Document
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AIAA 2000-1327
Flexible Wing Model for Structural
Sizing and Multidisciplinary Design
Optimization of a Strut-Braced Wing
F.H. Gern, A.H. Naghshineh-Pour,
E. Sulaeman, R.K. Kapania
Vir.ginia.Polytechnic Institute and State
Un=vers=ty, Blacksburg, VA
and
R.T.Haftka
Un=vers_ty of Florida,
Gainesvile, FL
41st AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics
and Materials Meeting & Exhibit
3-6 April 2000 / Atlanta, GA
For permission to copy or republish, contactthe American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, Virginia 20191-4344 AIAA-2000-1327 FLEXIBLE WING MODEL FOR STRUCTURAL WING SIZING AND MULTIDISCIPLINARY DESIGN OPTIMIZATION OF A STRUT-BRACED WING Frank H. Gern °, Amir H. Naghshineh-Pour +, Erwin Sulaeman*, and Rakesh K. Kapania I Department of Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA 24061-0203 Raphael T. Haftka i Department of Aerospace Engineering, Mechanical and Engineering Sciences University of Florida Gainesville, FL 32611-6250 Abstract c_ wing-box chord F,v vertical strut force (z-direction) This paper describes a structural and aeroelastic F._h horizontal strut force 0,-direction) model for wing sizing and weight calculation of a Lo# strut vertical offset length strut-braced wing. The wing weight is calculated using M, freestream Mach number a newly developed structural weight analysis module M(y) bending moment considering the special nature of strut-braced wings. A local lift distribution for element i qi(Y) specially developed aeroelastic model enables one to s wing-strut intersection (from wing root) consider wing flexibility and spanload redistribution u unit step function during in-flight maneuvers. The structural model uses Uah, Vab , Wab backwash, sidewash and downwash a hexagonal wing-box featuring skin panels, stringers, velocity, respectively and spar caps, whereas the aerodynamics part employs V(y) shear force a iinearized transonic vortex lattice method. Thus, the w bending deflection wing weight may be calculated from the rigid or W, engine weight flexible wing spanload. Y_ spanwise engine position (from root) The calculations reveal the significant influence of y spanwise coordinate lift coefficients at structural nodes the strut on the bending material weight of the wing. o;/3 The use of a strut enables one to design a wing with A wing sweep angle thin airfoils without weight penalty. The strut also 0 bending slope influences wing spanload and deformations. Weight /-, vortex strength savings are not only possible by calculation and iterative resizing of the wing structure according to the Introduction actual design loads. Moreover, as an advantage over the cantilever wing, employment of the strut twist Strut-braced wing configurations have been used moment for further load alleviation leads to increased both in the early days of aviation and today's small savings in structural weight.
airplanes. Adopting thin airfoil sections required external structural wing support to sustain the aerodynamic loads. However, external structures Nomenclature cause a significant drag penalty. Gradually. it was AR wing aspect ratio understood that the external bracing could be b wing span removed and lower drag could be achieved by c wing chord replacing the wing-bracing structure with a cantilever wing with an appropriate wing-box and thickness to "Research Associate, Member AIAA chord ratios.
* Graduate Student. Student Member AIAA Graduate Student However, along with the idea of the cantilever I Professor, Associate Fellow AIAA wing configuration with its aerodynamic advantages, Distinguished Professor, Fellow AIAA the concept of the truss-braced wing configuration Copyright © 2000 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.
American Institute of Aeronautics and Astronautics
alsosurvived. Thisis dueto the tireless effortsof
same payload range. Theyconcluded thatthestrut-
Werner Pfenninger atNorthrop in theearly1950's [1]
braced wingconfiguration reduces thetotalaircraft
andhis continuation of theseeffortsuntil the late
weight, even though wingandstrutweight increased
1980's. Using astrut ora truss offers theopportunity to
compared tothecantilever wing case, which isdueto
increase the wingaspect ratio andto decrease the
aerodynamic advantages of highaspect ratiowings.
induceddrag significantly without wing weight
Furthermore, theresults showed a fuelweight savings
penalties relative to a cantilever wing.Also,a lower of20%.
wingthickness becomes feasible reducing transonic
The strut-braced wing conceptoffers the
wave drag andhence resulting ina lower wingsweep.
possibility to reduce wing thickness withoutthe
Reduced wingsweep andhighaspect ratios produce
penalty of anincreased structural weight byreducing
natural laminar flow dueto low Reynolds numbers.
thebending moment onthewing.However, reduced
Consequently, a significant increase in the overall
wing thickness together with shorter wing chords
aircraft performance isachieved [2],[3].
result in smaller wing-box dimensions, thus
A number of strut-bracedwing aircraft
significantly reducing wing-box torsional stiffness
configurations have been investigated in thepast. In
andrendering thewingmore sensitive to aeroelastic
continuing Pfenninger's work, Kulfan and Vachal from
problems likeincreased static aeroelastic deformation
the Boeing Company performed preliminary design
orreduced flutter anddivergence speeds. Thepresent
studies andevaluated the performance of a large
approach highlights a possibility to remedythe
subsonicmilitary airplane[4]. They compared
problem of increased aeroelastic deformations by
performance andeconomics of acantilever wingwith
employment of the strutmoment induced on the
a strut-braced wing configuration. Two load
wing.
