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Optimization for Load Alleviation of Truss-Braced

Wing Aircraft With Variable Camber Continuous

Trailing Edge Flap

Sonia Lebofsky∗

Stinger Ghaﬀarian Technologies, Inc., Moﬀett Field, CA 94035

Eric Ting†

Stinger Ghaﬀarian Technologies, Inc., Moﬀett Field, CA 94035

Nhan Nguyen‡

NASA Ames Research Center, Moﬀett Field, CA 94035

Khanh Trinh§

Stinger Ghaﬀarian Technologies, Inc., Moﬀett Field, CA 94035

This paper focuses on load alleviation optimization for a high aspect ratio truss braced

wing (TBW) aircraft. The TBW aircraft model is based on the Subsonic Ultra Green

Aircraft Research (SUGAR) concept developed by Boeing, with the wing structures of

the model modiﬁed to include a novel aerodynamic control surface known as the Variable

Camber Continuous Trailing Edge Flap (VCCTEF). The purpose of the study is to inves-

tigate the eﬀectiveness of a Performance Adaptive Aeroelastic Wing (PAAW) technology,

speciﬁcally the VCCTEF, for alleviating load on the TBW wing during ﬂight maneuver.

The speciﬁc ﬂight maneuver under consideration in this study is a 2.5g pull-up maneuver.

Constrained gradient-based optimization is conducted to tailor the deﬂections of the VC-

CTEF such that bending moment along the wing is minimized at the 2.5g pull-up ﬂight

condition. Aerodynamic modeling for this study is conducted using a vortex-lattice method

code called Vorlax. A non-linear ﬁnite element analysis (FEA) method is constructed for

analyzing the structural deformation and resulting bending moment along the wing of the

aircraft with the inclusion of eﬀects from tension-stiﬀening due to axial loading in the truss.

This study is the ﬁrst phase of several studies, and involves optimization of a rigid wing

aircraft for preliminary analysis, with future studies incorporating ﬂexible wing structures

with aeroelastic interactions and deformations. The results of this ﬁrst phase positively

demonstrate the potential of utilizing the novel control surface on modern aircraft wing

designs for shaping control in order to provide load alleviation during ﬂight maneuver.

I. Introduction

With recent focus in the aviation industry on the need for reduced environmental impact and reduced

fuel burn, demand for green technologies and designs is expected to increase. Most large transport aircraft

today use the conventional tube-and-wing design and only incremental improvements have been made in

aerodynamic eﬃciency in the last century. In recent years, one such improvement is the use of lightweight

materials such as composites, which have been shown to allow for a signiﬁcant reduction in weight resulting

in reduced trim drag and thus improved energy eﬃciency. The Boeing 787 is an example of a modern air-

craft design that comprises lightweight structures. Another opportunity for further eﬃciency improvements

∗Engineer, Intelligent Systems Division, sonia.lebofsky@nasa.gov.

†Engineer, Intelligent Systems Division, eric.b.ting@nasa.gov.

‡Research Scientist, Intelligent Systems Division, nhan.t.nguyen@nasa.gov, AIAA Associate Fellow.

§Engineer, Intelligent Systems Division, khanh.v.trinh@nasa.gov.

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currently being investigated and pursued is in the form of high aspect ratio wing designs. However, as

wing aspect ratio increases, the need for maintaining suﬃcient load carrying capacity becomes increasingly

important. Traditional cantilever wing designs can only accommodate up to a certain aspect ratio beyond

which the wing root bending moment becomes too large imposing structural and weight limitations on the

wing design. Truss braced wing (TBW) aircraft concepts provide a structural solution for high aspect ratio

wing designs. The long slender wing includes structural bracing via the use of a truss member that provides

intermediate span supports in addition to the wing root attachment. These truss members generally support

a portion of the spanwise load carried by the wing and are loaded in tension.

The Subsonic Ultra Green Aircraft Research (SUGAR) TBW aircraft concept is a Boeing developed N+3

aircraft conﬁguration funded by the NASA ARMD Advanced Air Transport Technology (AATT) Project.1, 2

The SUGAR TBW is designed to be aerodynamically eﬃcient by employing an aspect ratio on the order

of 19, which is signiﬁcantly greater than the aspect ratio of conventional aircraft. The wings are braced at

approximately mid-span by two trusses, and two smaller jury struts, one on each wing, provide additional

reinforcement. Figure 1 shows an illustration of the SUGAR TBW aircraft concept.

