Morphing Wing: A Demonstration of Aero Servo Elastic Distributed Sensing and Control

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1 Morphing Wing: A Demonstration of Aero Servo Elastic Distributed Sensing and Control Sunil C. Patel Manoranjan Majji*, Bong Su Koh*, John L. Junkins +, Othon K. Rediniotis x Department of Aerospace Engineering Texas A&M Engineering College Station, Texas Abstract This paper details efforts made in the design, analysis, and control of a novel morphing wing for NASA utilizing cuttingedge intelligent material technology. The theoretical modeling of the aerodynamic characteristics of a morph-able wing has been achieved by applying Prandtl-Glauert s Lifting Line Theory. Using this Vortice-Lattice method in accordance with the computing language FORTRAN the drag, lift, and pitching moments of the morphing wing were calculated. The functional behavior that explains the aerodynamic response to the three twisting sections was studied. Relationships between motor outputs and achieved twist angles were derived from measurements; these relationships were then validated via sensor feedback systems. I. Introduction Morphing can be defined as the ability to morph, or to change the form or character of, to undergo transformation 1. When applied to an aerospace vehicle, it would refer to the capacity of a plane s wings to change shape during flight and thus providing some aerodynamic advantage. The concept of a morph able wing section is as old as the first airplane ever invented; the Wright Flyer II used a morphing wing as a way to control the aircrafts roll capability. All aircraft today use some sort of small degree of morphing in the form of control surfaces in order to pitch, roll, and yaw the aircraft. Some examples of these mechanisms are elevators, ailerons, and a rudder. A new definition of morphing has to be developed to the idea being an old one and therefore truly distinguishing an aircraft as morph able. A morphing wing can thus be defined as one which has the ability to either alter its shape in a continuous change along the chord or spar or to change its shape in a drastic manner. The Defense Advanced Research Projects Agency has developed a more technical and fine cut definition of a morphing aircraft as one that had the ability to perform either a 200% change in aspect ratio, a 50% change in wing area, a 5 degree change in wing twist, or a 20 degree change in wing sweep. Morphing wings of this type have taken several forms throughout their history from wings capable of twisting about a spar like the Wright Brother s aircrafts, variablesweep wings as the F-14 Tomcat, to telescoping wings. Undergraduate Research Assistant. Graduate Research Assistant, Student Member, AIAA. + Distinguished Professor, George J. Eppright Chair, AIAA Fellow. Associate Professor, AIAA Associate Fellow. Copyright 2005 by the American Institute of Aeronautics and Astronautics. 1

2 II. Motivation The traditional idea of an airplane is a set of rigid, fixed wings to provide lift and a combination of ailerons, elevators, and rudder to control roll, pitch, and yaw. Different types of wings have different types of aerodynamic characteristics such as a symmetrical wing has no lift generated when at and angle of attack of zero degrees; a cambered aircraft on the other hand has lift generated at an angle of attack of zero degrees. These traditional aircraft also use one set of configurations out of many to accomplish a given task. During traditional aircraft design, thousands of variables are reduced to a few key design variables, what Raymer refers to as the basic six : thrust to weight ratio (T/W), wing loading (W/S), wing thickness-to-chord ratio (t/c), wing taper ratio ( λ ), wing sweep ( Λ ), and wing aspect ratio (b 2 /S) 2. Different sized aircraft correspond to different sets of these quantities, which result in different performance capabilities. For example tanker aircraft for in air refueling are well-suited for long-duration cruising missions but are vastly different from quicker, more maneuverable fighters they help refuel. The goal of developing a morphing wing is that it will be able to accomplish contradictory missions such as the ones stated above through changes in wing shape. In general, wing shapes that are long and thick are well-suited for slow, gliding flight while short, thin swept wings allow for quick maneuvering and high speeds. The wing sections that manufacturers choose in the final design steps of an aircraft are usually a compromise between conflicting product capability. Changing the wing shape during the middle of a sortie brings the performance of a wing closer to the ideal concept of a wing. Where the ideal wing is a wing that is able to change with each mission it is assigned. An aircraft with a morph able wing will have better performance for a far wider variety of missions. It will have the versatility to perform contradictory missions with efficiency and have the adaptability to accomplish unforeseen tasks. This will also lead to a lesser need to design one type of aircraft for one type of mission; with the morphing wing you would have the capability of many aircraft in one. One of the nicest aspects of a morph able wing is its ability to