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Contents

1. Aerofoils ...............................................................................................................................6

1.1 Aerofoil Geometry & Definitions......................................................................................6

1.2 Aerofoil History & Families..............................................................................................6

1.3 Transonic Aerofoil Sections ..............................................................................................8

1.4 Design Lift Coefficient ....................................................................................................10

1.5 Maximum Lift Coefficient...............................................................................................11

1.6 Section Thickness ............................................................................................................11

1.7 Stall Characteristics .........................................................................................................13

1.8 Characteristic Curves.......................................................................................................13

2. High Lift Devices................................................................................................................15

2.1 Trailing Edge High Lift Devices .....................................................................................16

2.1.1 Plain Flap ..................................................................................................................16

2.1.2 Split Flap...................................................................................................................17

2.1.3 Slotted Flap ...............................................................................................................18

2.1.4 Fowler Flap ...............................................................................................................18

2.2 Leading Edge High Lift Devices .....................................................................................19

2.2.1 Slots/Slats..................................................................................................................19

2.2.2 Leading Edge Flaps...................................................................................................20

2.3 Part Span Effects .............................................................................................................21

2.4 3-D Effects.......................................................................................................................21

2.5 Extended Positions ..........................................................................................................22

3. Wing Planform Shape & Geometry....................................................................................23

3.1 Planform Shape & Geometry Definitions .......................................................................23

3.2 Aspect Ratio (A)..............................................................................................................24

3.3 Taper Ratio (λ) ................................................................................................................26

3.4 Wing Sweepback (Λ).......................................................................................................26

3.5 Wing Dihedral .................................................................................................................29

3.6 Wing Twist ......................................................................................................................30

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3.7 Wing Area & Wing Loading ...........................................................................................31

4. Other Wing Design Features...............................................................................................33

4.1 Vortex Generators............................................................................................................33

4.2 Spoilers ............................................................................................................................34

4.3 Stall Fences......................................................................................................................34

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List of Figures

1.1 Aerofoil geometry & definitions

1.2 Some early aerofoils

1.3 Pearcey “Peaky” section

1.4 Conventional & supercritical section comparisons

1.5 Vought F-8 Crusader with supercritical wing section

1.6 Different wing designs on Harrier I and US AV8-B version

1.7 Design lift coefficient selection

1.8 Critical Mach Number

1.9 t/c effect on Mcrit

1.10 Stall conditions (benign & severe)

1.11 Characteristic curves for NACA 2421 aerofoil

2.1 High lift device examples

2.2 Trailing edge high lift device mode of operation

2.3 Plain flap configuration

2.4 Split flap configuration

2.5 Slotted flap configuration

2.6 Fowler flap configuration

2.7 Boeing 727 triple-slotted Fowler flap configuration

2.8 Comparison of effectiveness of TE high ;lift devices

2.9 Slot/slat operation

2.10 Leading edge flaps

2.11 Tornado & Boeing 747 Krueger nose flaps

3.1 Planform shape & geometry

3.2 Mean aerodynamic chord definition

3.3 Wing sweepback effect on Mcrit and wave drag

3.4 Wing sweepback effect

3.5 Combined wing sweepback & thickness effects

3.6 Wing sweepback for subsonic leading edge

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3.7 Swept or straight wing selection – Lockheed F-104C Starfighter

3.8 Wing dihedral angle

3.9 Wing anhedral on BAe Harrier & Lockheed C-5 Galaxy

3.10 Wing washout

4.1 Vortex generators on Boeing 707 wing

4.2 Vortex generators on Javelin & Buccaneer wings

4.3 Spoilers on Airbus A319 and Boeing 777 wings

4.4 Stall fence example

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NOTATION

AF aerofoil section factor

b wing span

c wing chord length

C non-dimensional coefficient (e.g. CL = lift coefficient etc)

D drag

g gravitational acceleration

L lift

M Mach number, aircraft mass

S wing gross planform area

t aerofoil thickness

V velocity

W aircraft weight

α angle of attack

Λ sweepback angle

λ taper ratio

ρ density

Suffices

crit critical

D drag

L lift

r root

s stall

t tip

¼ quarter chord

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1. Aerofoils

1.1 Aerofoil Geometry & Definitions

These are shown in Fig 1.1.

Fig 1.1 Aerofoil geometry & definitions

chord line: straight line connecting leading edge (LE) and trailing edge (TE).

chord: length of chord line.

thickness: measured perpendicular to chord line as a % of it (subsonic typically 12%).

camber: curvature of section - perpendicular distance of section mid-points from chord

line as a % of it (subsonically typically 3%).

