Wing Aerodynamics Design

Post on 04-Apr-2015

996 views 44 download

Transcript of Wing Aerodynamics Design

04/11/23 Dr Derek Bray, DAPS 1

Aircraft Design -Wing Aerodynamics

Design

For more detailed notes please refer to www.rmcs.cranfield.ac.uk/aeroxtra

04/11/23 Dr Derek Bray, DAPS 2

Configuration - Overview• Aerofoil Selection

– Geometry & definitions, design/selection, families/types, design lift coefficient, thickness/chord ratio, lift curve slope, characteristic curves.

• High Lift Devices– Trailing edge and leading edge.

• Wing Planform Shape & Geometry– Aspect ratio, taper ratio, sweep, dihedral, wing area & loading.

• Other Wing Design Features– Vortex generators, wing stall fences, spoilers.

04/11/23 Dr Derek Bray, DAPS 3

Non-Dimensional Coefficients• Used for comparing wing aerodynamics

characteristics:

• Lift Coefficient (CL) =

• Drag Coefficient (CD) =

• Pitching Moment Coefficient (CM)

=Where A = aspect ratio, S = planform area, = mean chord, V = flight

speed, = air density, q = dynamic pressure.

21lift / /2 V S L qS 21drag / /2 V S D qS

21pitching moment / /2 V Sc M qSc

c

04/11/23 Dr Derek Bray, DAPS 4

Aerofoil Selection• Affects many aspects of aircraft performance:

– Cruise speed, stall speed, take-off and landing distances, handling qualities (especially near stall), overall aerodynamic efficiency, etc.

• Usually designed/selected with primary operating mode in mind, e.g. cruise flight for transport aircraft.

• Variable geometry (e.g. high lift devices) then used to match up better with low-speed requirements.

04/11/23 Dr Derek Bray, DAPS 5

Aerofoils – Geometry & Definitions

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

• Chord (c): length of chord line.

• Thickness (t): measured perpendicular to chord line as a % of it (subsonic typically 12%). • Camber (d): curvature of section - perpendicular distance of section mid-points from chord line as a % of it (subsonically typically 3%).

04/11/23 Dr Derek Bray, DAPS 6

Aerofoils – Geometry & Definitions

Other parameters of interest (with typical subsonic section values given) 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%),

• leading edge radius (as a % of chord length) (4%),• angle of attack - angular difference between chord line

and airflow direction.

04/11/23 Dr Derek Bray, DAPS 7

Aerofoil Design & Selection• Previously selected from existing catalogues considering

factors such as cruise drag, stall/pitching moment characteristics, thickness available for fuel/structure, ease of manufacture, etc.

• Nowadays custom-designed with existing computational (CFD) aerofoil design tools based upon desired aerofoil pressure distributions.

• Main aerofoil parameters affecting above:– Maximum t/c and its chordwise location, nose radius,

camber and its distribution, trailing edge angle.

04/11/23 Dr Derek Bray, DAPS 8

Early Aerofoil Families• A variety is shown below:

04/11/23 Dr Derek Bray, DAPS 9

Aerofoil Categories• Early – based on trial & error.

• NACA 4 digit – 1930’s.

• NACA 5-digit – aimed at pushing position of max camber forwards for increased CL,max.

• NACA 6-digit – designed for lower drag by increasing region of laminar flow.

• Modern – mainly based upon need for improved aerodynamic characteristics at speeds just below speed of sound.

04/11/23 Dr Derek Bray, DAPS 10

Aerofoils – NACA 4 Digit• Rarely used today except for in simple

symmetrical tailplane and fin sections.– 1st digit: maximum camber (as % of chord).

– 2nd digit (x10): location of maximum camber (as % of chord from leading edge (LE)).

– 3rd & 4th digits: maximum section thickness (as % of chord).

• Thus NACA 2412 has 2% camber at 40% chord from LE & is 12% thick (max).

04/11/23 Dr Derek Bray, DAPS 11

Aerofoils – NACA 5 Digit• Much better low-speed characteristics than 4

digit series.– 1st digit (x0.15): design lift coefficient.– 2nd & 3rd digits (x0.5): location of maximum camber

(as % of chord from LE).– 4th & 5th digits: maximum section thickness (as % of

chord).

