbe, 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, thegreater 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 surfacesmeet to create a series of vortices, termed a vortex sheet. These also drifttowards 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 adownwash component, must imply an expenditure of energy; an increase in(induced) drag. Vortex drag arises from introducing wings of finite span.

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 theresult of greater pressure difference. Greater pressure differences create moredownwash / stronger vortices.

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

The vortices tend to combine towards the wing-tip and so an ideal wing-planformwill create a lift distribution that minimises these vortices. This ideal is the so-called elliptical distribution or loading, which was attempted on the Spitfire byusing 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, andinversely proportional to the speed2.




4.11TOTAL DRAG

The effect of speed on zero-lift and induced drag can be shown on a singlegraph, 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.




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




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5. FORCES IN FLIGHT

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

5.1 FOUR FORCES

The first (and most common) case of an aircraft in flight is when the aircraft isconsidered to be straight and level (i.e. no change in heading or altitude), and atconstant 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 thesame point and no other forces are considered e.g. tailplane forces).

If the equilibrium of the forces is upset, e.g. Thrust (T) is increased, the aircraftwill accelerate (until the increase in drag balances the increases in thrust). If theLift 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. TheCP moves as the angle of attack changes, and the CG depends on the weightdistribution. This means that although L = W, their different lines of actionmeans that they create a couple. The different thrust and drag lines are alsolikely to create a couple. Ideally, the two couples should cancel each other.What is desirable is that a reduction in the thrust / drag couple should lead to anose-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 becreated to restore equilibrium. This is provided by the tailplane. Because thedistance from the CG is comparatively large, the size (area) of the tailplane canbe small. With a conventional tailplane, it is usual to find that it produces adownward 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 beginsby resolving the weight force into two components, perpendicular and parallelto the flight path. The forces in these directions can now be equated.

L = W cosθ

T = W sinθ + D

Two interesting and important facts emerge. If the aircraft is climbing, θ > O and

cosθ < 1

therefore Lift is less than Weight.

Similarly, sinθ > O and Thrust is greater than Drag.

We can therefore deduce that aircraft climb because of increased thrust, andnot increased lift. (Theoretically, this makes sense, because the aircraft gains height and therefore potential energy. The energy input is through the increasein thrust, itself resulting from the 'burning' or expenditure of fuel (chemicalenergy).




5.4 FORCES IN GLIDE & DESCENT

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

The equations becomes:

L = W cosθ

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

In the glide, T is assumed to be zero, and W sinθ = D. The weight component

now balances drag 'gap' - potential energy is now traded in order to maintainkinetic 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 dragspeed, coincident with best L/D ratio.

5.5 RATE OF CLIMB (PERFORMANCE)

Climb performance, or rate of climb (ROC), is theoretically a little morecomplicated. In the previous discussion, climb performance was considered interms of angle of climb and by equating forces. Rates of climb (usuallyexpressed 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. Butrate 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. Butthe fuel energy is expended in two areas; in maintaining speed whilst overcomingdrag, and in increasing altitude. But how much is used in each area?




The left-hand diagram shows that sinθ =

The right-hand diagram restates that sinθ =

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 climbperformance; 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 aircraftspeed. 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 whichrepresents excess power. If an aircraft on test fails to achieve the scheduledROC, then an investigation as to the possible cause should be made. Note theimportance of operating at the best climb speed.




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 areduced 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. Achange 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 inequilibrium). Change of direction therefore requires a resultant force, termed thecentripetal force (CPF); the force that must be present in order for a body tochange its direction of motion.

But the only forces available to act on an aircraft are aerodynamic forces, (thrustvectoring - forces will not be considered here), and changes to these forces are

dependent on changes in CL (itself dependent on α and shape changes).

Fundamentally, therefore, manoeuvre will depend on the changes in CL applied tothe main aerofoil (wing). Manoeuvres can be accomplished in the vertical(looping) plane or in the horizontal (banking) plane, (the combination of bothforms 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 tostop 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 toincrease the download on the tailplane. The resulting moment pitches the aircraftso as to increase the angle of attack of the mainplane , this increases CL. Theeffect 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 additionalforce or stress on the airframe and occupants. They experience the reaction tothe CPF, the centrifugal force (CFF). The excess of force is often termed the'g' force.




6.3 LOAD FACTOR

The 'g' force can be considered as a comparison between the lift generated andthe 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 asnegative and hence the Load Factor is also negative.

Because of the increased stresses, aircraft are designed with 'g' limits. Becauseviolent manoeuvres could result in over-stressing, aircraft are operated within 'g'limits, both positive and negative. Combat aircraft are designed to be moremanoeuvrable 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 changesheading. The pilot must bank the aircraft so that the horizontal component of liftprovides a CPF. But to maintain the vertical component equal and opposite toweight, 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 tanθ = where θ = angle of bank.

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




It should also be appreciated that increased angle of attack leads to increaseddrag 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 α, it was stated that the wing stalled beyond a certain α. This is known as the

stalling angle.

If an aircraft is flown straight and level and the thrust is reduced, the aircraft willreduce speed (drag is exceeding thrust). The pilot can maintain lift, by raising thenose to achieve a higher CL. At some point (speed), however, the aircraft willreach the stalling angle, the CL reduces and the aircraft stalls, suddenly losingaltitude.

L (=W) = ½ρv2S CL

To maintain equality, as v2 decreases, CL must increase. When CL reaches itsmaximum 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 indicatestheoretical 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 histraining. He learns to recognise and recover from it, and is encouraged to avoidit!

6.5.1STALLING SPEED

But it is important to appreciate that the stall is primarily dependent on angle of attack (α), 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 themaximum 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 basicstall speed.

Stall speed = basic stall speed

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

6.5.3AEROFOIL CONTAMINATION

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

weather conditions.




6.6 FLIGHT ENVELOPES

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

An example is shown below.




7. STABILITY

7.1 BASIC CONCEPT & DEFINITION

The aircraft has now been considered in both the steady flight path condition andduring changes of direction (manoeuvre). It is now necessary to investigatehow 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 isdisplaced 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.

7.2 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 hasnegative 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 todetermine the static stability of the system.




7.3 DYNAMIC STABILITY

So, following initial displacements the system may oscillate about the neutralposition 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). Intheory, such oscillations continue indefinitely. In practice, the oscillationssteadily 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 isdynamically unstable.

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

Most systems are designed to be statically and dynamically stable.

7.4 AIRCRAFT STABILITY

Considering the stability of an aircraft, we might ask two questions. Can itoscillate, 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 areconsidered 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, followingsome initial (probably random) displacement.

7.5 DESIGN FEATURES

If an aircraft is to be stable, it is obvious from the previous paragraphs that if theaircraft has been momentarily displaced relative to its flight path, there must be arestoring force or moment to return it to its original altitude. Recalling that amoment is the product of force and distance, we then deduce that anaerodynamic 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 thefin (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 willagain 'heads' towards the relative airflow - just like a weathercock heads intowind).

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

The manner in which the tailplane (horizontal stabiliser ) acts is similar inprinciple but somewhat more complicated in detail. The diagram below showsthe aircraft displaced in the pitching plane. Now two aerofoils are involved, themainplane 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 thereforeinherently unstable).