Other parameters of interest (with typical subsonic section values) include:

• position of maximum thickness (as a % of chord length aft of LE) (30%),

• position of maximum camber (as a % of chord length aft of LE) (40%), and

• leading edge radius (as a % of chord length) (4%).

• angle of attack - angular difference between chord line and airflow direction.

1.2 Aerofoil History & Families

The earliest serious work on the development of aerofoil sections began in the late 1800's.

Although it was known that flat plates would produce lift when set at an angle of incidence,

some suspected that shapes with curvature, that more closely resembled bird wings, would

produce more lift at greater efficiency. Phillips (1884) patented a series of aerofoil shapes after

testing them in one of the earliest wind tunnels. Chanute (1983) writes, “...it seems very

desirable that further scientific experiments be made on concavo-convex surfaces of varying

shapes, for it is not impossible that the difference between success and failure of a proposed

flying machine will depend upon the sustaining effect between a plane surface and one properly

curved to get a maximum of 'lift'.”

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At nearly the same time, Lilienthal had similar ideas. After carefully measuring the shapes of

bird wings, he tested various aerofoils on a 7m diameter "whirling machine". Lilienthal believed

that the key to successful flight was wing curvature or camber. He also experimented with

different nose radii and thicknesses.

Aerofoils used by the Wright Brothers closely resembled Lilienthal's sections: thin and highly

cambered. This was quite possibly because early tests of aerofoil sections were done at

extremely low Reynolds number, where such sections behave much better than thicker ones. The

erroneous belief that efficient aerofoils had to be thin and highly cambered was one reason that

some of the first airplanes were biplanes. The use of such sections gradually diminished over the

next decade.

Afterwards, a wide range of aerofoils was developed, based primarily on trial and error (Fig

1.2). Each is characterised by being considerably thicker than the Wright and Bleriot sections

with reduced lower section camber. Some of the more successful sections such as the Clark Y

and Gottingen 398 were used as the basis for a family of sections tested by the NACA in the

early 1920's - the 4-digit series.

Fig 1.2 Some early aerofoils

In 1939, Jacobs at the NACA in Langley, designed and tested the first laminar flow aerofoil

sections (NACA 5-digit series). These shapes had extremely low drag and the section shown

here achieved a lift to drag ratio of about 300. Nowadays, modern laminar flow sections still

find use on sailplanes (gliders).

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One of the reasons that modern aerofoils look quite different from one another is that the flow

conditions and design goals change from one application to the next. Below are some aerofoils

designed for low Reynolds numbers.

At very low Reynolds numbers (<10,000 based on chord length) efficient aerofoil sections can

look rather peculiar as suggested by the sketch of a dragonfly wing. The thin, highly cambered

pigeon wing is similar to Lilienthal's designs. The Eppler 193 is a good section for model

airplanes. The Lissaman 7769 was designed for human-powered aircraft.

Additionally, unusual aerofoil design constraints can sometimes arise, leading to some

unconventional shapes. The wide range of operating conditions and constraints, generally makes

the use of an existing, “catalogue” section, not best. These days, aerofoils are usually designed

especially for their intended application. Specific requirements could be to maximise CL,max, L/D

or to reduce transonic effects (i.e. increase Mcrit and reduce wave drag).

1.3 Transonic Aerofoil Sections

The basic aims of these types of sections are to delay and limit the amount of wave drag

associated with travelling at around Mcrit. This leads to aircraft which are able to fly faster at

greater aerodynamic efficiency.

Fig 1.3 Pearcey “Peaky” section

The original work in this area was done in the early 1960's by Pearcey at the NPL. This work

led to the development of the "peaky" section which found favour with many military and civil

transports in the 70's. Whitcomb at NASA Langley also used advanced computational

aerodynamics techniques at around the same time and came up with the supercritical section, so

named because it was found that some supersonic flow could be tolerated without a significant

drag increase. This was firstly used on the Vought F-8 Crusader aircraft. Typically, the

maximum local Mach numbers should not exceed about 1.2 to 1.3 on a well-designed

supercritical airfoil. This helps to produce a considerable increase in the available CL compared

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with entirely subcritical (or subsonic) designs. The supercritical and peaky sections are very

similar and are characterised by the following:

As compared with a conventional airfoil a supercritical airfoil has a reduced amount of

camber, an increased leading edge radius, smaller surface curvature on the suction side

and a concave rear part of the pressure side. This leads to substantial regions of

supersonic flow over the section, a strong aft subsonic loading and a relatively high

pitching moment.