• Thus NACA 23012 has CL of 0.3 with max camber at 15% chord from LE & is 12% thick (max).

04/11/23 Dr Derek Bray, DAPS 12

Aerofoils – NACA 6 Digit• Still represents good basis for some subsonic & high-

speed applications (e.g. Mach 2 F-15 uses 64A series). – 1st digit: identifies series type.

– 2nd digit (x10): location of minimum pressure (as % of chord from leading edge (LE)).

– 3rd digit: indicates acceptable range of CL above/below design value for satisfactory low drag performance (as tenths of CL).

– 4th digit (x0.1): design CL.

– 5th & 6th digits: maximum section thickness (%c)

• Thus NACA 632-315 is 6-series with minimum pressure 30% of chord back from LE, design CL of 0.3 ± 0.2 & is 15% thick (max).

04/11/23 Dr Derek Bray, DAPS 13

Modern Computationally-Designed Sections

• First use was to improve transonic behaviour – much pioneering work done by Pearcey at NPL in the 1960’s.

• Produced the peaky section, featuring:– Relatively flat upper surface

– Marked suction peak near to leading edge.

– Cusped trailing edge for increased rear loading.

04/11/23 Dr Derek Bray, DAPS 14

Supercritical Sections• These were developed by Whitcomb (NASA

Langley) – first flew on an F-8 in 1971.• Sections designed to minimize transonic effects

and allow aircraft to travel at higher speeds without suffering from too much wave drag.

• Sections feature:– Very flat upper surfaces to spread out lift.– Increased lower surface camber at rear end.– Increased leading edge radius to reduce leading edge

velocities.– Blunt trailing edge to increase structural strength.

04/11/23 Dr Derek Bray, DAPS 15

Supercritical SectionsThe effect regarding shock formation and its effect upon the pressure distribution is shown here.

Vought F-8 Crusader

04/11/23 Dr Derek Bray, DAPS 16

Supercritical Sections

• May be used in several ways:– Allow the aircraft to fly faster (increase Mcrit).– Increase the section thickness (for more fuel

capacity) or reduce sweep angle while maintaining same speed.

• Two main disadvantages:– Increased pitching moment– Thin at rear of section where flaps and ailerons are

generally situated.

• Used on many fighters, trainers and also transport aircraft (e.g. Boeing 777).

04/11/23 Dr Derek Bray, DAPS 17

Use of Supercritical Sections

Main requirement for the AV8-B was to improve payload/range capability.

Use of supercritical section allowed for thicker section to be used (thus larger fuel capacity) with less sweep but at the same Mcrit & cruise speed.

04/11/23 Dr Derek Bray, DAPS 18

Design Lift Coefficient• First consideration in initial aerofoil selection –

CL at which aerofoil has best L/D.

• Typical values are:– 0.5 for subsonic airliner in cruise.– 0.3 for fighter in cruise.

04/11/23 Dr Derek Bray, DAPS 19

Design Lift Coefficient• As a first approximation, it may be assumed for steady

level flight that:

Where W/S = wing loading

• W/S reduces as fuel is used up so if CL is to be kept constant then either V or must be reduced.

• Explains why long-range transports tend to cruise-climb.

212 LL W V SC 2

2L

WC

V S

04/11/23 Dr Derek Bray, DAPS 20

Maximum Lift Coefficient (CL,max)

• Can vary over a wide range for a basic 2-D aerofoil.

• Main influences are: camber, thickness and nose radius

(decreases as radius decreases).

• Typical values are:

– 1.6 for low speed aerofoils and advanced high-speed subsonic

– 1.0 for thin supersonic and older high-speed subsonic

• Main purpose of high-lift devices is to increase

available value of CL,max.

04/11/23 Dr Derek Bray, DAPS 21

Thickness/Chord Ratio (t/c)

• Affects CL,max and Mcrit (see later) and also wave drag

rise for transonic/supersonic designs.

• Value chosen is also influenced by structural design

and volume requirements.

• For low-speed subsonic aircraft relatively high t/c

values (up to 0.2) acceptable at wing root – gives good

structural depth with small profile drag penalty.

04/11/23 Dr Derek Bray, DAPS 22

Thickness/Chord Ratio (t/c) – cont.