conditions, a 2.5gmaneuver and1.67 taxibump were
Previously investigatedstrut-bracedwing
used toperform structural analyses. Theiroptimization
concepts considered thestruttoberigidlyattached to
andsensitivity analyses showed thathighaspect ratio
thewing. Therefore, strutbuckling during negative g
wings withlowthickness tochord ratios would result
maneuvers wasa majordesign issue, rendering the
inasignificant fuelconsumption reduction.
strutveryheavy in order to overcome thisbuckling
For thecantilever configuration, a ground strike
constraint [4], [5]. To avoid strut buckling,the
problem arose during taxiing. Thisissue wasresolved
present approach offersan innovative concept. A
byadding a strutto thewingstructure. Moreover, the
telescoping sleeve mechanism is employed to have
analysisindicatedthat the strut-braced wing
thestrut active onlyduring positive g maneuvers. For
configuration requires lessfuel(1.6%), andresults in
negative g maneuvers, thewingacts likea cantilever
lowertakeoff gross weight (1.8%)andlowerempty wing, renderingthe strut bucklingconstraint
weight (3%) compared to the cantileverwing
unnecessary. Furthermore, this arrangement allows
configuration. Cost comparisons showed that the
one to applya definedstrut force at the 2.5g
operating costs of thestrut-braced wingconfiguration
maneuver designload instead of the statically
wereslightlylessthanthose of the cantilever wing indeterminate one obtained from a rigid strut configuration because ofa lower takeoff gross weight.
attachment. Thisway,thestrutforce aswellasstrut
position canbe optimized in orderto achieve the
Parkfromthe BoeingCompany compared the
maximum benefits outofthedesign concept.
blockfuel consumption of a strutted wingversus a
cantilever wing[5].Even though heconcluded that the
To fully exploitthe synergism from the strut-
useof a strut savesstructural wing weight,the
braced wingconcept, anMDOapproach hasbeen
significant increase in the strutt/c to copewithits chosenfor aircraft design optimization.The
buckling atthe-1.0g load condition increased thestrut
multidisciplinary team consists of aerodynamics,
dragandhence did not appear practical for this
structures, andadetailed investigation ofinterference
transport aircraft dueto a higherfuel consumption drag.Theaerodynamic analysis uses simple models compared tothecantilever case.
forinduced drag, parasite drag, andinterference drag.
All analyses arelinked together, andtheperformance
Another study onstrut-braced wingconfigurations
of thestrut-braced wingaircraft is thenoptimized for
was conducted byTurriziani etal.[6].They addressed
minimum take-off-gross weight [3],[7],[8].
fuel efficiency advantages of a strut-braced wing
business jet employing anaspect ratioof 25overan
The MDOapproach hasbeenimplemented in
equivalent conventional wingbusiness jet with the
severalaircraft designs. Grossman et al. [9]
American Institute ofAeronautics and Astronautics
investigated the interaction of aerodynamic and
strut design, a vertical strut offset was considered as
structural design of a composite sailplane subject to
to achieve a significant reduction in wing/strut
aeroelastic, structural, andaerodynamic constraints to
interference drag.
increase theoverallperformance. Theyshowed that
Load Cases
themultidisciplinary design canyieldresults superior
To determine the bending material weight of the to the onesobtained fromthe sequential method.
strut-braced wing, two maneuver load conditions
Another example is theapplication of MDOtoaHigh
(2.5g maneuver, -1.0g pushover) and a taxi bump (-
Speed CivilTransport (HSCT). A significant efforthas
1.0g) are considered to be design critical. For the -
beenmadeat the Multidisciplinary Analysis and
1.0g pushover and for the -2.0g taxi bump, the strut is
Design (MAD) center of VirginiaTechto perform
not active and the wing acts like a cantilever beam.
MDOof anHSCT. Several methods were developed
Since the strut is not supporting the wing in these
for thebetter useof theMDOapproach for aircraft
cases, very high deflections of the wing are expected
conceptual andpreliminary design. Moreinformation
for the -2.0g taxi bump. As a result, an optimization about thisworkcanbeobtained from[10]and [11 ].
procedure is implemented to distribute the bending
Thepresented wingsizingmodule provides two
material to prevent wing ground strikes. To maximize essential features withintheMDOenvironment. First, the beneficial influence of the strut upon the wing it is used tocalculate thestructural wingweight, i.e.
structure, strut force and spanwise position of the
thebending material weight of thewing-box. It has
wing-strut intersection are optimized by the MDO
beenfoundthatcommonly available wing weight
code for the 2.5g maneuver load case.
calculation routines liketheNASA Langley developed
In order to attain acceptable aerodynamic
FlightOptimization System (FLOPS) [12] arenot
characteristics of the strut, an airfoil cross section is
accurate enough forthepresent approach. Therefore, a
considered. The strut is designed the way that it will
program hasbeen developed to accurately calculate
not carry aerodynamic forces during the cruise
thebending material weight of thewingbased ona
condition.
double platemodel. Thenon-structural wingweight
like flaps,slats, spoilers, ribsetc.is still calculated
Structural Assumptions
fromtheFLOPS equations by replacing theFLOPS
Preliminary studies have shown buckling of the bending material weight bytheactual one.
