Design and Validation of a New Morphing Camber System by Testing in the Price—Païdoussis Subsonic Wind Tunnel

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Article Design and Validation of a New Morphing Camber System by Testing in the Price—Païdoussis Subsonic Wind Tunnel

David Communier, Ruxandra Mihaela Botez * and Tony Wong

Laboratory of Applied Research in Active Controls, Avionics and AeroServoElasticity LARCASE, ÉTS, Montréal, QC H3C 1K3, Canada; [email protected] (D.C.); [email protected] (T.W.) * Correspondence: [email protected]

Received: 25 December 2019; Accepted: 3 March 2020; Published: 7 March 2020

Abstract: This paper presents the design and wind tunnel testing of a morphing camber system and an estimation of performances on an unmanned aerial vehicle. The morphing camber system is a combination of two subsystems: the morphing trailing edge and the morphing leading edge. Results of the present study show that the aerodynamics effects of the two subsystems are combined, without interfering with each other on the wing. The morphing camber system acts only on the lift coefficient at a 0◦ angle of attack when morphing the trailing edge, and only on the stall angle when morphing the leading edge. The behavior of the aerodynamics performances from the MTE and the MLE should allow individual control of the morphing camber trailing and leading edges. The estimation of the performances of the morphing camber on an unmanned aerial vehicle indicates that the morphing of the camber allows a drag reduction. This result is due to the smaller angle of attack needed for an unmanned aerial vehicle equipped with the morphing camber system than an unmanned aerial vehicle equipped with classical aileron. In the case study, the morphing camber system was found to allow a reduction of the drag when the lift coefficient was higher than 0.48.

Keywords: morphing camber; morphing trailing edge; morphing leading edge; wind tunnel testing; morphing wing

1. Introduction In an effort to reduce aircraft fuel consumption, researchers and engineers strive to optimize all aircraft flight phases. To this end, many studies have focused on optimizing aircraft weight (structure and materials), engine efficiency, aircraft trajectories, and aerodynamics, etc. The optimization of the aerodynamics of an aircraft is performed by modifying its shapes and/or its surfaces (wings, empennage, etc.). In terms of the shapes of the aircraft surfaces, they could be optimized according to the flight phases [1]. Some research has targeted the modification of the shapes of the surfaces during flight to adapt them to changing conditions and phases. This article presents a prototype of a Morphing Camber System (MCS) that enables an aircraft wing to modify its shape during flight. The MCS is intended to change the wing’s lift, which it does by having the lowest possible impact on the aircraft drag. As result, the morphing of the wing generates a smaller increase in drag than the present increase when classic control surfaces are used. The purpose of the MCS is to reduce the drag of the aircraft by replacing the slats, the aileron and the flaps with a morphing of the internal structure. In this paper, a new method to achieve the morphing of the internal structure is presented. This method consists of using slits on the ribs to make them compliant. Numerous theoretical studies have been carried out on the aerodynamic shape optimization of wing surfaces [2–6]. However, few functional mechanisms have been tested [7]; Blondeau [8] tested a

Aerospace 2020, 7, 23; doi:10.3390/aerospace7030023 www.mdpi.com/journal/aerospace Aerospace 2020, 7, x FOR PEER REVIEW 2 of 22 Aerospace 2020, 7, 23 2 of 22 [7]; Blondeau [8] tested a morphing aspect ratio in wind tunnel; Chanzy tested a morphing trailing edge in wind tunnel and in a flight test with a UAV integrating the morphing system [9]; Pecora et morphing aspect ratio in wind tunnel; Chanzy tested a morphing trailing edge in wind tunnel and in a al. tested a morphing trailing edge based on a full-scale wing of a civil regional transportation flight test with a UAV integrating the morphing system [9]; Pecora et al. tested a morphing trailing aircraft [10–12]; Radestock tested a morphing leading edge mechanism [13]; and Woods also tested edge based on a full-scale wing of a civil regional transportation aircraft [10–12]; Radestock tested a a morphing trailing edge system using a fish bone concept [14]. Numerical optimization studies are morphing leading edge mechanism [13]; and Woods also tested a morphing trailing edge system using generally hindered by their feasibility from a mechanical and thus, practical standpoint. a fish bone concept [14]. Numerical optimization studies are generally hindered by their feasibility Conversely, studies or “experimental analysis” on morphing mechanisms allow less aerodynamic from a mechanical and thus, practical standpoint. Conversely, studies or “experimental analysis” improvement than is ideal. The main obstacles in the design and testing of a morphing mechanism on morphing mechanisms allow less aerodynamic improvement than is ideal. The main obstacles are generally given by the weight, the power consumption of the morphing mechanism and the in the design and testing of a morphing mechanism are generally given by the weight, the power elasticity of the wing surface [15,16]. According to Weissharr [17], the fact that morphing systems consumption of the morphing mechanism and the elasticity of the wing surface [15,16]. According to are expensive, that morphing aircrafts are heavier than conventional aircrafts, and that morphing Weissharr [17], the fact that morphing systems are expensive, that morphing aircrafts are heavier than systems are complex and require exotic material are myths and demonstrated it by reviewing early conventional aircrafts, and that morphing systems are complex and require exotic material are myths morphing aircraft history. and demonstrated it by reviewing early morphing aircraft history. In previous studies, our LARCASE team has developed morphing wing mechanisms which, by In previous studies, our LARCASE team has developed morphing wing mechanisms which, by modifying the upper surface of the wing, allow the flow transition delay between the laminar and modifying the upper surface of the wing, allow the flow transition delay between the laminar and turbulent regimes around the wing [18–24]. This delay has the effect of reducing the drag generated turbulent regimes around the wing [18–24]. This delay has the effect of reducing the drag generated by by the wing. the wing. The present study aims to modify the camber of the wing with the aim to increase its lift The present study aims to modify the camber of the wing with the aim to increase its lift coefficient coefficient and lift to drag ratio(L/D). It is known that when the lift coefficient is increased, the and lift to drag ratio(L/D). It is known that when the lift coefficient is increased, the aircraft can fly with aircraft can fly with a lower angle of attack, thereby reducing its drag. a lower angle of attack, thereby reducing its drag.

2.2. Problem statement TheThe MCSMCS problemproblem is is simplified simplified by by dividing dividing the the wing wing into into its its three three sections: sections: the the leading leading edge, edge, the wingthe wing box andbox theand trailing the trailing edge. edge. Such aSuch morphing a morp systemhing system needs twoneeds actuating two actuating mechanisms mechanisms to morph to themorph leading the leading edge (Morphing edge (Morphing Leading Leading Edge (MLE)) Edge (MLE)) and the and trailing the trailing edge (Morphingedge (Morphing Trailing Trailing Edge (MTE)),Edge (MTE)), while while the wing the boxwing remains box remains fixed. fixed. InIn thisthis research, research, a NACA0012a NACA0012 airfoil airfoil is considered, is considered, which willwhich be morphedwill be morphed by the MCS by mechanism the MCS intomechanism a NACA4412 into a airfoil. NACA4412 This morphing airfoil. This is equivalent morphing tois modifyingequivalent the to greymodifying airfoil (NACA0012)the grey airfoil to the(NACA0012) black airfoil to (NACA4412),the black airfoil as (NACA4412), shown in Figure as 1shown. In this in figure,Figure these1. In this two figure, airfoil shapesthese two are airfoil each dividedshapes are into each three divided sections: into the three leading sections: edge, thethe center leading box edge, and thethetrailing center edge.box and The the center trailing box isedge. the sameThe center constant box shape is the and same is thus constant un-modified shape and for bothis thus airfoils un-modified while the for leading both andairfoils trailing while edges the areleading different and fortrailing both airfoils.edges are The different NACA0012 for both and NACA4412airfoils. The airfoils NACA0012 were consideredand NACA4412 because airfoils they havewere theconsidered same thickness, because and they the onlyhave dithefference same between thickness, their and shapes the liesonly in difference their cambers. between This istheir the reasonshapes whylies in this their new cambers. system isThis called is the a “Morphing reason why Camber this new System” system (MCS). is called a “Morphing Camber System” (MCS).