• For high-speed subsonic and transonic aircraft,

compressibility effects are more important and much

thinner sections used – typically 0.1 to 0.15 at wing root.

• Tip values are typically 2/3 of the root values, though not

necessarily a linear spanwise variation, especially if a

cranked trailing edge.

• For supersonic speeds t/c values of between 0.02 and 0.06

are typical , with small spanwise variations.

04/11/23 Dr Derek Bray, DAPS 23

Critical Mach Number (Mcrit)

• Mach number at which supersonic flow appears on the

upper surface, terminated by a shock wave.

• This produces a significant amount of drag and Mcrit is

usually defined as the Mach number giving an increase of

0.002 over its subsonic constant value.

04/11/23 Dr Derek Bray, DAPS 24

Critical Mach Number Estimation• Mainly dependent upon t/c, design standard of

aerofoil and lift coefficient (or angle of attack)

Typical t/c effect upon Mcrit for unswept wing.

04/11/23 Dr Derek Bray, DAPS 25

Critical Mach Number Estimation• Approximate formula for Mcrit is:

Mcrit = AF – 0.1 CL – t/c

• Where AF depends upon design standard of aerofoil section

but may be taken as 0.95 for advanced types:

• Hence for 2-D unswept aerofoils:

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

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

• See later notes for effect of sweep.

04/11/23 Dr Derek Bray, DAPS 26

Stall Characteristics

• This often plays 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 (generally

preferred, especially for light aircraft) – others experience

violent losses with rapid pitching moment changes.

04/11/23 Dr Derek Bray, DAPS 27

Stall Characteristics (cont.)

• Stall characteristics of thin aerofoils may be improved

with leading edge devices (slots, slats, etc.)

• Stall effects more important for high aspect ratio wings.

• Tip stalling is undesirable as it produces large roll rates.

04/11/23 Dr Derek Bray, DAPS 28

Lift Curve Slope (a)

• Theoretical 2-D value for lift-curve slope (a =

dCL/d) is 2 per radian = 0.11 per degree.

04/11/23 Dr Derek Bray, DAPS 29

Lift Curve Slope (a)

• Value falls with both aspect ratio and sweep angle.

• Approximate value is:

Where: A = aspect ratio, MN = flight Mach number,

¼ = sweep of quarter-chord line.

• Deployment of high lift devices usually has small effect

upon lift curve slope.

1

2 2

3 2 14

14

0.16/ 0.32 1 cos

cosD D N

Aa a M

04/11/23 Dr Derek Bray, DAPS 30

Characteristic Curves

• Available for all

classes of standard

aerofoils.

• Include plots of CD,

CL, L/D, CP, Mo &

geometry co-

ordinates.Example – NACA 2421

04/11/23 Dr Derek Bray, DAPS 31

High Lift Devices

• Used to reduce take-off and landing speeds/distances.

• Since stall speed (Vs) may be found from:

and touch-down speed 1.3 Vs,

lift-off speed 1.2 Vs

• Increase in either S or CL,max will reduce Vs and hence

touch-down and lift-off speeds.

,max2 /s LV W SC

04/11/23 Dr Derek Bray, DAPS 32

High Lift Devices – Further Comments

• Many different types available, both active and passive.

• All work in on or more of three ways:

– Increasing chord length (and thus wing area)

– Increasing camber (and thus CL,max).

– Improving state of boundary layer, thus increasing s and

CL,max.

• Generally categorised as leading-edge (LE) or trailing-

edge (TE) types with the latter usually preferable.

04/11/23 Dr Derek Bray, DAPS 33

High Lift Devices – Examples

04/11/23 Dr Derek Bray, DAPS 34

TE High Lift Devices • Simplest types (plain/split flaps) change camber to

increase CL,max.

• More complex types (slotted, Fowler) also increase wing area and possibly state of boundary layer to provide further increases.

• Usually occupy between 15% and 40% of chord.

• Maximum deflection angle varies with type but usually between 35o & 45o.

• Penalties of use: nose-down pitching moment (needs to be trimmed) & reduced effectiveness of LE devices.

04/11/23 Dr Derek Bray, DAPS 35

TE High Lift Devices

• TE flap deployment usually increases CL for a

given , increases CL,max

and reduces stall angle.

• Little change to lift curve slope.

