American Institute of Aeronautics and Astronautics 1

Investigation of Morphable Wing Structures for Unmanned Aerial Vehicle Performance Augmentation

Kamesh Subbarao*, Abhijit H. Supekar† and Kent Lawrence‡

The University of Texas at Arlington, Box 19018, Arlington, TX 76019-0018

In this paper, we propose a mechanism to continuously morph a wing from a lower aspect ratio to higher and to further extremities of a gull-configuration and an inverted gull- configuration. The mechanism comprises of a linear actuator for the extension of the wing and the servo motors to obtain the gull and inverted gull configurations. The initial design and preliminary finite element representation using just beams and plates were the benchmarks to proceed for the detailed structural analysis of the complete wing. From these results the modified CAD model developed to compute the vibrational mode frequencies to avoid any resonance conditions due to the combined operation of the servo motors and the structure. The preliminary aerodynamic analysis includes using COTS tools, to obtain basic aerodynamic parameters such as the lift curve slope, drag polar and the pitching moment slope as functions of angle of attack at different Reynolds numbers. A morphable balsa wood wing assembly is being built and will be tested in the wind tunnel for moderate operating speeds scaled on the basis of operation of a small sized fixed wing unmanned aerial vehicle (UAV) at the Aerodynamics Research Center, University of Texas at Arlington. These tests include obtaining the forces and moments from a Pyramidal six-component force balance; which are in turn utilized to evaluate the co-efficient of lift, drag and pitching moment at various angles of attack.

Keywords: Adaptive Wing Technology; Biomimetics; Linear Static Analysis; Modal Analysis; CFD;

I. Introduction

HE research and development activities in the adaptive wing technology continues as new ideas in morphing encompass more than the simple span extension or wing twisting initially envisioned. It’s common knowledge

that along a complete mission flight profile of an aircraft, the vehicle is subjected to widely varying aerodynamic conditions; thus traditional vehicle designs are essentially a compromise on aircraft performance due to the conventional fixed wing design. This is so because the design is optimized about a single operating point/regime (for e.g. cruise or loiter, depending on what phase the aircraft spends most of its time in), which leads to a sub-optimal performance at the off-design flight profile. However, utilizing an adaptive wing technology by emulating nature (birds wings, biomimetics), the wing geometry can be adjusted to changing the free-stream and load conditions, thereby allowing one to fully explore the flow potential at each point of the flight envelope and optimize the flight dynamics to a greater extent.

Inspired by bird flight, early aviation researchers have studied avian wings as the basics of developing man-made flight vehicles. This methodology is clearly seen in the work of Lilienthal1and Magnan2. In nature, one observes the relationship between Reynolds number and aerodynamic efficiency in birds where large species soar for extended periods of time while small birds have to flap vigorously (high frequency) to remain airborne. Also, the shape of the wing plays an important role in determining the type of flight of which the bird is capable. This restricts the bird in some ways and enhances the bird in others. Wing shape can be described in terms of two main parameters namely, aspect ratio and wing loading. Amongst birds there are four main kinds of wing types that the majority of birds use, although in some cases wings may fall between two of the categories. These types of wings are elliptical wings, high speed wings, high aspect ratio wings and soaring wings with slots. Additionally, the wing loading for small birds is less than that for large birds.

* Assistant Professor; Mechanical and Aerospace Engineering; Mail Stop 19018; E-mail: subbarao@uta.edu; Member, AIAA † Graduate Student; Mechanical and Aerospace Engineering; Mail Stop 19023; E-mail: abhijit.h.supekar@seagate.com;

Student Member, AIAA‡ Professor, Mechanical and Aerospace Engineering; Mail Stop 19018; E-mail: lawrence@uta.edu; Member, ASME, AIAA

T

AIAA Infotech@Aerospace Conference <br>and <br>AIAA Unmanned...Unlimited Conference 6 - 9 April 2009, Seattle, Washington

AIAA 2009-1829

Copyright © 2009 by Kamesh Subbarao. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

