Aerodynamic Book

8/8/2019 Aerodynamic Book

1/299an 05Section 6 Initial Sizing & Analysis Techniques

Copyright 2005 by Askin T. Isikveren All Rights Reserved

Section 6(iv)

Initial Sizing & AnalysisTechniques

PD340 TRADE STUDY AND FINAL CONFIGURATION SELECTION

(WILLIAMS FJ44-2 ENGINES)

20500

20600

20700

20800

20900

21000

21100

21200

21300

21400

21500

21600

21700

21800

21900

22000

310 315 320 325 330 335 340 345

Reference Wing Area (sq.ft)

MaximumTakeOffGrossWeight(lb)

W/S

TTC

Vopt

Range 1

VS

BFL

FEASIBLE SOLUTION=0.40

=0.35

=0.30

b=54 ft

b=54 ft

b=50 ftb=58 ft

Range 2

W/S=65 lb/sq.ft (317 kg/m2)

VS=90 kts @ MLW

BFL=3900 ft (1189 m)

TTC=18 min.

Vopt=375 KTAS or M0.65 @ FL 350

Range 1=700 nm (232 lb/PAX) & 850 nm (200 lb/PAX)

Range 2=800 nm (232 lb/PAX) & 950 nm (200 lb/PAX)

Aerodynamic Prediction, Devices &

Setting Requirements




Tier II Low-speed & High-speed

Aerodynamic Prediction

The importance of predicting low-speed and high-speed

aerodynamic qualities of aircraft cannot be understated

Vehicular definition relates to an initial appreciation of how the flight

envelope will look It is one of the integral components in formulating airplane operational

performance attributes

Prediction of low-speed and high-speed aerodynamic attributes

covers the following categories

Low-speed aerodynamics

Clean wing lift characteristics and maximum lift

Maximum lift generated by trailing and leading edge high-lift devices High-speed aerodynamics

Zero-lift drag

Vortex-induced drag at subsonic speeds

3D effects, trim and ancillary drag contributors

Total incremental drag due to OEI condition

Compressibility or wave drag due to volume and lift

Aerodynamic impact of winglets

Buffeting qualities


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Section6InitialSizing&

AnalysisTechniqu

es

3

Primary and secondary control surfaces and forces on a





Aerodynamic Prediction (cont.)

CLmax is the maximum lift coefficient the wing can generate

CLmax is dependent upon

Wing sweep

Wing aspect ratio

Wing thickness-to-chord

Flapping span and flap deflection angle

High-lift device configuration

In conceptual design, CLmax is often predicted by inspecting other

aircraft of similar configurations; as a general rule

Empirical methods are well suited to giving results with an adequatelevel of accuracy for conventional aircraft configurations and technology

levels

The primary goals are for highest (L/D)TO and (D/L)LD Predictions should not exceed approximately CLmax = 3.50 unless

suitable justification has been established

Parametric analysis techniques can be utilised to confirm the validity of

prediction results

, angle of attack, angle of attack

CCLL, Lift Coefficient, Lift Coefficient

CCLmaxLmax cleanclean

CCLmaxLmax landinglanding

CCLmaxLmax takeofftakeoff






An expedient method to establish clean wing CLmax and lift-curve

geometry

First identify the 3D CL using the Vortex-Lattice method; closed-form

Helmbold method is good enough as well Predict the zero-lift angle-of-attack; can read off 2D test data results as

an initial guess; non-linear lift is predicted to commence at oL + 10

Use the algorithm CLmax = 14 dCL/d to estimate the maximum liftcoefficient for 1g stall

oL

LiftCoefficient,C

L

Angle of Attack, (deg.)

43 2ARref

3

4 xdCL d

dCLd

= 10

Vortex-Lattice Calculations

Empirical Algorithm

1

2

3

4

stall

Predicting the lift characteristics of a clean finite wing






Examples showing distinction between 1g and minimum

aerodynamic stall definitions

Ref:Some

AspectsofAircraftDesign

and

AircraftOperation

Obert,

1996

Ref: AGARD CP-102

F-28 Mk 4000

Boeing 747






Note the reference configuration

Use fractional change theory

to predict the CLmax ofalternative layouts






Lift-to-drag ratio during takeoff manoeuvers

Instantaneous OEI climb gradient at V2 speed can be predicted using

the parametric correlation below

Increasing the incremental lift with high-lift devices has a tendency ofreducing the available lift-to-drag ratio, hence, is detrimental to climb

Ref: Delft University Press

Synthesis of Subsonic Airplane Design

Torenbeek, 1982

Method to estimate lift-to-drag ratio of design candidates with

high-lift devices deployed






Ref: 1981-6 No. 91

LAeronautique et LAstronautique, 1981

Details of wing planform, airfoil section and twist distribution

geometry for A310 transport


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AnalysisTechniqu

es

10

Itemized breakdown of total drag and physical explanatio



Copyright 2005 by Askin T. Isikveren All Rights Reserved 1

Predicting zero-lift drag

Basis is modified Eckerts equation for skin friction incorporating a

Reynolds number adjustment parameter

Mixed (laminar) flow adjustment can be incorporated thereafter Component build-up method is used to generate reference condition



0.002000

0.002500

0.003000

0.003500

0.004000

0.004500

0.005000

0 5000 10000 15000 20000 25000 30000 35000 40000

Vehicle Wetted Area (sq.ft)

Vehicula

rEquivalentSkinFrictionC

oefficient(-)

Unacceptably

Excessive

Advanced Passive

or Active Methods

Mean Line

Large Regionals & Large Business Jets

Small Regionals & Small Business Jets

Narrow-bodies

Wide-bodies

( )[ ] [ ]d2bRactf

Mc1Nlog

Ac

+=

equiv. sand roughness,

pressure & interferenceMach number

Survey of wetted areas and equivalent skin friction coefficients

Reynolds

number




R

LR

lvt

Top

Dwm

yeng

yeng

Predicting vortex-induced drag

Oberts empirical method is suitable for subsonic analysis (M>0.4)

Reduction in dCD/dCL2 due to slot-effect needs to be modeled as well

Incremental drag due to 3D effects and ancillary drag contributors Most common method is form factors that account for

3D effects

Ancillary interference

Excrescences

Trim (goal should be keep it small)

These values are computed based on thickness-chord ratios of the

wing, horizontal and vertical tails, and, the fineness ratios of thefuselage, nacelle and other appendages

OEI asymmetric drag estimation

Windmilling drag estimated using imaginary cut-off Reynolds number

It is an imaginary skin roughness (l/k) independent of engine size

Assuming this roughness level an equivalent skin friction is computed using

the Prandtl-Schlichting form of Eckerts equation

Drag due to asymmetry is then based

on equilibrium of moments



007.0AR05.1

CdCd

clean

2

L

D +

=

vortex-induced

drag factorref. aspect ratio

[ ]

w

R

vt

eng

opwmwm

DOEISq

tanl

yTDD

C

++=




Predicting wave drag

Difference in zero-lift drag coefficient between the fastest Mach number

(less than M =1.0) & Critical Mach is defined as transonic wave drag

Can produce reasonable initial estimate of Critical Mach using modified

Korns equation

Empirical exponential equation is then utilised to model the geometric

increase in drag within the drag rise and divergence regimes

Supersonic wave drag accounts for contributions due to volume

displaced by the vehicle as well as lift distribution



( )M

cos

ct

cos

C

10

1M

cos

1M

Qchd

m

2/3

Qchd2

L

REFQchdCR

=

ref. wing quarter chord sweep

airfoil technology operating lift coefficient

margin to divergence Mach

mean wing thickness

Mach number

CD

Constant CL

Constant CL

increasing CL

MCR MDD

CD = 0.0020


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AnalysisTechniqu

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Suggested target design and off-design cRef: Some Aspects of Aircraft Designand Aircraft Operation

