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1999-01-5621

Multidisciplinary Design Optimization of a Transonic Commercial Transport with aStrut-Braced Wing

F. H. Gern, J. F. Gundlach, A. Ko, A. Naghshineh-Pour, E. Sulaeman, P. -A. Tetrault, B. Grossman, R. K. Kapania, W. H. Mason and J. A. SchetzVirginia Polytechnic Institute and State Univ.

R. T. HaftkaUniversity of Florida

1999 World Aviation ConferenceOctober 19-21, 1999San Francisco, CA

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1

1999-01-5621

Multidisciplinary Design Optimization of a TransonicCommercial Transport with a Strut-Braced Wing

F. H. Gern, J. F. Gundlach, A. Ko, A. Naghshineh-Pour, E. Sulaeman, P. -A. Tetrault,B. Grossman, R. K. Kapania, W. H. Mason and J. A. Schetz

Virginia Polytechnic Institute and State Univ.

R. T. HaftkaUniversity of Florida

Copyright © 1999 by SAE International and the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

ABSTRACT

This paper details the multidisciplinary design optimiza-tion (MDO) of a strut-braced wing aircraft and its benefitsrelative to the cantilever wing configuration. The multidis-ciplinary design team is subdivided into aerodynamics,structures, aeroelasticity and synthesis of the various dis-ciplines. The aerodynamic analysis consists of simplemodels for induced drag, wave drag, parasite drag andinterference drag. The interference drag model is basedon detailed computational fluid dynamics (CFD) analysesof various wing-strut intersection flows. The wing struc-tural weight is partially calculated using a newly devel-oped wing bending material weight routine that accountsfor the special nature of strut-braced wings. The remain-ing components of the aircraft weight are calculatedusing a combination of NASA’s Flight Optimization Sys-tem (FLOPS) and Lockheed Martin Aeronautical Systemformulas. The strut-braced wing and cantilever wing con-figurations are optimized using Design Optimization Tools(DOT). Offline NASTRAN aerolasticity analysis prelimi-nary results indicate that the flutter speed is higher thanthe design requirement.

INTRODUCTION

Very few recent transonic transport aircraft designs divertfrom a low cantilever wing with either wing or fuselagemounted engines. Within that arrangement, few visualdissimilarities allow one to discern the various models(Fig. 1). It is unlikely that large strides in performance willbe possible without a significant departure in vehicle con-figuration.

Numerous alternative configuration concepts have beenintroduced over the years to challenge the cantilever wingdesign paradigm. These include the joined wing,blended-wing-body, twin-fuselage and the strut-braced

wing, to name only a few. This study exclusively com-pares the strut-braced wing concept (SBW) to the cantile-ver wing configuration.

Favorable interactions between structures, aerodynamicsand propulsion give the SBW potential for higher aerody-namic efficiency and lower weight than a cantilever wing(Fig. 2). The strut provides bending load alleviation forthe wing, allowing the wing thickness to be reduced for agiven wing load. Reduced wing thickness decreases tran-sonic wave drag and parasite drag. This favorable dragreduction allows the wing to unsweep for increasedregions of natural laminar flow and promotes further wingstructural weight savings. Decreased overall weight,along with increased aerodynamic efficiency permitsengine size reduction.

Figure 1. Conventional Cantilever Configuration

This strong synergism yields significant increases in per-formance over the cantilever wing. A MultidisciplinaryDesign Optimization (MDO) approach is necessary tofully exploit the interdependencies of various design dis-ciplines. Several SBW design studies have been per-formed in the past ([1]-[6]), though not with a full MDOapproach until quite recently ([7]-[9]).

2

This study was funded by NASA Langley with LockheedMartin Aeronautical Systems (LMAS) as an industrialpartner. The primary role of the LMAS interactions was toadd practical industry experience to the vehicle study.This was achieved by calibrating the Virginia Tech MDOcode to the LMAS MDO code for 1995 and 2010 technol-ogy level cantilever wing transports. LMAS also reviewedaspects of the Virginia Tech design methods specific tothe strut-braced wing [9]. One of the authors worked onlocation at LMAS to upgrade, calibrate and validate theVirginia Tech MDO code before proceeding with optimi-zations of cantilever and strut-braced wing aircraft.

Several SBW concepts have been investigated within thisproject. Design studies cover wingtip engines, under-wing engines, and fuselage-mounted engines with a T-tail. However, emphasis of this paper is placed on thestructural aspects of the optimization procedure for fuse-lage-mounted engine SBW configurations (Fig. 2). Sincedifferences in T-tail fuselage-mounted and under-wingengine cantilever designs are small, this study uses can-tilever optima with wing mounted engines, to make directcomparisons with the SBW.

Figure 2. SBW with Fuselage-Mounted Engines.

DESIGN OPTIMIZATION

GENERAL ASPECTS – The Virginia Tech Truss-BracedWing (TBW) code models aerodynamics, structures,weights, performance, and stability and control of bothcantilever and strut-braced wing configurations. DesignOptimization Tools (DOT) software by Vanderplatts R&D[10] optimizes the vehicles with the method of feasibledirections. Between 15 and 22 design variables are usedin a typical optimization. These include several geometricvariables such as wing span, chords, thickness to chordratios, strut geometry and engine location, plus additionalvariables including engine maximum thrust and averagecruising altitude. As many as 17 inequality constraintsmay be used (Table 1).

