Variable-span wing development for improved flight performance

Abstract

This paper describes the development and testing of a variable-span wing (VSW) concept. An aerodynamic shape optimisation code, which uses a viscous two-dimensional panel method formulation coupled with a non-linear vortex lattice algorithm and a sequential quadratic programming optimisation routine, is used to solve a drag minimisation problem to determine the optimal values of wing span for various speeds of the vehicle’s flight envelope while subject to geometric constraints. Structural design is performed using the finite element method for static analysis where the particular interface between wing parts is conveniently modelled. A full-scale prototype is built for ground testing the wing/actuator system. The wing is built in composite materials and an electro-mechanical actuation mechanism is developed using an aluminium rack and pinion system driven by two servomotors. Bench tests, performed to evaluate wing under load, showed that the system is capable of performing the required extension/retraction cycles and is suitable to be installed on a UAV airframe fully instrumented for evaluating the VSW concept prototype in flight. The data collected from the performed flights showed full functionality of the VSW and its aerodynamic improvements over a conventional fixed wing for the higher speed end of the flight envelope.

Keywords

Morphing aircraft telescopic wing variable-span wing UAV optimisation composite structure flight testing

Introduction

In recent years the development of morphing wing technologies has received a great deal of interest from the scientific community. These technologies potentially enable an increase in aircraft efficiency by changing the wing shape thus allowing the aircraft to fly near its optimal performance point at different flight conditions. Joshi et al. (2004) clearly demonstrated the advantages of these technologies where the flight envelope of a fixed geometry aircraft can be expanded so that new multi-role missions could be performed.

The design of adaptive mechanisms and structures, along with the development of smart materials that may allow bio-mimetic configurations of aircraft is highly desired in the near future. The new concepts and technologies developed up to now are a constant attempt to enhance the overall flight performance of aircraft, enabling new aircraft design approaches to be pursued and opening grounds for improved multi-mission flexibility.

These technologies can be divided into three different categories according to the type of geometric transformation implemented: out-of-plane transformations, aerofoil adjustments and planform changes. Out-of-plane transformations include twist, dihedral and spanwise bending. Regarding aerofoil adjustments, camber and thickness are the main geometric transformations. Finally, planform changes include variations of the wing’s chord, sweep and span. The very first concept of a morphing wing was developed by Makhonine on the MAK-10 aircraft. This vehicle had a telescoping mechanism where the outer panels of the wing slid inside the wing’s centre panels.

Several different concepts have been designed and tested in this field: from the pneumatic telescopic spars by Samuel and Pines (2007) and the inflatable wings by Cadogan et al. (2003) and Jacob et al. (2005), to the telescopic wing servo/pulley-actuated by Vale et al. (2011) and the zigzag (scissors-like) wing concept by Ajaj et al. (2013), among many others. Henry et al. (2005) also explored the effects on unmanned air vehicle (UAV) stability caused by asymmetric span variations. Since such a wing is very structurally demanding, Bae et al. (2005) proposed an aeroelastic and aerodynamic analysis of a variable wingspan for a cruise missile. Seigler et al. (2007) went further and built a fully adaptive wind tunnel model with seven degrees of freedom. A compliant skin supported by an internal honeycomb-like structure was tested on a span extending wing by Vocke et al. (2011). Some concepts tried to combine other morphing capabilities with span change. Gamboa et al. (2009) developed a wing concept for span extension and aerofoil thickness variation using a flexible compliant skin and Alemayehu et al. (2005) developed a telescopic span morphing wing with sweep change capability.

Despite the already large number of span morphing wing concepts devised and developed, very few reached sufficient maturity for flight tests. Manned flights with a telescopic wing were conducted with the FS-29 sailplane by the Akademische Fliegergruppe Stuttgart in 1975. A different concept, a batwing morphing concept from NextGen, has also been validated in flight after extensive design and wind tunnel testing (Bowman et al., 2007; Flanagan et al., 2007). More recently a telescopic wing UAV was developed through rapid prototyping technologies and demonstrated flight capability (Stern and Cohen, 2013).

Many projects have been done on aircraft morphing concepts, and much work is being carried out in this field: enhanced performance and increased energy efficiency of aircraft is of extreme importance and has driven the research (Barbarino et al., 2011). It is recognised that system performance and the advantages of such concepts are not easily grasped and therefore optimisation techniques are required during the design process. During concept development, even iteration between design and experiment is important. Much work has been done on aerodynamic shape optimisation of aerofoils and wings and multidisciplinary design optimisation of wing systems in order to enable shape changes to improve flight performance.

Alongside morphing technologies, the development of UAVs has undergone a major expansion in recent years. These vehicles are an excellent platform for testing new concepts of morphing wings. The use of UAVs for testing new concepts presents numerous advantages such as low development and operating costs, no flight crew is required and, since they are subjected to low aerodynamic loads, the use of several morphing technologies are potentiated.

This paper describes the design, development and testing of a variable-span wing (VSW) concept aimed at improving the performance of a small UAV which flies in the speed range between 11 and 40 m/s. It is interesting to note that practically no study in the literature provides flight performance results of the concepts presented, therefore this work not only summarises the design and development of a new telescopic span wing but also provides flight data on the VSW performance and also comparisons with a conventional fixed wing.

Aerodynamic optimisation

The main goal of this work is to design a wing for a small UAV that can perform in-flight span variations in order to reduce wing drag at a given flight speed. The aircraft fitted with the VSW should be capable of operating in the same range of speeds as with the original wing, from about the stall speed of 11 m/s to 40 m/s, with similar performance at low speed but better performance at high speed. The UAV under study is an experimental UAV developed by the Aerospace Sciences Department of University of Beira Interior. It is a high-wing pusher aircraft, with an electric brushless motor configured for 420 W, and the propeller placed behind its H-tail. The original wing structure is made of balsa wood ribs, a balsa wood torsion box and hard wood spars. The take-off weight of the aircraft, W, is 60 N. The original rectangular wing has a constant chord, c, of 0.25 m and a planform area, S, of 0.625 m². The aerofoil used is a SG6042, a low speed aerofoil with a good compromise between maximum lift coefficient and geometry simplicity. The cruise speed of the aircraft is about 20 m/s, and maximum speed about 40 m/s.

The shape and size of the VSW was obtained through a computational constrained aerodynamic shape optimisation aimed at determining the wing chord and span values that minimise its drag for a given speed range. The geometric constraints imposed on the wing design optimisation were dictated by component fitting, manufacturing simplicity and mechanism functionality considerations. A brief description of the optimisation procedure and its main results are given below but more detailed information can be sought in Mestrinho et al. (2011).