04/11/23 Dr Derek Bray, DAPS 36

TE High Lift Devices

Plain Flap

• Simplest type (similar to ailerons, etc.) – flap rotation changes camber to increase lift for given .

• Stall angle reduced as separation occurs earlier on more highly cambered upper surface.

• Maximum CL,max of about 0.75 for 40% chord at flap deflection of about 40o.

04/11/23 Dr Derek Bray, DAPS 37

TE High Lift Devices

Split Flap

• Takes form of hinged plate on lower surface.

• Produces slightly more CL,max than plain flap and lower change in pitching moment but more drag.

• Upper surface stalling effect is less pronounced than for plain flap so higher stall angle.

04/11/23 Dr Derek Bray, DAPS 38

TE High Lift Devices

Slotted Flap

• Flap moves slightly rearwards as it rotates to produce a slot.

• High pressure air from the lower surface then travels onto the upper to re-energise boundary layer and delay separation/stall.

• Cures problem of early separation suffered with plain flap.

                                                                                                                                  

04/11/23 Dr Derek Bray, DAPS 39

TE High Lift Devices

Slotted Flap – Further Comments

• Profile drag is much less than for plain & split flaps – better for take-off performance.

• Multiple slot arrangements often used to enhance effect though this increases cost & complexity issues – trend nowadays is for less slots.

• Produce a relatively large pitching moment change.

                                                                                                                                  

04/11/23 Dr Derek Bray, DAPS 40

TE High Lift Devices

Fowler Flap

• Very popular system – similar to slotted flap but moves much further back along tracks to significantly increase wing chord/area.

• Large lift increment available, CL,max of about 1.2 for 40% chord.

• Used on many jet transport aircraft and some fighters (e.g. F-111, Tu-22).

04/11/23 Dr Derek Bray, DAPS 41

Trailing Edge High Lift Devices

Triple slotted Fowler flap on Boeing 737.

Fowler flaps on C-5 Galaxy.

04/11/23 Dr Derek Bray, DAPS 42

TE High Lift Devices• Effect on 2-D wing – assuming use of 25%

chord flaps deflected by 30o.

                                                                                                                                  

04/11/23 Dr Derek Bray, DAPS 43

Leading Edge High Lift Devices• Recommended (ref Howe) that only

incorporated into aircraft design when:

(W/S)o / cos¼ FLE

• Where (W/S)o = take-off wing loading

¼ = quarter-chord sweep

FLE = 4000 N/m2 for combat a/c

= 5500 N/m2 for transport a/c

04/11/23 Dr Derek Bray, DAPS 44

Leading Edge High Lift Devices• Main categories of leading edge devices are:

– Leading edge flap (can take form of plain nose flap or droop nose).

– Krueger flap.

– Sealed slat.

– Slotted slat.

• Usually occupy between 10% and 20% of the available wing chord – typically 16%.

04/11/23 Dr Derek Bray, DAPS 45

Leading Edge High Lift DevicesLeading Edge Flap

• Usually only used on large transports.• Small effect, typically CL,max = 0.4. • Work by increasing camber (slightly) and reducing

severity of upper surface pressure peak.

04/11/23 Dr Derek Bray, DAPS 46

Leading Edge High Lift DevicesKrueger Flap• Nose flap formed by rotating part of

lower surface about a simple hinge.• Increases chord (area), nose radius &

camber.• Disadvantages include complexity,

costs & high profile drag. • Sometimes vented to re-energise upper

surface flow and increase stall angle.• Often used on large airliners (Boeing

747) and some fighters (Tornado). Variable Krueger flap

Boeing 747

Tornado

04/11/23 Dr Derek Bray, DAPS 47

Leading Edge High Lift DevicesSlot/Slat Systems• A slot is opened up and

high pressure air is forced from the lower surface onto the upper.

• This re-energizes the boundary layer and increases the stall angle and CL,max (typically by about 0.85).

04/11/23 Dr Derek Bray, DAPS 48

Leading Edge High Lift DevicesSlot/Slat Systems – Further

Comments• Usual system involves

movement of the forward section (slat) along a track to open up a slot.

• Problems/disadvantages:– Low drag affects landing

performance, system cost & complexity, pilot’s visibility impaired at high .

                                    

04/11/23 Dr Derek Bray, DAPS 49

High Lift DevicesPart Span Effects

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

– Presence of fuselage.