There are two side constraints to bound each design vari-able. Each design variable is scaled to have a valuebetween 0 and 1 at the lower and upper limits, respec-tively. Take-off gross-weight, economic mission take-offgross weight, and fuel weight are important examples forpossible objective functions that can be minimized.

The MDO code architecture is configured in a modularway such that the analysis consists of subroutines repre-senting various design disciplines. The primary analysismodules include: aerodynamics, wing bending materialweight, total aircraft weight, stability and control, propul-sion, flight performance and field performance (Fig. 3).

Numerous differences between the analysis details ofcantilever and SBW configurations are present in thedesign code, as is necessary for such dissimilar vehicles.The primary difference is in the analysis of the wingbending material weight, as discussed in the structuressection. The strut has parasite drag and interference dragat its intersections with fuselage and wing. Some geome-try differences are justified, such as setting the minimumroot chord for the cantilever wing to 52 feet to make roomfor wing-mounted landing gear and kick spar.

The SBW, without need for double taper, has the chordlinearly interpolated from root to tip. The SBW has a highwing and fuselage mounted gear. It is important to notethat, even though the external geometry of the fuselagefor all cases is identical, the fuselage weights will gener-ally be different.

Table 1. Optimization constraints

1. Aircraft Zero Fuel Weight Convergence

2. Range Calculated > Reference Range

3. Initial Cruise Rate of Climb > 500 ft/min

4. Cruise Section CLmax < 0.7

5. Fuel Weight < Fuel Capacity

6. CN Available > CN Required

7. Wing Tip Deflection < Max. Wing Tip Deflection at Taxi Bump Condition

8. Wing Weight Convergence

9. Max. Body and Contents Weight Convergence

10. Second Segment Climb Gradient > 2.4%

11. Balanced Field Length < 11,000 ft

12. Approach Velocity < 140 kts.

13. Missed Approach Climb Gradient > 2.1%

14. Landing Distance < 11,000 ft

15. Econ. Mission Range Calculated > 4000 nmi

16. Econ. Mission Section CLmax < 0.7

17. Thrust at Altitude > Drag at Altitude

3

Figure 3. Description of the MDO Process

MISSION PROFILE – The primary mission of interest isa 325-passenger, 7500 nautical mile range, Mach 0.85transport with a 500 nautical mile fuel reserve (Fig. 4).Range effects on take-off gross weight and required fuelweight are investigated. A minimum fuel design is alsoconsidered.

Several technology groups distinguish the 1995 and 2010technology level aircraft. A 1995 technology aircraft rep-resents an all-metallic benchmark similar to the Boeing777. The other aerodynamics grouping includes theeffects of riblets on the fuselage and nacelles, supercriti-cal airfoils, active load management for induced dragreduction and all moving control surfaces. Systems tech-nologies include integrated modular flight controls, fly-by-light and power-by-light, simple high-lift devices, andadvanced flight management systems. Airframe technol-ogies represent weight savings from composite wing andtails and integrally stiffened fuselage skins. The propul-sion technology is reflected in reduced specific fuel con-sumption.

Figure 4. Mission Profile

AERODYNAMICS – Numerous iterations of both the Vir-ginia Tech TBW code and Lockheed’s version of NASA’sFlight Optimization System (FLOPS) [16] were made sothat drag polars produced by each code are consistent atreference design conditions. The drag components con-

sidered in the Virginia Tech TBW code are parasite,induced, interference and wave drag. Unless specifiedotherwise, the drag model is identical to previous VirginiaTech SBW studies [8]. A detailed description of the dragcalculations can be found in [11].

Parasite Drag – To calculate the parasite drag, form fac-tors are applied to the equivalent flat plate skin frictiondrag of all exposed surfaces on the aircraft. The amountsof laminar flow on the wing and tails are estimated byinterpolating Reynolds number vs. sweep data for F-14and 757 glove experiments. Fuselage, nacelles, andpylon transition locations are estimated by an input tran-sition Reynolds number. Laminar and turbulent flat-plateskin friction form factors are calculated with LMAS formu-las in the Virginia Tech MDO tool. LMAS form factors forwing, tails, fuselage, and nacelles are applied to the skinfriction drag to obtain the parasite drag.

Induced Drag – The induced drag module uses a dis-crete vortex method to calculate the induced drag in theTrefftz plane [8]. Given an arbitrary, non-coplanar wing/truss configuration, it provides the optimum load distribu-tion corresponding to the minimum induced drag. Thisload distribution is passed to the wing sizing subroutine.An additional lift-dependent parasite drag componentwas added to correlate with LMAS drag polars at off-design conditions.

Wave Drag – The wave drag is approximated with theKorn equation, modified to include sweep using simplesweep theory [7], [8]. This model estimates the dragdivergence Mach number as a function of airfoil technol-ogy factor, thickness to chord ratio, section lift coefficient,and sweep angle.