American Institute of Aeronautics and Astronautics 2

Several approaches have been proposed over the years both in theory and in experiments that try to emulate some of the above mentioned bird wing characteristics3-14. The primary aim of the following work is to design and develop a mechanism for a wing to emulate most of the above mentioned characteristics of the bird flight for a single morphable wing and thus suggest a design to optimize the flight characteristics with the dynamic change of wing structure during flight. In spirit, this work is similar to the work carried out in Ref. [6] & [9], although the emphasis here is a systematic wing design and flight performance characterization. Further, Ref. [6] & [9] study a different mechanism for gull wing morphing as well as differential twist in wings for a Micro Air Vehicle (MAV) while the current work only focuses on differential telescoping and gull wing morphing. In addition, the wings are intended to be used in a small sized almost-ready-to-fly aircraft that’s significantly bigger than the MAV and has different actuator requirements.

In summary, it is not the goal of this paper to mimic bird kinematics. Rather, the objective is to select a biologically-inspired system to improve the range of achievable flying conditions for conventional aircraft. The rest of this paper focuses on the motivation, mechanism design and development, structural and vibrational analysis of the wing structure and preliminary CFD results. Future studies and results include the CFD and wind tunnel testing along with the mathematical modeling.

II. Biological Motivation Shape and aspect ratio of the bird wing are its most important characteristics that birds modify to suit the flight phase. Some of the bird flight phases are mentioned below:

a. short, broad, cupped wings for rapid takeoff and short-distance flight b. shorter and broader wings with slotted primary feathers for soaring flight c. flat moderately long, narrow, triangular wings for high-speed flight d. large, distinctly arched wings for flapping flight; long, narrow, flat pointed wings for gliding flight e. pointed, swept-back wings for hovering or motionless flight

The seagulls have been a biological inspiration due to its observed Flight Characteristics like slow low level flying, faster steep descend, differential wing extension, soaring at higher altitudes and a rapid take off. These variable characteristics are most desirable for a UAV being developed for surveillance and reconnaissance missions. The following are the wing shapes observed at the above mentioned flight phases (visual illustration is given by the accompanied photographs§):

1. TAKE-OFF (figure 1)a. higher angle of attack b. gull configuration c. short and high frequency flapping

Figure 1: Seagull taking-off

2. SOARING (at higher altitude) (figure 2)a. long and stretched out wings, hence a higher aspect ratio b. wings slightly above the body of the bird c. wings in a smaller gull configuration d. lower angle of attack

Figure 2: Seagull soaring at higher altitude

3. LOW LEVEL FLIGHT (slow and low level flight) (figure 3)a. wings are not completely stretched out i.e. wingspan is short and hence comparatively broader

§ Photographs presented here, courtesy of Acclaim Images (www.acclaimimages.com)

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b. wings in complete gull configuration (inverted ‘V’) or an inverted ‘L’ type configuration c. slightly higher angle of attack

Figure 4: Seagulls in flight disputing the ownership of a picnic sandwich at the beach

Figure 3: Seagull in a low level Figure 5: Seagull preparing Figure 6: Sea gull showing flight preparing to stoop down to land differential wing extension

4. STEEP DESCEND (figure 4)a. wings pointing downward and slightly swept forward b. negative angle of attack c. wings stretched out

5. LANDING (figure 5)a. higher angle of attack b. gull configuration c. slower flapping d. legs stretched out

Figure 6 shows a Seagull showing the Differential Wing Extension. The right-side wing is completely stretched out versus the left-side wing curled inward. Here, the seagull is preparing to turn left.

III. Mechanism Design and Development

Based on the above observed facts, follows the design and development of a simple 2-link mechanism to emulate the seagull wing:

(a) Shorter and broader wings for rapid takeoff and short-distance flight, and (b) Moderately long (and thus comparatively narrower) wings for high-speed flight.

