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Suleman Camber Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Published by: http://www.sagepublications.com can be found at:Journal of Intelligent Material Systems and StructuresAdditional services and information for http://jim.sagepub.com/cgi/alertsEmail Alerts: http://jim.sagepub.com/subscriptionsSubscriptions: http://www.sagepub.com/journalsReprints.navReprints: http://www.sagepub.com/journalsPermissions.navPermissions: http://jim.sagepub.com/content/22/10/1057.refs.htmlCitations: What is This? - Aug 1, 2011 OnlineFirst Version of Record - Sep 13, 2011Version of Record >> at Monash University on December 5, 2014jim.sagepub.comDownloaded from at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ http://jim.sagepub.com/content/22/10/1057 http://www.sagepublications.com http://jim.sagepub.com/cgi/alerts http://jim.sagepub.com/subscriptions http://www.sagepub.com/journalsReprints.nav http://www.sagepub.com/journalsPermissions.nav http://jim.sagepub.com/content/22/10/1057.refs.html http://jim.sagepub.com/content/22/10/1057.full.pdf http://jim.sagepub.com/content/early/2011/07/30/1045389X11416031.full.pdf http://online.sagepub.com/site/sphelp/vorhelp.xhtml http://jim.sagepub.com/ http://jim.sagepub.com/ Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber J. VALE,1 A. LEITE,1 F. LAU1 AND A. SULEMAN2,* 1IDMEC-Instituto Superior Tecnico, Lisbon, Portugal 2Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada ABSTRACT: An aero-structural design and analysis study of a telescopic wing with a con- formal camber morphing capability is presented. An aerodynamic analysis of a telescoping wing, first with a high speed airfoil followed by an analysis with a low speed airfoil is per- formed. The data obtained from these analyses is used to determine the optimum polar curves for drag reduction at different speeds. This information in turn provided the background for devising an optimal morphing strategy for drag reduction assuming that the telescoping wing airfoil has the capability to step morph between the high and low speed airfoils. Next, a conformal camber morphing concept is introduced. The concept is based on a non-uniform thickness distribution along the chord of a wing shell section that deforms from a symmetrical airfoil shape into a cambered airfoil shape under actuation. Structural optimization based on finite element models is used to obtain the shell thickness distribution for minimum shell section weight and best airfoil shape adjustment. Finally, a comparison study between the performance of an aircraft equipped with a morphing wing (telescopic wing combined with conformal camber morphing) and the performance of the same aircraft equipped with an optimized fixed wing for 30m/s cruise speed and 100N weight is presented. Aerodynamic optimization based on computational fluid dynamics models is used for the optimum fixed wing geometric parameters calculations. The optimal wing configurations for various perfor- mance parameters are calculated. The morphing wing generally outperforms the optimum fixed wing with the exception of a 10% reduction in rate of climb and 4% drag penalty at 30m/s cruise speed. Key Words: morphing, piezoelectric, actuator, control. INTRODUCTION MORPHING wings are a topic of recent researchinterest in aerospace engineering. Morphing solu- tions are intended to enable aircraft to adapt to different flight conditions, by changing their geometrical shape at different stages of flight as observed in bird flight. The goal is to improve efficiency of flight, to enable multiple mission profiles by the same aircraft, and to enlarge the flight envelope. The Wright brothers in 1899 explored ways to control the roll of the flyer by twisting the air- craft wing to produce lateral control. This became known as wing warping. Monner and Opitz (2009) have presented a compre- hensive review on the history of morphing efforts since 1990, including the morphing aircraft efforts that emphasized ‘smart materials’ and flow control device development. The NASA morphing program furnished valuable technologies, most of which await systems applications. Most importantly, this program, which was completed in 2004, identified a range of research that may have practical applications in aircraft design in the future. Concepts like camber variation along span (Manzo, 2006), lateral control via variable cant angle winglets (Bourdin et al., 2008), variable span wings (Bae et al., 2004), morphing airfoils (Secanell et al., 2006; Kerho, 2007), variable wing sweep (Hall et al., 2005), simultaneous variable span and chord (Aleixo et al., 2007; Gamboa et al., 2009), pneumatic telescopic wings (Blondeau and Pines, 2007), and rubber skin wings (Vale, 2007) have been studied in recent years. Other recent developments have led to wind tunnel testing and validation of two different concepts: a fold- ing wing from Lockeed Martin morphing concept (Ivanco et al., 2007; Chase, 2009) and the NextGen bat-wing morphing concept (Bowman et al., 2007; Flanagan et al., 2007; Love et al., 2007; Kudva, 2009). These projects proposed innovative, multi-mission air- crafts that were tested up to transonic speeds in the NASA/Langley transonic dynamics wind tunnel (TDT). *Author to whom correspondence should be addressed. E-mail:
[email protected] Figures 1�16 appear in color online: http://jim.sagepub.com JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 22—July 2011 1057 1045-389X/11/10 1057�17 $10.00/0 DOI: 10.1177/1045389X11416031 � The Author(s), 2011. Reprints and permissions: http://www.sagepub.co.uk/journalsPermissions.nav at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ Chase suggested supersonic designs that would require morphing innovation and, if successful, provide multi- mission unmanned air vehicles in the future. The NextGen prototype flew successfully and allowed vari- able sweep and span, while also increasing the wing area in some configurations by using a silicon skin which could stretch and increase wing area; however, it was not able to deliver an efficient airfoil shape. Turnok et al. (2009) and You and Crabtree (2009) have reported useful perspectives into design issues on the mechanisms for morphing, namely the importance of actuator selection and power requirements for successful system operation. Turnok discussed snap-through com- posite devices as one way of minimizing power require- ments and demonstrated an application to wing surface cambering. You and Crabtree discussed ideas for truss- like configurations that can lead to large shape change. Kota et al. (2009) introduced on a compliant trailing edge flap which has recently become a practical solution. Pendleton et al. (2009) have reported on the U.S. Active Aeroelastic Wing (AAW) project. The objective here was to take advantage of torsional aeroelasticity of the wing and the airstream to deform the wing in order to obtain lateral control. Although the program was com- pleted several years ago, the knowledge gained from the AAW project remains relevant. Attar et al. (2009) and Liu et al. (2009) addressed the aeroelasticity of rapidly changing morphing geometry on structural