Figure 1. NACA0012 and NACA4412 airfoils superimposed. Figure 1. NACA0012 and NACA4412 airfoils superimposed. To compare the efficiency of these two airfoils, an analysis of the L/D ratio is not enough. Indeed, an airfoilTo compare could have the aefficiency lower drag of andthese a highertwo airfoils L/D,, while an analysis having of a lowerthe L/D lift, ratio which is couldnot enough. be too lowIndeed, to allow an airfoil the aircraft could have to fly. a lower The variation drag and of a thehigher drag L/D, coe ffiwhilecient having with the a lower lift coe lift,ffi cient,which allows could directbe too visualizationlow to allow ofthe the aircraft airfoil to having fly. The the variatio smallestn of drag the givendrag coefficient a constant wi liftth value. the lift Thus, coefficient, when comparingallows direct the visualization variation of of Cl the with airfoil Cd forhaving NACA0012 the smallest airfoil drag versus given the a NACA4412constant lift airfoil,value. itThus, can bewhen seen comparing in Figure2 the that variation the NACA4412 of Cl with airfoil Cd for is more NACA0012 e fficient airfoil than versus the NACA0012 the NACA4412 airfoil airfoil, for a lift it coefficient Cl greater than 0.367.

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Aerospacecan be seen2020, 7in, 23 Figure 2 that the NACA4412 airfoil is more efficient than the NACA0012 airfoil3 for of 22 a lift coefficient Cl greater than 0.367.

Figure 2. Drag coeﬃcient variation with the lift coeﬃcient for NACA0012 (grey) and NACA4412 Figure 2. Drag coefficient variation with the lift coefficient for NACA0012 (grey) and NACA4412 (black). For Cl = 0.367, angle of attack of NACA0012 = 7.8◦ and angle of attack of NACA4412 = 2.97◦. (black). For Cl = 0.367, angle of attack of NACA0012 = 7.8° and angle of attack of NACA4412 = 2.97°.

This lift coefficient is obtained for an angle of attack of 2.97◦ for the NACA4412 airfoil, and of This lift coefficient is obtained for an angle of attack of 2.97° for the NACA4412 airfoil, and of 7.8◦ for the NACA0012 airfoil. It is therefore possible for an aircraft wing, equipped with an MCS, to increase7.8° for the its liftNACA0012 without havingairfoil. toIt is change therefore the anglepossible of attackfor an butaircraft only wing, by changing equipped its with shape an from MCS, a NACA0012to increase its to alift NACA4412. without having Furthermore, to change as the the an anglegle of of attack attack but of the only aircraft by changing could be its smaller shape withfrom ana NACA0012 MCS than with to a a NACA4412. classical wing, Furthermore, there is an additional as the angl reductione of attack in dragof the from aircraft other could aircraft be surfaces smaller (fuselage,with an MCS empennage). than with a classical wing, there is an additional reduction in drag from other aircraft surfacesA measurement (fuselage, empennage). of the total efficiency gain when considering all components (wing, fuselage, empennage,A measurement etc.) of the of UAVthe total is obtained efficiency by gain performing when considering comparative all flightcomponents tests for (wing, a UAV fuselage, with a conventionalempennage, wingetc.) of and the the UAV same is UAVobtained with by a morphingperforming wing. comparative flight tests for a UAV with a conventional wing and the same UAV with a morphing wing. 3. Design of the Morphing Camber System (MCS) 3. Design of the Morphing Camber System (MCS) The wing will be equipped with flexible ribs to morph its camber. The flexibility of the ribs is madeThe possible wing usingwill be vertical equipped slits. with Each flexible slit allows ribs to the morph ribs to its perform camber. a The small flexibility rotation of as the if a ribs pivot is connectionmade possible had using been addedvertical to slits. the system.Each slit By allows distributing the ribs the to slitsperform along a thesmall ribs, rotation the wing’s as if overalla pivot behaviorconnection becomes had been like added the one to of the a morphing system. By camber distributing system the (MCS). slits The along functionality the ribs, the and wing’s efficiency overall of thisbehavior approach becomes have beenlike demonstratedthe one of a usingmorphing the morphing camber leadingsystem edge(MCS). (MLE) The andfunctionality the morphing and trailingefficiency edge of (MTE)this approach concept ha developedve been demonstrated in [25,26]. The using maximum the morphing displacement leading of theedge MLE (MLE) and and the MTEthe morphing was determined trailing as edge follows: (MTE) concept developed in [25,26]. The maximum displacement of the MLE and the MTE was determined as follows: Xn = MaximumMaximum displacement displacement = ∑yi,𝑦, (1)(1) i=1 where: where: × 𝑦=l L , (2) y = × , (2) p where n is the number of slits, l the width of the slit, p represents the depth of the slit, and where n is the number of slits, l the width of the slit, p represents the depth of the slit, and finally, L finally, L represents the distance between the slit and the end of the rib [25]. represents the distance between the slit and the end of the rib [25]. Using the slit dimensions given in Table 1 and Table 2, a maximum MTE displacement y of Using the slit dimensions given in Tables1 and2, a maximum MTE displacement y of 1.33 in (33.78 1.33 in (33.78 mm), and a maximum MLE displacement y of 0.322 in (8.18 mm) were obtained using mm), and a maximum MLE displacement y of 0.322 in (8.18 mm) were obtained using Equations (1) Equation (1) and Equation (2). This displacement corresponds to the one observed on the model and (2). This displacement corresponds to the one observed on the model before the surface is installed before the surface is installed on the wing. on the wing.

AerospaceAerospace 20202020,, 77,, 23x FOR PEER REVIEW 44 ofof 2222 Aerospace 2020, 7, x FOR PEER REVIEW 4 of 22 Table 1. Slits’ dimensions on the trailing edge of the rib. TableTable 1. 1.Slits’ Slits’ dimensions dimensions on on the the trailing trailing edge edge of of the the rib. rib. Slit number 𝒍𝒏 (in) 𝑳𝒏 (in) 𝒑𝒏 (in) Slit number 𝒍𝒏 (in) 𝑳𝒏 (in) 𝒑𝒏 (in) Slit Number1 0.026ln (in) 4.911Ln (in) 0.416pn (in) 121 0.0260.026 0.026 4.6354.911 4.911 0.416 0.4 0.416 232 0.0210.026 0.026 3.6094.635 4.635 0.34 0.4 0.4 3 0.021 3.609 0.34 43 0.0210.021 3.3383.609 0.317 0.34 4 0.021 3.338 0.317 4 0.021 3.338 0.317 55 0.014 0.014 2.317 2.317 0.233 0.233 665 0.0140.014 0.014 2.0532.317 2.053 0.2050.233 0.205 6 0.014 2.053 0.205 Table 2.2. Slits’Slits’ dimensionsdimensions onon thethe leadingleading edgeedge ofof thethe rib.rib. Table 2. Slits’ dimensions on the leading edge of the rib. 𝒍 𝑳 𝒑 SlitSlit Number number 𝒏 (in)ln (in) 𝒏 (in)Ln (in) 𝒏 p(in)n (in) Slit number 𝒍𝒏 (in) 𝑳𝒏 (in) 𝒑𝒏 (in) 11 0.012 0.012 0.436 0.436 0.262 0.262 221 0.0140.012 0.014 0.6230.436 0.623 0.3060.262 0.306 332 0.0180.014 0.018 0.8170.623 0.817 0.3400.306 0.340 43 0.018 0.021 0.817 1.037 0.340 0.317 54 0.021 0.024 1.037 1.258 0.317 0.394 654 0.0240.021 0.026 1.2581.037 1.507 0.3940.317 0.413 65 0.0260.024 1.5071.258 0.4130.394 6 0.026 1.507 0.413 TheThe MLEMLE displacementdisplacement can alsoalso bebe obtainedobtained usingusing FiniteFinite ElementElement AnalysisAnalysis (FEA)(FEA) [[27]27] underunder The MLE displacement can also be obtained using Finite Element Analysis (FEA) [27] under CATIACATIA V5V5 withwith aa 3.3%3.3% errorerror withwith respectrespect toto itsits experimentalexperimentaldetermined determinedvalue value(Figure (Figure3 ).3). CATIA V5 with a 3.3% error with respect to its experimental determined value (Figure 3).

FigureFigure 3.3. MLE tip maximum displacement of 0.333 in (8.46 mm).mm). Figure 3. MLE tip maximum displacement of 0.333 in (8.46 mm). TheThe maximummaximum displacement displacement of of the the MTE MTE was was not obtainednot obtained directly directly from thefrom FEA, the asFEA, it was as limitedit was bylimited theThe CATIA by maximum the V5CATIA software displacement V5 software at a maximum atof athe maximum rotationMTE was ofrotation 10not◦ for ob of thetained 10° MTE for directly displacementthe MTE from displacement the (Figure FEA,4 ).as (Figure it was 4).limited by the CATIA V5 software at a maximum rotation of 10° for the MTE displacement (Figure 4).