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

As the centre of gravity moves aft, the aircraft becomes less stable, due to thechanging 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.

If an aircraft has 'dropped' a wing, it should be obvious from the precedingparagraphs that a moment to raise that wing is required. But how is this to beachieved? Consider the first diagram. An aircraft that has 'dropped' a wing willside-slip towards that wing because of the imbalance of the two forces whichhas 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 theintroduction of dihedral. The diagram indicates the angle concerned. Dihedralresults 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 tocreate a restoring moment which is tending to roll the aircraft back towardsstraight and level (at which point the side-slip stops and the restoring momentbecomes 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-areais mostly aft of the centre of gravity, then an additional effect is to yaw the aircraft

towards the dropped-wing.




In later studies, it will be appreciated that designers employ swept-wings to allowflight at high speeds. But an added bonus is that swept-wings encourage lateralstability. Consider the diagrams. In the first, the aircraft is flying straight andlevel.

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 tothe 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 atdifferent angles, and now has different components in respect of each wing. Itwill be recalled that it is the chordwise (or normal) component that creates lift

and reference to the diagram shows that greater chordwise component occurringover the dropped-wing will therefore generate more lift, so as to create a rollingmoment that restores the aircraft to (straight) and level flight.




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 centreof 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 aircraftthat 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 theaircraft. An aircraft that possessed all the features described would probably betoo stable. So a swept-wing, high-wing aircraft might incorporate anhedral (theopposite to dihedral) in order to reduce the degree of stability.

The above paragraphs have analysed features which create a moment so as torestore the aircraft towards its undisturbed or original position. They contributestatic 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.

7.6 CONTROL

The previous section has considered stability, where design features have beenincluded 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 benecessary to de-stabilise the aircraft. So it appears that stability andmanoeuvrability are conflicting requirements - increasing one characteristicdecreases the other.




To de-stabilise the aircraft, aerodynamic forces must be created for as long as isnecessary to cause a rotation about one or more of the axes. These forces arecreated simply by modifying the shape and angle of attack of the appropriateaerofoil. This is done generally by hinging the trailing-edge, thus allowing it torespond 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. Theymust 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 inopposite 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 doesso in the same direction as the turn. However, the rising (upward) wing ingenerating more lift also generates more (induced) drag than the descending

wing. This unbalance in the drag forces results in a moment which causes arotation (yaw) in the opposite direction to that first intended, hence, it is termedadverse yaw.

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

• Frise ailerons - where the leading-edge of the aileron is designed to

protrude into the airstream when the aileron is raised, thus causing extra(and equalising) drag.

• Differential ailerons - where the geometry of the control system is such as

will cause the down-going aileron to move through a smaller angle than theup-going aileron. This results in greater drag on the up-going aileron.

• Control coupling - where the rudder may be geared to the aileron control

system, so as to link same rudder movement to aileron movement.

• Spoilers - spoilers are often found on more sophisticated aircraft and maybe used for a variety if purposes. Basically, they reduce lift and increasedrag, and so their operation can reproduce what is required from the aileronsystem.

7.7 CONTROL ABOUT 3 AXES

To the maintenance engineer, the effect of the controls is very simple - asmovement of the control column produces a control-surface movement whichcreates 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 aboutanother axis.




7.8 AERODYNAMIC BALANCING

The purpose of control surfaces has now been defined and the basic operationhas been established. But what factors contribute to their effectiveness?Obviously, as they are aerodynamic devices, the same factors that governaerodynamic forces - speed, size and shape. In this case, shape is related to thedeflection angle.

It must not be overlooked that in deliberately creating an aerodynamic force bymoving a control-surface, this force is trying to move the surface back towards

the streamlined or neutral position. The surface will only deflect or remaindeflected as long as there is an input (force) from the control system. This input force will vary in proportion to the force output by the control-surface.

The input (force) is in fact a moment which must be applied at the hinge andwhich must always be large enough to produce the required control deflection.Due to increases in speed and size, it is quite possible that this hinge moment willrequire unacceptably large forces to be exerted by the pilot. This can beovercome by power assistance but aerodynamic methods have been developedas an alternative. This balancing of the forces required has led to the termaerodynamic balance.

Aerodynamic balancing, designed to reduce the physical effort of moving thecontrols can include:

• Horn balance

• Inset hinge

• Internal balance (sealed hinge)

• Balance tabs

In each case, the aim is to reduce the pilots contribution to the hinge momentnecessary to cause deflection.

The effect of the air-flow acting on the horn is to produce a moment assisting control movement.




The inset-hinge moves the hinge rearwards, thus moving closer to the Centre of Pressure of the control. Again, the hinge-moment reduces.

The sealed-hinge maintains a pressure difference between the upper and lower

surfaces. This results in a net pressure force acting forward of the hinge,creating a moment assisting deflection.

7.9 BALANCE OF TABS

The action of Tabs need some explanation. A tab is a small hinged surfaceforming part of the trailing-edge of the control surface itself.

Consider that an aircraft is tail heavy (aft CG). The pilot must apply a steadypush force to maintain straight and level flight. He must maintain a hingemoment. It a tab is added, and deflected in the opposite direction to the controlsurface deflection, it will create a hinge moment to assist the pilot. When the tabdeflection is large enough, the effect of the tab exactly balances the effect of the

control. The pilot could then take his 'hands-off' the control, the aircraft would bein equilibrium; it is said to be "trimmed".




Several types of tab exist, their operation is the same in terms of theaerodynamic principle.

Examples include:

Fixed tabs,

Trim tabs,

Balance tabs e.g. geared, servo and spring tabs.

7.10 FIXED & TRIM TABS

Fixed and Trim tabs are used to maintain a control deflection, so as to trim theaircraft.

A fixed tab can only be adjusted on the ground, by an engineer followingconsultation with the pilot. It is only truly effective therefore for a given set of conditions, e.g. a particular weight and CG position, a particular thrust setting,and at a particular speed. (This would typically be a cruise configuration).

The fixed tab is obviously simple, but its effect has been shown to be limited. A

trim tab can be adjustable, operated by the pilot in the cockpit. The classicmethod of operation is by a handwheel, positioned and operated instinctively, ie.Movement of the elevator trimwheel is similar to the response required by theaircraft. (Note however that the pilot should move his control column, and then trim-out the load).

On light aircraft, it is usual to find an adjustable trim-tab only fitted to theelevators. Larger aircraft will generally have such tabs fitted to all three controls.For example, a multi-engined aircraft with (one) engine failure would develop astrong yawing tendency, which would be opposed by a large rudder deflection,maintained by rudder trim.




7.11BALANCE TABS

Whereas trim tabs maintain control deflection, balance tabs assist deflection. Aerodynamic balance tabs are then further categorised according to themechanical principle of their operation.

The geared tab is connected by a link to some part of the fixed structure.Movement of the control surface by the pilot will cause a deflection of the tab,dependent on the geometry or gearing.

If the tab is operated directly by the pilot, the tab is termed a servo tab. A servotab is considered to lack effectiveness at low speeds. The main control surface isnot connected to the control system, it "floats". If a large deflection is required,the servo tab must be able to generate a sufficient moment to cause this. At lowspeed this is difficult.