Figure 1: Boeing SUGAR TBW aircraft concept.

Research into the TBW as a viable future generation aircraft is presently being conducted. Owing to its

high aspect ratio wing constructed from ﬂexible modern materials, signiﬁcant bending deformations, twisting

deformations, and aeroelastic interactions are expected for the aircraft. These deformations and aeroelastic

interactions may result in adverse aerodynamic eﬀects such as increased drag as the wing deforms to a

non-optimal shape, as well as adverse structural eﬀects as loading on the structure is increased during ﬂight

maneuvers. Previous conceptual studies, such as a 2010 study titled “Elastically Shaped Future Air Vehicle

Concept,”3were conducted to address such issues. The study produced results demonstrating potential

aerodynamic and load alleviation beneﬁts from using active control technology to tailor the wing shape

during ﬂight. A Performance Adaptive Aeroelastic Wing (PAAW) technology control surface known as the

Variable Camber Continuous Trailing Edge Flap (VCCTEF) was proposed as a control eﬀector3,4 to act as

a wing shaping device. Several previous conceptual design studies have been conducted investigating the

potential of the VCCTEF system for drag reduction at oﬀ-design cruise ﬂight conditions for a ﬂexible wing

aircraft representative of a current generation commercial aircraft model.5–7 These studies produced results

showing that a VCCTEF system does have potential for eﬀectively reshaping the aircraft wing during ﬂight

for signiﬁcant drag reduction beneﬁts. Experimental wind tunnel studies were also conducted to show the

beneﬁt and potential of a VCCTEF system on a ﬂexible wing.8–10 These previous studies were primarily

focused on drag minimization and were performed for older generation aircraft designs. It is of interest to

assess the capabilities of a PAAW system like the VCCTEF on more modern or future aircraft designs, and

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also to address not only drag minimization, but also the potential for using a wing shaping device to provide

load alleviation during ﬂight maneuvers such as pull-up or coordinated turn.

The TBW represents an N+3 testbed for evaluation of the load alleviation and drag reduction capabilities

of the VCCTEF system. This current study is an initial assessment of the VCCTEF capabilities on the TBW.

In particular, this study involves an investigation into whether the VCCTEF can be used to shape the wing

such that the spanwise lift distribution on the wing is modiﬁed in such away to provide load alleviation

on a rigid wing aircraft. Drag minimization for a ﬂexible wing TBW is to be conducted in future studies.

An aerodynamic model of the TBW is created using a vortex-lattice method, and an automatic geometry

generation tool is used to deﬂect the ﬂaps of the VCCTEF system. A non-linear ﬁnite element analysis

is used to determine the wing deformations and internal bending moments. Constrained gradient-based

optimization is performed to determine the optimal ﬂap deﬂections resulting in minimized bending moment

due to a 2.5g pull-up maneuver. This study represents a preliminary analysis of the performance beneﬁt of

the VCCTEF system and its utility in adaptive wing shaping for load alleviation during ﬂight.

II. Aircraft and VCCTEF Model Framework

The TBW aircraft model used for this study is based on the Boeing SUGAR 765-095 aircraft, which was

developed through a collaboration between the NASA Fixed Wing Project, Boeing Research and Technology,

and a number of other organizations.11 The aircraft has an aspect ratio of 19.56, with a wing span of 170

ft. It is designed to ﬂy at a Mach number of 0.7, with an optimal cruise CLof 0.766. The CAD geometry of

the aircraft provided for this study had wings already deformed to a 1g loaded shape, not jig-shape wings.

Therefore, any aerodynamic and structural ﬁnite element analysis of the aircraft would need to take this

built-in 1g shape into account.

The TBW aircraft model was modiﬁed for this study to include the VCCTEF, as shown in Fig.2. The

number of spanwise ﬂap sections was arbitrarily set to 10, and each ﬂap was sized to be of approximately

equal width. For the spanwise ﬂap layout, some consideration was taken for the location of the wing/truss

juncture and the location of a proposed folding wing hinge, such that a single ﬂap would not span these

points. Between each ﬂap section is a 6” section of a ﬂexible supported material, or elastomer, joining the

adjacent ﬂaps and allowing for a continuous trailing edge with no drag producing gaps. Additionally, each

ﬂap section has two individually commanded chord-wise camber segments, as showing in Fig. 3, allowing

for a spanwise distribution of variable camber.

