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Aeroelastic Analysis of Wing Twist for Roll Control of a Micro Air Vehicle

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Title:
Aeroelastic Analysis of Wing Twist for Roll Control of a Micro Air Vehicle
Creator:
Troner, David B.
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[Gainesville, Fla.]
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University of Florida
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English

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Subjects / Keywords:
Aerodynamic lift ( jstor )
Aeroelasticity ( jstor )
Ailerons ( jstor )
Aircraft ( jstor )
Aircraft design ( jstor )
Aircraft roll ( jstor )
Aircraft wings ( jstor )
Stiffness ( jstor )
Structural deflection ( jstor )
Velocity ( jstor )
Aeroelasticity
aerodynamics
aircraft structures
micro air vehicle
wing twist
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Undergraduate Honors Thesis

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Abstract:
With increasing growth of micro air vehicles and flexible aircraft structures, new ways to control aircraft are needed where conventional trailing edge control surfaces are not feasible. This project performs a preliminary analysis on the feasibility for using wing twist to control the roll of a micro air vehicle. The aeroelastic effects of this wing twist are analyzed over a design space of material selection (specifically torsional rigidity) and trim velocity. The analysis is performed in ASWING software on a generic micro air vehicle developed by the Munitions Directorate of the Air Force Research Laboratory called the GenMAV. The results present a design tradeoff between the increased ability to induce a roll moment and the decreased lift-to-drag ratio as flexibility and wing twist are increased. The results are then compared with a conventional trial in which the GenMAV’s elevons are used to generate an equivalent roll moment for the same trim conditions. A comparison of these results shows an increase in performance utilizing wing twist for the trim case analyzed, and an increased capacity to generate large roll moments for rapid maneuvering. ( en )

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Aeroelastic Analysis of Wing Twist for Roll Control of a Micro Air Vehicle David B. Troner Undergraduate Honors Thesis Summa Cum Laude B.S. in Aerospace Engineering University of Florida Flight Control Laboratory Fall 2015

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David Troner | University of Florida | Fall 2015 1 A CKNOWLEDGEMENTS I wish to express my gratitude to Dr. Rick Lind for the use of his lab and for his continual support and guidance throughout this project. I also wish to thank George Armanious for his help throughout the research and for the guidance with the ASWING software package. A spec ial thanks goes out to Dr. Mark Dre la and the team at MIT that developed the ASWING software package, without which this project would not be possib le.

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David Troner | University of Florida | Fall 2015 2 A BSTRACT With increasing growth of micro air vehicles and flexible aircraft structures, new way s to control aircraft are needed where conventional trailing edge control surfaces are not feasible. This project p er forms a preliminary analysis on the feasibility for using wing twist to control the roll of a micro air vehicle. The aeroelastic effects of this wing twist a re analyzed over a design space of material selection (specifically torsional rigidity) and trim vel ocity. The analysis is performed in ASWING software on a generic micro air vehicle developed by the Munitions Directorate of the Air Force Research Labo ratory called the GenMAV. The results present a design tradeoff between the increased ability to induce a roll moment and the decreas ed lift to drag ratio as flexibility and wing twist are increased. The results are then compared with a conventional trial in which the s. A comparison of these results shows an increase in performance utilizing wing twist for the trim case analyzed , and an increased capacity to generate large roll moments for rapid maneuvering.

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David Troner | University of Florida | Fall 2015 3 T ABLE OF C ONTENTS Acknowledgements ................................ ................................ ................................ ................................ ....... 1 Abstract ................................ ................................ ................................ ................................ ......................... 2 1 Nomenclature ................................ ................................ ................................ ................................ ....... 5 2 Introduction ................................ ................................ ................................ ................................ .......... 6 3 Aeroelasticity Overview ................................ ................................ ................................ ........................ 7 4 Modeling ................................ ................................ ................................ ................................ ............... 9 4.1 Generic Micro Air Vehicle (GenMAV) ................................ ................................ ........................... 9 4.2 ASWING Software ................................ ................................ ................................ ....................... 11 5 Wing Twist for Roll Co ntrol Study ................................ ................................ ................................ ....... 11 5.1 Background ................................ ................................ ................................ ................................ . 11 5.2 Trim Conditions ................................ ................................ ................................ ........................... 12 5.3 Desi gn Space ................................ ................................ ................................ ............................... 13 5.4 Performance Criteria and Process ................................ ................................ .............................. 14 5.5 Results ................................ ................................ ................................ ................................ ......... 15 5.6 Wing Twist Study Conclusions ................................ ................................ ................................ .... 20 6 Baseline Roll Comparison with Conventional Ailerons ................................ ................................ ....... 20 6.1 Background ................................ ................................ ................................ ................................ . 20 6.2 Trim Conditions ................................ ................................ ................................ .......................... 21 6.3 Performance Criteria and Process ................................ ................................ .............................. 22 6.4 Aileron Sensitivity Analysis ................................ ................................ ................................ ......... 22 6.5 Results ................................ ................................ ................................ ................................ ......... 24 6.6 Aileron Study Conclusion ................................ ................................ ................................ ............ 25 7 Conclusion ................................ ................................ ................................ ................................ ........... 26 8 Future Work ................................ ................................ ................................ ................................ ........ 26 9 References ................................ ................................ ................................ ................................ .......... 28