Obert, 1996




Buffet Envelop

It is an additional en route limitation to the aircraft flight envelop

Defines an upper threshold of flight level after an appreciation of climb

and cruise specific excess power residuals, and, maximum cabinpressure differential are considered

Buffeting is characterized by

Breaks in CL-, cm- or cx- curves and emergence of pressure divergenceon any of the lifting surfaces or fuselage

The derivation of these boundaries are commonly performed using

extrapolated wind tunnel data to full-scale and subsequently verified with

flight testing

Initial prediction methods can become mathematically quite extensive which

do not easily lend themselves to simplification In reaching and surpassing the threshold for buffeting the aircraft must

permit full controllability

This means flow separation on a swept wing at high Mach number should not

initiate too far outboard to prevent strong roll or pitch-up tendencies

Airworthiness rules stipulate cruise flight has to be limited to lift

coefficients where n = 1.30 can be reached without encountering buffet

Free from buffet within the operationally expected envelop is desirable



Explanation of buffeting envelop for transport aircraft

Ref: AIAA 88-2043

The Integration of CFD and

Experiment: An Industry ViewpointBengelink, 1988

Ref: AIAA-2002-0002

Design of the Blended-Wing-Body

Subsonic Transport

Liebeck, 2002






Buffet boundary for MD80 transport

Predicted and flight test derived buffet boundary for L-1011

Ref:

SomeAspectsofAircraftDesign

andAircraftOperation

Obert,

1996




Aerodynamic Devices

These are appendages that either enhance performance or fix

problems, i.e. either lead to successful operation and/or

certificated airworthiness

Winglets With greater emphasis being placed on improving aircraft cruise

efficiency winglet devices offer the most attractive drag reduction

Another reason for selecting winglets is the aesthetic appeal

There are two categories

The conventional winglet; AR=1.5

Blended winglets typified by a high aspect ratio (AR=3.5) and integrated by

way of pronounced filleted transition geometry between the wing and wingletstructures

Benefits of winglets can be itemized as follows

Decreased fuel burn and increased payload range attributes achieved

through an aerodynamic performance improvement, i.e. net vehicular drag

reduction

Higher cruise altitude and OEI drift-down ceiling

due to a net vehicular drag reduction enabling a

greater amount of specific excess power at given

altitude and speed Improved takeoff performance higher effective

OEI lift-to-drag and therefore higher second

segment climb gradient for given reference speed;

allows for higher TOGWs

Reduced engine maintenance the option of

retaining the original takeoff performance levels

prior to installation of winglets promotes a reduced

thrust concept

Lower airport noise levels exploiting the reduced thrust concept

Vortex Generators

Flow over a lifting surface may tend to separate prematurely leading to

stall, diminished control authority, greater drag or even noise

The separation can be either chordwise or spanwise

Separation can occur at low-speed or high-speed (transonic flow)

BBJ with AviationPartners winglet




To correct this situation a series of vortex generators or vortilons near

the wing or control surface leading edge are usually installed

These energize the airflow over the surface and thereby assist in delaying the

onset of flow separation

This is a common solution to imperfections like poor manufacturing tolerance

Thin plates attached to engine nacelles or along the forward portion ofthe fuselage body are called strakes also shed vortices to energize

local flow or even correct directional stability at high angles of attack

Not a desirable solution

Can be avoided for the wing if thoughtful consideration is given to wing

thickness, section contour distribution and washout

Measure of insufficient upfront work done on a new design if artificial devices

are employed to fix problems during flight testing

Perpetual strides in CFD capabilities will have a tendency to minimise use ofvortex generators, or, at least establish a rationale that employing them is the

best compromise

Aerodynamic Devices (cont.)

Examples of vortex generators for high-speed (GV left) and low-

speed (Legacy right)




Aerodynamic Devices (cont.)

Stall Strips

Are spanwise strips added to the wing

leading edge to ensure stall begins at

that location first They provide more docile (acceptable)

stall characteristics

It is an effective method to ensure

proper stall progression, however,

may also lead to unacceptable

high-speed drag penalty

Do not require these when leading edge high-lift device is used

Wing Fences Act as barriers to deter cross-flow, thereby possible separation which

could lead to tip stall

High-speed drag penalty

Ventral Fins

Are surfaces that protrude from the

underside of the aft fuselage in an

inverted V configuration They improve stall protection by

scooping up air under the tail helping

to push the nose down at high alpha

Another benefit is enhanced

directional stability at

sideslip and higher angles

of attack

Ancillary benefit Can avoid the need of a

stability augmentation

system through inherent

improved directional stability

at high Mach numbers and

altitudes, and, increased

Dutch-roll damping

Generates drag through greater wetted area and interference




Setting Requirements for Low-speed &

High-speed Aerodynamics

Whenever an initial technical assessment is undertaken a

preliminary list of wing aerodynamic design requirements needs to

be generated

Primary considerations include Aircraft performance and handling

Aircraft certification

The list constitutes a roadmap and is formulated by collaborative efforts

between conceptual design, aerodynamics and operational

performance functions

The most important component is the wing design

It is an iterative process and requires input from all three groups mentioned

above

Issues concerning design philosophy generate fundamental questions about

how the goals are to be achieved

Requisite number of development wings

Requisite number of production wings (if a family concept)

Scope of trade-off analysis and declaration of optimisation parameters

Low-speed requirements and targets that need to be defined are

All speed targets are with respect to 1-g stall concept

Max expected L/D for each flap and/or slat angle

Expected L/Ds at 1.13VS and 1.23VS for respective takeoff and landing

configurations

Stable L/D versus CL at 1.13VS and 1.23VS and VFE Expected CD at

V2 (1.13Vs) for each permissible takeoff flap configuration

Mid-AUW, typical descent speed (e.g. 250 KCAS) in the clean configuration

(idle power)

VAPP (1.3VS), in the clean configuration

VREF (1.23VS) in the landing configuration

Alpha = 0.0 in ground effect for each takeoff flap configuration

Expected CLmax for each flap and/or slat angle assuming both clean and

with icing contamination

Number of unprotected (anti-ice or de-ice) slat panels should be taken into

account





High-speed Aerodynamics (cont.) Small Runback Ice behind ribs and edges of protected slat panels

Double-Horn (3 in.) shapes on winglet (if applicable), wing-body fillet and

landing lights

Takeoff ice on all forward facing aerodynamic surfaces including protected

slat panels should not result in stall speed increase of more than 3 KCAS Landing ice on all forward facing aerodynamic surfaces including protected

slat panels should not result in stall speed increase of more than 5 KCAS

Delayed Turn-on ice on all slat panels should not advance stall onset ahead

of stall warning (Plus 1 sec., if applicable)

