American Institute of Aeronautics and Astronautics

1

Integrated Structural, Flight Dynamics and Aeroelastic

Analysis of the ANCE X-3d as a Flexible Body

Luis A. Hernández1

Universidad Simón Bolívar, Caracas, Miranda, 1080-A, Venezuela

Pedro J. Boschetti2

Universidad Simón Bolívar, Naiguatá, Vargas, 1160, Venezuela

and

Pedro J. González3

Instituto Tecnológico de Aeronáutica, São José Dos Campos, SP, 12228-900, Brazil

The objective of this paper is to generate simplified structural configurations for the ANCE

X-3d by considering the influence of structural flexibility on the flight dynamic characteristics

and the aeroelastic phenomena. This aircraft consists of an unswept wing with double tail

boom structure and two vertical stabilizers. Two structures were designed by an analytical

approach and finite element models to create suitable structural arrangements for the wing,

tail booms, and stabilizers, and carbon-fiber composite materials were selected for this

purpose. Knowing the stiffness and mass properties of the main structural components,

reduced order aero-structural models were developed to quantify the influence of the

flexibility on the aircraft aerodynamics and stability characteristics. Flight dynamic

evaluation of the airplane considering the flexibility of the structure was performed at

different velocities and altitudes. The resultant flutter and divergence velocities fulfill the

design criteria.

Nomenclature

Ak = circulation Fourier mode coefficients

CD0 = minimum drag coefficient

CL0, CM0 = lift and pitching moment coefficients at zero angle of attack

CLq, CDq, CMq = variation of lift, drag, and pitching moment coefficients with pitch rate

CLα, CDα, CMα = lift, drag, and pitching moment slopes

CYβ, Cℓβ, Cnβ = variation of side force, rolling, yawing coefficients with sideslip angle

CYp, Cℓp, Cnp = variation of side force, rolling, yawing coefficients with roll rate

CYr, Cℓr, Cnr = variation of side force, rolling, yawing coefficients with yaw rate

D = control state vector

E = control error-integral vector

E = young modulus, Pa

EI = bending stiffness, Nm2

iF = beam force-stress resultant

JF = global beam force-stress resultant

G = shear modulus, Pa

GJ = torsional stiffness, Nm2

h0 = stick fixed neutral point

k = lift dependent drag factor or induced drag factor

1 Undergraduate student, Program in Mechanical Engineering, Sartenejas Valley. 2 Associate Professor, Department of Industrial Technology, Camurí Grande Valley, Senior Member AIAA. 3 PhD Candidate, Aerospace Engineering Division, São José dos Campos, Member AIAA.

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AIAA Scitech 2019 Forum

7-11 January 2019, San Diego, California

10.2514/6.2019-0824

Copyright © 2019 by Luis A. Hernández, Pedro J. Boschetti, Pedro J. González. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA SciTech Forum

American Institute of Aeronautics and Astronautics

2

h0 = stick fixed neutral point

iM = beam moment resultant

JM = global beam moment resultant

n = load factor

ir = beam -section location

ER = earth referenced global position

SS = shear strength, Pa

T = air temperature

iu = beam-section velocity

U , U = aircraft absolute position, acceleration

U, Uc = state vector, commanded state vector

Vs, Vcr, Vcar, VD= stall speed, cruise speed, Carson speed, dive speed

VF, VDIV = flutter speed, torsional divergence speed

Xc, Xt = compression strength, tensile strength

δ1, δ2, δ3 = aileron, elevator, rudder deflection

δF = control deflections

i = beam-section rotation

= aircraft orientation Euler angles vector

= system eigenvalue

ρ = air density

ζ = damping ratio

ω = frequency

ωF = flutter frequency

i = local beam-section rotation

, = aircraft absolute rotation, angular velocity

I. Introduction

IRCRAFT structural design is an interdisciplinary process. The airframe structural components must be capable

of withstanding the loads generated in critical flight conditions, to ensure the physical integrity of the aircraft in

the complete flight envelope and provide enough stiffness to reduce the influence of the structural flexibility on the

aerodynamic characteristics and dynamic response of the aircraft, as well as preventing the appearance of potentially

destructive aeroelastic phenomenona.1 In general, the dynamic and aeroelastic analysis of the complete airplane

represents a highly complex task and for this reason, it is treated as a separate problem in the design process with

direct influence on the structural sizing of the airframe. However, for the design team to accomplish a complete

rational analysis of the aircraft dynamic response, a significant effort must be done to develop accurate mathematical

models and obtain valuable experimental data to proceed with the validation of the numerical results and the

subsequent certification process of the aircraft, which demands a large amount of computational and experimental

engineering analyses.2 The aeroelastic phenomena represent a hazard to the safe operation of the aircraft, consequently

it is required mitigating the unstable behavior of the structure, which generally involves important modifications of

the structural design, increasing the financial risk of the project and affecting the initial time estimation for the design

phase.3 For this reason, it can be advantageous to generate a simplified model in an earlier phase of the structural

design process in order to gain valuable insight about the dynamic response of the aircraft that could serve as feedback

for the structure team and as input data to the aeroelastic and flight dynamic engineers. Another potential advantage

of this approach is that it allows exploring different structural configurations using low-cost computational models to

evaluate the sensitivity of the aircraft dynamic response to the structural characteristics of the main components and

the possible failure scenarios.2

The objective of this paper is to generate simplified structural configurations for the Unmanned Airplane for