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David Troner | University of Florida | Fall 2015 4 T ABLE OF F IGURES Fig. 1 . Fig. 2 . Geometry of the GenMAV 10 Fig. 3 . Trim conditions for wing twist study 12 Fig. 4 . Win g twist study 14 Fig. 5 . Plots depicting lift to drag ratio as a function of trim velocity over design space 15 Fig. 6 . Plots depicting lift to drag ratio as a function of trim v elocity and to 17 Fig. 7 . Plots depicting roll moment as a fun 19 Fig. 8 . Trim conditions for aileron study 21 Fig. 9 . Aileron 22 Fig. 10 . Roll moment 22 Fig. 11 . Wing t wist . 23 Fig. 12 . Lift to Drag ratio comparison for both c ases 24 T ABLE OF T ABLES T ABLE I : M ATERIAL D ESIGN S PACE FOR W ING T WIST S TUDY T ABLE II : E FFECTS OF D ESIGN V ARIABLES ON L IFT TO D RAG R ATIO T ABLE III : R OLL M OMENTS AND L IF T TO D RAG R ATIO D UE TO W ING T WI ST AT T RIM C ONDITION T ABLE IV : L IFT TO D RAG R ATIO AND R OLL M OMENT D UE TO A ILERON D EFL ECTION AT T RIM C ONDITION

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David Troner | University of Florida | Fall 2015 5 1 N OMENCLATURE Variable Description Units Aileron Deflection Angle of Attack Angle of Incidence Bending Stiffness Chord Length Coefficient of Drag n/a Coefficient of Lift n/a Density Drag Force Dynamic Pressure Elevator Deflection Lift Force Roll Moment Rudder Deflection Shear Modulus Side Slip Angle Torsional Stiffness Trim Velocity Wing Planform Area b Wing Span Wing Twist Angle

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David Troner | University of Florida | Fall 2015 6 2 I NTRODUCTION Wing twisting to control the roll of an aircraft has been around for over a century. In fact, the very first successful aircraft, the Wright Flyer built by the Wright Brothers, u tilized wing warping to control the aircraft. Birds use wing twist to control precise maneuvers and generate propulsion. So what has led to the decline of wing twist in favor of conventional ailerons over the past century ? In part, a major driver for ailer ons was the use of stiffer materials for aircraft structures. As balsa and pine wood was replaced with aluminum and composites, wing flexibility was taken as a detriment and sought to be minimized rather than actively used for aircraft control. The use of ailerons, which change the shape of only a small portion of the wing in a predictable manner through rotating a hinged lifting surface, allow for precise and predictable roll control with stiffer wings. Aeroelasticity, which is the interactions of aerodyna mic forces and aircraft structural dynamics, was largely an unpredictable factor that could lead to flutter , control reversal, and even buckling of the aircraft lifting surfaces if the materials are too flexible. However, modern analysis tools such as ASWI NG and ZAERO can be used to analyze the effects of aeroelasticity in flight. These analysis tools bring about a new phenomenon, the ability to design an aircraft to utilize aeroelasticity and flexibility as a benefit. A growing market for flexible structur es in aviation is the use of unmanned aerial vehicles (UAVs) and in particular, micro air vehicles (MAVs). These vehicles are often designed to take the impact of crashes regularly, and a key feature is their portability. Flexible structures enables both t hese goals, as flexible structures can often withstand impacts better than more brittle carbon fiber or composites, and they allow for the structure to be manipulated to take up less space for transport. A flexible aircraft wing is often designed with a stronger leading edge to take most of the structural strength and a more flexible trailing edge section to achieve the desired camber needed for lift. This poses a problem for the use of conventional ailero ns, as these are a trailing edge device that are not feasible with more flexible trailing edges. Hence the motivation for the re emergence of wing twist for roll control, which is a key option for controlling these flexible M AVs. Wing twist can be induced in a number of methods ranging from mechanical servos to active materials that change shape as a result of an applied current. For example, a joint DARP A/AFRL/NASA study commissioned a Northrop Grumman led Smart Wing Program which has explored the use of shape memory alloys (SMA) for active wing twist [ 5 ] . Hinge less control surfaces such as the SMAs used