Expected CLmax in the landing configuration

Expected CLMU (in ground effect at aircraft tip-back geometry limit minus

1 is approximately CLshaker in free air) with no wing tip separation

Special relationships and guidelines gathered through experience are

CLmax lowest takeoff flap > CLmax landing / 1.21

CLmax clean > CLmax landing / 1.50

No significant lift loss due to residual de-icing fluids in aerodynamic critical

zones during lift off in ground effect

Acceptable stall characteristics, uncontaminated and with icing assumptions

Number of unprotected (anti-ice or de-ice) slat panels should be taken into account

Small Runback Ice behind ribs and edges of protected slat panels

Double-Horn (3 in.) shapes on winglet (if applicable), wing-body fillet and landinglights

Takeoff ice on all forward facing aerodynamic surfaces including protected slat panels

Delayed Turn-on ice on all slat panels

Double-Horn (1.5 in.) ice on all slat panels

No winglet separation up to V2 5 KCAS for all takeoff flaps

No significant buffeting up to VFE for all flap and/or slat configurations

Wing Stall Progression

Should be preceded by trailing edge separation and/or buffeting of the inboard/mid-

wing

Onset should not be defined by leading edge separation

Should initiate on the inboard/mid-wing at the trailing edges

For underwing podded engines, flow over the wing behind the nacelles should remain

attached and be adequately energised up to higher angles of attack

Outboard wing leading edge should be adequately protected to higher angles of

attack with no significant losses in roll control effectiveness

Approach and Landing Phase

Pitch attitudes of 0-2 at VREF in the landing configuration

Pitch attitudes at touch-down (VREF 10 KCAS at 50 ft), in the landing configuration,

is less than the aircraft tip-back geometry limit by at least 2





High-speed Aerodynamics (cont.)

Pitch attitudes of less than 4 at VAPP in the clean configuration

No abrupt changes in pitch stability with increasing alpha up to maximum

alpha

Dihedral stability for all low speed configurations

Wing tip, flaps, underwing podded engine ground clearances up to 10 in roll,geometry limit in pitch or combination of both

High-speed requirements and targets that need to be defined are

Expected maximum M*L/D at design cruise speed

Expected L/D at

High AUW, maximum climb speed, initial cruise altitude

Mid-AUW, typical climb speed, intermediary cruise altitude

MAXRange

No unnacceptable handling characteristics up to MAX(roll-off, sudden pitch-up, severe buffetting, etc.)

Performance Requirements @ Shaker

CL

CLMAX (no ice)

CLShaker (no ice)

Manoeuvre

Margin

20

10

Reference Speed

CLREF

3 % or 5% Margin

No Ice

With Ice

Definition of target CL- characteristics; note stick-pusher needsto be accounted for aft-fuselage mounted engine configuration





High-speed Aerodynamics (cont.) Expected CD at

High AUW, typical climb speed, initial cruise altitude

Mid-AUW, maximum climb speed, intermediary cruise altitude

High AUW, typical cruise speed, initial cruise altitude

High AUW, maximum cruise, initial cruise altitude

MDD number at mid-AUW and initial cruise altitude

Buffet boundaries margin of 1.4 g at

High AUW, intermediate speed, initial cruise altitude

Mid-AUW, MMO, intermediary cruise altitude

Special relationships and guidelines gathered through experience are

Speed stability (slope of L/D versus CL) assured at low AUW, MFC/VFC kink

(thrust lapse rate included) CD always increases with Mach and CL particularly for intermediate to high

speeds

Shock waves strength and movement should not be abrupt with increasing

Mach up to MMO or alpha (CL) up to 1.5g

Typical aircraft pitch angles during cruise

Should not exceed +1.5-2.0 for most cases within the typical operations envelop

Good design practise to ensure +0 for all operations

Wing loading to ensure passenger comfort and operational efficiency

Stable dihedral and weathercock characteristics up to MMO/VMO

Gradual degradation in stability derivatives up to MFC/VFC

No aileron aerodynamic reversal up to MFC/VFC






Additional Reading

Young, A.D., The Aerodynamic Characteristics of Flaps, Aeronautical

Research Council Reports and Memoranda, Ministry of Supply, UnitedKingdom, 1953

Aerodynamics, Jet Transport Performance Methods, D6-1420, Seventh

Edition, Boeing Flight Operations Engineering, May 1989

Obert, E., Forty Years of High-Lift R&D An Aircraft Manufacturers

Experience, AGARD DCP 505, September, 1993

Obert, E., The Aerodynamic Development of the Fokker 100, ICAS-88-

6.1.2, 1988 Schaufele, R.D., Ebeling, A.W., Aerodynamic Design of the DC-9 Wing and

High-Lift System, Douglas Aircraft Div., McDonnell Douglas Corp., AIAA

Paper No. 670846, 1967, pp 2575-2583

Shevell, R.S., Aerodynamic Bugs: Can CFD Spray Them Away?, AIAA-85-

4067, AIAA 3rd Applied Aerodynamics Conference, October 1985

Getting a Lift Out of Winglets, Business and Commercial Aviation,

February 1998, pp. 56-65

Dees, P., Stowell, M., 737-800 Winglet Integration, SAE Paper 2001-01-

2989, 2001 World Aviation Congress, September 2001

Isikveren, A.T., Quasi-analytical Modeling and Optimization Techniques for

Transport Aircraft Design, Section 7, Predicting Low-Speed and High-

Speed Aerodynamic Attributes, Report 2002-13, Royal Institute of

Technology (KTH), Ph.D. Thesis, Department of Aeronautics, Sweden, 2002


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2001-01-2989

737-800 Winglet Integration

Paul DeesBoeing Commercial Airplanes

Michael StowellAviation Partners Boeing

Copyright 2001 Society of Automotive Engineers, Inc.

ABSTRACT

A joint venture called Aviation Partners Boeingsuccessfully integrated winglets into the Next-Generation737-800 by retaining performance improvements with

minimal weight penalty on the existing 737 wing design.Program challenges included developing both retrofitand production configurations using a common wingletdesign, causing minimal impact on all customers, andcausing minimal disruption to the 737 productionprocess. Winglet benefits along with improvedperformance include reduced engine wear andenhanced visual appeal.

INTRODUCTION

The 737-800 wing was originally designed and certifiedwithout winglets. The flight testing of winglets for the

Boeing Business Jet (BBJ) indicated the expected gainsin aerodynamic efficiency were real, as also wereincreases in flight loads. The technical challenge thenbecame how to add winglets to the already existing 737wing design, keeping the improved aerodynamicefficiency with minimal structural weight penalty andminimal systems changes. The program challenge thenwas how to integrate winglets into both existing fleetaircraft and into new production aircraft. Anotherprogram challenge was how to minimize cost of the flighttest and certification effort of several distinct wingconfigurations, preferably using a common wingletdesign. To meet these challenges, a joint venture calledAviation Partners Boeing (APB) was formed betweenThe Boeing Company and Aviation Partners, Inc. wherethe patented blended winglet technology (Reference 1)was developed. Boeing has primary responsibility forproduction winglets and APB has primary responsibilityfor retrofit winglets on in-service airplanes.