control roll, pitch, and yaw without the need of ailerons, elevators, and rudder. This would lead to an elimination of these parts which in part would lead to potential increase in reliability and a reduction of aircraft maintenance. Another important factor in their elimination is the removal of seams along the wing which would mean a longer duration of laminar flow in the direction of the chord line. This would lead to a greater fuel efficient aircraft which is lower in weight also. For military aircraft the seamless wing would greater increase the stealth of the plane when in comes to radar detection. Birds are the primary source of motivation for the development of a morphing wing. The versatility and control that even the most complex fixed-wings planes can accomplish pales in comparison to the performance versatility that birds can achieve with a simple move of their wings. Several researchers are studying these wings in hopes to better understand how birds can perform such complex maneuvers. Figure 1 shows some of the many different configurations a bald eagle can achieve. Figure: 1 Bald Eagle in Various Wing Configurations III. Past Research As mentioned previously, the morphing wing is an old concept with the Wright brothers actually designing the first aircraft, the Wright Flyer I in 1903, that utilized a morphing concept which they referred to has wing warping. They used a series of pulleys and cables that twisted the wing to change directions. They too were inspired by the flight of birds when the observed a turkey buzzard over the Miami, Ohio river 3. Several attempts to develop morphing wings have been made in the U.S. throughout the past few decades. The B-1B bomber 4 developed in the mid-1980 s had a blended-wing body that was capable of varying its sweep, providing for wingspans between 78 and 180 feet. The upswept position allowed the B-1B to takeoff in shorter distances and provided increased range, and the swept position allowed it to achieve higher speeds. The Navy s F-14 Tomcat 5 also uses variable sweep wings to achieve different wingspans ranging from 38 to 64 feet (a range of 20 to 68 degrees), resulting in a range of aerodynamic characteristics. The variable sweep allows the F-14 to land and takeoff of short runways of aircraft carriers while still allowing it to maintain speed and maneuverability in flight (Figure: 2). The large wing pivot mechanism, however, spans the entire diameter of the fuselage and greatly increases the weight of the plane. 2

3 control algorithms for the control of actuation systems on morphing wings. Figure: 2 F-14 Tomcat with Wings Swept Back The Mission Adaptive Wing 6 was a joint project between the United States Air Force and the National Aeronautics and Space Administration to apply morphing technology to an F-111 test bed plane. It was one of the first attempts at a smooth, variable-camber wing. The shape of the airfoil s cross-sections adapted to suit the specific task of the plane. Hydraulic servo-systems were used to change camber on the leading and trailing edges, resulting in a possible leading-edge rotation of +2 to -21 degrees and trailing edge rotation of +4 to -22 degrees. Sliding panels located on the lower edge allowed for chord changes resulting from the variable camber, and the wing was covered with a flexible plexi-glass skin. One of the more recent morphing wing projects involved the addition of an active aero elastic wing to an F/A 18A Hornet 7. Pre-production wings for the Hornet that were deemed too flexible to be used on the actual plane during manufacturing were fitted onto a Hornet. The wings were flexible enough to twist were small amounts at high speeds, resulting in decreased drag and an increase in range. IV. Current Research The recent developments in the field of smart materials have spurred research in the field of morphing wings where those materials can be used to make a 21 st century intelligent wing. One of the most prominent morphing projects is NASA s own Aircraft Morphing Program which is a 6 year program aimed at developing smart devises for implementing in airframe application to enable self-adapting flight resulting in dramatic improvements in aircraft efficiency and affordability 11. The program focuses on shape-memory alloys and other smart technology to create shape alterations in the wing. Research on morphing wings is also being conducted at many universities across the United States. Many research groups are developing morphing wing designs at universities such Virginia Polytechnic and State University, University of Florida, and University of Maryland 8. Several other universities are developing V. Project Goals The stated goals of the project in this research paper is to explore mathematical models which explain the aerodynamics of the morphing wing, derive control laws which achieve desired lift and moment values upon twisting the different sections of the morphing wing, and explain the coupling action between the three sections of the wing. The final goal of this project will be to build a UAV with the morphing technology which reaches velocities of 20 m/s. Different types of smart actuation technology are being researched by a separate group of students. The particular type of morphing