Principles of flight - 081 POF

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081 PRINCIPLES OF FLIGHT

G LONGHURST 1999 All Rights Reserved Worldwide
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COPYRIGHTAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or

transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,without the prior permission of the author.

This publication shall not, by way of trade or otherwise, be lent, resold, hired out or otherwise circulatedwithout the author's prior consent.

Produced and Published by the

PROFESSIONAL PILOT STUDY CENTRE

EDITION 1.01.00 1999

This is the first edition of this manual, and incorporates all amendments to previous editions, in whateverform they were issued, prior to July 1999.

EDITION 1.01.00 COPYRIGHT 1999 G LONGHURST

The information contained in this publication is for instructional use only. Every effort has been made to ensurethe validity and accuracy of the material contained herein, however no responsibility is accepted for errors or

discrepancies. The texts are subject to frequent changes which are beyond our control.

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TABLE OF CONTENTS


Aerodynamic Principles

Lift

DragStalling

Lift Augmentation

Control

Forces in Flight

StabilityHigh Speed Flight

Limitations
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081 Principles of Flight



Units

Systems of Units

Newton's Laws of Motion

The Equation of Impulse

Basic Gas Laws

Airspeed Measurement

Shape of an Aerofoil

The Equation of Continuity

Bernoullis Theorem


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Chapter 1 Page 1 G LONGHURST 1999 All Rights Reserved Worldwide

1Aerodynamic Principles

Units1. In order to define the magnitude of a particular body in terms of mass, length, time,acceleration etc., it is necessary to measure it against a system of arbitrary units. For example, onepound (lb) is a unit of mass, so the mass of a particular body may be described as being a multiple

(say 10 lb), or sub-multiple (say lb) of this unit. Alternatively the mass of the body could havebeen measured in kilograms, since the kilogram (kg) is another arbitrary unit of mass.

Systems of Units2. There are a number of systems of units in existence and it is essential when making

calculations to maintain consistency by using only one system. Three well-known consistent systemsof units are the British, the c.g.s. and the S.I. (Systeme Internationale). These are illustrated inFigure 1-1below:


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FIGURE 1-1

Units of

Measurement

3. The S.I. system of units is the one most commonly used. In this system, one Newton is theforce that produces an acceleration of 1 M/s when acting upon a mass of 1 kg.

Newton's Laws of Motion4. The motion of bodies is usually quite complicated, involving several forces acting at the sametime as well as inertia and momentum. Before considering the Laws of Motion, as described by SirIsaac Newton, it is necessary to define force, inertia and momentum.

BRITISH C.G.S. S. I.

SYSTEM

LENGTH Foot Centimetre Metre (m)

TIME Second Second Second (s)

ACCELERATION Ft/s C/s M/s

MASS Pound Gram Kilogram (kg)

FORCE Poundal Dyne Newton (N)


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5. Force is that which changes a body's state of rest or of uniform motion in a straight line. Themost familiar forces are those which push or pull. These may or may not produce a change ofmotion, depending upon what other forces are present. Pressure acting upon the surface area of a

piston exerts a force that causes the piston to move along its cylinder. If we push against the wall ofa building a force is exerted but the wall does not move, this is because an equal and opposite force isexerted by the wall. Similarly, if a weight of 1 kilogram is resting upon a table there is a force(gravitational pull) acting upon the weight but, because an equal and opposite force is exerted by thetable, there is no resultant motion.

Force Can Be Quantified6. Where motion results from an applied force, the force exerted is the product of mass andacceleration, or:

F= ma

Where: F = Force m = mass and a = acceleration7. Inertia is the tendency of a body to remain at rest or, if moving, to continue its motion in astraight line. Newton's first law of motion, often referred to as the law of inertia, states that everybody remains in a state of rest or uniform motion in a straight line unless it is compelled to changethat state by an applied force.


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Momentum

8. The product of mass and velocity is called momentum. Momentum is a vector quantity, in

other words it involves motion, with direction being that of the velocity. The unit of momentum hasno name, it is given in kilogram metres per second (kg m/s). Newton's second law of motion statesthat the rate of change of momentum of a body is proportional to the applied force and takes place inthe direction in which the force acts.

9. Newton's third law of motion states that to every action there is an equal and oppositereaction. This describes the situation when a weight is resting upon a table. For a freely falling bodythe force of gravity (gravitational pull), measured in Newtons , acting upon it is governed by:

F = mg

where g is acceleration due to gravity 9.81M/s, and m is themass of the body in kilograms.

10. If the same body is at rest upon a table it follows that, since there is no motion, there must bean equal and opposite force exerted by the table.

Motion with Constant Acceleration

11. When acceleration is uniform, that is to say velocity is increasing at a constant rate, the

relationship between acceleration and velocity can be expressed by simple formulae known as theequations of motion with constant acceleration. Under these circumstances velocity increases by thesame number of units each second, so the increase of velocity is the product of acceleration (a) andtime (t). If the velocity at the beginning of the time interval, (the initial velocity), is given the symbol(u) and the velocity at the end of the time interval, (the final velocity), is given the symbol (v) then thevelocity increase for a given period of time can be expressed by the equation:


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v = u + a.t

12. If it is required to calculate the distance travelled (s) during a period of motion with constant

acceleration, this can be done using the equation:

13. By substitution, using the above two equations, it is possible to develop two more equations:

And:

These are the equations of motion with constant acceleration.

The Equation of Impulse14. Given that the momentum of a body is the product of its mass and its velocity it follows that,providing mass and velocity remain constant, momentum will remain constant. A change of velocitywill occur if a force acts upon the body because:

s1

2--- u v+( )t=

s ut1

2---at2+=

v2 u2 2as+=

F ma=

A d i P i i l


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And therefore

15. If the force acts in the direction of motion of the body for a period of time (t), the resultantacceleration will cause a velocity increase from (u) to (v). This must also cause an increase inmomentum from (mu) to (mv). Combining the equations F = ma and v = u+at gives:

Which transposes to:

16. The change in momentum (final momentum minus initial momentum) due to a force actingon a body is the product of that force and the time for which it acts. This change in momentumcalled the impulse of the force and is usually identified by the symbol J. Hence:

Or:

a

F

m----=

v u tF

m----

+=

Ft mv mu=

J Ft=

J mv mu=


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A d i P i i l


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Charles' Law

21. Charles Law states that the volume of a fixed mass of gas at constant pressure expands by 1/

273 of its volume at 0C for every 1C rise in temperature. In other words, the volume of a givenmass of gas is directly proportional to its (absolute) temperature, providing its pressure does notchange.

22. This may be expressed mathematically as:

Pressure Law

23. The pressure law is the result of experimentation during the nineteenth century by a professorcalled Jolly and states that the pressure of a fixed mass of gas at constant volume increases by 1/273of its pressure at 0C for every 1C rise in temperature. In other words, the pressure of a given massof gas is directly proportional to its temperature, providing its volume does not change.

24. This may be expressed mathematically as:

V1

T1------ V

2

T2------ or V

T---- cons ttan=

=

P1

T1------

P2

T2------ or

P

T--- cons ttan=

=

A d i P i i l


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The Ideal Gas Equation

25. The three equations expressing the Gas Laws can be combined into a single or Ideal Gas

Equation which may be expressed mathematically as:

Static Pressure26. The static pressure of the atmosphere at any given altitude is the pressure resulting from themass of an imaginary column of air above that altitude. In the International Standard Atmosphere(ISA) at mean sea level the static pressure of the atmospheric air is 1013.25 millibars (mb), whichequates to 14.7 pounds per square inch (psi) or 29.92 inches of mercury (in. Hg). ISA mean sea level

conditions also assume an air density of 1.225 kilograms per cubic metre (kg/m) and a temperatureof +15C (288A). The standard notation for static pressure at any altitude is (P).

