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Morphing Structural Concepts Evaluation Criteria Using Dimensionless Analysis and Computer Simulation

José J. Granda §, Ignacio Q. Sandoval *,

§* California State University, Sacramento. Department of Mechanical Engineering Sacramento, California, 95819

Lucas G. Horta†

† NASA Langley Research Center, Structural Dynamics Branch, Structures and Materials Competency, Hampton, VA 23681

ABSTRACT

Predicting the behavior of new airplanes or space structures that undergo large geometry changes in flight

present an engineering and scientific challenge. NASA’s Morphing Project and the International Space Station program are both facing these challenges. The task at hand is the study of methodologies to assist engineers and scientists in evaluating and analyzing these so called “morphing” structures. In order to establish a methodology several approaches from dimensionless parameter determinations to solid modelling and computer simulation methods have been used. The determination of critical parameters and in which way they can be used to gain an appreciation of the value of a concept is an integral part of this research. Computer models that use finite element models combined with state of the art dynamic system simulation techniques such as Bond Graph Modelling are presented to demonstrate not only the concept but also structural performance under loads. Several factors from weight, structural responses, volume, and mechanical/electrical power are all considered to establish a criterion to compare different designs. Also presented is historical data to compare new designs to existing designs on the basis of weight.

I. Introduction The study of morphing structures for potential uses in aircraft has been investigated from several angles originating at the start of the 20th century. New morphing wing concepts are constantly being developed and introduced by various organizations. These organizations include private companies, educational institutions, and government agencies. Since one of NASA’s objectives is to foster development of varied concepts and encourage the creation of new technology, materials, and production processes, a concept evaluation criterion is needed. The general objective of most evaluation criteria is to highlight and reward concepts with desirable features while penalizing those with less desirable characteristics. The objective of this particular effort is the development of an evaluation matrix that highlights concept morphing features/design technology and only compares the relative difference between each of the selected concepts. The challenge lies in creating such a relativistic feature based evaluation matrix.

II. Generation of Morphing Concepts and Analysis Solutions Several morphing concepts have been generated in order to establish a spectrum of possible concepts that use different mechanisms to achieve the change of shape of a structure in flight. Morphing a structure requires the relative motion of its members. In order to achieve this, articulations are necessary. These determine the degrees of freedom and the external inputs necessary to cause the motions and the internal components that will carry on the relative displacements. These elements are pin joints, slide joints, revolute joints, classified by the degrees of freedom they allow. Several morphing concepts have been considered starting first with kinematics considerations to establish the feasibility of motion and what source will cause such motion. Four two dimensional concepts have been chosen. Each is discussed in more detailed below. __________________________ § Professor, Department of Mechanical Engineering, email: grandajj@ecs.csus.edu AIAA Member * Graduate Student, Department of Mechanical Engineering, email: sandovali@ecs.csus.edu † Assistant Branch Head, Structural Dynamics Branch. email: l.g.horta@larc.nasa.gov AIAA Associate Fellow

46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference18 - 21 April 2005, Austin, Texas

AIAA 2005-2111

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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In order to study the feasibility of the concepts, kinematics analysis of motion in a two-dimensional and in three-dimensional space was considered. This technique was supplemented with dynamic analysis software programs. A combination of several software programs with sequential interfaces assisted in this effort. These include SOLIDWORKS, Working Model 2-D, NASTRAN 4D, CAMP-G, MATLAB, and SIMULINK.

A. Solid links, cable system model The first concept is a wing formed by three sections and moved by a single input. A set of cables connected to a single source at the base generates the motion of the wing.

Fig 1. Single input linkages and cable concept

This concept was studied using Working Model 2-D. The links are represented by blocks with the proper rigid body inertial properties. This software package allows complete concept motion analysis. This allowed also performing load calculations based on the actual concept movements (forces, velocities, accelerations, displacements, etc.). This concept involves the use of cables, small pulleys and a motor as a power source. B. Variable Truss with actuated links This concept is based on the use of a structural truss whose articulations are pin joints capable of rotating in a clockwise or counterclockwise direction. The internal cross members are actuators, which also serve as structural members for added rigidity and articulation. This concept model and its motion were modeled using Working Model 2-D. This concept presents a challenge to the design of actuators whether hydraulic or electrical actuators are

Fig 2. Articulated variable link truss

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used. These factors and the increase in complexity obviously and its consequences on weight and cost were part of the study to develop a criteria evaluation matrix that can be used for decision-making. C. Articulated Plates Concept Taking inspiration from the flexible metal bands such as those found in wristwatches, this concept is comprised of a set of plates with pin joins and a set of sliders on both front and rear of each adjoining plate to produce the morphing motion. Each minor displacement of consecutive plates contributes to an overall major displacement of the assembly (at the tip). Hydraulic actuators acting between the plates produce the motion.

Fig 3. Articulated Plates Concept.

This concept was studied using Working Model2D. The forces required by the inner plate actuators were calculated as functions of time during the dynamic motion. The actuators either compress or extend and since their ends are attached to each par of plates, produce the morphing motion.