configurations. Attar et al. (2009) were concerned with identifying new instability phenomenon early in the design process while Liu et al. (2009) addressed the need for an unsteady aerodynamics method to accurately predict unsteady airloads for stress and dynamic response calculations. In this article, an aero-structural computational design, analysis, and optimization of a telescoping wing with conformal camber morphing is presented. The major contribution of the present article is on the quantification of performance parameters of a complete aircraft with a morphing wing (variable span and camber) compared to the case of an aircraft designed with a wing optimized for cruise. The results presented provide a contribution to the state-of-the-art in morph- ing aircraft by identifying the flight segments that most benefit from the morphing solutions. TELESCOPIC WING DESIGN The telescoping wing can continuously change the wing span by having an inner wing that slides in and out of the outer wing. For the case in this study, the inner and the outer wings have a 1m semi-span and the inner wing can be further deployed up to a maximum of 0.75m. The structural solution adopted to achieve the variable span capability consists of a hollow outer wing which supports loadings by having leading and trailing edge composite carbon fiber reinforcement as well as composite carbon fiber reinforcements evenly spaced along the span to substitute conventional ribs. From the leading and trailing edge to the interior of the outer wing there are carbon fiber structures for sup- port and sliding guidance of the leading and trailing edges of the inner wing. The inner wing is a conventional wing with fixed ribs and a fixed spar. Both wings are covered with carbon fiber composite shells and actua- tion is done by attaching the mechanism to the inner wing and forcing the relative movement between inner wing and outer wing spars. Figure 1 illustrates the morphing wing span increase sequence. The wing is designed for a 98N MTOW. The struc- ture is designed to withstand approximately 290N (145N for half wing) of lift and the respective drag, corresponding to approximately 3 g loading when fully extended. Coupled Field Analysis In order to computationally represent a telescopic wing, and assuming a quasi-static behavior, several dis- crete models that simulate the wing at various span con- figurations have been created. These configurations are representative of the wing behavior in static conditions and are shown in Table 1. The models were used first for the dimensioning of the morphing wing structure and then for the aerodynamic performance quantification. Figure 2 shows the FEM and CFD meshes used for the coupled field analysis using Ansys-CFX� software (Ansys Inc., 2007a, b). Coupled field analysis or multifield analysis is a com- bination of analysis from different engineering disci- plines that interact with each other to solve a global Figure 1. Span increase sequence. 1058 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ engineering problem, where the input of one field depends on the results from another. In a fluid-structure analysis, the fluid pressure causes the structure to deform, which in turn causes the fluid solution to change and therefore interaction between the two physic fields is required to achieve a converged solution. This interaction is simulated using the FEM code to solve the structural problem with the loads provided by the CFD code calculation, which in turn receives from the FEM code the displacements of the relevant nodes to calculate new aerodynamic forces. A convergence study, based on the airflow at 30m/s and a wing angle of attack of 8�, in a domain that extends 4 chords length upstream from the leading edge, 8 chords length downstream from the leading edge, 4 chords length above and below the leading edge, and 2.5 spans length spanwise, led to a CFD mesh of 12,67,779 elements. The CFD code solves the unsteady Navier�Stokes equations in their conservative form with the finite volume method. Near wall prism layer elements were used for refinement around the wing and a k-" turbu- lence model was used. For the FEM mesh the convergence study based on maximum deformation and maximum Von Mises stress led to a mesh with a total of 98,750 elements, of which the majority is of shell type for the simulation of wing skin and ribs. Beam elements are used for simulation of the spars. Detailed descriptions of the model character- istics and analysis procedures can be found in Leite (2008). It was observed that as long as the wing structure is sufficiently stiff in order to prevent structural failure, differences in CD due to structural deformation do not exceed 3% and are much lower for CL. Therefore, aero- elastic effects are negligible in these static analyses and coupled field analysis is unnecessary to determine the aerodynamic coefficients. Thus, only aerodynamic anal- yses were performed for the telescoping wing. Telescoping Wing with a High Speed Airfoil The high speed airfoil for the telescoping wing studied considered here is the NACA0012. This airfoil is Figure 2. Internal structure mesh (left) and wing deformation at approximately 3 g loading (145.3 N, 8� AOA fully extended) and the fluid field model mesh. Table 1. Morphing wing configurations. Outer wing chord (m) Inner wing chord (m) Half wing span (m) 0.22 0.20 1.00, 1.25, 1.50, 1.75 Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1059 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ generally used for high speed flight due to its symmetry and low relative thickness. Figure 3 shows the polar CD versus CL curves for the four different telescoping wing configurations in level flight at sea level. Each curve represents a different wing span. The lift and drag coef- ficients are calculated using the maximum wing area configuration of the telescoping wing. As expected, some configurations are more efficient than others, depending on the CL required for flight. Because the CL and CD coefficients are calculated using always the same wing area, the required CL for level flight depends directly on the airspeed. As airspeed increases, the required CL decreases, and there are points where the curves cross each other, which means that a new configuration will reduce drag from that air- speed value on to higher airspeeds. Therefore, it is pos- sible to create an approximation to the optimum polar curve for the telescopic wing by selecting the sections of the polar curves between the crossing points with the adjacent configurations polar curves, as shown in Figure 4. Changing from maximum to minimum span results in a stall speed increase of 36.2% (10� AOA) and wing drag reduction of 62.3% at maximum speed (CL< 0.1). Telescoping Wing with a Low Speed Airfoil Now, consider a telescoping wing with a high maxi- mum lift coefficient for better low speed performance such as the Eppler-434. Using CFD models and the same methodology as for the low speed case, the polar curves for different span configurations were obtained, as shown in Figure 5. The optimal polar curve for the telescoping wing with Eppler-434 airfoil is shown in Figure 6. Changing from maximum to minimum span results in stall speed increase of 31.9% (10�AOA) and wing drag reduction of 73.4% at maximum speed (CL< 0.1). 