– Interruptions for powerplants & pylons.

• LE devices also limited by wing tip shape.

• TE devices limited by provision for ailerons.

04/11/23 Dr Derek Bray, DAPS 50

High Lift Devices3-D Effects• 2-D lift values not obtained on a finite span

wing, especially if swept.• Losses will be due to tip losses and spanwise

angle of attack variations.• Approximations for loss factors are:

– LE Devices: 0.85 cos¼

– TE Devices: 0.67 cos¼

• For all 3-D swept values of unswept CL,max, multiply by cos¼ for approximate effect.

04/11/23 Dr Derek Bray, DAPS 51

Typical Effectiveness of TE High Lift Devices

Device (all TE) 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

04/11/23 Dr Derek Bray, DAPS 52

Typical Effectiveness of High Lift Devices

Device 2-D CL,max 3-D CL,max

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

04/11/23 Dr Derek Bray, DAPS 53

High Lift DevicesExtended Positions• Two (or more) extended positions – at least for

landing and take-off.• Take-Off – High lift/drag requirement so TE

flap deflection about half of landing setting and LE slots at about 2/3 of maximum landing values.

• Landing – Need high lift and drag so use maximum flap and slot deflections.– Limits due to pitching moment and mechanical

design constraints.

04/11/23 Dr Derek Bray, DAPS 54

Wing Planform Shape & Geometry

• A reference (trapezoidal) wing shape is used for all initial calculations.

04/11/23 Dr Derek Bray, DAPS 55

Wing Planform Shape & Geometry• Aerofoil pitching data is generally provided

about the ¼ chord line where (subsonically) the pitching moment is essentially constant with changing (aerodynamic centre).

• Primary planform parameters of interest are:– Aspect ratio (A) = b2/S– Taper ratio () = ct/cr

– Sweep angle ()

• Leading or trailing edge sweep is sometimes changed (crank).

04/11/23 Dr Derek Bray, DAPS 56

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

aerodynamic design characteristics.

• MAC = 2

2

2 41 ( / ) 1(1 ) (1 )3 3rc S A

04/11/23 Dr Derek Bray, DAPS 57

Aspect Ratio (A)

• Aerodynamic preference is for a high aspect ratio as this is the most efficient at reducing lift-induced (trailing vortex) drag

CD,i = CL2 / Ae

• Especially important for low speed performance, when lift-induced drag is dominant.

04/11/23 Dr Derek Bray, DAPS 58

Aspect Ratio (A) – Further Comments

• However, a high aspect ratio leads to a high wing structural mass so a compromise is needed with due consideration given to aerofoil and other geometric parameters.

• A limit may also be imposed by maximum allowable span, e.g. on naval aircraft and airliners due to airport gate widths.

• Wing-tip folding may be used but this is a complex, costly and heavy option.

04/11/23 Dr Derek Bray, DAPS 59

Aspect Ratio (A) – ExamplesAircraft 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

04/11/23 Dr Derek Bray, DAPS 60

Aspect Ratio (A) – ExamplesAircraft Wing Span (m) Aspect Ratio

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

L1011-250 47.35 6.95

MD-11 51.77 7.5

DC10-30 50.42 7.5

04/11/23 Dr Derek Bray, DAPS 61

Aspect Ratio (A) – ExamplesAircraft Wing Span (m) Aspect Ratio

Combat Aircraft & Trainers

BAe Hawk 200 9.39 5.3

Sepecat Jaguar 8.69 3.12

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

04/11/23 Dr Derek Bray, DAPS 62

Taper Ratio ()

• Defined as the ratio of the tip chord to the root chord.

• Wing taper is primarily chosen to produce a near-elliptical spanwise lift distribution – this reduces the trailing vortex drag component.

• This is preferable to employing an elliptical planform shape as it is much less complicated in terms of design, manufacture and assembly.

04/11/23 Dr Derek Bray, DAPS 63

Taper Ratio () – Further Comments

• Wing taper is also of structural benefit:– The centre of pressure is moved inboard to reduce

the wing bending moment.– The wing thickness and chord is largest at the root,

where the bending moment is largest.

• Too much taper can lead to tip-stalling and can also reduce the area available for the ailerons and high-lift devices.