Figure 2: TBW aircraft with VCCTEF system.

Figure 3: Cross-section of variable camber ﬂap section.

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III. Modeling

III.A. Aerodynamic Model: Superposition Vortex-Lattice Approach

Aerodynamic analysis for the load alleviation optimization of the TBW with VCCTEF is performed using

a vortex-lattice ﬂow solver called Vorlax.12 Although Vorlax is a low ﬁdelity tool, it does provide a rapid

method for estimation of aerodynamic force and moment coeﬃcients given an input geometry. Therefore the

vortex-lattice method is chosen for this study due to its computational eﬃciency. However, It is important

to keep in mind the limitations of vortex-lattice aerodynamic modeling when assessing the results of this

study. For example, Vorlax is an inviscid, incompressible code not capable of capturing transonic eﬀects

such as shock formation. Although the ﬂight condition for the TBW is transonic at M = 0.7, it was deemed

that transonic eﬀects would not play a critical role in the evaluation of load alleviation beneﬁt. However, for

future studies, particularly ones involving drag assessments, a transonic correction involving the integration

2D transonic small-disturbance theory results will be included in the model. For conceptual design studies

such as this one, particularly involving optimizations with many iterations, the trade-oﬀ in ﬁdelity for a

rapid solution is acceptable.

Vorlax models a lifting surface as a vortex sheet formed by the mean camber surface of the compo-

nent. While this generally provides a reliable aerodynamic prediction for simple lifting surfaces such as a

cantilevered wing, the method may become less reliable as more complex geometries are introduced, such

as multiple lifting surfaces located in close proximity in the stream-wise direction like those on the TBW.

However, due to the vortex-lattice method’s basis in potential ﬂow theory, the principal of superposition

of aerodynamic solutions holds. A previous study showed the possibility of using various superposition

combinations for the TBW aircraft.13 For this study, the TBW full conﬁguration is decomposed into three

components: 1) fuselage+wings+tail, 2) fuselage+truss+tail, 3) fuselage+tail. The aerodynamic solution

for each conﬁguration is obtained separately, and then the aerodynamic solution for the full conﬁguration is

obtained by adding the ﬁrst two conﬁgurations and subtracting the third, as diagrammed in Fig. 4. This

approach separates the wing and truss lifting surfaces, and therefore it is important to note that aerodynamic

interference eﬀects between bodies is not accounted for.

Figure 4: Aerodynamic superposition method for the TBW model.

III.B. Geometry Generation and Flap Deﬂection

A geometry generation tool was developed in order to automatically generate a mesh of the TBW geometry

for input into Vorlax. An example of the generated aircraft mesh used for this study is shown in Fig. 5. As

can be seen from the ﬁgure, engine nacelles and pylons are removed from the geometry. While the weight

of the engines is accounted for in the 1g shape of the wing, the aerodynamic eﬀects and interferences of the

engines and nacelles are neglected. For the purpose of this study, only the unimpeded aerodynamic eﬀects

of the VCCTEF are considered without the added complexity of engine interference. The small jury struts

were also removed from the model for simplicity.

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Figure 5: Mesh of TBW geometry created using geometry generation tool.

Modiﬁcation to the shape of the wing due to deﬂections of the cambered segments in the VCCTEF is

accounted for in the geometry generation tool. Flap deﬂections are modeled by deﬁning the hinge line for

the ﬂap and then rotating the aft portion of the wing section about that hinge line by the provided deﬂection

angle. The result is a new wing section with the modiﬁed camber.