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1m Wing polar curves for configurations with NACA0012 airfoil Half span 1.25m Half span 1.5m Half span 1.75m 1 1.2 Figure 3. Polar curves of the telescopic wing with NACA0012 airfoil for different span configurations. 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1m, NACA0012 Optimum polar curve for drag reduction (NACA0012) Half span 1.5m, NACA0012 Half span 1.25m, NACA0012 Half span 1.75m, NACA0012 1 1.2 Figure 4. Optimum polar curve for telescopic wing with NACA0012 airfoil. 1060 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ Morphing Strategy Figure 7 compares the two telescoping wings with high and low speed airfoils. It is clear that the airfoil influences significantly the high and low speed perfor- mance of the telescopic wing. Using the same reasoning used to find the optimal polar curves for each telescop- ing wing with the high and low speed airfoils, we can now find the optimal polar curve assuming it is possible to perform a step change in the airfoil shape from Eppler 434 to NACA0012. Figure 8 clearly shows the morphing strategy for level flight of an aircraft with a telescoping wing that allows changing the airfoil. The aircraft should take off with maximum span and with the Eppler-434 airfoil configu- ration, increase speed maintaining the airfoil and reduc- ing the span and change the airfoil to NACA0012 when the inner wing is fully retracted at high speed. The inverse strategy should be used as speed decreases. Table 2 summarizes the morphing strategy. This procedure is a rough graphical optimization for a morphing strategy that does not include the influence of the remaining parts of the aircraft on the drag perfor- mance but is useful as a starting point to assess the pos- sible benefits of changing configuration in cruise. For instance, changing from Eppler-434 to NACA0012 at high speeds (low CL values) leads to a reduction in wing drag up to 30.1%, while increasing span in 75% at low speeds with Eppler-434 allows an increase in pay- load of 5.8% along with a 3.3% drag reduction rela- tively to the telescoping wing with NACA0012. These benefits encourage the development of a camber morph- ing concept described next. CAMBER MORPHING Camber change has been successfully used in general aviation for many years. The use of flaps and leading edge devices with various degrees of complexity to change wing camber (and to increase chord) is 0.1 0.08 0.07 0.05 0.03 0.01 0.09 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1m Wing polar curves for configurations with Eppler-434 airfoil Half span 1.25m Half span 1.5m Half span 1.75m 1 1.2 Figure 5. CD vs CL curves of the telescopic wing with Eppler-434 airfoil for different span configurations. 0.1 0.08 0.07 0.05 0.03 0.01 0.09 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1m, Eppler434 Optimum polar curve for drag reduction (Eppler-434) Half span 1.25m, Eppler434 Half span 1.5m, Eppler434 Half span 1.75m, Eppler434 1 1.2 Figure 6. Optimum polar curve for telescopic wing with Eppler-434 airfoil. Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1061 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ common with the goal of increasing lift at low speeds and allowing take-off and landing on shorter runways (Shea and Smith, 2008). This is normally achieved with some penalty in the maximum AOA, and at the expense of a higher drag and sacrifice of the wing’s efficiency, that is, reducing the maximum lift-to-drag ratio (L/D). Such drag penalties or significant reductions in max- imum AOA (as would happen in leading edge devices without slots) are due to discontinuities in the airfoil shape (in the case of flaps) or boundary layer separation at low AOA (in the case of leading edge devices). To mitigate such penalties, slots are introduced, both in flaps or leading edge devices, to help maintain a smooth aerodynamic flow around the wing and prevent flow separation (Coiro et al., 2009; Marquez et al., 2009). The objective of these devices is to adapt the air- craft to different flight conditions, namely take-off and landing, for which they have been designed and devel- oped since the onset of early aviation. In this context, the benefits of increasing camber with- out creating discontinuities in the airfoil shape and how it can be applied to a telescopic wing is discussed next. 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1.25m, Eppler434 Half span 1.5m, Eppler434 Half span 1.75m, Eppler434 Optimum polar curve for drag reduction (Step change in airfoil shape assumed) Half span 1m, NACA0012 1 1.2 Figure 8. Optimum polar curve for telescoping wing assuming a step airfoil shape change. 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1m, Eppler434 Half span 1.25m, Eppler434 Half span 1.5m, Eppler434 Half span 1.75m, Eppler434 Optimum polar curves for drag reduction (Eppler-434 and NACA0012) Half span 1m, NACA0012 Half span 1.25m, NACA0012 Half span 1.5m, NACA0012 Half span 1.75m, NACA0012 1 1.2 Figure 7. Optimum polar curves for telescopic wing with Eppler-434 and NACA0012 airfoils. Table 2. Summary of morphing strategy for level flight. CL Airfoil Half span (m) AOA (�) CD � 0.284 NACA0012 1.00 0�5.92 0.011�0.017 0.284�0.441 Eppler 434 1.25 0.85�3.62 0.017�0.024 0.441�0.702 Eppler 434 1.5 2.28�6.00 0.024�0.036 0.702�1.230 Eppler 434 1.75 5.01�12 0.036�0.086 1062 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ Figure 9 presents the polar curves of two wings with the same span and different camber airfoils: the NACA0012 symmetric airfoil and the NACA7312 with 7% maxi- mum camber. Both airfoils have the same relative thick- ness. The curves illustrate how increasing the airfoil camber can be beneficial when higher CL values are required, not only because of a higher CL value before stall but also because of a higher lift-to-drag ratio. This is true because the two curves are related to smooth airfoils without discontinuities. An aileron or flap gen- erally increases CL but decreases the lift-to-drag ratio. In the case illustrated in the figure, changing from NACA0012 to NACA7312 increases the CL at an AOA of 10� by 53.1% while the maximum lift-to-drag ratio increases by 34.9%. Design of a Conformal Camber Morphing In a telescoping wing, issues related to the design and implementation of flaps and/or leading edge devices arise (Han et al., 2007; Samuel and Pines, 2007) due to an increase in system complexity, or when using camber change without the loss of wing efficiency at higher speeds. The use of a conformal camber change presents several advantages: . Camber change without loss of efficiency would allow the wing to produce the required lift at different cruise speeds with smaller changes in the AOA, allow- ing fuselage drag to be minimized in these flight con- ditions and cockpit visibility could be enhanced by mounting the wing in a proper position. . Camber change without loss of efficiency would allow adaptation of the wing to high speeds (symmetric air- foils) and low speeds (cambered airfoils), without compromizing