The spring tab is an effective compromise. In effect, a tab is created whenneeded, and deleted when not required.

At low speeds, no assistance is needed and the pilot moves the control surfacewithout tab deflection. If the speed rises, the increasing air resistance requiresthe pilot to apply an increasing hinge moment via the control system. At somestage, the forces in the control system overcome the spring forces, which allowsthe link to pivot and create a movement of the tab. The greater the force, themore the link and tab will move, the greater will be the assistance to the pilot.




7.12LIFT AUGMENTATION

One of the greatest attractions of air transport is its relatively high speed andconsequent ability to travel great distances in minimum time. This is important tooperator and passenger alike. This has resulted in the development of aerofoilswhich have low drag but also low lift coefficient. (This means that the lift isderived 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 compensatefor 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 thestalling speed will be relatively high for a modern aerofoil. This has a profounddisadvantage as far as airfield performance is concerned, as it means that take-off and landing distances are lengthened considerably.

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 LiftAugmentation.

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 aswell), slats and slots (typically on the leading-edge), and systems which allowsome control of the boundary-layer behaviour.

Flaps are used change the shape of the wing. They generally consist of ahinged trailing-edge to the mainplane, extending from just inboard of theailerons, 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 hingingdownwards. (Hence, the area increases as well as the CL value). The differenttypes 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 usualto modify the leading-edge in order to present the wing at a more favourableangle. 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 theaerofoil 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. theengine) 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 α. The graphs confirm the information

given on the diagram listing the devices in detail.




7.13 USE OF HIGH LIFT DEVICES

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




7.14 FLAPS, SLOTS & SLATS

High-Lift Devices

Increaseof

maximumlift

Angleof basicaerofoil

atmax. lift

Remarks

Basic Aerofoil

-- 15°Effects of all high-liftdevices depend onshape of basic aerofoil.

Plain or Camber Flap

50% 12°

Increase camber.Much drag when fullylowered. Nose-downpitching moment.

Split Flap

60% 14°

Increase camber.Even more drag thanplain flap. Nose-downpitching moment.

Zap Flap

90% 13°

Increase camber andwing area. Much drag.Nose-down pitchingmoment.

Slotted Flap

65% 16°Control of boundarylayer. Increase camber.Stalling delayed. Notso much drag.

Double-slotted Flap

70% 18

Same as single-slottedflap only more so.Treble slots sometimesused.

Fowler Flap

90% 15°

Increase camber and

wing area. Best flapsfor lift. Complicatedmechanism. Nose-down pitching moment.

Double-Slotted Flower Flap

100% 20°

Same as Fowler flaponly more so.Treble slots sometimesused.

table continue….




table continued….

High-Lift Devices

Increaseof

maximumlift

Angleof basicaerofoil

atmax. lift

Remarks

Krueger Flap

50% 20°

Nose-flap hinging aboutleading edge. Reduceslift at small deflections.Nose-up pitchingmoment.

Slotted Wing

40% 20°Controls boundarylayer. Slight extra dragat high speeds.

Fixed Slat

50% 20°

Controls boundary

layer. Increasescamber and area.Nose-up pitchingmoment.

Movable Slat

60% 22°

Controls boundarylayer. Increasescamber and area.Greater angles of attack. Nose-uppitching moment.

Slat and Slotted Flap

75% 25°

More control of

boundary layer.Increased camber andarea. Pitching momentcan be neutralised.

Slat and Double-SlottedFowler Flap

120% 28°

Complicatedmechanisms. The bestcombination for lift;treble slots may beused. Pitching momentcan be neutralised.

Blown Flap

80% 16°Effect depends verymuch on details of arrangement.

Jet Flap

60% ?Depends even more onangle and velocity of jet.




7.15 DRAG DEVICES

In the preceding section, mention was made of aerofoils with low dragcoefficients which result in reduced fuel consumption.

But how do these aircraft with low drag / 'slippery' shapes slow down quickly or descent at steep angles without accelerating to dangerously high speeds?

The design will normally include devices whose purpose is the provision of extra-

drag, such spoilers and airbrakes. They are designed to produced high-drag(whilst possibly maintaining lift) and to avoid variation in pitching-moment or trim.

They may vary considerably in appearance and location, and may have varyingdegrees of movement, depending on the flight-phase. An example is shown inthe diagram below.

Conventional low-speed ailerons have certain disadvantages, which can beeliminated by the use of flight spoiler . When raised differentially, they will

create a rolling moment, and also a tendency to yaw. They will be activated inthis sense by normal inputs from the manual flight control system or the autopilot.

Spoilers may also be raised symmetrically in order to create high-drag or todestroy lift (when they are often termed lift-'dumpers') during the landing-runs(hence the common-term 'ground' spoilers).

Airbrakes are fitted to bring about a large increase in drag, thus allowing theaircraft to lose speed or descend steeply and quickly. Careful positioning bydesign should avoid any significant change in balance or trim.




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8. HIGH SPEED FLIGHT

8.1 HIGH SPEED AIRFLOW

Compressibility. At subsonic speeds, flow through a venturi can be said toobey the predictions of Bernoulli's Theory. That is, to maintain a constant massflow, pressure energy (static pressure) is converted to kinetic energy (dynamicpressure) at the throat of the duct. At relatively small speeds, up to about half the

speed of sound this is correct to within a small and acceptable degree of error.However, there is always an error if Bernoullis' Theory alone is used for calculation purposes.

This error is due to the fact that Bernoullis' Theory is based on the flow of anincompressible medium, water. However, air which is the medium we areconcerned with is highly compressible and so at high air speeds 'compressibilityerrors' are introduced and must be accounted for. In fact even at low speeds,the density of the air will change slightly, but this is such a small effect that it cangenerally be ignored. However, this is not the case in high speed flow wherecompressibility is a major factor.

8.2 SHOCK WAVES

Noise, or sound is a series of pressure variations transmitted through the air andcan be generated from a variety of sources. In fact every part of an aircraft flyingthrough the air is vibrating and therefore every point on the airframe is producingsound waves (pressure waves) which emanate in all directions. If the aircraftwere stationery (e.g. hovering Harrier Aircraft) the pressure waves would beconcentric, like the ripples on a pond when a stone is dropped.

These pressure waves move outwards at the speed of sound.

If the point is moving, seediagram (b) below, the pressure

waves will no longer beconcentric but closer together inthe direction of movement. Thefaster the point travels the closer together will become thesoundwaves in that direction.

Diagram (c) below, shows thesituation where the point istravelling at the same speed asthe pressure waves (the speed of sound). In this situation the

pressure waves build up toproduce a shock wave. Theshock wave can be considered asa build-up of all the pressurewaves emitted by the point andas such produces a very thin lineof highly compressed air whichmoves with the point and is atright angles to the directions of airflow.




8.2.1MACH ANGLE & MACH CONE

The diagram below shows what will happen if the point emitting the pressurewaves is travelling faster than the speed of sound.

The angle, or α, is called the Mach Angle and by simple trigonometry

it will be clear that:

sin α = =

The point emits a pressure wave at position A and by the time the point hasreached D the pressure wave has attained a radius A.E. All subsequentpressure waves emitted between A and D will have reached the tangent D.E.,which is known as a Mach Line.