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David Troner | University of Florida | Fall 2015 7 in the Smart Wing Study can provide improved aerodynamic performance as these devices all but eliminate the discontinuities from deployed conventional con trol surfaces , thereby delaying the onset of flow separation and stall characteristics. Utilization of wing twist has additionally been studied for use on manned aircraft in the X 53 Active Aeroelastic Wing (AAW) Program, a joint effort by NASA, the Air Force, and Boeing researchers. This program modified an F 18 fighter aircraft to equip it with flexible wings from a pre production prototype to use a combination of active and passive aeroelastic control to produc e a highly flexible, light weight control system [10] . Flight control software was developed to actively command trim settings to facilitate wing twist to minimize loads at high speeds. This project successfully demonstrated the use of actively controlled wing warping technology for aircraft roll at transonic speeds, and provides a benchmark for future aircraft designs to use this technology such as fighters, UAVs, and high altitude long endurance (HALE) aircraft [6]. This report aims to study the effects o f wing twist as a method of roll control as compared with the use of a conventional trailing edge device . 3 A EROELASTICITY O VERVIEW Aeroelasticity encompasses the interaction of the structural, aerodynamic, and inertial forces that act upon an aircraft in fl ight. These interactions build off each other, and may have a significant impact on the control and stability characteristics of the aircraft . Static aeroelasticity is of primary concern for this study. Static aeroelasticity focuses on the steady state def lections of flexible aircraft surfaces in a trimmed equilibrium condition. A key concern in static aeroelastic analysis is divergence, which is a structural failure due to the aerodynamic forces overcoming the restoring forces of the structure, which is mo st common in wing torsion [2]. With this potential adverse effect, the stiffness of the structure is a key parameter for aeroelastic analysis, since the stiffness directly relates to the restoring forces that res ist deformation of the surface. For aircraft , aeroelasticity arises wh en the aerodynamic forces cause structural deformation of the aircraft surfaces. The deformed surfaces have different aerodynamic properties and thus generate

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David Troner | University of Florida | Fall 2015 8 different loads which in turn causes dif ferent structural deformations. In trimmed steady state flight, this cycle continues until equilibrium is reached. This aeroelastic cycle is depicted below. Fig. 1. Aeroelasticity cycle. Aeroelastic interactions influence flight performance in many ways, including st ability derivatives that affect the aircraft dynamic response to perturbations, control effectiveness and even control reversal of control surfaces, and aircraft dynamic stability to include flutter [10]. In addition, as structural weight is minimized wit h new composite materials being introduced and with the advent of advanced statically unstable aircraft systems with high authority feedback control systems, aeroelastic effects are becoming even more significant. These changes tend to decrease the frequen the importance of aeroelastic study in the design of control systems for these systems to limit adverse effects of dynamic aeroelasticity such as flutter [9]. Clearly, a eroelasticity is an important concern as the aircraft structural materials are made more flexible. However, aeroelasticity and flexible structures, if properly understood, may be actively controlled to provide optimal performance for an aircraft. This conc erns the field of aeroservoelasticity, which uses interactive flight controls to modify the aeroelastic dynamic response of an aircraft to increase performance and stability [10].

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David Troner | University of Florida | Fall 2015 9 4 M ODELING 4.1 G ENERIC M ICRO A IR V EHICLE ( G EN MAV ) The definition of what constitutes a micro air vehicle varies, but in general, a MAV is an aircraft that is generally the size of a bird or smaller. MAVs generally operate in low Reynolds number flight regimes due to their smaller sized wings [2]. The market for micro air vehicles has seen large growth over the past decade as these small, unmanned aircraft allow them to be particularly useful in both maneuverability and portability to accomplish missions that would be more difficult or impossible wi th larger platforms. The emerg ence of smaller sensor platforms further increases the potential of micro air vehicles for surveillance and other missions . This study utilizes a generic micro air vehicle platform developed at the Munitions Directorate of the Air Force Research Laboratory at Eglin Air Force Base in Florida called the GenMAV [8]. The GenMAV wa s designed to provide a baseline platform to perform experiments on MAVs in a collaborative environment , and multiple experiments have been conducted on t his MAV platform . The GenMAV has a high wing configuration with a circular fuselage and conventional tail [8]. The horizontal and vertical stabilizers are used for control via a rudder and elevons . It is constructed predominately of carbon fiber, and has a wingspan of 61 cm and length of 42 cm. The GenMAV has a flight ready mass of 1.02 kg and is powered by a nose mounted electric motor. The GenMAV is designed for flight speeds of around 15 m/s [ 1 ]. The experimental testing and modeling used to generate the detailed ASWING model of the GenMAV were performed previously by J. Babcock, and outlined in his Ph.D. dissertation, Aeroservoelastic Design for Closed Loop Flight Dynamics of a MAV [2]. The GenMAV utilizes elevons rather than ailerons to roll the aircra ft; however, ASWING treats the elevons functioning as elevators and the elevons functioning as ailerons as separate control be referred to throughout this rep ort as ailerons, since they are functioni ng as such in the ASWING model. The GenMAV model was selected for this study due to its detailed prior modeling with experimental validation and due to its flight and structural properties generalizable to many MAVs .