one or the other. . In a telescoping wing, use of flaps or ailerons is com- plex or impossible. To have an aileron/flap type other than the split flap implies using an inner wing chord much smaller than the outer wing chord, resulting in less lifting surface. Camber change without loss of efficiency would allow substitution of flaps. . Also for a telescopic wing, aileron position would be at maximum in the tip of the outer wing, which would produce less roll ratio when the wing is extended and rotational inertia is higher. Camber change without loss of efficiency would allow substitution of ailerons in roll control. The requirements of the telescopic wing described above imply that any mechanism intended to change the camber of the airfoil of the outer wing has to fit in the narrow space between the outer and inner wing, if actuation is to act directly on the skin or ribs of the wing. There is no point in changing the camber of the inner wing without changing the camber of the outer wing, because, in that case there will be interference between the inner and outer wing, even when the wing is fully extended, unless the inner wing chord is much smaller than the outer wing chord. One solution consists of using a composite wing skin with embedded actuators such as piezoelectric patches or shape memory alloy strings among the fiber, but the actuation density needed to achieve the desired airfoil shape would possibly be high, and the increase in con- trol complexity could also be prohibitive. On the other hand, the usefulness of having a mechanism that allows radical changes in airfoil shape is questionable, since the possible aerodynamic benefits would most likely be overcome by the penalties inherent to the probable high actuation density. Following an incremental capability approach, the goal here is to add a moderate camber morphing capa- bility, aerodynamically more efficient than flap, without adding prohibitive complexity to the telescoping wing. The choice was to approach the airfoil shape of a NACA0012 without actuation and a NACA7312 when fully actuated or vice versa, thus varying the airfoil camber from 0 to 7%, and with the expectation that the camber change is smooth along the course of actu- ation, which was likely to be true and verified after- wards. The choice of this airfoils family was based on previous work done in studying these airfoils (Secanell et al., 2006) and therefore on data availability. Any other family of airfoils could be chosen as long as there is a possible correlation between actuation and geometrical changes. The basic idea is to actuate a shell with the shape of one airfoil and a specific thickness distribution that deforms (or morphs) into the other airfoil shape as illus- trated in Figure 10. In order to achieve this, one has to observe the airfoils and figure out what could hinder the morphing from one shape to the other: . The airfoil cannot be clamped to the fuselage at all points in the wing root. It is critical that the wing root 0.08 0.07 0.05 0.03 0.01 0.09 0.06 0.04 0.02 0 0 0.2 0.4 0.6 CL C D 0.8 Half span 1.33m NACA 7312 Half span 1.33m NACA 0012 Wing polar curves for 1.33m half span configurations 1 1.2 Figure 9. Polar curves for two wings with same span and different camber airfoil. Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1063 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ varies camber. Otherwise the �CL is critically reduced at low speeds and also there would be the problem of fitting the inner wing inside the outer wing with varying camber along the span. . The spar cannot be clamped to the fuselage either. For load transfer from the wing skin (shell) to the spar, the spar must be connected to the shell in some way, and if the shell deforms, the spar should be allowed to follow the deformation. . The deformed shell has to be able to sustain its shape under loading and to within some limits around the desired shape. This means that a base thickness should be used for load bearing. . The base thickness of the shell should be a compro- mize between shell weight, actuation force, and load- bearing capability. If any of these three items is out- side the acceptable range, camber morphing will not be practical. . The length of the upper side of the cambered NACA7312 is higher than the length of the lower side and the length of the symmetric NACA0012 upper and lower sides is in between them. Trying to morph NACA7312 into NACA0012 or vice versa would be very difficult, since the leading edge of either airfoil would have to be flattened to morph into the other (Figure 11). That would make it expen- sive in terms of actuation energy and power since the leading edge has to be stiff enough to withstand the loading without significant deformation. Also, there would be a significant change in the wing’s mount angle (1.5�) when morphing form one airfoil to the other. The last issue raised in an important one, since if no solution is found, it is not feasible to perform the airfoil morphing and the other issues become redundant. The lengths of the upper and lower sides of NACA7312 rel- ative to the length of one side of the NACA0012 are shown in Table 3, as well as the change in maximum camber if the NACA0012 was modified to have the upper and lower sides with the same length as the upper and lower sides of NACA7312. The maximum camber is less than 0.4% and the aero- dynamic differences to the original NACA0012 are expected to be very low. The most significant differences occur in the trailing edge, where the boundary layer is thicker; so the geometrical changes should not be impor- tant to aerodynamics. A feasible solution to circumvent these issues is to sacrifice the perfect symmetry of NACA0012 and modify it to the shape shown in Figure 12. This way the leading edge does not need to be flattened and the change in the mount angle would not be so high. The camber morphing concept is therefore based on having a shell with the shape of a slightly modified Figure 10. The morphing sequence and the comparison between NACA0012 and and NACA7312 airfoils: CL vs AOA (Hepperle, 2006 a). Figure 11. NACA0012 leading edge intersecting NACA7312 at half length of the NACA7312 total perimeter length. The leading edge of NACA0012 would have to be flattened to morph into NACA7312 airfoil. 