Aerodynamic analysis and optimisation

Simple medium-fidelity aerodynamic analysis algorithms were implemented and integrated with other aerodynamic analysis programs and optimisation algorithms in order to assemble the wing aerodynamic shape optimisation tool.

The aerodynamic analysis implemented in the code is done in two steps (Gamboa, 2007). First, the two-dimensional (2D) aerodynamic coefficients as functions of angle of attack (AOA) and Reynolds number (Re) at specified wing sections across the span of the wing are obtained using the solver of the XFOIL code (Drela, 2001). Then, a non-linear vortex lattice method (VLM) is used to obtain the lift distribution and the induced drag. The VLM algorithm implemented is based on the steady linear VLM from Katz and Plotkin (2001) and is coupled with an iterative decambering approach (Mukherjee et al., 2003). In calculating the total lift of the vehicle it is assumed that only wing and horizontal tail contribute to lift. The tailplane lift is calculated such that the pitching moment about the centre of gravity (CG; assumed at wing quarter chord position) is zero. Therefore, for a negative wing pitching moment, typical of positive cambered aerofoils, the wing lift must be greater than the weight to compensate for the negative tail lift. This affects not only the induced drag of the wing but also the parasite drag since it flies at a higher AOA.

In this tool, empirical weight information for the wing, the tailplane and the vertical tail was introduced to allow for the variations in aerofoil relative thickness, wing area, aspect ratio and taper ratio. The weight formulation is based on Raymer (2006) and is described by Gamboa (2007).

The gradients of the objective function and constraints are computed using forward finite-differences. The constrained aerodynamic shape optimisation is carried out with the sequential quadratic programming (SQP) constrained optimisation algorithm of FFSQP3.7 (Zhou et al., 1997). SQP has been shown to produce good results by Secanell and Suleman (2005).

Aerodynamic shape optimisation

The VSW planform geometry is illustrated in a schematic form in Figure 1. In this study, the wing does not exhibit any dihedral or any sweep (the quarter chord line lies along the y-axis) and is made of one rectangular inboard part (inboard fixed wing (IFW)) and a rectangular outboard part (outboard moving wing (OMW)) which slides in and out of the IFW for span changes. Taking into account fuselage dimensions and the geometric characteristics of the wing, four wing sections were defined from the root to the tip for the optimisation problem, as shown in Figure 1, where the lateral position of station 4 is the only one allowed to vary during the optimisation process. The positions of sections 2 and 3 are automatically defined given the highest value of the position of section 4 (maximum semi-span) in such a way that the OMW when fully retracted fits completely inside the IFW (between fuselage side and section 3) and when fully extended maintains a 0.1 m overlap with the IFW for structural reasons. The maximum wing span is 2.5 m, the same value as in the original fixed wing.

Several optimisation problems were studied by Mestrinho et al. (2011) but, for brevity, only the one that led to the implementation of the wing prototype is presented here. In this case, the OMW aerofoil is a SG6042 aerofoil modified to have a straight lower surface, the OMW chord length is fixed and equal to 0.25 m and no stall speed constraint is imposed. The optimisation statement is shown below, for two sets of design variables, span, b, and AOA, α, where the angles are in degrees:

Minimise : f = \int_{V_{i}}^{V_{f}} D (α, b, V) dV

(1)

\begin{matrix} L (α, b, V) = W \\ Subject to : & - 5 < α \leq 20 \\ 1.475 < b \leq 2.5 \end{matrix}

(2)

In the objective function of equation (1), the integral between the initial and final speed values, V_i and V_f, respectively, was calculated using Simpson’s rule where drag, D, was computed at five different speeds: 15, 20, 25, 30 and 35 m/s. For each one of these speed values there are two design variables, AOA and span, totalling 10 design variables for this optimisation problem. For the wing fully extended the increase in wing weight was computed as 3.6 N resulting in a take-off aircraft weight of 63.6 N. For the OMW fixed chord of 0.25 m, the IFW chord resulted in a value of 0.2822 m from an offset of 3 mm around the OMW aerofoil. Based on the aerodynamic shape optimisation results, the plots of Figure 2 were obtained for the VSW and the original fixed wing.

Figure 2(a) shows that the VSW has better performance than the original wing only at speeds above 25 m/s, indicating that the present design allows better performance at the higher speed end of the envelope. At 30 m/s the VSW has about 10% less drag than the original one. At a speed of 40 m/s the drag reduction increases drastically to 28%. At low speeds, the original wing outperforms the new wing, although presenting only slightly better results. The original wing was designed for low speeds, and near the design point it was expected to have better performance than the new wing because of the higher relative thickness of the aerofoil in the IFW and because of the less efficient aerofoil resulting from the lower surface simplification of the SG6042 aerofoil. Therefore, the new wing presents a slightly higher total drag at low speeds when it is fully extended, which is only compensated at higher speeds, when the wingspan starts to decrease. For example, one can see that above 20 m/s a major span reduction takes place (see Figure 2(b)), when the new wing performance surpasses the original wing, until the minimum span of 1.475 m is reached at a speed of 35 m/s. Stall speed increased too, from 10.75 m/s in the original wing to 11.5 m/s in the new wing. The increased weight of the wing had an important effect in the wing performance at low speeds. Lift-to-drag ratio of the VSW is slightly reduced below 19 m/s, then is maintained up to 23 m/s but is greatly increased at higher speeds (see Figure 2(c)). Clearly the increased drag below 25 m/s seen in Figure 2(a) is due to the increased weight of the VSW.

Fuselage drag was not considered in this study but clearly the smaller variation in AOA of the VSW may result in reduced fuselage pressure drag allowing further benefits in the aircraft overall drag curve. In the range 17.5–30 m/s the variation in AOA of the VSW is only around 2° whilst that of the original wing is 4.5°.

Structural design

The structural components of the wing were developed with a combination of composite materials and hard and soft wood which provide good general strength and stiffness. The sizing of the structure was performed using structural analysis models with the finite element method (FEM) considering limit material stresses and required structural stiffness. A brief description of the structural analysis and their main results is given below but more detailed information can be sought in Santos et al. (2013).

Materials and wing structure

The IFW uses a monocoque type of structure with a sandwich skin of carbon/foam/carbon which is required to both provide the correct shape and resist shear loads. From inside out, the load carrying thick skin has a layer of 48 g/m² glass/epoxy, a layer of 185 g/m² carbon/epoxy, a layer of 2 mm porous PVC foam (55 kg/m³), a layer of 185 g/m²carbon/epoxy, and finally another layer of 48 g/m² glass/epoxy. The PVC foam core was incorporated between the carbon fibre layers to allow embedding of the main spar and to give adequate stiffness to the skin. All fibre fabric layers are plain weave oriented at 0° along the wing span. The glass layers do not have a structural role but are added to reduce the porosity of the carbon/epoxy layers. The complete assembled skin has a thickness of 2.5 mm, which creates a fairly acceptable small discontinuity between the IFW and the OMW. Spar caps inside the IFW are composed of rectangular beams made of pultruded carbon fibre with a cross-section of 16 mm × 1.7 mm. For greater strength and stiffness, the spar extends along the complete fixed wing span of 1.475 m.