• A typical design value is: 1 24

14

0.2 cosA

04/11/23 Dr Derek Bray, DAPS 64

Improving Spanwise Lift Distribution• Even when an elliptical or

tapered wing is used its intersection with the fuselage will still produce a dip in the lift distribution.

• Less critical for a high wing location.

• Many combat aircraft counter the effect by using a cambered non-circular fuselage.

04/11/23 Dr Derek Bray, DAPS 65

Wing Sweep ()• Usually defined along the ¼ chord line.

• Generally used on high-speed aircraft to:– Increase Mcrit, and/or

– Reduce peak wave/compressibility drag.

04/11/23 Dr Derek Bray, DAPS 66

Wing Sweep () – Further Comments

• Only the velocity component normal to the leading edge is accelerated, so the higher the sweepback angle the higher the value of Mcrit.

04/11/23 Dr Derek Bray, DAPS 67

Wing Sweep () – Further Comments

• Sweepback much more common than sweepforward as it also gives stability and general layout advantages.

• Sweptforward wings are also prone to aeroelastic divergence effects.

• Sweep angle is kept as low as possible for given design flight conditions and aerofoil configuration as large sweep implies structural & handling penalties.

04/11/23 Dr Derek Bray, DAPS 68

Sweep Effects – High Subsonic Speeds• Methods for calculating 2-D Mcrit values

presented earlier.• Approximate 3-D swept corrections are:

– For 0o 1/4 35o

– For 1/4 > 45o

• Interpolate for 35o 1/4 45o

crit 3D crit 2D 1/ 4(M ) /(M ) 1/ cos

0.6

crit 3D crit 2D 1/ 4(M ) /(M ) 1/ cos

04/11/23 Dr Derek Bray, DAPS 69

Sweep Effects – High Subsonic Speeds

Combined effects of sweep and t/c

Shown here for a subsonic airliner, cruise CL = 0.5

04/11/23 Dr Derek Bray, DAPS 70

Sweep Effects – Supersonic Speeds

Another advantage of sweepback at supersonic speeds is gained by retaining a subsonic leading edge so that it lies inside the Mach line (cone) and shock wave generated.

This means that subsonic aerofoil sections are still aerodynamically efficient.

This reduces wave drag increment, loss in CL and also trim change requirement.

04/11/23 Dr Derek Bray, DAPS 71

Sweep Angle Selection For Supersonic Speeds

• The increment in zero-lift drag is close to a minimum when:

– For t/c 0.06 and 1 A(M2 – 1)1/2 4• As an approximation, for 1.1 M 3.0

– Optimum

• Example: M = 1.6, LE = 57.3o.

2LE1 cot 0.8M

1 oLE cos (1/ ) 6M

04/11/23 Dr Derek Bray, DAPS 72

Supersonic Leading Edges

• The Mach cone angle increases as M increases so that at very Mach numbers the sweep must be very high to retain a subsonic leading edge.

• This reduces the available wing area and eventually there is a limit above which unswept leading edges become preferable.

04/11/23 Dr Derek Bray, DAPS 73

Supersonic Leading Edges

Straight wings used on many high-speed fighters and missiles – such aircraft have poor low-speed performance characteristics.

Lockheed F-104C Starfighter

04/11/23 Dr Derek Bray, DAPS 74

Wing Dihedral/Anhedral ()• Often incorporated for lateral/rolling stability/control

purposes.• Also often used for general layout reasons, e.g.

increased ground clearance requirements for wing-mounted powerplants & stores (dihedral), reduction of length of tip-mounted outriggers on Harrier (anhedral).

Typical range of values between –3o and 5o.

04/11/23 Dr Derek Bray, DAPS 75

Anhedral• Too much dihedral (or combination of dihedral/high

wing/sweep) can lead to dutch roll (lateral dynamic stability problem).

• Many swept high wing aircraft therefore adopt anhedral to alleviate this effect.

BAe Harrier Lockheed C-5 Galaxy

04/11/23 Dr Derek Bray, DAPS 76

Wing Area & Wing Loading• Depends upon geometric parameters but mainly

determined by relationships with performance requirements and available thrust.