Fig 1.4 Conventional & supercritical section comparisons

Fig 1.5 Vought F-8 Crusader with supercritical wing section

Certain precautions have to be taken with supercritical aerofoil designs. Several have looked

promising initially, but encountered problems when actually incorporated into an aircraft design.

Typical difficulties include the following:

• Too much aft loading can produce large negative pitching moments with trim drag and

structural weight penalties.

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• The adverse pressure gradient on the aft lower surface can produce separation in extreme

cases.

• The thin trailing edge may be difficult to manufacture.

• Supercritical, and especially shock-free, designs are often very sensitive to Mach and CL

and may perform poorly at off-design conditions.

• The appearance of drag creep is quite common, a situation in which substantial section

drag increase with Mach number occurs, even at speeds below the design value.

Fig 1.4 shows the pressure distribution of a typical modern supercritical section with a weak

shock at its design condition.

Fig 1.6 Different wing designs on Harrier I and US AV8-B version

1.4 Design Lift Coefficient

This is one of the first considerations in the initial selection procedure of an aerofoil. For many

aircraft, its selection will be based on optimising cruise conditions, i.e.:

L = W = ½ ρ V2 S CL (1.1a)

which may be rearranged to give:

CL = (2 / ρ V2)(W / S) (1.1b)

where W/S is known as the wing loading.

Optimum performance will be attained if the aircraft can fly at or close to this CL as this will

give the best trade-off in terms of L/D. As the aircraft uses up fuel then the value of W/S will

reduce, which means that either V or ρ has to be reduced to maintain a constant value of CL. A

reduction in V is clearly undesirable and this explains why long-range aircraft tend to cruise-

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climb. In reality, traffic control regulations mean that aircraft have to adopt step-climb profiles

instead.

Fig 1.7 Design lift coefficient selection

Typical cruise values for the design lift coefficient will be around 0.5 for a subsonic airliner

down to 0.3 for a high manoeuvrability fighter.

1.5 Maximum Lift Coefficient

This is another very important term for an aircraft design and crucially affects stall, and hence

also take-off and landing, performance. It can vary over a very wide range for a basic 2-D

areofoil and is considerably influenced by parameters including the nose radius (decreasing with

increasing radius), camber and thickness. Typical values are:

1.6, for low speed aerofoils and advanced high-speed subsonic.

1.0, for thin supersonic and older high-speed subsonic.

The main purpose of high lift edvices is to increase the available value of CL,max.

1.6 Section Thickness

The selection of the value of this parameter is particularly important for high-speed subsonic,

transonic and supersonic designs as it affects the critical Mach number (Mcrit) and wave drag

component. Its value may also be driven by structural and fuel volume requirements as there are

trade-offs between aerodynamic, structural and range performance. The term Mcrit is explained

in Fig 1.8.

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Fig 1.8 Critical Mach Number

For low-speed subsonic aircraft, relatively high t/c values, up to around 0.2, are acceptable at the

wing root as this gives good structural depth with a small profile drag penalty. For high subsonic

and transonic designs, compressibility effects and wave drag are much more important and

considerably thinner sections are required, typically around 0.1 to 0.15 at the root. For high-

speed supersonic designs even thinner sections are needed, between 0.02 and 0.06.

The tip values are usually considerably less than the root values, around 2/3 of the root value

though the spanwise variation is not necessarily linear, especially if there is a cranked trailing

edge.

Fig 1.9 t/c effect on Mcrit

A useful approximate formula for Mcrit is (ref Howe):

Mcrit = AF – 0.1 CL – (t/c) (1.2)

Where AF depends upon design standard of aerofoil section but may be taken as 0.95 for

advanced types:

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Hence for 2-D unswept aerofoils:

– Subsonic airliner (CL = 0.5), Mcrit = 0.9 – (t/c) (1.2a)

– Fighter (CL = 0.3), Mcrit = 0.92 – (t/c) (1.2b)

1.7 Stall Characteristics

This can often play an important role in subsonic aerofoil selection. Important factors are:

• Suddenness & magnitude of lift loss.

• Increase in pitching moment.

Some aerofoils have a gradual reduction in lift and this is generally the preferred case, especially

for light aircraft. Others may experience much more violent losses, with rapid pitching moment

changes. The stall characteristics of thin aerofoils may be improved considerably with the use of

leading edge devices (slots, slats, etc.). Stall effects tend to be more important for high aspect

ratio wings, and therefore usually slower aircraft designs. Another factor of concern is tip

stalling; this is highly undesirable as it produces large roll rates (covered in more detail later).