Angle alpha (a) is known as the Mach Angle.

Viewed three dimensionally, the point will be emitting pressure waves as spheresand so in reality a point produces a Mach Cone, see diagram below.

The effect of the irregularity can only be felt within the 3-D Machcone which has a surface made up of Mach lines.

The mach cone could be considered as being made up of a series of mach lines

and so the included angle of a mach cone will be 2α.

The Mach Angle only holds true for a weak shock wave at some distance fromthe point (or aircraft) where is may be referred to as a Mach Wave, see diagrambelow. Nearer the aircraft, where the shock wave is stronger, the shock waveprogressively becomes a 'normal' shock wave, i.e. at 90º to the airflow.




In practice a fully formed, strong shockwave travels slightly faster than the speedof sound and so will be in front of the mach cone.

The bow shock wave becomes progressively weaker further out from the Aircraft eventually becoming a very weak 'Mach Wave'.

8.3 GROWTH OF A SHOCKWAVE SYSTEMThere are three accepted terms which are used when considering airflow inrelation to the speed of sound. They are pertinent to airflow over the any shapeof object, but for this discussion we will use airflow over an aerofoil section.These terms are:

• Subsonic Flow - In this condition the air flowing over the aerofoil is

subsonic (below the speed of sound) at all points of the aerofoil.

• Transonic Flow - In this condition part of the aerofoil will be experiencing

subsonic flow and part will be experiencing supersonic flow (faster than thespeed of sound).

• Supersonic Flow - In this condition all parts of the aerofoil are experiencing

supersonic flow.

As the aerofoil accelerates from subsonic to transonic through to fully supersonic,shock waves will form and move in relation to the aerofoil. As this greatly effectsthe drag, lift and stability of an aerofoil (and whole aircraft) it is important tounderstand the process.

8.4 SPEED OF SOUND

The speed of sound is the speed at which the pressure waves or vibrations areactually propagated through the medium (material) concerned. The speed is a

function of the material characteristics, such as density, bulk modulus, etc. for example, sound travels over 10 times faster through steel than through air.

In air, the speed of sound is proportional to the square-root of the air-temperature(in degrees Kelvin). At sea-level, where the temperature is assumed to be 288K,the speed if sound is approximately 330 m/s.

At altitude, the speed of sound

(a) = 330

Because of the significance of the speed of sound to the pressure waveprorogation, the aircraft speed (V) is often considered in terms of Mach Number,

which enables us to asses the aircraft speed immediately in relation to the speedof sound.




Mach Number (M) =

(Note that the actual flight speed is the True Airspeed (TAS) which is Indicated Airspeed (IAS) corrected for density at altitude.)

The speed of sound is adjusted according to the ‘local’ (actual) air temperature.

8.5 MACH NUMBER

The following explanation references the various 'events' to the speed of the free

stream airflow, or to be more precise, the Mach Number of the free streamairflow. The stated mach numbers however are only an approximation or generalisation as it will be different for each differing shape or aerofoil dependinglargely on its camber and fineness ratio.

• Subsonic - At free stream airflows up to approximately M = 0.6, airflow over

all points of the aerofoil is subsonic. However it accelerates up to the point of maximum camber and then decelerates towards the trailing edge, seediagram below.

• Transonic - As free-stream airflow increases to approximately M = 0.8,

airflow at the point of maximum camber reaches sonic speed (M = 1.0). Aweak shock wave termed an Incipient Shock Wave, forms at the point of maximum camber at right angles to the surface and local airflow.

As the free-stream airflow increases in speed the shockwave strengthens andinclines backwards, see diagram below.




• High Transonic - As the free stream airflow continues to gain speed up to

sonic speed (M = 1.0), the incipient shockwave move backward toward thetrailing edge and increases in strength, see diagram below.

• Supersonic - As the free stream airflow reaches supersonic speed (e.g.

M = 1.1) the strengthened shock wave has moved back and attached itself tothe trailing edge, see diagram below.

A Bow Shock Wave also forms some distance in front of the leading edge.This may be known as the Normal shockwave as it is initially at 90º to thefree-stream airflow but with increasing speed it strengthens and inclinesbackward.

• High Supersonic - As the free-stream airflow increases to the region of

M = 2.0, the bow wave attached to the leading edge and inclines back at an

increased angle. The tail wave angle is also increased with speed, seediagram below. At this point the shock waves are considered to be 'fullydeveloped'.




8.6 EFFECTS OF A SHOCKWAVE

As we saw previously shockwaves form at a point where the local airflow over anobject becomes sonic or supersonic. At other points the airflow is still subsonic. As a shockwave is physically extremely thin (a few thousandths of a millimetre)the effects it has on the airflow as it passes through it are extremely dramatic.

The diagrams below show the five stages of shock wave formation from fullysubsonic to fully supersonic over a symmetrical aerofoil at 0º angle of attack.

• Subsonic - The diagram (a) below the aerofoil is all subsonic and there is a

relatively small turbulent wake aft of the transition point where the laminar boundary layer becomes turbulent.

• Transonic - As the free-stream airflow increases speed to the value where

the local airspeed at the point of maximum camber is sonic (M = 1.0) andIncipient Shock Wave forms. This is initially very weak and at 90º to the

airflow.

This speed is the point at which a variety of adverse effects start to be felt andit is therefore called the Critical Mach Number . The Incipient Shock Wavehas four effects on the (sonic) airflow as it passes through:

i. The airflow speed is instantaneously reduced.

ii. The density of the air is instantaneously increases (compressed).

iii. The pressure is instantaneously increased.

iv. The temperature is instantaneously increased.

The diagram (b) below shows conditions when the free-stream airflow has

further increased in speed (but is still subsonic). At this point three veryimportant changes take place:

i. An area forward of the shock wave (inside the dotted lines) is now

supersonic, caused by the increase of airspeed over the camberedsurface.

ii. Aft of the shockwave the air is,

SubsonicHigher in density (compressedHigher in pressureHigher in temperature

iii. As the shockwave develops and strengthens, the 'transition point'moves forward to near the shockwave causing the boundary layer toseparate from the aerofoil surface. This is called Shock Induced

Separation which causes a large, turbulent subsonic wake.




• High transonic - The diagram (c) shows the free-stream airflow at M = 1.0.

The shockwave has moved back taking the 'transition point' and the shockinduced separation back with it. The supersonic area forward of the shockwave has grown. Airflow aft of the shockwave is still reduced to supersonicspeed.

• Supersonic - The diagram (d) below shows the position with the free-

stream airflow supersonic in which:

i. A bow shockwave has formed.

ii. An area around the stagnation point of the aerofoil has supersonicairflow.

iii. The original shockwave has moved to the trailing edge.

iv. There is no separation flow over the aerofoil.

v. As the air passes through the shock waves the speed, pressure,density and temperature are modified by each successiveshockwave, but the initial high airspeed ensures that the airflowremains supersonic throughout.

vi. A small turbulent subsonic wake is still present.