Ecological Conservation (ANCE X-3d)4,5 by considering the influence of structural flexibility on the flight dynamic

characteristics and the initial analysis of aeroelastic phenomena as part of the structural design process. The ANCE

X-3d has been developed to patrol oil extraction areas in order to look for oil leaks to minimize the response time of

emergency squads and reduce the environmental damage that these events could produce to the ecosystem and to the

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conservation of the natural environment and wildlife.

The aircraft is a twin-boom monoplane, with a maximum

takeoff mass of 182.055 kg, wingspan of 5.187 m,

geometric mean chord of 0.604 m, and wing area of

3.1329 m2. Figure 1 illustrates a sketch of the airplane.

Figures 2 and 3 show the flowchart corresponding to the

classic aircraft structural design process and that one

used in the present investigation, respectively. The main

difference in Fig. 3 with respect to the first diagram lies

in the fact that the structural sizing now is dependent on

the level of influence of the aircraft flexibility on the

overall flight characteristics.

In order to proceed with the dynamic analysis of the

ANCE X-3d as a flexible body, it was necessary to obtain

the stiffness and mass distributions of the airframe main

structural elements. For this purpose, two structures were

designed by an analytical approach and finite element

models to generate suitable structural arrangements for

the wing, tail booms, and stabilizers. Carbon-fiber

composite materials were selected because of their high

mechanical properties and weight-saving characteristics.

Reduced order aero-structural models were developed

with the objective of quantifying the influence of the

flexibility on the aircraft aerodynamics and stability

characteristics. Finally, an aeroelastic analysis was

carried out to predict the divergence and flutter velocities

to ensure that both phenomena occurred outside the flight

envelope of the ANCE X-3d, and that they achieved the

design criteria.

II. Structural Design

A. Load Estimation

The critical loads over the different components of

the vehicle were determined by evaluating the

aerodynamic loads over a range of flight conditions in

order to select the maximum load case for each of the

structural components. The maximum load factors were

computed using the program Coquivacoa, which

calculates in-flight states in time domain of a subsonic

airplane considering atmospheric and control

disturbances that may appear during flight, using a

classic four-order Runge-Kutta method.6 This software

calculates the critical load factors at asymmetric flight

conditions considering the maximum deflection of the control surfaces for each individual component, which is ±15

deg.7 Open-loop simulations were carried out to obtain the maximum load factor values using the corresponding flight

parameters of each flight condition. Flight envelope diagrams at sea level and for cruise altitude are drawn based on

the data attained by these simulations according to the FAR Part 23 (Ref. 8); these are shown in Fig. 4.

The vortex lattice models of this airplane previously used to simulate the flow field around the ANCE X-3d (Refs.

9,10) are employed to obtain the lift distribution over the aerodynamic surfaces (wing, horizontal stabilizer, and

vertical stabilizer) for the given flight conditions.

Figure 1. Axonometric view of the ANCE X-3d.

Figure 2. Flowchart for the classic aircraft structural

design process.

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B. Structural Configuration

The main structural components are designed using composite materials to take advantage of their elevated

mechanical properties and low weight to strength ratio.11 The composite material selected is ACP Standard Carbon

Fiber.12 Finite element models are developed using ANSYS software13 in order to compute the stress and deformation

distributions over the airframe structural elements for the critical load case determined in the previous section. The

computational model of the composite laminate is constructed using ANSYS ACP14 to generate an accurate

representation of the composite structure.

Figure 4. Velocity as function of load diagram at sea level (left) and for cruise altitude (right).

-2

-1

0

1

2

3

4

5

0 10 20 30 40 50 60

Lo

ad f

acto

r

Velocity, m/s

ManeuverGust 25 ft/sGust 50 ft/sEnvelope

-2

-1

0

1

2

3

4

5

0 10 20 30 40 50 60 70

Lo

ad f

acto

r

Velocity, m/s

Maneuver

Gust 25 ft/s

Gust 50 ft/s

Envelope

Figure 3. Flowchart for the modified aircraft structural design process.

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Two structural configurations were designed herein.

Table 1 presents a comparison of the mechanical

characteristics of both structural configurations. The

second design has a higher wing torsional stiffness in the

section located between the fuselage and the wing-tail

boom joint (sec. 2) and a lower bending stiffness in the

same section. The tail boom bending stiffness is also

increased for the first section compared to the first

structure. The second section’s (sec. 1) torsional and

bending stiffness are reduced for the wing and tail boom.

These variations in stiffness properties are mostly

achieved by changing the composite laminate

configuration using 0 deg, 90 deg and ±45 deg plies.