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David Troner | University of Florida | Fall 2015 10 The geometry of the ASWING GenMAV model is shown below in Fig. 2. Fig. 2 . Geometry of the GenMAV .

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David Troner | University of Florida | Fall 2015 11 4.2 ASWING S OFTWARE ASWING is a software program developed my Dr. Mark Drela at the Massachusetts Institute of Technology to allow for rapid aerodynamic, control response, and structural analysis for aircraft design and evaluation. ASWING is particularly suited for analysis of aircraft with flexible wings and fuselages with higher aspect ratio [3]. ASWING allows for the prediction of static and quasi static loads and deformations of aircraft in a trimmed condition . ASWING utilizes a nonlinear Bernouli Euler beam representation for surface and fuselage structures, and uses a lifting line representation to model the aerodynamic surface characteristics with use of the Prandtl Glauert transf ormation in wind aligned axes to capture compressibility effects . The aeroelastic effects are captured through coupling of t he aerodynamic and structural formulations in a single nonlinear system , which is then solved by a full Newton method [3 ,4 ] . ASWING has been validated against analytical cases in both static and dynamic cases, and has been used in many other projects for aeroelastic analysis [2]. For this reason and for its capabilities described above, ASWING was chose n as an ideal software to perform the following analysis on wing twist since it allows for rapid configuration changes and captures aeroelastic effects. 5 W ING T WIST FOR R OLL C ONTROL S TUDY 5.1 B ACKGROUND A key area of interest in this report is the use of wing twist as a replacement for ailerons found on most modern aircraft. The feasibility of wing twist is dependent on many factors, most importantly the ability to actuate a twist in the wing. This may be performed by smart materials that change shape as a result of an applied electric current or by physical actuators. The following study does not focus on the means for twist, but rather serves as a preliminary study to assess the implications of a deformed wing shape on the trim aerodynamics of an aircraf t. As previously mentioned, micro air vehicles provide an excellent platform for wing twist study due to the numerous applications of flexible wings and the relative low risk and inherent low structural factors of safety needed as compared with larger airc raft platforms.

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David Troner | University of Florida | Fall 2015 12 The basis of this study is to determine how a given geometrical twist of the wing shape induces a roll moment. While rolling is a dynamic maneuver, the aircraft is analyzed in trim in a quasi static equilibrium state such that the governing equations are solved to give a non zero roll moment yet have a roll rate of zero. 5.2 T RIM C ONDITIONS The GenMAV aircraft is trimmed in the ASWING software for straight and level flight with one constrained to zero deflection and the roll moment ( ) is left unconstrained. The elevators and rudder are constrained to give zero angular acceleration about the y and z axes, respectively, as is desirable for straight and level flight. The full trim conditions of the GenMAV for this study is detailed below in Fig. 3 . In Fig. 3 , each variable in the top row is constrained by a given trim variable in the left hand column, linked by a white square. To read the chart, follow the column from each constrained variable in the top row down the column until a white square is reached. Then follow the row which contains the white square to the left side to reach the constraining variable and its value. Fig. 3 . Trim conditions for wing twist study.