Dynamic Pressure

27. Air has density (mass per unit volume) and consequently air in motion has energy and mustexert pressure upon a body in its path. Similarly, a body moving in air will have a pressure exertedupon it that is proportional to its rate of movement, or velocity (V). This pressure due to motion isknown as dynamic pressure and is given the notation (q).

28. Energy due to motion is kinetic energy (K.E.) and in the S.I. system of units is measured injoules (j). From Bernoullis equation for incompressible flow the kinetic energy due to air movementmay be calculated using the formula:

P1V1

T1-------------

P2V2

T2------------- or

PV

T-------- cons ttan=

=



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29. To calculate kinetic energy in joules, density () must be in kilograms per cubic metre (kg/m)and velocity (V) in metres per second (m/s). One joule is the work done when a force of 1 newtonmoves the point of application of the force 1 metre in the direction of the force.

30. If a volume of moving air is brought to rest, as in an open-ended tube facing into theairstream, the kinetic energy is converted into pressure energy with negligible losses. Hence, dynamic

pressure:

31. It should be noted that dynamic pressure cannot be measured in isolation, since ambient

atmospheric pressure (static pressure) is always present also. The sum of the two, (q+P), is knownvariously as total pressure, stagnation pressure or pitot pressure and is given the notation (H or Ps).

Therefore, dynamic pressure:

KE1

2---V2=

q1

2---V2=

q q P+( ) P=



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Viscosity

32. Viscosity is a measure of the internal friction of a liquid or gas and determines its fluidity, or

ability to flow. The more viscous a fluid, the less readily it will flow. Unlike liquids, which becomeless viscous with increasing temperature, air becomes more viscous as its temperature is increased.The viscosity of air is of significance when considering scale effects in wind tunnel experiments andin terms of friction effects as it flows over a surface. Changes of density do not affect the airviscosity.

Density33. Density () is defined as mass per unit volume. The density of air varies inversely withtemperature and directly with pressure. When air is compressed, a greater mass can occupy a givenvolume or the same mass can be contained in a smaller volume. Its mass per unit volume hasincreased so, by definition, its density has increased.

34. When the temperature of a given mass of air is increased it will expand, thus occupying agreater volume. Assuming that the pressure remains constant the density will decrease because themass per unit volume has decreased.

35. Both the above statements assume that the air is perfectly dry. When air is humid, that is itcontains a proportion of water vapour, it becomes less dense. This is because water vapour weighs

less than air and so a given volume of air weighs less if it contains water vapour than if it were dry.Its mass per unit volume is less.



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Airspeed Measurement

Indicated Airspeed (IAS)36. The speed displayed on the airspeed indicator (ASI) is known as indicated airspeed. It doesnot include corrections for instrument errors and static pressure measurement errors (pressure error),both of which are very small. The indicated airspeed will differ progressively from actual flight speedas altitude increases and, consequently, density () decreases (q = V). The notation for IAS is

(VI).

Calibrated Airspeed (CAS)

37. Also known as Rectified Airspeed (RAS), this is the speed obtained by applying theappropriate instrument error and pressure error corrections to the ASI reading. The notation for

CAS is (Vc).

Equivalent Airspeed (EAS)

38. The equation for IAS (dynamic pressure) is derived from Bernoullis equation, which assumesair to be incompressible. Below about 300 knots the compression that occurs when the airflow is

brought to rest (as in the pitot tube) is negligible for most practical purposes, becoming increasinglysignificant above that speed. EAS is obtained by applying the compressibility correction to CAS.The notation for EAS is (Ve).



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True Airspeed (TAS)

39. The true airspeed is the actual flight speed relative to the surrounding atmosphere, regardless

of altitude. It must, therefore, take account of air density and is obtained by applying the formula:

where

40. TAS is given the notation (V). At 40,000 ft, where standard density is one-quarter sea leveldensity, TAS will be twice EAS (0.25 = 0.5). British ASIs, in common with most others, arecalibrated for ISA mean sea level density (0), where EAS = TAS. At all greater altitudes TAS will begreater than EAS by a proportional amount.

Shape of an Aerofoil41. The terminology for the dimensions that determine the shape of an aerofoil section is shownin Figure 1-2below.

TASEAS

------------=

relative air density

0-----= =



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FIGURE 1-2

Aerofoil Section

Chord Line

42. A straight line joining the leading edge to the trailing edge of the aerofoil.

Chord (c)43. The distance between leading and trailing edge measured along the chord line.

Thickness/Chord Ratio

44. The maximum thickness of the aerofoil section, expressed as a percentage of chord length. A

typical figure is about 12 per cent. The distance of the point of maximum thickness from the leadingedge, on the chord line, may also be given as a percentage of chord length. Typically it is about 30percent.



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Mean Camber Line

45. A line joining the leading and trailing edges which is equidistant form the upper and lower

surfaces along its entire length.

Camber

46. The displacement of the mean camber line from the chord line. The point of maximumcamber is expressed as a percentage and is the ratio of the maximum distance between mean camber

line and chord line to chord length. The amount of camber and its distribution along the chorddepends largely upon the operating requirements of the aircraft. Generally speaking, the higher theoperating speed of the aircraft the less the camber (i.e. the thinner the wing).

Nose Radius

47. The nose or leading edge radius is the radius of a circle joining the upper and lower surfacecurvatures and centred on a line tangential to the curve of the leading edge.

Angle of Attack ()48. The angle between the chord line and the relative airflow (RAF). This may also be referred to

as incidence, but must not be confused with the angle of incidence. Furthermore, it is essential todifferentiate between the angle of attack and pitch angle, or attitude, of the aircraft. The latter is, ofcourse, measured relative to the horizontal plane.



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Angle of Incidence

49. The angle between the aircraft wing chord line and the longitudinal centreline of the aircraft

fuselage.

The Wing Shape

50. The shape of an aircraft wing in planform has a great influence on its aerodynamiccharacteristics and will be discussed in depth in later chapters. The terminology describing the

dimensions that determine wing shape is listed below.

Wing Span

51. The straight-line distance measured from tip to tip. See Figure 1-3.



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FIGURE 1-3

Wing Span

Wing Area

52. The plan surface area of the wing. In a wing of rectangular planform it is the product of spanx chord.



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Aspect Ratio

53. The ratio of wing span to mean chord or to wing area.

Wind Loading

54. The weight per unit wing area.

Root Chord55. The chord length at the centreline of the wing (the mid-point along the span).

Tip Chord

56. The chord length at the wing tip.

Tapered Wing

57. A wing in which the root chord is greater than the tip chord.

Taper Ratio

58. The ratio of tip chord to root chord usually expressed as a percentage.

Quarter Chord Line

59. A line joining the points of quarter chord along the length of the wing.

span

2



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Swept Wing

60. A wing in which the quarter chord line is not parallel with the lateral axis of the aircraft. See

Figure 1-4.