Table 2 shows the mass values of the main components

for both configurations, and it can be observed that the

mass of the second structure is 45.9% less than the mass of the first one. These values correspond only to the mass of

the structural elements and do not represent real mass distribution of the complete airframe. Figure 5 illustrates the

structure geometry and the location of the different sections.

III. Structural and Mass Model

A. Aswing Mathematical Modelling

The Aswing software is aimed at the overall evaluation of the aerodynamics, structural and control system

implementation on flexible aircraft of moderate to high aspect ratio.15,16,17 The program allows making quick design

modifications to get insight into structural failure, flight dynamic response, stability characteristics and aeroelastic

phenomena appearance in a wide range of flight conditions. The complete nonlinear system is solved by means of a

full Newton method. The structural model consists of nonlinear connected beams with arbitrary mass, inertia, and

stiffness distributions. The lifting-line based aerodynamic model allows considering general aerodynamic sections

with control-surface deflection. Compressibility effects are considered using the Prandtl–Glauert correction in wind

axes. The complete aircraft dynamics can be computed including the airplane response to atmospheric gust encounters

with a general state-feedback law governing control-surface deflections and thrust configuration.15

The general unsteady problem is represented using the two vectors shown in Eqs. (1) and (2), where E is a control-

error integral vector. The system is treated in nonlinear residual form as presented in Eq. (3), where Uc is the

commanded state vector.15

Table 1. Bending and torsional stiffness of the main structural components.

Design 1 Design 2

EIxx, Nm2 EIyy, Nm2 GJ, Nm2 EIxx, Nm2 EIyy, Nm2 GJ, Nm2

Wing beam sec. 1 56600 56600 32000 23672.4 23672.4 52893.3

Wing beam sec. 2 56600 56600 32000 13011.7 13011.7 3128.1

Tail boom sec. 1 19600 19600 14700 26778.3 26778.3 6351.2

Tail boom sec. 2 18100 18100 13600 9118.6 9118.6 3594.2

Horizontal tail* 2550 8210 234 2550 8210 234

Vertical tail* 14.4 230 17.4 14.4 230 17.4

Table 2. Total mass of the main structural components.

Design 1 Design 2

Mass, kg Total mass, kg Mass, kg Total mass, kg

Wing beam 2.023 4.045 1.754 3.509

Tailboom 7.732 15.465 3.225 6.449

Horizontal tail 0.804 0.804 0.804 0.804

Vertical tail 0.240 0.480 0.240 0.480

Total - 20.79 - 11.24

Figure 5. Simplified structural model in ANSYS.

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( )i i i i i i J J J J k Er M F u r M F A R U U = U E (1)

1 2( ...)F F =D (2)

( , , ; )c =R U U D U 0 (3)

The corresponding linearized system can be written as follows:15

+ + =

R R RU U D R

U DU (4)

This linearized system of equations in Eq. (4) is the base of the Aswing solution for steady state, time-domain,

frequency-response and eigenvalue analysis. Eigenvalue calculation is achieved by Eq. (5) to obtain the corresponding

nontrivial solutions X̂ for the unknown eigenvalues .15

ˆ ˆ =AX MX (5)

= = −

R RA M

U U (6)

An instability of eigenmode is indicated if ℝ ( ) 0 (Ref. 15). This could represent a flight instability as in the

common case of unstable spiral mode or a structural instability like flutter, which is an undesirable condition because

one goal during the design process is that the structural modes must be stable.

B. Aswing Structural and Mass Model

The structural and mass properties presented in Tables 1 and 2 were used to create the structural and mass models

used by Aswing. These data were also employed to build a simplified beam-like finite element model in ANSYS.

Natural frequencies and mode shapes of the structures are calculated by both methods and these are shown in Table

3, and Figs. 6 and 7 illustrate the corresponding mode shapes. For the first design, the natural frequencies achieved by

both methods present an agreement below 10% except for the fourth mode shape, which has a difference of 11.54%.

An analogous result is attained in the case of the second design, where the natural frequency of the second mode

presents a difference of 11.78% between both methods. The difference may be a direct result of the simplified beam-

like FEM model used for extracting the mechanical properties of the structural elements. It should be noted that for

the second design, it was not possible to obtain the corresponding sixth mode shape so the comparison is made using

the first five modes.

C. Aswing Aerodynamic Model

The geometry of the ANCE X-3d is modeled in Aswing using five surfaces and three bodies, and this is illustrated

in Figs. 6 and 7. The aerodynamic and stability coefficients estimated by Aswing are compared with those coefficients

presented in previous published works18-20 achieved by wind tunnel testing and using other numerical and empirical

methods. Table 4 shows the aerodynamic parameters and stability coefficients calculated for the airplane with Aswing

Table 3. Natural frequencies obtained for both proposed structures. Design 1 Design 2

Mode ANSYS, Hz Aswing, Hz Percental

difference ANSYS Hz Aswing, Hz

Percental

difference

1 2.13 2.11 1.33 6.88 7.5 9.07

2 6.48 6.43 0.7 8.69 9.71 11.78

3 6.64 6.66 0.25 12.53 12.67 1.13

4 19.08 21.28 11.54 21.3 20.82 2.32

5 20.01 18.03 9.88 22.21 21.1 5.23

6 20.78 19.71 5.13 - - -

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Figure 6a. Mode shapes (first to fourth) for the first structural configuration (D1) calculated with ANSYS (left)

and Aswing (right).