The airfoil technology factor was selected by Lockheed toagree with the LMAS wave drag. Finally, the wave dragcoefficient of a wing strip is calculated from the critical

BaselineDesign

GeometryDefinition

StructuralOptimization/

Weight

RangePerformance

Aerodynamics

Stability andControl

Propulsion

Optimizer

InducedDrag

Friction andForm Drag

Wave Drag

InterferenceDrag

Offline CFDAnalysis

Initial Design Variables

Weight

Updated Design Variables

FieldPerformance

L/DSFC

Objective Function,Constraints

11,000 ft

T/O Field Length

11,000 ft

LDG Field Length

Climb

Mach 0.85 Cruise

140 KnotApproachSpeed

Mach 0.85

7500 Nmi Range 500 Nmi Reserve

4

Mach number. The total wave drag is found by integratingthe wave drag of the strips along the wing.

Interference Drag – The benefits of a strut-braced wingconfiguration are accompanied by a potential interfer-ence drag penalty at the junction of the strut with thefuselage and the wing. The interference drag betweenthe wing-fuselage and strut-fuselage intersections areestimated using Hoerner equations based on subsonicwind tunnel tests [12].

The drag of wing-strut junctions can be important in tran-sonic flow because of the presence of shock waves andseparated flow regions. In order to alleviate the problemassociated with a sharp wing-strut angle, the strutemployed here is given the shape of an arch and inter-sects the wing perpendicularly. Analyses for an archradius ranging from 1 ft to 4 ft were performed with Com-putational Fluid Dynamics (CFD) tools. Unstructuredgrids were obtained with the advancing-front methodol-ogy implemented in the code VGRIDns [13], [ 14]. TheEuler equations were solved using the CFD code USM3D[14], [15] at the cruise Mach number of 0.85.

A very convenient way to extract the interference dragpenalty from a CFD calculation consists in subtractingthe drag of the wing alone from the drag of the strut-braced wing design obtained with CFD. The resultingnumber is a DCD penalty associated with the presence ofthe strut. As the arch radius is increased, the drag pen-alty decreases almost exponentially. From these results,a curve fit is produced and used in the present analysis toaccount for the drag of the wing-strut junction.

The drag polars output from the Virginia Tech MDO tooland LMAS modified FLOPS agree within 1% on averagefor cantilever wing designs.

STRUCTURES – Due to the unconventional nature ofthe proposed concept, commonly available weight calcu-lation models for transport aircraft (such as the NASALangley developed FLOPS) are not accurate enough. Aspecial bending weight calculation procedure was thusdeveloped, taking into account the influence of the strutupon the structural wing design. In addition to the strutdesign, a vertical strut offset was considered as toachieve a significant reduction in wing/strut interferencedrag.

Load Cases – To determine the bending material weightof the strut-braced wing, two maneuver load conditions(2.5g maneuver, -1.0g pushover) and a taxi bump (-2.0g)are considered to be design critical. For the -1.0g push-over and for the -2.0g taxi bump, the strut is not activeand the wing acts like a cantilever beam. Since the strutis not supporting the wing in these cases, very highdeflections of the wing are expected for the -2.0g taxibump. As a result, an optimization procedure is imple-mented to distribute the bending material to prevent wingground strikes. To maximize the beneficial influence ofthe strut upon the wing structure, strut force and span-

wise position of the wing-strut intersection are optimizedby the MDO code for the 2.5g maneuver load case.

In order to attain acceptable aerodynamic characteristicsof the strut, an airfoil cross section is considered. Thestrut is designed the way that it will not carry aerody-namic forces during the cruise condition.

Structural Assumptions – Preliminary studies haveshown buckling of the strut under the –1.0g load condi-tion to be the critical structural design requirement in thesingle-strut configuration, resulting in high strut weights[8]. To address this issue, an innovative design strategyemploys a telescoping sleeve mechanism to allow thestrut to be inactive during negative g maneuvers andactive during positive g maneuvers. Thus, under the –1.0g case, the wing acts like a cantilever beam and forthe positive g maneuvers, the wing is a strut-bracedbeam.

Even more wing weight reduction can be obtained byoptimizing the strut force and wing-strut junction location.On a typical optimum single-strut design, this means thatthe strut would first engage in tension at some positiveload factor. This can be achieved by assuming a slack inthe wing-strut mechanism. The optimum strut force at2.5g is different from the strut force that would beobtained at 2.5g if the strut were engaged for all positivevalues of the load factor. Therefore, the slack load factoris defined as the load factor at which the strut engagesfor the first time. It is important to have the slack load fac-tor always positive, otherwise the strut would be pre-loaded at the jig shape to achieve the optimum strutforce.

Double Plate Model – For calculating the wing-bendingweight of single strut configurations, a piecewise linearbeam model, representing the wing structure as an ideal-ized double plate model, was used (Fig. 5).

Figure 5. Double plate model for bending weight calculation

This model is made of upper and lower skin panels,which are assumed to carry the bending moment. Thedouble-plate model offers the possibility to extract thematerial thickness distribution by a closed-form equation.The cross-sectional moment of inertia of the wing-boxcan be expressed as:

(1)

d

Cb

t

2

)()()()(

2 ydycytyI b=

5

where t(y) is the wing skin thickness cb(y) is the wing-box chord, and d(y) is the wing airfoil thickness. To obtainthe bending material weight, the corresponding bendingstress in the wing is calculated from:

(2)

where σmax denotes the maximum stress, M(y) is thebending moment of the wing, and I(y) denotes the cross-sectional moment of inertia.