Figure 4. MTE tip displacement of 1.01 in (25.65 mm) for a 1010°◦ rotation of servomotor. Figure 4. MTE tip displacement of 1.01 in (25.65 mm) for a 10° rotation of servomotor. WeWe note,note, however, however, that that the the displacement displacement of theof the MTE MTE is linearly is linearly proportional proportional to the to rotation the rotation angle ofangle the Weof servomotor the note, servomotor however, (Table (Table 3that). As the 3). shown displacementAs shown in Table in 3Tablof, a the rotatione 3, MTE a rotation ofis linearly 13.4 of◦ 13.4°(angle proportional (angle corresponding corresponding to the rotation to the to angle of the servomotor (Table 3). As shown in Table 3, a rotation of 13.4° (angle corresponding to

AerospaceAerospace 20202020,, 77,, x 23 FOR PEER REVIEW 55 of of 22 22 theAerospace calculate 2020 , maximum7, x FOR PEER displacement REVIEW of 1.33 in (33.78 mm)) for the MLE tips is obtained for5 itsof 22 deformationcalculate maximum of 1.357 displacement in (34.47 mm), of 1.33which in (33.78corresponds mm)) for to thea 2.06% MLE tipsrelative is obtained error. This for its displacement deformation isofthe reduced 1.357 calculate in once (34.47 maximum the mm), surface which displacement is correspondsinstalled on of tothe 1.33 a wi 2.06% inng (33.78because relative mm)) the error. heat-shrinkablefor This the displacementMLE tips plastic is isobtained reducedused to forhide once its thethedeformation slits surface folds is back installedof 1.357 on itself, onin (34.47 the which wing mm), reduces because which the the corresponds width heat-shrinkable of the to slits. a 2.06% plastic relative used to error. hide theThis slits displacement folds back onis itself,reduced which once reduces the surface the width is installed of the on slits. the wing because the heat-shrinkable plastic used to hide the slits foldsTable back 3. MTE on itself, tip displacement which reduces values the according width of to the the slits.servomotor angle of rotation. Table 3. MTE tip displacement values according to the servomotor angle of rotation. Servomotor angle Tip displacement Table 3. MTE tipServomotor displacement Angle0° values according Tipto0 the in Displacement servomotor angle of rotation.

Servomotor0◦ 5° angle Tip0.549 displacement in0 in 5◦ 10°0° 1.010 in0.549 in 10 1.01 in ◦13.4°5° 1.3570.549 in in 13.4◦ 1.357 in The impact of each morphing system10° on the overall wing1.01 inbehaviour is obtained thanks to the two previous studies on the MTE ((Figure13.4° 5) [25,26]) and on1.357 the MLEin (Figure 6). The impact of each morphing system on the overall wing behaviour is obtained thanks to the two The impact of each morphing system on the overall wing behaviour is obtained thanks to the previous studies on the MTE ((Figure5)[25,26]) and on the MLE (Figure6). two previous studies on the MTE ((Figure 5) [25,26]) and on the MLE (Figure 6).

Figure 5. MTE system.

Figure 5. MTE system. Figure 5. MTE system.

FigureFigure 6. 6. MLEMLE system. system.

The MCS is a combination of these two morphing systems and it maintains the dimensions of the The MCS is a combination of these twoFigure morphing 6. MLE system. systems and it maintains the dimensions of theslits slits for thefor trailingthe trailing edge (Tableedge 1(Table) and the1) leadingand the edge leading (Table edge2), as (Table shown 2), in Figureas shown7. Consequently, in Figure 7. it becomes possible to identify potential interactions between the MTE system and the MLE system Consequently,The MCS it is becomes a combination possible of tothese identify two morphingpotential interactions systems and between it maintains the MTE the dimensions system and of aerodynamic performance. thethe MLE slits system for the aerodynamic trailing edge performance. (Table 1) and the leading edge (Table 2), as shown in Figure 7. Consequently, it becomes possible to identify potential interactions between the MTE system and the MLE system aerodynamic performance.

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FigureFigure 7.7. MCS design in CATIA V5.V5. Figure 7. MCS design in CATIA V5. ToTo comparecompare MCS MCS performances performances with with those those of aof non-morphing a non-morphing system, system, the prototypethe prototype of the of MCS the To compare MCS performances with those of a non-morphing system, the prototype of the mustMCS havemust thehave same the dimensionssame dimensions as the non-morphingas the non-morphing system system (reference (reference wing): wing): 10 in (254 10 in mm) (254 chord, mm) MCS must have the same dimensions as the non-morphing system (reference wing): 10 in (254 mm) 12chord, in (304.8 12 in mm) (304.8 in span.mm) Thein span. MCS The has aMCS morphing has a morphing section span section of 9.5 inspan (241.3 of 9.5 mm) in with(241.3 1 inmm) (25.4 with mm) 1 chord, 12 in (304.8 mm) in span. The MCS has a morphing section span of 9.5 in (241.3 mm) with 1 onin (25.4 each sidemm) ofon the each morphing side of the section morphing that cannot section be that morphed. cannot Thebe morphed. last 0.5 in The (12.7 last mm) 0.5 ofin remaining(12.7 mm) in (25.4 mm) on each side of the morphing section that cannot be morphed. The last 0.5 in (12.7 mm) spanof remaining was needed span to was embed needed the wing to embed to the the circular wing base to the of thecircular aerodynamic base of the loading aerodynamic scales. The loading total of remaining span was needed to embed the wing to the circular base of the aerodynamic loading spanscales. in The contact total with span the in airﬂowcontact waswith 11.5 the inairflow (292.1 was mm). 11.5 in (292.1 mm). scales. The total span in contact with the airflow was 11.5 in (292.1 mm). TheThe morphingmorphing sectionsection ofof thethe wingwing isis composedcomposed ofof threethree ribs,ribs, whichwhich areare connectedconnected byby rodsrods toto itsits The morphing section of the wing is composed of three ribs, which are connected by rods to its trailingtrailing andand leading edges. edges. These These connections connections allow allow the the ribs ribs to to move move in inparallel, parallel, which which results results in an in trailing and leading edges. These connections allow the ribs to move in parallel, which results in an anidentical identical morphing morphing along along the the span span of of the the morphing morphing section. section. To To obtain obtain a very goodgood aerodynamicaerodynamic identical morphing along the span of the morphing section. To obtain a very good aerodynamic behavior,behavior, aa heat-shrinkableheat-shrinkable plasticplastic waswas installedinstalled onon thethe surfacesurface ofof thethe wing.wing. WhenWhen thisthis plasticplastic waswas behavior, a heat-shrinkable plastic was installed on the surface of the wing. When this plastic was installedinstalled overover thethe slits,slits, thethe morphingmorphing surfacesurface moved,moved, maximizingmaximizing thethe spacingspacing betweenbetween thethe slitsslits andand installed over the slits, the morphing surface moved, maximizing the spacing between the slits and preservingpreserving thethe maximummaximum displacementdisplacement ofof morphingmorphingfor forthe thecontrol controlsurfaces. surfaces. preserving the maximum displacement of morphing for the control surfaces. FigureFigure8 8 shows shows the the internal internal structure structure of of the the wing wing with with its its MCS. MCS. In In previous previous prototypes prototypes (MTE (MTE Figure 8 shows the internal structure of the wing with its MCS. In previous prototypes (MTE andand MLE),MLE), thethe servomotorsservomotors werewere ﬁxedfixed onon thethe centralcentral rib.rib. TheThe MCSMCS requiredrequired twotwo servomotors;servomotors; twotwo and MLE), the servomotors were fixed on the central rib. The MCS required two servomotors; two servomotorservomotor bracketsbrackets were were added added next next to to the the central central rib rib on on the the wing wing structure. structure. All All other other features features of the of servomotor brackets were added next to the central rib on the wing structure. All other features of designthe design (ribs with(ribs slits,with mainslits, spars,main controlspars, rods,control control rods,arms), control as arms), shown inas Figureshown8 ,in were Figure designed 8, were in the design (ribs with slits, main spars, control rods, control arms), as shown in Figure 8, were thedesigned MTE, forin the the MTE, rear part for the of the rear wing, part orof inthe the wing MLE,, or forin the the MLE, front partfor the of thefront wing. part of the wing. designed in the MTE, for the rear part of the wing, or in the MLE, for the front part of the wing. MTE Servomotors MTE Servomotors