Fig 1.10 Stall conditions (benign & severe)

1.8 Characteristic Curves

Aerodynamic data may be found for all classes of aerofoil, including CL, CD and L/D (see Fig

1.11 for an example). Other data may also be available, e.g. pitching moment, centre of pressure,

section geometry and co-ordinates.

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Fig 1.11 Characteristic curves for NACA 2421 aerofoil

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2. High Lift Devices

High lift devices are used on aircraft in order to reduce landing and take-off speeds and

distances. Wings are generally designed for cruise conditions (or specific manoeuvre conditions

for fighter aircraft) and this is usually not best for low-speed operations. High lift devices offer a

means by which the wing geometry may be changed to better match up with the low-speed

requirements. The devices can be active or passive with the latter category comprising either

leading edge or trailing edge types.

Fig 2.1 High lift device examples

Consider an aircraft in steady level flight at stall (minimum speed) conditions:

L = W = ½ ρ V2 S CL (2.1)

This can be rearranged to give:

stall speed (Vs) = [(2 W) / (ρ S CL,max)] (2.2)

It is then clear that an increase in either S or CL,max will reduce Vs and hence touch-down and

lift-off speeds (typically 1.3 Vs and 1.2 Vs respectively).

High lift devices all work in one (or a combination) of three basic ways:

• increase chord length (c), and therefore wing area, S

• increase camber, and therefore CL,max

• improve the state of the upper surface boundary layer to increase the stall angle (αs) and

hence CL,max.

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2.1 Trailing Edge High Lift Devices

The simplest types of trailing edge devices (plain and split flaps) change only the camber of the

aerofoil to increase CL,max. More complex types (slotted and Fowler flaps) also increase the wing

area (S). The effect is not just felt locally over the flap surface, but over the entire wing surface.

The flap area varies from aircraft to aircraft but typically occupies between 15% and 40% of the

aft chord. The maximum deflection angle used depends upon the type of flap, but will typically

be between 35o and 45

o for landing cases.

Penalties associated with their use include:

• complexity, cost, mass and volume

• a nose-down pitching moment, requiring a trim change

• an intensification of the leading edge peak suction, reducing the effectiveness of leading

edge devices.

In any case, the primary mode of operation is to shift the lift curve up vertically, to produce

more lift at a given angle of attack (Fig 2.2)

Fig 2.2 Trailing edge high lift device mode of operation

2.1.1 Plain Flap

The simplest trailing edge device is a plain flap which has been used as a high lift device on

many light aircraft since the 1st World War. Its operating principle is simple, in that its extension

causes a change in the overall section camber. As discussed in the Lift notes, this brings about an

increase in the amount of lift. In fact, the zero-lift incidence angle is reduced with virtually no

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effect upon the lift-curve slope. However, flap extension does reduce the section stall angle, as

separation will occur earlier over a more highly cambered upper surface.

The maximum lift will occur with a flap deflection of about 40o to 45

o, typically giving a

∆CL,max of about 0.75 for a flap which covers about 40% of the chord.

They are rarely used on modern aircraft as high-lift devices, only as control surfaces (e.g.

ailerons, elevators and rudders).

Fig 2.3 Plain flap configuration

2.1.2 Split Flap

This takes the form of a flat metal plate, hinged on the lower surface at its forward edge. This

has a smaller effect upon the upper surface than for a plain flap, resulting in less of a reduction

in the stall angle and a slightly higher ∆CL,max. It does, however, produce more pressure drag,

though this is an advantage during landing.

Fig 2.4 Split flap configuration

Split flaps are not very common any more, though they can still be found on many Cessnas and

DC-3s. The main advantage of split flaps is that they are very structurally strong and, as a result,

can be extended at high speeds. Their effect upon pitching moment is also less severe than for a

plain flap.

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2.1.3 Slotted Flap

These are similar to plain flaps, except that a small slot opens up when moved into the extended

position. This leads to high pressure air moving from the lower surface through the gap to the

upper surface, thus re-energising the upper surface boundary layer and delaying the premature

separation problem associated with plain flaps. The profile drag is less for such flaps, leading to

improved take-off performance. It also allows the use of flap angles around 45o.

Fig 2.5 Slotted flap configuration

There are many fighter aircraft applications - e.g. F-5, F-14, F-18, Su-17, MiG-23 and AV-8B,

while multiple slots are sometimes used to increase lift still further (F-1, Hawk, Su-24, Jaguar

and Tornado). One disadvantage associated with their use is that they produce a relatively large

pitching moment change which has to be trimmed out by the pilot.