III.C. Non-Linear Finite Element Analysis

The ﬁnite element analysis (FEA) for this study uses stick beam models for both the wing and the truss,

deﬁned along the elastic axes for each component. Each component beam is divided into nelements with

6 degrees of freedom at each node, and the FEA is used to numerically approximate the solution of the

governing structural partial diﬀerential equations through discretization into matrix equations.14–16 A couple

of modiﬁcations are made to the general FEA method in order to account for some unique features of the

TBW model. Firstly, the elastic axis deﬁnitions for the wing and truss, as supplied by Boeing, do not

connect. That is, the end node of the truss that should join to the wing does not actually lie on the wing

elastic axis. Therefore, a master-slave relationship is implemented such that compatibility in deformation

between the end node of the truss and the corresponding joint node on the wing is imposed. Secondly,

the FEA for this study includes the eﬀects of geometric non-linearity due to tension stiﬀening in the truss

member. The presence of axial loading in the structure causes an increase in bending and torsional stiﬀness.

The eﬀect of the tensile force in the structure is included as additive terms to both the bending and torsion

components of the structural stiﬀness matrix,

Ks

i=Zli

0

N0T

uEAN 0

u0 0 −N0T

uEAeyN00

v

0N0T

θ(GJ +T k2)N0

θ0 0

0 0 N00T

wEIy yN00

w+N0T

wT N 0

w−N00T

wEIy zN00

v

−N00T

vEAeyN0

u0−N00T

vEIy zN00

wN00T

vEIz zN00

v+N0T

vT N 0

v

(1)

where the subscript iindicates the ith beam element; Nu,Nv, and Nθare the ﬂap-wise bending, chord-wise

bending, and torsional FEA shape functions with the primes indicating the order of derivative; Tis the

tensile force; and k2is the radius of gyration of the element such that Ixx =Ak2. Since the total tensile

force Tin the truss is not known prior to the solution, the problem is non-linear and is solved using an

iterative method, as outlined in Fig. 6. The tension in the truss is ﬁrst initialized to zero and the FEA

static solution is found. From the resulting static deformation, the tensile force in the truss elements can be

calculated. The structural stiﬀness matrix is updated with the calculated tensile force and the FEA solution

is recomputed. This process is repeated until convergence is achieved. In this study, convergence is deﬁned

as being reached when the vertical deﬂection of the wing tip is no longer signiﬁcantly changing between

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iterations. A detailed discussion and analysis of the tension stiﬀening non-linear FEA as implemented for

the TBW is provided in a previous study.17

Figure 6: Flowchart outlining stiﬀness matrix updating process for structure with tension stiﬀening.

IV. Optimization

With the aerodynamic and non-linear FEA models built, it is possible to consider shape optimization of

the wing for maneuver load alleviation. In this case, shape optimization is achieved through deﬂection of

the VCCTEF system, resulting in a change of bending, twist, and camber along the wing span. For this

study, the maneuver load being considered is a 2.5g pull-up maneuver. While a pull-up maneuver involves

an elevator deﬂection to initiate the maneuver, the change in lift due to the elevator deﬂection is typically

small compared to the total CLand is ignored. For this study, the aircraft is analyzed at the ﬁnal total

CLresulting from the 2.5g pull-up maneuver. For the TBW, CLat 1g ﬂight is 0.766, therefore the CLfor

following analysis is CL= (2.5)(0.766) = 1.915. As the lift on the wing is increased due to pull-up, the

ﬂap-wise bending moment on the wing also increases and may become the critical load on the wing. For this

load alleviation optimization study, the goal is to determine a VCCTEF deﬂection resulting in a reduction

of the wing ﬂap-wise bending moment at the increased 2.5g loading.

IV.A. Load Alleviation: Minimization of Bending Moment

In general, for a cantilever wing the maximum ﬂap-wise bending moment occurs at the wing root. However,

the TBW has the addition of a truss member and can no longer be assumed to behave in the same manner

as a single cantilever. Therefore, the ﬁrst step in this analysis is to determine where on the clean wing

(VCCTEF stowed) the ﬂap-wise bending moment is critical at 2.5g. The bending moment along the wing is

calculated in the local beam element axis system using the FEA solution at 2.5g loading and the FEA element

shape function for bending. The ﬂap-wise bending moment for each wing beam element is approximated as,

Wi(η) = hφ1(η)φ2(η)φ3(η)φ4(η)i

w1i

w0

1i

w2i

w0

2i

=Nw(η)wi(2)

where the wivector contains the vertical deﬂection and slope at the ith element nodes, and the vector Nw(η)

contains the Hermite polynomial shape functions given by,

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NT

w=

φ1(η)

φ2(η)

φ3(η)

φ4(η)

=

1−3η2+ 2η3

lη−2η2+η3

3η2−2η3

l−η2+η2

(3)

where η∈[0,1] is the local coordinate and lis the element length.