• Wing area often expressed as: – wing loading = Mg/S or W/S, where:– M = aircraft mass, W = weight, S = gross wing

planform area.• Usually taken at design take-off mass condition.• Highly interconnected with aircraft’s thrust/weight

ratio for performance optimisation so a credible estimate is required early in the design process.

04/11/23 Dr Derek Bray, DAPS 77

Practical Range of Wing Loading• Vary over a wide range but close correlations between

certain categories so may be used for initial selection.

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

04/11/23 Dr Derek Bray, DAPS 78

Practical Range of Wing Loading

Class of Aircraft Wing Loading Range (N/m2)

Large executive jet 4000

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+

04/11/23 Dr Derek Bray, DAPS 79

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, known as washout.

• An increase in angle of attack towards the tip is washin.• A wing may also be aerodynamically twisted by using

different aerofoil sections.

04/11/23 Dr Derek Bray, DAPS 80

Aerodynamics v Structure Conflict• Direct conflict between wing aerodynamic and

structural requirements since low wing mass needs low values of A, , and high t/c.

• Common to compromise using a structural design parameter (SP):

Where n is the ultimate maximum normal load factor (greater of manoeuvre and gust conditions)

1.25

1/ 4SP sec/

nA

t c

04/11/23 Dr Derek Bray, DAPS 81

Aerodynamics v Structure Conflict (cont.)• Typical SP values are:

– Executive jets 12 – 13– Subsonic military strike/trainer 18– Supersonic military strike/intercept 18 – 20– Long range supersonic 10– High performance sailplane > 30– Others 15 - 16

• A good compromise between the aerodynamics and structure may be made with the following correlation:

1.6

0.41/ 40.8

SPcosA= /t c

n

04/11/23 Dr Derek Bray, DAPS 82

Other Wing Design Features• Many other aerodynamic design aids and

features are incorporated onto modern wings.

• Some of the following are described below:

– Vortex generators

– Spoilers & Air Brakes

– Stall fences

– Tip plates and tanks

– winglets

04/11/23 Dr Derek Bray, DAPS 83

Vortex Generators• Small metal plates attached to the wing upper surface

to generate vortices, re-energise boundary layer and delay separation and stall effects.

Boeing 707 wing

04/11/23 Dr Derek Bray, DAPS 84

Vortex Generators• May be used for several applications:

– Swept-wing transonic designs – to alleviate potential shock stall problems (e.g. Harrier, Buccaneer, Javelin).

– To improve control surface effectiveness (e.g. Embraer 170).

– On STOL aircraft to improve low-speed performance (e.g. C-17).

Javelin Buccaneer

04/11/23 Dr Derek Bray, DAPS 85

Spoilers & Air Brakes• Opposite function to high-lift devices in that they

“destroy” the wing lift.• Usually hinged flaps located on wing upper surface

ahead of the TE flaps.• Gliders tend to use simpler surfaces which rise

vertically out of the wing.

Airbus A319 Boeing 777

04/11/23 Dr Derek Bray, DAPS 86

Spoilers – Further Comments• Used to:

– Dump lift after touch-down, thus preventing aircraft from bouncing back up into the air.

– Allow controlled descents without gaining excessive aircraft speed.

– Increase drag to reduce landing distance.– Provide roll control through differential operation,

either:• In conjunction with ailerons, or• As primary roll control method, leaving entire

trailing edge free for flap use.

04/11/23 Dr Derek Bray, DAPS 87

Stall Fences• Used on highly-swept wings to alleviate tip-stalling

problems (due to thickening boundary layer of outwards flowing velocity component).

MiG-19 wing

04/11/23 Dr Derek Bray, DAPS 88

Tip Plates & Tip Tanks

• Reduce strength of wing-tip vortices and thus reduce lift-induced drag.

• However, produce an increase in skin friction drag.

• Use not recommended nowadays for reducing drag.

MiG-19 wingLearjet 23

04/11/23 Dr Derek Bray, DAPS 89

Winglets• Winglet produces its own closed vortex system

which partially cancels main wing trailing vortices.• This reduces spanwise downwash and thus lift-

induced drag.• Usually fitted above the tip for ground clearance

reasons.• Cheaper, easier & more aerodynamically efficient to

increase wing span instead and for full effect should be designed from outset, rather than as ad-hoc feature.

• May also be used as lateral stability/control surfaces.MiG-19 wing