2.1.4 Fowler Flap

This is similar to a slotted flap but moves much further rearwards along a set of tracks to

increase the wing area and thus provide a second means of increasing the overall CL,max. There is

therefore a very large lift increment available; typically ∆CL,max is around 1.2 for a 40% chord

flap.

Fig 2.6 Fowler flap configuration

Compared with the other flap types described earlier, these tend to be relatively complex, more

costly and heavier. This is particularly so if combined with slots and split into multiple sections,

as is often the case on civil jet airliners. Fig 2.7 shows the triple-slotted flap system on a Boeing

727 airliner. Without such a system, the aircraft would suffer from its landing and take-off

speeds being too high.

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Fig 2.7 Boeing 727 triple-slotted Fowler flap configuration

Fig 2.8 Comparison of effectiveness of TE high ;lift devices

2.2 Leading Edge High Lift Devices

There are two basic categories of leading edge high lift devices - (i) slots/slats, and (ii) leading

edge flaps.

2.2.1 Slots/Slats

The usual system involves moving a section of the leading edge upper surface forwards and

downwards along a track, opening up a slot as it does so. The moving section is known as the

slat while the gap opened up is the slot. The air then flows through this slot, thus re-energising

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the upper surface boundary layer and delaying upper surface separation and consequently stall.

This therefore gives an increment to CL,max, typically about 0.85. This increase is only achieved

due to the fact that the aircraft can operate at higher angles of attack, and this can produce

visibility problems. Additionally the low drag of the system impairs the landing performance.

Fig 2.9 Slot/slat operation

Some aircraft have simpler fixed slots/slats but incur a large cruise drag penalty. Many aircraft

combine both leading edge slot/slat systems and trailing edge flaps to give even higher

increments to CL,max. The effects for a slot/slat system and combined slot/slat plus trailing edge

flap system are shown in Fig 2 and 3 respectively. Note that the slots tend to extend the lift

curve while the flaps displace it.

2.2.2 Leading Edge Flaps

There are two basic types:

• a plain flap, hinged at the mid-depth position, and

• a droop nose, hinged on the lower surface.

Fig 2.10 Leading edge flaps

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The overall effect is the same for both types, however, in that the camber is increased slightly

and the severity of the peak upper surface pressure is reduced, thus increasing both the stall

angle and CL,max. The overall effect is quite small, typically giving a CL,max increment of about

0.4. Disadvantages associated with their use include increased cost, complexity, mass and

impaired pilot visibility. They only tend to be used on large civil transport aircraft.

A Krueger flap is a nose flap formed by rotating part of the lower surface about a simple hinge.

This increases the wing chord (and hence the wing area), as well as the nose radius and camber.

Disadvantages include complexity, costs & a high profile drag increment.

They are sometimes vented, in order to re-energise the upper surface flow and to the increase the

stall angle. They are often used on large airliners (e.g. Boeing 747) and some fighters (e.g.

Tornado).

Fig 2.11 Tornado & Boeing 747 Krueger nose flaps

2.3 Part Span Effects

High lift devices cannot be used over the full wing span because of:

• the presence of the fuselage

• interruptions necessary for powerplants & pylons.

LE devices are usually also limited by the wing tip shape while TE devices are further limited by

provision requirements for ailerons.

2.4 3-D Effects

The theoretical 2-D lift values will not obtained on a finite span wing, especially if it is swept.

Losses will be present due to tip effects and also because of spanwise angle of attack variations.

Approximations for loss factors are (ref Howe):

LE Devices: 0.85 cos Λ1/4 (2.3a)

TE Devices: 0.67 cos Λ1/4 (2.3b)

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Some typical unswept 2-D and 3-D values are given below (ref Howe).

Device 2-D ∆CL,max 3-D ∆CL,max

Basic subsonic aerofoil 1.6 1.5

Basic supersonic aerofoil 1.0 0.95

Plain flap 20% chord 0.8 0.55

Plain flap 40% chord 1.1 0.75

Split flap 20% chord 0.9 0.6

Plain flap 40% chord 1.4 0.95

Single slotted flap 20% chord 1.2 0.8

Single slotted flap 20% chord 1.8 1.2

Double slotted flap 40% chord 2.5 1.65

Triple slotted flap 40% chord 2.9 1.9

Fowler flap 20% chord 1.2 0.8

Fowler flap 40% chord 1.8 1.2

Fowler + Split flap 40% chord 2.2 1.45

Plain LE flap 15% chord 0.5 0.4

Vented slat 18% chord 1.0 0.85

Krueger flap 20% chord 0.8 0.65

2.5 Extended Positions

There will generally be two or more extended positions – in the minimum for different landing

and take-off cases. For take-off, there is high lift/drag requirement, so the TE high lift device

deflection will be at about half of the maximum setting with LE slots set at about 2/3 of

maximum values. For landing, there is a need for both high lift and high drag so the maximum

LE & TE flap and slot deflections are used.