The total length of the OMW is 625 mm, where 525 mm is the stroke and 100 mm is the overlap with the remaining IFW so that bending and torsion moments can be effectively transmitted from the OMW to the IFW. The structural configuration used in the moving wing part is very conventional: the wing is composed of ten 2 mm thick balsawood ribs, a 240 g/m² carbon fibre/epoxy skin and a I-section spar consisting of 8 mm × 0.8 mm pultruded carbon spar caps with a 1.5 mm balsa wood spar web. The main spar confers sufficient bending stiffness while the ribs provide the correct wing shape. The ribs are bonded to the skin and spar with epoxy glue.

The cross-sections of the wing are represented in Figure 3 clearly showing the different structural layouts adopted for the inboard and outboard parts of the wing as necessary to allow the motion of the OMW inside the IFW. The circular tubes in the OMW are present to allow the span actuation system components to move inside it and although they have no special structural function they contribute to the stiffness of the OMW both in bending and in torsion.

The material properties for the PVC foam, the balsa wood and the pultruded carbon/epoxy elements were obtained from the manufacturer’s datasheet. The woven carbon/epoxy composite properties were obtained experimentally following ASTM D3039/D3039M (ASTM (2014)). This standard contains guidelines to determine the ultimate tensile strength of the composite and the longitudinal elastic modulus. Five rectangular carbon/epoxy specimens were hand laminated with a fibre orientation of 0° /90° balanced and symmetric, for which the specified dimensions are 25 mm in width, 250 mm in length and 1.1 mm in thickness. The specimens were tested in a Shimadzu universal testing machine up to rupture, with a test speed of 2 mm/min and with the data being recorded in the form of a load/strain curve. The maximum registered load was used to determine the ultimate tensile strength of the specimens and from the curve’s slope the elastic moduli, E₁ and E₂, were computed. Since the skin material has identical fibre fractions at 0° and 90° both longitudinal elastic moduli are assumed to be the same. The results were statistically analysed revealing the sample mean (average), the sample standard deviation and the sample coefficient of variation, in percentage. The properties of the different materials used in the VSW structure are summarised in Table 1.

Table 1.

Material properties.

Property	Woven carbon/epoxy	Pultruded carbon/epoxy	Balsa wood	PVC foam (Airex C70.55)
Density ρ, kg/m³	1600	1500	120	55
Longitudinal modulus E₁, GPa	51	120	1.28	0.045
Longitudinal modulus E₂, GPa	51	8	0.0192	0.045
Shear modulus G₁₂, GPa	5	5	0.04736	0.022
Poisson ratio ν₁₂	0.1	0.3	0.488	0.0227
Poisson ratio ν₂₃	0.1	0.3	0.231	0.0227
Tensile strength 1, MPa	600	1100	19.9	1.0
Tensile strength 2, MPa	600	—	—	1.0
Shear strength, MPa	90	70	1.07	0.7

Numerical model

The numerical model of the VSW wing was developed in ANSYS Mechanical using the ANSYS Parametric Design Language (APDL) (ANSYS, 2013) with shell and beam elements according to the model shown in Figure 3. An APDL script was written to handle geometry creation, material definition, section properties and meshing.

The IFW was discretised using SHELL181 elements. The sandwich skin was modelled with three layers built as offset surfaces from the aerofoil contour according to its own thickness. These three layers constitute the carbon/epoxy faces and PVC sandwich. In the locations of the embedded spar, the PVC foam layer was replaced with unidirectional pultruded carbon/epoxy elements. Likewise, the OMW skins, ribs, I-shaped spar web and circular spar were discretised using SHELL181 type elements. The OMW I-spar cap is discretised using BEAM188 elements.

The SHELL181 element is suitable for analysing thin to moderately-thick shell structures. It is a four-node element with six degrees of freedom at each node: translations in the x, y and z directions, and rotations about the x, y and z axes. This type of element is well-suited for linear, large rotation, and/or large strain nonlinear applications. In addition, the change in shell thickness is taken into account in nonlinear analyses. The BEAM188 is suitable for analysing slender to moderately thick beam structures. The element is a linear, quadratic, or cubic two-node beam element in three dimensions. BEAM188 has six degrees of freedom at each node. These include translations in the x, y and z directions and rotations about the x, y and z axes. This element is well suited for linear, large rotation and/or large strain nonlinear applications.

The peculiar structure used by the VSW, required the use of contact elements, in order to correctly model the interface. This contact in the overlap surface between the IFW and the OMW was modelled with a shell to shell contact using TARGE170 (target element for 3D geometries) and CONTA173 (contact element for 3D shells without mid side nodes). Since the distinction between the contact and target surfaces is not clear in the interface, a symmetric contact (or ‘two-pass contact’) was created. In this type of contact, each surface is designated to be both a target and a contact surface. Then, two sets of contact pairs between the contacting surfaces are generated. The symmetric contact is less efficient than asymmetric contact. One other reason to use this type of contact in this particular situation is to reduce penetration between contact surfaces. The contact elements’ behaviour is standard in order to simulate the flexible contact on the interface.

The wing was considered to be built-in at the root. In addition, the centre portion of the innermost rib of the OMW is constrained along the y axis to simulate the constraint imposed by the rack and pinion actuator mechanism and thus avoid outward sliding of the OMW. Figure 4 shows the different assemblies that make up the finite element model as well as the complete wing model.

Static analysis

In order to validate the numerical model, experimental deflection results of a wing prototype of the wing were used. In the experiment, the VSW with the span fully extended was clamped at its root and was statically tested with two loading cases: (a) bending with a concentrated load of 5 N applied at 35% of the OMW tip chord and (b) torsion with a couple of 1.1 Nm at the IFW tip chord. For the former loading case, both experimental and numerical deformations are evaluated at constant 35% chord position along the wing span. In the other loading case, the deformations are evaluated along the IFW tip chord. The results from the numerical study and the experimental tests are shown in Figure 5.