• High Supersonic - The diagram (e) below shows conditions with the free-

stream airflow further increased in speed.

i. All airflow is now fully supersonic with no subsonic area at thestagnation point.

ii. The bow wave is now attached to the leading edge.

iii. The wake is further reduced and is now supersonic.




8.7 SHOCK INDUCED SEPARATION

As stated earlier, when the incipient shockwave forms, the boundary layer separates from the point at which the shockwave meets the airframe causing alarge turbulent wake. This can happen at any point on the wings, tailplane or fuselage where the local speed of the air reaches sonic or supersonic. Shockinduced separation has four detrimental effects, which are:

• Shock induced drag

• Buffet

• Rapid centre of pressure changes

• High speed/low incidence stall (shock stall)

8.8 SHOCK INDUCED DRAG

Shock induced drag is the combination of two effects which cause an extremerise in drag around the transonic region.

This drag reduces from its peak as speed further increase, but never returns toit's subsonic levels.

The two components of shock-induced drag are:

• Wave Drag - The changes in speed, pressure, density and temperature of

the airflow which happen in the shockwave require energy. This dissipation of energy is observed as an increase in drag.

• Boundary Layer Drag (Viscous Drag) - This is always present at any

speed of flight, but as shock-induced separation occurs, the much larger turbulent wake produces a correspondingly high drag.

8.8.1BUFFET

This is caused by the turbulent wake striking the airframe (fuselage, wingstailplane etc) with considerable force causing a high amplitude 'vibration' whichphysically shakes the whole aircraft.




8.8.2HIGH SPEED / LOW INCIDENCE STALL ( SHOCK STALL)

Shock induced separation, when it occurs over the wings had as effect similar tothe high incidence stall. The large, turbulent wake produced aft of the incipientshockwave acts in a similar manner to that produced by the high incidence stall.The turbulence destroys, or at best reduces the lift produced by the area of wingover which it occurs.

If the incipient shockwave forms far enough forward on the wing, enough lift islost, which coupled with the rapid increase in drag (shock induced), causes the

aircraft to stall. This happens at a very small angle of attack and is totallyindependent of it.

8.9 CENTRE OF PRESSURE CHANGES

The diagram below shows the pressure distribution you might expect at subsonicspeeds with the approximate position of the centre of pressure this distributionwould produce.

However, once the shockwaves form, this situation will change. As we sawearlier as the air passes through the shockwave it is slowed down. Moreimportant when we are considering lift is the effect on pressure and density.These both rise.

The pressure over the top surface reduces rapidly up to the shockwave wherepressure and density instantly rise. This may contribute to shock stall. Thepressure then continues to rise toward the trailing edge. This has the effect of moving the centre of pressure forward producing a nose up pitching moment onthe aircraft. This effect is only apparent in the transonic range. As theshockwave moves to the trailing edge the centre of pressure returns toapproximately its original position. This effect may be cancelled or reversed bysimilar effects on the lower surface.

As shock induced separation occurs the shock wave may also rapidly oscillate back and fore over the wing. This causes a rapid up and down movement of the

nose accentuating buffet.The movement of the centre of pressure associated with shock-wavedevelopment results in trim changes throughout the transonic speed-range.This requires an automatic response or correction input to the pitch controlsystem, which is termed Mach Trim.




8.10 CONTROLLED SEPARATION - CONICAL VORTEX LIFT

As stated earlier, a wing with a sharp leading edge is subject to boundary layer separation at small angles of attack. If the leading edge is swept back at anacute angle this property can be used to produce lift. The diagram below showsthe highly swept inboard section of Concorde's wing. This wing is designed sothat the airflow over the sharp leading edge is encouraged to separate. In factConcorde flies with separated flow at all speeds and angles of attack.

This is possible because when the air separates it rolls up into conical vorticesover the wing, see diagram below. As these vortices are rotating at high speed,

the pressure within them is low and therefore lift is produced.

Whilst Concorde is designed to fly with separated flow at all speeds, other aircraftsuch as the F16 are designed to fly with attached flow at low angles of attack andseparated flow at high angles of attack.

8.11TRANSONIC FLIGHT

Supersonic flight, whilst glamorous is almost totally the realm of the military. Thisis because high speed is a vital necessity for some military operations, withspeed over-riding all other considerations.

Civil aviation, with the one exception of Concorde, has remained in the subsonicand transonic speed range, mainly because of financial considerations, in whichthe aircraft designer must balance two opposing requirements when decidingon the cruise speed of an aircraft:

• A Gas Turbine (Jet) engine is more fuel efficient at high speeds.

• As an aircraft reaches the transonic region a sharp increase in drag is

encountered due to wave drag and shock induced separation. This meanshigher fuel consumption.




Taking these two effects into consideration it has been found that flying at speeds just below the onset of wave drag is the most economical. However, to obtainthe highest cruise speeds possible a great deal of design work has been directedat delaying the onset of shockwave formation and reducing its effect.

8.12CRITICAL MACH (MCRIT)

This high cruise speed introduces a further term i.e. Critical Mach Number (MCRIT). This is the aircraft speed (expressed in terms of Mach Number) at which

detrimental effects like shock wave formation, shock induced separation andbuffet first occur. It is therefore vital that this speed is not reached or exceeded innormal operation. MCRIT will vary from aircraft to aircraft but M0.7 to M0.8 is arepresentative valve and coincides with the buffer boundary.

8.12.1 TRANSONIC WING PLANFORM

Most (if not all) aircraft which are designed to cruise at transonic speed haveswept wings. This is because it has been found that a swept wing will delay theonset of the compression (high speed) effects such as shockwave formation.This is because the free-stream airflow meets the leading edge of a swept wingat an angle. The vector of this airflow can be divided into two components, one

parallel to the wing (spanwise component) and one at ninety degrees to the wing(normal component).

Velocity components on a swept wingOnly the normal component contributes to the generation of lift

It has been found by observation and experiment that as long as the velocity of the normal component is subsonic, the flow patterns and characteristics will besimilar to ordinary low speed flow. This may be true even if the normal andspanwise components add up to a supersonic free stream velocity.

From this it appears that:

Normal component = free stream velocity × cosine of sweep angle.

Therefore the amount of sweep required to maintain subsonic flow characteristicsmust increase with aircraft speed.

8.13SWEEP BACK

Unfortunately swept wings have detrimental characteristics that must bebalanced against their advantages.

The detrimental characteristics are:




• Lift Generation - The normal velocity component is the only component of

flow that effects shock formation. Unfortunately it is the only component thateffects lift. Therefore to generate the same amount of lift as a straight wing itmust be larger and heavier.

(Lift = ½ ρV2.S.CL. so if V2 is reduced S must be increased to maintain a

constant lift).

• Drag - Although lift is dependent on the normal component, drag is

dependent on both components. Therefore a swept wing will have a poorer lift to drag ratio than an equivalent sized straight wing.

• Tip Stall - In a swept wing configuration, trailing vortex generation and

resulting downwash differs from that of a straight wing. In a swept wing thetrailing vorticity and hence downwash is not as strong as the tips. In somecases there may even be an upwash.

This has two results:

i. The wingtips have a higher angle of attack and stall before the inner wing causing the C of P to move forward. This produces a divergentupward pitching moment.

ii. Ailerons become ineffective. As a result the benefits of wing-sweep must be balanced against the badcharacteristics. This limits the amount of sweep employed and therefore toan extent, the aircraft speed.