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David Troner | University of Florida | Fall 2015 13 5.3 D ESIGN S PACE The d esign space c overed ranges in material flexibility from nylon to extremely stiff and ranges in trim velocity from 10 30 m/s as the wing was twisted up to 4 degrees at the tip . The velocity was increased in 2.5 m/s increments, and the stiffness of only the wing is varied. The wing was twisted in a linear fashion with the root at zero twist angle relative to the fuselage, and the tip twisted to an angle ( ) up to 4 degrees in 1 degree increments. The wings were twisted in an equal and opposite manner with the local angle of incidence ( ) of the wing along the span varying by the following equation, with y as the distance along the y axis and the wing span as b . [1] Th e wing was twisted in this manner to emulate a simple servo device which twists the tip of the wing while the root is attached rigidly to the fuselage. The wing was twisted about an elastic axis taken at the mid chord. Wing twist induced by an active material or other means may take a different twist distribution along the span, and alternate distributions may be addressed in future work. The twist angle was limited to maximum 4 degrees of variation si nce, as to be shown in Section 6 , further deflection angles generate too large a roll moment to be compared reasonably with ailerons. The trim velocity range was chosen to capture off design trim performance since higher and lower airspeeds play an important role in the aeroelastic forces generated, and a key concern to the feasibility of flexible wings is the ability to retain performance in off design conditions for take off, landing, or maneuvering flight. The GenMAV to drag ratio is around 18 m/s, and as will be shown, the lift to drag ratio drops more rapidly as the aircraft is slowed from this value than if the airspeed is increased. Thus, the 10 30 m/s range was chosen to ca pture a large performance spectrum, particularly in terms of the lift to drag ratio. The material flexibility was selected as a design variable since the flexibility of the aircraft is paramount to this study, and variations in material torsional stiffness provide a benefit to the aircraft designer wishing to use these results for material selection . Only the torsional stiffness is varied in this study in an effort to separate the effects of torsional and bending stiffness and focus solely on torsional stif fness effects. The bending stiffness is kept at an extremely high value ( ) to give an essentially stiff wing in bending . The torsional stiffness values were chosen

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David Troner | University of Florida | Fall 2015 14 to approximate that of actual materials. The original GenMAV model of predominately carbon fiber was scaled based on the shear modulus ( G ) to achieve the desired torsional stiffness ( ) input for the ASWING model. The se design points are detailed below in Table I . T ABLE I : M ATERIAL D ESIGN S PACE FOR W ING T WIST S T UDY [7 ] M ATERIAL S HEAR M ODULUS ( ) S CALE F ACTOR GJ ( ) N YLON 4.1 0.12 0.0398 Tin 18 0.55 0.17455 Aluminum 6061 T6 24 0.727 0.23273 Carbon Fiber 33 1 0.32 Titanium Grade 5 41 1.24 0.39758 Stainless Steel 77 2.34 0.75861 Stiff n/a n/a 1000 5.4 P ERFORMANCE C RITERIA AND P ROCESS The main performance factor used to evaluate the trial results is the lift to drag ratio . This paramet er was chosen since it is commonly used as a design parameter in wing design and this study is intended as a preliminary study to analyze the effects of wing twist as a design tool. The steps of this study are outlined in the following figure. Fig. 4 . Wing twist study process flow chart .

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David Troner | University of Florida | Fall 2015 15 5.5 R ESULTS First, the effect of trim velocity on lift to drag ratio over varying wing twist angles and torsional stiffness were studied. The results of these trials are shown below. Fig. 5 . Plots depicting lift to drag ratio as a function of trim velocity over design space.

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David Troner | University of Florida | Fall 2015 16 First to be noted, the results for nylon differ greatly from the other results . W ith this highly flexible scenario, as the wings are twisted , the aerodynamics forces deform the wings a large amount which leads to large deflections that have detrimental effects on the aerodynamic propert ies of the wing including the li ft to drag ratio. Thus , a nylon wing is not recommended for this specific aircraft, which with very thin wings has a low torsional stiffness. The following analysis will thus exclude Nylon. Nylon still may be a suitable materia l for an aircraft with thicker wings. A few key trends are readily evident . First, as the trim velocity is decreased from the design speed of roughly 18 m/s, the effects of wing twist on lift to drag ratio decreased and the results begin to converge over the four twist angles . This relationship is largely independent of the torsional stiffness. The convergence may be primarily due to the fact that with decreasing airspeed, the dynamic pressure ( ) decreases, and lift and drag then decrease as they are proportional to this dynamic pressure. Therefore, as the trim velocity decreases, the aerodynamic forces resulting from the wing twist decrease resulting in wing twist having less of an effect on the lift to drag ratio. The relationship between the ae rodynamic forces, dynamic pressure, and trim velocity is sho wn below in Eq. 2 through Eq. 4. T he wing planform area ( ) remains unchanged and the coefficient of lift and drag are largely a function of the airfoil and angle of attack, which only varies loc ally up to the maximum 4 degrees. [ 2 ] [ 3 ] [ 4 ] Another trend stemming from this relationship is the increased negative effects of wing twist at trim velocities higher than the design velocity. The plots show that as wing twist is increased, the lift to drag ratio decreases at a faster rate for higher velocities. Also evident is that this rate of decrease of the lift to drag ratio increases with decreasing torsional stiffness. These effects are summarized in the following table.