Observing Figure 5(a), which presents the vertical deflection along the span due to tip load, it is clear that a general good agreement exists between experimental and numerical data. It is important to note the change of slope of the deflected shape at the OWM/IFW interface. In fact, the IFW aerofoil contour in the proximity of the interface expands in the thickness direction and a small gap appears on the top side of the IFW, resulting in the slope discontinuity observed in this region. The interface in the numerical model appears to be slightly stiffer, since the maximum deflection is underestimated. Also it is noticeable the high stiffness of the OMW, evidenced by the linear deformation of this component. Regarding the torsion due to the tip couple (Figure 5(b)), it is possible to conclude that the torsion angle is similar in both the numerical and the experimental situations. This indicates that the torsional stiffness of the finite element model is correct. From both tests, it becomes evident that the developed finite element model represents with good approximation the elastic characteristics of the prototype wing.

In order to enhance the knowledge about the performance of the developed structure, the wing deformation induced by aerodynamic loading with varying load factor was studied. More particularly, two loading factors were considered, 4 and 6, corresponding to total lift forces of 120 and 180 N, respectively, on a single wing for a takeoff weight of 60 N. The loading was considered to have an elliptic distribution and was applied along the span at 25% chord position. The deflections obtained from this study are shown in Figures 6 and 7. From both figures, the widening of the wing thickness at the IFW tip due to the moment transmitted from the OMW is clearly seen. The tip deflection varies from 0.032 m at the 4g condition and 0.048 m at the 6g load case, corresponding to relative deflections with respect to half-span of 2.6% and 3.8%, respectively. These values are well below the typical maximum relative deflection of 10% typically allowed in wing designs at limit load, but necessary to allow the seamless motion of the OMW under high loads.

For the maximum load factor case, the maximum stress index distribution, from the maximum strength criteria, is obtained to visualise high stress concentration areas which may require further attention in the structural elements design and to identify oversized areas that can be subject of weight reductions for increased structural efficiency. As expected, two highly stressed regions stand out in Figure 8: the OMW leading edge skin in the IFW/OMW overlap region and upper and lower rib area on the second and first ribs of the IFW in the same IFW/OMW interface region. The maximum stress index reaches values near 1.0 in these balsa ribs. When the OMW deflects under load, the bending moment transmitted from the OMW to the IFW should produce a linear reaction force distribution over the 0.1 m overlap distance, should the structure be completely rigid. However, the effect observed in Figure 8(b), where the upper and lower skins slightly move apart at the IFW tip chord, makes this reaction distribution to be non-linear and have peak values at the overlap extremities (OMW root chord and IFW tip chord). This effect overloads the lower part of the first OMW rib and the upper part of the second OMW rib due to the vertical compressive reaction that is exerted on them by the IFW sandwich skin. The maximum stress index observed on the leading edge of the IFW in the interface area is close to 0.5, therefore not critical, although this results from bending of the leading edge skin as the upper and lower IFW skin move apart in the interface.

Overall, the wing structure exhibits adequate strength requiring, though, three improvements to make it more efficient: (a) increasing the width of the first two balsa ribs of the OMW to reduce the stress levels; (b) stiffening the rib contour at the tip of the IFW to reduce the aerofoil section deformation; and (c) reducing the weight of the OMW towards the tip.

Flutter speed analysis

An aeroelastic analysis using the typical aeroelastic section with unsteady linearised potential theory together with the aerodynamic strip theory was performed to determine the speed margin between the maximum flight speed and the onset of the flutter mode of vibration. The details of the study formulation can be found in Gamboa et al. (2013). Flutter analysis was performed for sea-level standard conditions where the air density is greatest and the flutter critical speed will be lowest. From the results obtained in the study, a speed margin of 44.5% ensures safe operations of the VSW during the flight tests programme.

Prototype development

A working prototype was implemented to allow the pursuit of several ground and flight validation and evaluation tests. The actuation mechanism and manufacturing techniques used to build the wing are briefly presented below.

Actuation concept

The VSW concept presents a very pragmatic layout: a hollow wing (IFW) inside of which a smaller conventional wing slides (OMW) actuated by a simple electromechanical mechanism consisting of a servomotor, a pinion and a rack. The pinion is driven by the servomotor installed at the centre of the wing assembly and pushes/pulls the rack which is attached to the OMW to make it slide inside the IFW. The maximum span length was set equal to the original fixed wing: 2.5 m. For this total span, it was estimated that both inboard and outboard wing parts would have a length of 0.625 m and that 0.1 m of minimum wing overlapping would allow sufficient wing stiffness in the full extended configuration. Knowing these dimensions and fuselage width one was able to estimate the IFW and OMW lengths. The overall system was developed in a CAD/CAM tool and is illustrated in Figure 9 where the main components are highlighted.

Wing prototype

The hand-layup and vacuum bagging lamination approach was chosen, since this technique allows a lightweight structure to be obtained with low cost and reduced complexity. The cure process was performed under controlled temperature conditions in two steps (cure and post-cure) so that the mechanical properties of the composite parts could be known with confidence. Moulds were produced to build the various skin parts.

The VSW actuation mechanism was designed to allow in-flight extensions and retractions of the wing as required. A simple rack and pinion system actuated by a servomotor was selected as the best suited for the purpose: it is light and fast enough if actuated properly. In future work, development of an automatic span extension controller should be facilitated by this choice. It was the control simplicity that led to the choice of a servo-mechanism as a means to actuate the wing. The rack rod used to push/pull the OMW is made of aluminium and is 0.8 m long, which is enough to span the wing length of 0.625 m and the stroke needed of 0.525 m. The two elements can be observed from Figure 10. In order to select the material and size of the rack several factors were addressed: weight, availability, size and price. Given that the rack is a critical element of the control system which is part of a moving system subject to vibrations, adding to buckling and flexural stiffness considerations and manufacturing issues, a section of 9mm × 5mm was adopted. The material selected for the pinion was bronze to reduce friction. In the future, lightweight materials may be considered.

The selection of the servomotors followed again a series of considerations regarding availability, low price, high speed, high torque, low weight and incorporation of metal gears, being the latter a prerequisite to carry out the necessary modifications. Combining the best compromise, a pair of Hitec HS-805MG servos was purchased. The actuation shaft of the servomotor was modified to receive a bronze pinion designed to be compatible with the rack and provide the adequate combination of torque and speed to the OMW motion. The feedback potentiometer of the servo was removed and an external potentiometer was installed with a nylon pinion designed to provide the correct travel for the OMW motion. In Figure 10 it is possible to see the actuation pinion and the feedback potentiometer reduction pinion.