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Figure 6b. Mode shapes (fifth to sixth) for the first structural configuration (D1) calculated with ANSYS (left)

and Aswing (right).

Figure 7a. Mode shapes (first to second) for the second structural configuration (D2) calculated with ANSYS

(left) and Aswing (right).

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Figure 7b. Mode shapes (third to fifth) for the second structural configuration (D2) with ANSYS (left) and

Aswing (right).

Table 4. Aerodynamic parameters and stability coefficients obtained by different methods in rad-1.

Digital

DATCOM20 AVL18 PANAIR18 CMARC20

Wind

tunnel19

Aswing

Rigid First structure Second structure

k 0.0364 0.0506 0.0493 0.0488 0.0464 0.0541 0.0579 0.0558

h0 0.792 0.826 0.893 0.958 - 0.9422 0.7935 0.9195

CD0 - - - - 0.0317 0.0295 0.0264 0.0253 CL0 0.311 0.3111 0.3089 0.3273 0.3424 0.2775 0.3 0.2592

CM0 -0.081 -0.1 -0.009 -0.096 - -0.0557 -0.0901 -0.0746

CDα 0.128 0.152 0.13 0.173 - 0.1332 0.0968 0.1182

CLα 5.6379 4.8128 4.2743 5.4202 4.34302 4.4347 2.7864 4.0868

CLq 8.474 10.157 - 6.221 - 11.28533 -5.27969 7.2287

CMα -3.054 -2.773 -2.75 -3.839 - -3.07 -1.515 -2.736

CMq -26.075 -28.13 - -18.663 - -35.4193 -15.7436 -25.46

CYβ -0.761 -0.527 - -0.327 - -0.33695 -0.32642 -0.3287 CYp -0.083 -0.055 - -0.005 - -0.05698 -0.02627 -0.092

CYr - 0.455 - 0.421 - 0.2529 0.24221 0.2538

Cℓβ -0.059 -0.057 - -0.138 - -0.01309 -0.0195 -0.0331

Cℓp -0.53 -0.546 - -1.127 - -0.52969 -0.52611 -0.5319

Cℓr 0.069 0.091 - 0.211 - 0.11902 0.10184 0.1081

Cnβ 0.175 0.132 - 0.189 - 0.11632 0.11289 0.1116

Cnp -0.031 -0.001 - -0.032 - -0.03512 -0.03067 -0.0298

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as a rigid body and for both proposed structures at Carson speed (45 m/s) at sea level. Figure 8 shows the lift coefficient

as a function of angle of attack and the drag polar curve of the airplane. A very good correlation can be observed

between the values of induced drag factor, lift slope and stability coefficients achieved by experimental and numerical

methods and those calculated by Aswing for the rigid body model. The minimum drag coefficient estimated by Aswing

is 6.9% smaller than the one achieved by wind tunnel testing because the Aswing aerodynamic model does not have

landing gear, engine and camera. The stability coefficients obtained for the first structure present significant

differences respect to those ones of the second structure and the airplane as a rigid body. The pitch slope attained for

the first structure is 65.51% and 44.62% smaller than the one estimated for a rigid body and for the second structure,

respectively, representing a reduction of static stability. The lift and drag slopes obtained for the first structure is

37.2% and 27.3% less than those estimated for the airplane as a rigid body, respectively. Hantrais-Gervois and

Destarac21 describe that CLα rotates around the zero-lift point because of the wing elastic twist distribution and if the

wing twist variation is moderate, a drag polar invariance with flexibility is expected at the cruise point for airplanes

of moderate aspect ratio (RA≈9). The lift and drag slopes for the second structure show a decrease of 8.51% and 12.63%

when compared with the rigid body results, respectively; however, it is noticed that there is no significant rotation of

the lift curve for the flexible body, which could be explained by the increase of torsional stiffness in the first section

of the wing structure. As expected, the drag polar curve shows no significant sensitivity to the flexibility of the airplane

structure, according to the observation in Ref. 21, but the induced drag factor calculated for the second structure is

smaller compared to the one for the first structural configuration. The resultant maximum lift-drag ratio value of the

airplane as a rigid body estimated by Aswing is 12.52. For the first and second structures the resultant maximum lift-

drag ratio are 12.79 and 13.31, respectively. As flexibility increases, the maximum lift-drag ratio also rises.

