Aerodynamic Book
Transcript of Aerodynamic Book
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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
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2/299an 05Section 6 Initial Sizing & Analysis Techniques
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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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Primary and secondary control surfaces and forces on a
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4/299an 05Section 6 Initial Sizing & Analysis Techniques
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Tier II Low-speed & High-speed
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
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5/299an 05Section 6 Initial Sizing & Analysis Techniques
Copyright 2005 by Askin T. Isikveren All Rights Reserved
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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
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6/299an 05Section 6 Initial Sizing & Analysis Techniques
Copyright 2005 by Askin T. Isikveren All Rights Reserved
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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
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7/299an 05Section 6 Initial Sizing & Analysis Techniques
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Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
Note the reference configuration
Use fractional change theory
to predict the CLmax ofalternative layouts
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8/299an 05Section 6 Initial Sizing & Analysis Techniques
Copyright 2005 by Askin T. Isikveren All Rights Reserved
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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
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9/299an 05Section 6 Initial Sizing & Analysis Techniques
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Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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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Itemized breakdown of total drag and physical explanatio
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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
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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
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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
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
007.0AR05.1
CdCd
clean
2
L
D +
=
vortex-induced
drag factorref. aspect ratio
[ ]
w
R
vt
eng
opwmwm
DOEISq
tanl
yTDD
C
++=
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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
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
( )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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Suggested target design and off-design cRef: Some Aspects of Aircraft Designand Aircraft Operation
Obert, 1996
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15/299an 05Section 6 Initial Sizing & Analysis Techniques
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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
Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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
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Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
Buffet boundary for MD80 transport
Predicted and flight test derived buffet boundary for L-1011
Ref:
SomeAspectsofAircraftDesign
andAircraftOperation
Obert,
1996
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17/299an 05Section 6 Initial Sizing & Analysis Techniques
Copyright 2005 by Askin T. Isikveren All Rights Reserved 1
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
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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)
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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
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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
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Setting Requirements for Low-speed &
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
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Setting Requirements for Low-speed &
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
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Setting Requirements for Low-speed &
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
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Tier II Low-speed & High-speed
Aerodynamic Prediction (cont.)
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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LOW-SPEED & HIGH-SPEED AERODYNAMICS 77
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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CONCEPTUAL AIRCRAFT DESIGN METHODS78
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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CONCEPTUAL AIRCRAFT DESIGN METHODS80
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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CONCEPTUAL AIRCRAFT DESIGN METHODS82
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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CONCEPTUAL AIRCRAFT DESIGN METHODS84
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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CONCEPTUAL AIRCRAFT DESIGN METHODS86
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