The ﬂap-wise bending moment for a beam element is deﬁned as,

My=EIy y

d2W

d2x=EIy y 1

l2d2W

d2η=EIy y 1

l2d2Nw(η)

d2ηwi(4)

Therefore, the local ﬂap-wise bending moment along the ith beam element is calculated as,

Myi=EiIyyi1

l2

ih−6 + 12η l(−4+6η) 6 −12η l(−2+6η)i

w1i

w0

1i

w2i

w0

2i

(5)

Note that in the local beam axis, ﬂap-wise bending moment is My, about the local y-axis, and is positive

when resulting in upwards bending of the wing, as indicated in Fig. 7.

Figure 7: Local wing axis system and positive ﬂap-wise bending moment.

The ﬂap-wise bending moment along the span of the wing for 2.5g is shown in Fig. 8. As mentioned in

Section III, the wing model provided for the analysis already has 1g loaded shape built in, and it is unknown

what the bending moment is for this 1g load. Therefore, the values for the bending moment at 2.5g are not

absolute values, but rather incremental values obtained by using the incremental loading between 1g and

2.5g in the FEA. It is clear from the ﬁgure that the maximum Myoccurs not at the wing root, but rather at

the juncture of the wing and the truss.aThis is because the truss constrains the wing at the juncture point,

acting as an eﬀective root. Thus, for the load alleviation optimization, it is the ﬂap-wise bending moment

at the wing/truss juncture that is the objective to be minimized, herein called JBM for juncture bending

moment.

aThe discontinuity in the bending moment is due to the wing elastic axis not being straight. At the juncture node the local

beam axis changes direction, resulting in a slightly diﬀerent local bending moment at the node for each adjoining element.

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Figure 8: Flap-wise bending moment along clean wing.

IV.B. Constraints

In order to achieve a feasible result, the optimization for the minimization of ﬂap-wise bending moment at

the wing/truss juncture is subject to several constraints. Firstly, the total CLfor the aircraft is ﬁxed at

the 2.5g value of CL= 1.915. Also, due to the elastomer material between adjacent ﬂaps, it is assumed

that there is some relative limit on ﬂap deﬂection. Therefore, a constraint of ±2 degrees between adjacent

VCCTEF sections is imposed. If no further constraints were imposed, the optimizer would drive the solution

to one where the JBM is reduced with no restrictions on the shape of the lift distribution on the wing. This

could result in a solution where the VCCTEF is deﬂected in such a way that the lift distribution is pushed to

a triangular shape with the Clat the root and the bending moment at the root both increasing beyond any

limit. If the Clat the root were to go beyond a stall value, then the solution would be unacceptable, even

if JBM was successfully minimized. Therefore, a constraint on spanwise Clvalue is imposed. Aerodynamic

stall data for the TBW is not available, but it is assumed to be at approximately α= 12 degrees, where αis

the aircraft angle of attack, which is a typical value for current commercial aircraft. Following from this stall

assumption, α= 10 degrees is assumed to be a conservative limit for where non-linear aerodynamics begins.

Thus the TBW spanwise Cldistribution at α= 10 degrees is calculated using Vorlax, and the Clvalue at

the root location is determined to be the critical value, Cl,critical. Throughout the optimization, Clvalues at

spanwise locations along the wing are monitored and constrained to remain below Cl,critical . Finally, as the

optimization proceeds, it is desirable that lift load does not shift from the wing to other components that are

not as well designed to carry lift, such as the truss. This constraint is imposed by holding the aircraft angle

of attack constant, ensuring that the total lift values being carried by any one component will not change.

The constraint angle of attack, α0, is the TBW angle of attack for clean wing at CL= 1.915 as calculated

using the aerodynamic model.

Constraints used in optimization are typically mathematically deﬁned such that they are feasible when

≤0. For example the angle of attack constraint for this problem would be represented by the relationship,

g=α−α0≤0 (6)

which also indicates that the constraint is considered to be active when g= 0. For the purpose of this

optimization, all of the problem constraints are assumed to be active when within a buﬀer of ±0.01 from

zero in order to allow for ease of convergence.