Limits on the actual angle settings are due to associated pitching moment and mechanical design

constraints.

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3. Wing Planform Shape & Geometry

3.1 Planform Shape & Geometry Definitions

Most workers use as system of definitions along the lines of the following:

Fig 3.1 Planform shape & geometry

Wing Area (S): usually based on an equivalent or reference trapezoidal planform which

neglects the effects of leading edge and trailing edge extensions and also wing tip curvature.

This section is extrapolated to the aircraft's centre-line to give a so-called gross planform area. A

net area has the fuselage area subtracted from it, though it is the gross area which is mainly used

elsewhere. A wetted area is also sometimes needed, especially for skin friction drag

calculations. This is based on the total exposed planform area so is approximately twice the

reference value.

Wing Span (b): the tip-to-tip distance across the wing.

Wing Root Chord (cr): the chord of the trapezoidal wing section taken at the aircraft centre-

line.

Wing Tip Chord (ct): the chord of the trapezoidal wing section taken at the wing tip.

Aspect Ratio (A or AR): the ratio of wing span to mean chord but may be defined more usefully

as:

A = b2 / S (3.1)

The term is highly important as it crops up frequently throughout aerodynamics and aircraft

design work.

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Sweepback Angle (Λ): can be defined in several ways but most usually as the sweepback angle

of the quarter-chord line (Λ¼); this is approximately coincident with the aerodynamic centre

position for subsonic aircraft . Other sweep angles are sometimes also given for the leading and

trailing edges.

Taper Ratio (λ): defined as the ratio of the tip chord to root chord (ct / cr).

Wing Crank: refers to a local change in leading or trailing edge sweepback angle.

Mean Aerodynamic Chord (MAC): Used as a reference dimension for many aerodynamic

design characteristics.

Fig 3.2 Mean aerodynamic chord definition

It may be found from the following:

( ) ( )

2 22 41 1

3 1 3 1r

SMAC c

A

λ λλ λ

= + = −

+ + (3.2)

3.2 Aspect Ratio (A)

The aerodynamic preference is for a high aspect ratio wing, as this is the most efficient way to

reduce lift-induced (trailing vortex) drag, as discussed in the drag notes. This is especially

important for low-speed operations, when the relative effect of lift-induced drag becomes more

important.

The main trade-off is in terms of structural mass, so a compromise is generally needed, with due

consideration given to the aerofoil selection and other geometric properties. There may also be

some other limit imposed on the maximum allowable span, e.g. on large airliners due to airport

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gate widths or on naval aircraft operating from ships. A possible solution is to use wing-tip

folding (e.g. the Buccaneer) but this tends to be complex, costly and heavy.

Some specific examples of aircraft aspect ratios are given below (Ref Howe):

Civil Transport Aircraft Wing Span (m) Aspect Ratio

Narrow-Body Jet Transports

A319, A320-200 34.1 9.5

Boeing 737 28.9 8.8

Boeing 757 38.05 8.0

MD-81 32.0 9.6

Regional Turboprops

BAe Jetstream 41 18.29 10.26

Embraer 120 19.78 9.9

Shorts 330-200 22.76 12.3

Wide-Body Jet Transports

A310-200 43.9 8.8

A340-200 60.3 10.0

Boeing 747-200C 59.6 6.94

Boeing 747-400 64.3 7.87

Boeing 767-200 47.57 8.0

Boeing 777-200 60.9 8.68

L-1011-250 47.35 6.95

MD-11 51.77 7.5

DC10-30 50.42 7.5

Combat Aircraft & Trainers Wing Span (m) Aspect Ratio

BAe Hawk 200 9.39 5.3

Sepecat Jaguar 8.69 3.12

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Grumman F-14A 11.6 – 19.54 2.07 – 7.28

MDD F-15E 13.05 3.01

Lockheed F-16C 9.45 3.0

MDD F/A-18E 11.43 3.52

Su-27 14.69 3.57

Eurofighter Typhoon 10.52

Panavia Tornado 8.6 – 13.9 2.78 – 7.27

3.3 Taper Ratio (λ)

As described in the Drag notes, wing taper is primarily chosen to produce a near-elliptical

spanwise lift distribution in order to reduce the trailing vortex drag component. This is far

preferable to employing an elliptical planform shape as it is much less complicated in terms of

design, manufacture and assembly.