1064 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ airfoil to meet the upper and lower side lengths of the airfoil it is going to morph to, and actuate it by joining the upper and lower trailing edges, taking advantage of the thickness distribution to guarantee the morphed air- foil shape. It was decided to morph from the symmetric to the cambered airfoil for safety reasons. The symmet- ric one is supposed to be used at higher speeds and therefore it has higher probability of being subjected to higher loadings when unpredictable situations occur. Having an already stressed structural member in this situation is not advisable. Airfoil Thickness Distribution for Conformal Camber Morphing Finding the thickness distribution along the shell in order to morph from one airfoil shape to the other is a relatively simple task, involving optimization and FEM analysis. The optimization processes minimizes the weight of the shell while maintaining its actuated shape close enough to the NACA7312 airfoil with or without aerodynamic loading. This requirement addresses some of the issues raised above. Table 4 summarizes the FEM model material, geometrical, and load data. The aerodynamic loading was obtained using a one- way coupled FEM-CFD analysis for the NACA7312 air- foil with an AOA of 10� at 15m/s. This pressure loading is integrated and applied directly to the nodes of the FEM model. The nodal load is then scaled to represent the lift that the rib has to withstand when the wing is making a 3 g turn The design variables include the two thickness distri- butions as functions of the spatial coordinate x that lies along the chord of the modified NACA0012 airfoil. Each of the thickness distribution functions is for the upper and lower side of the shell, respectively. The upper side thickness distribution function starts at x0¼ 0 with thickness h0. From xi to xiþ1, the thickness varies line- arly form hi to hiþ1, for i¼ 1 to 4. The lower side thick- ness distribution function is described in the same way by replacing the index i¼ 1 to 4 by i¼ 5 to 8. Note that the design variables xi can exceed the chord of the air- foil, in which case it means that the number of design variables may exceed what is needed. The lower limit imposed on the thickness distribution is based on the requirements stated earlier. The base thickness should guarantee good load-bearing capability and acceptable actuation force and weight. A sensitivity study led us to choose 0.5mm as the minimum value. Geometrical limitations impose a maximum of 3mm in thickness since the inner wing chord should not be too small and this thickness value imposes an inner wing chord 20% smaller than the outer wing chord. At the leading edge the thickness upper limit is 2mm to allow the accommodation close to the leading edge of a circu- lar section spar with the maximum diameter possible. For geometrical constraints, it is imposed that the average absolute error in the position of the nodes of the deformed shell relative to the expected shape at the shell root section is less than 0.6mm (2% of maximum thickness), and that the maximum absolute error does not exceed 1.2mm (4% of maximum thickness). A tol- erance of 0.005mm for these constraints is allowed. Actuation energy constraints are based on limiting the maximum actuation power needed. This maximum is assumed to occur when actuation is deforming the shell (and not returning to the undeformed state) at the limit of maximum deformation. Since actuation energy in this case is related to deformation energy, and the deforma- tion energy is proportional to the quantity of material in the shell, it is assumed that minimizing shell weight will minimize the energy required. Also the force required is proportional to the bending stiffness of the shell. Minimizing shell weight by changing its thickness, as in this case, will therefore minimize the required force, thus minimizing power requirement. For these reasons no explicit actuation power or force constraint is applied. For structural constraints, it is imposed that the Tsai�Wu index does not exceed 0.85with orwithout load- ing,meaning that nomore than 85%ofmaximum stresses are reached. A tolerance of 0.5% is allowed for this con- straint. The optimization problem is stated inTable 5. The value of c is the length of the upper side chord. Table 4. FEM model material, geometrical and load data. Material - Bidirectional carbon fiber-epoxy composite Young’s modulus (GPa) Ex¼60 Ey¼ 60 Ez¼ 20 Density (kg/m3) 1600 Failure criteria �x¼ 250 �y¼ 250 �z¼ 35 (Max. stress)(MPa) �xy¼ 20 �yz¼20 �xz¼ 20 Geometry Upper side chord (m) 0.261 Lower side chord (m) 0.246 Shell span (m) 0.025 Loading 3 G Loading (N) Fx¼�5.99 Fy¼42.94 Fz¼�0.12 Table 3. Length ratios of the upper and lower sides of the NACA7312 and the modified NACA0012 airfoils rela- tive to the original NACA0012 airfoil. Airfoil Upper side length ratio Lower side length ratio Maximum camber NACA0012 1.000 1.000 0.0% NACA7312 1.042 0.986 7.00% at x/c¼ 0.300 Mod NACA0012 1.042 0.986 0.37% at x/c¼ 0.986 Figure 12. Modified NACA0012 airfoil. Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1065 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ The optimization algorithm used was the function fmincon in the MatLab Optimization Toolbox. This opti- mization algorithm is a gradient based method that uses finite differences to calculate the gradient of the objec- tive function and constraints. Results The optimal design set and its respective objective function and constraint values are shown in Table 6. The thickness distribution and aerodynamic loading are shown in Figure 13. The figure also shows the unactuated unloaded and loaded results and the actuated unloaded and loaded results superimposed to the desired cambered airfoil shape. Table 6 shows that the constraints aremain- tained within the tolerance permitted. It shows also that variable h4 and x4 are not influencing the solution since x3 is already stationed after the trailing edge of the shell. On the other hand, the design variables affecting the lower side may not be enough for the calculation of the optimum weight, since x8 is not at the trailing edge or aft. Nevertheless we do not foresee a significant weight reduction by including extra design variables for the lower side and recalculating and therefore no extra design variables were considered. Actuation force results show that the actuation force is greater when there is no aerodynamic loading, which suggests that the aerodynamic force helps the deformation of the shell to the desired shape in this loading condition. Different loading conditions could lead to increased actuation force, therefore some safety margin on the design of the actuation mechanism should be used. Using a 3mm diameter screw for join- ing both upper and lower airfoil trailing edges as the actuation mechanism (substituting the actuator ele- ments of Figure 14) and considering a 0.15 friction coefficient, the actuation torque estimate based on the maximum actuation force results is 0.098Nm (Shigley and Mischke, 2003). This value is considered acceptable. Table 5. Statement for the optimization of the shell weight. Objective function: min F ¼ � Vg Constraints Design variables Loaded Unloaded Upper side Lower side P n i¼0 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q n � 0:61 mm P n i¼0 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q n � 0:61 mm 0:5 mm � h0 � 2 mm 0:5 mm � h1 � 3 mm 0 � x1 � c 0:5 mm � h5 � 3 mm 0 � x5 � c MAX2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q � 1:21 mm MAX2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q � 1:21 mm 0:5 mm � h2 � 3 mm x1 � x2 � x1 þ c 0:5 mm � h6 � 3 mm x5 � x6 � x5 þ c 0:5 mm � h3 � 3 mm x2 � x3 � x2 þ c 0:5 mm � h2 � 3 mm x6 � x7 � x6 þ c TWmax � 0:85 TWmax � 0:85 0:5 mm � h4 � 3 mm x3 � x4 � x3 þ c 0:5 mm � h2 � 3 mm x7 � x8 � x7 þ c Table 6. Optimal design results. Objective function: min F ¼ 0:25N Constraints Design variables Loaded Unloaded Upper side Lower side P n i¼0 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q n ¼ 0:54 mm P n i¼0 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q n ¼ 0:58 mm h0 ¼ 2:00 mm MAX2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q ¼ 1:20 mm MAX2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y � yið Þ2 q ¼ 1:20 mm h1 ¼ 0:84 mm x1 ¼ 4:03 mm h5 ¼ 1:24 mm x5 ¼ 17:80 mm h2 ¼ 2:83 mm x1 ¼ 134:00 mm h6 ¼ 0:96 mm x6 ¼ 60:35 mm TWmax ¼ 0:26 TWmax ¼ 0:25 h3 ¼ 0:84 mm x3 ¼ 343:92 mm h7 ¼ 1:39 mm x7 ¼ 110:33 mm Actuation Force ¼ 0:30:08 N Actuation Force ¼ 164:13 N h4 ¼ 2:00 mm x4 ¼ 593:92 mm h8 ¼ 0:74 mm x8 ¼ 220:32 mm 1066 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ PERFORMANCE STUDY Quite a few aircraft performance parameters, related to different flight conditions, can be estimated using the CL and CD versus AOA functions. These parameters are: range, loiter time, maximum speed, stall speed, maximum climb angle (CA), maximum rate of climb (RoC), and best glide angle (GA) (Roskam and Lan, 1997). Traditionally, the estimates for these performance parameters are determined early in the design stage of the aircraft as its values can be obtained analytically. For a morphing wing, for which CL and CD depend also on the configuration, the performance parameters are not so easy to calculate and therefore optimization is a tool that needs to be used to determine the best con- figuration of the wing for a given flight condition. Also, for a morphing wing, drag at a given cruise speed can also be optimized, adding to the list of performance parameters that require specific optimized wing config- urations. To assess correctly the performance benefits, a comparison between the morphing wing and an opti- mum fixed wing is required. Aerodynamic Coefficients for the Morphing Wing Since structural deformation caused by aerodynamic loading does not affect significantly the aerodynamics of Figure 14. Wing FEM model parts: shell sections (top left); spars (bottom left); polymer cover (top right); actuator elements (bottom right). Figure 13. (a) Thickness distribution; (b) Aerodynamic loading; (c) Unactuated unloaded; (d) Unactuated loaded; (e) Actuated unloaded; and (f) Actuated loaded. Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1067 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ the wing as long as the wing structure is stiff enough, it allows one way coupled-filed analysis by solving the unloaded (but actuated) structural problem and passing the mesh deformation to the fluid solver for each of the configurations analyzed. The accuracy of the results was assessed afterwards using a two-way coupled-field anal- ysis for some specific values of AOA in the configura- tions more susceptible to higher deformation (maximum span configuration and null camber actuation), namely zero lift and near stall AOA, once the aerodynamic coef- ficients of the unloaded configurations are obtained. Here, as shown in Figure 14, the wing structure is mod- elled as follows: . Five shell sections with the optimized thickness dis- tribution calculated in the previous section for the outer wing and five shell sections with a scaled thick- ness distribution for the inner wing, which has a chord of 80% of the outer wing chord, to work as the classical wing ribs in maintaining the wing sec- tions shape. . An outer wing spar placed between the outer wing leading edge and the inner wing leading edge, an inner wing spar and an actuation spar which slides inside the inner wing spar as the span is increasing or decreasing, and an outer wing trailing edge spar to help bear some of the loading and prevent unaccept- able deformation of the wing cover at the trailing edge. . Rigid polymer sections on the remaining wing surface. . Actuator elements at the trailing edge of the shell sections to model the actual real actuators and assess the actuator force necessary. Displacements of both the outer and inner wing sur- faces are transmitted to the CFD mesh with the excep- tion of the interior nodes displacements at the wing tips, since there are no FEM nodes there. The CFD mesh adapts by placing the tip nodes inside the area contained by the tip edge nodes, which in turn receive displace- ments from the FEM model nodes. The CFD mesh used does not have the traditional boundary layer ele- ments and therefore cannot predict accurately separa- tion, which is the reason why the AOA is limited to 10�. For the same domain size as in section 2.1 a mesh with 14,86,970 elements was used. Viscous drag was cal- culated based on wall functions using the k-" turbulence model. Figure 15 shows four different configuration meshes. Four different span configurations are analyzed and for each one four different camber airfoils are analyzed in a total of 16 different configurations. Each of these Figure 15. CFD surface meshes for four different wing configurations. 1068 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ configurations is analyzed at 6 different AOA ranging from �5� to 10� and a speed of 30m/s, giving a total of 96 CFD analyses and 16 FEM analyses. The data obtained from these analyses is then interpolated to obtain analytical lift and drag functions of 4 different parameters: span; camber (or actuation course); AOA and speed. Appendix A shows the functions for the 16 CL versus AOA and CD versus AOA curves obtained from the computational analyses. The reference wing area is the fully deployed wing area (0.8129m2) and air density is 1.185 kg/m3 (air at 25�C). These functions can be interpolated to build approximate analytic func- tions that encompass all CL and CD values within the configuration variables of the morphing wing, suitable to use in performance parameters optimization. Optimum Fixed Wing Aerodynamic Coefficients A fixed wing can be optimized for one specific perfor- mance parameter at a time or it can be a compromise between two ormore opposing requirements. In commer- cial aircraft, wing geometry is optimized for maximum range at a specific cruise speed and altitude. Design alti- tude for long-range flights at the design cruise speed in order to save fuel is one possible desired solution. Here, we perform an aerodynamic optimization to obtain the optimum fixed wing geometry for minimum drag in cruise at 30m/s, with aircraft weight of 100N. The wing root and tip airfoils are of the same airfoil family of the morphing wing (NACA0012 toNACA7312) and their camber is allowed to vary between 0 and 7%, as the camber of the morphing wing. The reasons behind these geometrical limits are comparability with the morphing wing, which has the same airfoil family as base geometry, and limitation of the design space for computational speed. The root chord has a fixed length of 0.25m to be able to accommodate a spar that allows approximately the same load-bearing capability as the morphingwing, but the tip chord can be reduced allowing wing taper. Minimum span is the same as the morphing wing’s to limit minimum wing area and therefore allow- ing the wing to carry extra load without excessive increase in AOA. The design variables are: half span [1, 1.7] (m); tip chord [0.167, 0.250](m); root maximum camber [0.00, 0.07]; tip maximum camber [0.00, 0.07]; AOA [0, 10]. The optimization process starts by generating the