D. Articulated Spine Concept The articulated spine concept is also composed of a set of plates and pins. The main idea is to use an optimum shape plate in a way such that the forces generated by the actuators will be located at the furthest possible point with the intent to reduce the forces necessary by using mechanical advantage to generate the torsion moments via the use of leverage.

Fig 4. Articulated Spine Concept

The number of actuators increased compared to the previous one, but the forces required of each decrease due to the increased efficiency in mechanical advantage that provide the shape of each link. Since the actuators are located at the end of each plate, the forces produce higher moments with respect to the joint and thus the force required is less.

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E. Three Dimensional Models A three section articulated folding wing is composed of two cylindrical joints. This concept was achieved by combining solid modeling techniques with finite element and dynamic system simulations. Using software like Solid Works or Pro Engineer, the concept and its motion were generated and tested. This involved the joints and the actuators that in this case produce joint rotation.

Fig 5. Three sections articulated three-dimensional wings

An interface between SOLIDWORKS, and NASTRAN4D using data base compatibility techniques was used to develop a solid model and then import it into NASTRAN4D to transform it into a finite element model. Once this was achieved, the dynamic system analysis was used to study the displacements, stress, accelerations and forces as functions of time. This is equivalent to analyze the structure in actual flight conditions. F. Morphing Concepts and Bond Graph Modeling Bond Graph Modeling fundamentals are presented very nicely in Ref. 2. The technique is also presented as it applies to the aerospace industry. See Reference 1. Physical components of systems are represented with symbols that identify their unique function and mathematical constitutive equations of each element based on power and energy transformations. The connections between elements are called ‘bonds”. The complete system is presented in a topological graph that relates it to reality and thus the name Bond Graph. The technique is suitable for automation of the modeling process. In this case CAMP-G (Computer Aided Modeling Program) was used to automatically generate the model is the form of a State Space Model in the form of MATLAB .m files. In order to show the relative merits of Bond Graph modeling in predicting motion and relative performance, a simple extend wing concept is presented here. This wing concept is shown in the unmorphed and morphed positions in Figures 6 and 7 respectively. These models were produced by CAMP-G; the associated motion simulations were produced using MSC Nastran4D, MATLAB and SIMULINK. A topological assembly of the dynamic elements represents the real system. CAMP-G software interfaces with the user who inputs graphically the model bond graph. It generates the MATLAB and SIMULINK models, which in turn perform the dynamic simulation. The technique has been used in modeling space vehicles and structures such as the International Space Station. A detailed explanation of these applications is presented in Ref. 3 and Ref. 4. The morphing concept involves sliding plates so that the area of the wing can be extended or contracted. The principles behind this model can be used to model wings that fan out or components rotate. This model is an opportunity to compare the technologies that have been in place as regular engineering practice with the more recent automated techniques offered by bond graph models.

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Fig. 6 Extend Wing in the Unmorphed Position Fig. 7 Extend Wing in the Morphed Position 1) Bond Graph Model Development In order to develop the bond graph model for the wing actuation, it is first necessary to breakdown the wing system into simple mechanical components. The main fixed wing base can be assumed to be a structure mounted to an aircraft fuselage. The moving/extend section will also be modeled as a mass on frictionless rollers (for illustrative purposes only since friction can also be added). The structure compliance of the connections (main fixed wing to structure and the moveable wing section) will be modeled using simple spring and damper models. To add the effects of gravity, the aircraft wing centerline will be assumed to have a banked angle (structure camber) to help with the creation of lift during take-off. The complete wing extend model is shown in Fig 8.

Fig. 8 Dynamic System Approximation For The Extend Wing Concept

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2

1

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For the purpose of illustration of the technique some of the characteristic values were used for inputs in the

generated MATLAB files for stiffness values, damper and mass values. All initial conditions are assumed to be zero. 2) System Bond Graph Using the system modeled in Figure 8, a system bond graph was generated. The sections numbered 1, 2, 3 of Figure 8 and their attached damper and stiffness elements are represented in the Bond Graph model shown in Figure 9. The bond graph symbols correspond to the physical elements shown in Figure 8. Each inertia element is represented by an I element and the SE elements represent gravitational forces. The C and R elements are between the masses and therefore they kinematically experience the relative velocity between the I elements. This relative velocities are represented by the 0 junctions. The I elements are attached to 1 junctions representing common velocities. The 0 junctions represent common forces. The spring and damper elements are between the primary and smaller mass elements. The bond graph topologically represents that relation between the dynamic elements (I, C, R, SE) and the corresponding physical elements.

Fig 9. CAMP-G generated Bond Graph Model with wing sections One can sketch the Bond Graph on paper or directly enter it into CAMP-G by choosing from the menu elements on the left hand side as shown in Figure 9. Then, these elements are placed on the screen. The computer assigns

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bond numbers just for unique identification of the variables and also the causality which indicates the interaction and represent mathematically the constitutive relations of each of the elements in relation to each other, is automatically generated by CAMP=G. For tracking purposes, each bond is assigned a number. This assists in identifying the force and velocity variables for the system. The complete bond graph consists of the elements, bonds that represent the interconnections and power flow directions, which represent the energy flow and keep the system kinematically consistent with the motion of the sliding sections.