AVIATION PARTNERS BOEING BACKGROUND

Aviation Partners Boeing is a limited liability corporationowned by The Boeing Company (Boeing) and theprincipals of Aviation Partners Incorporated (API). APIs

primary business is the application of performanceimprovement technology to business jets. The jointventure company was formed after Boeing BusinessJets contracted API to design and certify winglets on the737-700 IGW business jet. The purpose of the jointventure is to create a mechanism for an exchange ofdata between API and Boeing with the goal of improvingthe performance of Boeing products in production and inthe retrofit market. Boeing has access to APIs BlendedWinglet technology for applications on current aircraft inproduction as well future airplane programs. The jointventure allows APB access to Boeing basic airplanedata, which will facilitate design and certification efforts

in the retrofit market.

WINGLET BENEFITS

Figure 1 - Blended winglet on 737-800


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The addition of 8 foot tall Blended Winglets to the 737-800 (see Figure 1) increases the aerodynamic efficiency.For a given amount of lift, drag is reduced.

Direct economic benefits to the airlines includecombinations of these items (not all are availablesimultaneously):

Decreased fuel burn

Increased payload-range

Improved take-off performance

Reduced engine maintenance

Lower airport noise levels

Figure 2 shows the flight-test derived winglet block fuelburn improvement, which increases with cruise range. Itis based on an average of eastbound and westboundmissions and is common to both retrofit and production

winglets.

Figure 2 Winglet block fuel burn improvement

Other less tangible benefits include high-tech visualappearance and airline passenger appeal(environmentally friendly).

Figure 3 Blended winglet construction

Figure 3 shows the 737-800 Blended Wingletconstruction. The winglet is approximately 70%graphite-epoxy by weight.

RETROFIT WINGLETS

APB has primary responsibility for the retrofit (postdelivery and in service) winglet installations. In theaircraft retrofit environment many of the challenges toinstall winglets on the airplane are different compared tothe production modifications.

Many of the aerodynamic driven changes to the 737-800

are the same for the retrofit and production versions.

Changes common between the 737-800 retrofit andproduction aircraft with winglets are:

Winglet

Stabilizer Trim settings

Auto-throttle

Flight Management Computer (FMC) data

Figure 4 Retrofit winglet aircraft modifications

Most of the structural changes required differ betweenthe 737-800 retrofit and production aircraft. Figure 4shows the primary retrofit changes and Figure 5illustrates the structural modifications required for the737-800 winglet retrofit.

Figure 5 Retrofit wing modifications

Adding winglets increased both the wing dynamic andstatic flight loads significantly. An economically viable


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retrofit program minimizes the recurring costs of theinstallation. This is difficult because the retrofitmodification is limited by existing parameters in the basicairplane. For example, increasing skin thickness may bethe most efficient means of increasing the wing bendingstrength, however skin replacement is not cost effectivefor retrofit. For the Retrofit 737-800 the wing strengthwas increased by the addition of straps and angles tothe stringers located inside the wing-box as shown inFigure 5. Modification to the wing was minimized by thedevelopment of a Speed-brake Load Alleviation System.This system changes the angle of the in-flight speed-brakes in critical flight conditions to reduce wing loading.

Wing service life goals were achieved by reworkingexisting fasteners in the lower wing skin. The fastenerswere removed and replaced with interference fit, specialfasteners for fatigue life improvement.

The increased pitch inertia at the wingtips by the additionof winglets aggravated critical flutter modes. A reductionin the low altitude operating speed was avoided byadding 90 pounds of ballast per wing in the outboard

leading edge. Also, replacement of the removable outer2 bay skin panels improved flutter tip modes.

PRODUCTION WINGLETS

Boeing has primary responsibility for the in-lineproduction winglet installations. The winglets are builtwithin Boeing to the same drawings as the APB retrofitwinglets.

Figure 6 Production winglet installation modifications

The retrofit configuration used a load-alleviation system

to handle the increased flight loads. The productionwinglet installation met the challenge by carefullydesigning minimal additional bending and torsionalstiffness into the wing. The structural provisions weredesigned to minimize weight impact on customers whochose not to purchase the optional winglets. They werealso designed to minimize the impact of winglets on theBoeing production facilities, especially final assembly.Flutter considerations drove a significant effort to controlwing torsional stiffness and winglet weight and center ofgravity. Systems changes were also required to supportthe addition of winglets. An overview of the required

changes for the production winglet installation is shownin Figure 6.

The wing structural changes are shown in Figure 7. Theprimary changes were upper and lower skin panel gagechanges and stringer gage changes over the outboard2/3 of the wing. To minimize the weight penalty forcustomers who do not choose winglets, these changesstop at rib 25, and the configuration is known as partialprovisions. Partial provisions also include new ribs 25through 27 with additional strength as needed. As withthe retrofit, some specific fastener locations are coldworked to meet fatigue requirements. Some minorstrengthening is required in the center wing.

Figure 7 Production winglet structural changes

The customers that choose winglets have new upperand lower outboard skin panels from ribs 25 to 27 and75 pounds of flutter ballast per wing that is required tomeet the flutter certification requirements of being flutterfree at 15% greater airspeeds then Mdive/Vdive. Itwould have been possible to trade flutter ballast weight

for greater increases in wing skin panel thickness, butthat was rejected as it would have penalized customersnot choosing winglets.

As with the retrofit, an absolute seal is installed toprohibit any flammable fuel vapors from the inboard wingfrom reaching any potential ignition sources in thewinglet.

Since the winglets improve cruise performance, a new 800 winglet model engine database (MEDB) for the flightmission computer (FMC) is required and is selected viapin select. Likewise, a new Autothrottle is used with

winglets and includes a winglet setting via dipswitch.These system changes are common with the retrofitinstallation. All of the position and navigation lighting ison the winglet, as with the retrofit configuration (Figure8). The aft position light installation is in a low dragstreamlined fairing on the inboard portion of the winglet.The early production winglets have a small light shieldinboard of the forward anti collision lights to preventstrobe flashing from entering the cockpit. The new 6stall management yaw damper (SMYD) accommodatesthe shields impact on stick shaker speeds and is pin-selectable. A retrofittable lighting product improvementis in development to eliminate the light shield.


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Figure 8 Production winglet lighting

Another small systems change is required due to thewinglet aerodynamics altering the stabilizer trim angles.This manifests itself as updated stabilizer trim switchlocations and a winglet greenband light plate in thecockpit. Autothrottle, FMC, SMYD, and stabilizergreenband changes are shown in Figure 9.

Figure 9 Systems changes

FLIGHT TEST AND CERTIFICATION

Five different 737 aircraft were flight tested from 1998 to2001 to validate and to certify the winglet installations. Asummary of these flight test programs is shown in Figure10. Boeing and APB held joint flight test programswherever possible to minimize cost and share data.

Prototype winglet performance and loads were flown in1998 and 1999 on the YC001 (737-800) and YG001(737-700 BBJ) airplanes. The BBJ winglet installationwas certified on YG032 in 2000. It is similar but not

identical to the 800 retrofit winglet installation, whichwas certified using YC020 flight test data. An exampleof cooperation between Boeing and APB is the use ofYC020 flutter flight test data to correlate with Boeingcomputational methods in support of the productionwinglet flutter certification. This allowed a reduction inYC714 flight test hours by avoiding additional flutter flighttesting.

Figure 10 Flight test summary

APB worked with assistance from BCA to achievecertification for the retrofit installation with the FAA andJAA and obtained the Supplemental Type Certificate(STC) in May, 2001. Certification of the Boeingproduction installation, with assistance from APB,occurred also in May and was done by Program Letter ofDefinition (PLOD).