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David Troner | University of Florida | Fall 2015 17 T ABLE II : E FFECTS OF D ESIGN V ARIABLES ON L IFT TO D RAG R ATIO Action Effect on Lift to Drag Ratio Effect on Lift to Drag Ratio Increase V Increase GJ Increase Next, the effects of torsional stiffness and trim velocity were analyzed separately for each value of wing twist. The results of these trials are shown as follows . Fig. 6 . Plots depicting lift to drag ratio as a function of trim velocity and torsional stiffness.

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David Troner | University of Florida | Fall 2015 1 8 Key trends evident fr om the plots again compliment the previous results that for a given angle of twist, the most pronounced decreases in the lift to drag ratio occur at higher velocities and with more flexible materials, as is expect ed. What these plots provide over the previous results is a sense of the relative weights of changes of torsional stiffness and changes in trim velocity on the lift to drag ratio. The lift to drag ratio changes more drastically over the velocity design spa ce than it does over the torsional stiffness design space. Thus, an incremental change in trim velocity of 2.5 m/s carries more effect on the lift to drag ratio than an incremental change in torsional stiffness between the materials. In fact, from a torsio nal stiffness of to a torsional stiffness of , the lift to drag ratio only changes by 0.12 in its worst case of maximum wing twist (4 degrees) and maximum trim velocity (30 m/s). This result is important for designers, since it indicate sizable effect on the lift to drag ratio and other design factors can drive the material selection such as price and ability of the shape to be deformed at a desired rate or magnitude. However, as shown by the previous results for nylon, as the torsional stiffness becomes very low the effects of torsional stiffness do dominate the performance parameters such as lift to drag ratio. The final trial for this study was to anal yze the generated roll moment for a given wing twist. This result is important since the purpose of the wing twist is ultimately to roll the airplane via a roll moment. The results of this trial are shown below.

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David Troner | University of Florida | Fall 2015 19 Fig. 7 . Plots depicting roll moment as a function of design space variables. The plots illustrate three important relationships. First, holding all other factors constant, increasing the wing twist leads to a rather large increase in the generated roll moment. Second, the roll moment incre ases with increasing trim velocity as expected, since again higher velocities lead to a great er lift (and drag) force which generates a larger roll moment. This effect is exacerbated as the wing twist increases because the angle of attack of the wing tip w ill be larger than the local angle of attack at the root by a value equal to the wing twist angle. The larger the wing twist, the greater the wing tip angle of attack is relative to the aircraft angle of attack and thus a greater lift force at the tip whic h generates a larger roll moment due to the large moment arm from the center of gravity to the wing tip. These relationships are shown below in the following equations. [5] [ 6 ] [7]

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David Troner | University of Florida | Fall 2015 20 Further evident from these results is that as the torsional stiffness is decreased, the rate at which the roll moment increases with velocity changes from predominantly linear to predominantly in terms of roll moment for a given trim velocity and wing twist. 5.6 W ING T WIST S TUDY C ONCLUSIONS As with all desi gn problems in aerospace engineering, this study shows an important tradeoff . As the material is made more flexible, there are reductions in lift to drag ratio which are exacerbated at larger wing twists. However, the ultimate goal of wing twist is to achi eve a desired roll moment, and both increasing wing twist and decreasing the material torsional stiffness result in higher roll moment for a given trim velocity. Increasing flexibility can even increase the roll moment to such an extent that less wing twist is needed to achieve a desired roll moment. Thus, the designer must ca refully weigh the relative contributions of trim velocity, torsional stiffness, and wing twist angle to achieve an optimal design. This selection will of course vary for each aircraft configuration; however, the trends still apply within a reasonable desig n range and should aid the designer in material selection for wing twist design. Selecting a trim velocity close to the design velocity in an effort to limit the adverse effect of flexibility on lift to drag ratio while allowing for moderate flexibility su ch as with Tin may provide an optimal tradeoff for the GenMAV model. This trim condition is compared to a baseline aileron roll generation in the following section to evaluate the relative cost benefit of using wing twist over ailerons for roll control. 6 B ASELINE R OLL C OMPARISON WITH C ONVENTIONAL A ILERONS 6.1 B ACKGROUND In an effort to evaluate the benefit of utilizing wing twist for roll control, the trim condition described above is compared with the similar trim condition using ailerons. Specifically, the trim condition is as follows.