on which this project is build on is the application of a wing twist with a smooth distribution along the span. Actuated Section at 33% Span Actuated Section at 66% Span Section Rotated by Angle θ1 Section Rotated by Angle θ2 Actuated Section at 100% Span Spar Stiff in Torsion and Bending Section Rotated by Angle θ3 Figure: 3 A Schematic of the Wing Twist VI. Wing Design As shown in figure 3 above, the morphing wing is divided into three independent sections where each one can rotate about the spar creating wing twists. The first section rotates -5 to +5 degrees, the second section rotates -10 to +10 degrees, and the third section rotates -15 to +15 degrees relative to the preceding section. This is all accomplished with the use of four concentric tubes that run through the length of the structure where twist is accomplished by rotating one section of rod by the use of D/C servos. With the wing made of a flexible ABS plastic material the wing has the ability to flex and then bend back 3

4 to shape once the force of the rotating motors is stopped. In order to maximize flexibility in torsion, the structure consists of front and rear supports at the three locations of twist. The wing was manufactured in three sections and then fastened together with bolts for rigidity and the ability to absorb stress concentrations. The temporary skin which covers the structure is made up of a very flexible elastomer which in the future will be reinforced with carbon nanotubes for structural and actuation purpose. VII. Theoretical Aerodynamics In the Prandtl Model a wing section is replaced by a bound vortex of constant circulation. The theory is based on Helmholtz laws which says a bound vortex cannot end at the wing tips but rather form a complete circuit, or it must extend to infinity or a boundary of the flow. It follows that a stationary line vortex normal to the moving stream is the equivalent of an airfoil as the resultant force is concerned 9. Quantitatively, in practice b <<V t for steady flight and the configuration becomes essentially a horseshoe vortex fixed to the wing and extending to infinity. Actual finite wings are made up of a superposition of horseshoe vortex elements of various strengths, an infinite number of theses lead to a continuous distribution of circulation and therefore of lift as a function of y. V b Figure: 4 Bound Vortex y b/2 V t X Equation 1.1 is the general equation of the lifting line theory. The only unknown in the integro-differential equation is the circulation. Unfortunately, its solution is only straight forward for a few cases, one of those cases being for elliptical lift distributions (1.2). d 2 1 b / 2 dy wing αa (y 0 ) = + dy (1.1: Lifting Line Equation) m 4 b / 2 ov c V Π y0 y 2 y = s 1 (1.2: Circulation for an Elliptical Distribution) b / 2 1 = m0scsv 2 An sin nθ (1.3: Circulation for an Arbitrary Distribution) n= 1 Where: m = lift curve slope c = chord V = velocity far upstream = circulation 0 α = absolute angle of attack b = span along the wing a Glauert in 1937 considered circulation distributions expressed by Fourier series approximations which led to the development of equation 1.3. This equation works for any arbitrary lift distribution and gives the correct circulation ( ) so that once the circulation is known you can input it into the Lifting Line Equation (1.1) and calculate the absolute angle of attack which leads to finding all the basic aerodynamic quantities like C L, C D, C M, etc. This Prantle-Glauert model works well with wing sections because the wing is cut into many arbitrary sections along the span from the root to the tip where each point that it is virtually cut is analyzed for the absolute angle of attack using equations 1.3 and 1.1 respectively, the more sections you cut the wing into the better accuracy you can achieve. VIII. Analyzing Prandtl-Glauert Through FORTRAN The Prantle-Glauert approach was found to be very favorable when analyzing the morphing wing due to the fact that three separate independent sections twist, and any method used would have to split up the wing into many parts to account for the independent twisting sections which is exactly the approach the Fourier series approximations take. Because the entire method is built on calculating the absolute angle of attack at each section of the wing the twisting of the sections is taken as just an increase or decrease of the total angle of attack. The Prantle-Glauert method was very efficiently applied using the computing language FORTRAN due to the much iteration that it took to completely analyze the morphing wing. Dr. Leland Carlson of Aerospace Engineering at Texas A&M University had written a Prantle-Glauert code (named PRAND2G) in 1997 which was modified to take into account the three separate twisting sections and cuts the morphing wing theoretically into 19 separate sections and calculates each points absolute angle of attack (Figure: 6). Figure: 5 Horseshoe Vortices 4