Wing taper is also of structural benefit:

• the centre of pressure is moved inboard, thus reducing the wing bending moment.

• wing thickness and chord is largest at the root, where the bending moment is largest.

Too much taper can lead to undesirable tip-stalling phenomena, and will also reduce the area

available for ailerons and high-lift devices.

A typical design value (ref Howe) is:

0.25 2

1/ 40.2 cosAλ = Λ (3.3)

3.4 Wing Sweepback (Λ)

This is an extremely common wing design feature and is used on most modern aircraft designed

to operate at speeds above about Mach 0.6. The sweepback angle itself is normally defined in

terms of the angle that the quarter-chord line is displaced from a line perpendicular to the

aircraft centre-line.

The main reasons for its use will be covered on the High Speed Flight notes, but is reviewed

here:

• to increase the critical Mach number; and

• to reduce the peak wave or compressibility drag (Fig 3.3).

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Fig 3.3 Wing sweepback effect on Mcrit and wave drag

It is also possible to use sweepforward to achieve similar effects, though its use is much less

common, mainly due to aeroelastic divergence problems. Sweepforward can also give other

advantages in terms of stability and overall layout.

Sweepback works by geometrically reducing the airflow velocity component perpendicular to

the wing leading edge. This is the component which passes over the aerofoil section and is thus

subjected to flow accelerations, leading to supersonic flow formation on the upper surface. The

higher the sweep angle, the lower the affected flow component (Fig 3.4).

Fig 3.4 Wing sweepback effect

Generally the sweep angle is designed to be as low as possible for a given aerofoil configuration

and set of flight conditions, as increased sweep implies structural and handling penalties.

The combined effects of wing sweep and aerofoil section thickness are shown below on Fig 3.5

(for a typical airliner design). It is up to the wing designer to come up with a suitable

combination of the two which will give the desired Mcrit value while still meeting the other

constraints imposed by the overall design.

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Fig 3.5 Combined wing sweepback & thickness effects

Wing sweepback is also commonly employed on supersonic aircraft wing designs, with the

intention of maintaining a subsonic leading edge and thus reduce wave drag. This is covered in

more detail in the High Speed Flight notes. The Mach angle reduces as Mach number increases,

meaning that the sweepback angle has to increase for increasing aircraft speed. This is the

rationale behind swing-wing aircraft, such as the F111, F-14 Tomcat and Tornado, all have

multi-role capabilities and can operate effectively at low subsonic speed (with low sweep

angles), or at high supersonic speeds (with high sweep angles).

Fig 3.6 Wing sweepback for subsonic leading edge

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Fig 3.7 Swept or straight wing selection – Lockheed F-104C Starfighter

For very high supersonic speeds, the amount of sweep required for a subsonic leading edge

becomes impractical (Fig 3.7), due to the greatly reduced wing area, and the designer then

reverts to a straight unswept low aspect ratio wing instead, e.g. Lockheed F-104 Starfighter.

3.5 Wing Dihedral

Fig 3.8 Wing dihedral angle

Dihedral is the upward angle of the wing from the vertical when seen from the front, or nose of

the aircraft (Fig 3.8). If each wing is angled 5° up from the horizontal, then the wing is said to

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have 5° of dihedral. The primary use of wing dihedral is to provide lateral static stability. It is,

however, also often used for layout purposes, e.g.

• to increase ground clearance for wing-mounted powerplants/stores,

• to reduce the length of the wing tip-mounted outriggers on a Harrier, by the use of

negative dihedral (or anhedral), see Fig 3.9.

Fig 3.9 Wing anhedral on BAe Harrier & Lockheed C-5 Galaxy

Since there is a direct trade-off between stability and manoeuvrability, aircraft with high

manoeuvrability requirements tend to have much less dihedral, indeed many have anhedral

instead.

Too much dihedral (or a combination of dihedral/sweepback and a high wing) can lead to too

much lateral stability and also a nasty dynamic lateral stability phenomenon known as Dutch

Roll. As a consequence, many high wing/swept wing aircraft use anhedral instead of dihedral to

reduce Dutch Roll effects.

Typical values tend to be:

Swept Wing (30o): high wing: -3°, low wing: 0°

Unswept Wing: high wing: 0°, low wing: 3° to 5°

3.6 Wing Twist

The wing is often twisted, usually to reduce tip-stalling effects. The usual method is to reduce

the angle of attack moving towards the tip; this is known as washout. The opposite is to increase

the angle of attack moving towards the tip, known as washin. A wing may also be

aerodynamically twisted by using different aerofoil sections along the span.