Because Tip-stalling is generally undesirable, one method of reducing thistendency is to reduce the angle of attack at the tips, in comparison to that of the inboard wing-sections. This is achieved by ‘twisting’ the wing betweenroot and tip so as to reduce the angle of incidence at the tip. This is termed‘wash-out’.

• Boundary Layer Separation - In addition to the problem of upwash, the tips

of a swept wing are also inherently prone to a thicker, more turbulentboundary layer which makes them prone to boundary layer separation beforethe inner wing. This adds to the previous problem of tip stall.

This problem can be controlled by the use of several devices as shown in thediagram below. These control the spanwise flow of air which is the cause of the thickening boundary layer at the wingtips.




Devices for inhibiting flow separation on swept wings(a) Wing fence, (b) Vortilon, (c) Saw-tooth leading edge

i. Wing fences mounted chordwise extending back from the leading

edge, see diagram (a) above. These effectively split the wing intoseparate sections and also shed a vortex which rotates in theopposite direction to the wingtip vortex.

ii. A saw tooth or dog tooth leading edge, see diagram (c) above, mayalso be used. This also generates a vortex.

iii. The vortilon, see diagram (b) above, is a small fence which extendsforward from beneath the leading edge to create a vortex over the topsurface at high angles of attack.

iv. Vortex Generators are small 'brackets' attached near the leadingedge. These shed small vortices which mix with the thickening

boundary layer to re-energise it and so prevent or delay separation.They may extend over the whole span or just part of it.

8.14 INSTABILITY

Another disadvantage is the common-tendency to demonstrate a degree of dynamic instability, particularly with respect to lateral and directional stability.There instabilities are often ‘coupled’ and produce a phenomenon called ‘DutchRoll’. This is overcome by sensing the resultant motion and then generating anautomatic response or correction to the rudder. Such a system is commonlyfound on swept-wing aircraft and is termed ‘yaw damping’.




8.15 THE SUPER CRITICAL WING

The diagram below shows the pressure distribution over an aerofoil designed for low speed operation. This has a high degree of camber which causes highspeeds of flow over the top surface with a large suction peak at the leading edgeand a steep adverse pressure gradient towards the trailing edge.

Low Speed Aerofoil Pressure Distribution

Mach number below 1.0 over surfaceNote: Leading edge suction peak and adverse pressure gradient

on top surface

These properties produce supersonic flow over the top surface and a strongincipient shockwave. Even at relatively low free stream airflow velocities.Therefore this is not a shape suitable for high transonic airspeeds. Thesupercritical wing, see diagram below, has been developed to overcome theseproblems.

'Roof Top' Pressure DistributionLocal surface Mach number is close to 1.0 between A and B

This design, is used on most modern transonic airliners and although there willbe slight differences between aircraft, the basic design is the same.

The main features are:

• The camber is reduced at the front.

• The camber is increased at the rear.

• The thickness is reduced as much as possible without detracting from the

strength and stiffness of the structure.

This had the effect, with a given free-stream airflow of lowering the 'local' highairflow speeds at the leading edge and reducing the adverse pressure gradientover the rear of the aerofoil. This gives a pressure distribution with a more evenspread of pressure known as a roof top distribution with a shock-free

recompression at increased free-stream airflows.




8.16 SHOCK-FREE COMPRESSION

As the air over the wing accelerates and becomes supersonic, the expectedresult is for a shockwave to form. This shockwave is the result of a series of 'weak compressive waves' coalescing into a shockwave, see diagram below.

This can be observed in a wind tunnel. The incipient shockwave forms at adistance from the aerofoil surface and as it 'strengthens' it grows in length toattach itself to the surface.

If the aerofoil can be designed so that the weak compressive waves are angledso that they will coalesce outside the supersonic flow region, a shockwave willnot form and shockless re-compression will occur as in the diagram below.

Weak compression waves in supersonic region reach sonicboundary before forming shock wave

Despite the possibilities of shock-free re-compression some supercritical aerofoilsdo fly with a weak incipient shockwave.

The diagram below shows an aerofoil with a large area of supersonic airflow over the forward part ending in a weak shockwave.

Peaky Pressure DistributionFlow on top surface is supersonic up to weak shock wave

This produces an aerofoil capable of higher wing-loadings (more lift) but with a

minimum wave drag penalty.




8.17 THE TRANSONIC AREA RULE

To produce minimum Boundary Layer Normal Pressure (or Form) Drag a bodymust be streamlined. That is, it must have a high fineness ration with amaximum thickness about halfway along its length and a gradual change incross-section area.

It has been found that for an aircraft in transonic flight to meet these conditions,the total cross-section including the wings, tailplane etc must be taken into

account. In some designs this had led to the fuselage being "wasted" tocounteract the large cross-section change caused by the wings and empenage.

This however, has been normally restricted to military designs as a civil aircraftrequires an untapered fuselage.

Area rule, then, is where the designer has carefully ‘controlled’ the developmentof the total cross-sectional area (c.s.a) from fore to aft, avoiding sudden changes which are known to promote premature formation of shock-waves. Area-rule was investigated by a NACA aerodynamicist (Whitcomb) whoconducted experiments which evaluated the variation in CD of similar (but notidentical) shapes at transonic speeds, as the diagram shows.




The other diagrams show the typical change in appearance when area-rule isapplied to an aircraft, and also the additional aerodynamic benefits resulting fromextending or ‘stretching’ the upper deck on a Boeing 747.

8.18BUFFET BOUNDARY

As we have seen, buffet is the result of shock-induced separation and the rapidmovement of the incipient shockwave back and forth along the wing chord line.

Not only can buffet be a warning of imminent shock-stall, it is in itself a condition

which can threaten the safety of the aircraft. For this reason the 'buffet boundary'is the marker for the top speed of a transonic aircraft.




8.19 AIRFLOW THROUGH AN OBLIQUE SHOCKWAVE

Airflow, when it passes through a 'normal' shockwave, (i.e. the shockwave is a t90º to the flow) is slowed down (to a sub-sonic speed), but its direction is notaltered. If the shockwave is an oblique shockwave, inclined at an angle to theflow, this is not the case. The diagram below shows the effect of an obliquewave.

The velocity vector V1, can be divided into two. A vector normal (at 90º) to theshockwave Vn and one Tangential (parallel) to the wave V t. The wave only hasan effect on the normal vector, reducing it.

Therefore Vt behind the wave is unchanged but Vn2 is shortened (speedcomponent reduced). So V2 must be inclined outward in relation to V1.

8.20 SUPERSONIC AEROFOIL SECTIONS

Previously we have considered airflow over chambered wings. These may beadequate for subsonic or transonic flight but are not suitable for fully supersonicflight. To generate lift with minimum drag at supersonic speeds, totally differentaerofoil cross-sections are required. These utilise to the full, the shockwaves produced and their effect of compressing air; and mach waves which expand air as it passes through them.

We are therefore studying Compressive Airflow.




8.20.1 FLAT PLATE AEROFOIL

The most efficient supersonic aerofoil is a flat plate held at a small angle of attack, see diagram below.