Sweep Angle

61. The angle between the quarter chord line and the lateral axis of the aircraft. SeeFigure 1-4.



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FIGURE 1-4

Sweep Angle

Mean Aerodynamic Chord62. The chord line passing through the geometric centre of the plan area of the wing (ie. thecentroid). SeeFigure 1-5.



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FIGURE 1-5

Mean

Aerodynamic

Chord

Dihedral63. The upward inclination of the wing to the plane through the lateral axis. See Figure 1-6.



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FIGURE 1-6

Dihedral

Anhedral

64. The downward inclination of the wing to the plane through the lateral axis. See Figure 1-7.

FIGURE 1-7

Anhedral

The Equation of Continuity65. The equation of continuity states that mass cannot be either created or destroyed. Air massflow is a constant.



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e ody a c c p es


66. Figure 1-8illustrates the streamline flow of air through a cylinder of uniform diameter. Theair mass flow is the product of the density of the air (), the cross-sectional area of the cylinder (A)and the flow velocity (V). At any point along the cylinder:

FIGURE 1-8

Streamline Flow

67. Mass flow = AV = constant is the general equation of continuity, which applies to bothcompressible and incompressible fluids. In compressible flow theory it is convenient to assume thatchanges in density can be ignored at speeds below about 0.4 Mach and a simplified equation ofcontinuity:

Airmass flow AV cons ttan= =

AV cons ttan=



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y p


68. Consider now the streamline airflow through a venturi tube as illustrated at Figure 1-9.Given that mass flow is constant at any point and is the product of AV then at point Y, since thecross-sectional area (A) is reduced, velocity (V) must increase in order to maintain the equation of

continuity.

FIGURE 1-9

69. In other words, a reduction in cross-sectional area (as in a venturi tube) produces an increasein velocity and vice-versa.

Bernoullis Theorem70. A gas in motion possesses four types of energy. Potential energy (due to height), heat energy,pressure energy and kinetic energy (due to motion). Bernoulli demonstrated that in an ideal gas insteady streamline flow the sum of the energies remains constant. At low subsonic (less than 0.4mach) flow air can be conveniently regarded as an ideal gas (incompressible and inviscid). In thesecircumstances Bernoulli's Theorem can be further simplified by assuming there is no transfer of heator work in or out of the gas and by ignoring the insignificant changes in potential energy and heatenergy.

71. For practical purposes then, in streamline flow of air around an aircraft wing at low subsonicspeed:



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y p


pressure energy + kinetic energy = constant

72. This can be expressed as:

73. Where P = static pressure. In other words, static pressure + dynamic pressur = constant.

74. From this simplified Bernoulli's Theorem it is evident that an increase in velocity of gas flow

results in a decrease in static pressure, and vice versa. Hence at point Y in Figure 1-9the increase invelocity of airflow will produce a decrease in pressure.

P 1

2---V2 cons ttan=+



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p g


Lift

Airflow Round an Aerofoil

Two-dimensional Flow

Three Dimensional Flow

Wake Turbulence

Lift

Lift


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2Lift

Airflow Round an Aerofoil1. As stated in the previous chapter the relationship between pressure and velocity in the airflowpatterns around an object is that defined by Bernoulli. The airflow impacting on the object at a pointnear its leading edge will be brought to rest, or stagnate. At the stagnation point the velocity is zero

and the pressure equal to the total pressure of the air stream, that is to say ambient atmosphericpressure plus dynamic pressure. As the airflow divides and passes around the object the increases oflocal velocity, characterised by closely spaced streamlines, produce decreases of local static pressure.Pressures in excess of ambient atmospheric pressure are conventionally referred to as positive (+) andpressures below ambient atmospheric pressure as negative (-). The type of airflow around the bodywill be either Steady Streamline Flow or Unsteady Flow.

Steady Streamline Flow

2. In this type of airflow the flow pattern can be represented by streamlines. Where thestreamlines appear close together high local velocities, greater than the free stream velocity, exist.Where the streamlines are widely separated velocity is lower than free stream velocity. Steady

streamline flow can be divided into two types.

(a) Classical Linear Flow. In this flow pattern the streamlines basically follow thecontours of the body, with no separation of the airflow from the surface. Figure 2-1illustrates classical linear flow around an aerofoil.

Lift


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FIGURE 2-1

(b) Controlled Separated Flow or Leading Edge Vortex Flow. It is possible to design anaerofoil such that the airflow close to the surface separates at the leading edge andforms a controlled vortex. The main streamline flow is then around this vortex. Thishas advantages with swept-wing and delta wing planforms, as will be shown in laterchapters. This is shown at Figure 2-2.

FIGURE 2-2

Leading Edge

Vortex Flow

Lift


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Unsteady Flow

3. Unsteady Flow occurs when the airflow separates from the surface of the body and the flow

parameters (eg. speed, direction, pressure), at any point, vary with time. The flow thus cannot berepresented by streamlines.

Two-dimensional Flow4. An aerofoil section has only two dimensions, from leading edge to trailing edge and from

upper surface to lower surface, known as chord and its thickness. Hence, when considering airflowaround it, the consideration is limited to flow in two dimensions only.

Aerodynamic Forces on Surfaces

5. Associated with the velocity changes as air flows around an aerofoil there will, as has already

been explained, also be pressure changes. If the aerofoil is inclined to the airflow as shown inFigure 2-3, it will be seen from the streamlines that the velocity over the upper surface is greater thanthat over the lower surface. According to Bernoulli, the greater the velocity the lower the localpressure, so there is a pressure difference between the upper and lower surfaces such that a force willbe acting upwards.

Lift


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FIGURE 2-3

Airflow Around an

Aerofoil

6. The angle at which the aerofoil is inclined to the airflow is called the angle of attack (). Thegreater the angle of attack, the greater the pressure difference and therefore the greater the upwardforce produced. This is true up to the point at which the airflow separates from the upper surface,

known as the point of stall. As the airflow approaches the leading edge of the aerofoil it is turnedtowards the lower pressure on the upper surface. This effect is known as upwash. As it leaves thetrailing edge it returns to its original, free stream location and this is termed downwash. The upwardforce produced as air flows over the aerofoil is the source of lift.

7. Figure 2-4illustrates the aerodynamic forces acting upon an aerofoil inclined at an angle ofattack () to the relative airflow.

Lift


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FIGURE 2-4

Aerodynamic

Forces Acting on

an Aerofoil

8. The resultant of all the aerodynamic forces acting on the wing is also referred to as the TotalReaction. The lift force is the component of the resultant force acting perpendicular to the relativeair flow. The component of the resultant force acting parallel to the relative airflow is known asdrag.

Streamline Pattern and Pressure Distribution

9. Let us now consider the pressure distribution around a symmetrical aerofoil. A symmetricalaerofoil is one in which the chord line and the mean chord line are co-incident. Figure 2-5a showsthe streamline pattern around a symmetrical aerofoil at zero degrees angle of attack and Figure 2-5bshows the pressure distribution for the same situation.

Lift


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FIGURE 2-5

Symmetrical

Aerofoil at Zero

Lift Angle of

Attack

(a) Streamline

Flow

(b) Pressure

Distribution

10. Notice from Figure 2-5(b) how the pressure distribution around the aerofoil can beconveniently represented in vector form. The pressure at any point on the upper and lower surfacesof the aerofoil is represented by a vector at right angles to the surface and whose length is

proportional to the difference between absolute pressure at that point and free stream static pressure.Conventionally, pressures higher than ambient, ie. positive, are represented by a vector plottedtowards the surface and for negative values, the vector is plotted away from the surface.