If the wing is designed according to the fully-stressed cri-terion, the allowable stress σall can be substituted intoEq. (2) for σmax. Substituting I(y) into equation (2), thewing panel thickness can be specified as:

(3)

This skin thickness is modified by the results obtainedfrom the tip displacement constraint optimization. Thebending material weight of the half-wing therefore is:

(4)

where is the structural span with .

Vertical Strut Offset – To reduce the wing/strut interfer-ence drag, a vertical offset between strut and wing isimplemented. The vertical offset member is designed fora combined bending/tension loading. In this context, thehorizontal component of the strut force is of special con-cern (Fig.6). Since this horizontal force results in a con-siderable bending load on the offset piece, its weightincreases dramatically with increasing strut force and off-set length.

As a result, it is imperative to employ MDO tools to obtainoptimum values for vertical offset, strut force, and span-wise wing/strut breakpoint. By this way, it is possible totrade off the two contrary design requirements: (i) areduced offset length to reduce strut loading, (ii) anincreased offset length to reduce the wing/strut interfer-ence drag. After a complete design optimization with thevertical strut offset as an active design variable, the influ-ence of the offset weight on the total strut weightbecomes comparably small. For the wing bending weightand especially for the TOGW it is almost immaterial.

Figure 6. Vertical strut offset and applied loads

Figure 7 depicts the bending moment distributions on thewing for the design critical load cases of the fuselagemounted engine SBW design. Due to the vertical strutoffset, an additional bending moment is induced into thewing at the wing/strut breakpoint, leading to a discontinu-ity in the bending moment distribution. Since the strut isinactive in compression, the bending moment distribu-tions for the -1.0g pushover as well as for the 2.0g taxibump do not exhibit this discontinuity.

Figure 7. Bending moment distributions for the design critical load cases of the fuselage mounted engine SBW

AEROELASTICITY

Hexagonal Wing-Box Model – Although the double platemodel renders very accurate estimates for the wingbending material weight, it is not suitable for calculationof the wing-box torsional stiffness. Nevertheless, tor-sional stiffness becomes essential when calculating wingtwist and flexible wing spanload, as well as for the incor-poration of aeroelastic constraints and design variablesinto the MDO optimization.

)(2

)()(max yI

ydyM=σ

allb ydyc

yMyt

σ)()()(

)( =

dyycytWsb

bwb ρ)()(22/

0∫=bs Λ= cosbbs

Wing Lower Surface

Wing Neutral Axis

Structural Strut Offset

Vertical Strut Force

Horizontal Strut Force

AerodynamicStrut Offset

-2.0E+07

-1.5E+07

-1.0E+07

-5.0E+06

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

0 20 40 60 80 100 120

Wing Half Span (Ft)

Ben

din

g M

om

ent

(F

t-L

b)

2.5G Maneuver-1.0G Pushover-2.0G Taxi Bump

6

Therefore, a hexagonal wing-box model provided byLMAS was implemented into the code (Fig. 8). In contrastto the double plate model, the hexagonal wing-box allowscomputation of bending and torsional stiffness with a highdegree of accuracy. Based upon Lockheed Martin’s expe-rience in wing sizing, the wing-box geometry varies in thespanwise direction with optimized area and thicknessratios for spar webs, spar caps, stringers, and skins. Fur-thermore, minimum gauges and maximum stress cutoffscan be accurately applied.

Figure 8. Hexagonal wing-box and applied sectional forces and moments

Figure 9. Flutter boundary vs. altitude for different flight conditions of the fuselage mounted strut-braced wing configuration

Computational Aeroelasticity – Beyond rendering accu-rate quantities for bending and torsional stiffness, thehexagonal wing-box is suitable to create input data andrealistic sizing for detailed finite element analyses. Cur-rently, the panel thickness distributions from the doubleplate model are used to create a hexagonal wing-boxaccording to the spanwise variation of the respectivecross sectional data.

To obtain the spanwise distribution of the moments ofinertia, the overall cross sectional area of stringers, sparcaps, and skins are matched with the respective crosssections of the double plate model. With this data, adetailed finite element model of the structural wing-box iscomputed and analyzed using NASTRAN. It consists of630 grid points, 1239 rod elements, and 3232 plate ele-ments. The structural material is an equivalent isotropiccomposite model same as the one used in wing-bendingweight calculations. The fuel load is distributed into 47mass elements. For unsteady aerodynamics, the DoubletLattice method with compressibility correction for sub-sonic flight is employed. Aerodynamic loads are simu-lated using 300 box elements.

To calculate the flutter speed, 10 structural vibrationmodes are considered. In this model, no strut structure isincluded. Figure 9 illustrates the flutter boundaryobtained using the PK method in terms of the true airspeed. At each altitude, flutter is related to the fundamen-tal wing bending and torsional modes. However, at30,000 ft flight level, flutter occurs due to coupling of theyawing mode with the first torsional mode.