Main spars Main spars

MLE Control arms MLE Control arms

Figure 8. MCS internal assembly. Figure 8. MCS internal assembly. 4. Prototype Manufacturing Figure 8. MCS internal assembly. 4. Prototype Manufacturing 4. PrototypeThe prototype Manufacturing of the MCS requires wood as raw material, while the other parts are made from commerciallyThe prototype available of the material MCS requires and hardware. wood as All ra thew material, wooden pieces,while the with other the soleparts exception are made of from the The prototype of the MCS requires wood as raw material, while the other parts are made from spar,commercially were cut withavailable a LASER material cutting and machine, hardware. enabling All the the wooden pieces to pieces, be connected with the (with sole glue) exception together. of commercially available material and hardware. All the wooden pieces, with the sole exception of Tothe ensure spar, were the correct cut with positioning a LASER of cutting the pieces machine, during enabling gluing, the the pieces jigs were to be also connected done with (with plywood glue) the spar, were cut with a LASER cutting machine, enabling the pieces to be connected (with glue) andtogether. cut using To ensure the LASER the correct machine. positioning These jigs of providethe pieces the during exact spacinggluing, the between jigs were the ribsalso todone obtain with a together. To ensure the correct positioning of the pieces during gluing, the jigs were also done with plywood and cut using the LASER machine. These jigs provide the exact spacing between the ribs plywood and cut using the LASER machine. These jigs provide the exact spacing between the ribs

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Aerospace 2020,, 7,, xx FORFOR PEERPEER REVIEWREVIEW 7 of 22 morphing span of 9.5 in (241.3 mm) with an overall span of 12 in (304.8 mm), the angle of incidence of to obtain a morphing span of 9.5 in (241.3 mm) with an overall span of 12 in (304.8 mm), the angle theto obtain ribs and a morphing the perpendicularity span of 9.5 ofin the(241.3 ribs mm) according with an to theoverall main span spars of (Figure12 in (304.89). mm), the angle of incidence of the ribs and the perpendicularity of thethe ribsribs accordingaccording toto thethe mainmain sparsspars (Figure(Figure 9).9).

Figure 9. Morphing ribs placed in the manufacturing guide. Figure 9. MorphingMorphing ribsribs placedplaced inin thethe manufacturingmanufacturing guide.guide. The prototype was manufactured in two phases. First, the central section was constructed. This The prototype was manufactured in two phases. First,t, thethe centralcentral sectionsection waswas constructed.constructed. ThisThis section corresponds to the MCS of the wing, with a span of 9.5 in (241.3 mm). Each rectangular part of section corresponds to the MCS of the wing, with a span of 9.5 in (241.3 mm). Each rectangular part the wing surface was LASER-cut to ensure the straightest slits possible, as shown in Figure 10. of the wing surface was LASER-cut to ensure the straightest slits possible, as shown in Figure 10.

Figure 10. CentralCentral section section of of the the wing wing corresponding corresponding to the MCS.

InIn orderorder toto obtainobtain thethe surfacesurfacesurface atat thethethe leadingleadingleading edge,edge, thethe balsabalsa leavesleaves werewere moistenedmoistened andand thenthen shaped intointo moldsmolds (Figure(Figure 1111).). The molds were alsoalso cutcut withwith aa LASERLASER cuttingcutting machinemachine onon plywood.plywood.

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Figure 11. Leading edge mold. Figure 11. LeadingLeading edgeedge mold.mold.

5. The Price–Païdoussis Wind Tunnel 5. The Price–Païdoussis Wind Tunnel The LARCASELARCASE laboratorylaboratory is is equipped equipped with with the the Price–Païdoussis Price–Païdoussis subsonic subsonic wind wind tunnel tunnel (Figure (Figure 12), The LARCASE laboratory is equipped with the Price–Païdoussis subsonic wind tunnel (Figure which12), which has alreadyhas already been been used used in many in many LARCASE LARCASE projects projects [19,25 [19,25,28–30]).,28–30]). 12), which has already been used in many LARCASE projects [19,25,28–30]).

Figure 12. Price–Païdoussis subsonic wind tunnel of LARCASE. Figure 12. Price–PaïdoussisPrice–Païdoussis subsonicsubsonic windwind tunneltunnel ofof LARCASE.LARCASE.

This openopen circuitcircuit wind wind tunnel tunnel (Figure (Figure 13 )13) is modularis modular and and allows allows test chamberstest chambers of di ﬀoferent different sizes. This open circuit wind tunnel (Figure 13) is modular and allows test chambers of different Thesizes. test The chamber test chamber used forused wing for wing testing testing with thewith MCS the MCS is 2 ft is (0.609 2 ft (0.609 m) tall, m) 3tall, ft (0.914 3 ft (0.914 m) wide m) wide and sizes. The test chamber used for wing testing with the MCS is 2 ft (0.609 m) tall, 3 ft (0.914 m) wide 4and ft (1.2194 ft m)(1.219 long m) (Figure long 14(Figure). This 14). test chamberThis test sizechamber enables size measurement enables measurement of model aerodynamic of model and 4 ft (1.219 m) long (Figure 14). This test chamber size enables measurement of model performanceaerodynamic atperformance speeds ranging at speeds from 6ranging m/s to 35from m/ s.6 m/s to 35 m/s. aerodynamic performance at speeds ranging from 6 m/s to 35 m/s.

Figure 13. Dimensions of the Price–Païdoussis subsonic wind tunnel. Figure 13. DimensionsDimensions ofof thethe Price–PaïdoussisPrice–Païdoussis subsonicsubsonic windwind tunnel.tunnel.

Aerospace 2020, 7, 23 9 of 22 Aerospace 2020,, 7,, xx FORFOR PEERPEER REVIEWREVIEW 9 of 22

Figure 14. Dimension of the test chamber of the wind tunnel. Figure 14. DimensionDimension ofof thethe testtest chchamber of the wind tunnel. To obtain results, the wind tunnel was equipped with an aerodynamic loading scale whose design To obtain results, the wind tunnel was equipped with an aerodynamic loading scale whose and implementation are explained in [28,31,32] (Figure 15). The aerodynamic loading scales allowed design and implementation are explained in [28,31,32] (Figure 15). The aerodynamic loading scales measurement of the forces [31] to control a servomotor installed in the test wing [28] and to control the allowed measurement of the forces [31] to control a servomotor installed in the test wing [28] and to change of the angle of attack of the wing during testing [32]. For the tests of the wing with the MCS, control the change of the angle of attack of the wing during testing [32]. For the tests of the wing a servomotor control was added to the interface. The interface had to be modiﬁed to allow the display with the MCS, a servomotor control was added to the interface. The interface had to be modified to of the forces according to the second servomotor. allow the display of the forces according to the second servomotor.

Figure 15. Aerodynamic loading scales. Figure 15. Aerodynamic loading scales. 6. Results 6. Results During wind tunnel tests, the aerodynamic forces of drag and lift were measured on the MCS. All testsDuring were wind carried tunnel out attests, a speed the aerodynamic of 20 m/s, for anforces air density ofof dragdrag of andand 1.18 liftlift kg werewere/m3. Themeasuredmeasured leading onon and thethe trailing MCS.MCS. Alledges tests of thewere wing carried were out morphed at a speed according of 20 tom/s, their for angle an air values density presented of 1.18 inkg/m³. Table 4The. leading and trailing edges of the wing were morphed according to their angle values presented in Table 4. Table 4. Morphing cases studied in wind tunnel. Table 4. Morphing cases studied in wind tunnel. Case StudyTable 4. Morphing cases MTE studied Angle in wind tunnel. MLE Angle Fixed wingCase study MTE Nangle/AN MLE angle /A MCSFixed 0 wing N/A 0◦ N/A 0◦ MCS 5MCS 0 0° 5 ◦ 0° 5◦ MCS 10 10◦ 10◦ MCS 5 5° 5° MTE 5 5◦ 0◦ MCS 10 10° 10° MTE 10MCS 10 10° 10 ◦ 10° 0◦ MTE 5 5° 0° MTE 10 10° 0° For each of these cases, theMTE drag 10 (Figure 16) 10° and the lift (Figure 0° 17) forces variation curves with the angleFor each of attack of these were cases, plotted the drag using (Figure measurements 16) and the carried lift (Figure out in 17) the forces wind variation tunnel. curves From thesewith the angle of attack were plotted using measurements carried out in the wind tunnel. From these