strut under the -l.0g load condition to be the critical
Second, the wing sizing modulefeatures an
structural design requirement in the single-strut
idealized hexagonal wing-box model which hasbeen
configuration, resulting in high strut weights [3]. To
providedfor the projectby Lockheed Martin
address this issue, an innovative design strategy
Aeronautical Systems in Marietta,Georgia. The
employs a telescoping sleeve mechanism to allow the
hexagonal wing-box permits accurate computation of
strut to be inactive during negative g maneuvers and
thewing's torsional stiffness, therefore enabling one to
active during positive g maneuvers. Thus, during the
investigate aeroelastic effectslike staticaeroelastic
-l.0g maneuver, the wing acts like a cantilever beam
deformation, maneuver loadalleviation, andto use
and for the positive g maneuvers, the wing is a strut- flexiblespanload distributions asdesign loads. Asa braced beam.
result, themodel canbeemployed toresize thewing
Even more wing weight reduction can be obtained
according totheactual in-flight maneuver loads. This
by optimizing the strut force and wing-strut junction
procedure usuallyleadsto significant wing weight
location. For a typical optimum single-strut design, reductions.
this means that the strut would first engage in tension at some positive load factor. This can be achieved by Structural Wing Modeling providing a slack in the wing-strut mechanism. The optimum strut force at 2.5g is different from the strut Due to the unconventional nature of the proposed force that would be obtained at 2.5g if the strut were wing concept, commonly available weight calculation engaged for all positive values of the load factor.
models for transport aircraft (such as the NASA Langley developed Flight Optimization System The slack load factor is defined as the load factor FLOPS [12]) are not accurate enough. A special at which the strut initially engages. It is important to bending weight calculation procedure was thus have the slack load factor always positive, otherwise developed, taking into account the influence of the the strut would be pre-loaded at the jig shape of the strut upon the structural wing design. In addition to the wing to achieve the optimum strut force. To prevent American Institute of Aeronautics and Astronautics
thestrutfromengaging anddisengaging during cruise
where qi(y) denotes the local lift distribution
dueto gustloads, theupper limit for theslack load
for element i, ¢ and fli denote the lift coefficients at factor issetto0.8during theoptimization.
nodes i and i+l , and Yi and y,÷ldenote the node Double Plate Model coordinates in the y-direction. The piecewise model in global coordinates is shown in Figure 2.
For calculating the wing-bending weight of single strut configurations, a piecewise linear beam model, representing the wing structure as an idealized double plate model, was used first (Figure I).
i cb i Rool Y n-I i i-I 3 2 i Figure 1: Double plate model for bending weight calculation Figure 2: Piecewise aerodynamic loads representation This model is made of upper and lower skin panels, which are assumed to carry the bending moment. The The shear force and moment equations are double-plate model offers the possibility to extract the obtained from the spanwise lift distribution by material thickness distribution by a closed-form applying the well-known beam equations. Since for equation. The cross-sectional moment of inertia of the the -1.0g load case, the strut is not active, the load wing box can be expressed as: distribution is identical to the one obtained for a cantilever wing. Therefore, it is not displayed here.
l(y) = t(y)ch(y)d2(y) (1) For the 2.5g maneuver case, the strut is active, adding an additional shear force and bending moment to the where tO') is the wing skin thickness, CbO') is the wing.
wing box chord, and d(y) is the wing airfoil thickness.
To obtain the bending material weight, the As a result, the shear force develops to: corresponding bending stress in the wing is calculated V(y)= W,u[y-(b/2- y,)]+ F_,u[y-(b/2- s)] from: M(v)d(y) O'ma x -- " (2) - foq(y)dy (5) 21(y) Consequently, the bending moment on the strut- where O'max denotes the maximum stress, M(y) is braced wing is obtained by integration of the shear the bending moment of the wing, and 1(3,) denotes the force along the span: cross-sectional moment of inertia.
M(y)=-V(y)y-W_eu[y-(b/2- Ye)] If the wing is designed according to the fully- stressed criterion, the allowable stress o'ajl can be + F,_(b/2- s)u[y-(b/2- s)]- ;_'yq(y)dy substituted into Eq. (2) for Crmax. Substituting I0, ) into equation (2), the wing panel thickness can be specified + W, (b/2 - y, )u[y-(b/2 - y, )] (6) as_ + FshLotrU[y-(b/2- s)]
t(y) - IM(y)I (3)
ch(y)d(y)Cr,, In Eq. (6) u(y) is a unit step function defined as: Wing Bending Moment Distribution {0 if y<0 (7) u(y)= if 3'->0 The local lift distribution can be written as: The structural boundary conditions are: (4) q,(Y)= I (_ '- y'+') °' +/_-7-"-_7,(Y-Y') ]
LO,- Y,+,) w,÷, - ._w '8' 0(b/:)=o
(8a, b)
,,,(b/2)-- 0
American Institute of Aeronautics and Astronautics Thecalculated panel thickness is modified by the spanload, as well as for the incorporation of results obtained fromthetip displacement constraint aeroelastic constraints into the MDO optimization.
optimization. Therefore, thebending material weight
Therefore, a hexagonal wing-box model was ofthehalf-wing is: implemented into the wing weight calculation eb, 12 module. This model was provided by Lockheed W., = 2J,, t(y)c,,(y)pdy (9) where b_ is the structural span with b = b/cosA.