Figure 10. CAMP-G Bond Graph including actuators. The Bond Graph shown in Figure 10 includes the actuators that control the R and C elements. The 0 junction between the 1 junctions on bonds 23 and 24 indicate that the actuators will act to affect the relative motion between the first and the third section and that such action is relative with respect to those sliding sections. The arrows above the C and the R elements indicate their control system. This model was entered into CAMP-G. The software generated a similar bond graph with the exact causality shown. The interface to MATLAB was then used to generate MATLAB ready .m files. These files are also used to enter data about system physical parameters that control the simulation and will shed light on system performance characteristics. The computer generates automatically the State Space Matrices A, B, C, and D, transfer functions, outputs, etc. These allow to generate bode and root locus diagrams which in turn are used to design the control system. The CAMP-G state space model is then delivered to SIMULINK, a MATLAB toolbox. It is used to generate block diagrams of the system equations. These block diagrams add insight into the inner workings of the how the particular system characteristic values and how they are used for predicting system performance.

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III Development of Morphing Structure Concept Evaluation Criteria Flexible wings undergoing large shape changes introduce many variables not present in conventional fixed wings designs. The proposed morphing concepts and their associated dynamic variables challenge the traditional methods used to compare design. In particular, the greatest challenge involves the development of base generic comparison parameters that can be applied to the plethora of concepts already in existence and yet still be capable of highlighting the relative merits of each concept. For the most part, these concepts span the range from complex articulating mechanisms, advanced aero-elastic wing skin materials, shape memory metal/polymer actuators, to novel in-flight wing boundary layer manipulators for vehicle flight enhancement and performance. Since one of the objectives of the morphing project is to foster the development of new concepts, evaluation criteria must be developed to highlight the relative merits of each concept independent of the scale of the concept. For this purpose, the evaluation criteria need to include dimensionless parameters that highlight concept merits independent of scale. This work builds on previous efforts by NASA to develop non-dimensional evaluation parameters based on the Buckingham Pi Theorem. The proposed criteria matrix is designed to evaluate and rank 39 characteristics of morphing wings. Most of these characteristics focus on establishing the morphing envelope and how the morphing affects traditional aerodynamic evaluation factors. Since a majority of the concepts only involve the wing structure, the criteria are tailored toward the evaluation of wing concept merits by the use of several methods. Some of these wing parameters require concept-loading factors derived via physical testing or software evaluation. A majority of these wing characteristics are dimensionless to allow for a relative comparison between concepts regardless of scale. A. GEOMETRIC VARIABLES One of the several sets of variables involved in morphing wings is the geometry. For illustration purposes, a sample of the many factors considered during this research is presented as set of diagrams containing illustrative descriptions of the critical geometric variables

Fig 11. Wing width factor

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Fig 12 Wing rotation

Error!

Fig 13. Wing load, weight factors

In creating an evaluation matrix, consideration was given to developing parameters capable of highlighting concept features regardless of scale and dimensions. Since most concepts are simply at the technology demonstrator stage, they vary considerably in scale and detail. The best method for accomplishing this task is using and developing dimensionless parameters. Several techniques are available that help accomplish this task. The

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Buckingham Pi Theorem methodology along with several other traditional methods is used to produce custom dimensionless units for concept evaluation (Ref 8, 9). These include the creation and use of 3-D models, finite element analysis and simulation, and data mining with regression analysis to develop concept factors that can be compared to established aerodynamic wing factors. In addition to more traditional factors, the matrix also includes factors for articulation, technology, material, type of actuator, and deflection/loading.

B. MORPHING FACTORS

. The following concept characteristics were selected for evaluation. These include: wing area, sweep, wing thickness, taper ratio, twist, wing orientation, time to actuate (unmorphed to morphed), wing weight, power consumption, complexity/maintainability, and inventory/infrastructure support. A summary table of each factor is shown in Table 1. These factors in turn can be used to evaluate any potential concept.

Morphing Concepts Factors

TABLE 1. Morphing Concept Factors

After selecting the appropriate wing parameters, the next task involved the calculation of the factors and the factor units. Since the goal was to develop scale independent factors (for relative comparison), priority was given to the development of dimensionless units where appropriate. For example, to calculate the unmorphed deflection factor, a distributed wing load with a magnitude equal to a percentage of the concept weight was applied. The tip deflection factor (measured in inches) is calculated by dividing the wing deflection by the total length of the wing concept. This dimensionless factor was compared to that of other proposed concepts to obtain a relative idea of deflection. Other factors are calculated in a similar manner. In order to facilitate the calculation process and expedite concept feature comparisons, the factor calculations were programmed into an Excel spreadsheet. The user/evaluator only has to fill in the appropriate concept dimensions and FEA results to have the software automatically calculate the concept factor values. The final calculated values are then automatically summarized in a factors table. An example of such table generated for the three section articulated wing shown as a three-dimensional model in Figure 5. The general factors calculations for this concept are shown in Table 2.as follows:

Wing Width Factor Distributed Wing Load Factor

Material Factor Envelope Articulation Factor

Wing Thickness Factor Max Deflection Factor

Weight Power Ratio Factor

Envelope Time Factor

Wing Rotation Angle

Wing Weight Load Factor Articulation Per Weight Factor

Articulation Power Factor

Envelope Factor (X-Y-Z)