Aerospace 2020, 7, 23 10 of 22 Aerospace 2020, 7, x FOR PEER REVIEW 10 of 22 Aerospace 2020, 7, x FOR PEER REVIEW 10 of 22 measuredmeasured values,values, the performanceperformance of thethe wingwing withwith thethe MCSMCS waswas studied.studied. The drag coefficients’ coefficients’ measured values, the performance of the wing with the MCS was studied. The drag coefficients’ variationvariation showedshowed in FigureFigure 1616 thatthat thethe wingwing withwith thethe MCSMCS generatedgenerated moremore dragdrag thanthan aa fixedfixed wingwing variation showed in Figure 16 that the wing with the MCS generated more drag than a fixed wing (without(without controlcontrol surface) surface) for for an an angle angle of of attack attack higher higher than than7 −◦7°and and that that its its stall stall angle angle was was lower lower by 4by◦. (without control surface) for an angle of attack higher than− −7° and that its stall angle was lower by The4°. The diff erencedifference in the in variation the variation of the of drag the coedragfficient coefficient obtained obtained for each for morphing each morphing case was case too smallwas too to 4°. The difference in the variation of the drag coefficient obtained for each morphing case was too besmall analyzed to be analyzed from Figure from 16 Figure. 16. small to be analyzed from Figure 16. 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2 0.15 0.15

Drag coefficient Cd Drag coefficient 0.1

Drag coefficient Cd Drag coefficient 0.1 0.05 0.05 0 0 -20 -15 -10 -5 0 5 10 15 20 25 -20 -15 -10 -5 0 5 10 15 20 25 Angle of attack MCS 0 Angle of attackMCS 5 MCS 010 MCSMTE 510 MCSMTE 105 MTEFixed 10 wing MTE 5 Fixed wing Flapped wing Flapped wing Figure 16. Drag coefficient variation with angle of attack. Figure 16. Drag coefficient coeﬃcient variation with angle of attack.attack.

1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 -0.2 Lift coefficient Cl coefficient Lift -0.2 Lift coefficient Cl coefficient Lift -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -20 -15 -10 -5 0 5 10 15 20 25 -20 -15 -10 -5 0 5 10 15 20 25 Angle of attack Angle of attack MCS 0 MCS 5 MCS 010 MCSMTE 510 MCSMTE 105 MTEFixed 10 wing MTE 5 Fixed wing Flapped wing Flapped wing FigureFigure 17.17. Lift coecoefficientﬃcient variationvariation withwith angleangle ofof attack.attack. Figure 17. Lift coefficient variation with angle of attack. The lift coefficient variation curves, Figure 17, show that the MTE acts on the variation of the The lift coefficient variation curves, Figure 17, show that the MTE acts on the variation of the lift coefficient of the wing by causing a shift to the left, for a positive angle. The MLE has no effect lift coefficient of the wing by causing a shift to the left, for a positive angle. The MLE has no effect on the value of the lift coefficient for an angle of attack of 0° and the slope of the variation of the lift on the value of the lift coefficient for an angle of attack of 0° and the slope of the variation of the lift coefficient. coefficient.

Aerospace 2020, 7, 23 11 of 22

The lift coefficient variation curves, Figure 17, show that the MTE acts on the variation of the lift coefficient of the wing by causing a shift to the left, for a positive angle. The MLE has no effect on the valueAerospace of 2020 the, lift7, x coeFORffi PEERcient REVIEW for an angle of attack of 0◦ and the slope of the variation of the lift coeffi11cient. of 22 Figure 18 shows that the L/D variations with the angle of attack values are close to each other for eachFigure of morphing 18 shows camber that cases. the L/D The variations maximum with L/D the tends angle to shift of attack to the values left of theare curvesclose to (closer each toother the forangle each of attackof morphing 0◦) when camber the morphing cases. The of maximum the camber L/D increases. tends to It shift is also to shownthe left that of the the curves MCS reduces (closer tothe the L/D angle of the of wing attack for 0°) angles when of the values morphing of 5◦ to of the the stall camber angle, increases. but for angles It is also smaller shown than that 5◦, the the MCS reducesgives the the highest L/D of L/ D.the wing for angles of values of 5° to the stall angle, but for angles smaller than 5°, the MCS gives the highest L/D.

30 25 20 15 10 5

Lift on drag ratio L/D drag ratio on Lift 0 -5

-10 -20-15-10-50 5 10152025 Angle of attack MCS 0 MCS 5 MCS 10 MTE 10 MTE 5 Fixed wing Flapped wing

Figure 18.18. Lift on drag ratio variation with the angle of attack.attack

Figure 1919 showsshows aa modiﬁcationmodification of of wing wing behavior behavior during during the the stall sta whenll when camber camber morphing morphing is at is 10 at◦ (case10° (case MC 10).MC These 10). behaviorsThese behaviors of the drag of andthe liftdrag coe ﬃandcient lift variation coefficient curves variation with the curves morphing with of the morphingtrailing and of leading the trailing edges and are identicalleading edges to those are observed identical during to those independent observed during analyses independent of the MTE analysesand MLE of systems the MTE [25 and]. It canMLE thus systems be seen [25]. that It thecan presencethus be seen of the that MLE the systempresence does of notthe generateMLE system any doesinterferences not generate on the any MTE interferences system and on that the thereMTE issystem no additional and that drag there due is no to theadditional combination drag due of the to thetwo combination systems on the of the same two wing. systems on the same wing.

0.8

0.75

0.7

0.65

0.6

Lift coefficient Cl coefficient Lift 0.55

0.5

0.45 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Angle of attack MCS 0 MCS 5 MCS 10 MTE 10 MTE 5 Fixed wing Flapped wing Figure 19. Lift coefficient variation with the angle of attack around the stall angle.

Aerospace 2020, 7, x FOR PEER REVIEW 11 of 22

Figure 18 shows that the L/D variations with the angle of attack values are close to each other for each of morphing camber cases. The maximum L/D tends to shift to the left of the curves (closer to the angle of attack 0°) when the morphing of the camber increases. It is also shown that the MCS reduces the L/D of the wing for angles of values of 5° to the stall angle, but for angles smaller than 5°, the MCS gives the highest L/D.

30 25 20 15 10 5

Lift on drag ratio L/D drag ratio on Lift 0 -5 -10 -20-15-10-50 5 10152025 Angle of attack MCS 0 MCS 5 MCS 10 MTE 10 MTE 5 Fixed wing Flapped wing

Figure 18. Lift on drag ratio variation with the angle of attack

Figure 19 shows a modification of wing behavior during the stall when camber morphing is at 10° (case MC 10). These behaviors of the drag and lift coefficient variation curves with the morphing of the trailing and leading edges are identical to those observed during independent analyses of the MTE and MLE systems [25]. It can thus be seen that the presence of the MLE system Aerospace 2020, 7, 23 12 of 22 does not generate any interferences on the MTE system and that there is no additional drag due to the combination of the two systems on the same wing.

0.8

0.75

0.7

0.65

0.6

Lift coefficient Cl coefficient Lift 0.55

0.5

0.45 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Angle of attack MCS 0 MCS 5 MCS 10 MTE 10 MTE 5 Fixed wing Flapped wing Figure 19. Lift coecoefficientﬃcient variation with thethe angleangle of attackattack aroundaround thethe stallstall angle.angle.

The following figures and discussion will only consider the MCS 0, MCS 5, MCS 10, and Fixed Wing cases to improve the visibility of the curves. However, these curves alone cannot assess the effectiveness of the wing with the MCS because of the fact that for a given angle, the MCS provides more lift, but generates more drag, than a fixed wing. In the next section, the methodology to conclude on the effectiveness of the MCS is discussed.

7. Discussion During the design of an aircraft, we seek to obtain a target lift value. To allow an analysis of the performance of the wing with the MCS, it is preferred to represent the drag coefficient variation with the lift coefficient. These curves made it possible to identify the configuration that generates the least drag, given a target lift coefficient value. This idea allows to define its specific morphing configuration for drag minimization, for each flight case of an aircraft, characterized by a needed lift. The drag coefficient variation differences are small between each case study. As we want to establish the effectiveness of the MCS for its use on an aircraft, we can reduce the number of measurements displayed by keeping only the measurement for positive lift coefficients and by removing the measurements corresponding to the stall angles. Thus, in Figure 20, the values obtained for each case studied are compared. It can be observed that a fixed wing allows obtaining the least drag in the range of lift coefficients allowed by the NACA0012 airfoil. However, this wing has no control surface for controlling the aircraft, which means that this configuration is not functional for an aircraft. Aerospace 2020, 7, x FOR PEER REVIEW 12 of 22

The following figures and discussion will only consider the MCS 0, MCS 5, MCS 10, and Fixed Wing cases to improve the visibility of the curves. However, these curves alone cannot assess the effectiveness of the wing with the MCS because of the fact that for a given angle, the MCS provides more lift, but generates more drag, than a fixed wing. In the next section, the methodology to conclude on the effectiveness of the MCS is discussed.