AIRLINE OPERATIONS

The first flight with certified 737-800 winglets was byHapag Lloyd on May 8th, 2001.

Initial production winglet customers included SouthAfrican Airways through GATX, Air Berlin, ILFC, andAmerican Trans Air. Initial retrofit winglet customersincluded Hapag-Lloyd as launch customer and Air Berlin.

POTENTIAL FUTURE PROGRAMS

APB believes a tremendous interest in winglets exists inthe passenger and freighter market place. Currentcommitted 737 retrofit programs beyond the 737-800 are

the 737-700 and the 737-300. Figure 12 details thestatus of all the 737 winglet programs.

Figure 12 737 Winglet program status


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CONCLUSIONS

1. APB blended winglets were successfully integratedand certified onto the Boeing 737-800, both as

retrofit and production installations.2. Properly integrated winglets provide substantial

value to their operators.

3. The expected winglet performance benefit wasmaintained with minimal weight penalty despite

increased wing loads.4. Proper treatment of additional winglet loads and their

impact on flutter were required for a successfulprogram.

5. A joint development and flight test program was animportant ingredient to support the certificationefforts.

6. A common design approach for both retrofit andproduction winglet installations provides maximum

fleet commonality for the winglet customers.

REFERENCE

Gratzer, Louis B., Blended Winglet, US Patent5,348,253, granted September 20, 1994.

CONTACT

Retrofit winglet sales information is available from TomVanDerHoeven at 1-800-winglets.

Production winglet sales information is available fromJames Wilkinson at (206) 766-1380.


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LOW-SPEED & HIGH-SPEED AERODYNAMICS 75

7 Predicting Low-Speed and High-Speed Aerodynamic

Attributes

The importance of predicting low-speed and high-speed aerodynamic qualities ofaircraft cannot be understated. The implication to vehicular definition relates to an initial

appreciation of how the flight envelope will look as well as being one of the integral

components in formulating the aeroplanes operational performance attributes. The main

aim is to develop methodologies where the designer has an ability to approach the design

solution in a more sophisticated manner; not only in terms of departing from the usual

more simplified approach premise, but an account of the impact a technological decision

makes to the end result. These two primary goals must also be tempered by an appreciation

for reduction in the analysis complexity. This is surmised as being achievable by first of all

soliciting the designers philosophical requirements and translating this notion into single

all-encompassing algorithms that provide visibility to the designer. Secondly, the

methodologies must be impervious to stoppage when key information required on the part

of the designer is found to be lacking.

7.1 Low-Speed Aerodynamics: LiftTo consistently support design studies of not only quite complex conventional

planforms (with multiple cranks, dihedral, etc.), but also of more exotic layouts such as

multi-surface and non planar wings, it was recognised the algorithm to compute maximum

lift attributes adhere to a quasi-analytical philosophy. This task can be achieved by

concurrent utilisation of dedicated software to quantify the fundamental parameter of clean

wing lift-curve slope with well-established empirical methodologies.

7.1.1 Clean Wing Lift Attributes and Maximum Lift

The clean wing maximum lift can be computed for any original multi-surface or non-

planar planform geometric definition using a three-dimensional Vortex-Lattice Method93

(VLM), which calculates aerodynamic properties of multi-wing designs that are swept

(symmetric or otherwise skewed), tapered, cambered, twisted and cranked with dihedral.

Unlike what is offered by classical VLM approaches, one particular approach models the

wake coming off the trailing edge of every lifting surface as flexible and changing shape

according to the flight state considered. With a distorting wake, non-linear effects such as

the interaction of multiple surfaces can be simulated more consistently. The source of the

basic theory for the VLM with flexible wake is cited as Moran94, and an exemplar of

software embodying these principles is one authored by Melin95

. Succinctly, the classicalhorse-shoe arrangement of other VLM programs has been replaced with a vortex-sling

arrangement. It basically works in the same way as the horse-shoe procedure with the

exception that the legs of the shoe are flexible and consist of seven (instead of three)

vortices of equal strength. Since the primary assumption of any VLM is linearity, two seed

computations are conducted for the lifting surface system at angles of attack (AoA or )where collinearity is likely as depicted in Figure 23 and labelled as Step 1; two such

candidates are suggested as = 0 and +4.Following the protocol mapped out in Figure 23, the next step is to identify the zero-

lift AoA (oL); this is found by extrapolating the lift-curve slope (dCL/d) back to the pointat which CL = 0. The slope dCL/d itself is quantified by comparing the computed VLMlift at the two seed AoA VLM calculations. Wing lift carry-over into the fuselage body can

be accounted for by factoring the original (wing only) dCL/d with a calibrated variation of


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CONCEPTUAL AIRCRAFT DESIGN METHODS76

oL

LiftCoefficient,CL

Angle of Attack, (deg.)

43 2ARref3

4 xdCL

d

dCLd

= 10

Vortex-Lattice Calculations

Empirical Algorithm

1

2

3

4

stall

Figure 23. Predicting the lift characteristics of a clean finite wing using quasi-analytical

techniques (1-g stall concept shown).

a method given by Pitts et al96

wing

L

vehicle

L

ddC

ddC

=(134)

where

gross

2

h

wingLgross

neth

S

d

ddC2S

S

b

d1

+

+= (135)

is related to the fuselage external maximum width (dh), the net or exposed wing planform

area (Snet) and the gross wing planform area (Sgross). The parameter is a calibrationconstant and was derived to equal 3.2. As a final point, Pitts et al stipulates that the use ofEqn. (135) is only applicable for wing-body configurations not violating the constraint of

dh / b < 0.2.

From known data3,97-101, Step 3 involves an AoA increment of = 10 to yield anestimate of the cessation of the linear portion of the curve (usually around = 8) or the

beginning of non-linear lift leading eventually to stall. The final step involves adding 4times the vehicular dCL/d to the now corrected CL computed for Point 3 in Figure 23 to

predict the clean wing CLmax adhering to a 1-g stall concept, or, simply given as

( )vehicle

LregsmaxL

d

dC064.0114C

+= o (136)


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When s = 1, the impulse function, regs = (s,1), introduces a multiplier derived frominformation presented by Obert3, otherwise is zero for s < 1. An appropriate parameter

value is invoked in accordance with the analysis being conducted, i.e. under the premise of

a power-off 1-g stall concept (s = 0), or, the minimum speed in a stall manoeuvre in

accordance with FARs (s = 1) respectively.

If the value is of interest, the corresponding AoA for stall (stall) can be estimated aswell. A suggested empirically derived method based on the same data3,97-101 quoted earlier.

Working off the equivalent reference wing aspect ratio as the only independent variable for

analysis, stall is found by incrementing the AoA at Point 3 shown in Figure 23 by (43 -2ARref) / 3, or alternatively put, by combining all the steps detailed above can be simplified

to read

3

AR273oLstall

+= (137)

Eqn. (137) is taken to be applicable for the 1-g stall concept only. Since the AoA for

stall will differ between the 1-g stall break and minimum speed in a stall manoeuvre, it is

suggested that Eqn. (137) be incremented by an additional 1.0 to model theminimum speed (FARs) in stall manoeuvre AoA.