Total Power Consumption Factor

Joint Actuation Factor Concept Wing Control

Wing. Envelope Change Factor

Wing to Actuator Weight Factor

Volume Actuation Factor Concept Wing Control Function

Wing Volume Factor

System Joint Factor Envelope Weight Factor

Concept Wing Load Factor

Wing Volume Change Factor

Time Frame for Morphing Envelope Power Factor

Comparison Graphs

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Calculated Factors For Three Dimensional Morphing Concept (Fig. 5)

1) Wing Width Factor (Constant Width Wing)

0

8) Wing Sweep Angle 0

15) Wing Length Factor -.04601

22) System Actuator Facto 4.00

Total # of Actuators 2 2) Wing Width Factor

(Change in Wing Root) 0

9) (X-Y Top) Envelope X-Coord. Y-Coord. 326 87.4 Unmorph 311 87.4 Morphed .9539 Factor Value

16) Distributed Wing Load Factor

60.6 (w/o Actuators) 55.045 (with Actuators)

Unmorphed

23) Total Power Consumption

18143.33333 lbs-ft/sec 32.98787879 HP

3) Wing Width Factor ( Wing Tip Root)

0

10)(X-Z Side) Envelope X-Coord. Z-Coord. 326 9.835 Unmorph 311 160 Morphed 15.5198 Factor Value

17) Distributed Wing Load Factor

60.6 (w/o Actuators) 55.045 (with Actuators)

Morphed

24) Wing to Actuator Weight Factor 22.32 (w/o Actuators) 23.32 (with Actuators)

4) Wing Width Factor (Average Wing Chord)

0

11)(Y-Z Side) Envelope Y-Coord. Z-Coord. 87.4 9.835Unmorph 87.4 160 Morphed 16.27 Factor Value

18) Max Deflection Factor

0.000103681 Unmorphed

10X Wing Weight

25) System Joint Factor 4.00

Total # of Joints 2

5) Wing Width Factor (Max Wing Chord)

0

12) Total Wing Envelope X-Crd. Y-Crd. Z-Crd. 326 87.4 9.85 Unmrph 311 87.4 160 Mrph 240.867 Factor Value

19) Max Deflection Factor

0.000131511 Morphed

10X Wing Weight

26) Time Frame for Morphing

10.00 seconds

6) Wing Thickness Factor

(Ave. Wing Thickness) 0

13) Wing Volume Factor

15.519

20) Wing Weight Load Factor

6.13E-05(w/oActuators) 6.13E-05(withActuatrs) Unmorphed

27) Material Factor

1.00

Material Types 1 7) Wing Rotation

Angle 0

14) Wing Vol. Change Factor

14.5198

21) Wing Weight Load Factor

2.8E-05(w/oActuators) 2.8E-05 (withActuators)

Morphed

28) Weight Power Ratio Factor

0.615101Sec/Ft(w/oactuatrs) 338.3060812 lbs/HP 0.642660298Sec/Ftwithactatrs 353.4631637 lbs/HP

Table 2. Concept Factors Calculated for Three Dimensional Concept ( Fig 5)

In a similar fashion each of the factors proposed in Table 1 can be calculated for each Morphing concept. Shown in Table 3 are the calculations for the Distributed Wing Stress Factor. The calculated factor is then automatically inserted into the summary table shown in Table 2.

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Distributed Wing Stress Factor (umorphed)

Wing Weight (w/o actuators) Material: Major Wing Components: Quantity Weight. (lbs) Total Each (lbs.) Properties

1 Alum.2024-T3, Spar Type 1 1 4260 4260 YS = 50kpsi 2 Alum.2024-T3 Spar Type 2 1 4220 4220 YS = 50kpsi 3 Alum.2024-T3, Spar Type 3 1 2680 2680 YS = 50kpsi 4 Alum 2024-T3 Spar Type 4 0 0 0 YS = 50kpsi 5 Alum.2024-T3 Spar Type 5 0 0 0 YS = 50kpsi 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 0 10 0 0 0 11 Miscellaneous 0 0 0

Total Wing Weight (lbs) 11160

Total Wing Weight (w/o Actuators): 11160 lbs Total Wing Weight (with Actuators): 11660 lbs 10X Max Wing Weight (distributed) 116600 lbs Max Stress (from analysis) 103000 psi Material YS (Least Strong) 50,000 psi

Max wing Stress factor 0.485436893 (Material YS/ Max Stress Unmorphed)

Table 3. Wing Stress Factor Calculation

Comparisons between varied and unique concepts can now be made based on the selected matrix comparison factors. The factor calculations using an Excel spreadsheet are shown in Table 3. At the same time the factor summary table shown in Table 2 is created and updated allowing the creation of an active database of comparison factors. In order to illustrate the concept in detail for another factor, such calculations for factors 22, 23 the “Actuators” and “Power factors”, their calculations are shown in Table 4.