7. Discussion During the design of an aircraft, we seek to obtain a target lift value. To allow an analysis of the performance of the wing with the MCS, it is preferred to represent the drag coefficient variation with the lift coefficient. These curves made it possible to identify the configuration that generates the least drag, given a target lift coefficient value. This idea allows to define its specific morphing configuration for drag minimization, for each flight case of an aircraft, characterized by a needed lift. The drag coefficient variation differences are small between each case study. As we want to establish the effectiveness of the MCS for its use on an aircraft, we can reduce the number of measurements displayed by keeping only the measurement for positive lift coefficients and by removing the measurements corresponding to the stall angles. Thus, in Figure 20, the values obtained for each case studied are compared. It can be observed that a fixed wing allows obtaining the least drag in the range of lift coefficients allowed by the NACA0012 airfoil. However, this wing Aerospacehas no 2020control, 7, 23 surface for controlling the aircraft, which means that this configuration is13 ofnot 22 functional for an aircraft.

0.12

0.1

0.08

0.06

0.04 Drag coefficient Cd Drag coefficient

0.02

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Lift coefficient Cl MCS 0 MCS 5 MCS 10 Fixed wing

Figure 20. DragDrag coefficient coeﬃcient variation with the lift coefficient coeﬃcient variation.

The fixedfixed wingwing configuration configuration was was studied studied for for the the comparison comparison of its of result its result with thosewith ofthose an MCSof an 0 MCSconfiguration. 0 configuration. The diff Theerences differences in these in two these cases two for ca theses variationfor the variation of drag coeof dragfficient coefficient with the with angle the of angleattack of (Figure attack 20 (Figure) came from20) came the interferencefrom the inte betweenrference the between MCS and the aerodynamic MCS and aerodynamic fluid around fluid the wing.around The the variation wing. The of thevariation MCS 0 of and the MCS MCS 10 0 drag and coe MCSfficient 10 drag values coefficient are too close values for theare lifttoo coe closefficient for valuesthe lift betweencoefficient 0.25 values and 0.5between to define 0.25 which and 0.5 configuration to define which would configuration generate less would drag than generate the other less dragconfiguration. than the other For a liftconfiguration. coefficient value For a lesslift thancoefficient 0.1, the value MCS less 0 case than generates 0.1, the lessMCS drag; 0 case similarly, generates for lessa lift drag; coeffi similarly,cient value for greater a lift coefficient than 0.5, the value MCS greater 10 case than generates 0.5, the less MCS drag. 10 Therecase generates is no lift coelessffi drag.cient valueThere foris no which lift coefficient the MCS 5value case for generates which the less MCS drag, 5 butcase for generates lift coeffi lesscient drag, values but lessfor lift than coefficient 0.25 and valuesbetween less 0.5 than and 0.6,0.25 the and MCS between 5 case is0.5 very and close 0.6, the to the MCS MCS 5 10case case. is very It would close therefore to the MCS be preferred 10 case. toIt wouldmake the therefore transition be betweenpreferred the to MCSmake 0 the case transiti and theon MCS between 10 case the when MCS the0 case lift coeandffi thecient MCS required 10 case to make the aircraft fly will be between 0.5 and 0.6. The drag generated by the wing during a flight will be minimized.

8. Application of results with the UAS-S4 Ehécatl The Unmanned Aerial System (UAS) S4 Ehécatl is an autonomous flight system. It includes an onboard camera, an autopilot and the sensors necessary for its operation. The UAS-S4 Ehécatl model was developed in Mexico by Hydra Technologies in 2002 and made its first flight in 2006. It is therefore a continuous development project for almost 15 years. The UAS-S4 Ehécatl is used by the Mexican army and police. As part of the research developed at the Research Laboratory in active control, avionics and aeroservoelasticity (LARCASE), we use it to develop new methods of analysis, design and manufacturing applied to morphing wings. The geometries for the UAS-S4 in this paper are in Table5.

Table 5. Geometrical data of the UAS-S4.

Geometry Value Wing Surface S 2.9769 m2 Root chord CR 656.159 mm Wing span b 4.19 m Wing Taper Ratio λ 0.6057 Aerospace 2020, 7, 23 14 of 22

To measure the impact of the MCS on the drag and lift forces of the UAS-S4, we must calculate the Cd0 and clα values from the lift and drag coeﬃcient values using Equation (3). The value of clα can be calculated using the equation:

cl Cl = ∝ , (3) ∝ cl 1 + π AR∝ e ∗ ∗ where the aspect ratio (AR) of the wing is:

AR = b/c, (4) and the Oswald coeﬃcient for a straight wing is: e = 1.78 1 0.045 AR0.68 0.64, (5) ∗ − ∗ −

The value of Clα is obtained from the lift coeﬃcient linear variation curves with the angle of attackAerospace (Figure 2020, 7, x21 FOR), and PEER the REVIEW equations of these curves are presented in Table6. 14 of 22

0.8 0.6 0.4 0.2 0

Lift coefficient Cl Lift coefficient -0.2 -0.4 -0.6

-0.8 -20 -15 -10 -5 0 5 10 15 20 25 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing

Figure 21. Lift coefficient coeﬃcient variation curve with the angle of attack.

Table 6. Equation of lift coeﬃcient variation with the angle of attack. Table 6. Equation of lift coefficient variation with the angle of attack.

Studied Cases Cl equation of Variation Clα Studied cases Cl equation of variation Clα Fixed wing y = 0.0446x 0.0112 0.0446 Fixed wing y=0.0446x-0.0112− 0.0446 MC 0 y = 0.043x + 0.0294 0.043 MC 5MC 0 y = y=0.043x+0.02940.0421x + 0.1138 0.043 0.0421 MC 10MC 5 y y=0.0421x+0.1138= 0.041x + 0.1885 0.0421 0.041 MC 10 y=0.041x+0.1885 0.041 The span of the wing in the wind tunnel was 11.5 in. Because the floor of the wind tunnel acts The span of the wing in the wind tunnel was 11.5 in. Because the floor of the wind tunnel acts as a symmetry plane with respect to the aerodynamics flow around the wing, the span considered as a symmetry plane with respect to the aerodynamics flow around the wing, the span considered for the calculation must be 23 in., and the chord has 10 in. The aspect ratio AR = 2.3 and the Oswald for the calculation must be 23 in., and the chord has 10 in. The aspect ratio AR = 2.3 and the Oswald coefficient value e = 0.9989 were obtained. These values allow us to calculate the cl corresponding to coefficient value e = 0.9989 were obtained. These values allow us to calculate the ∝𝑐𝑙 corresponding the wing airfoil for each case study. The cl values are presented in Table7. ∝ to the wing airfoil for each case study. The∝ 𝑐𝑙∝ values are presented in Table 7.

Table 7. Values of 𝑐𝑙∝ for each case study.

Case study clα Fixed wing 0.0449 MC 0 0.0433 MC 5 0.0423 MC 10 0.0412

The value of 𝐶𝑑 is calculated using the equation:

𝐶𝑑 =𝐶𝑑−𝐶𝑑, (6) where:

𝐶𝑑 = , (7) ∗∗

From the equations of Cl, the induced drag 𝐶𝑑 for each case studied was calculated (Figure 22). The value of Cd was obtained using the drag coefficient variation curve with the angle of attack (Figure 23). The equations of these polynomial (2nd order) curves are presented in Table 8. From the

Aerospace 2020, 7, 23 15 of 22

Table 7. Values of cl for each case study. ∝

Case Study clα Fixed wing 0.0449 MC 0 0.0433 MC 5 0.0423 MC 10 0.0412

The value of Cd0 is calculated using the equation:

Cd = Cd Cd , (6) 0 − i where: Cl2 Cd = , (7) i π AR e ∗ ∗ From the equations of Cl, the induced drag Cdi for each case studied was calculated (Figure 22). The value of Cd was obtained using the drag coeﬃcient variation curve with the angle of attack (FigureAerospace 202023)., 7 The, x FOR equations PEER REVIEW of these polynomial (2nd order) curves are presented in Table8.15 From of 22 the induced drag Cdi and the total drag Cd, the value of drag of the skin friction Cd0 is determined (Figureinduced 24 drag). 𝐶𝑑 and the total drag Cd, the value of drag of the skin friction 𝐶𝑑 is determined (Figure 24).

0.16

0.14

0.12

0.1

0.08

0.06

0.04 Induce drag coefficient Cdi drag coefficient Induce 0.02

0 -20 -10 0 10 20 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing Figure 22. Induced drag coeﬃcient Cd variation with the angle of attack. Figure 22. Induced drag coefficient 𝐶𝑑i variation with the angle of attack.