7.1.2 Maximum Lift Generated by Trailing and Leading Edge

High-Lift Devices

High-lift produced by flap and slat deflection is estimated based on methods presented

by Young102. This reference uses empirical correlation from assorted accumulated data and

predicts with adequate accuracy the aerodynamic characteristics of high lift devices. The

methods are not explained in great detail here; however, the salient features will be

appropriately noted. A similar and more detailed working account may be found in a

design review done by Pazmany103 and Isikveren et al104.

Making allowances for effective chord, flap incidence and part span, the increment

due to the presence of any trailing edge flap is given by

)(f)1cc(C)6(F

)AR(F)cc(CC WmaxLLflapsL

+= (138)

where (c/c) is the effective chord ratio; F(AR) is the function relating the vehicular

dCL/d and the aspect ratio, and this is standardised to an AR = 6.0; C LmaxW is themaximum clean wing lift attainable, f () is a correction to the lift increment for a sweptwing, and

[ ][ ]

= +

+

C c c c c

b b b b b b b b

L f f

f f f f

1 1 2 1 1 2 22 22

3 22 3 21 3 12 3 11

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

(139)

1(cf/c) is a function of effective chords, 2() is a function of the flap angle and is

determined from experimental data (varies from one flap to another). The subscript 22denotes the influence of an auxiliary flap or vane if applicable. The operation [3(bfx2/b) -


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3(bfx1/b)] is a part span correction factor, and, x = 2 and 1 define the outboard and inboard(due to a central cut-out) ends respectively.

The first task is to take Eqn. (138), its coupled constituent Eqn. (139), and introduce

not only the fixed functional values related to design intent supplied by Young, but a

parameter to account for the stall concept adopted per chosen airworthiness regulations.

Additionally, by incorporating supplementary simplifications for sake of brevity, i.e. linear

sensitivity to AR, an all-purpose fixed quantity for effective chord, introduction of a

continuous functional form for the f() correction parameter, the final algorithm describingchange in lift due to trailing edge device deflection is proposed here as

( ) Qchd3flapflapgeofowldslotTE

flapsL cos1b3ARk20

520C

++=

(140)

The two design related impulse functions, dslot = (s,1) and fowl = (s,1), representthe relative increase in lift compared to the default single-slotted flap prediction assuming

double slotted of Douglas type and Fowler flapping arrangements respectively. The

constant kgeo is equal to 2.183 x 10-3 and is universally applicable for all (chord extending)

flaps considered. The flap deflection angle in degrees is denoted by flap with bflap definingthe part-span flap including fuselage carry-through, expressed as fraction of total reference

wingspan.

A series of fixed flap settings corresponding with deflection optima based on

experimental results given in literature1,3-5,39 for given high-lift device types have been pre-

selected for field calculations. Single slotted flaps tentatively have pre-designated

deflection optima of 7

o

, 15

o

and 35

o

for intermediate takeoff, maximum takeoff and landingconfigurations respectively. For double slotted flaps of Douglas type, initial guesses for

optimal flap deflections have been assumed to be approximately 10o, 20o for intermediate

and maximum takeoff, and 45o for landing. Congruous with the double slotted premise, the

Fowler assumes 10o, 20o and 45o for intermediate takeoff, maximum takeoff and landing

configurations respectively. Although optimal flap deflection is dependent upon a given

vehicular configuration and ambient conditions in which the aircraft operates, these

selected values were found to be very close to actual deflections used on contemporary

aircraft and hence adopted for simplicity. Regardless of this directive, the algorithm used to

determine CLmax given above permits an opportunity to truly optimise flap setting for the

operational performance scenario considered; providing an extension is made to allow

cubic interpolation of CLmax for the given intermediary flap setting.These trailing edge high-lift devices may also be complemented by the introduction of

leading edge slats. Occasions where a slat lift increment is desired, a tentative maximum

deflection of 20o is assumed based on experimentation and actual examples64,97,105. The

increment in lift due to slat is only introduced for maximum lift prediction, i.e. maximum

optimal flap deflection usually pertaining to landing configuration. Furthermore, an upper

permissible boundary of CLmax = 3.50 which is universally applicable to all devices has

been artificially set in keeping with conclusions drawn from surveys presented by Obert3.

Young102 suggests a rather simplified expression relating lift increment due to slat to the

slat wing chord fraction. In the end, a more consistent approach exhibiting functional

similarity with Eqn. (140) was chosen to be a more accurate model

Qchd

3

flapgeoLEflapsLcosbARkC = (141)


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where all other parameters retain the previously given definitions, except for kgeo, now

taken to be 0.0470, and bflap is the slat part-span fraction.

To complete the entire prediction exercise, a trimmed lift coefficient needs to be

produced. As outlined by McCormick34 a complete treatment involves augmenting

untrimmed vehicular lift coefficient according to the relative distance between vehicular

centre of gravity (xcg) and aerodynamic centre (xac) locations, and then incrementing

contributions due to generated moment coefficient about the aerodynamic centre and the

moments created because of increase in drag due to trim. Such an approach requires a

detailed array of information; to simplify matters, sufficient accuracy can be achieved by

dropping the terms dependent upon moment coefficient and increase in drag.

( )

+= accg

t

maxLtrimL xxl

MAC1CC (142)

Many aircraft manufacturers adopt the simplified functional form given by Eqn. (142)

in their respective aerodynamic data handbooks. Default values for the non-dimensional

relative MAC distance (xcg xac) can be assumed as -0.05 for aft-fuselage mounted

vehicles, otherwise equal to approximately -0.15 for all other configurations.

7.1.3 Establishing the Accuracy of Clean Wing and High-Lift PredictionOnce each of the analytical and empirical constituents is combined to form the final

algorithm, a wide-ranging analysis has shown predictions are relatively consistent with

actual aircraft lift data. Using a generic supercritical profile as a basis for this investigation,

namely the MS(1)-0313, Figure 24 elucidates this by demonstrating a typical bandwidth of

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Vehicle Actual CLmax (-)

Error,,

inP

redictedCLmax

(-)

TE (or LE) Flaps Neutral

Max TE (or LE) Flaps = +10%

= +5%

= -5%

= -10%

Figure 24. Prediction accuracy of algorithm to compute CLmax using quasi-analytical

techniques. High-lift device set to neutral and maximum deflection shown.


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error ( = predicted actual) with respect to manufacturer quoted values falls within a 5%splay. More saliently, the study indicates there exists a good likelihood maximum lift

predictions will not exceed an error of around = 0.15 irrespective of flap deflection.

The benchmarking data comprised either known aerodynamic performance or wasderived from vehicular stalling speeds. The aircraft used for this validation exercise were:

Boeing BBJ176; Bombardier Aerospace Learjet 4578, Learjet 60106, Challenger CL-60451,

Global Express64, CRJ20079, CRJ70080 and CRJ90081; Cessna Citation Excel82; Dassault

Aviation Falcon 2000107 and Falcon 90053; Embraer ERJ 135108, ERJ 140109, ERJ 14584;

Fokker Aircraft Fokker 70110 and Fokker 100111; Gulfstream Aerospace GIV-SP89 and GV-

SP90; PD340-2 19 PAX regional jet conceptual design study112; and, Saab Aerospace Saab

340113 and Saab 2000114. Note that all aircraft assuming maximum flap deflection data

points are displayed in Figure 24; data pertaining to neutral flap deflection is shown where

the original manufacturer information was available.