IV. Flight Dynamics

Table 5 presents the eigenvalues of the dynamic modes of the airplane as both a rigid and a flexible body computed

by Aswing in cruise altitude (2438 m) and velocity equal to 51 m/s (Carson speed). The eigenvalues obtained for the

airplane as a rigid body using Aswing for phugoid, short period, and Dutch roll are complex and have negative real

parts, indicating that after a disturbance the response would decay sinusoidally in time. The root for the roll mode is

real and negative, representing a stable and heavily damped rolling motion. The root for spiral motion is positive,

indicating a slightly divergent spiral motion. The eigenvalues obtained in previous studies present similar behavior,

expected for spiral mode. Because of the mass model employed by Aswing herein only has the mass of the main

structure, there are no correlations between the values estimated by this model and those obtained in previous studies,

which used inertial properties estimated for the complete aircraft. Table 5 shows a moderate variation of the damping

and frequency of the flight dynamic modes for the second structure, and for the first structure it is observed a smaller

sensitivity of the eigenvalues concerning aircraft flexibility.

Figure 8. Lift coefficient as a function of angle of attack (left) and drag polar curve (right).

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-20 -15 -10 -5 0 5 10 15 20

Lif

t co

effi

cien

t

Ange of attack, deg

Wind Tunnel

ASWING rigid

ASWING flex. D1

ASWING flex. D2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.02 0.04 0.06 0.08 0.10

Lif

t co

effi

cien

t

Drag coefficient

Wind Tunnel

ASWING rigid

ASWING flex. D1

ASWING flex. D2

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Table 6 compares the dynamic characteristics of the airplane when it is considered a rigid body and using the first

and second structures, and it is observed that the modification in the stiffness and mass distributions has an important

influence on the short period and Dutch roll frequencies and on the roll mode. A moderate variation of the short period

and Dutch roll modes for the second structure (D2) is appreciated in Figs. 9 and 10 at sea level and cruise altitude,

respectively. For the first structure (D1), the short period and Dutch roll modes do not present significant changes.

The phugoid and spiral modes remain practically invariant for both structures at sea level and cruise altitude.

Figures 11 to 13 illustrate the variation of the flight mode eigenvalues with velocity for both structural

configurations. The results indicate that the effect of flexibility increases with velocity, however, all the flight modes

are stable in the velocity range of the ANCE X-3d. For the phugoid mode, the damping diminishes with velocity until

56 m/s and 66 m/s for the first and second structures, respectively, at sea level, and then this value remains relatively

constant. The damping value for phugoid mode reduces until 50 m/s and 70 m/s for the first and second structures,

respectively, for the cruise altitude. Figures 14 to 17 present a similar behavior in the root-locus plot. Figures 18 to 20

compare the damping as a function of velocity at sea level and cruise altitude for the first and second structural

configurations. The phugoid mode shows a slight variation in damping between both structural configurations, and

the damping for Dutch roll and short period modes are quite different.

V. Aeroelastic Analysis

Figures 21 to 26 illustrate the root-locus and damping as a function of velocity at sea level, for cruise altitude, and

service ceiling, respectively, for the first structural configuration (D1), and Fig. 27 to 32 for the second structure (D2).

For the first structural configuration, the results show that flutter occurs outside the flight envelope of the vehicle

fulfilling the design requirements. The flutter velocity is equal to 86 m/s at sea level, 80 m/s for cruise altitude and

78 m/s for service ceiling. Additionally, the flutter mode corresponds to the asymmetric torsion of the wing structure.

Figures 22, 24, and 26 present damping modes as a function of velocity of the critical aeroelastic modes, and a fast

reduction of damping for high velocities values can be observed. For cruise altitude, flutter velocity is 4.17% higher

than the maximum permissible value of 1.2VD established in Ref. 22. Figures 27, 29 and 31 show the symmetric

in-plane bending (SYM. B IP), symmetric out-of-plane bending (SYM. B OP), asymmetric in-plane bending (ASYM.

B IP), asymmetric out-of-plane bending (ASYM. B OP) and torsional structural modes at sea level, for cruise altitude

and at service ceiling. It is observed that the torsional mode of the horizontal tail structure becomes unstable at 79 m/s,

77 m/s, and 93 m/s at sea level, for cruise altitude, and at service ceiling, respectively, which represents a drastic

reduction of flutter velocity compared to the results of the first structure. This result also suggests a lack of torsional

Table 5. Dynamic modes eigenvalues at cruise flight condition.

Digital

DATCOM20 AVL20 CMARC20

Aswing

Rigid First structure Second

structure

Phugoid Real -0.0093 -0.0093 -0.0097 -0.04109 -0.03387 -0.02922

Im (±) 0.2308 0.2306 0.244 0.303 0.30315 0.25093

Short Period Real -2.0737 -1.9172 -1.912 -3.6207 -3.04246 -4.4274

Im (±) 4.1976 4.0325 4.7212 6.09775 5.71142 9.61222

Dutch Roll Real -0.4701 -0.3545 -0.454 -1.055 -1.01497 -1.66534

Im (±) 3.127 2.6987 2.4785 3.57246 3.59889 5.0911

Roll Real -4.2369 -4.3371 -6.7322 -16.9461 -20.309 -58.223

Spiral Real -0.0037 0.0042 -0.0289 0.01353 0.01213 0.01228

Table 6. Comparison of the dynamic characteristics of the airplane

Rigid First

structure

Second

structure

Difference

rigid-1st

str.