(i) Un-extended Short and Broad Wing (ii) Telescopically extended long & (comparatively) narrow wing

Link A Link B

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(iii) Gull Wing Configuration (iv) Inverted-Gull Wing Configuration

Figure 7: Preliminary Mechanism Configurations

The morphable wing’s two-link structure is telescopic in nature. The telescopic actuation is performed by a linear actuator consisting of a rack and pinion arrangement driven by continuous rotation (speed controlled) servo motor, thus changing the shorter and broader wings to moderately long. The cross-sectional area remains almost constant but the aspect ratio does change due to the telescopic action. This forms the second case of our study i.e. the “Extended-Wing” configuration, typically used by birds for gliding flight. Thus we obtain a variable aspect ratio wing. It is one of the objectives of this work to observe the changes in the aerodynamic loading due to a dynamic change in the wing aspect ratio. Figure 8a shows the unextended wing configuration modeled in CATIA V5 R15. Link-A is termed as the extendible wing which is stored inside the main wing i.e. the Link-B. Figure 8b shows the extended wing configuration. The extendible wing is in its extreme position and thus has the highest aspect ratio. The figure also shows the ribs and spars that form the basic wing configuration. The fuselage forms the fixed end of the wing. The locations for the servo motors used to obtain the extension as well as the gull mechanism have been specified in the Figure 8b.

Figure 8a: Case 1 – Unextended Wing Configuration Figure 8b: Front-isotropic view of the extended wing configuration

The telescopic actuation is performed by a linear actuator consisting of a rack and pinion arrangement driven by continuous rotation servo motor, thus changing the shorter and broader wings to moderately long. The cross-sectional area remains constant but the aspect ratio does change due to the telescopic action. Figure 8c shows the rack base which also houses the space for the gull-mechanism’s servo motor and bell-crank type arrangement, which would move with the telescopic extension of the wing. The main rod and the gull-mechanism rod form the rotational joints of this wing structure.

Extendible Wing Extension motor

Rack and Pinion arrangement

Push-rods

Gull motor

Figure 8c: Telescopic and gull mechanism It is also observed that for a seagull when in the gull configuration, the angle between the two limbs of the seagull wing is approximately 30o (see Refs. [3], [14]). To morph the aircraft wing to the further extremities of the “Gull”

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and “Inverted-Gull” configurations, we have used a push-rod and a bell-crank type of an arrangement driven by the gull-mechanism servo motor.

Figure 8d: Gull wing configuration Figure 8e: Inverted-Gull wing configuration

Thus a relative motion between the two links of the mechanism is achieved and the angle between the outer main wing and the inner extendible wing can be varied by the push-rods and a servo motor through +60 degrees. Also, the angle between the outer wing and the aircraft structure can be varied by using a bevel gear-set, where the outer wing angle would vary from +30 degrees with respect to the aircraft’s fixed fuselage. The 3D models have been created in CATIA V5 R14 as shown in Figures 8d and 8e. The model is simulated using the I-DEAS NX11 - Mechanism Module to verify the required degrees of freedom for the mechanism to operate.

The preliminary construction is to be tested in the low speed subsonic wind-tunnel and as such based upon the tunnel dimension (width – 36 inches, height – 24 inches and length – 72 inches) the maximum semi-wingspan of the wing was limited to 30 inches to avoid the wall effects of the wind tunnel. The outer wing thus measures up to 20 inches and the inner (telescopic/extendable wing) measures 10 inches span wise. The wing loading for model aircrafts of this size is typically about 18 - 24 oz/sq. ft. A value of 12.8 oz/sq. ft. is assumed initially for design consideration at a flight speed of 33 mph. Further, we note that sea-gulls typically weigh about 5oz - 38oz and fly at a speed ranging between 15 to 38 mph (see Ref. [3]) and this information was additionally used to size the wing structure.

Based on the methodology outlined in Ref. [16] and the density of air, the preliminary sizing is carried out. Note, while the aspect ratio is varied from 5 to 8 (morphing strategy), the wing with aspect ratio 5 is the broader one capable of supporting the model aircraft with more weight, resulting in lesser weight restrictions for the model aircraft and also satisfying the first construction requirement of the wing. With a wing loading of 12.8 oz/sq. ft., the wing is capable of carrying weight up to 36 oz. Further calculations lead us to a wing that has a chord of 9 inches and maximum height of the elliptical cross-section of 1.62 inches (NACA 0018 profile).