IV. Design Concept Performance Prediction Using Real World Wing Data A. DATA SEARCH AND GRAPH TABLES: In addition to the aforementioned concept factors and simulation/modeling software, real world correlations can be made using available aircraft wing data. Traditionally, design tables have been used to establish preliminary aircraft designs. These tables are based on historical trend/design data that aims to predict aircraft performance. One such derived parameter is wing load. Depending on whether the aircraft will function as a civilian flyer, fighter, jet bomber, or cargo craft, the wing loading will clearly evolve from and depend on the aircraft type and mission. The wing load is a parameter that evolves from the mission requirements of the aircraft. In particular, it is defined as the total take-off weight of the aircraft (fully loaded with fuel and mission equipment) divided by the total wing area. The wing load has units of pounds per square foot. This singular parameter is not only characteristic of a particular type of aircraft, but also a key predictor of aircraft performance. For example, a given wing load can be used to predict (via charts) take-off distance, landing distance, acceleration, climb, range, turn rate, flight ceiling,

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C ) Actu a to rs22 ) T o ta l typ e a nd qu an tity o f ac tu a to rs

D es crip tio n : Q u an tity: W e ig h t T o ta l T im e to A c tu a te -S e con ds Actu a to r typ e 1 (ea ch , lbs ) (u n m o rph ed to m orp he d)

1 ) S c re w /m o to r type 4 0 .5 1 0Actu a to r typ e 2

2 ) N on e 0 0 0 .00 1Actu a to r typ e 3

3 ) N on e 0 0 0 .00 1Actu a to r typ e 4

4 ) N on e 0 0 0 .00 1Actu a to r typ e 5

5 ) N on e 0 0 0 .00 1T o ta l Ac tu ato r W e ig h t (lb s ) 2

Act. T yp e 1 A c t. T yp e 2 Ac t. T yp e 3F orce D is tance (ft) P ow e r F o rce D is tance(ft) P ow e r F o rce D is tance (ft)

1 6 0 0 0 .17 10 .2 0 0 0 0 02 6 0 0 0 .17 10 .2 0 0 0 0 03 3 0 0 0 .17 5 .1 0 0 0 0 04 3 0 0 0 .17 5 .1 0 0 0 0 05 0 0 .1 0 0 0 0 0 06 0 0 .1 0 0 0 0 0 07 0 0 .1 0 0 0 0 0 08 0 0 .1 0 0 0 0 0 09 0 0 .1 0 0 0 0 0 0

1 0 0 0 .1 0 0 0 0 0 0T ota l P ow er A c t. T yp e 1 lb s -ft/sec 30 .6 T ota l P ow er A c t. T yp e 2 lb s -ft/se c 0 T ota l P ow er A c t. Typ e 3 lbs -ft/se cT ota l P ow er A c t. T yp e 1 H P 0 .05 5 63 6 T ota l P ow er A c t. T yp e 2 H P 0 T ota l P ow er A c t. Typ e 3 H PA ctua to r P ow er C onsum ption F ac to r T ype 1 1 A c tua to r P ow er C onsum ption F ac to r T ype 2 0 A ctua to r P ow er C onsum ption F ac to r T ype 3

Act. T yp e 4 A c t. T yp e 5F orce D is tance (ft) P ow e r F o rce D is tance(ft) P ow e r C h e ck : T o ta l P o w e r C o n s u m

1 0 0 .1 0 0 0 0 lbs -ft/se c2 0 0 0 0 0 0 H P3 0 0 0 0 0 04 0 0 0 0 0 05 0 0 0 0 0 06 0 0 0 0 0 07 0 0 0 0 0 08 0 0 0 0 0 09 0 0 0 0 0 0

1 0 0 0 0 0 0 0T ota l P ow er A c t. T yp e 4 lb s -ft/sec 0 T ota l P ow er A c t. T yp e 5 lb s -ft/se c 0T ota l P ow er A c t. T yp e 4 H P 0 T ota l P ow er A c t. T yp e 5 H P 0A ctua to r P ow er C onsum ption F ac to r T ype 4 0 A c tua to r P ow er C onsum ption F ac to r T ype 5 0S ys te m A c tu a to r F a c to r (= T o ta l # ac tua to rs X [( to ta l # ac tu a to rs / to ta l n um be r o f a c tua to rs A ) + ( to ta l # a c tu a to rs / to ta l n um b er o f ac tu a to rs B ) + ( to ta l # a c tu a to rs / to ta l n um b er o f ac tu a to rs "n ")]

Actu ato r T yp e 1 2 3 4 5Actu ato r Q u a n tity 4 0 0 0 0Actu ato r T yp e F ac to r 1 0 0 0 0T o ta l Actu a to rs 4

T o ta l S yste m A ctu a to r F ac to r 16 .0023 ) P o w er F ac to rs T o ta l a c tua to r po w e r co nsu m ption / T o ta l ac tu a to r typ e p ow e r con sum ption (fo r e a ch a c tu a to r typ e )

Actu ato r T yp e 1 2 3 4 5P o w e r C o n s u m p tio n B y T y p e 3 0 .6 0 0 0 0 lb s -ft/secP o w e r C o n s u m p tio n B y T y p e 0 .05 56 3 6 0 0 0 0 H PP o w e r C o ns u m p tio n F a c to r B y T yp e 1 0 0 0 0T o ta l P o w e r C o n s u m p tio n

lbs -ft/se c 3 0 .6H P 0 .05 56 3 6

and glide rate (per design of aircraft Ref. 6, 7, 8). Since wing load is such a useful performance predictor, being able to define a concept factor that is similar to wing load will aid in understanding the concept’s potential use and application. For this reason being able to make a correlation between wing load of a complete aircraft (fully mission loaded) and the wing load of a single concept wing has proven fruitful.