The results should be corrected using a more accuratetransonic unsteady aerodynamics modeling to simulatethe transonic dip effect. Also, aeroelastic constraintsmust be included into the optimization.

WEIGHTS – The aircraft weight is calculated by incorpo-rating several different methods. The majority of theweights equations come from NASA Langley’s FlightOptimization System (FLOPS) [16]. Many of the FLOPSequations were replaced with those suggested by LMAS.The LMAS and original FLOPS methods do not have theoption to analyze the strut-braced wing with the desiredfidelity. Therefore, the bending material weight from theFLOPS equations is replaced by the bending materialweight obtained from the piecewise linear wing load mod-els described above [17].

The wing bending weight is calculated using the panelthickness results or hexagonal wing-box cross sectionsfrom the piecewise linear beam model for the differentload cases (Fig. 10). The overall panel thickness distribu-tion of the wing is obtained by considering the highestvalue of the panel thickness or cross section at eachspanwise position (envelope). To account for suddenchanges in the material distribution, an additional 1%weight penalty is applied.

Hexagonal Wing-Bo

Airfoil

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 0.2 0.4 0.6 0.8 1

z/c

x/c

L

M

Aerodynamic Center

Shear Center (Elastic Axis)

Center of GravityN·g·m

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000 1200 1400 1600 1800

Flutter Speed (fps)

Alt

itu

de

(103

ft)

1.15 Vd Flight Envelope

Isolated Wing, full fuel

Wing-Strut, full fuel

Wing-Strut, zero fuel

Isolated Wing, zero fuel

7

Before linking the wing weight module to the MDO code,it has been validated using the 747-100 wing. The resultsobtained from the double plate model as well as the hex-agonal wing-box show good agreement with the actual747-100 and with the results obtained from FLOPS [16]and Torenbeek [18].

Figure 10. Panel thickness distributions for the different load cases (fuselage mounted engine configuration)

The total weights for the different components (strut, off-set, wing) are obtained using the FLOPS equations.Here, the wing bending material and strut tensionweights are being multiplied by a technology factor toaccount for the weight reduction achieved by the employ-ment of composite materials by the year 2010.

After computation of the load carrying weights, a 10%non-optimum factor is applied to account for manufactur-ing constraints. The total wing weight is calculated usingthe FLOPS equations with the overall load carryingweight, i.e. wing, strut, and offset. The total weights of thedifferent components are determined according to theratio of their contributions to the load carrying weight.

LMAS provided a weight estimate for the telescopingsleeve mechanism based on landing gear componentdata. Weights calculated in the Virginia Tech transportoptimization code are identical to FLOPS with the excep-tion of nacelle, thrust reverser, passenger service, land-ing gear, wing, fuselage and tail weights. The aboveweights are now calculated from proprietary LMAS for-mulas. Weight technology factors are applied to majorstructural components and systems to reflect weight sav-ings due to advances in technology levels from compos-ite materials, advanced electronics and othertechnologies described above.

Some aircraft weights are implicit functions, and internaliteration loops are typically required for convergence.However, utilizing the optimizer to converge the zero fuelweight of the aircraft showed to be more efficient by pro-viding smoother gradients. DOT also selects the fuelweight so that the range constraint is not violated. Other

weights such as the maximum body and contents weightand wing weight converge efficiently with the lagging vari-able method [10].

STABILITY AND CONTROL – The horizontal and verti-cal tail areas are first calculated with a tail volume coeffi-cient sizing method. The tail volume coefficients weredetermined based on Lockheed statistical data. A verticaltail sizing routine was developed to account for the oneengine inoperative condition [8], [17]. The engine-outconstraint is met by constraining the maximum availableyawing moment coefficient to be greater than therequired yawing moment coefficient. As specified by FARrequirements, the aircraft must be capable of maintainingstraight flight at 1.2 times the stalling speed with theoperable engine at its maximum available thrust. The lat-eral force of the vertical tail provides most of the yawingmoment required to maintain straight flight after anengine failure [11].

The maximum available yawing moment coefficient isobtained at an equilibrium flight condition with a givenbank angle and a given maximum rudder deflection. FAR25.149 limits the maximum bank angle to 5°, and somesideslip angle is allowed. The stability and control deriva-tives are calculated using empirical methods of DATCOMas modified by Grasmeyer [8], [20]. In order to allow a 5°aileron deflection margin for maneuvering, the calculateddeflection must be less than 20-25°. The calculated avail-able yawing moment coefficient is constrained in the opti-mization problem to be greater than the required yawingmoment coefficient. If the yawing moment constraint isviolated, a vertical tail area scaling factor is applied by theoptimizer.

PROPULSION – A GE-90 class high-bypass ratio turbo-fan engine is used for this design study. An engine deckwas obtained from LMAS, and appropriate curves forspecific fuel consumption and maximum thrust as a func-tion of altitude and Mach number were found throughregression analysis. The general forms of the equationsare identical to those found in Mattingly [21] for high-bypass ratio turbofan engines, but the coefficients andexponents are modified.