5 Original equation which took the entire wing into account without any breaks. Case: 2 30 < TH ( I ) Twist (I) = (Tw3 - Tw2)*Cos[3*(TH ( I ) )-30 )] + Tw2 2 Where: Tw2 = 1st section twist Tw3 = 2nd section twist Case: 3 0 < TH ( I ) Twist (I) = (Tw4 - Tw3)*Cos[3*(TH ( I )) ] + Tw3 (2.4) 3 Figure: 6 PRAND2G Code The original equation was replaced by three if statements which took into account the three separate twisting sections. There was actually only one line in the original code which incorporated the twist into the calculations (2.1). Twist (I) = (Tw2 - Tw1)*Cos(TH ( I ) ) + Tw1 (2.1) Where: Tw1 = root twist Tw2 = tip twist The modified code incorporates three cases which correspond to the three sections of twist the morphing wing is capable of rather than the one section like the original code had. It takes equation 1.1 and makes it a piece wise function ( ). Once these equations were derived they were incorporated into the code using if statements. Where: Tw3 = 2nd section twist Tw4 = 3rd section twist VIIII. Summary of the PRAND2G Code There are nine main inputs that the code needs to be able to give output data. First it needs a Mach number input because the program calculates the solution for incompressible flow but contains a Mach number plan form and solution correction based on 3D Prantle-Glauert compressibility correction theory but for incompressible flow a value of 0 can be inputted. The second input is the angle of attack that you wish the wing section to be at. It is important to note that a value other than 0 must be inputted. This is the case because the solution needs two angles of attack to obtain two solutions and thus obtain the lift curve slope. The value of 0 is automatically used so a value other than 0 must be inputted. The third input parameter needed is 6 coordinate points defining the platform for the right hand side of the wing. These must be entered clockwise from the apex of the wing (Figure: 7). Case: 1 60 < TH ( I ) Twist (I) = (Tw2 - Tw1)*Cos[3*(TH ( I ) )-60 )] + Tw1 (2.2) 1 Where: Tw1 = root twist Tw2 = 1st section twist Figure: 7 The fourth and fifth input parameters are root twist and tip twist of the wing respectively. This part of the 5

6 code was the only part that had to be modified so that the program could account for the three extra twists the morphing wing can experience with actuation. So the program now asks for the root twist and three additional twist angles. The sixth and seventh input parameters are the 0 lift angle of attack and the ratio of the actual 2D lift curve slope over 2π. For the instance of the morphing wing the 0 lift angle attack is theoretically 0 because the wing is symmetrical. The ratio of the 2D lift curve slope over 2π is 1 because under the present version of the code these values are assumed to be the same at every section. The eighth and ninth input parameters are the change in 0 lift angle of attack if trailing edge flaps are used and the y value of flap extent. For our application we are not utilizing flaps so a value of 0 can be inputted for both quantities. X. Output Data The PRAND2G code creates a JUNKP file every time the program is ran so that the data can be observed in an organized fashion. This file can be read by using the windows program notepad. The output file gives data on the coefficient of lift, the coefficient of induced drag, airfoil loading, and the ratio of lift to drag. This set of data is given for the angle of attack of 0 and the angle of attack you input in parameter number 2. Additional output data involves the lift curve slope, the basic and additional coefficient of lift, the new zero lift angle of attack incorporating twist, and the percentage of variation from an elliptical wing. XI. Significance of Modified PRAND2G Program There are three main significant points of the PRAND2G code. First it gives a method for physics based model for the aerodynamic characteristics of a morphing wing. Second we have theoretical data to compare with the experimental data collected from wind tunnel experiments. Third and finally if the theoretical data coincides with the experimental data there is the possibility to generate configurations that produce desired lift, drag, and pitching moments. So it is evident that with this code the deciphering of the aerodynamics of the morphing wing is much more in depth with this new tool and also the time saved from not having to do wind tunnel test for hours on end. XII. Current Results: 1) Input Output Mapping of Theoretical PRAND2G Data using GLOMAP 9 The PRAND2G code was run 300 times for mapping different inputs (angle of attack, twist 1, twist 2, and twist 3) to outputs (C L, C D, and rolling moment). Once all the output data was in a format that could be read in Mat lab, GLOMAP 10 (a non-linear function approximator whose order can be changed) was utilized to find the relationship between the three twisting sections and C L, C D, and rolling moment. The angles of attack tested were 0, 6, and 12 degrees with a variety of different twist configurations. The results showed that C L increases as each section of the morphing wing is twisted and increases more when the first section is twisted because there is much more surface area at the first section. For the maximum amount of lift all three sections of the wing could be twisted at maximum capacity. The data also showed that the rolling moment is very sensitive to twist inputs which lead to the point that regular ailerons would not be needed with the morphing wing and the aircraft can be rolled by twisting one side of the wing. The data also showed, as expected, as the CL increases the induced drag increases which increases the total drag of the wing section, although the order of magnitude of the lift is much greater than the total drag. When all of the data was reviewed GLOMAP gave the result of the morphing wing being multi-linearly coupled between the three twisting inputs and the aerodynamic outputs, the angle of attack was, of course, coupled linearly with the aerodynamic forces. Figure: 8 C L vs. Twist Sections Figure: 8 Rolling Moment vs. Twist Sections 6