During the linear actuation of the telescopic wing, the wing planform area increases and consequently the wing loading decreases, until it reaches the least value of 9.6 oz/sq. ft., when the semi-wingspan equals 30 inches. The angle made by the limbs of typical sea-gull wing is approximately 60 degrees (see Ref. [3]). The mechanism is designed to incorporate this angle between the two links and consequently the angle between the outer wing and the aircraft body is assumed to be 30 degrees. When the wing forms the gull or the inverted gull configurations, the wing loading reduces to 12.22 oz/sq. ft., which is less than the design wing loading value.

IV. Structural Analysis

The preliminary design approach is conservative and hence an elliptical pressure distribution having its aerodynamic center (0.25 times the chord length) of the cross-section was assumed for the structural as well as the actuator calculations of the mechanism. Before constructing the actual 3D model, the analysis for the just basic wing structure was done in ANSYS using 3D spar elements as shown in Figure 9. The material properties of balsa wood were used for these preliminary calculations.

300 300

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Figure 9: Applied boundary conditions for 3D beam elements and plate/shell elements

The deflection after the elliptical loading in the above figure was of the order of 0.43 inches at the farthest end in the un-extended wing position. An improvised model using 3D beam elements and plate/shell elements was created, which further reduced the deflection to 0.15 inches. Here the, actuator along with is components and the extendable part of the telescopic wing were not modeled. These will also add to the global stiffness matrix and thus reduce the deflection. The 3D model then was created in I-DEAS NX11 and CATIA V5 R14 as shown in Figures 10 and 11. The model was simulated using the I-DEAS NX11 - Mechanism module to verify the required degrees of freedom for the mechanism to operate.

Figures 10, 11: Arrangement inside wing structure without motors and gear-sets

Figures 12 and 13 show the case of static analysis of the un-extended wing structure and the telescopically extended wing along with gull configuration as well as the inverted- gull configuration were all performed using ANSYS WORKBENCH. It shows (in red) that the maximum deflection increases from 0.077 inches for the un-extended wing case to 0.036 inches for the case of telescopic extension of the wing.

Figure 12: Maximum deflection of 0.077 inches Figure 13: Maximum deflection of 0.036 inches

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The wing structure was modified at some of the weak components for design safety and stability in vibration. Delrin rods (at the joints) have been used to strengthen the weakest component in the mechanism. Similar to the above two cases of un-extended and extended wing, the maximum deflection and the forces and moments transferred by morphing the wing are shown in Figures 14 and 15. The left figure shows the respective configuration and the right figure shows the deflection obtained after applying the loads. The maximum deflection obtained is shown in red.

Figure 14: Gull configuration along with a maximum deflection of 0.090 inches

Figure 15: Inverted-Gull configuration along with a maximum deflection of 0.087 inches

The forces and moments transferred by morphing the wing dynamically are obtained from ANSYS directly. These results demonstrate the practicality of the structure developed. A maximum Von - Mises Stress of 525 psi is observed in the servo motor foundation for the Gull configuration. The material used here is balsa wood and based on the material properties; the factor of safety obtained is 1.3. Also, the maximum Von - Mises Stress of 691 psi is observed in the Nylon rack used for the telescopic motion. The factor of safety obtained in this case is 9.6. Further, the vibration analysis showed that the lowest frequency amongst the above mentioned configurations was 9.3 Hz for the extended wing configuration.

The above mentioned analysis leads one to size the various motors used for the linear as well as the rotational actuation. We obtain the motor torques from the force analysis of the above configurations. Since the choice of speed for motor actuation is not to change the wing shape rapidly but a gradual change so as to avoid any unnecessary excitation of the structural modes, the motors were chosen to be of a lower frequency than the above. The gear-sets were sized on the similar lines. Nylon (Plastic) spur rack and pinion along with bevel gears, suit the purpose of higher strength to weight ratio. The servo motors torques were obtained to be 17.2 oz-in, 90 oz-in and 343 oz-in for telescopic actuation, varying the angle between inner and outer wing, and varying the angle between outer wing and fuselage respectively.