After the actuation system was developed, a platform capable of supporting the servos and effectively transmitting the forces to the VSW moving parts, subject to geometric constraints dictated by the fuselage size of the UAV, was built. Considering all of this, the result was a plywood board 3 mm thick, supported by two 6 mm thick lugs of the same material bonded to the wing tube and spars as seen in Figure 10. In this figure, the upper board supports the pinion’s servo shafts and the rack’s guiding rollers at the top. The function of the rollers is to align and maintain the racks in contact with the corresponding pinion’s teeth. In order to reduce friction to an acceptable minimum, ball bearings were placed in all contact holes between shafts and supporting structure. In order to keep the weight low, the rollers were lathe machined from a 10 mm aluminium circular rod.

Wing mass

All components were weighed in order to evaluate the difference in mass between the conventional wing and the telescopic wing. Table 2 presents the main component masses and the total mass of the prototype wing. The resin used to impregnate the composite skins is included in the mass of the different assemblies. The wing’s total mass, including the actuation mechanism, is around 2.19 kg, as opposed to 1.38 kg of the original wings developed for the Olharapo UAV (with the original flight control system of servos and cables and the wing supporting part that attaches to the fuselage). This is an increase of about 0.81 kg: 59% of wing mass or 14% of total vehicle mass. This value represents 0.44 kg more than the 0.37 kg first estimated with a preliminary wing prototype and assumed in the aerodynamic optimisation of the wing. The increased mass was due mainly to the servos selected which had to be more powerful and hence larger than initially anticipated and to the heavier rack and pinion transmission. In the future, this negative mass margin should be reduced through structure and actuating system optimisation.

Table 2.

Mass of major assemblies of the telescopic wing and mass of the original Olharapo UAV wing.

Assembly	Mass, kg
OMW (including rack)	0.57
IFW	0.97
Actuation bay	0.65
VSW (total)	2.19
Original wing	1.38

Ground testing

Bench tests were performed to evaluate the performance of the overall system. In order to achieve this, two separate types of tests were conducted: structural and actuator system testing. A more detailed description of the tests performed may be found in Felício et al. (2011).

Structural tests

Structural tests were performed with the objective of evaluating the strength and stiffness of the VSW. These tests also helped to validate the structural model as described above. More specifically, the wing tip deflection was measured when subjected to different loads representing a range of flight load factors. The flight loads were simulated by placing sand bags on the upper surface of the wing. For simplicity, the wing load distribution was considered constant in the IFW and triangular in the OMW portion. Load factors between approximately 0g and 4.5g were applied. Furthermore, all of the sand bags were distributed along the main wing spar in order to avoid unnecessary torsion of the telescopic wing assembly. The tip deflection was determined by reading off a scale placed behind the wing tip.

The variation in tip deflection with increasing load factor was in-line with the numerical predictions. As expected, the increase in load factor led to a considerable increase in the wing tip vertical deflection. Furthermore, a slight slope discontinuity was observed at the position where the movable wing enters the fixed wing, particularly at higher load factors. However, the OMW showed to be quite stiff. The overlap of 100 mm between both wing parts resisted the bending loads by deforming the aerofoil contour shape: effectively increasing the aerofoil thickness, situation also modelled by the FEM analysis. This localised bending produced a small gap between the IFW upper skin and the OMW upper skin which became more apparent at higher load factors, reaching a value close to 2 mm under a 4.5g load.

Actuation system tests

The actuation system was subjected to a series of tests aimed at measuring the telescopic wing extension and retraction times under various load factors. Full cycle times (extension followed by retraction) were measured using a digital stopwatch. The results of half-cycle actuation times for different load factors are shown in Table 3. It becomes clear that the time of retraction/extension increased as load factor was raised. This was already expected, since increasing the load factor increases friction between wing parts and, hence, the servomotor had more difficulty in overcoming the increased force.

Table 3.

Half-cycle actuation times of the VSW using the Hitec HS-805MG servos.

Load factor	0	1	2	3	4
Time, s	1.8	2.0	2.3	2.5	3.0

Flight testing

As a result of the referred development and ground testing it was concluded that the designed VSW is suitable to be installed on a UAV for in-flight concept evaluation. For that purpose, a previously developed UAV airframe was modified and instrumented to serve as a suitable test bed with flight data acquisition, telemetry and first-person view (FPV) capabilities (Sousa et al., 2013). Figure 11(a) illustrates the UAV fitted with a conventional fixed wing while Figure 11(b) shows the UAV prototype fitted with the telescopic wing.

UAV instrumentation

The core of the UAV instrumentation is the Pixhawk autopilot. Pixhawk is a fully-featured autopilot system developed by the PX4 open-hardware project. It features a 32-bit ARM Cortex M4 and sensor technology from ST Microelectronics and a NuttX real-time operating system. It has also dual gyroscope and dual accelerometer (ST Micro L3GD20 3-axis 16-bit gyroscope, ST Micro LSM303D 3-axis 14-bit accelerometer/magnetometer and Invensense MPU 6000 3-axis accelerometer/gyroscope). To perform navigation, the Pixhawk also uses an Ublox LEA-6H GPS. The Pixhawk autopilot allows full logging of the various flight parameters and sensor data at 50 Hz (or faster) to a microSD card. This greatly facilitates inflight data logging and further data processing.

In order to measure the angle of attack, α and angle of sideslip, β of the UAV, an alpha-beta probe was built. The probe is made up of two very low-friction magnetic encoders whose output gives a voltage that is proportional to the angle of rotation. Each encoder shaft is connected to one vane in order to allow the encoders to adjust to the surrounding flowfield. The probe is also featured with a pitot-static tube to measure airspeed connected to a Measurement Specialties 4525DO differential pressure sensor with 6.9 MPa measurement range (maximum airspeed of about 100 m/s). Figure 12 shows the assembled alpha–beta probe.

Figure 13 shows the various components used in UAV Olharapo. The Pixhawk autopilot was mounted as close as possible to the CG. The remaining components were fitted in such a way to allow proper CG centring and also to limit interferences between sensitive components (long-range receiver) and high-power sources (electric motor and electronic speed controller). The UAV is powered from two lithium polymer batteries: one dedicated to the electric motor and another dedicated to the control systems. There is also a backup NiMh battery to power the UAV systems in case of the main battery failure.

Software

The Pixhawk autopilot can run two different flight softwares: the PX4 native flight control stack and the APM.Plane flight control stack. The latter was chosen given the higher maturity level of the code and also because of the previous team experience in its operation. Since the hardware has available rate gyroscopes, accelerometers, magnetometers, GPS, airspeed and barometric pressure measurements, it is essential to fuse all data to build an attitude and heading reference system (AHRS). This is used to provide attitude information of the UAV, including heading, pitch, yaw and roll angles. In order to fuse all data reliably an extended Kalman filter (EKF) algorithm is used in APM.Plane. The algorithm used in the software estimates a total of 22 states. More information can be found in Riseborough (2014).