/-----'-Hexagonal Wing-Box L Vertical Strut Offset °_ I 0 o3 To reduce the wing/strut interference drag, a f " _ I-..-.--- Airfoil vertical offset between strut and wing is implemented. ool The vertical offset member is designed for a combined _°' _-_ IT T _ t- bending/tension loading. In this context, the horizontal • o 03 / component of the strut force is of special concern .0o4 (Fig.6). Since this horizontal force results in a considerable bending load on the offset piece, its weight increases dramatically with increasing strut °_ N.g.m _ Center of Gravity force and offset length.
Shear Center (Elastic Axis) Wing Neutral Axis Aerodynamic Center Figure 4: Hexagonal wing-box and applied sectional Wing Lower Surface forces and moments Martin Aeronautical Systems in Marietta, Georgia.
StructuraIStrut Offset 'I Based upon Lockheed Martin's experience in wing Aerodynamic I" sizing, the wing-box geometry varies in the spanwise Strut Offset direction with optimized area and thickness ratios for Horizontal Strut Force spar webs, spar caps, stringers, and skins. By keeping these ratios fixed, it is still possible to reduce all geometric data of the wing-box to one independent thickness which is allow to vary in the spanwise Vertical Strut Force direction. Therefore, despite the complexity of the geometry, a closed solution for the material thickness Figure 3: Vertical strut offset and applied loads can still be found by employing the piecewise linear As a result, it is imperative to employ MDO tools load representation.
to obtain optimum values for vertical offset, strut In contrast to the double plate model, the force, and spanwise wing/strut breakpoint. This way, it hexagonal wing-box allows computation of bending is possible to trade off two contrary design and torsional stiffness with a high degree of accuracy.
requirements: (i) reduced offset length to reduce strut Furthermore, minimum gauges and maximum stress loading, (ii) increased offset length to reduce cutoffs can be accurately applied.
wing/strut interference drag. After a complete design optimization with the vertical strut offset as an active Aerodynamic Modeling design variable, the influence of the offset weight on The aerodynamic loads are calculated based on the total strut weight becomes comparably small. For the well-accepted vortex lattice concept (VLM). For the wing bending weight and TOGW it is almost this purpose, a linearized transonic VLM code was immaterial.
developed. To account for compressibility effects, the airflow density is corrected according to the Hexagonal Wing-Box Model freestream Mach number using a linear Although the double plate model renders very accurate approximation. Although not capable of transonic estimates for the wing bending material weight, it is shock predictions, this modification allows very not suitable for calculation of the wing-box torsional accurate calculations of local lift coefficients. To take stiffness. This torsional stiffness becomes essential into account the spanwise variation of the sectional when calculating wing twist and flexible wing American Institute of Aeronautics and Astronautics
pitchanddihedral, aswellasthechordwise variation
features 40 spanwise and 5 chordwise vortex panels
of the airfoil camber surface, the flow tangency
distributed equally along the wing span.
boundary condition is formulated as: In a first step. the wing deformation including sectional twist angle, dihedral (bending slope) and U sin(a-6)cosy = w,,j, cos),cosd (10) deflection, is calculated from the initial wing + v,b sin ),cos 6 - u,b cos )'sin fi spanload. Since the aircraft wing is being optimized where a, y and 6 are the angle of attack, dihedral, for mimimum induced drag by the MDO code, this and slope of the mean camber line, respectively, for initial spanload usually is close to an elliptical one.
each point on the curved surface. The induced To obtain an elliptical lift distribution during velocities u,b, v,b and w,h represent the backwash, cruise, the wing is being pre-twisted and jig twisted.
sidewash and downwash velocities, respectively, The pre-twist of the wing planform is calculated acting on any arbitrary point C (Xoy,.,z,.) of the lifting using Lamar's design program LAMDES [ 13]. Since, surface due to a bound vortex AB having the vortex for a swept wing, the sectional streamwise angle of strength /" and the end points A (x,,y,,za) and B attack is a combination of twist angle and bending (xb, yh, Zb) (see Appendix A).
slope, the wing bending deformation significantly The developed lifting surface aerodynamic code influences the aerodynamic effectiveness of the has been validated with several well documented test lifting surface. Therefore in order to achieve the cases, among them a delta wing of aspect ratio AR = 2, desired twist distribution of the wing during cruise, as well as the unswept and swept wings investigated the wing is jig twisted to account for the changes in by Weissinger (Figure 5).
the local twist due to the bending deformation.
Gimmestad from the Boeing Company showed that consideration of the jig twist for wing sizing of 0.1 i ..........................................................
.................... i the B-52 resulted in a 10% reduction in the design 0.m _- __._,..._.._,.:::::_ loads [14]. Therefore, considering the jig twist during preliminary design may result in significant structural O m 0 8 _ weight savings. This holds even more true for the 0.07-- present case where an MDO approach allows weight savings in one component to carry through the overall ..O 0,06 design of the respective aircraft configuration. In the "6" 0,05 present code, the jig twist is calculated from the actual wing deformation by subtracting the bending "5 0.04 slope from the structural twist of the wing-box.
0.03 Present DPM In the following iteration procedure, the lift Present VIM 0.0"2 distribution is recalculated according to the actual wing deformation, yielding a new (flexible) spanload.