Lift


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11. At the leading edge of the aerofoil, where the streamlines diverge, positive pressure exists.Where the airflow is forced to divide and flow around the aerofoil the streamlines are close togetherand high local velocities and negative static pressure exists. The negative pressures are the same

above and below the aerofoil, so with no pressure difference between upper and lower surfaces nolift is generated. The angle of attack at which this occurs is referred to as the zero lift angle of attack,for that particular aerofoil. It should be noted that a stagnation point also occurs at the trailing edge,where the flow velocity decreases to free stream velocity.

12. Consider now the symmetrical aerofoil at a positive angle of attack as shown in Figure 2-6.

The greatest local velocities occur where the streamlines are forced into the greatest curvature asshown at Figure 2-6a. Consequently the highest velocities occur over the forward part of the uppersurface. Upwash is generated ahead of the aerofoil, moving the forward stagnation point under theleading edge and creating an area of decreased local velocity below the forward part of the lowersurface. Behind the aerofoil downwash is generated.

Lift


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FIGURE 2-6

Symmetrical

Aerofoil at Positive

Angle of Attack (a)

Streamline Flow

(b) Pressure

Distribution

13. Figure 2-6(b) illustrates the pressure distribution from which it can be seen that there is amarked pressure differential between upper and lower surfaces, creating positive lift.

Lift


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14. A practical aircraft wing would not normally be of symmetrical aerofoil section, but wouldhave some positive camber since such a section is capable of producing lift even at very low angles ofattack.

15. Figure 2-7 illustrates the pressure distribution around a conventional cambered aerofoilinclined at a small positive angle of attack.

FIGURE 2-7

Pressure

Distribution

Around a

Cambered

Aerofoil at a Small

Positive Angle of

Attack

Lift


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16. At point A at Figure 2-7, total pressure (pitot pressure, stagnation pressure) prevails and thisis the forward stagnation point. As the air passes over the upper surface towards point B, it ismoving into an area of reducing pressure and point B is where minimum pressure exists on the upper

surface Beyond B, pressure is increasing until total pressure is recovered at the rear stagnation pointC and thus the air travelling from B to C is moving against an adverse pressure gradient. This ismost significant as the only way the air can travel against this adverse pressure gradient is by virtueof its kinetic energy and should this be insufficient the air flow will break away or separate from thewing. This concept is fully covered in Chapter 4 under Stalling.

17. Furthermore, if points A and C are stagnation points and there is negative pressure on bothupper and lower surfaces, then points X on the upper surface and Y on the lower surfaces are pointsof static pressure. To reduce the effect of the pressure reduction on the lower surface the curvature ofthe lower wing surface is kept to a minimum.

Effect of Angle of Attack on Pressure Distribution

18. Figure 2-8 illustrates the pressure distribution around a conventional cambered aerofoilthrough the working range of angles of attack. Such an aerofoil produces lift at zero degrees angle ofattack because the aerofoil over the upper surface, with its greater curvature is accelerated more thanover the lower surface creating a pressure differential and thus positive lift. It follows, therefore, thatthe zero lift angle of attack is a negative value (for this particular aerofoil it is -4) when thedecreased pressure above and below the aerofoil is equal and hence no lift is generated.

Lift


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19. As the angle of attack is progressively increased, the negative pressure above the upper surfacesteadily increases, whilst that below the lower surface decreases. Beyond about +8the pressurebelow the lower surface becomes positive. Thus, it can be seen that with increasing angle of attack,

the pressure differential between upper and lower aerofoil surface increases. However, at the lowerangles of attack, it is the pressure reduction on the upper surface which is largely responsible for thelift generated whereas at the higher incidence, it is both the reduced pressure on the upper surfaceand the increased pressure on the lower surface which contribute to lift generation.

Lift


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FIGURE 2-8

Pressure

Distribution

Around anAerofoil

Lift


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Flow Separation at High Angles of Attack

20. Beyond about +14 in this typical aerofoil the low-pressure area on the upper surface

suddenly reduces as the airflow separates from the surface, becoming unstable and turbulent insteadof streamline, significantly reducing the total lift. The contribution to the total lift produced by theincreased pressure on the lower surface however, remains relatively unchanged. This occurs at thecritical or stalling angle of attack. At angles of attack beyond the stall the aerofoil may be regardedas a flat plate inclined to the airflow, as shown in Figure 2-9and the lift produced is as a result of thestagnation pressure and flow deflection below the plate, but this is more than offset by the high drag

force due to the plates resistance to the airflow. Stalling is fully covered in Chapter 4.

Lift


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FIGURE 2-9

Flat Plate Effect

Centre of Pressure

21. The pressure differential between the upper and lower surfaces can be convenientlyrepresented by a single aerodynamic force acting at a particular point on the chord line. This point isknown as the centre of pressure (CP). Both the resultant aerodynamic force and hence lift, and thepoint through which it acts (CP) vary with angle of attack.

Lift


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22. From Figure 2-8it can be seen that as the angle of attack increases, the magnitude of the forceincreases and the centre of pressure gradually moves forwards towards the leading edge until thepoint of stall when, with the aerofoil past its stalling angle of attack (or critical angle), the force

reduces and the CP moves rapidly rearwards. With a cambered aerofoil, the centre of pressuremovement over the normal operating range of angles of attack is no further forward thanapproximately 25 - 30% chord, measured from the leading edge. With a symmetrical aerofoilsection there is virtually no movement of the CP over the working range of angles of attack, insubsonic flight.

23. The movement of the CP with angle of attack is shown for a cambered aerofoil atFigure 2-10.

Lift


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FIGURE 2-10

Centre of

Pressure

Movement

Lift


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24. Let us now briefly consider moments, couples and coefficients.

Moment

25. The moment of a force about any point is the product of the force and the perpendiculardistance from the line of action of the force to that point. See Figure 2-11.

FIGURE 2-11

Moment of a

Force

Lift


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Couple

26. Two equal forces acting parallel but in opposite directions are called a couple. The moment

of a couple is the product of one of the forces and the perpendicular distance between them. SeeFigure 2-12.

FIGURE 2-12

Moment of a

Couple

Lift


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Coefficients

27. When considering lift, drag and pitching moments, it is much more convenient to use their

respective co-efficients, CL,CD,CM. These co-efficients are non-dimensional and independent ofdensity, scale of the aerofoil and velocity prevailing at the time such studies are carried out. Theydepend on the shape of the aerofoil and vary with angle of attack.

Aerodynamic Centre

28. An aircraft pitches about the lateral axis which passes through the centre of gravity. Thewing pitching moment is therefore the product of lift and the distance between CG and CP of thewing. But, as we know, the position of the CP is not fixed and moves with changes in angle of attackand therefore, calculation of the pitching moment is quite involved and complicated.

29. The pitching moment and hence its coefficient (CM) depends not only on the lift force and the

position of the CP, both of which change with change in angle of attack, but also the point about

which the moment is considered.

30. For example, if we take a point of reference arbitrarily towards the leading edge then the nosedown pitching moment about this point (B), increases with increasing angle of attack because,although the centre of pressure movement is forward, its effect is less than that of the increasing liftforce, as shown in Figure 2-13.