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IV.C. Optimization Method

With the objective function and all constraints determined, the full optimization problem is posed as follows,

Minimize: JBM (δ)

Subject to: CL,total =CL,2.5g= 1.915

±2 degrees between adjacent ﬂaps

max(Cl(y)) ≤Cl,critical

α=α0

where it is indicated that JBM is a function of the VCCTEF deﬂections, δ, which are the design variables

for the problem.

Optimization is carried out using a gradient-based constrained optimization method called the Method

of Feasible Directions (MFD).18–20 MFD takes into account the gradient of the objective function as well

as the gradient of each constraint to determine a feasible (no violated constraints) and useable (reduction

in objective function) search direction. Gradients for the problem are approximated using forward ﬁnite

diﬀerence. A ﬂowchart outlining the optimization procedure is given in Fig. 9.

Figure 9: TBW load alleviation optimization procedure.

V. Results

V.A. VCCTEF Design Variable Parametrization

The design variables for the optimization problem are the deﬂection angles of the VCCTEF. As outlined in

Section II, the VCCTEF system is made up of 10 individual spanwise ﬂap sections, each with two chord-wise

segments controlling the variable camber. For this study, a circular arc camber shape is assumed. Therefore,

it is the deﬂection angle of the trailing edge chord-wise ﬂap segment, δ2, that is varied to achieve load

alleviation, with the other ﬂap segment following in a circular arc such that δ1=1

2δ2. The deﬂection angles

of the chord-wise segments are illustrated in Fig. 10.

Figure 10: Deﬂection angles of VCCTEF chord-wise ﬂaps.

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One way to approach the optimization problem is to have all 10 values of δ2be independent design

variables. However, the forward ﬁnite diﬀerence method used to approximate the gradient of the objective

function requires that the aerodynamic model be run once for every design variable, which can result in

signiﬁcant run time and increased cost as the number of design variables is increased. Therefore, for this

analysis, the deﬂections are parametrized using a shape function in order to reduce the number of design

variables for the problem. The shape function used is a Chebyshev cubic polynomial,

δ2=c1+c2τ+c3(2τ2−1) + c4(4τ3−3τ) (7)

where,

τ=F lap No. −1

N o. of F laps −1(8)

Therefore, there are only four design variables for the optimization problem, namely the coeﬃcients of

the parametrization function, c1,c2,c3, and c4.

V.B. Load Alleviation Results

The ﬂap-wise bending moment along the wing beam axis before and after optimization is shown in Fig. 11,

and the percent and absolute value reductions from clean wing to optimized wing are given in Table 1. In

the ﬁgure the 36.7% reduction in JBM is clearly seen. In fact, the optimization results in a reduction of

ﬂap-wise bending moment along the majority of the wing span. However, there is some increase in bending

moment at the wing root. This is not surprising, as it is expected that the optimization would drive the lift

distribution to increase at the root in order to alleviate the loading at the joint. However, as shown in Table

1, the absolute increase in root bending moment (RBM) is approximately 1.6 times less than the absolute

decrease in JBM. Also, the ﬁnal RBM value is not signiﬁcantly larger than the ﬁnal moment value at the

critical joint location. Therefore, the increase in RBM is considered acceptable in relation to the overall

reduction in JBM.

0 10 20 30 40 50 60 70 80 90

−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4x 105

Span, y (ft)

My (lb−ft)

Clean Wing

Optimized

Figure 11: Flap-wise bending moment along wing span, clean wing and optimized.

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Table 1: Reduction in bending moments from clean wing to optimized wing, percent diﬀerence and absolute

diﬀerence.

Percent Reduction, % Absolute Value Reduction (kb-ft)

JBM 36.7 1.43×105

RBM -49.7 -8.53×104

The optimized ﬂap deﬂection resulting from the JBM minimization is shown in Fig. 12. The ﬁgure shows

the total deﬂection angle of the trailing edge camber segment, with the understanding that the other camber

segment follows in a circular arc. Since it is expected that the optimizer would drive the ﬂaps to a shape

that moves the wing loading inboard towards the root, the resulting deﬂection shape of ﬂaps down inboard

toward ﬂaps up outboard follows what is expected. Figure 13 shows the deﬂected ﬂaps on the aircraft model,

with the deﬂections magniﬁed 2x for visibility.