- >-. VLM I 0.01 I Considering the new spanioad, all structural wing o...................... I.................... 1 .................... !...................
F...... i parameters like bending stiffness, torsional stiffness, 0 0.5 1 1.5 2.5 3.5 4 and wing weight are recalculated and then again used spanwise y for computation of the flexible spanload. The wing Figure 5: Validation of the VLM for Weissinger's bending weight is calculated using the panel swept wing (AR = 5, taper ratio = 0.5, A = 35 °, angle thickness results or hexagonal wing-box cross of attack = 5.8 °) sections from the piecewise linear beam model for the different load cases. The overall panel thickness distribution of the wing is obtained by considering Flexible Wing Sizing the highest value of the panel thickness or cross For accurate wing sizing, the wing has been section at each spanwise position (envelope) [8]. To subdivided into 81 structural nodes representing the sustain the total lift for the respective load cases, the spanwise grid points for the application of the total aircraft incidence is recalculated after each piecewise linear loads. To account for increasing iteration step thus ensuring the correct lift for in- gradients in the spanload towards the wing tip, cosine flight maneuvers.
spacing is being used. The aerodynamic lifting surface American Institute of Aeronautics and Astronautics Thetotalwingweight, i.e.including thesecondary main effect of considering the flexible wing load is
structure like ribs,flapsetc.is calculated usingthe
due to the recalculation of the bending deformation FLOPS equations [12].Forthispurpose, thebending after the first step and the resulting reduction in the material weightin FLOPS is beingreplaced by the sectional angle of attack (wash-out). This high
bending material weightobtained fromthe present
torsional stiffness is further manifested by the fact model.
44000 -- Validation To check the integrity of the results, the structural _' 43000 Flexible wing, jig twletld analysis code has been validated using available data • Flexible wing, jig twisted, engine moment for the 747-100. The bending material weight _ 42000 computed from the piecewise linear load model is m compared with the bending material weights given by Torenbeek [15] and FLOPS [12]. Figure 6 highlights E 41000 the good agreement of both the double plate model and o) _= "o the hexagonal wing-box model with the actual 747- ¢ 100 weights for the assumption of an elliptical _40000 spanload, i.e. a rigid wing model. However, only the hexagonal model allows computation of the wing-box I I I I I I I I I I = 39000 torsional stiffness, thus enabling one to consider the 0 I 2 3 4 5 6 7 8 9 10 No. of iterations influence of pre-twist, jig twist, and flexible load distribution.
Figure 7: Bending material weight convergence As it can be seen, application of the flexible wing history for a 747-100 type wing weight calculation procedure as described above can that the influence of the engine twist moments is very result in significant weight savings for a 747-100 small, as it can also be seen from Figure 7.
configuration. Interestingly, this potential has already The passive load alleviation due to the wash-out 90000 effect results in an inboard shifting of the lift loads 80000 and therefore reduced bending moments on the 70000 outboard sections of the wing. Although the wing 60000.
structure is resized after each iteration step, the 50000 flexible wing spanload rapidly converges to its final m 40000 .$ 2.4 3= 30000 2.2 20000 10000 1.8 747-100 Torenbeek FLOPS Double Hexagonal He:cagonaJ 1.6 Rate (rigid) (flexible) I 1,4 [[] Bending weight [] Secondary struclure] 1.2 a Figure 6: Comparison of wing bending material U 1 weights and total wing weights for the 747-100 0.8 been demonstrated with a flying derivative of this 0.6 airplane, namely the 747-400.
0.4 The bending weight convergence history for this 0.2 i I i r I I I I = i I I r i l I I configuration is depicted in Figure 7. The structural 0.25 0.5 0,75 1 wing weight is rapidly converging to its final value, Nondimensional wing span exhibiting only small variations after the first iteration step. The reason for this behavior is the relatively high Figure 8: Spanload convergence for the 747-100 torsional stiffness of this wing-box. Therefore, the type flexible wing American Institute of Aeronautics and Astronautics
distribution(Figure 8). The wing deformation
performance of the strut-braced wing is optimized
calculated for a 2.5gmaneuver forsuch anoptimized
with the Design Optimization package DOT [16].
wingstructure isdepicted inFigure 9.
Using a typical long range mission profile _cruise Mach number 0.85, range 7500Nmi, initial cruise altitude >31,000ft, 325 passengers_ the results indicate an overall increase in performance of the strut-braced wing configuration compared to its cantilever counterpart [8]. Figure 10 and Table 1 show the details of the investigated aircraft configuration.
Table 1: Strut-braced wing aircraft parameters Wing halfspan 108.44 fl Strut breakpoint 74.52 ft Wing sweep (3/4 chord) 25.98 ° Strut sweep (3/4 chord) 19.01 °
Figure9: Bending Deformation of the747-100 type
Aerodynamic strut offset 2.74 ft
wingconfiguration
Wing root chord 32.31 ft 14.76 ft Wing breakpoint chord 6.77 ft Wing tip chord Strut-Braced Wing Configuration 6.62 ft Strut chord (constant) The strut-braced wing aircraft is obtained from an 13.75 % Wing root t/c MDO process as it has been described in [3] and [8].