Flight mechanics

Reference systems

There are numerous reference systems used in aerospace applications. In this work, it is important to describe four reference systems: the topodetic, the vehicle carried vertical, body and wind. The topodetic or Earth fixed reference is considered to be fixed in space with the orientations of the axes: x is directed north, y axis to east and z axis down. The vehicle carried vertical axis system is used to define the attitude of the airplane using the Euler angles: pitch angle, θ, bank angle, ϕ, and heading, ψ. This reference system is obtained by a translation of the topodetic axis system to the vehicle CG. The body axis system has its origin coincident with the vehicle’s CG. In a symmetric airplane x and z axes are in the plane of symmetry. The positive direction of the body axis angular velocities: roll rate, p, pitch rate, q, and yaw rate, r (about x, y and z, respectively) and the body axis velocities: u, v and w (in x, y and z direction, respectively) are shown in Figure 14. This reference system and the vehicle carried vertical are related through the Euler angles (pitch, roll and heading). Figure 14 also shows the relationship between wind axis and body axis.

From Figure 14 the components of the airspeed vector (V) in the body axes (u, v and w) can be extracted. These are

\begin{matrix} u = & V \cos (α) \cos (β) \\ v = & \sin (β) \\ w = & \sin (α) \cos (β) \end{matrix}

(3)

Euler equations of motion

After defining the reference axes system, the equations of motion for an airplane that is assumed to be rigid can be derived as (the equations are shown here with no further derivation; more details can be found in Duke et al. (1988) and Etkin and Reid (1996))

\begin{matrix} \overset{\cdot}{u} = & \frac{(X_{T} + X_{a})}{m} - g \sin (θ) - qw + rv \\ \overset{\cdot}{v} = & \frac{(Y_{T} + Y_{a})}{m} + g \sin (ϕ) \cos (θ) - ru + pw \\ \overset{\cdot}{w} = & \frac{(Z_{T} + Z_{a})}{m} + g \cos (ϕ) \cos (θ) + qu - pv \end{matrix}

(4)

where X_a, Y_a and Z_a are the total aerodynamic force components in each direction given by

\begin{matrix} X_{a} = & - D \cos (α) \cos (β) - Y \cos (α) \sin (β) + L \sin (α) \\ Y_{a} = & - D \sin (β) + Y \cos (β) \\ Z_{a} = & - D \sin (α) \cos (β) - Y \sin (α) \sin (β) - L \cos (α) \end{matrix}

(5)

where L, D and Y are lift, drag and sideforce, respectively.

The thrust vector is defined as

\begin{matrix} [T] \end{matrix} = [\begin{matrix} X_{T} \\ Y_{T} \\ Z_{T} \end{matrix}]

(6)

where X_T, Y_T and Z_T are the total thrust force components along the x, y and z body axes. In this particular case these are zero because a gliding flight with the engine turned off is considered. The presented system of linear equations is solved with respect to lift (L), drag (D) and aerodynamic lateral force (Y), and the lift-to-drag ratio is obtained by dividing L by D.

Sensor corrections

Since not all sensors can be located near the vehicle CG, it is necessary to apply some corrections. Of particular interest is the angle of attack and angle of sideslip corrections, since the sensors used to measure these quantities are moderately displaced from the UAV fuselage, in order to reduce aerodynamic interference from the UAV body. From Duke et al. (1988) the corrections are found to be

α_{c} = α_{m} - \frac{{qx}_{α} - {py}_{α}}{V}

(7)

β_{c} = β_{m} - \frac{{rx}_{β} - {pz}_{β}}{V}

(8)

where α_c and β_c are the corrected values of angle of attack and angle of sideslip, respectively, and x_α and y_α are the x and y distances of the AOA sensor from the CG and x_β and z_β are the x and z distances of the angle of sideslip (AOS) sensor from the CG.

Drag polar representation

In order to compute the drag polar, lift and drag coefficient should be calculated. Lift coefficient can be directly calculated from its definition and using the flight path angle to calculate the component of the weight during the glide. Thus,

C_{L} = \frac{W \cos (γ)}{0.5 ρ V^{2} S_{ref}}

(9)

where γ is the flight path angle, W the UAV weight, ρ the air density and S_ref the reference wing area (of the fixed wing). The flight path angle can be computed from

γ = \arctan (\frac{1}{L / D})

(10)

Finally, the drag coefficient is calculated noting that

C_{D} = \frac{C_{L}}{L / D}

(11)

Flight performance results

The main purpose of the flight data is to provide information to compare a conventional fixed wing with the designed VSW in terms of aerodynamic efficiency. The aerodynamic efficiency is assessed using gliding flights. Each flight consists of a series of power-off descents at different airspeeds that are achieved by simply changing the elevator trim position. A total of 45 flight tests were performed, totalling about 30 flight hours. All flights took place in Castelo Branco’s airfield, Portugal, which has an altitude of 375 m.

The variable span wing and fixed wing have different weights (21.5 and 13.5 N, respectively) as mentioned before. Therefore, the CG position was carefully measured so that it is maintained at the same chord position for both wings. This allows a more direct comparison of the performance curves, since the lift-to-drag ratio (L/D) curve as function of airspeed moves along the airspeed axis when changing the CG, due to trim adjustments. The take-off weight of Olharapo UAV with the conventional wing is 54.5 N and with the VSW is 65.5 N and the CG was located at 28.6% and 28.9% of each wing chord, respectively. The VSW was tested in two different wingspan configurations: full wingspan (2.5 m) and minimum wingspan (1.55 m). It should be emphasised that the wing reference area used throughout the calculations is the conventional fixed wing area of 0.625 m².

Experimental procedure

A typical flight path for data acquisition starts with an initial climb until the UAV reaches a certain altitude. The altitude to reach is highly dependent on the speed condition that will be analysed, since the sink rate greatly increases with forward speed. Then the electric motor is turned off and motor brake is automatically activated, allowing the propeller blades to retract (reducing propeller drag). As the gliding flight is initiated, the elevator trim is set to establish the airspeed. The dynamics of the UAV and the wind characteristics determine the time it takes to converge. This can clearly be seen in Figure 15 as a damped sinusoidal motion. The UAV is then allowed to loose altitude until a minimum and throttle is restored, in order to regain the altitude. This cycle is repeated until the energy stored in the battery is not sufficient to perform more flight cycles, thus proceeding to the landing stage.

A sample of the flight testing procedure is shown in Figure 15. It is possible to observe the variation of absolute altitude (AGL), angle of attack (α), pitch angle (θ) and airspeed, during a typical gliding flight in good weather conditions.