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David Troner | University of Florida | Fall 2015 21 Under this condition, the following roll moments were generated using wing twist. T ABLE III : R OLL M OMENTS AND L IFT TO D RAG R ATIO D UE TO W ING T WIST AT T RIM C ONDITION W ING T WIST (D EGREES ) G ENERATED R OLL M OMENT (N M ) L IFT TO D RAG R ATIO 0 1 2 3 4 To compare the use of ailerons to this wing twist case, it is necessary to find the relationship between aileron deflection and generated roll moment. Once this is found, the aircraft is then trimmed for that given aileron deflection, and the lift to drag ratio is found. 6.2 T RIM C ONDITIONS Similar to the wing twist trials the aircraft is tri mmed for straight and level flight with on e key difference. In this trial, the aileron is trimmed to give a desired roll moment corresponding to the values in Table III. The trim case is shown below in the same format as for the wing twist case. Fig. 8 . Trim conditions for aileron study.

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David Troner | University of Florida | Fall 2015 22 6.3 P ERFORMANCE C RITERIA AND P ROCESS Again the main performance factor used to evaluate the trial results is the lift to drag ratio. This allows for a direct comparison with the wing twist results for generating the same roll moment. The process is illustrated below. Fig. 9 . Aileron study process flow chart. 6.4 A ILERON S ENSITIVITY A NALYSIS To match the generated roll moment between the two cases, the roll moment generated for a given aileron deflection at the trim condition was found and is plotted below. Fig. 10 . Roll moment for a given aileron deflection.

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David Troner | University of Florida | Fall 2015 23 Neglecting other factors that are not changed in the trim case , the roll moment for a given aileron deflection ( ) is related by the slope of the above plot ( ) as follows. [ 8] This follows the relatively linear ( ) relationship shown in the plot, with the slope from the trendline. This generated roll moment is also related to a given wing twist as shown in Table III. Thus, the aileron deflection and wing twist can be related through the roll moment each generates. This relationship is plotted below. Fig. 11 . Wing twist roll moment relationship. Since both aileron deflection and wing twist are linearly related to roll moment, it follows that they are linearly related to each other. This plot reve als a key benefit of wing twist over ailerons: a small wing twist generates a roll moment that would require a large aileron deflection. In fact, for the GenMAV , every degree of wing twist is equivalent to roughly 16 degrees of aileron deflection. This wil l play an important role in the lift to drag ratio, as to be discussed. A caveat, this relationship is specific to the GenMAV which has aileron (elevons) with a low aileron effect iveness of . Aircraft with a higher aileron effectiveness will not need to deflect the ailerons as much to achieve the same roll moment for a given wing twist. However,

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David Troner | University of Florida | Fall 2015 24 this study is intended to be focused on aircraft similar to the GenMAV where flexibility is key and elevons are much more feasible than ailerons which may have a larger effectiveness. 6.5 R ESULTS The results of the aileron study is shown below in Table IV. T ABLE IV : L IFT TO D RAG R ATIO AND R OLL M OMENT D UE TO A ILERON D EFLECTION AT T RIM C ONDITION A ILERON D EFLECTION ( DEGREES ) G ENERATED R OLL M OMENT (N M ) L IFT TO D RAG R ATIO 0 14.93 9.79 30.91 8.01 49.13 5.35 66.53 3.56 The results from Tables III and IV are combined to compare the lift to drag ratios for both cases. This is plotted as follows. Fig. 12 . Lift to Drag ratio comparison for both cases. The plot reveals a result that the lift to drag ratio decreases much more rapidly to generate an increasing roll moment for the aileron case than the wing twist case. This is largely due in part to the large deflections the ailerons must undergo to achieve the desired roll moment as compar ed