Difference

rigid-2nd

str.

Difference

1st str-2nd

Phugoid ζ -0.1344 -0.11103 -0.11565 21.05% 16.2% 4.17%

ω, rad/s 0.303 0.30315 0.25093 0.05% 20.75% 17.23%

Short period ζ -0.8598 -0.88259 -0.90828 2.58% 5.33% 2.91%

ω, rad/s 6.09775 5.71142 9.61222 6.76% 36.56% 68.3%

Dutch roll ζ -0.2832 -0.27143 -0.3109 4.34% 8.9% 14.54%

ω, rad/s 3.57246 3.59889 5.0911 0.73% 29.83% 41.46%

Roll Real -16.946 -20.309 -58.223 16.56% 70.89% 186.68%

Spiral Real 0.01353 0.01213 0.01228 11.51% 10.18% 1.21%

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Figure 9. Eigenvalues obtained at Carson speed (45 m/s) at sea level.

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

-6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

Dutch Roll Rigid

Dutch Roll D1

Dutch Roll D2

Short Period Rigid

Short Period D1

Short Period D2

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.03 -0.02 -0.01 0 0.01 0.02

Imag

inar

y p

art

Real part

Phugoid Rigid

Phugoid D1

Phugoid D2

Spiral rigid

Spiral D1

Spiral D2

Figure 10. Eigenvalues obtained at Carson speed (51 m/s) in cruise altitude (2438 m).

-13

-11

-9

-7

-5

-3

-1

1

3

5

7

9

11

13

-6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

Dutch Roll Rigid

Dutch Roll D1

Dutch Roll D2

Short Period Rigid

Short Period D1

Short Period D2

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.03 -0.02 -0.01 0 0.01 0.02

Imag

inar

y p

art

Real part

Phugoid Rigid

Phugoid D1

Phugoid D2

Spiral rigid

Spiral D1

Spiral D2Dow

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Figure 11. Variation of Dutch roll eigenvalues with velocity at sea level (left) and cruise altitude (right).

0

2

4

6

8

10

12

14

16

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

Imag

inar

y p

art

Real part

B.H Rigid

B.H Flexible D1

B.H Flexible D2

0

2

4

6

8

10

12

14

16

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

Imag

inar

y p

art

Real part

B.H Rigid

B.H Flexible D1

B.H Flexible D2

Figure 12. Variation of short period eigenvalues with velocity for sea level (left) and cruise altitude (right).

0

5

10

15

20

25

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

S.P Rigid

S.P Flexible D1

S.P Flexible D2

0

2

4

6

8

10

12

14

16

18

20

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

S.P Rigid

S.P Flexible D1

S.P Flexible D2

Figure 13. Variation of phugoid eigenvalues with velocity at sea level (left) and cruise altitude (right).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-0.05 -0.04 -0.03 -0.02 -0.01 0.00

Imag

inar

y p

art

Real part

Phugoid Rigid

Phugoid D1

Phugoid Flexible D20.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-0.06 -0.05 -0.04 -0.03 -0.02 -0.01

Imag

inar

y p

art

Real part

Phugoid Rigid

Phugoid D1

Phugoid Flexible D2

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Figure 14. Root-Locus of Dutch roll, short period and phugoid with velocity at sea level for the first structure

(D1).

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

-6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real Part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Dutch

Short period

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

-0.10 -0.08 -0.06 -0.04 -0.02 0.00

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Phugoid

Figure 15. Root-Locus of Dutch roll, short period and phugoid with velocity at sea level for the second structure

(D2).

-25

-20

-15

-10

-5

0

5

10

15

20

25

-6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

26 m/s36 m/s46 m/s56 m/s66 m/s76 m/s86 m/s

Dutch roll

Short period

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-0.08 -0.06 -0.04 -0.02 0.00

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Phugoid

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Figure 16. Root-Locus of Dutch roll, short period and phugoid with velocity for cruise altitude for the first

structure (D1).

-12

-7

-2

3

8

-5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

Short period

Dutch roll

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-0.10 -0.08 -0.06 -0.04 -0.02 0.00Im

agin

ary p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

Phugoid

Figure 17. Root-Locus of Dutch roll, short period and phugoid with velocity for cruise altitude for the second

structure (D2).

-25

-20

-15

-10

-5

0

5

10

15

20

25

-6 -5 -4 -3 -2 -1 0

Imag

inar

y p

art

Real part

30 m/s 40 m/s

50 m/s 60 m/s

70 m/s 80 m/s

90 m/s 100 m/s

Dutch roll

Short period

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-0.08 -0.06 -0.04 -0.02 0.00

Imag

inar

y p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

100 m/s

Phugoid

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Figure 18. Dutch roll damping as a function of velocity at sea level (left) and cruise altitude (right).