7.23% Breakpoint t/c For the optimization, the aircraft configuration is 6.44% Wing tip t/c parameterized into 19 design variables.
Strut t/c 8.0% Realization of a successful design requires a tight Strut force 215387.1 lb coupling of several disciplines to exploit the synergism Engine nacelle diameter 12.54 ft in the strut-braced wing concept. Therefore, a 20.33 ft Fuselage diameter multidisciplinary approach is essential. The 1411.02 fie Wing flap area multidisciplinary team is broken down into 4237.30 fie Wing reference area aerodynamics, structures, and a detailed investigation 3355901b Aircraft zero fuel weight of interference drag. The aerodynamic analysis 504833 Ib Take-off gross weight consists of simple models for induced drag, parasite drag, and interference drag. The interference drag model is based on computational fluid dynamics (CFD) analyses of various wing-strut intersection Numerical Results flows. A performance routine is used to evaluate the design constraints and the objective function, TOGW.
Flexible Strut-Braced Wing Spanload All these analyses are linked together, and the The strut-braced wing as described in the previous section has been analyzed with the new module.
Figure 11 shows the spanload distribution on the wing for the 2.5g maneuver obtained from the iteration process. As a first step, the wing structure was kept constant. Spanload and wing deformation were converged to their actual distributions.
Basically, the strut-braced wing exhibits the same load alleviation behavior as its cantilever counterpart (Figure 11). Due to the upward bending of the wing, lift loads are shifted inboard because of the reduction Figure 10: SBW with Fuselage-Mounted Engines of the sectional angle of attack on the outboard wing American Institute of Aeronautics and Astronautics 2.4 2.2 1.8 . _"-;-I_.=; ,,.
1.6 _1.4 -- 'k,_ m,m % 1.2 1 _' % .',q._ %.
...................... Rigid Wing "._x _ 0.8 .............. Iteration no. 1 _'-_'1_ I,_t .......... Iteration no. 2 "" :_\ 0.6 .......... Iteration no. 3 " ._, _._ ^ 4 r- .... Fie]tibia wing (strut in elas. axis) _', '_ Iteration no 4 ::':_1._" ' 0.4 u. F .... Fle_dble wing (strut at front spar) "_ .............. ,temtton no § _ 0.2 0.2 _" _,
.... o.' 5 .... 0'.5 .... o. 5 .... I
0(_ I I i I I J _ ' ' I I I l i I ' ' _ _ I 0.25 0.5 0.75 1 Nondimensionalwing span Nondlmensional wing span Figure 11: Spanload distribution for the strut-braced Figure 13: Strut-braced wing spanload convergence wing in a 2.5g maneuver for the 2.5g maneuver. The strut is attached to the wing-box front spar sections (wash-out). For a rigid wing, the spanload for the 2.5g maneuver would be the cruise spanload scaled the aircraft incidence, Figure 12 displays the by the load factor 2.5, i.e. an almost elliptical one.
convergence history of the root lift coefficient. The procedure rapidly converges towards the final value, Figure 11 also depicts one major advantage of the exhibiting a behavior similar to the one observed strut-braced wing from the aeroelastic point of view: a previously for the cantilever wing aircraft.
chordwise offset of the strut attachment to the wing- box produces a twist moment acting on the wing. By Wing Sizing From Flexible Spanload attaching the strut to the wing-box front spar instead of Consideration of the actual maneuver spanloads the wing elastic axis, this moment literally is twisting usually results in a significant reduction in the design down the wing leading edge. As a result, even more loads [14]. Since the influence of the strut moment load is shifted inboard, producing a much higher load offers even more potential for maneuver load alleviation effect than for a conventional wing.
alleviation, the impact of flexible wing sizing may As mentioned before, the aircraft incidence has to even be higher than for the cantilever wing. As a next be adjusted after each iteration step to sustain the total step, the wing structure has been resized according to lift for the respective load factor. As an indicator for the actual spanload distribution after each iteration 2.3 2.3 r _ _.._=----o----g .... • ........... • ............. _..........• .... • 2.2 2.2 T ¢/ / "\v / ",r"...... -- ......
_ 2 j_ k / 2.1 I]_ /i 'L9 1.9 _ ] I _ Root Ct*c/c m 18 _ -_a-----R OO' Ct "C/¢'" j 1.8 1.7 I I I I I I I I I I 170 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 No. of iterations No. of Iterations Figure 12: Convergence history of the strut-braced Figure 14: Root lift coefficient convergence for the wing root lift coefficient strut-braced wing in a 2.5g maneuver. The strut is attached to wing-box front spar American Institute of Aeronautics and Astronautics step. Figure 13 depicts the spanload distributions for 40,000 _0"=2.5g flexible, -lg rigid I .,_ the first five iteration steps and Figure 14 displays the _.,.11=2,5g and-lg flexible convergence history of the root lift coefficient. Due to E 38,000 7= the structural resizing, the convergence of spanload 36,000 and aircraft incidence becomes slower.
Weight calculation from the flexible design loads 34,ooo reveals the significant influence of the strut moment on t- ._ 32,000 maneuver load alleviation and wing weight, depicts the o) .= convergence history of the wing bending material 30,000 weight for three different strut attachments: at the wing-box front spar, in the wing elastic axis, and at the 28,000 wing-box rear spar. Compared to the rigid wing 0 0.2 0.4 0.6 0.8 weight, sizing the wing using the actual design loads Chordwise strut position leads to lower weights for all three cases.