7.2 Zero-Lift Drag Estimation - The Equivalent Length MethodA common method for determining the zero-lift drag (CDo) of aircraft components is

an assumption that the constituents friction drag is equivalent to a flat plate having the

same wetted area and characteristic length. In this way, a very preliminary assessment of

the complete vehicular zero-lift drag estimation may be accomplished by summation of

these individual components. By creating a hybrid approach where the component build-up

method is benchmarked against a standardised closed form expression, economy of effort

can be achieved without incurring excessive degradation in predictive powers. A tool for

estimating zero-lift drag is the friction coefficient equation based on experimentation done

by Eckert115, which accounts for fully turbulent flow and compressibility effects. By

assuming an appropriate reference condition of Mach number and flight level, the

component build-up method may be employed and a characteristic equivalent length forthe entire vehicle can be derived from its equivalent skin friction coefficient - a quantity

commonly used for aircraft comparison exercises. This equivalent characteristic length

may in turn be reintroduced into Eckerts equation and solved for any other Mach number

and flight level combinations the aeroplane encounters.

7.2.1 Derivation of The Equivalent Characteristic Length Method

Assuming the boundary layer is fully turbulent and accommodating effects due to

compressibility on skin friction, the friction coefficient (cf turb) according to Eckert based

on wetted area is given by

( ) ( )d2bRturbf

Mc1Nlog

Ac

+= (143)

where M is the instantaneous Mach number, constants A = 0.455, b = 2.58, c = 0.144 and d

= 0.58 are coefficients of proportionality derived by Eckert, and, the Reynolds number

(NR) in atmospheric flight at given speed and flight level can be expressed as

b

slssls

slsR lVN

= (144)

The identity sls/sls is approximately equal to approximately 6.9x104 s/m2, and lb is

any specified representative length of the body.


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The results obtained by an approximate turbulent theory such as the one given by Eq.

(143) assumes a smooth adiabatic flat plate. In actual flight conditions, typical values of

skin friction exceed the predicted value significantly. This circumstance does not

necessarily invalidate the use of Eckerts equation, but rather, raises the requirement of

additional adjustments to reflect actual physical observations. The first correction calls for

account of an equivalent sand roughness. The traditional method utilises the concept of a

cut-off Reynolds number4, which is determined using the characteristic length and skin

roughness derived from a table of values presented for different surfaces. Other sizable

contributions to the final value of skin friction includes dissimilar boundary layer

development and velocity profiles between streamlined shapes and the flat plate analogy,

and, pressure effects due to frontal area. Instead of relying on a sequence of discretised

computations, the aim here is to formulate a single-step prediction procedure for skin

friction coefficient that can incorporate these adjustments.

Examination of Eq. (143) reveals the theoretical turbulent skin friction coefficient is

primarily a function of Reynolds number with a supplementary account of compressibilityeffects. In view of this situation, any adjustment that takes into account actual-flight

corrections should be expressed as being proportional to Reynolds number, or,

algebraically incorporated into the (log NR)b term. With this idea in mind, Eq. (143) would

be modified to read as

( )[ ] [ ]d2bRactf

Mc1Nlog

Ac

+= (145)

where the parameter act = 1 produces a skin friction result synonymous with Eckerts

original theory, otherwise, for values act 1 constitutes an additional correction torepresent equivalent sand roughness, pressure and interference effects. Based on anelaborate amount of experimentation done in wind tunnel and flight-testing, Poisson-

Quinton116 was able to quantify the difference between actual values of skin friction and

theoretical turbulent friction assuming a smooth adiabatic flat plate. The results showed a

simple linear proportionality between cfand cf turb, namely,

turbfactf cc = (146)

By initially equating Eq. (145) with a factorised Eq. (146) using the binomial

construct, solving for the constant of proportionality, act, and then re-arranging the interimresult such that act becomes the subject, the Reynolds number adjustment parameter

becomes

( ) Rb1act Nlog1act 10

= (147)

Assuming an actual flight Reynolds number of around 20 x 106 where act was foundto equal approximately 1.45 as cited in Poisson-Quintons results116, produces a correction

ofact = 0.105, which would then be introduced into the modified Eckerts equation givenby Eq. (145). The Reynolds correction coefficient ofact = 0.105 can be thought of as amean curve adjustment, representative of conventional technology/manufacturing


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levels, and therefore has been presented as the basis for establishing predictions at the

very initial design stage. Consideration must also be given to the fact a practical lower

limit ofact = 1.30 (or potential CDo reduction of up to 10% from the mean curve) has beenderived when analysing some narrow bodies and larger aircraft types from data supplied by

Obert3, and this factor is in turn synonymous with a Reynolds correction coefficient of act= 0.197.

Eq. (143) represents a condition where fully turbulent flow exists. It would be prudent

to give scope in accommodating mixed laminar and turbulent flow, hence permit the

designer to set a minimum goal of what proportion laminar flow shall occur over the

characteristic length of the body constituent in question. Since an algorithm to quantify a

realistic turbulent skin friction coefficient has been established with Eq. (143), this can be

used as a basis to formulate an extension such that a realistic skin friction assuming mixed

flow is produced. Working off a basic assumption that momentum thickness at given

transition point is synonymous for both laminar and turbulent flows (see Figure 25), the

final skin friction can be produced by summing the friction coefficients for partly laminarand turbulent flow2.

lb

Figure 25. The premise of mixed laminar and turbulent flow used to derive an

augmented realistic skin friction coefficient2.

Matching the momentum thickness of the laminar and fully turbulent boundary layer

at transition point T gives

xcxc turbfTlamf = (148)

where cf lam is the skin friction coefficient for laminar flow, xT is the point along the body

characteristic length where flow transition occurs and x is a distance ahead of thetransition point where fictitiously the onset of fully turbulent flow takes place. It can be

shown34 the total flat plate friction coefficient for a mixed laminar and turbulent flow is

calculated from

( )lamfturbfb

Tturbff cc

l

xcc = (149)

In this equation, cf turb is computed assuming a Reynolds number based on a body

characteristic length starting from the fictitious onset of turbulent flow to the end of the

The aircraft surface can have many irregularities. These include gaps and steps, protruding flush rivetheads, and, surface waviness due to airframe construction, dynamic distortion and cabin pressurisation.


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body, and, cf lam is calculated based on the entire length of assumed laminar flow, or

distance xT. Substitution of Eq. (148) into Eq. (149) can produce an alternate form

turbf

b

Tf c

lxx1c

+= (150)

Since cf turb also depends on x, an iterative procedure is required to solve for x inEq. (150). A valid form of simplification is in order here. Introducing a presumption the

fictitious distance x consistently exhibits linear proportionality with xT for low to mid-range values of x / lb, scope can be given to dispense with the transcendental nature ofEq. (150), hence permit a reduction in complexity. Investigations found that for xT / lb

values less than approximately 0.40, the total skin friction coefficient for mixed laminar

and turbulent flow can alternatively be expressed as

turbf

b

Tmff c

l

x1c

= (151)

The constant of proportionality, mf, assists in ascertaining what proportion of thecompletely turbulent flow premise imparts an influence on the mixed flow result.