-0.99

-0.97

-0.95

-0.93

-0.91

-0.89

-0.87

-0.85

20 40 60 80 100

Rea

l p

art

Velocity, m/s

Dutch Roll D1

Dutch Roll D2

-1.00

-0.98

-0.96

-0.94

-0.92

-0.90

-0.88

20 40 60 80 100

Rea

l p

art

Velocity, m/s

Dutch Roll D1

Dutch Roll D2

Figure 19. Short period damping with velocity at sea level (left) and cruise altitude (right).

-0.98

-0.96

-0.94

-0.92

-0.90

-0.88

-0.86

-0.84

-0.82

20 40 60 80 100

Rea

l p

art

Velocity, m/s

Short Period D1

Short Period D2

-1.00

-0.98

-0.96

-0.94

-0.92

-0.90

-0.88

-0.86

-0.84

-0.82

20 40 60 80 100

Rea

l p

art

Velocity, m/s

Short Period D1

Short Period D2

Figure 20. Phugoid damping with velocity at sea level (left) and cruise altitude (right).

-1.000

-0.998

-0.996

-0.994

-0.992

-0.990

-0.988

25 35 45 55 65 75 85

Rea

l p

art

Velocity, m/s

Phugoid D1

Phugoid D2

-1.000

-0.998

-0.996

-0.994

-0.992

-0.990

35 45 55 65 75 85

Rea

l p

art

Velocity, m/s

Phugoid D1

Phugoid D2Dow

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Figure 21. Root-locus as a function of velocity at sea level for the first structure (D1).

S.P, D.R, phugoid

0

25

50

75

100

125

150

175

200

-50 -40 -30 -20 -10 0

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Wing asymmetric

torsion

Tailboom symmetric

bending

Unstable

40

42

44

46

48

50

52

54

56

-12 -8 -4 0 4 8 12

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Figure 22. Damping as a function of velocity at sea level for the first structure (D1).

-10

-8

-6

-4

-2

0

2

4

0 10 20 30 40 50 60 70 80 90 100

Dam

pin

g,

s-1

Velocity, m/s

Tailboom symmetric bending

Wing asymmetric torsion

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Figure 23. Root-locus as a function of velocity for cruise altitude for the first structure (D1).

S.P, D.R, phugoid

0

25

50

75

100

125

150

175

200

-50 -40 -30 -20 -10 0 10

Imag

inar

y p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

Wing asymmetric

torsion

Tailboom symmetric

bending

Unstable

40

42

44

46

48

50

52

54

56

-12 -8 -4 0 4 8 12

Imag

inar

y p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

Figure 24. Damping as a function of velocity for cruise level for the first structure (D1).

-15

-10

-5

0

5

10

0 10 20 30 40 50 60 70 80 90 100

Dam

pin

g,

s-1

Velocity, m/s

Tailboom symmetric bending

Wing asymmetric torsion

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Figure 25. Root-locus as a function of velocity at service ceiling for the first structure (D1).

0

25

50

75

100

125

150

175

200

-125 -100 -75 -50 -25 0 25 50

Imag

inar

y p

art

Real part

47 m/s

57 m/s

67 m/s

77 m/s

87 m/s

97 m/s

107 m/s

Tailboom symmetric

bending

Wing asymmetric

torsion

Unstable

15

20

25

30

35

40

45

50

-10 -8 -6 -4 -2 0 2 4

Imag

inar

y p

art

Real part

47 m/s

57 m/s

67 m/s

77 m/s

78 m/s

Figure 26. Damping as a function of velocity at service ceiling for the first structure (D1).

-6

-5

-4

-3

-2

-1

0

1

2

40 45 50 55 60 65 70 75 80

Dam

pin

g,

s-1

Velocity, m/s

Tailboom symmetric bending

Wing symmetric torsion

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Figure 27. Root-locus as a function of velocity at sea level for the second structure (D2).

Unstable H.T

Torsion

40

60

80

100

120

140

160

180

-40 -30 -20 -10 0 10 20 30

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

79 m/s

96 m/s

Tailboom SYM.

B (IP)

Tailboom SYM. B (OP)

Tailboom

ASYM. B (OP)

Unstable

250

270

290

310

330

350

370

390

-10 -8 -6 -4 -2 0 2

Imag

inar

y p

art

Real part

26 m/s

36 m/s

46 m/s

56 m/s

66 m/s

76 m/s

86 m/s

96 m/s

Wing ASYM. B (IP)

Figure 28. Damping as a function of velocity at sea level for the second structure (D2).

-30

-25

-20

-15

-10

-5

0

5

0 10 20 30 40 50 60 70 80 90 100

Dam

pin

g,

s-1

Velocity, m/s

Tailboom SYM. B (in plane)Tailboom - ASYM. B (out of plane)H.T Torsion

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Figure 29. Root-locus as a function of velocity for cruise altitude for the second structure (D2).