Figure 16: Influence of the chordwise strut position on Nevertheless, it becomes obvious that employment of the wing bending material weight the strut moment is an important design factor.
It is important to note that an identical wing result, lift loads are shifted outboard instead of featuring a thin airfoil would suffer from significant inboard. This special way of "load aggravation" leads weight penalties if designed without a strut. Figure 15 to higher bending moments and higher bending indicates a 43% weight penalty for the rigid wing material weights (Figure 17).
sizing and a 29% weight penalty for the flexible design The chordwise strut position and the resulting loads in such a case. Presently, the MDO optimization twist moment not only influence spanload and 50000t structural wing weight, but also wing bending and twist deformations. For the 2.5g maneuver, the 48000 • Stria1 in wing elastic axis upward bending of the wing significantly decreases Strut at wing-box Iront spar 46000 by moving the strut towards the leading edge of the p-.
Wing without strut ,_ 44oo0 wing (Figure 18). In the same way, the wing twist is being reduced.
.........• , ......... Strut at wing-box mar spar 42000 o o o o o o o o o _40000 Since the strut is not active during the -1.0g "C @ pushover, the downward deflections for this 38000 E maneuver usually are relatively high. Depending on 0136000 .E the chordwise strut position, the wing structure is "_C 34000 resized according to the actual design loads.
32000 2.4 30000 '\"it"" '= ..m .... • .... • ....• -.m -• • 2.2 28000 '_ I "t"- = _t-- = 'T-- n T- t 2 1 2 3 4 5 6 7 8 9 10 No. ofiterations 1.8 1,6 Figure 15: Bending material weight convergence for different strut attachments =_ 1,4 _ 1.2 considers the rigid lift distribution for wing sizing.
_ l Therefore, runtime application of flexible spanloads 0,8 may result in an optimum wing configuration different from the investigated one. 0.6 0,4 -_ Figure 16 highlights the influence of the 0.2 _-- ......... ,oration no. 5 chordwise strut position on the wing bending material weight. The bending material weight increases if the O_ = _ _ = I n = i _ I _ _ i i I a _ _ _ I 0.25 0.5 0.75 1 strut is attached to the rear parts of the wing-box. By Nondimensional wing span moving the strut backward in the chordwise direction, Figure 17: Spanload convergence for the 2.5g maneuver.
the influence of the strut moment is inverted, i.e. it The strut is attached to the wing-box rear spar literally is pulling the leading edge upward. As a American Institute of Aeronautics and Astronautics Therefore, also forthe-l.0g pushover, thedeflections The strut also influences spanload distributions, slightly depend onthestrut position (Figure 19).
wing deformations. Weight savings are not only possible by calculation and iterative resizing of the wing structure according to the actual design loads.
Moreover, as an advantage over the cantilever wing, employment of the strut twist moment for further load alleviation leads to increased savings in structural weight.
Ongoing investigations focus on the influence of the strut upon the flutter behavior of the strut-braced wing and on a complete incorporation of the flexible wing sizing routine into the strut-braced wing aircraft i design process, i.e. the MDO environment.
N ,lo Acknowledgments This project is funded by NASA Langley Grant X NAG 1-1852. Part of the work was done under Figure 18: Strut-braced wing deformation for the 2.5g subcontract from Lockheed Martin Aeronautical n Systems in Marietta, Georgia. The authors would like to thank Bob Olliffe from Lockheed Martin Aeronautical Systems for the valuable input and discussions concerning the structural data for the hexagonal wing-box model. Finally, the authors want to thank all their colleagues from the strut-braced wing team for their active contributions throughout the project.
..k References [1] Pfenninger, W., "Design Considerations of Large Subsonic Long Range Transport Airplanes with Low Drag Boundary Layer Suction," Northrop Aircraft, X Inc., Report NAI-54-800 (BLC-67), November 1954.
Figure 19: Downward deflections for the -1.0g [2] Joslin, R.D., "Aircraft Laminar Flow Control," pushover Annual Review of Fluid Mechanics, Annual Reviews Inc., Vol. 30, pp. 1-29, Palo Alto, CA, 1998.
Conclusions [3] Grasmeyer, J.M., Naghshineh-Pour, A.H., A structural model for wing sizing and weight Tetrault, P.A., Grossman, B., Haftka, R.T., Kapania, calculation of a strut-braced wing has been developed. R.K., Mason, and W.H., Schetz, "Multidisciplinary To consider the influence of the actual design loads on Design Optimization of a Strut-Braced Wing Aircraft the flexible wing, static aeroelastic deformations and with Tip-Mounted Engines," MAD Center Report 98- flexible wing spanloads have been calculated. 01-01, Virginia Tech, January 1998.
Validation of the module with an existing aircraft wing [4] Kulfan, R.M., and Vachal, J.D., "Wing Planform and comparison with results from other sources Geometry Effects on Large Subsonic Military showed very good agreement with the present model. Transport Airplanes," Boeing Commercial Airplane Company, AFFDL-TR-78-16, February 1978.
The calculations revealed the significant influence [5] Park, H. P., "The Effect on Block Fuel of the strut on the bending material weight of the wing.