The engine size is determined by the maximum thrustrequired to meet several constraints. These constraintsare thrust at average cruise altitude, available rate ofclimb at initial cruise altitude, balanced field length, sec-ond segment climb gradient, and missed approach climbgradient. The dimensions of the engine nacelles vary asthe square root of required thrust, and the engine weightis assumed to be linearly proportional to the enginethrust. The specific fuel consumption model is indepen-dent of engine scale. A specific fuel consumption tech-nology factor is applied to reflect advances in enginetechnology.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 120Wing half span ft

Pan

el t

hic

knes

s in

tip constraint2g taxi bump-1g maneuver2.5g maneuver

8

PERFORMANCE – The range is calculated by theBreguet range equation [11]. The L/D ratio, flight velocity,and specific fuel consumption are determined for theaverage cruising altitude and Mach number. The initialweight is 95.6% of the take-off gross weight to accountfor fuel burned during climb to the initial cruise altitude. Areserve range of 500 nautical miles allows for emergencyairport re-routing, extra loiter time while waiting for land-ing clearance at the end of a maximum range missionand strong headwinds.

Figure 11. Minimum TOGW Designs

Take-off and landing performance utilizes methods foundin Roskam and Lan [22]. The field performance subrou-tine calculates the second segment climb gradient, bal-anced field length, missed approach climb gradient, andthe landing distance. All calculations are done for hot dayconditions at sea level. Sample drag polars for the aircraftat take-off and landing were provided by LMAS [11].Trends are the same for both SBW and cantilever config-urations. The actual drag polars use correction factorsbased on total aircraft wetted area and wing aspect ratio.The second segment climb gradient is the ratio of rate ofclimb to the forward velocity at full throttle while oneengine is inoperative and the gear is retracted.

Roskam and Lan methods are also used to determinethe landing distance [22]. Three legs are defined: the airdistance from clearing the 50-foot object to the point ofwheel touchdown including the flare distance, the free rolldistance between touch-down and application of brakes,and finally, the distance covered while braking. The liftcoefficient on landing approach is the minimum CL asso-ciated with either V=1.3Vstall or the CL to meet the tailscrape requirement. The drag coefficient is calculatedwith gear down.

The missed approach climb gradient is calculated in thesame way as the second segment climb gradient with afew exceptions. First, the weight of the aircraft at landingis assumed to be 73% of the take-off gross weight asspecified by LMAS. Second, all engines are operational.Third, a landing drag polar distinct from the take-off dragpolar is used. In the present study, the FAR minimummissed approach climb gradient constraint is never vio-lated.

Table 2. Parametric properties of aircraft designs for minimum take-off gross weight (TOGW)

Cantilever Wing

SBW

Span (ft) 223.2 227.0Sw (ft

2) 5120 4233AR 9.73 12.17Root t/c 14.50% 14.28%Tip t/c 7.80% 6.15%Wing Λ1/4 (deg) 33.3 29.9Strut Λ1/4 (deg) 20.1η Strut 68.9%η Engine 37.0%Max Thrust (lbs) 75133 59572Cruise Altitude (ft) 41160 40322L/D 23.34 25.40Wing Wt. (lbs) 63774 60745Bending Matl (lbs) 48076 43326Fuel Wt. (lbs) 184948 159883TOGW (lbs) 535643 492332% TOGW Improv. 8.1%% Fuel Improv. 13.6%% Thrust Reduction 20.7%Section Cl Limit ACTIVE ACTIVE2nd Segment Climb ACTIVE ACTIVEBalanced Field Length

ACTIVE

Engine Out ACTIVE

Fuselage-EngineSBW

Cantilever Wing

Table 3. Minimum Fuel Optimum Designs

CantileverWing

SBW

Span (ft) 256.2 262.3Sw (ft^2) 5800 4694AR 11.32 14.65Root t/c 13.06% 12.37%Tip t/c 5.31E-02 5.29%Wing Λ1/4 (deg) 32.3 28.3Strut Λ1/4 (deg) 21.2η Strut 66.6%Max Thrust (lbs) 70919 57129Cruise Altitude (ft) 43826 42248L/D 26.13 29.08Wing Wt. (lbs) 89373 86260Bending Matl (lbs) 74846 68543Fuel Wt. (lbs) 176646 150147TOGW (lbs) 554963 509881% TOGW Improve-ment

8.1%

% Fuel Improvement 15.0%Section Cl Limit ACTIVE ACTIVE2nd Segment Climb ACTIVEBalanced Field Length ACTIVE

9

OPTIMIZATION RESULTS

MIMIMUM TAKE-OFF GROSS WEIGHT – Table 2 showsthe parametric results for TOGW minimization and Fig.11 gives an impression of the geometric differences ofthe investigated aircraft designs. Note that the cantileverwing has a trailing edge break to permit landing gearstowage. A comparison of the cantilever and SBWdesigns shows that in general, the SBW aircraft have lesswing area, higher aspect ratio and a reduced wing sweepcompared to their cantilever counterparts.

MINIMUM FUEL CONSUMPTION – Fuel burn is likely tobe an increasingly important factor in aircraft design fromtwo perspectives. First, as the Earth’s petroleumresources are depleted, the cost of aviation fuel will rise.Any reduction in fuel demand will be welcome if the fuelprice becomes a larger part of transport life cycle cost.Second, strict emissions regulations stemming from envi-ronmental concerns will limit the amount of pollutant dis-charge permitted by an aircraft. Beyond engine design,reducing the overall amount of fuel consumed for a givenflight profile by improved configuration design will alsoreduce the total amount of emissions. Table 3 shows theminimum fuel weight results.