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V. Computational Fluid Dynamics

The aerodynamic analysis is performed using FLOTRAN developed by ANSYS Inc., to obtain basic aerodynamic parameters such as the lift curve slope, drag polar and the pitching moment slope as functions of angle of attack at different Reynolds numbers. ANSYS FLOTRAN™ is a powerful finite element based CFD analysis tool with steady-state or transient fluid flow and heat transfer capabilities. Conventionally, the aerodynamic characteristics are simplistically modeled as functions of angle of attack to be used later in stability and control analyses as well as flight performance calculations. However with the morphable geometries, it is essential that the aerodynamic characteristics be modeled not only as functions of the angle of attack but also the morphing parameters (such as the angle between the inner and outer wing, wing span, aspect ratio, etc).

The following air flow assumptions were made for the FLOTRAN solution:

a. Steady State b. No-slip at Fluid/Solid Interface c. Turbulentd. Incompressible e. Isothermal f. Subsonic

To verify the accuracy of FLOTRAN solution, analysis was performed on 2D NACA 0018 Airfoil. The section was simulated at an air flow speed of 33 mph i.e. 14750 mm/sec. One of the simulation results for the airfoil at zero degrees angle of attack are shown in figures 16 and 17. Figure 16 shows the Pressure plot. As expected, the red color showing the area of maximum pressure is observed at the point of stagnation seen in the velocity plot depicted in blue color. The symmetry in airflow is as expected to the theoretical results for airflow over a symmetric airfoil. Values for Lift and Drag at each angle of attack are obtained through the nodal integration on the nodes along the Fluid/Solid Interface.

Figures 16 & 17: 2D Airfoil at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

The accuracy results were judged on the basis of the plots of co-efficient of lift and the co-efficient of drag versus the angle of attack in degrees obtained through simulations, in comparison with the Theoretical Co-efficient of Lift versus the Angle of attack in degrees. From Figure 18, it is observed that for a 2D case, the accuracy of the FLOTRAN solution remains constant after about 1000 iterations. The figure also shows that for the FLOTRAN solution, divergence from the linear solution is observed at a higher angle of attack (after 10 degrees) due to the separation of flow at the trailing edge.

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Comparision between 500, 1000 and 2000 Iterations

-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

0 5 10 15 20 25

angle of Attack (degrees)

Co-

effic

ient

of L

ift

cl_500cl_1000cl_2000cl_Theo

Figure 18: Comparison between co-efficient of lift obtained through various iterations for a 2D airfoil

Similar procedure is being verified for a 3D case for an infinite wing. For a 3D case, about 1500 iterations are assumed to be sufficient. The section in all the figures below is taken at 25% of the chord to show the span-wise symmetry in the pressure and the velocity distribution at zero degrees angle of attack at various configurations. The dark blue region in the pressure plots (left) corresponds to the high velocity region in the velocity plots (right).

The following results are obtained for a 3D case of an Infinite Wing at zero degrees angle of attack.

Figure 19 & 20: 3D Infinite Wing at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

Figure 21 shows a comparison between co-efficient of lift obtained through theoretical calculations versus those values obtained from FLOTRAN. The span efficiency factor of 0.75 is used for the theoretical calculations.

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1500 Iterations

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 2 4 6 8 10 12

Angle of Attck (degrees)

3D_cl_15003D_cd_1500Infinite_wing_Theo_clFinit_wing_Theo_cl2D_cl_10002D_cd_1000

Figure 21: Comparison between co-efficient of lift obtained through various iterations for a 3D airfoil versus the Theoretical results

As expected, the drag obtained in the 3D infinite wing case is greater than obtained in the analysis of the 2D airfoil. The following results are obtained for a 3D case of an un-extended wing at zero degrees angle of attack. An elliptical pressure distribution is observed at the quarter chord verifying the assumption made for the initial wing design calculations. This wing is shorter and broader, with a lower aspect ratio.