0.14

0.12

0.1

0.08

0.06

Drag coefficient Cd Drag coefficient 0.04

0.02

0 -20 -15 -10 -5 0 5 10 15 20 25 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing

Figure 23. Drag coefficient Cd variation with the angle of attack.

Table 8. Equation of drag coefficient variation with angle of attack.

Studied cases Cd equation of variation Fixed wing y = 0.000364x2 − 0.000397x + 0.010814 MC 0 y = 0.000368x2 − 0.000446x + 0.022767 MC 5 y = 0.000347x2 + 0.000788x + 0.028511 MC 10 y = 0.000333x2 + 0.001496x + 0.028223

Aerospace 2020, 7, x FOR PEER REVIEW 15 of 22 induced drag 𝐶𝑑 and the total drag Cd, the value of drag of the skin friction 𝐶𝑑 is determined (Figure 24).

0.16

0.14

0.12

0.1

0.08

0.06

0.04 Induce drag coefficient Cdi drag coefficient Induce 0.02

0 -20 -10 0 10 20 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing Aerospace 2020, 7, 23 16 of 22 Figure 22. Induced drag coefficient 𝐶𝑑 variation with the angle of attack.

0.14

0.12

0.1

0.08

0.06

Drag coefficient Cd Drag coefficient 0.04

0.02

0 -20 -15 -10 -5 0 5 10 15 20 25 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing

Figure 23. Drag coefficient coeﬃcient Cd variation with the angle of attack.

Table 8. Equation of drag coeﬃcient variation with angle of attack. Table 8. Equation of drag coefficient variation with angle of attack. Studied Cases Cd Equation of Variation Studied cases Cd equation of variation 2 Fixed wing y = 0.000364x2 0.000397x + 0.010814 Fixed wing y = 0.000364x − 0.000397x− + 0.010814 MC 0 y = 0.000368x2 0.000446x + 0.022767 MC 0 y = 0.000368x2 − 0.000446x− + 0.022767 MC 5 y = 0.000347x2 + 0.000788x + 0.028511 MC 5 y = 0.000347x2 + 0.000788x2 + 0.028511 Aerospace 2020, 7, x FOR PEER MCREVIEW 10 y = 0.000333x + 0.001496x + 0.028223 16 of 22 MC 10 y = 0.000333x2 + 0.001496x + 0.028223

0.09 0.08

0.07

0.06

0.05

0.04

0.03 Skin fricton drag Cd0 Skin fricton 0.02

0.01

0 -20 -10 0 10 20 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing

Figure 24. Skin friction drag variatio variationn with the angle of attack.

As shown in Figure 20, for the same lift value, the fixed wing generates less drag. However, as seen in Figure 17, for the same lift value, the angle of attack of the MCS is lower than that of the fixed wing. This observation implies that the angle of attack of the fuselage for an aircraft using the MCS will be lower than the angle of attack of the fuselage of a conventional aircraft. The variation of the drag coefficient with the lift coefficient is recalculated using the UAS-S4 wing and fuselage geometry as the fuselage geometry needs to be considered. The drag and lift coefficients of the fuselage were obtained using the UAS-S4 in-house simulator for flight conditions corresponding to the wind tunnel tests (20 m/s) [33]. The drag and lift performance of the wings were obtained by using Equations (3), (4) and (8) to (10) with the previously calculated clα and Cd0 values, and by use of the wing geometry of UAS-S4. The equation for modeling the drag coefficient of the fuselage with the angle of attack (AoA) from the drag coefficients used in the simulator at a speed of 20 m/s is: 𝐶𝑑 = 1.442834 ∗ 10 ∗ 𝐴𝑜𝐴 + 7.472932 ∗ 10 ∗ 𝐴𝑜𝐴 − 3.14648307 ∗ 10 ∗ 𝐴𝑜𝐴 + (8) 4.434891635 ∗ 10, The equation for modeling the lift coefficient of the fuselage with the angle of attack (AoA) from the drag coefficients used in the simulator at a speed of 20 m/s is: 𝐶𝑙 =3.08∗10 ∗ 𝐴𝑜𝐴 + 6.872 ∗ 10 ∗ 𝐴𝑜𝐴 + 3.33018 ∗ 10 ∗ 𝐴𝑜𝐴 − 8.16467 ∗ 10, (9)

In Equations (8) and (9), the angle of attack (AoA) is in degrees. The drag and lift coefficients of the fuselage were expressed according to the surface of the wing. This allows adding the coefficients of the fuselage to the coefficients of the wings. Thus, we could estimate the total drag and lift coefficients according to the following equations:

𝐶𝑙 =𝐶𝑙+𝐶𝑙, (10)

𝐶𝑑 =𝐶𝑑 +𝐶𝑑 +𝐶𝑑 +𝐶𝑑, (11) where:

Aerospace 2020, 7, 23 17 of 22

As shown in Figure 20, for the same lift value, the fixed wing generates less drag. However, as seen in Figure 17, for the same lift value, the angle of attack of the MCS is lower than that of the fixed wing. This observation implies that the angle of attack of the fuselage for an aircraft using the MCS will be lower than the angle of attack of the fuselage of a conventional aircraft. The variation of the drag coefficient with the lift coefficient is recalculated using the UAS-S4 wing and fuselage geometry as the fuselage geometry needs to be considered. The drag and lift coefficients of the fuselage were obtained using the UAS-S4 in-house simulator for flight conditions corresponding to the wind tunnel tests (20 m/s) [33]. The drag and lift performance of the wings were obtained by using Equations (3), (4) and (8) to (10) with the previously calculated clα and Cd0 values, and by use of the wing geometry of UAS-S4. The equation for modeling the drag coefficient of the fuselage with the angle of attack (AoA) from the drag coefficients used in the simulator at a speed of 20 m/s is:

Cd = 1.442834 10 6 AoA3+ 7.472932 10 5 AoA2 3.14648307 10 4 AoA+ 0 f ∗ − ∗ ∗ − ∗ − ∗ − ∗ , (8) 4.434891635 10 3 ∗ − The equation for modeling the lift coeﬃcient of the fuselage with the angle of attack (AoA) from the drag coeﬃcients used in the simulator at a speed of 20 m/s is:

Cl = 3.08 10 6 AoA3+ 6.872 10 5 AoA2 + 3.33018 10 3 AoA f ∗ − ∗ ∗ − ∗ ∗ − ∗ − , (9) 8.16467 10 3 ∗ − In Equations (8) and (9), the angle of attack (AoA) is in degrees. The drag and lift coefficients of the fuselage were expressed according to the surface of the wing. This allows adding the coefficients of the fuselage to the coefficients of the wings. Thus, we could estimate the total drag and lift coefficients according to the following equations:

Clt = Cl + Cl f , (10)

Cdt = Cd0 + Cd0 f + Cdi + Cdi f , (11) where: 2 Cl f Cd = , (12) i f π AR e ∗ ∗ Equation (13) will be used for calculating the Oswald coeﬃcient [1] because of the fact that the wing of UAS-S4 is trapezoidal with a sweep angle ΛLE = 6.353◦ and AR = 10.4785.

0.68 0.15 e = 4.61 1 0.045 AR (cos ΛLE) 3.1, (13) ∗ − ∗ ∗ −

By use of Equation (3) for the calculation of Clα of the wing and the values of Cl0 of the test wings, the variation curves of the lift coeﬃcient of the wing with the angle of attack can be traced in Figure 25. Then, Equations (9) and (10) give the lift coeﬃcient variations for the wing and fuselage assembly (Figure 26). Aerospace 2020, 7, x FOR PEER REVIEW 17 of 22 Aerospace 2020, 7, x FOR PEER REVIEW 17 of 22

𝐶𝑑 = , (12) 𝐶𝑑 = ∗∗, (12) ∗∗ Equation (13) will be used for calculating the Oswald coefficient [1] because of the fact that the Equation (13) will be used for calculating the Oswald coefficient [1] because of the fact that the wing of UAS-S4 is trapezoidal with a sweep angle 𝛬 = 6.353° and AR = 10.4785. wing of UAS-S4 is trapezoidal with a sweep angle 𝛬 = 6.353° and AR = 10.4785. . . 𝑒=4.61∗1 − 0.045 ∗ 𝐴𝑅. ∗ cos 𝛬. −3.1, (13) 𝑒=4.61∗1 − 0.045 ∗ 𝐴𝑅 ∗ cos 𝛬 −3.1, (13) By use of Equation (3) for the calculation of Clα of the wing and the values of Cl0 of the test By use of Equation (3) for the calculation of Clα of the wing and the values of Cl0 of the test wings, the variation curves of the lift coefficient of the wing with the angle of attack can be traced in wings, the variation curves of the lift coefficient of the wing with the angle of attack can be traced in AerospaceFigure 25.2020 Then,, 7, 23 Equations (9) and (10) give the lift coefficient variations for the wing and fuselage18 of 22 Figure 25. Then, Equations (9) and (10) give the lift coefficient variations for the wing and fuselage assembly (Figure 26). assembly (Figure 26). 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0

Lift coefficient Cl coefficient Lift -0.2

Lift coefficient Cl coefficient Lift -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -20 -10 0 10 20 -20 -10 0 10 20 Angle of attack MCS 0 Angle of attack MCS 5 MCS 0 MCS 5 MCS 10 Fixed wing MCS 10 Fixed wing Figure 25. Lift coefficient variation with angle of attack for the UAS-S4 wing. Figure 25. Lift coefficient coeﬃcient variation with angleangle of attack for the UAS-S4 wing.