Lift


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FIGURE 2-13

31. Now, about a point towards the trailing edge (A) the nose up pitching moment increasesprogressively with increasing incidence as shown at Figure 2-14.

Lift


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FIGURE 2-14

Pitching Moment

Change About

Point A

32. It follows, therefore, that if about the leading edge, the nose-down pitching momentprogressively increases and about the trailing edge, the nose-up pitching moment progressivelyincreases, then there must be a point somewhere on the chord line between points A and B aboutwhich there is no change in pitching moment with changes in angles of attack. This point is thewing aerodynamic centre, shown at Figure 2-15and is, at subsonic speeds, approximately at quarterchord (ie. 25% chord from the leading edge).

Lift


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FIGURE 2-15

Pitching Moment

About Wing

AerodynamicCentre

33. This can be represented graphically at Figure 2-16which shows curves of CMplotted against

CLwhere, conventionally, nose-up pitching moments are referred to as positive, and nose-down,

negative.

Lift


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FIGURE 2-16

Cmagainst CL

Lift


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34. It can be seen from Figure 2-16that at zero lift there is a residual pitching moment present.It is negative, and, by definition, remains constant about the aerodynamic centre up to the stall (ieCLmax). By reference to Figure 2-17which shows the pressure distribution around our cambered

aerofoil section at its zero lift angle of attack, it can be seen that the resultant forces due to thepressure reduction torwards the trailing edge on the upper surface and towards the leading edge onthe lower surface produce a nose-down (negative) pitching moment.

35. The pitching moment coefficient CMat the zero lift angle of attack is referred to as CMoas

shown in Figure 2-16.

Lift


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FIGURE 2-17

Pressure

Distribution at

Zero Lift Angle ofAttack

Lift


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Three Dimensional Flow36. When considering airflow around an aircraft wing the flow becomes three-dimensional. This

is because there is an element of spanwise flow above and below the wing in addition to thechordwise flow already discussed.

Spanwise Flow

37. When an aircraft wing is producing lift the local static pressure on the upper surface is lower

than that on the lower surface. Air will flow from an area of higher pressure to one of lowerpressure. Since a wing is of finite length, this means that air will flow from the under surface, aroundthe wingtip, to the upper surface. Consequently, a spanwise flow of air occurs from the rootoutwards towards the tip on the under surface, around the tip, and from the tip inwards towards theroot on the upper surface. The effect is illustrated at Figure 2-18.

FIGURE 2-18

Spanwise Flow

38. The flow at any point on the trailing edge leaving the upper surface will, therefore, be movingin a different direction from that leaving the lower surface as shown at Figure 2-19.

Lift


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FIGURE 2-19

Upper and Lower

Surface Flow

39. Thus the flow at the trailing edge of the wing where the upper and lower surface flows meet isof a vortex nature and these vortices are continuously shed all along the trailing edge, shown atFigure 2-20in which the trailing edge is viewed from behind.

FIGURE 2-20Trailing Edge

Vortices


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62/475

Lift


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Induced Downwash

41. The effect of these trailing vortices is to produce a downward airflow, or downwash which

influences the whole flow over the wing with two important consequences:

(a) The effective angle of attack is reduced by the modified relative airflow and thus thelift generated is also reduced. This is shown at Figure 2-22. Furthermore, the dragcharacteristics of the wing are adversely affected and this induced or vortex drag willbe covered in detail in Chapter 3.

(b) The flow over the tailplane in a conventional aircraft design will be affected by thedownwash such that its effective incidence is also reduced with importantconsequences in respect of longitudinal stability, which is covered fully in Chapter 8.

FIGURE 2-22

Downwash Effect

on Angle of Attack

Lift


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42. The magnitude of the downwash is determined by the vortex formation which in turn is aconsequence of spanwise flow. Spanwise flow results from wing tip spillage, the magnitude of whichis determined by the pressure differential between upper and lower surfaces. In other words, any

parameter which increases the pressure differential will also increase downwash and its effects.

Spanwise Lift Distribution

43. The distribution of lift along the span of the wing depends upon a number of variables, one ofwhich is the variation of chord length along the span (in other words, the wing planform). A

rectangular planform (i.e. constant chord throughout the span) wing creates most of its trailingvortices at the tips, consequently downwash is greatest at the tips. A tapered wing, with the chordprogressively narrowing toward the tip, produces a greater proportion of lift at the centre and thetrailing vortices are greatest towards the wing root.

44. Theoretically a constant downwash condition along the span can be achieved if the liftincreases from zero at the tip to a maximum at the root in an elliptical fashion as shown in

Figure 2-23. Such a condition is highly desirable for the reduction of induced drag, (explained fullyin Chapter 3), and one way of achieving it is with a planform in which the chord increases ellipticallyfrom tip to root. There are, however, manufacturing and structural difficulties with such a planformand it has been found that a close approximation to elliptical spanwise lift distribution is possibleusing a tapered wing with varying aerofoil section.

Lift


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FIGURE 2-23

Elliptical Lift

Distribution

45. A convenient way to consider lift distribution is to use the ratio of the lift coefficient at anygiven point on the wing span (the local lift coefficient) (Cl), to the overall wing lift coefficient (CL),

and plot this against the semi-span distance. When this is done for an elliptical planform wing aconstant value is obtained from root to tip since:

46. Figure 2-24shows spanwise lift distribution in this format for a number of wing planforms.The elliptical planform (A) has only been used in a few cases, most notable being the Spitfire. Therectangular planform (B) is often used for light private aircraft and trainers, because of its favourable

stall characteristics. Larger aircraft invariably use tapered wings, in order to limit structural weightand maintain stiffness, with a taper ratio of between 20% and 45% (C) and (D).

Cl

CL------ 1.0=

Lift


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FIGURE 2-24

Spanwise Lift

Distribution

Lift


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Wake Turbulence47. The trailing vortices produced by a wing when it is creating lift extend for a considerable

distance behind the aircraft. The greater the lift being produced, the stronger these vortices will be.With a large aircraft these vortices create significant turbulence in the wake of the aircraft and takeseveral minutes to dissipate. This wake turbulence is sufficient to seriously affect the controllabilityof other aircraft entering it and pilots are strongly advised to maintain a specified separation whenfollowing a large aircraft, especially in close proximity to the ground (i.e. during the take-off andlanding phase). The separation required will depend upon the relative sizes of the aircraft and may

be several miles if the following aircraft is much smaller than the leading one.

48. In addition, the strength of the vortices is universally proportional to aircraft speed andaspect ratio. The increased angle of attack, for a given weight, associated with low speed andstronger vortices from a low aspect ratio wing will result in increased wake turbulence.Furtheremore, when trailing edge flaps are extended, extra vortices are shed from the flap tips whichtend to weaken the tip vortices and hasten vortex breakdown.

49. The vortex strength will, therefore, be greatest with increased aircraft weight, reduced speedand clean configuration ie. shortly after take-off.

50. This wake turbulence is influenced by proximity of the aircraft to the ground and also windconditions. The vortices slowly descend under downwash influence to approximately 1000ft below

the aircraft until when, in ground effect, they drift outwards from the generating aircrafts track.Any prevailing cross-wind, between 5-10kts, will retain the upwind vortex on the generatingaircrafts track ie. on the runway after take-off.