Figure 22 & 23: 3D Un-extended Wing at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

The following results are obtained for a 3D case of an extended wing at zero degrees angle of attack. These plots are similar to the above results from the simulation for an un-extended wing. The difference lies in the lift and the drag due to the telescopic extension. This wing is moderately long (and thus comparatively narrower) with an increase in the aspect ratio.

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Figure 24 & 25: 3D Extended Wing at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

The following results are obtained for a 3D case of a wing in Gull Configuration at zero degrees angle of attack. These plots show the change in the pressure distribution over the wing surface due to morphing it to Gull configuration.

Figure 26 a & 27 a: 3D Wing in Gull Configuration at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

Figure 26 b & 27 b: 3D Wing in Gull Configuration at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

The following results are obtained for a 3D case of a Wing in Inverted-Gull Configuration at zero degrees angle of attack. These plots show the change in the pressure distribution over the wing surface due to morphing it to Gull configuration.

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Figure 28 a & 29 a: 3D Wing in Inverted-Gull Configuration at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

Figure 28 b & 29 b: 3D Wing in Inverted-Gull Configuration at zero deg angle of attack showing Pressure Plot (left) and Velocity Plot (right)

Based on these results a mathematical model will be developed for the lift curve and the pitching moment as a function of the angle of attack as well as the configuration parameters for the Gull and the Inverted-Gull cases. This mathematical model will finally be validated via wind tunnel tests on an in-house manufactured balsa wood wing at low speed subsonic conditions (quasi steady conditions).

VI. Balsa Wood Wing Prototype

The prototype of the wing along with the mechanism described in section III is being developed at the Aerodynamics Research Center, University of Texas at Arlington. As a part of the mechanism, Nylon (Plastic) spur rack and pinion along with bevel gears, suit the purpose of higher strength to weight ratio. The servo motors torques were obtained to be 17.2 oz-in, 90 oz-in and 343 oz-in for telescopic actuation, varying the angle between inner and outer wing, and varying the angle between outer wing and fuselage respectively.

The Balsa Wood was bought from Hobby Lobby Inc. and National Balsa Co., the FUTABA servo motors were procured from Hobby Town Inc. and the plastic gears were bought from Quality Transmission Components and Stock Drive Products / Sterling Instruments. The following photographs show the progress on its development:

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Figure 30 & 31: The Balsa Wood Wing from the Front View (right) and the Side View (left) clearly showing the Wing Nose, Spars, the Extension Mechanism, Cross-sectional supports and Wing Tail

Figure 32: The Balsa Wood Wing along with the 3 servo motors placed at their operating locations.

The development of the entire wing is a part of the future work to be carried out.

VII. Wind Tunnel Tests The balsa wood wing will be tested in a Low Speed Wind Tunnel at the Aerodynamics Research Center,

University of Texas at Arlington. A six-component small pyramidal balance measures the Lift, Drag, Side Force, Pitching Moment, Yawing Moment and Rolling Moment for the mounted wing. This strain gauge balance system si used to support a wing model in a wind tunnel, adjust its angle of attack over a plus-minus 25 degree range, adjust its angle of yaw over a 360 degree range and separate and measure the six force and moment components which determine the resultant force exerted by the air stream on the model. The components are separated mechanically and measured through individual strain gauge load cells and readout is accomplished through appropriate electrical equipment. Component ranges of minus 50 to plus 100 pounds in Lift, minus 50 to plus 50 pounds in Drag and Side Force, minus 100 to plus 100 inch pounds in Rolling, Yawing and Pitching moments are recommended although overloads of at least 50% may be sustained. Adjustable stops on each load cell limit the deflection to a safe value (Ref. [17]). The wind tunnel test results are a part of the future work.