7 CL CL vs. Angle of Attack 0,0, ,0,0 2.67,0, ,2.5,0 first two sections at a constant twist and varying the third and recording the values of how the first two sections change as the third one was varied. Once a series of five runs were complete one of the first two would be increased in value while the other was still held constant and as before the third would be varied and outputs of how the first two sections change were recorded. This method was run until each section was twisted through all of the different ranges. Once all the data was collected GLOMAP 10 was used again see what the relationships between the section twists were ,0,2 0,0, ,1.5,2 2.67,2.5, Angle of Attack (degrees) Figure: 9 C L vs. Angle of Attack (2D) CD vs. CL CD ,0, ,0,0 2.67,0,0 0,1.5,0 0,2.5,0 0,0,2 0,0, ,1.5,2 2.67,2.5, CL Figure: 9 C D vs. C L XIII. Current Results: 2) Input Output Mapping of Coupled Twist Sections using GLOMAP 10 The morphing wing uses a telescoping rod to have the ability to twist the three independent sections as explained prior sections. The wing structure consists of an ABS plastic which is able to deform when the correct forces are applied. Due to the fact that the entire structure (all three sections) is connected using bolts when one section is twisted the other two also feel some movement and because of this coupling action the only way to be sure about what angle each section is at to be able to give the proper inputs a input/output mapping of the coupled twisting sections had to be carried out. To test the coupling action between the three sections magnetic sensors were utilized and mounted to each twisting sections. These sensors sensed a change in the magnetic field and were able to give feedback in degrees of motion they were experiencing. The experiment to achieve a relationship between sections was done by holding the Figure: 10 Plots of Coupling Relationships 7

8 What was discovered was that the coupling between sections is non-linear as can be seen from figure: 10. The second section is not very coupled at all but still undergoes some minor changes when the other two sections are twisted. Figure: 11 Residual Error Plots of Twist Sections The large residual errors even with 4 th degree GLOMAP approximator reveals the high non-lineareality of the structure which could not be modeled accurately (Figure: 11). This led us to conclude that more test runs have to be completed (only 80 were run during this test) to derive the proper relationships, although as explained before we do know that the relationship will be non-linear. XIV. Conclusion The PRAND2G FORTRAN code has been modified and used to show its applicability for future comparison with wind tunnel testing results. The conclusion that can be made from the PRAND2G code is that the aerodynamic characteristics of the morphing wing are multi-linearly dependent on the three twisting sections. The coupling actions between the three twisting sections are non-linearly dependent on each other. With these facts being known proper control laws can be derived so that the precise outputs of the aerodynamic characteristics can be foreseen when different configurations are inputted into the system. With this recent progress the novel morphing wing idea is one step closer to the final product which is a UAV that is designed with a morph-able wing. XV. Acknowledgment This work was sponsored by the Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles (TiiMs), funded by NASA Cooperative Agreement No. NCC A special acknowledgment to Dr. John L. Junkins, Manoranjan Majji, and Bong Su Koh at Texas A&M University. XVI. References 1) 2) Raymer,D., Vehicle Scaling Laws for Multidisciplinary Optimization, AIAA , 39 th AIAA Aerospace Sciences Meeting, Reno, NV, Jan ) Marks, P., The next 100 years of flight-part two, The New Scientist 4, Dec ) Federation of American Scientists. B-1B Lancer ) Federation of American Scientists. F-14 Tomcat. Oct April ) Kenneth L. Bonnema and Stephen B. Smith. AFTI/F- 111 Mission Adaptive Wing Flight Research Program. Pages , San Diego, California, ) J.R. Wilson. Active Aeroelastic Wing: A New/Old Twist On Flight. Aerospace America, 40(9):34-37, Sep ) Arrison, L., Birocco, K., Gaylord, C., Herndon, B., Manion, K., Metheny, M., AE/ME Morphing Engineering Department, Virginia Polytechnic Institute and State University, May ) Arnold M. Kuethe., and C.Y.Chow., Foundations of Aerodynamics : Bases of Aerodynamic Design, John Wiley and Sons, New York, ) J. L. Junkins, P.Singla, et.al., Orthogonal Global/Local Approximation in N dimensions: Applications to Input- Output Approximation, International Conference on Space Structures, Cinque-Terre, Italy. 8