Lift


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Lift51. Lift is defined as that component of the total aerodynamic force which is acting perpendicular

to the direction of flight. The magnitude of the total aerodynamic force, and therefore the liftgenerated, is dependent upon a number of variables of which the following are the most important:

(a) Free stream velocity (V)

(b) Air density ( )

(c) Wing area (S)

(d) Angle of attack ()

(e) Wing planform and aerofoil section

(f) Surface condition (rough or smooth)

(g) Air viscosity ()

(h) Compressibility of the air.

52. The last two variables, viscosity and compressibility of the air, and their effect on lift will be

discussed in subsequent chapters.

53. However, the major factors are dynamic pressure (V), wing surface area (S) and therelative pressure distribution existing on the surface, ie. the coefficient of lift (CL).

Lift


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Coefficient of Lift (CL)

54. The simplified equation for calculating aerodynamic force is VS multiplied by a

coefficient proportional to the change in force that occurs when angle of attack is changed. Thiscoefficient is the lift coefficient (CL) and the equation for lift is:

L = CL VS

CLfor a given aerofoil section and planform allows for varying angle of attack and other variables

not included in the equation. By transposition of formula it can be seen that:

55. The coefficient of lift is the ratio of lift pressure to dynamic pressure.

Effect of Angle of Attack

56. It is convenient to represent lift in coefficient form (CL) and then consider the factors affecting

lift in terms of CLwhich can then be depicted graphically. It is possible from experimentation to

obtain values of CLand plot them against angle of attack for a given wing at constant airspeed andair density.

CLlift

1

2---V2S----------------=

Lift


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57. Figure 2-25 shows a graph of CL against angle of attack () for a moderately camberedaerofoil section. It will be seen that the curve is linear for the greater part, with the coefficient of liftbeginning to fall off at about +14. The lift coefficient reaches a maximum value at about +15(CL

max) as the section reaches stalling angle (stall), otherwise known as the critical angle (crit).Therefore any further increase in angle of attack results in marked reduction in CL.

Lift


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FIGURE 2-25

Lift Curve

Lift


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Effect of Camber

58. The slope of the CL/curve is constant regardless of the camber of the aerofoil, but values of

CLare greater for any given angle of attack in sections of increased camber. This is illustrated atFigure 2-26.

FIGURE 2-26

Effect of Camber

on the Lift Curve

Lift


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59. Note that the curve passing through the origin at Figure 2-26 is representative of asymmetrical wing section. At zero angle of attack such a section produces no lift since the pressuredistribution on the upper and lower surfaces is identical and there is thus no pressure differential. As

we know from our pressure distribution studies earlier in this chapter, the angle of attack at whichthe CLis zero is known as the zero-lift angle of attack. For a symmetrical aerofoil it is 0and for a

cambered section, typically between -2and -4.

Effect of Leading Edge Radius

60. The shape of the leading edge largely determines the stall characteristics of a wing. A bulbousleading edge with a corresponding large radius results in a well-rounded peak to the CL curve

whereas a small leading edge radius will encourage a leading edge stall as the airflow will be less ableto negotiate the sharper corner at large angles of attack. The peak to the CLcurve is much more

pronounced and the small radius produces a correspondingly more abrupt stalling characteristic.

Lift


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FIGURE 2-27

Effect of Leading

Edge Radius on

the Lift Curve

Lift

Eff f A R i


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Effect of Aspect Ratio

61. The effective angle of attack is reduced by induced downwash, ie. the downward component

of airflow at the rear of the wind caused by trailing edge vortices. A wing of infinite span has no tipvortices, no induced downwash and therefore no reduction in the angle of attack and it is a wing ofhigh aspect ratio which approaches this condition of infinite span. Conversely, a wing of low aspectratio, having greater trailing edge vorticity will have a greater reduction in the effective angle ofattack and thus produce less lift than a wing of high aspect ratio, with the same wing area.Figure 2-28shows the effect of aspect ratio on the CLcurve.

Lift

FIGURE 2 28


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FIGURE 2-28

Effect of Aspect

Ratio on the Lift

Curve

Lift

Eff t f S b k


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Effect of Sweepback

62. If an aircrafts wings are swept back and the wing area remains the same, the aspect ratio

( /area) must be less than its equivalent straight wing. Therefore, the effect on the CLcurve for

a swept wing compared to a straight wing is similar to that for a low aspect ratio wing whencompared to a high aspect ratio wing . This effect is shown at Figure 2-29.

FIGURE 2-29

Effect of

Sweepback on theLift Curve

span2

Lift

63 N th l thi d t t f th di ti t d ti i C f hi hl t


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63. Nevertheless, this does not account for the distinct reduction in CLMAX for highly swept

wings, however this is fully explained in Chapter 4, Stalling.

Effect of Surface Condition64. Roughness of the wings surface, especially at or near the leading edge has a considerableeffect particularly on CLMAX. Figure 2-33shows the reduction in CLMAXfor a roughened leading

edge when compared to a relatively smooth surface. Any roughness of the wing surface beyond 25%has little effect on CLMAXor the curve gradient.

Lift

FIGURE 2 30


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FIGURE 2-30

Effect of Leading

Edge Roughness

on the Lift Curve

Lift

Eff t f I d F t


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Effect of Ice and Frost

65. Ice or frost deposits on the aircraft surface will invariably have a detrimental effect upon the

performance of the aeroplane. In either case the aerodynamic shape will be changed and theboundary layer performance will be altered such that turbulence and separation occur more readilythan with a clean aircraft. Since the wing is responsible for the vast majority of the lift generated theformation of ice or frost on its surface may cause considerable changes to the aerodynamiccharacteristics of the aircraft.

Ice at the Stagnation Point66. There are essentially two effects of large ice formations on the leading edge of the wing. Inthe first place the contour of the aerofoil section may be considerably changed, as shown atFigure 2-31.

FIGURE 2-31

Effect of Ice onLeading Edge

67. This will almost certainly induce severe local pressure gradients, reducing boundary layervelocity locally and possibly causing leading edge separation, with consequent loss of lift. Secondly,some forms of ice have great surface roughness that significantly increases surface friction. Thisreduces the boundary layer energy and increases drag. The overall effect is a decrease in themaximum lift coefficient and an increase in drag.

Lift

68 The effects in practical terms are that the aircraft will require more power to maintain a given


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68. The effects in practical terms are that the aircraft will require more power to maintain a givenairspeed, the stalling speed will be higher and the stalling angle of attack will be lower.

69. Leading edge icing is most likely to occur during flight in icing conditions and should beprevented at the onset by the correct use of anti-icing procedures. Its effect will be most noticeable atthe low flight speeds associated with approach and landing, where the higher stalling speed willrequire a higher landing speed.

Surface Ice and Frost

70. A thin layer of ice or frost on the upper surface of the wing may not significantly change theaerodynamic contour of the aerofoil section. However, the surface roughness, especially of hardfrost, can increase surface friction and reduce boundary layer energy sufficiently to promote a loss oflift by as much as 25%. There will also be an increase of drag due to the increased skin friction.

71. The loss of boundary layer energy will lead to separation and a reduction in the stalling angle

of attack. The maximum lift coefficient will be reduced and stalling speed will be increased.72. Surface coatings of frost can occur in flight, but are more commonly associated with groundformation. Application of adequate ground de-icing and anti-icing procedures in conditions whereice or frost may form on the upper surfaces of a parked aircraft are essential prior to flight. The lossof lift and increased drag due to such coatings will seriously reduce take-off performance, to theextent that the aircraft may have difficulty in becoming airborne. Even if it does, its climb

performance may be degraded to the point where obstacles cannot be cleared.