Being a flat plate, it has sharp leading edge which encourages the bowshockwave to attach itself readily.

A feature of many designs of supersonic aerofoil is a razor sharp leading edgewhich is employed for that purpose.

8.20.2 GENERATION OF LIFT

8.20.2.1 Flow Under the Aerofoil (Flat Plate)

The (supersonic) airflow approaches the aerofoil and is undisturbed until itencounters the bow shockwave which is attached to the leading edge andextends downward and backward at an angle. (Oblique shockwave).

As the air encounters the shockwave, it is:

i. Slowed down

ii. Compressed

iii. The pressure rises

iv. The temperature rises

v. Deflected instantaneously to flow parallel to the aerofoil undersurface.

The pressure rise produces a lifting force on the aerofoil.

As the flow reaches the trailing edge, it encounters an expansion wave. Anexpansion wave is an area bounded by two weak shock waves termed machlines. These mach lines are attached to the trailing edge and form a divergingfan shaped area. As the air passes through this area, it is:

i. Accelerated to its original velocity

ii. Expanded

iii. The pressure drops to its original value

iv. The temperature drops

v. It is gradually deflected to its original course.




8.20.2.2 Flow Over the Aerofoil

At the leading edge, extending upward, is an expansion wave identical to that atbelow the trailing edge and this has the identical effect, which is to:

i. Accelerate the airflow

ii. Expand it

iii. Reduce the pressure

iv. Reduce the temperaturev. Gradually deflect the flow within the expansion wave until it flows

parallel to the top surface.

The reduced pressure causes a suction over the aerofoil producing lift.

As the airflow reaches the trailing edge it encounters a shockwave which:

i. Decelerates it

ii. Deflects it instantaneously back to its original direction of flow

iii. Compresses it

iv. Raises its pressure to its original value

v. Raises its temperature

Unfortunately a flat-plate aerofoil has two major draw backs:

• It is not able to withstand the structural forces that would be applied to it.

• At subsonic speeds its lift generating capacity is almost zero.

Because of this, the lift producing effect of the flat plate is used on variations of this shape and therefore are two main cross-sectional shapes which arecommonly used as practical supersonic aerofoils. These are:

• The Double Wedge

• The Bi-Convex Form

8.20.3 DOUBLE WEDGE AEROFOIL SECTION

The double wedge, like the flat plate uses shockwaves and expansion waves toproduce lift in supersonic flight.

Life the flat plate it must also have a small angle of attack for efficient liftproduction. In fact for the best lift/drag ratio the front-top and rear-lower surfacesshould be parallel to the free-stream airflow.




As this attitude the aerofoil produces shockwaves and expansion waves asshown in the diagram above. Thus air under the forward, lower surface is at ahigh pressure and that over the upper rear surface is as a lower pressure.Elsewhere it has all the same characteristics of the free-stream airflow.

8.20.4 BI-CONVEX AEROFOIL SECTION

This shape also produces pressure differences and lift by shockwaves andexpansion waves and as it is a symmetrical shape it must also have a small

angle of attack to do this.The diagram below shows a bi-convex aerofoil with its shockwave and machlines causing an extended area of expansion over the complete upper and lower surfaces.

This bi-convex aerofoil acts in a similar way to the double wedge. The airflowunder the aerofoil first encounters a shockwave which raises its density andpressure. These steadily reduce to original values as the airflow passes througha 'field' of expansion waves.

Over the top surface, the airflow first passes through a 'field' of expansion waveswhich gradually reduces its pressure and density to a minimum. These arereturned to their original values as they encounter the trailing-edge shockwavewhich re-compresses the air.

8.20.5 PRESSURE DISTRIBUTION

The diagram below shows the pressure distribution for each of the forms alongwith the location of the centre of pressure. As can be seen the centre of pressureis in the middle of the aerofoil and the pressure is evenly distributed giving a zeropitching moment.

It must be emphasised that these are basic shapes only. Any aerofoil sectionused on an aircraft would use a complex adaptation of these basics to optimisehigh speed flight but still maintain adequate low speed performance for take-off and landing.




8.21 SUPERSONIC WING PLANFORMS

Air, flowing at subsonic speeds can be influences by objects many metresupstream. This is evident when watching airflow in a wind tunnel using a smokegenerator. A change in an aerofoil's angle of attack will greatly effect the path of the oncoming air before it reaches the aerofoil. The effect can be attributed to anobject (aerofoil etc), transmitting pressure waves upstream at the speed of sound. These 'warn' the oncoming air of its presence. The air can then flowsmoothly round the object.

In supersonic airflow this cannot happen. As the object is travelling faster thanthe speed of sound, the pressure waves cannot propagate upstream in front of the object. In fact an object (or point), can only effect the air within its mach conewhich is in effect downstream. Conversely, the airflow within a mach conealthough still supersonic may be influenced by events upstream (as far as theapex of the mach cone) and so may act as if it is sub-sonic.

These are important considerations when the design of supersonic wings isconsidered.

8.21.1 THE UNSWEPT SUPERSONIC WING

In the unswept wing, see diagram below, supersonic airflow causes a mach coneto be produced by each wing tip and a mach wedge is produced by the leadingedge. As the wing tip can only effect the area within its mach cone the majority of the wing acts like an infinitely long wing. This means there is no span-wise flowover the inboard part of the wing and all flow is two dimensional.

Within the tip mach cone, the airflow is influenced by pressure waves generatedby points of the wing upstream. It therefore has 'advanced warning' that there issomething to encounter further downstream. The nett result is that within themach cone a span-wise flow (as in subsonic flow) is possible and a pair of wing-tip vortices are produced.

With an unswept supersonic wing a sharp leading edge is required. This is toensure that the bow shockwave attaches as soon as possible thus reducing thewave drag.

Unfortunately a sharp leading edge will cause boundary layer separation and stallat relatively small angles of attack. This means an aircraft with straightsupersonic wings has a high landing speed which is dictated by the small angle

of attack that can be tolerated.




8.21.2 THE SWEPT SUPERSONIC WING

The mach cone generated by any point on a wing is governed by the machnumber of the airstream. The higher the airspeed the smaller the mach angle. If the whole leading edge can be placed in this mach cone then low speed handlingadvantages can be gained.

8.21.2.1 Subsonic Leading Edge

The diagram below shows a wing with a degree of sweep greater than the machcone. In this configuration any airflow entering the mach cone produced by pointB will be influenced by pressure waves emanating from point B. This has theeffect of 'warning' the air that an obstacle is in its path and the air will then actsub-sonically and floe smoothly over the wing, even though it may still betravelling supersonically.

In this configuration the wing is said to have a subsonic leading edge. Thismeans a rounded leading edge may be employed, which will enhance the wingslow speed characteristics delaying boundary layer separation at high angles of attack, allowing a slower landing speed and better low speed performance.

Swept wing with subsonic leading edge Airflow approaching section AA is influences by point B, but A

Cannot affect B

The diagram below shows a complete wing with a mach cone generated from theleading 'point'. (In reality this would be generated from the aircraft nose).