root and tip airfoils analytically and then creates the upper and lower wing surfaces and the control volume. A mesher is then used to mesh the volume with a relatively coarse mesh to speed up the process, the CFD problem is solved, and results are obtained. The optimization algo- rithm uses this procedure to calculate the best design set. Table 7 presents the optimization results and Appendix A presents the CL and CD functions of the AOA obtained after the optimization using a refined mesh. FULL AIRCRAFT CONSIDERATIONS The full aircraft considerations used in the perfor- mance parameters optimization are as follows: . Fuselage and tail contribution to lift is null. . Fuselage, tail, and engine drag variation with AOA is null. . Friction drag coefficient of aircraft body (fuselage, tail, engine) CD0¼ 0.0196 (calculated with morphing wing reference area). . Air density 1.185 kg/m3 (air at 25�C). . Available power Pav¼ 4.85 hp. . Total aircraft weight of 100N for the fixed wing optimization. . Total aircraft weight of 111N for the morphing wing optimization, accounting for the increased wing weight when compared to the fixed wing according to Table 8. Actuation system and fixed wing weight estimates are arbitrary. . 10N fuel weight. . 0.0056N/s fuel consumption. . Propeller efficiency �(U), with maximum at 60m/s as shown in Figure 16 (Hepperle, 2006b). The assumption of tail, fuselage, and engine drag var- iation with AOA being null is a simplification made 0.8 0.7 0.5 0.3 0.1 0.6 0.4 0.2 0 0 8070605040 U (m/s) Propeller efficency 302010 Figure 16. Propeller efficiency with speed. Table 8. Weight estimates for morphing and fixed wing. Wing structure weight (from FEM model) 18.1 N Actuation system weight (10% of structural weight) 1.8 N Fixed wing weight estimate (50% of structural weight) 9.05 N Table 7. Aerodynamic optimization results. Design variable Span Tip chord Root camber Tip camber Value 1.0 m 0.167 m 4.60% 0.00% Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1069 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ because of the variety of configurations that could be chosen for these aircraft parts, leading to possibly sig- nificantly different results and increasing the complexity of the analyses. For instance, the higher the variation of fuselage drag with AOA, the less significant the possible drag reductions obtained from morphing will be. Therefore, the results obtained should be seen as non- conservative and point out to the maximum benefits that can be expected. Also the absence of results concerning actuation requirements for span variation forced the assumption of an arbitrary weight increase estimate and the inclusion of results considering extra weight penalty, therefore providing a small sensitivity analysis on the performance parameters variation with weight. Performance Parameters Optimization For the morphing wing aerodynamic parameters opti- mization the design variables are: AOA [�6, 10] (�); half span [1, 1.70] (m); camber actuation [0, 100] (%); speed [0, 150] (m/s). In some performance parameters speed is fixed (e.g., optimizing drag at a specific speed). In other cases the parameter is calculated at all speeds between stall speed and maximum speed and then its maximum or minimum value (depending on the parameter) is con- sidered optimum (e.g., range or glide angle). It is noted that minimizing drag and maximizing range are not exactly the same, as it may appear from Table 9 since the objective function and constraints are the same. In fact, when minimizing drag we obtain the wing configuration for which the aircraft drag is mini- mum at a given speed and weight while when maximiz- ing range means we obtain the variations on the wing configuration while fuel is being burned and therefore weight is reducing. For the fixed wing aerodynamic parameters optimization the design variables are only two: AOA [�6, 10](�); speed [0, 150](m/s). Results Although the analytical calculation could have been performed for the fixed wing, a numerical optimiza- tion analysis was carried out, since the procedure was already programmed and readily available. As observed in Table 10, the greatest penalty of the morphing wing usage is in the maximumRoC, which is reduced by 9.91% relatively to the fixed wing maximum RoC. The other penalty is the extra drag in cruise at 30m/s, of 4.15%. Table 10. Performance parameters results and comparison between morphing and fixed wing. Wing Morphing Optimum Relative difference Span (m) 1�1.7 1 0�70% Camber 0�7% 4.2% at root, 0% at tip Area (m2) 0.52�0.81 0.42 23.81�92.86% Max speed (m/s) 56.87 56.26 1.07% Stall speed (m/s) 12.23 19.18 �36.24% Drag at 20 m/s 9.08 10.58 �14.15% Drag at 30 m/s 15.32 14.71 4.15% Drag at 56 m/s 46.67 48.04 �2.84% Max climb angle (�) 22.64 22.14 2.28% Max RoC (at 40 m/s) 9.69 10.75 �9.91% Max range (km) 284.70 at 19 m/s 284.97 at 26 m/s �0.09% Max range (at 26 m/s) 270.25 284.97 �5.17% Min glide angle (�) 3.55 6.04 �41.26% Max endurance (min) 251.07 157.17 59.74% Table 9. Performance parameters optimization: objective functions and constraints. Parameter Objective function Constraints Max speed Min �U T¼D; L¼W Stall speed Min U L¼W Drag at speed U Min D L¼W Max climb angle (CA) and rate of climb (RoC) at speed U Min 90�CA¼ 90 tan-1((T�D)/L) 0�CA� 90; L cos(90�CA)¼W Max range at speed U Min D T¼D; L¼W Max loiter time Min C¼DU/(PZ(U)) 0�C� 1; L¼W; Min glide angle (GA) Min GA¼ tan-1(D/L) 0�GA� 90; L(cos(GA)þ tan(GA)sin(GA))¼W 1070 J. VALE ET AL. at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ On the benefits side, one can see a stall speed reduction of 36.24% which is also related to the 59.74% increase in maximum endurance since smaller speed means smaller drag. Adding flaps to the fixed wing would reduce these differences although it is not likely to mitigate completely the morphing benefits. Range remains practically the same (0.09% reduction) due to the lower speed flight capability, although at 26m/s (speed at which the range with the fixed wing is maximum) the range of the morph- ing wing is 5.17% lower. Drag at low speeds is signifi- cantly reduced due to morphing but at high speeds there is also a small reduction, meaning that camber morphing capability compensates the extra wing area that the morphing wing has relative to the fixed wing, even at the smaller span configurations.Glide angle decreases sig- nificantly (41.26%), which is an advantage in case of engine malfunction; maximum climb angle also increases by 2.28%. It can be inferred that the morphing wing gen- erally outperforms the optimum fixed wing. Some remarks should be made concerning the weight estimates in Table 8 because if they introduce consider- able error, the performance of the morphing wing may not be as good, as shown in Table 10. In the limit, we can assume the extra weight of the morphing wing is its total weight and then check the performance parameters comparison. The total aircraft weight for the morphing wing optimization is then 120N. Table 11 shows the comparison for this case. The major benefits in stall speed, endurance, and glide angle remain significant (33.71% decrease, 47.17% increase, and 41.26% decrease respectively). The