Table 4 Actuator and Power Factor Calculation

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In an effort to establish this relationship, a reference search was undertaken at the NASA Langley technical library in cooperation with the reference librarians. Our collective search yielded an aircraft wing weight study published in 1971 that proved to be a major cornerstone in deriving a concept wing load factor (Ref. 5). The objective of this study was to establish an empirical formula for estimating wing weight based on structural integrity, control surface, and other design factors prior to actual wing construction. This particular study listed the wing weights (including control surfaces) minus hydraulic fluids and fuel for over forty different types of aircraft ranging from small civilian to jet powered transport. A full listing is included in Table 5. It is important to note that military fighter aircraft data is not included. The significance of this data was that only wing weights were listed without any reference to total aircraft weight. Most aircraft charts summarize overall system characteristics and rarely mention individual subsystem weights. The only task remaining was to find and document information on total aircraft weight and wing area for each of the listed types of aircraft. This information/data was required to insure that a complete wing load calculation could be completed since the actual data in the study was derived by dividing the wing weight by the wingspan to the second power (lbs/(ft)^2). Due to the many varied types and manufacturers of aircraft (not to mention fabrication date), data from one source would not be easily found. Table 6 can be used as reference, it shows typical wing loading based on aircraft mission. B. EVALUATION DATA AND GRAPH GENERATION: A spreadsheet was developed to assist with calculating the traditional wing load factor. These values can be seen in column 6 titled “Wing Load” (Table 5). Column two is divided by column three. This column is titled “Mod Wing Load”. This factor was calculated by dividing only the wing weight by the wing area. This factor was created to show a correlation between total aircraft weight and wing weight. Having obtained these values for all the aircraft involved, correlation graphs were generated as shown in Figure 14. This graph is very insightful for the following reasons. First, it clearly shows that there is a correlation between wing weight and total aircraft weight. Second, it shows that this correlation is consistent even when different types of aircraft (civilian flyers vs. transport planes) were considered. The R Squared correlation factor shows that the data is best approximated by a polynomial function; and that this correlation is within 94 percent accuracy. The plot of the aircraft data clearly shows a correlation between wing weight and aircraft type. This piece of information is highly significant since it can now be used to derive a traditional wing load value while only still at the wing concept level. This implies that a concept wing can be developed and analyzed for morphing performance independent of aircraft take-off weight. By simply using the chart, it is now possible to predict the type of aircraft that the concept wing is best suited for. As already mentioned, this information is only good for first approximations. For concept refinement and to properly track effects of structural changes, more sophisticated follow-up evaluation methods (FEA, CFD, etc.) will be required. In trying to understand the data variance, a second plot was generated to look at the scatter in the wing weight as a percentage of total aircraft weight. Figure 15 shows that as the aircraft take-off weight increases, the wing weight tends to decrease. Unfortunately, the data correlation can only be approximated with a polynomial fit that has an R-squared of 14. In any other case, this would not be considered to be good correlation. What should be noted is that the wing weight range starts at six and extends up to sixteen percent for the aircraft used in the study. This would imply an average weight value of 10 percent with a delta of four percent. In using these results to further understand the concept wing load graph, it can be assumed that a minimum variance threshold of four percent above and below the concept wing load line can be expected. This data also lends itself to further constructive manipulation. By combining concept wing load with traditional wing load and aircraft take-off weight, its possible to predict hypothetical aircraft take-off weight that’s appropriate for use with the concept wing under consideration. This graph can be seen in Figure 16. This plot shows concept wing load versus predicted aircraft take-off weight (based on the compiled aircraft data shown in table 3.) Figure 17. shows the traditional wing load vs. take-off weight for the aircraft data compiled during this study. This plot was generated to show the general trend for wing load and for use as a baseline for comparing the predicted aircraft weight when using concept wing load values.

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Table 5. Selected Aircraft Wing Data