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Lift

Lift Coefficient and Speed for Constant Lift


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Lift Coefficient and Speed for Constant Lift

75. In straight and level flight the lift is equal to the weight and:

76. Wing area (S) does not change and. at constant altitude, density () remains essentiallyconstant. In order to maintain constant lift both the lift coefficient (CL)and speed (V) must be kept

constant or, if one increases the other must decrease proportionately. Since varying angle of attackvaries (CL), and the optimum angle of attack has been shown to be about +4, maintaining constant

lift is best achieved by adjusting airspeed. The relation between the lift coefficient and speed, forconstant lift, is shown in the graph atFigure 2-33.

Lif t CL1

2---V2S=

Lift

FIGURE 2-33


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FIGURE 2-33

Lift Coefficient and

Airspeed

Relationship forConstant Lift

77. During flight the weight will progressively decrease as fuel is used and the lift must decreaseaccordingly, or the aircraft will climb. The ideal aerodynamic solution to this is to reduce airspeedprogressively, but in commercial operations, for ease of flight planning and other reasons, it isnormal to fly at constant speed and trim the aircraft to reduce angle of attack (incidence)progressively.


Dra


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Drag

Zero Lift Drag

Lift Dependent Drag

Total Drag

Speed Stability

Drag

Drag


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3Drag

1. The total drag force acting upon an aircraft in flight is the sum of all the components of thetotal aerodynamic force that are acting parallel and opposite to the direction of flight. Total drag ismade up of those factors arising from the generation of lift (Lift Dependent Drag) and those whichare present when no lift is being generated (Zero Lift Drag).

Zero Lift Drag2. When an aircraft in flight is not generating any lift there is no component of the totalaerodynamic force acting perpendicular to the flight path. Consequently all of the aerodynamicforce must be acting parallel and opposite to the direction of flight. This force is known as zero lift,or parasite, drag and comprises surface friction drag, form drag and interference drag.

Profile Drag

3. Otherwise known as boundary layer drag, profile drag is the term used to describe thecombined effects of boundary layer normal pressure drag (form drag) and surface friction drag.

Drag

Form Drag


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Form Drag

4. We have already seen that when moving air is either totally or partially brought to rest on the

surface of an object, a pressure greater than static pressure, that is to say total, or stagnationpressure, is acting on the surface of the body. The velocity differences between leading and trailingedge mean that there are also pressure differences, pressure at the low velocity trailing edge beinggreater than at the relative high velocity leading edge. This adverse pressure gradient opposes theairflow across the surface, creating pressure drag. Form drag is otherwise known as boundary layernormal pressure drag and can form a significant portion of the total drag force acting on the aircraft.

5. Consider a circular flat plate, which is placed in a wind tunnel so that the flat surface of theplate is at right angles to the flow of air. If, over the entire surface area, the air was broughtcompletely to rest, a pressure equal to the dynamic pressure would be felt at all points. The forcethus created would be equal to the dynamic pressure multiplied by the surface area of the plate, orVS, where S is the surface area.

6. The situation is complicated somewhat since the air is not brought totally to rest over thewhole surface. Some of the air flows around the edges, resulting in the formation of a low pressurearea behind the back of the plate. This effectively creates a suction, which tends to retard the airflowpassing the plate (or the passage of the plate through the air).

7. A turbulent wake will form behind the plate, in the case of a flat plate the amount ofturbulence will be considerable and the drag factor therefore will be extremely high. With a

streamlined wing the amount of turbulence will be much lower and therefore the drag factor will beconsiderably reduced. We can therefore see that the shape as well as the frontal area will affect theamount of drag produced. It is the shape, which gives us the co-efficient of drag (CD), and the total

form drag formula now reads:

Drag

1 2


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8. It is clear that a flat plate is a most inefficient shape to try and move through the air. If wenow consider a sphere of the same diameter as a flat plate placed in the airflow, it is not hard tovisualise that this shape will produce considerably less drag than the flat plate. The nature of theairflow around these two objects is illustrated at Figure 3-1.

FIGURE 3-1

Airflow Around aFlat Plate and

Sphere

9. It is seen at Figure 3-1that the very large turbulent wake created by the flat plate has nowbeen replaced by a much smaller one as the air flows more smoothly around the surface of the sphereand the suction drag created behind the sphere is thus reduced. The total amount of form drag

created by the sphere is calculated in exactly the same way , however the co-efficient of

drag for the sphere is very much smaller than that for the flat plate.

Form Drag CD1

2---V

2S=

CD( 1

2---V

2S )

Drag

10. Now consider a streamlined aerofoil (ignoring any lift which it may generate), as illustrated at


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( g g y y g ),Figure 3-2. This shape has a very low co-efficient of drag, since the air can follow the surface of theshape almost to the trailing edge before it separates from the surface of the aerofoil and becomes

turbulent. The turbulent wake produced by a streamlined shape is therefore very small. It is notpossible to entirely eliminate the turbulent wake, but within limits the streamlined body can beextended with a consequent reduction in the co-efficient of drag value.

FIGURE 3-2

Airflow Around a

Streamlined

Aerofoil

11. Clearly it would be impractical to extend the length of the aerofoil beyond certain sensiblelimits since the increased weight would outweigh the improvement in the co-efficient of drag. In anyevent, beyond a certain length, the effect of friction between the air and the aerofoil surface preventsany further reduction in the drag factor. The amount of streamlining of a body is expressed as afineness ratio, which is its length divided by its maximum thickness, as shown at Figure 3-3.

Drag

FIGURE 3-3


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Fineness Ratio

Coefficient of Drag (CD)12. As with lift, drag is an aerodynamic force and may be considered as a coefficient and it is thiscoefficient which is the major factor in this drag formula CDVS. By transposition it can be seen

that:-

13. The coefficient of drag is the ratio of drag pressure to dynamic pressure.

14. Figure 3-4shows a graph of CDagainst angle of attack (). From this it can be seen that atlow angles of attack the drag coefficient is low and it changes only slightly with small changes ofangle of attack. As angle of attack increases however, drag increases and at the upper end of the range even small changes in angle of attack produce a significant increase in drag. At the stall a largeincrease in drag occurs.

CDdrag

1

2---V2

S

-----------------=

Drag

FIGURE 3-4


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Drag Curve

Drag

FIGURE 3-5


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Lift Curve

Drag

The Lift/Drag Ratio


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The Lift/Drag Ratio

15. Clearly an aerofoil is at its most efficient when it is generating the greatest possible lift for the

least possible drag. From Figure 3-5it will be seen that maximum lift is generated at an angle ofattack of about 15,ie. the stalling angle. From Figure 3-4it is seen that the least drag occurs at anangle of attack of about -2. Neither of these angles is practical for normal flight and neither issatisfactory, as the ratio of lift to drag is low in each case. What is needed is an operating angle ofattack at which the lift force is high for a low drag force. In other words, a high ratio of lift to drag.

16. By combining Figure 3-4and Figure 3-5values of CLand CDfor each angle of attack can be

obtained and the ratio CL/CD calculated for each angle. A graph of CL/CDratio against angle of

attack can then be plotted, from which the best lift/drag ratio angle of attack is evident. Such agraph is illustrated at Figure 3-6, from which it can be seen that the best lift/drag ratio occurstypically at about +4. At this angle the ratio of lift to drag is likely to be between 12:1 and 25:1,depending upon the aerofoil section used and is referred to as the optimum angle of attack.