Consumption of a Strutted vs. Cantilever Wing for a The use of a strut enables one to design a wing with Short Haul Transport Including Strut Aeroelastic thin airfoils without weight penalty. Designing an Considerations," AIAA-78-1454-CP, Los Angeles, identical thin airfoil wing without strut would result in California, Aug. 21-23, 1978.
a 40% increase in wing weight.
American Institute of Aeronautics and Astronautics [6]Turriziani, R.V.,Lovell, W.A.,Martin, G.L.,Price, Appendix: Vortex Lattice Formulation
J.E., Swanson, E.E., and Washburn, G.F., "Preliminary
Using the Helmholtz method to derive the vortex
DesignCharacteristics of a Subsonic Business Jet
line downwash and with
Concept Employing anAspect Ratio25StrutBraced
n= (11)
Wing," NASA CR-159361, October 1980.
it can be shown that the induced velocities
[7] Grasmeyer, J.M., "Multidisciplinary Design
Optimization of a Strut-Braced WingAircraft,"MS develop into the following equations: Thesis, Virginia Tech, April1998.
Downwash:
[8] Gem,F.H.,Gundlach, J.F.,Ko,A., Naghshineh-
(12) Pour, A.,Sulaeman, E.,Tetrault, P.-A., Grossman, B., Kapania, R.K., Mason, W.H., J.A.Schetz, andHaftka,
R.T.,"Multidisciplinary DesignOptimization of a
xo<y_h - x_j,y_< x
Transonic Commercial Transport witha Strut-Braced
( x o< y _ - x o,,Y:c)+ ( x o?:_ - XobZo< ) + ]72 ( y:<z_ - Y=,Z:c ) Wing,"1999 WorldAviation Congress, 99WAC-30,
San Francisco, CA,Oct.19-21, 1999
XbcX, h+_(yb, y,t,+Z_) xoex.,, + f12 ( Y.<.Yb + Z_hZ_e )] [9] Grossman, B., Strauch, G.J.,Eppard, W.M., 4Xebc + fl2(y2 + zeb¢) -
Gurdal,Z., andHaftka,R.T.,"Integrated Aerody-
namic/Structural Design of a Sailplane Wing," AIAA-
86-2623, Dayton, Ohio, October 20-22, 1986.
,yo<I,- x- I
y2o<+z% /x2oc + + z2o<)
[10] Giunta,A.A., Balabanov, V., Haim, D.,
Grossman, B., Mason,W.H., Watson, L.T., and
Haftka,R.T.,"Multidisciplinary Optimization of a
Supersonic Transport UsingDesign of Experiments
Note that forM.=0, z = 0, and T= 0, Eq. (12)
Theory and Response SurfaceModeling,"The
reduces to the formula used by Bertin and Smith [17].
Aeronautical Journal, pp.347-356, October 1997.
[11] Hutchison, M.G.,Unger, E.R.,Mason, W.H., Backwash:
Grossman, B., Haftka,R.T.,"Variable Complexity
Aerodynamic Optimization of a High Speed Civil
u, b _ = (13) Transport Wing,"Journal of Aircraft, Vol. 31,No. 1, pp.110-116, 1994.
-- YaeZah + YahZac X , + 2 , ,
[12]McCullers, L.A., FLOPS User's Guide, Release
(x,,y,b--X,o),,)+(X,eZ_--X#bZ,,) fl (),,Z,b--Y,bZ_c) 5.81, NASA Langley Research Center.
+ '(y,cyo + z. )_xo<xo + + 1
[13] Lamar, J.E., "A Vortex Lattice Method for the Mean Camber Shapes of Trimmed Non-Coplanar Ix2b<+fl2(y2b<+Z2b<) iX2<,, + f12 (y2,,<- + Z2<,<) j Planforms with Minimum Vortex Drag," NASA TN Sidewash: D-8090, June, 1976 [14] Gimmestad, D., "An Aeroelastic Optimization Procedure for Composite High Aspect Ratio Wings," v: b _ = (14) AIAA Paper No. 79-0726, April, 1979 - x_z_o + X.bZ_< x [ 15] Torenbeek, E., "Development and Application of (x_<y,, b- x_by<,<)+(x:<z,, b- XabZac) + fl2(y:<z:_,-- YobZo<) a Comprehensive, Design Sensitive Weight Prediction Method for Wing Structures of Transport Category
I + + zo ) x:<Xo + fl2(yo<y: +
Aircraft," Delft University of Technology, Report LR- [ i x2_+fl_(y2°'+z2_) - 4x'#_+ff(Y2"+z2'_) 693, Sept. 1992.
[16] Vanderplaats Research & Development, Inc., DOT User's Manual, Version 4.20, Colorado Springs,
x.. )
+ yZ_< +Z2o< t 4x2:<+f12(y2:.+Z2.<) CO, 1995.
[17] Bertin, J.J., Smith, L.L., Aerodynamics for .4.
Engineers, 2 nd Ed., Prentice Hall, Englewood Cliffs,
]
t
/ [18] Katz, J. ,Plotkin, A., Low-Speed Aerodynamics, Note that forM.=0, Eqs. (12) to (14) reduce to McGraw-Hill, New York, 1991 the formulae used by Plotkin and Katz [ 18].
American Institute of Aeronautics and Astronautics