Air Craft Description MAX WO Wing Area Wing Span Wing Weight Wing Load Mod Wing Load Ww/WtBeechcraft Bonanza 2295 181 32.83 259 12.68 1.43 0.112854Beechcraft Musketeer 2750 146 32.75 276 18.84 1.89 0.100364Cessna 172B Skyhawk 2200 174 36 236 12.64 1.36 0.107273Cessna 210 3800 175.5 36.75 261 21.65 1.49 0.068684Cessna 150A 1500 160 33.33 213 9.38 1.33 0.142Cessna 140 1450 167 32.83 180 8.68 1.08 0.124138Cessna 180 2550 174 36 254 14.66 1.46 0.099608Cessna 185 1727 174 35.83 266 9.93 1.53 0.154024Beagle B206 7,500 214 45.83 765 35.05 3.57 0.102Beechcraft Twin Bonanza 6300 277 45.25 633 22.74 2.29 0.100476Beechcraft Queen Air 8200 294 50.25 670 27.89 2.28 0.081707Convair 340 47000 920 105.33 5,300 51.09 5.76 0.112766Curtis C-46 45000 1360 108 6108 33.09 4.49 0.135733Fairchild Provider 60000 1223 110 6200 49.06 5.07 0.103333Fokker F-27 42000 753.5 95.17 4424 55.74 5.87 0.105333Grumman Gulfstream 35100 610.3 78.5 3700 57.51 6.06 0.105413Hawker Siddeley 748 46500 810 98.5 5250 57.41 6.48 0.112903Handley Page Herald 43000 886 94.33 4365 48.53 4.93 0.101512Nord Aviation 262 23370 600 71.67 2698 38.95 4.50 0.115447Scottish Aviation Twin Pioneer 14602 669.521 76.542 2121 21.81 3.17 0.145254Shorts Skyvan 12500 373 64.083 1223 33.51 3.28 0.09784Transall C-160 112200 1721 131.25 12422 65.19 7.22 0.110713Vickers Viking 34000 882 89.25 3350 38.55 3.80 0.098529Bristol Britannia 155000 2075 142.3 12,580 74.70 6.06 0.081161Canadair CL-44 208606.3 2073.89677 142.2536 15580 100.59 7.51 0.074686Boeing Stratocruiser 145800 1769 141.25 14411 82.42 8.15 0.098841Douglas DC-6 97200 1463 117.5 7508 66.44 5.13 0.077243Douglas DC-7C 143000 1637 127.5 11115 87.35 6.79 0.077727Lockheed L749 Constellation 133000 1647 63.89 11093 80.75 6.74 0.083406Lockheed L1049 120000 1650 123 11542 72.73 7.00 0.096183Lockheed L-1649A 156000 2012.19512 150 16535 77.53 8.22 0.105994Lockheed C-130E Hercules 175000 1745 132.58 11697 100.29 6.70 0.06684Lockheed C-133 284102.1 2673.15512 179.70037 27371 106.28 10.24 0.096342Republic Rainbow 100630.5 1639.50356 129.14016 12300 61.38 7.50 0.122229Vickers Viscount 700 64500 963 81.83 6100 66.98 6.33 0.094574Vickers Vanguard 141000 1527 118.583 14400 92.34 9.43 0.102128Aero Jet Commander 1123 20700 308 44.417 1322 67.21 4.29 0.063865BAC 111 One-Eleven Srs. 300-400 88500 1003 88.5 9656 88.24 9.63 0.109107BAC 111 One-Eleven Srs. 500 104500 1031 93.5 10104 101.36 9.80 0.096689Douglas DC-9/30 121000 1000.7 93.417 9300 120.92 9.29 0.07686Fokker F-28 fellowship 65000 822.4 77.33 7025 79.04 8.54 0.108077Lockheed Jetstar 38940 542.5 54.42 2700 71.78 4.98 0.069337Hawker Siddeley Trident1C 144000 1462 98 12420 98.50 8.50 0.08625BAC VC-10 309931 2845.17919 146.3326 34320 108.93 12.06 0.110734Boeing B-47 206700 1428 116 17250 144.75 12.08 0.083454Boeing 707-120 257000 2433 130.83 24000 105.63 9.86 0.093385Boeing 707-320 333600 3050 145.75 30000 109.38 9.84 0.089928Douglas DC-8/10 325000 2868 142.42 26500 113.32 9.24 0.081538General Dynamics 990 253000 2250.3 120 26865 112.43 11.94 0.106186C-141 Starlifter 316600 3228 160 34701 98.08 10.75 0.109605Lockheed C-5A 837000 6200 223 79000 135.00 12.74 0.094385

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Table 6. Typical Wing Loading Per Aircraft Mission Profile

y = 9.0603x1.0722

R2 = 0.9371

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Concept Wing Load (Lbs/Ft^2)

Win

g Lo

ad (L

bs/F

t^2)

Wing Load VS. ConceptWing Load

Power (Wing Load VS.Concept Wing Load)

Fig 14 Wing Load Vs. Concept Wing Load

Mission Requirement Wing Loading (lbs/Ft^2)

Long Range 125 ±15 Short/Medium Range 95 ±15 Short TO&L 65 ±25 Light Civil 20 ±10 Combat Fighter 55 ±15 Combat Intercept 135 ±15 High Altitude 45 ±15

17

y = 979.46x2.334

R2 = 0.9327

05000

100001500020000250003000035000400004500050000550006000065000700007500080000850009000095000

100000105000110000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00

Concept Wing Loading (Lbs/Ft^2)

Pred

icte

d C

once

pt A

ircra

ft W

eigh

t (Lb

s)

Concept wing loading Vs. TotalWeightPower (Concept wing loadingVs. Total Weight)

y = -0.0043Ln(x) + 0.1464R2 = 0.141

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 100000 200000 300000 400000 500000 600000 700000 800000 900000

Total Take-off Weight (lbs)

Win

g W

eigh

t/Tot

al ta

ke-o

ff W

eigh

t

Wing weight percent VS. Total Weight

Log. (Wing weight percent VS. TotalWeight)