MINIMUM TOGW VS. MINIMUM FUELCONSUMPTION – For minimum TOGW and minimumfuel cases, the SBW is superior for the selected objectivefunctions. While the SBW has an 8.1% decrease inTOGW, the savings in fuel consumption are even moreimpressive. A SBW has a 13.6% lower fuel burn than acantilever configuration when optimized for minimumTOGW, and a 15% lower fuel weight when both are opti-mized for minimum fuel weight.

The minimum-fuel-SBW has a higher wingspan toincrease the L/D and fly at higher altitudes. The mini-mum-fuel-SBW TOGW is 8.1% lower than an equivalentcantilever design, and 3.6% higher than a minimum-TOGW-SBW. The SBW L/D increases from 25.4 to 29.1going from the minimum-TOGW to the minimum-fuelcase, and from 21.7 to 26.1 for the cantilever configura-tion. This improved aerodynamic efficiency is achieved byincreasing the wing span, and comes at a cost in struc-tural weight.

Airport noise pollution can limit the types of aircraft per-mitted to use certain urban airfields and impose opera-tional restrictions on those that do. Minimizing enginesize can also be expected to reduce the noise generatedif the engine is of similar design. Minimum TOGW SBWengine thrust is reduced by 20.7% over the equivalentcantilever design, probably reducing airport noise pollu-tion by a similar amount.

Figure 12. Effect of range on take-off gross weight

Figure 13. Effect of range on fuel weight

RANGE EFFECTS – The SBW becomes increasinglydesirable as the design range increases. Figures 12 and13 show the effects of range on TOGW and fuel weight.The TOGW reduction relative to the cantilever configura-tion steadily improves from 5.3% at a 4,000 nautical milerange up to 10.9% at 12,000 nautical miles. The fuelweight savings fluctuates within about 11-16%, generallyimproving with increasing design range. These resultsare for minimum TOGW designs, however greater fuelburn improvements are expected for SBW aircraft opti-mized for minimum fuel weight. Maximum fuel weight isset at 400,000 pounds.

At 12,000 nautical miles an aircraft can reach any desti-nation on Earth. The SBW maximum range is 13,099nautical miles at the maximum fuel weight, whereas thecantilever configuration can only reach 11,998 nauticalmiles, or the SBW has 8.4% greater maximum range.Therefore, the SBW can either have a reduced fuelweight for a given range or an increased range for a givenfuel weight relative to the cantilever configuration.

Take -Off Gros s Weight vs. Range

300000

400000

500000

600000

700000

800000

900000

4000 6000 8000 10000 12000 14000

Range

Tak

e-O

ff G

ross

Wei

gh

t (l

bs.

)

Conventional

SBW

Fuel W eight vs. Range

50000

100000

150000

200000

250000

300000

350000

400000

450000

4000 6000 8000 10000 12000 14000

Range

Fu

el W

eig

ht

(lb

s)Conventional

SBW

10

CONCLUSIONS

Virginia Tech transport studies have shown the potentialof the SBW over the traditional cantilever configuration.After much added realism by a major airframe manufac-turer, the MDO analysis shows that the SBW still demon-strates major improvements over the cantilever wingconfiguration. A significant reduction in TOGW wasfound, but the greatest virtue of the SBW is the improvedfuel consumption and smaller engine size. These resultsindicate that the SBW will cost less, limit pollutant dis-charge and reduce noise pollution for urban airports.Advantages of the SBW increase with range, suggestingthat this configuration may be ideal for larger, long-rangetransports.

The special design of the strut-braced wing necessitatedthe development of a wing sizing module suitable to fullyexploit the benefits of this structural configuration. Aftervalidation with existing aircraft like the 747-100, the mod-ule was used for wing sizing and structural weight com-putation of the SBW. The great potential of the outlinedwing sizing procedure lies in the consideration of jig twist,strut moment, wing flexibility, and flexible wing spanload.Consideration of the actual in-flight maneuver loads notonly increases the accuracy in wing sizing but also givesthe potential for further weight savings. This is especiallyimportant within a multidisciplinary design environmentwhere due to synergistic interaction even small weightsavings in one component are very likely to result in fur-ther weight reductions for other components.

Further benefits of the SBW are expected to becomeapparent in future studies. The cooperative relationshipwith LMAS focused on adding realism to the SBW designeffort for direct comparisons with the cantilever design.Realism often takes the form of weight penalties andexpanded performance analysis, which inevitablydetracts from SBW theoretical potential. Presently, effortsare underway to identify technologies and strut/trussarrangements to exploit the strengths of the strut. Limit-ing the SBW design arrangements so that the aircrafttakes the appearance of a cantilever wing may not be themost appropriate approach to realize the full potential ofthe SBW.