As the whole of the wing is within the mach cone it will act sub-sonically. i.e. theair will flow over it without generating leading edge shockwaves. Unfortunatelyas the wing is 'subsonic' it will allow spanwise flow and therefore wingtip vortices(and drag) will be produced.

If the leading edge were forward of the mach cone it would act as a supersonicedge with all the associated shockwaves and their effects.

8.21.3 SUBSONIC & SUPERSONIC TRAILING EDGES

The same arguments may be used to predict the flow over the trailing edge, seediagram below. If the trailing edge is 'subsonic' no trailing edge shockwave willform.

If the trailing edge is supersonic, see diagram below, a trailing edge shockwavewill form.




8.21.4 SUPERSONIC ENGINE INTAKES

A final consideration of shock-wave formation concerns not the aerofoil or airframe airflows but that through engine intakes of gas-turbines.

It should be appreciated that the airflow into the engine compressor should besub-sonic. So a supersonic airflow must be slowed-down. This is normallyachieved by designing the intake ducts so as to create shock waves, throughwhich the velocities will be reduced. An additional benefit is that the pressure

increased, which is what is required as it passes on through the compressor.The intake-geometry necessary for this to happen may be ‘fixed’ or moreprobably variable. (A good example is the complex intake system on Concordewhich took considerable time and effort to develop, but which was essential if theperformance targets were to be achieved).

(Variable-geometry intake (Concorde))




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9. HELICOPTER AERODYNAMICS

The Aerodynamics Module has so far considered heavier - than - air vehicles thatare able to fly by depending on fixed wings (relative to the fuselage), moving relative to the surrounding air. The lift force is proportional to this movement(speed) and to the angle of attack.

The same principle applies equally to the helicopter. It is often described as arotary wing aircraft, because the wings or blades rotate relative to the fuselageand to the air. This of course gives the helicopter its main feature - the fuselagedoes not need to move relative to the air so it can ascend vertically or hover. (Itis useful to differentiate between the helicopter and autogyro. The autogyro hasrotary wings (blades) but as these are not powered, the ability to climb verticallyor hover is absent).

Helicopters may have more than one rotor, each rotor may have 2 or moreblades. Like a fixed-wing aircraft, the larger the helicopter, the greater the power required and the greater the number of blades. Many helicopters have a tail-rotor, this is simply to overcome the torque-reaction of the main-rotor, but alsoprovides yaw control. They must also have some form of device to allow therotor to rotate, following the possible failure of the engine.

When considering aerofoil performance, a critical parameter is the angle of attack, the angle between chord line relative airflow. A helicopter blade canmove in a somewhat complicated manner for reasons which will become clear,but it requires the introduction of several terms or definitions at this stage.

Definitions - refer to diagrams.

• Shaft axis - the axis of the main rotor shaft.

• Axis of rotation - the axis of rotation of the rotor head and blade assembly.(It is not necessarily the same as the shaft axis).

• Plane of rotation - the plane of rotation of the rotor head / blade assembly,

which is at right-angles to the axis of rotation.




• Tip path plane - the path of the rotor tips, parallel to the plane of rotation.

• Blade pitch - similar to the angle of incidence in fixed-wing terminology, it is

the angle between the chord-line and the plane of rotation.

• Rotor thrust and drag - equivalent to Lift and Drag and expressed relative

to the plane of rotation.• Coning angle - rise of blade due to thrust, thus the blade forms an angle

with the plane of rotation.




9.1 CYCLIC & COLLECTIVE CONTROLS

A helicopter is able to move vertically or horizontally, and its path can be acombination of both. Whatever the movement, it is the result of the rotor bladeforces being altered, in both magnitude and direction.

Vertical movement is achieved by increasing the pitch (blade angle) of all therotating blades, thus increasing the angle of attack and the lift. A lever, usuallyfound lying horizontally to the left of the pilot, is raised in a vertical sense. It is

known as the collective pitch lever . Just as drag increases when lift increases,the rotor drag increase necessitates an increase in power, in order to maintainrotor RPM, see diagram. (This is often achieved automatically by governor andcomputer).

Horizontal movement is achieved by 'tilting' the rotor disc in the direction of therequired movement. This tilting of the disc provides a horizontal component inaddition to the vertical force. Tilting is achieved by increasing the blade pitch on

one side whilst decreasing the pitch on the opposite side. This requires eachblade to alternately increase then decrease its pitch during 360º of disc rotation.This represents a cyclical change in pitch and therefore leads to the term cyclicpitch being applied to the lever which corresponds to the control column found onfixed wing aircraft.




9.2 ANTI-TORQUE CONTROL

The torque applied by the power unit to the rotor (and in turn to the airflow)results in an equal and opposite reaction being applied to the fuselage. Giventhat the shaft axis is vertical, this means that the fuselage will yaw. Use of a finand rudder is not possible (when hovering, there is no relative airflow) and so ahorizontal force creating a corrective moment must be generated. This is doneby a tail-rotor, replacing a fin and rudder, and driven by the power-unit. Because

a variation in main rotor torque requires a corresponding variation in tail-rotor force, the tail-rotor blade pitch is variable and is controlled by rudder-pedals. Thisallows the tail-rotor to both balance the torque, but also to deliberately yaw theaircraft.

The previous paragraphs have introduced the basic concept of rotary-wingaerodynamics, and have highlighted the cyclical nature of the aerodynamicforces. The torque reaction required a second rotor to oppose it, in the absenceof fixed aerodynamic control surfaces. These factors introduce their ownproblems which necessitate solutions that lead to added complexity.




9.3 EFFECT OF THE TAIL ROTOR

The torque reaction of the main rotor is overcome by moment provided by the tailrotor. Recalling basic physics, a torque is being balanced by a torque, but herethe balancing torque is not itself a couple, but a force multiplied by a distance.Considering forces, the tail-rotor force is unbalanced, and acts as though tryingto move the helicopter sideways. This is termed tail-rotor drift. It could bereduced by placing the tail-rotor as far as possible from the main rotor, but this is

not practical. The usual solution is to tilt the main disc to produce a sidewaysforce in the opposite direction, either automatically or manually.

If the tail-rotor force is below the sideways force of the main rotor, as outlinedabove, another couple will be created which tends to roll the helicopter. Hence itis termed tail-rotor roll. It can be alleviated by raising the line of action of the tailrotor force to the same level as the corrective force of the main rotor.

9.4 MAIN ROTOR HEAD CONFIGURATION & MOVEMENT

A blade has to be able to rotate about its chord axis, i.e. to alter its pitch, either cyclically or collectively.

As a result of these changes, the blades will also tend to rise or fall (remember the tip path is not the same as the plane of rotation, but creates a coning angle).To reduce bending stresses, blades are often allowed to 'flap' upwards or downwards by a flapping-hinge.




Similarly, variation in dragging-forces is accommodated by a drag-hinge. Theeffect of drag varies cyclically for several reasons and so the instantaneousposition of the blade may lead or lag about its main position. The drag-hingeallows movement backwards and forward but this movement is restricted bysome form of drag-damper.

Following a cycle pitch input, the variation in blade angle during rotation of therotor disc is theoretically complicated but practically less-so, as the blademovements about the hinges leads to the so-called 'flapping to equality'.

Documents

Basic Aerodynamics module 4