Experimentation has found a useful value for this parameter is approximately mf = 0.74for all xT / lb < 0.40. The upper boundary of assumed laminar flow fraction is a reasonable

one for design prediction purposes since an example of the most successful flight testing of

combined passive and active laminar flow control technology achieved laminar flow up to

30% of wing chord117

. In addition, experimentation conducted in a more operationallypragmatic sense commonly produces transition at 15% wing chord117.

The component build-up method for zero-lift drag at given Mach number and flight

level is given as

W

I

1i

i

wet

i

f

h,MDo S

Sc

C

== (152)

where the product iweti

fSc is the drag area of each component i. By choosing an appropriate

reference condition of Mach number and altitude, an equivalent skin friction coefficientrepresentative of the entire vehicle can be produced with the congruent relation

==

I

1i

i

wet

i

f

I

1i

i

wetf ScSc (153)

The parameter fc is the equivalent skin friction for the sum of all constituent wetted

areas produced using the equivalent flat plate analogy representing the entire aeroplane. It

The reference condition for Mach and flight level is open to the designers willingness to trade larger errorsin low speed for more accurate high-speed zero-lift drag or visa versa. Experimentation has found that a

speed near the final vehicle MRC or LRC at an altitude 4000 ft lower than the intended certified ceiling aregood reference conditions for a balanced error distribution.


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is now proposed that this notion of equivalence can be extended to quantify a characteristic

length as well. Since the entire vehicle has been replaced by the flat plate premise with a

corresponding value for fc , by rearranging Eckerts equation, Eq. (143) can be solved for

an equivalent characteristic length (l) given by the identity

[ ]

V

10l

slssls

sls

Mc1c

A b/d2b/1

f

=

+

(154)

Reintroducing this relation to Eckerts equation, and assuming the error in NRdue to a

now fixed equivalent characteristic length (i.e. independent of Mach number or flight level

effects) is small, a general zero-lift drag equation, designated hereon as the Equivalent

Characteristic Length Method (ECLM), which accounts for all variations of Mach numberand flight level can be given approximately as

[ ] Wwet

d2

b

slssls

sls

h,MDo S

S

Mc1lVlog

AC

+

(155)

For a detailed analytical treatment of en route performance, drag is an integral

parameter and has the primary requirement of being differentiable with respect to the

airspeed V for all cases. Eq. (155) appears to be in a form that is quite complex, and more

poignantly, not configured for a more in-depth calculus treatment. It was identified that thisproblem may be avoided via the use of logarithmic differentiation. By utilising the relation

x = eln x, Eq. (155) can be alternatively expressed as

[ ]

+

=

2

sls

2

slssls

slsb

fa

Vc1lndlVlnlnbexp10lnAc (156)

which is in a form ready for differentiation albeit the complexity has not been reduced.

7.2.2 Gauging the Robustness of the Equivalent Characteristic Length Method

An interesting question is to what extent the equivalent characteristic length

assumption is compatible to the exact component build-up method, and, more importantly

what is the upper threshold of relative errors the designer may expect. In an effort to

theoretically gauge the magnitude of inherent errors produced by this approach, the ECLM

expression was reconfigured as an error function with respect to the exact component

build-up method. The most expedient way to observe this would be the comparison of

resultant equivalent skin friction errors analytically and do so for a range of contemporary

regional transport and business jet Reynolds number regimes based on complete vehicular

characteristic lengths. If Eckerts general equation is partitioned into Reynolds number and

compressibility dependent constituents, in conjunction with some algebraic manipulation,

Eq. (143) then becomes


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b

2

b2

1f

llog1

c

+

= (157)

where the compressibility term is described by

[ ]d21 Mc1A

+= (158)

and the Reynolds number dependent constituent is defined as

= Vlog

slssls

sls2 (159)

-10.0%

-5.0%

0.0%

5.0%

10.0%

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5Reynolds Number Based on Vehicular Characteristic Length (x10

6)

RelativeErrorofVehicularZero-LiftDrag(-)

+40%

+20%

+30%

+10%

-10%

-40%

-30%

-20%

0%

+70%

+60%

+50%

Error in l

Error in l

Figure 26. Resilience of ECLM accuracy for a given error in vehicular characteristic

length and en route Reynolds number based on vehicular characteristic length.

Now, by introducing the notion of error factor defined as the ratio of the fixed

vehicular characteristic length quantity derived from a reference Mach and flight level to

the exact value of vehicular characteristic length, or l = l/lexact, the relative error of anequivalent characteristic length assumption can be gauged by considering deviations from

the exact value of exactfc through a fractional comparison


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b

R

l

f

f

Nlog

log1

c

c

exact

+= (160)

Figure 26 (previous page) shows the variation of resultant prediction error compared

to the exact vehicular equivalent skin friction of zero-lift drag with Reynolds number based

on vehicular characteristic length whilst assuming various errors in the l ratio. To putReynolds number based on vehicular characteristic length into context, small business jets

typically operate at around NR = 106, regional aircraft and larger business jets between NR

= 1.5 x 106 and 2.0 x 106, and larger regional and narrow-body aircraft from NR= 3.0 x 106

and higher. For a typical en route Reynolds number of 1.5 x 106 based on vehicular

characteristic length for regional transports, an error of -24% in l compared to lexact

corresponds to a +5% overestimation of equivalent skin friction or total zero-lift drag.

Conversely, for the same Reynolds number, a -5% underestimation of zero-lift drag is

tolerated by a +33% error in equivalent characteristic length from the exact value. Thisresult demonstrates the resilience of ECLM.

7.3 Vortex-Induced Drag at Subsonic SpeedsMany methods exist in quantifying this phenomenon and the most simplest of them is

the Oswald Span Efficiency Method which assumes the vortex-induced drag coefficient of

three dimensional wings with an elliptical lift distribution equals the square of the lift

coefficient divided by the product of the aspect ratio and . Additional drag produced bynon-elliptical lift distributions is made by using the Oswald Span Efficiency Factor (e),

which effectively reduces the aspect ratio. The vortex-induced drag factor35 is given as

eAR

1

Cd

Cd2

L

D

=

(161)

Numerous estimation methods for e have been developed but they mostly tend to

produce optimistically high values compared values of real aircraft. Obert3 offers an

empirically derived equation for the vortex-induced drag factor applicable for Mach

numbers greater than about 0.40, based on actual aircraft regardless of power plant

installation, assuming typical centre of gravity locales, inclusion of wing twist effects, and

compressibility effects neglected.

007.0AR

05.1

Cd

Cd

clean

2

L

D +

=

(162)

Eq. (162) does not appear to account for the distinction of power plant installation

philosophy, i.e. clean wing, underwing podded or on-wing nacelle configurations, and the

direct impact this has on span loading distribution. As an exercise, Eq. (162) was compared

to Eq. (161) and Oswald span efficiency factor solved for a variety known e values of

equipment with different power plant installation philosophies not covered by the

statistical survey. Interestingly, the continuous functional form offered by Obert seemed to

match the values for these known examples with an adequate degree of accuracy. This

leads the author to believe a correlation between aspect ratio and power plant installation


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The ht parameter represents horizontal tail placement non-dimensionalised by dv withrespect to the vertical tail tip and FRP water-line. Similarly with the wing, the vertical tail

form factor was amended to read as

+

+=4

mm

vtailc

t240

c

t425.0 (166)

The fuselage form factor is predicated by body slenderness ratio. Assuming a

st

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