Data post-processing

All flight tests were recorded on-board on a microSD card, allowing later processing of the data. The post-processing of the data is a methodical procedure composed by the following steps:

identification of the gliding flights starting and a finishing instant, based on graphical analysis of the airspeed and altitude data;

correction of AOA and angle of sideslip due to their offset position as given by equations (7) and (8);

computation of L, D and L/D by the solution of equation (4) for each instant during the glide;

computation of average L/D during the whole glide;

computation of averages of all values of interest during the glide: α, β, γ and ρ_atm;

computation of C_L and C_D using equations (9) and (11);

storage of all data to the corresponding database (fixed wing or VSW as function of span position);

repeat steps 2–7 until all flights are computed.

The C_L and C_D curves for each studied case (fixed wing, VSW fully extended and VSW fully retracted) are approximated with a parabola using the least-squares method, in order to obtain the asymmetric quadratic drag polar of the form

C_{D} = C_{D 0} + K_{1} C_{L} + K_{2} C_{L}^{2}

(12)

Drag polars

Figures 16 and 17 show the experimental data and the parabolic approximations for the UAV fitted with the conventional wing, with the VSW in full-span configuration and minimum span configuration. Observing Figure 16, which shows both the experimental data and the parabolic approximation, it is visible that a strong correlation exists between the two, being the correlation coefficient (R²) of 0.85. The equation of the approximation is

C_{D} = 0.0903 - 0.1652 C_{L} + 0.1988 C_{L}^{2}

(13)

Observing Figure 17, which shows the drag polar of the VSW with full-span and minimum span, one can conclude that the experimental data and the parabolic approximation agrees well, being the correlation coefficient equal to 0.91 in both situations. The equations of the approximation are, for full-span and minimum span, respectively,

C_{D} = 0.1393 - 0.2873 C_{L} + 0.2793 C_{L}^{2}

(14)

C_{D} = 0.0780 - 0.1282 C_{L} + 0.2115 C_{L}^{2}

(15)

Lift-to-drag ratio

After computing the drag polar approximation for each test condition, the lift-to-drag ratio as a function of airspeed is recomputed using the parabolic curves at sea-level conditions. The results here presented are for the complete aircraft.

Considering Figure 18, it is visible that the maximum L/D occurs with the fixed wing at an airspeed of 14.6 m/s, with a value of 9.7. The maximum L/D with the VSW occurs with the maximum span, reaching a value of 9.3 at 15.6 m/s. Therefore, at low speed the VSW is less efficient than the conventional wing. This was to be expected due to mainly three aspects as discussed in Aerodynamic shape optimisation: less efficient aerofoil in OMW, thicker aerofoil in the IFW and chord discontinuity in the transition from the IFW to the OMW. The first two mentioned aspects are closely related, since the IFW aerofoil was generated as an offset of the OMW. In order to make this possible the OMW aerofoil was modified to have a flat lower surface, which in turn reduced the performance of the local aerofoil. At higher speeds the fixed wing and the VSW with full-span show very similar characteristics. However, when the airspeed reaches 19 m/s the conventional wing becomes slightly better. This behaviour carries on up to the maximum measured speed of 30 m/s. The VSW with the minimum span has inferior performance at low speed, being the maximum L/D of 7.8 at 16.8 m/s. This was to be expected given the dramatic area reduction (40%). However, with the increase of the airspeed to 18.8 m/s, the benefits clearly start to be seen. At this airspeed the L/D exceeds that of the conventional wing. The benefit continues to increase, with the VSW in the minimum span configuration being 35% better than the original fixed wing at 30 m/s. The curve trends suggest that the benefit should continue to increase even further for higher speeds (as suggested by the numerical study in the section ‘Aerodynamic optimisation’).

Note that, comparing Figure 2(c) with Figure 18, the former showing the numerical predictions for L/D of the wings alone and the latter showing the L/D curves obtained from the experimental data for the complete UAV, one can see the same trends in both wings at similar airspeeds.

Conclusions

A fully functional VSW system was developed covering areas from aerodynamic optimisation and structural design, through prototyping and flight testing. The main conclusions of the work done in the design and development of the variable-span morphing wing concept presented are:

Aerodynamic design optimisation allowed the sizing of a VSW which reduces the drag × speed integral in the design speed range of the vehicle. At low speeds, the original wing has slightly better performance than the VSW, due to the performance reduction of the modified SG6042 aerofoil, the higher relative thickness ratio of the IFW aerofoil and the increased vehicle weight. However, this performance trend is inverted beyond 25 m/s, in the speed range where retraction of the OMW occurs, which reduces the wing area and consequently the total wing drag. For example, at 35 m/s the drag of the VSW was reduced by 22% from the original fixed wing.

Even though structural tests revealed some discrepancies between the experimental and the finite element model deflections, the trends and magnitudes are similar. The differences are mainly due to the modelling of the interface between IFW and OMW, the uncertainty in material properties and also due to manufacturing imperfections of the prototype wing. Nevertheless the design was generally confirmed in the loading tests.

Both deployment and load tests revealed satisfactory performance of the VSW concept. However, deployment can be improved by increasing the skin stiffness at the IFW tip with an internal stiff rib (between sandwich facings). In alternative, this can also be achieved using an external lighter rib similar to an end plate around the perimeter of the aerofoil.

In-flight concept evaluation of the UAV fitted with the variable span wing demonstrated full flight capability and confirmed numerical estimates of performance and showed improvements produced by the VSW over a conventional fixed wing for speeds above cruise speed.

Overall, the increased structural and power related weight and complexity introduced by the VSW design proposed is justified by the increased speed flight envelope. In principle, it is possible to design a VSW that extends the speed boundaries for lower and higher speeds relative to a fixed wing designed for a given main design speed.

Footnotes

Acknowledgements

The authors are grateful for the contributions of João Mestrinho, João Felício and Lino Miguel to various aspects of the development of the VSW concept, in particular manufacturing and instrumentation.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work presented herein has been partially funded by the European Community’s Seventh Framework Programme (FP7; grant agreement 314139). The CHANGE project (Combined morphing assessment software using flight envelope data and mission based morphing prototype wing development) is a level 1 project funded under the topic AAT.2012.1.1-2 involving nine partners. The project started on 1 August 2012. The work presented herein has also been partially funded by the Portuguese Science Foundation (FCT - Fundação para a Ciência e Tecnologia, PhD Grant SFRH/BD/90159/2012).

References

Ajaj

Saavedra Flores

Friswell

Allegri

Woods

BKS

Isikveren

Dettmer

(2013) The Zigzag wingbox for a span morphing wing. Aerospace Science and Technology 28: 364–375. DOI:10.1016/j.ast.2012.12.002.