Fig 15 Wing Weight Variance Vs. Total Aircraft Weight (from compiled aircraft data)

Fig 16. Predicted Aircraft Weight Based On Concept Wing Load

18

y = 10.099x2.1249

R2 = 0.9201

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

130000

140000

150000

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00

Wing Load (Lbs/Ft^2)

Airc

raft

Wei

ght (

Max

. tak

e-of

f)

Wtake-off VS. Wing Load

Power (Wtake-off VS. Wing Load)

Fig 17 Curve Fit of Wing Load Vs. Aircraft Weight Based On Compiled Aircraft Data CONCLUSIONS Several innovative and challenging concepts for morphing aerospace structures have been presented. Several technologies were combined to generate the concepts and their models in order to conduct first order assessments. The software Working Model2D was used to study the kinematics and dynamics of the several concepts in two dimensions. SOLIDWORKS was used to generate three-dimensional models. An interface software program was used to enter the models into NASTRAN4D where finite element modeling calculations and dynamic animation was performed. Also presented was the application of automated modeling tools such asCAMP-G (Computer Aided Modeling Program with graphical input) to this class of morphing structures. Using the bond graph modeling technique a sliding morphing wing structure was reduced to a state space model, which automatically was exported to MATLAB and SIMULINK. The combination of these analysis tools is necessary to conduct the required calculations for the different evaluation factors introduced in this paper. Results from the combined tools were then fed into a spreadsheet, which in turn produced an evaluation criteria matrix to compare morphing concepts. The evaluation criteria matrix general system modeling, and simulation examples presented have proven to be effective in helping make efficient design decisions prior to making full design commitments. As results indicate, the derived matrix and the selection criteria are capable of providing a relativistic comparison of concept features with ease. The critical factors involved will greatly depend on the skill and experience of those individuals tasked with creating the concepts to insure that sufficient detail and accuracy in system performance is modeled. The aircraft wing data tables and graphs provide a quick reference/comparison for concept evaluation. Since the objective of the graphs is to predict an approximate wing load for the concept wing and an approximate aircraft weight in which these wings can be used, these data tools increase the insight offered into the operational characteristics of the concepts. Having wing load factor values then allows the use of most aerodynamic tables and charts to predict aircraft performance. As with all data derived from general charts and tables, the results are

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approximate and help give an idea of where the design currently stands. For the purpose of relative aerodynamic concept merit evaluation, its accuracy is acceptable. In addition, this exercise has clearly pointed out the effectiveness of existing software programs SOLIDWORKS, WORKING MODEL 2-D, MSC NASTRAN, AND CAMP-G, and MATLAB AND SIMULINK to model and predict complex morphing wing system/concept performance at an early development stage without the need to commit vast amounts of time. Once the most promising concepts have successfully passed these baseline evaluations, more rigorous FEA, kinematics, dynamic, CFD simulations, and prototype development can proceed to arrive at the most optimized and refined morphing wing solutions and applications. Of course this becomes the starting point for prototype and wind tunnel testing, which this time starts on solid ground after several hurdles have been sorted out and the room for error has been reduced or eliminated.

ACKNOWLEDGMENT

The authors acknowledge the ideas of Nick Zentil, Nicholas Haviland, Zachary Schultz, Kamran Aghashiri, Luke Mallat, and Steve Moore undergraduate students at the California State University, Sacramento.

REFERENCES: 1Granda J, Montgomery R. “Automated Modeling And Simulation Using The Bond Graph Method For The Aerospace

Industry” Proceedings of the 2003 AIAA Modeling and Simulation Technologies Conference 11-14 Austin, Texas August 2003

2Karnopp, Margolis, Rosenberg. System Dynamics. Wiley 2000. 3Montgomery R, Granda J. “Using Bond Graphs for Articulated, Flexible Multi-bodies, Sensors, Actuators, and Controllers

with Application to the International Space Station”. Proceedings of the International Conference on Bond Graph Modeling and Simulation ICBGM 2003. Orlando, Florida, January 2003.

4Elramady Alyaa, Granda J.J., “Modal Analysis of the Zvesda Mission of the Space Station With Bond Graphs”

Proceedings of the 2005 Internatinal Conference on Bond Graph Modeling and Simulation. New Orleans, January 2005. 5Quick estimation of wing structural weight for preliminary aircraft design, Aircraft Engineering, February 1972. 6Aircraft Design: A conceptual Approach, third edition, AAIA Education Series published 1999, by Daniel P. Raymer, pg 62

and chapter 15 Pgs 467-480 statistical weight equations and airplane component weights (materials and structures). 7Design of Aircraft, Prentice Hall, Pearson Education, published 2003, by Thomas C. Corke.

8Essentials of Engineering Fluid Mechanics, third edition, Intext Educational Publishers, published 1973, by Reuben M.

Olson. 9Aerodynamics, first edition, Mcgraw-Hill Book Company, published 1946, by A. Wiley Sherwood. 10Binder: Aircraft Data For Concept Wing Load Calculations, Compiled data with web site source information. 11Sandoval, Ignacio. Masters Thesis. Department of Mechanical Engineering, California State University, Sacramento 2005.