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David Troner | University of Florida | Fall 2015 25 with the wing twist. This indicates a major lift to drag savings for using wing twist over ailerons to generate larger roll moments. A word of caution, however. The drag calculated due to aileron deflection is not modeled entirely in an accurate manner in ASWING. ASWING models drag in vector form as follows [4] . [9] In Eq. 9, is the perpendicular component of the velocity , is the unit normal, and is the coefficient of pressure drag, and is the coefficient of skin friction drag. With the pressure drag a key component to the drag force, the pressure drag is calculated as follows [4] . [10] This linear approximation is intended to model drag devices such as spoilers rather than conventional trailing edge surfaces such a s ailerons, since these trailing edge devices have a profile drag that is roughly quadratic with surface deflection rather than linear. However, since the trailing edge devices, namely the elevons, were constrained to zero (for roll considerations antisymm etric), the linear drag factors are zero such that the linear vs. quadratic relationship is a non factor in the pure roll case. Inaccuracies in drag from the elevons do show up in the pitch consideration; however, the inaccuracies in approximation play int o both the elevons and the wing twist case in pitch only and thus can be neglected since the key difference between the two is analyzed only in the roll axis. 6.6 A ILERON S TUDY C ONCLUSION Even with these inaccuracies in the modeling of drag due to aileron defl ection and the limited scope of the direct comparison of ailerons to wing twist, the results do pose important qualitative results . First, wing twist has the potential to perform as well if not better than ailerons in terms of lift to drag ratio for high roll moment scenarios. Second, wing twist can be used to generate a relatively large roll moment for a small wing twist. Therefore, wing twist would be ideal for MAVs that are designed to be highly maneuverable and undergo large roll rates. An exampl e of such a

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David Troner | University of Florida | Fall 2015 26 vehicle would be a MAV modeling a bat, where flexible wings and high maneuverability are desirable. 7 C ONCLUSION These studies reveled that there may be a benefit to the use of wing twist over elevons for this specific aircraft configuration. Ul timately, there are many more design factors (to be discussed in Section 8) to be considered before making an absolute determination on the benefit of wing twist. However, this study does show that wing twist may be beneficial to achieve larger roll moment s with small deflections, especially as material stiffness is decreased. Key trends in the studies showed that decreased material stiffness does not linearly relate to changes in roll moment and lift to drag, but instead has a larger effect when varied fro Carbon Fiber results. Decreasing the torsional stiffness was further shown to increase in a linear manner to incr easing in a quadratic manner with trim velocity as the torsional stiffness is decreased. However, this positive effect of decreased torsional stiffness comes at a decrease in lift to drag ratio, and it is ultimately up to the designer to balance this trade off with other factors such as actuator power required to select the best use of wing twist for roll control for a more flexible aircraft. 8 F UTURE W ORK This is a preliminary study on the effects of torsional stiffness on a MAV model, the use of which is in tended to be beneficial in the use of wing twist for roll control. As such, there is much room to expand the design space, performance parameters, and overall aircraft configurations. For example, the t orsional stiffness distributions may be changed to a n on constant model along the span to analyze the effects of changing material or thickness along the wing span. The range of material stiffness may be expanded on to include the range of stiffness between that of Tin and Nylon that still may converge for th e given GenMAV model. Additionally, differing performance metrics other than lift to drag ratio may be analyzed based on the goals. To fully understand the effects of aeroelasticity, future wo rk should include a study of the combined effects

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David Troner | University of Florida | Fall 2015 27 of varied torsional and bending stress together on not only on the wing surfaces but on the empennage as well. Experimental validation of the results may be achieved through wind tunnel testing of the GenMAV model and physical twisting of the wings to match the configurations in this study . While this analysis is geared towards that of a small MAV, aeroelasticity and the use of wing twist for roll control can apply to larger aircraft, especially high altitude long endurance (HALE) aircraft. Thus , the Reynolds number can be varied to analyze the aeroelastic effects on these larger configurations. Additionally, alternative methods for twisting the wing may be studied. This report used a linear twist; however active materials may resul t in non linear twisting along the span and these distributions may yield differing results than those presented in this report. Following these computational results, designing a controller to control wing twist using actuators or active materials would b e a logical next step. A trade study on the relative cost benefit of using wing twist that incorporates actuation limitations and weight and power costs should be investigated before a complete design decision is made. Finally, this analysis can be expande d to investigate the utilization of wing or even vertical and horizontal tail twist to control yaw and pitch in addition to roll.

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David Troner | University of Florida | Fall 2015 28 9 R EFERENCES [1] a MAV, AIAA Atmoshperic Flight Mechanics Conference , 2012. [2] Babcock Loop Flight Dynamics o [3] [4] escription Steady Formulation [5] Fleming , G. and Burner , A., "Deformation Measurements of Smart Aerodynamic S urfaces", Proc. A SPIE 3783, Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for a Solids, 228 (October 13, 1999); doi:10.1117/12.365741 . [6] A New Twist in Flight Research: The F NASA a Aeronautics Book Series , 2013. [7] The Engineering Toolbox Available: a http://www.engineeringtoolbox.com/modulus rigidity d_946.html . [8] a a Sciences Meeting and Exhibit, AIAA 2007 0667, Reno, NV, Jan. 2007. A doi:10.2514/6.2007 667. [9] Journal of Aircraft , a vol. 25, 1988, pp. 563 571. [10] Weisshaar, T. ,