Unstable H.T

Torsion

40

60

80

100

120

140

160

180

-40 -30 -20 -10 0 10 20

Imag

inar

y p

art

Real part

30 m/s40 m/s50 m/s60 m/s70 m/s80 m/s77 m/s100 m/s

Tailboom SYM. B (OP)

Unstable

250

270

290

310

330

350

370

390

-10 -8 -6 -4 -2 0 2

Imag

inar

y p

art

Real part

30 m/s

40 m/s

50 m/s

60 m/s

70 m/s

80 m/s

90 m/s

100 m/sWing ASYM. B (IP)

Figure 30. Damping as a function of velocity for cruise altitude for the second structure (D2).

-25

-20

-15

-10

-5

0

5

0 10 20 30 40 50 60 70 80 90 100 110

Dam

pin

g,

s-1

Velocity, m/s

Tailboom SYM. B (in plane)Tailboom ASYM. B (out of plane)H.T Torsion

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Figure 31. Root-locus as a function of velocity at service ceiling level for the second structure (D2).

Unstable H.T

Torsion

40

60

80

100

120

140

160

180

-40 -30 -20 -10 0 10 20

Imag

inar

y p

art

Real part

47 m/s

57 m/s

67 m/s

77 m/s

87 m/s

97 m/s

107 m/s

Tailboom SYM. B (OP)

Unstable

250

270

290

310

330

350

370

390

-20 -15 -10 -5 0 5

Imag

inar

y p

art

Real part

47 m/s

57 m/s

67 m/s

77 m/s

87 m/s

97 m/s

107 m/s

Wing ASYM. B (IP)

Figure 32. Damping as a function of velocity at service ceiling level for the second structure (D2).

-18-16-14-12-10

-8-6-4-2024

40 50 60 70 80 90 100 110

Dam

pin

g,

s-1

Velocity, m/s

Tailboom SYM. B (in plane)Tailboom ASYM. B (out of plane)H.T Torsion

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stiffness for the horizontal

stabilizer. The flutter velocity

remains outside the flight

envelope, and the flutter velocity

is 0.26% higher to 1.2VD for

cruise altitude.

The wing torsional divergence

velocity is calculated by an

analytical approach1 at different

altitudes. Table 7 shows that the

resultant torsional divergence

velocities are higher than the

maximum aircraft velocity at

each specific flight condition.

However, the divergence velocity

exhibits a significant reduction for the second structure, which could be explained due to the torsional stiffness

distribution presented in Table 1. Table 7 summarizes the torsional divergence and flutter velocities for both structures.

VI. Conclusions

A general methodology is presented to account for flight dynamic response and aeroelastic phenomena

characteristics on the initial structural design of the ANCE X-3d main components using low-detail reduced aero-

structural models. This procedure proved to be useful in obtaining an overall evaluation of the aircraft flight dynamic

sensitivity to the structural flexibility affected by earlier modifications in the design process. The aeroelastic analysis

allowed obtaining valuable insight into the nature of the unstable aeroelastic modes and the stiffness properties linked

with the appearance of structural instabilities.

The simplified structural design of the ANCE X-3d proved to be a useful approximation to obtain an initial

structural definition of the airframe, significantly reducing computational modelling time by neglecting secondary

components that do not perform a structural function. The low computational cost of the reduced order beam-like

model also represents an important advantage due to the possibility of evaluating the physical response of the structure

for different geometric configurations, without the need to take special care of the airframe details that have a

negligible impact on the final structural properties.

The results have shown that structural flexibility does not have a significant influence on the aerodynamic and

stability characteristics of the ANCE X-3d. The aerodynamic performance has a moderate sensitivity to the wing

torsional stiffness in the section located between the fuselage and the wing-tail boom joint, but do not present an

important variation regarding the rigid body model. The ANCE X-3d flight dynamic modes are stable in the flight

envelope and they do not show a drastic modification as a consequence of aircraft flexibility, which satisfies the design

criteria.

The initial aeroelastic analyses suggest that the ANCE X-3d can operate in any condition located inside the flight

envelope with enough margin against aeroelastic phenomena. The results of the structural sensitivity analysis show

that flutter appearance is closely related to the wing first section torsional stiffness.

References 1Bisplinghoff, R. L., Ashley, H., and Halfman, R. L. Aeroelasticity. Dover Books on Aeronautical Engineering, New York,

1996, Chaps. 1, 8. 2Taylor, M.R., Weisshaar, A.T. and Surukhanov, V., “Structural Design Process Improvement Using Evolutionary Finite

Element Models,” Journal of Aircraft, Vol. 43, No. 1, 2006, pp. 172-181.

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Table 7. Torsional divergence and flutter velocities for both structural

configurations.

First structure Second structure

Sea level

ωF, rad/s 43.21 141.49

VF, m/s 86 79

VDIV, m/s 467 188.6

Cruise

altitude

ωF, rad/s 43.40 140.65

VF, m/s 80 77

VDIV, m/s 525 212.4

Service

ceiling

ωF, rad/s 43.10 140.70

VF, m/s 78 93

VDIV, m/s 663 268

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