Content uploaded by Nhan Nguyen
Author content
All content in this area was uploaded by Nhan Nguyen on May 04, 2016
Content may be subject to copyright.
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.
1 of 14
American Institute of Aeronautics and Astronautics
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
2 of 14
American Institute of Aeronautics and Astronautics
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.
3 of 14
American Institute of Aeronautics and Astronautics
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.
4 of 14
American Institute of Aeronautics and Astronautics
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
5 of 14
American Institute of Aeronautics and Astronautics
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,
6 of 14
American Institute of Aeronautics and Astronautics
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.
7 of 14
American Institute of Aeronautics and Astronautics
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.
8 of 14
American Institute of Aeronautics and Astronautics
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.
9 of 14
American Institute of Aeronautics and Astronautics
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.
10 of 14
American Institute of Aeronautics and Astronautics
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
11 of 14
American Institute of Aeronautics and Astronautics
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.
12 of 14
American Institute of Aeronautics and Astronautics
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.
References
1Bradley, M. K., and Droney, C. K., “Subsonic Ultra Green Aircraft Research: Truss Braced Wing Design Exploration,”
Contractor Report, The Boeing Company, June 2014.
2Bradley, M. K., Droney, C. K., and Allen, T. J., “Subsonic Ultra Green Aircraft Research: Truss Braced Wing Aeroelastic
Test Report,” Contractor Report, The Boeing Company, June 2014.
3Nguyen, N., “Elastically Shaped Future Air Vehicle Concept,” NASA Innovation Fund Award 2010 Report, Oct. 2010,
Submitted to NASA Innovative Partnerships Program.
4Nguyen, N., Trinh, K., Reynolds, K., Kless, J., Aftosmis, M., Urnes, J., and Ippolito, C., “Elastically Shaped Wing
Optimization and Aircraft Concept for Improved Cruise Efficiency,” AIAA Aerospace Sciences Meeting, AIAA-2013-0141,
January 2013.
5Lebofsky, S., Ting, E., and Nguyen, N., “Aeroelastic Modeling and Drag Optimization of Aircraft Wing with Variable
Camber Continuous Trailing Edge Flap,” 32nd AIAA Applied Aerodynamics Conference, AIAA-2014-2443, June 2014.
6Lebofsky, S., Ting, E., and Nguyen, N., “Multidisciplinary Drag Optimization of Reduced Stiffness Flexible Wing Aircraft
with Variable Camber Continuous Trailing Edge Flap,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference, AIAA-2015-1408, January 2015.
7Rodriguez, D. L., Aftosmis, M. J., Nemec, M., and Anderson, G. R., “Optimized Off-Design Performance of Flexible
13 of 14
American Institute of Aeronautics and Astronautics
Wings with Continuous Trailing-Edge Flaps,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference, AIAA-2015-1409, January 2015.
8Nguyen, N., Livne, E., Precup, N., Urnes, J. M., Nelson, C., Ting, E., and Lebofsky, S., “Experimental Investigation of a
Flexible Wing with a Variable Camber Continuous Trailing Edge Flap Design,” 32nd AIAA Applied Aerodynamics Conference,
AIAA-2014-2441, June 2014.
9Livne, E., Precup, N., and Mor, M., “Design, Construction, and Tests of an Aeroelastic Wind Tunnel Model of a
Variable Camber Continuous Trailing Edge Flap (VCCTEF) Concept Wing,” 32nd AIAA Applied Aerodynamics Conference,
AIAA-2014-2442, June 2014.
10Nguyen, N., Ting, E., and Lebofsky, S., “Aeroelastic Analysis of Wind Tunnel Test Data of a Flexible Wing with a
Variable Camber Continuous Trailing Edge Flap (VCCTEF),” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics,
and Materials Conference, AIAA-2015-1405, January 2015.
11Bradley, M. K., and Droney, C. K., “Subsonic Ultra Green Aircraft Research: Phase I Final Report,” NASA Contractor
Report NASA/CR-2011-216847, Boeing Research and Technology, April 2011.
12Miranda, L. R., Elliot, R. D., and Baker, W. M., “A Generalized Vortex Lattice Method for Subsonic and Supersonic
Flow Applications,” NASA CR-2865, 1977.
13Ting, E., Reynolds, K., Nguyen, N., and Totah, J., “Aerodynamic Analysis of the Truss-Braced Wing Aircraft Using
Vortex-Lattice Superposition Approach,” 32nd AIAA Applied Aerodynamics Conference, AIAA-2014-2597, June 2014.
14Hodges, D. H., and Pierce, G. A., Introduction to Structural Dynamics and Aeroelasticity, Cambridge University Press,
2002.
15Hughes, T., The Finite Element Method Linear Static and Dynamic Finite Element Analysis, Prentice Hall, Inc., 1987.
16Craig, Jr., R. R., and Kurdila, A. J., Fundamentals of Structural Dynamics, Second Edition, John Wiley & Sons, Inc.,
2006.
17Nguyen, N., Ting, E., and Lebofsky, S., “Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced
Wing Aircraft,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA-2015-1840,
January 2015.
18Vanderplaats, G. N., and Moses, F., “Structural Optimization by Methods of Feasible Directions,” Computers & Struc-
tures, Vol. 3, 1973, pp. 739-755.
19Vaderplaats, G. N., Multidisciplinary Design Optimization, Monterey, CA, 2007.
20Sadek, E., “Application of Methods of Feasible Directions to Structural Optimization Problems,” Computers & Structures,
Vol. 17, No. 2, 1983, pp. 183-191.
14 of 14
American Institute of Aeronautics and Astronautics