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Fig 3.10 Wing washout

3.7 Wing Area & Wing Loading

The wing area is clearly dependent upon geometric parameters but is mainly determined initially

by relationships with performance requirements and available thrust. Wing area is often more

usefully expressed as wing loading = Mg / S or W/S,

where:

M = aircraft mass, W = weight, S = gross wing planform area.

This is usually taken at the design take-off mass condition.

Wing loading is highly interconnected with the aircraft’s thrust/weight ratio for performance

optimisation, so a credible estimate is required very early in the aircraft design process. Values

vary over a wide range but there are close correlations to be found between specific aircraft

categories and these may be used for initial selection if undertaking an aircraft design. Some

typical ranges are given below (ref Howe).

Class of Aircraft Wing Loading Range (N/m2)

Ultra light 200 – 400

Light single piston engine 500 – 800

General single turboprop 1000 – 1800

General twin piston engine 1000 – 2000

Small commuter turboprop 1500 – 2000

Large commuter turboprop 2000 – 3000

Small executive jet 2200

Medium executive jet 3000

Large executive jet 4000

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Military jet trainer 2500 – 3000

Turboprop transport 3000 – 4000

Naval strike/interceptor 3500 – 4000

Land-based strike/interceptor 4000 – 5000

Supersonic bomber/transport 5000

Subsonic long-range bomber 5000 – 6000

Short/medium range jet transport 5500 – 6500+

Long range jet transport 6200 – 7000+

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4. Other Wing Design Features

4.1 Vortex Generators

Vortex generators are small, low aspect ratio metal surfaces which are attached to the upper

surface of a wing and develop strong tip vortices. These vortices draw in air from the passing

airstream and mix it with the sluggish boundary layer. The net effect is that the boundary layer is

re-energised, leading to a beneficial delay in separation.

Fig 4.1 Vortex generators on Boeing 707 wing

They can be used for several reasons and applications:

On swept wing transonic aircraft. These are likely to have a region of supersonic flow over

the upper surface, terminated by a shock wave which produces an adverse pressure gradient and

an increased likelihood of separation (known as shock stall). Vortex generators reduce the

likelihood of the shock stall phenomenon and have been used on aircraft such as the Javelin and

Buccaneer (Fig 4.2).

Fig 4.2 Vortex generators on Javelin & Buccaneer wings

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To improve control surface effectiveness. The separation problem poses other problems in that

the control surfaces are usually located along the trailing edge of a wing. When the flow

separates from the wing, these control surfaces have little or no air flowing over them and they

become ineffective. Thus, not only will the aircraft lose lift when the wing stalls, but the pilot

may not be able to control the aircraft. To remedy this deficiency, vortex generators are often

placed shortly before the control surfaces to create a faster flow of air over the surfaces making

them more effective (e.g. on an Embraer-110 regional jet).

On STOL aircraft. These aircraft operate at low speeds during takeoff and landing. Aircraft

like the C-17 Globemaster III use vortex generators to create a higher-speed flow over the wings

and control surfaces at these conditions to improve performance and controllability.

4.2 Spoilers

These act in the opposite sense to high lift devices in that their purpose is to destroy the wing

lift, rather than increase it. They usually take the form of simple hinged surfaces, located on the

wing upper surfaces, ahead of the trailing edge flaps. They are used for several purposes:

• To dump lift after touch-down, thus preventing the aircraft from bouncing back up into

the air. Landing distances are therefore considerably reduced.

• To increase the aircraft drag, to allow controlled descents without gaining excessive

airspeed.

• To increase the aircraft drag when landing, again reducing landing distances.

• To provide roll control through differential operation, either in conjunction with the

aerofoils or as a primary means, thus leaving the entire trailing edge free for flap use.

Fig 4.3 Spoilers on Airbus A319 and Boeing 777 wings

4.3 Stall Fences

These are sometimes used on swept wing aircraft which suffer from undesirable tip stalling

effects. This is due to the presence of a spanwise flow component which has a thickening

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boundary layer as the flow moves out to the tip. Since separation is more likely to occur with a

thick boundary layer, a stall condition is most likely to occur first of all at the tip. This will

produce a large roll effect due to the long moment arm. A stall fence, as shown in Fig 4.4,

disrupts this spanwise flow component and helps to alleviate the tip-stall problem.

Fig 4.4 Stall fence example