penalty in RoC increases significantly (from 9.97% to 16.54% RoC reduction). Range has now a reduction of 4.53% and drag at 30m/s increases by 6.34%. All other perfor- mance parameters show decrease in benefits and increase in penalties. This limit case shows the importance of weight pen- alty on the morphing concept technology. There can be a level of weight penalty that can be tolerable where most of the performance parameters benefit from morphing and morphing technology would be an obvi- ous choice. On the other hand, comparing the morphing wing with a fixed wing, that is, a compromise between cruise drag and endurance for instance would probably reduce the advantages of the morphing wing compared to the fixed wing performance. Other consideration is how much one is willing to sacrifice a performance parameter in order to benefit the other performance parameter using morphing. For example, how much of the RoC would one be willing to sacrifice in order to gain 60% increase in maximum endurance? If the fixed wing is to perform multiple tasks, how often will it have to operate in non-optimal conditions that justifies the increase in construction complexity, maintenance, or cost? How critical is it if the fixed wing aircraft underperforms a task, or simply does not perform it? Is morphing capability introduction justifiable in such cases? Further studies will have to be done to create a tool that can answer these questions and establish criteria to assess if morphing capability is beneficial or not for the mission profiles that an aircraft is intended to perform. CONCLUDING REMARKS A morphing telescopic wing concept with airfoil shape change capability was designed and studied computationally using coupled fluid-structure analysis. Strategies for drag reduction using span morphing were obtained. A concept of airfoil camber morphing based on non-uniform thickness distribution was designed and studied. Based on the optimization results, the concept is feasible both in terms of geometric changes and actua- tion requirements. The airfoil camber concept was then introduced in a wing with telescoping capabilities and a study was Table 11. Performance parameters results and comparison between morphing wing with extra weight penalty and optimum fixed wing. Wing Morphing Optimum Relative difference Span (m) 1�1.7 1 0�70% Camber 0�7% 4.2% at root, 0% at tip Area (m2) 0.52�0.81 0.42 23.81�92.86% Max speed (m/s) 56.8 56.26 0.96% Stall speed (m/s) 12.71 19.18 �33.71% Drag at 20 m/s 9.39 10.58 �11.21% Drag at 30 m/s 15.65 14.71 6.34% Drag at 56 m/s 46.83 48.04 �2.52% Max climb angle (�) 21.12 22.14 �4.58% Max RoC (at 40 m/s) 8.97 10.75 �16.54% Max range (km) 272.05 at 20 m/s 284.97 at 26 m/s �4.53% Max range (at 26 m/s) 259.68 284.97 �8.87% Min glide angle (�) 3.55 6.04 �41.26% Max endurance (min) 231.3 157.2 47.20% Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1071 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/ carried out to obtain the aerodynamic coefficients vari- ation with the geometrical changes of the morphing wing. This procedure allowed the analytical description of the aerodynamic behavior of the morphing wing, suit- able for fast optimization of the wing configuration for the best values of different performance parameters. Comparison between the morphing wing performance and a fixed wing optimized for cruise at 30m/s was per- formed, accounting for weight penalties on the morph- ing wing structure and actuation system relative to the fixed wing weight. For reasonable (although arbitrary) weight estimates, results show that the most significant penalties are in maximum RoC (9.91% reduction) and drag at 30m/s (4.15% increase), which is the speed for which the fixed wing is optimized. The greatest benefits are for stall speed, endurance, and glide angle (36.24% decrease, 59.74% decrease, and 41.26% increase, respec- tively). Negligible penalties and benefits are in range and climb angle (�0.09% decrease and 2.28% increase, respectively). The morphing wing generally outperforms the optimum fixed wing. When comparing the optimum fixed wing with the morphing wing with extra weight penalty, it is observed that performance is penalized, although major benefits remain significant. Further studies are needed to establish criteria to fully assess the morphing benefits. Nevertheless, the present study provides useful insights to the field of morphing aircraft and provides some foundation for future research in morphing wings. ACKNOWLEDGEMENTS This work was possible due to the funding provided to the project SMORPH by the European Science Foundation (ESF) and the Fundação para a Ciência e Tecnologia (FCT) and the funded project POCTI-EME- 61587-2004. The author José Vale would like to also thank the FCT for the Graduate Fellowship. 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You, Z. and Crabtree, J. 2009. ‘‘Mechanisms for Large Shape Change in Morphing Aircraft,’’ In: RTO-NATO Morphing Vehicles Symposium, 20�24 April, Évora, Portugal. APPENDIX A Table A1. CL and CD vs AOA functions for the morphing wing. Configuration (half span, actuation) CL vs AOA CD vs AOA (1.70, 1.00) 9.348 E�02*AOAþ5.918 E�01 �1.149 E�05*AOA3þ 6.040 E�04*AOA2þ 8.713 E�05*AOAþ 3.466 E�02 (1.70, 0.67) 9.387 E�02*AOAþ4.299 E�01 �7.858 E�06*AOA3þ 5.9128 E�04*AOA2�2.928 E�05*AOAþ2.7518 E�02 (1.70, 0.33) 9.409 E�02*AOAþ2.296 E�01 �5.195 E�08*AOA3þ 5.500 E�04*AOA2� 4.616 E�05*AOAþ 2.175 E�02 (1.70, 0.00) 9.341 E�02*AOAþ1.358 E�02 6.376 E�06*AOA3þ4.724 E�04*AOA2�1.742 E�04*AOAþ1.893 E�02 (1.47, 1.00) 8.046 E�02*AOAþ4.797 E�01 �1.383 E�05*AOA3þ 5.661 E�04*AOA2þ 5.429 E�05*AOAþ 2.942 E�02 (1.47, 0.67) 8.084 E�02*AOAþ3.464 E�01 �7.471 E�06*AOA3þ 5.055 E�04*AOA2þ 4.530 E�07*AOAþ 2.378 E�02 (1.47, 0.33) 8.090 E�02*AOAþ1.843 E�01 8.009 E�07*AOA4�8.538 E�06*AOA3þ4.415 E�04*AOA2þ 1.715 E�04*AOAþ 1.877 E�02 (1.47, 0.00) 8.055 E�02*AOAþ1.219 E�02 5.048 E�06*AOA3þ4.202 E�04*AOA2�1.384 E�04*AOAþ1.660 E�02 (1.23, 1.00) 6.709 E�02*AOAþ4.078 E�01 2.292 E�07*AOA4�1.099 E�05*AOA3þ4.729 E�04*AOA2þ 3.742 E�04*AOAþ 2.795 E�02 (1.23, 0.67) 6.717 E�02*AOAþ2.967 E�01 5.262 E�07*AOA4�1.075 E�05*AOA3þ4.153 E�04*AOA2þ 4.359 E�04*AOAþ 2.085 E�02 (1.23, 0.33) 6.729 E�02*AOAþ1.608 E�01 5.500 E�07*AOA4�6.124 E�06*AOA3þ3.801 E�04*AOA2þ 3.191 E�04*AOA1þ1.609 E�02 (1.23, 0.00) 6.679 E�02*AOAþ1.065 E�02 3.109 E�07*AOA4þ5.086 E�07*AOA3þ3.601 E�04*AOA2� 2.063 E�05*AOAþ 1.422 E�02 (1.00, 1.00) 5.274 E�02*AOAþ3.356 E�01 �7.542 E�06*AOA3þ 4.024 E�04*AOA2þ 7.154 E�04*AOAþ 2.500 E�02 (1.00, 0.67) 5.348 E�02*AOAþ2.357 E�01 6.777 E�07*AOA4�1.217 E�05*AOA3þ3.626 E�04*AOA2þ 6.932 E�04*AOA1þ1.719 E�02 (1.00, 0.33) 5.328 E�02*AOAþ1.280 E�01 3.209 E�04*AOA2þ3.222 E�04*AOAþ1.313 E�02 (1.00, 0.00) 5.284 E�02*AOAþ8.155 E�03 3.458 E�04*AOA2�1.652 E�04*AOAþ1.171 E�02 Table A2. CL and CD vs AOA functions for the optimum fixed wing. Configuration (half span, camber) CL vs AOA CD vs AOA (1.00, 4.6�0.0%) 8.7 E�02 AOAþ 2.3 E�01 �2.4 E�06 AOA3þ 5.4 E�04 AOA2þ 3.9 E�04 AOAþ2.4 E�02 Aero-Structural Optimization and Performance Evaluation of a Morphing Wing with Variable Span and Camber 1073 at Monash University on December 5, 2014jim.sagepub.comDownloaded from http://jim.sagepub.com/