1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0

Lift coefficient Cl coefficient Lift -0.2

Lift coefficient Cl coefficient Lift -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 -20 -10 0 10 20 -20 -10 0 10 20 Angle of attack MCS 0 Angle of attack MCS 5 MCS 0 MCS 5 MCS 10 Fixed wing MCS 10 Fixed wing FigureFigure 26.26. Lift coecoefficientﬃcient variation withwith angleangle ofof attackattack forfor UAS-S4UAS-S4 (wing(wing ++ fuselage). Figure 26. Lift coefficient variation with angle of attack for UAS-S4 (wing + fuselage).

Equation (7) allows the calculation of the induced drag coefficients for the UAS-S4 wing from the lift coefficients of the wing. Then, with Equation (11), the combination of wing and fuselage drag coefficients of the UAS-S4 are plotted (Figure 27). Aerospace 2020, 7, x FOR PEER REVIEW 18 of 22

Equation (7) allows the calculation of the induced drag coefficients for the UAS-S4 wing from Aerospacethe lift 2020coefficients, 7, 23 of the wing. Then, with Equation (11), the combination of wing and fuselage19 of 22 drag coefficients of the UAS-S4 are plotted (Figure 27).

0.12

0.1

0.08

0.06

0.04 Drag coefficient Cd Drag coefficient

0.02

0 -20 -10 0 10 20 Angle of attack MCS 0 MCS 5 MCS 10 Fixed wing

Figure 27.27. Drag coefficient coeﬃcient variation with angle of attack for UAS-S4.

Once the drag and lift coecoefficientfficient variationvariation curvescurves are obtained,obtained, the graph representing the variation ofof thethe drag drag coe coefficientfficient with with the the lift lift coe coeffifficientcient is plottedis plotted (Figure (Figure 28). 28). As seenAs seen in Figure in Figure 29, for 29, a liftfor coea liftfficient coefficient greater greater than 0.48, than the 0.48, wing the with wing a morphing with a ofmorphing the camber of ofthe 10 camber◦ (MCS 10)of 10° generates (MCS less10) draggenerates than less a fixed drag wing. than Thisa fixed value wing. corresponds, This value in corresponds, Figure 26, to in an Figure angle 26, of attackto an angle of 11◦ offor attack a fixed of wing11° for and a fixed of 7◦ forwing a wing and withof 7° a for morphing a wing ofwith the a camber morphing of 10 ◦of. Thisthe camber observation of 10°. indicates This observation that for the aircraftAerospaceindicates lift2020 that coe, 7, xffifor FORcient the PEER greateraircraft REVIEW thanlift coefficient 0.48, the MCS greater will than be more 0.48, advantageous the MCS will thanbe more the fixed advantageous wing.19 of 22 than the fixed wing. These values were calculated0.12 for a wing with a NACA0012 airfoil whose performances were obtained in the wind tunnel. This is not the airfoil used in the current UAS-S4, but it is a close one; the values are useful for potential gain that can be provided using an MCS on the UAS-S4. 0.1

0.08

0.06

0.04 Drag coefficient Cd Drag coefficient

0.02

0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Lift coefficient Cl MCS 0 MCS 5 MCS 10 Fixed wing

Figure 28. DragDrag coefficient coeﬃcient variation with lift coefficient coeﬃcient for the UAS-S4.

0.07

0.065

0.06

0.055

0.05

0.045 Drag coefficient Cd Drag coefficient 0.04

0.035

0.03 0.35 0.45 0.55 Lift coefficient Cl MCS 0 MCS 5 MCS 10 Fixed wing

Figure 29 Drag coefficient variation with lift coefficient for UAS-S4 (zoom).

9. Conclusions In this article, a new system allowing the complete morphing of the camber, from the airfoil leading edge to its trailing edge, was presented from its design to its validation in a wind tunnel. The design of this system provides an easy-to-manufacture and lightweight MCS for the wing structure. The MCS will consequently not penalize the performance of the aircraft from its weight point of view. The method used to calculate the maximum displacements of the MLE and of the MTE makes it easy to size the slits without having to perform an FEA optimization process. In order to apply this method, the thickness of the material remaining at the slits must allow the rib to bend without causing its plastic deformation. To ensure this bending, anisotropic materials, such as

Aerospace 2020, 7, x FOR PEER REVIEW 19 of 22

0.12

0.1

0.08

0.06

0.04 Drag coefficient Cd Drag coefficient

0.02

0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Lift coefficient Cl MCS 0 MCS 5 MCS 10 Fixed wing Aerospace 2020, 7, 23 20 of 22 Figure 28. Drag coefficient variation with lift coefficient for the UAS-S4.

0.07

0.065

0.06

0.055

0.05

0.045 Drag coefficient Cd Drag coefficient 0.04

0.035

0.03 0.35 0.45 0.55 Lift coefficient Cl MCS 0 MCS 5 MCS 10 Fixed wing

FigureFigure 29.29 DragDrag coefficient coeﬃcient variation variation with with lift lift coefficient coeﬃcient for UAS-S4 (zoom).

These values were calculated for a wing with a NACA0012 airfoil whose performances were 9. Conclusions obtained in the wind tunnel. This is not the airfoil used in the current UAS-S4, but it is a close one; the valuesIn arethis useful article, for apotential new system gain allowing that can bethe provided complete using morphing an MCS ofon the the camber, UAS-S4. from the airfoil leading edge to its trailing edge, was presented from its design to its validation in a wind tunnel. 9.The Conclusions design of this system provides an easy-to-manufacture and lightweight MCS for the wing structure.In this The article, MCS a will new consequently system allowing not penalize the complete the performance morphing ofof thethe camber,aircraft from theits weight airfoil leadingpoint of edge view. to The its trailing method edge, used was to presentedcalculate th frome maximum its design displacements to its validation of in the a windMLE tunnel.and of Thethe designMTE makes of this it system easy to provides size the an slits easy-to-manufacture without having to and perform lightweight an FEA MCS optimization for the wing process. structure. In Theorder MCS to apply will consequently this method, notthe penalizethickness the of performancethe material ofremaining the aircraft at the from slits its must weight allow point the of rib view. to Thebend method without used causing to calculate its plastic the deformation. maximum displacements To ensure this of bending, the MLE anisotropic and of the MTE materials, makes such it easy as to size the slits without having to perform an FEA optimization process. In order to apply this method, the thickness of the material remaining at the slits must allow the rib to bend without causing its plastic deformation. To ensure this bending, anisotropic materials, such as wood or carbon ﬁbers in the direction of the length of the rib will be more eﬀective than isotropic materials, such as steel or aluminum. The wind tunnel tests, despite having a lower than expected maximum morphing capabilities due to the manufacturing method, showed that the MCS improved the aerodynamic performance of the wings and of the UAS-S4. The MTE and MLE systems were also shown to be independent. The MTE acted on the lift of the wing, and the MLE acted on the stall angle, thus independent control of both systems was allowed. Wind tunnel performance scaling was used to determine the potential gain from using an MCS on the UAS-S4. The next step will be to design an MCS with the dimensions used for the UAS-S4 wing.

Author Contributions: Investigation, methodology, writing, D.C.; Supervision, Writing—review & editing, R.M.B. and T.W. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to sincerely thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for the Canada Research Chair Tier 1 in Aircraft Modelling and Simulation New Technologies funding, as well as the McGill University Michael Païdoussis and Stuart Price for the donation of the Price–Païdousis wind tunnel at the LARCASE, ÉTS. Conﬂicts of Interest: The authors declare that there is no conﬂict of interest regarding the publication of this paper. Aerospace 2020, 7, 23 21 of 22

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