Alemayehu

Leng

McNulty

Mulloy

Somero

Tenorio

(2005) Virginia Tech Morphing Wing Team Spring 2005 Final Report. Technical report, Aerospace and Mechanical Engineering Departments, Virginia Tech.

ANSYS (2013) Mechanical APDL Structural Analysis Guide. Technical report, ANSYS, Inc., USA.

ASTM (2014) In: Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials - D3039/D3039M. West Conshohocken, PA: ASTM International. DOI:10.1520/D3039_D3039M-14.

Bae

Seigler

Inman

(2005) Aerodynamic and static aeroelastic characteristics of a variable-span morphing wing. Journal of Aircraft 42: 528–534. DOI:10.2514/1.4397.

Barbarino

Bilgen

Ajaj

Friswell

Inman

(2011) A review of morphing aircraft. Journal of Intelligent Material Systems and Structures 22(9): 823–877. DOI:10.1177/1045389X11414084.

Bowman

Sanders

Cannon

Kudva

Joshi

Weisshaar

(2007) Development of Next Generation Morphing Aircraft Structures. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Honolulu, Hawaii: American Institute of Aeronautics and Astronautics. DOI:doi:10.2514/6.2007-1730.

Cadogan

Graham

Smith

(2003) Inflatable and rigidizable wings for unmanned aerial vehicles. AIAA paper 6630: 2003. DOI:10.2514/6.2003-6630.

Drela

(2001) XFOIL 6.94 User Guide. Technical report, Massachusetts Institute of Technology & Astro Harold Youngren Aerocraft, Inc.

10.

Duke

Antoniewicz

Krambeer

(1988) Derivation and Definition of a Linear Aircraft Model. Technical report, Scientific and Technical Information Division of NASA, Edwards, California, United States of America.

11.

Etkin

Reid

(1996) Dynamics of Flight, Stability and Control,3rd edn. New York: John Wiley & Sons.

12.

Felício

Santos

Gamboa

Silvestre

(2011) Evaluation of a variable-span morphing wing for a small UAV. In: 52nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Denver, CO: American Institute of Aeronautics and Astronautics. DOI:10.2514/6.2011-2074.

13.

Flanagan

Strutzenberg

Myers

Rodrian

(2007) Development and flight testing of a morphing aircraft, the NextGen MFX-1. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Honolulu, Hawaii: American Institute of Aeronautics and Astronautics. DOI:10.2514/6.2007-1707.

14.

Gamboa

(2007) Multidisciplinary Design Optimization of Morphing Aircraft. PhD Thesis, Departamento de Ciências Aeroespaciais, Universidade da Beira Interior, Covilhã, Portugal.

15.

Gamboa

Santos

Silva

Santos

(2013) Flutter Analysis of a Composite Variable-Span Wing. In: 4th international conference on integrity, reliability and failure, Funchal.

16.

Gamboa

Vale

Lau

PFJ

Suleman

(2009) Optimization of a morphing wing based on coupled aerodynamic and structural constraints. AIAA Journal 47: 2087–2104. DOI:10.2514/1.39016.

17.

Henry

Blondeau

Pines

(2005) Stability analysis for UAVs with a variable aspect ratio. In: 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Austin, TX, pp. 1–10.

18.

Jacob

Simpson

Smith

(2005) Design and Flight Testing of Inflatable Wings with Wing Warping. SAE Technical Paper 2005-01-3392 DOI:10.4271/2005-01-3392.

19.

Joshi

Tidwell

Crossley

Ramakrishnan

(2004) Comparison of Morphing Wing Strategies Based Upon Aircraft Performance Impacts. In: 45th AIAA/ASME/ASCE/AHS/ASC structures structural dynamics materials conference, Palm Springs, CA, vol. 2, pp. 1–7. DOI:10.2514/6.2004-1722.

20.

Katz

Plotkin

(2001) Low-Speed Aerodynamics,2nd edn. Cambridge: Cambridge University Press.

21.

Mestrinho

Gamboa

Santos

(2011) Design optimization of a variable-span morphing wing for a small UAV. In: 52nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. Denver, CO: American Institute of Aeronautics and Astronautics. DOI:10.2514/6.2011-2025.

22.

Mukherjee

Gopalarathnam

Kim

(2003) An iterative decambering approach for post-stall prediction of wing characteristics from known section data. In: 41st aerospace sciences meeting and exhibit. Reno, NV: American Institute of Aeronautics and Astronautics. DOI:10.2514/6.2003-1097.

23.

Raymer

(2006) Aircraft Design: A Conceptual Approach, 4th edn (AIAA Education Series). AIAA.

24.

Riseborough

(2014) APM. Plane navigation extended Kalman filter - overview and theory. Available at: http://plane.ardupilot.com/wiki/common-apm-navigation-extended-kalman-filter-overview (accessed 30 September 2014).

25.

Samuel

Pines

(2007) Design and testing of a pneumatic telescopic wing for unmanned aerial vehicles. Journal of Aircraft 44: 1088–1099. DOI:10.2514/1.22205.

26.

Santos

Gamboa

Santos

Silva

(2013) Structural design of a composite variable-span wing. In: 4th international conference on integrity, reliability and failure, Funchal.

27.

Secanell

Suleman

(2005) Numerical evaluation of optimization algorithms for low-Reynolds-number aerodynamic shape optimization. AIAA Journal 43(10): 2262–2267. DOI:10.2514/1.12563.

28.

Seigler

Neal

Bae

Inman

(2007) Modeling and flight control of large-scale morphing aircraft. Journal of Aircraft 44(4): 1077–1087. DOI:10.2514/1.21439.

29.

Sousa

Santos

Gamboa

(2013) Control systems for UAV flight testing. In: International conference on engineering ICEUBI2013 engineering for economic development, Covilhã.

30.

Stern

Cohen

(2013) VAST AUAV (Variable Airspeed Telescoping Additive Unmanned Air Vehicle). In: Rapid 2013 conference and exposition, including 3D imaging. Pittsburgh, PA: SME.

31.

Vale

Leite

Lau

Suleman

(2011) Aero-structural optimization and performance evaluation of a morphing wing with variable span and camber. Journal of Intelligent Material Systems and Structures 22: 1057–1073. DOI:10.1177/1045389X11416031.

32.

Vocke

Kothera

Woods

BKS

Wereley

(2011) Development and testing of a span-extending morphing wingJournal of Intelligent Material Systems and Structures 22(9): 879–890. DOI:10.1177/1045389X11411121.

33.

Zhou

Tits

Lawrence

(1997) User’s Guide for FFSQP Version 3.7. Technical report, Electrical Engineering Department and Institute for Systems Research, University of Maryland, United States of America.