The SBW is likely to have a more favorable reaction fromthe public than other configurations, especially for thosewho suffer from a fear of flying. Affirmative passengerand aircrew acceptance is probable because other thanthe addition of a visually innocuous strut and a high wing,there is little to distinguish the SBW from the existing air-liner fleet. Radical appearances of the blended-wing-body, joined wing, or other candidate configurations maycause apprehension in many flying patrons.

ACKNOWLEDGMENTS

This project is funded by NASA Langley Research GrantNAG 1-1852. Part of the work was done under subcon-tract from Lockheed Martin Aeronautical Systems inMarietta, Georgia. NASA deserves much credit for hav-ing the vision to pursue bold yet promising technologieswith the hope of revolutionizing air transportation. Lock-heed Martin Aeronautical Systems provided valuablecontributions in data, design methods and advice.

REFERENCES

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2. Gunston, B., Giants of the Sky: The BiggestAeroplanes of All Time, Patrick Stephens Limited,Wellingborough, UK, pp. 240-250.

3. Kulfan, R.M., and Vachal, J.D., “Wing PlanformGeometry Effects on Large Subsonic Military Trans-port Airplanes,” Boeing Commercial Airplane Com-pany, AFFDL-TR-78-16, February 1978.

4. Jobe, C.E., Kulfan, R.M., and Vachal, J.D., “WingPlanforms for Large Military Transports,” AIAA-78-1470, 1978.

5. Turriziani, R.V., Lovell, W.A., Martin, G.L., Price, J.E.,Swanson, E.E., and Washburn, G.F., “PreliminaryDesign Characteristics of a Subsonic Business JetConsept Employing an Aspect Ratio 25 Strut-BracedWing,” NASA CR-159361, October 1980.

6. Smith, P.M., DeYoung, J., Lovell, W.A., Price, J.E.,and Washburn, G.F., “A Study of High-AltitudeManned Research Aircraft Employing Strut-BracedWings of High-Aspect Ratio,” NASA CR-159262,February, 1981.

7. Grasmeyer, J.M., Naghshineh_Pour, A., Tetrault, P.-A., Grossman, B., Haftka, R.T., Kapania, R.K.,Mason, W.H., Schetz, J.A., Multidisciplinary DesignOptimization of a Strut-Braced Wing Aircraft with Tip-Mounted Engines, MAD 98-01-01, 1998.

8. Grasmeyer, J.M., Multidisciplinary Design Optimiza-tion of a Strut-Braced Wing Aircraft, MS Thesis, Vir-ginia Polytechnic Institute & State University, April1998.

9. Martin, K.C., Kopec, B.A., “A Structural and Aerody-namic Investigation of a Strut-Braced Wing TransportAircraft Concept”, NAS1-96014, November 1998.

10. Vanderplaats Research & Development, Inc., DOTUser’s Manual, Version 4.20, Colorado Springs, CO,1995.

11. Gundlach, J.F., Multidisciplinary Design Optimizationand Industry Review of a 2010 Strut-Braced WingTransonic Transport, MAD 99-06-03, 1999

11

12. Hoerner, S.F., Fluid Dynamic Drag: Practical Informa-tion on Aerodynamic Drag and Hydrodynamic Resis-tance, published by Mrs. Hoerner, 1965. Currentaddress: P.O. Box 65283, Vancouver, WA 98665.

13. Pirzadeh, S., “Structured Background Grids for Gen-eration of Unstructured Grids by Advancing-FrontMethod”, AIAA Journal, Vol. 31, February 1993, pp.257-265.

14. Frink, N.T., Pirzadeh, S., and Parikh, P., “An Unstruc-tured-Grid Software System for Solving ComplexAerodynamic Problems”, NASA CP-3291, May 1995.

15. Frink, N.T., Parikh, P., and Pirzadeh, S., “A FastUpwind Solver for the Euler Equations on Three-Dimensional Unstructured Meshes”, AIAA-91-0102,1991.

16. McCullers, L.A., FLOPS User’s Guide, Release 5.81.Text file included with the FLOPS code.

17. Naghshineh-Pour, A.H., Kapania, R., Haftka, R., Pre-liminary Structural Analysis of a Strut-Braced Wing,VPI-AOE-256, June 1998.

18. Torenbeek, E., "Development and Application of aComprehensive, Design Sensitive Weight PredictionMethod for Wing Structures of Transport CategoryAircraft," Delft University of Technology, Report LR-693, Sept. 1992.

19. Roskam, J., Methods for Estimating Stability andControl Derivatives of Conventional Subsonic Air-planes, Roskam Aviation and Engineering Corp.,Lawrence, KS, 1971.

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21. Mattingly, J.D., Heiser, W.H., and Daley, D.H., AircraftEngine Design, AIAA, Washington, D.C., 1987.

22. Roskam, J., and Lan, C.-T. E., Airplane Aerodynam-ics and Performance, DARCorporation, Lawrence,KS, 1997.

CONTACT

Dr. Frank H. GernMultidisciplinary Analysis and Design (MAD) Center forAdvanced VehiclesDepartment of Aerospace and Ocean EngineeringVirginia Polytechnic Institute and State UniversityBlacksburg, VA 24061-0203, USA

Phone: (540) 231-4860Fax: (540) 231-9632Email: fgern@aoe.vt.eduhttp://www.aoe.vt.edu