Figure 12: Optimized deﬂections of trailing edge ﬂap segments.

Figure 13: Optimized VCCTEF deﬂection, magniﬁed two times for visibility.

Figure 14 shows the 2.5g spanwise lift distribution on the wing before and after optimization. The

optimized lift distribution is of the expected shape, with lift increasing inboard of the wing/truss juncture

and decreasing outboard of the juncture. Also included on the plot is the lift distribution for the wing at

the α= 10 degree limit, which is included for visualization of the eﬀect of the Clcr itical constraint. The

optimized lift distribution does increase slightly above the constraint lift distribution, but this is an artifact

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of the ±0.01 buﬀer that was imposed on the constraint, as mentioned in Section IV.B. The impact of the

ﬁxed αconstraint is visualized in Fig. 15 and Table 2. As can be seen from the results, the truss does not

take on any extra lift as a result of the optimization. Also, as desired, the total lift on the wing also remains

unchanged with the optimal deﬂection of the ﬂaps only resulting in a modiﬁcation to the shape of the lift

distribution.

Figure 14: Spanwise lift distribution along wing, clean wing and optimized.

0 10 20 30 40 50 60 70 80 90

0

2

4

6

8

10

12

14

16

18

20

Span, y (ft)

Cl*c

Clean Wing

Optimized

Truss for Clean Wing

Truss for Optimized Wing

Figure 15: Spanwise lift distribution along wing, clean wing and optimized, for both wing and truss.

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Table 2: Angle of attack and lift, clean wing and optimized.

Angle of Attack (deg) CLon Wing CLon Truss

Clean Wing 8.67 1.49 0.25

Optimized 8.67 1.48 0.25

VI. Conclusion

This paper presents a study into the use of a PAAW technology, speciﬁcally a VCCTEF, for wing

shaping in order to provide load alleviation during a 2.5g pull-up ﬂight maneuver. The aircraft model

used in this study is a Truss Braced Wing aircraft with rigid wings. The speciﬁc objective for measuring

load alleviation is to minimize bending moment at the critical location of the wing/truss juncture point

on the wing through deﬂection of the VCCTE ﬂaps. The analysis involved using a vortex-lattice method

to determine the aerodynamic loading on the wing and truss structures of the aircraft, and a non-linear

FEA to calculate the deformation and bending moment along the wing. The non-linear component of the

FEA arises from the fact that the truss member is axially loaded, resulting in tension-induced stiﬀening of

the structure. Several constraints were imposed on the problem in order to ensure that the results were

feasible. These constraints included a limit on the local lift load on the wing to ensure stall load is not

exceeded, and a constraint to ﬁx the angle of attack to ensure that total load on the wing does not change

or transfer to the weaker truss member. It was shown that within the bounds of the constraints, and the

limitations of the lower ﬁdelity aerodynamic modeling tool, the VCCTEF system could be used eﬀectively

to reduce the bending moment on the wing due to the load from a 2.5g pull-up maneuver. An optimal ﬂap

deﬂection conﬁguration found by the optimizer resulted in a 36.7% reduction in ﬂap-wise bending moment

at the wing/truss joint location. While this optimal ﬂap deﬂection does also results in a 49.7% increase in

the ﬂap-wise bending moment at the wing root, the absolute increase at the root is 1.7 times less than the

absolute decrease at the wing/truss joint. Furthermore, the root bending moment after optimization does

not exceed the original maximum bending moment on the wing, and in fact is only marginally larger than the

optimum value of the wing/truss joint moment, and so is not considered critical. This study illustrates the

potential of a PAAW system such as the VCCTEF for eﬀectively providing ﬂight maneuver load alleviation

through active wing shaping. Future studies will involve analyzing the eﬀectiveness of the VCCTEF on a

ﬂexible wing TBW aircraft, including both load alleviation from other ﬂight maneuvers, as well as drag

minimization at oﬀ-design ﬂight conditions.

VII. Acknowledgment

The authors would like to thank the Advanced Air Transport Technology (AATT) Project under the

Fundamental Aeronautics Program of NASA Aeronautics Research Mission Directorate (ARMD) for funding

support of this work. The authors would also like to acknowledge Boeing Research and Technology for

providing the Truss Braced Wing aircraft models.

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