Drag

FIGURE 3-6


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Lift/Drag Curve

Drag

17. At the zero lift angle of attack the lift/drag ratio is zero, but increases significantly for small


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increases in angle up to the optimum angle of attack of about +4. Beyond this the lift/drag ratiodecreases steadily since, although lift is increasing, drag is increasing at a greater rate. At the stall the

lift/drag ratio falls off markedly.

Surface Friction Drag

18. Modern aircraft have skin surfaces, which appear to be very smooth and polished. A closerinspection under a magnifying glass would reveal an irregular pitted surface, with the irregularitieshaving massive dimensions when compared to the individual molecules of air flowing over thesurface. It is not surprising then that the air immediately in contact with the aircraft surface isbrought virtually to rest. This impedes the flow of air layer by layer until the point is reached wherethe air is flowing freely at free-stream speed. The total depth of air, which is flowing at less than99% of free-stream velocity, is known as the boundary layer. The force required to overcome theshearing friction within the boundary layer is known as surface friction drag and is determined bythe surface area of the aircraft, the viscosity of the air and the rate of change of velocity through theboundary layer, as illustrated at Figure 3-7.

Drag

FIGURE 3-7


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Boundary Layer

19. Within the boundary layer, and certainly within the free-stream air, it is hoped that theairflow will be laminar from the leading edge almost to the trailing edge. At a point known as thetransition point, the smooth flow breaks down into a turbulent flow, which creates a much thickerboundary layer, see Figure 3-8.

Drag

FIGURE 3-8


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Transition Point

20. The effect of surface friction is, not surprisingly, far more marked in the turbulent part of theboundary layer than in the laminar part. It is therefore desirable to hang on to the laminar flow fora long as possible.

21. One of the main factors affecting the position of the transition point is the pressuredistribution of the upper surface of the wing. Transition tends to occur at the minimum pressurepoint on the top surface, and this tends to occur at the point of maximum thickness of the wing itself.Therefore, by designing a wing where the maximum thickness occurs well back from the leading edgethe laminar flow is increased, and the surface friction consequently reduced. A conventional wingand a laminar flow wing are shown atFigure 3-9.

Drag

FIGURE 3-9


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Aerofoil Sections

Interference Drag

22. Where two boundary layers meet, as at the junction between wing and fuselage, turbulentflow will ensue, leading to an increased pressure difference between leading and trailing surface areasand resulting pressure drag. The effect can be largely reduced in subsonic flight by adequate fairingat the junctions.

Profile Drag and Airspeed

23. Any form of profile drag will increase with increasing airspeed, as shown in the graph atFigure 3-10and is in fact, proportional to the square of the speed.

Drag

FIGURE 3-10

f


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Profile Drag -

Speed Curve

Lift Dependent Drag24. When an aircraft is generating lift additional drag is produced. This comprises induced(vortex) drag plus increases in the components that make up zero lift drag.

Drag

Induced Drag


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g

25. As has been stated, the tip and trailing edge vortices create a downwash that angles the

relative airflow to the direction of flight. The effect of the vortices is to direct the airflow downwardsfrom the trailing edge. The angle between the airflow as it would be without induced drag, and theactual airflow, is termed the downwash angle. See Figure 3-11.

FIGURE 3-11

Downwashed

Airflow

26. This induced downwash flow aft of the trailing edge influences the flow over the whole wing,(see Chapter 2-41), such that the effective angle of attack is reduced. As a result, the lift generated isalso reduced and can only be restored by increasing the angle of attack. This increase in angle ofattack will tilt rearwards the total reaction vector and thus the component parallel to the direction offlight is increased. This increase in drag, due to the wing vortices is induced (vortex) drag and isshown in Figure 3-12.

Drag

FIGURE 3-12

I d d (V )


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Induced (Vortex)

Drag

Drag

27. Figure 3-12(a) represents a section of a two dimensional wing, ie. one of infinite span which isproducing lift but has no trailing edge vortices


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producing lift, but has no trailing edge vortices.

28. Figure 3-12(b) represents the same section but whose wing is of a finite span and thus having

trailing edge vortices and hence induced downwash flow. The reduced effective angle of attackresults in a reduction in the lift generated as shown.

29. In order to restore the lift to its two dimensional value (ie. value without downwash as atFigure 3-12(a), the angle of attack must be increased and the subsequent inclination of the totalreaction vector causes an increase in the component parallel to the direction flight (ie. induced drag).

Effect of Airspeed

30. The lift generated by a wing can be increased by increasing the angle of attack for a givenairspeed or by increasing the airspeed for a given angle of attack. The faster you fly, the lower theangle of attack necessary for the lift required and, the lower the angle of attack the less the

downwash, thus reducing the induced drag, see Figure 3-13.

Drag

FIGURE 3-13

Eff t f S d


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Effect of Speed on

Induced Drag

Drag

31. Suppose, whilst maintaining level flight, the airspeed were to be doubled. The dynamicpressure producing lift (V) would be quadrupled In order to maintain level flight the angle of


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pressure producing lift (V) would be quadrupled. In order to maintain level flight the angle ofattack would have to be reduced, thereby inclining the lift vector forward and reducing induced drag.

Hence, induced drag decreases with increased airspeed being inversely proportional to the square ofthe speed, as shown in the graph at Figure 3-14.

FIGURE 3-14

Induced Drag -

Speed Curve

Drag

Effect of Aspect Ratio


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32. Aspect ratio is defined as the ratio of the overall wing span to the mean chord. Since the

magnitude of the induced drag of a wing depends upon the magnitude of the tip vortices, anythingthat can be done to reduce these vortices must reduce induced drag. The longer and narrower a wingthe less the proportion of airflow around the tips to that over the remainder of the wing andtherefore the less the influence of the tip vortices. In other words, less downwash so less induceddrag than for a wing of the same area, but lower aspect ratio. This is illustrated at Figure 3-15.

FIGURE 3-15

Effect of AspectRatio on Induced

Drag

Drag

33. The greater the aspect ratio, then, the lower the induced drag of the wing. Taken to itsultimate conclusion a wing of infinite span would have no induced drag at all Clearly this is not


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ultimate conclusion, a wing of infinite span would have no induced drag at all. Clearly this is notfeasible in the practical sense, although it can be proved in a wind tunnel experiment with a wing

extending the full width of the tunnel. For aircraft in which low drag at moderate airspeed is afundamental requirement, high aspect ratio wings are essential. Examples are sailplanes, long rangepatrol aircraft and medium speed transports.

Effect of Planform

34. Since induced drag decreases with increasing airspeed the need for high aspect ratio wings isless important for aircraft designed to operate at high subsonic or supersonic speeds. Indeed, forthese a low aspect ratio is important because thin aerofoil sections are necessary, demanding a shortwingspan for structural reasons. Concorde, for example, has an aspect ratio of less than 1:1,whereas a high performance sailplane may have an aspect ratio of 45:1 or greater. Clearly, withaircraft in which normal operations demand a low aspect ratio, high induced drag at the low speedsof take-off and landing has to be accepted. Similarly, training aircraft that benefit from the

favourable stall characteristics of a rectangular planform wing suffer from greater induced drag thanwould be the case with a tape

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Principles of flight - 081 POF