VIII. Future Work & Summary Along with initial calculations and using deflection results from ANSYS a Static Divergence Speed will be

calculated. Also, based on the results of the CFD analysis, a mathematical model will be developed for the lift curve slope, drag polar and the pitching moment slope as functions of angle of attack at different Reynolds numbers. This numerical model will finally be validated via wind tunnel tests on an in-house manufactured balsa wood wing at low speed subsonic conditions (quasi steady conditions). A mathematical model will then be developed to be used to

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estimate the UAV flight performance as well as stability and control characteristics. Finally, the objective to characterize the vehicle dynamic response as well as the aerodynamic benefits (improved control authority) is thus achieved via differential telescopic extension and change in gull angle configuration (symmetric as well as asymmetric).

References 1Lilienthal, O., “Birdflight as the Basis of Aviation”, Markowski International, Hummestown, PA, 2001. 2Magnan, A., “Bird Flight and Airplane Flight”, NASA TM-75777, 1980. 3P J Grant, “Gulls- A Guide to Identification”, Princeton University Press; 2nd edition (August 1, 1997) 4Leonard D. Wiggins, Matthew D. Stubbs, Christopher O. Johnston, Harry H. Robertshaw, Charles F. Reinholtz,

and Daniel J. Inman, “A Design and Analysis of a Hyper-Elliptic Cambered Span (HECS) Wing”, 45th

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 19 - 22 April 2004, Palm Springs, California

5Egon Stanewsky, “Aerodynamic benefits of adaptive wing technology”, Aerospace Science and Technology (1270-9638). Vol. 4, no. 7, pp. 439-452. Oct. 2000

6Mujahid Abdulrahim, Helen Garcia, Gregory F. Ivey, and Rick Lind, “Flight Testing A Micro Air Vehicle - Using Morphing For Aeroservoelastic Control”, AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, Aug. 11-14, 2003

7GregW Pettit, Harry H. Robertshaw and Dan J. Inman, “Morphing wings for unmanned aircraft”, Smart Materials Bulletin, Feature Article, November, 2001

8Jae-Sung Bae , T. Michael Seigler, Daniel J. Inman, In Lee, “Aerodynamic and Aeroelastic Considerations of A Variable - Span Morphing Wing”, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference; Palm Springs, CA; Apr. 19-22, 2004

9Mujahid Abdulrahim and Rick Lind, “Flight Testing and Response Characteristics of a Variable Gull-Wing Morphing Aircraft”, AIAA Guidance, Navigation, and Control Conference and Exhibit 16 - 19 August 2004, Providence, Rhode Island

10Helen M. Garcia , Mujahid Abdulrahim and Rick Lind, “Roll Control for a Micro Air Vehicle using active wing morphing”, AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, Texas, Aug. 11-14, 2003

11Spillman, J., “The Use of Variable Camber to Reduce Drag, Weight and Costs of Transport Aircraft”, Aeronautical Journal, Vol. 96, Jan. 1992, pp. 1-8.

12Blondeau, J., Richeson, J., and Pines, D.J., “Design, Development and Testing of a Morphing Aspect Ratio Wing Using an Inflatable Telescopic Spar”, AIAA Paper 2003-1718, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference and Exhibit, Norfolk, VA, April 7-10, 2003.

13Cone, C. D., “The Aerodynamic Design of Wings with Cambered Span Having Minimum Induced Drag”, NASA TR-R-152, 1963

14Tianshu Liu, K. Kuykendoll, R. Rhew, and S. Jones, “Avian Wing Geometry and Kinematics”, AIAA Journal Vol. 44, No. 5, May 2006

15Peter G. Ifju, David A. Jenkins, Scott Ettinger, Yongsheng Lian, Wei Shyy, Martin R. Waszak, “Flexible-Wing-Based Micro Air Vehicles”, AIAA 2002-0705, AIAA Aerospace Sciences Meeting and Exhibit, 40th, Reno, NV, Jan. 14-17, 2002

16Andy Lennon, “Basics of R/C Model Aircraft Design – Practical Techniques for building better models”, Published by Air Age Inc.

17http://maepro.uta.edu/arc/ (Aerodynamics Research Center), University of Texas at Arlington