Low Reynolds Number Aerodynamics, Phase 3: Micro Air Vehicle Airfoil, Aspect Ratio, and Planform Optimization

Low Reynolds Number Aerodynamics, Phase 3: Micro Air Vehicle Airfoil, Aspect Ratio, and Planform Optimization Johnathan Moore, 10 th Grade 3553 Ridgeway Rd. Bellbrook, OH 455-1967 Abstract The purpose of this project is to design a fully operational Micro Air Vehicle (MAV) that conforms to the DARPA and International MAV Competition regulations. A MAV is defined as a micro-sized aircraft in which no linear dimension exceeds 6. This is the third phase of a five year project researching low Reynolds number aerodynamics. The engineering goal of this phase is to conduct Computational Fluid Dynamics (CFD), run a Design of Experiments (DoE), conduct Multidisciplinary Design Optimization (MDO), and fabricate a fully operational MAV. The CFD program XFOIL was used to optimize three airfoils for three figures-of-merit: maximizing the lift coefficient, minimizing the drag coefficient, and achieving a pitching moment of zero. A DoE was conducted to reduce the full factorial of wind tunnel and computational experiments down to the desired number. In the case of the wind tunnel experiments, the number of test articles was reduced from 27 to 18. An MDO methodology was implemented to achieve the optimum MAV configuration. In this optimization procedure, an analytical code was written to optimize the MAV configuration for flight endurance subject to a maximum dimension of six inches. Both one and two panel wing configurations were optimized. The optimum configuration had a two-panel geometry, and the predicted endurance was 38 min. and 48 sec. This project has shown that CFD, DoE, and MDO approaches can be used to generate a feasible MAV configuration. A MAV geometry has been optimized for flight duration, and a prototype has been built and flighttested. 1.0 Introduction to Micro Air Vehicle Development The concept of a Micro Air Vehicle (MAV) has only been around for ten years, therefore, there is not much known about these micro-sized aircraft. The first operational MAV was designed by the AeroVironment Inc. in 1999. Their final configuration was capable of carrying a fully operational remote control system, a CMOS camera, and a microprocessor that relayed information back to a control center 3. The University of Florida hosted the first annual Micro Air Vehicle Competition in 1997, in which universities compete within what are now four categories: Surveillance, Endurance, Ornithopter, and Design Report. Recently, numerous research institutions have addressed the problems relating to MAV development, as has the Air Force and Navy. Most previous research conducted on MAVs has been based around generating an operational configuration, and not on sufficiently understanding the low Reynolds number regimen in which these MAVs operate. This lack of Low Re knowledge is currently hindering a truly optimal MAV geometry. However, this field of Aerodynamics is steadily growing, and perhaps the flow about these MAVs will be sufficiently understood in the upcoming years. The following project will focus on the development of a fully operational MAV that abides by the International Micro Air Vehicle Competition regulations, while also following the DARPA guidelines. 2.0 Procedure and Results This project is the third phase of a five phase project, and this third phase will be segregated into two parts; Phase 3a and Phase 3b. Phase 3a will focus on optimizing the airfoils to be used in the wind tunnel analysis, running a Design of Experiments to reduce the number of wind tunnel tests required, conducting Multidisciplinary Design Optimization, and lastly fabricating a fully functional Phase 3a MAV. Phase 3b (not discussed in this paper) will consist of running 500-1000 wind tunnel tests at varying velocities and angles of attack with each of the test articles fabricated in Phase 3a. This wind tunnel data will then be entered into the already functional MDO code and the optimizer will optimize on the actual force data. This is thought to produce valid results, on which a final Phase 3 micro air vehicle will be based upon. 2.1 Computational Fluid Dynamics The Computational Fluid Dynamics (CFD) program XFOIL 1 was used to produce three preliminary airfoils 1

that would later be incorporated into the test articles. Three airfoils were optimized, each for a different figure of merit. The figures of merit were to produce the maximum C L, minimum C D, and a C M as close to zero as possible. These particular figures of merit were selected because they were thought to be the most influential in maximizing flight duration. In order to optimize the airfoils, some parameters must be set as constants. The Reynolds number was set at 60,000-80,000; representative of a 5-6 aircraft flying at 35 ft/sec. The preliminary airfoil for each figure of merit was selected by an airfoil filtering process in which characteristics of low Re airfoils were used to omit airfoils in the database that are not characteristic of low Reynolds number airfoils. The constraints that defined a low Reynolds number airfoil were a maximum thickness of 14.0%, a minimum thickness of 8.0%, a camber < 4%, and only reflex airfoils were to be accepted. This narrowed the airfoil selection down to approximately 60. The graphs of C L, C D, C L /C D, and C m for each of these airfoils were computed and carefully analyzed. The resulting airfoils, polars, and specifications are shown below. Figure of Merit: Minimum C D Maximum thickness: 8.62% at 26.1% chord Maximum camber: 1.45% at 38.3% chord Leading edge radius: 0.5512% Trailing Edge thickness: 0.250% C D Polar: Figure of Merit: Maximum C L Maximum thickness: 11.34% at 27.2% chord Maximum camber: 1.86% at 37.0% chord Leading edge radius: 1.0004% Trailing edge thickness: 0.250% C L Polar: Figure of Merit: Minimum C M Maximum thickness: 8.19% at 27.5% chord Maximum camber: 2.78% at 25.0% chord Leading edge radius: 0.3739% Trailing edge thickness: 0.252% C M Polar: 2

2.2 Design of Experiments In order to optimize more than one independent parameter (variable), each parameter must be tested with the other. So, since three independent parameters are being optimized (airfoil, aspect ratio, and planform), and there are three of each, 27 test articles are required to fill the design space (3 airfoils x 3 AR s x 3 Planforms = 27 articles). It is beyond the scope of modern engineering practice to run the full factorial of experiments. Instead, a Design of Experiments (DOE) was conducted. A Design of Experiments was run to determine a subset of all possible airfoil, aspect ratio, and planform combinations. This DOE code tries to select the independent parameters is such a way that the individuals in the subset are mathematically orthogonal to each other. This helps reduce redundancies in the wind tunnel and analytical experiments and helps the optimization process. In this case, the full factorial of designs was 27, and the desired number was 18. Therefore, the DoE produced a combination of independent parameters that represented the design space in the most accurate manner. The DOE was run twice in order to see if there are more than two possible methods of accurately representing the design space, and there was. The second trial was chosen since it distributed the design variables is such a way that the design space was represented more completely than the first trial. 2.3 Multidisciplinary Design Optimization (MDO) 2.3.1 Introduction to MDO A Multidisciplinary Design Optimization (MDO) methodology was developed to achieve the optimum MAV configuration. Although the wind tunnel data and CFD data produce force data, the maximum or minimum force is not necessarily optimal for any given configuration. Therefore, a MDO approach is implemented, in which the optimal MAV configuration can evolve in a computer simulated environment. The optimizer can then stretch and squeeze the planforms, airfoils, and aspect ratios into intermediary shapes. This will produce a result that is perhaps more optimal than just selecting the planform that best satisfies a given figure of merit. 2.3.2 Objective The objective of the MDO is to maximize the endurance of a Micro Air Vehicle such that the maximum linear dimension does not exceed 6 inches. 2.3.3 Approach The approach to conducting the MDO is to (1) fix everything except the wing shape. (2) Conduct a series of experiments using a Design of Experiments (DoE) to generate a series of designs. (3) Apply a response surface methodology to find a mathematical surface (equation) that can be used in an optimization procedure to find the optimal design variables. MATLAB 6 was used to conduct all MDO procedures. 2.3.4 MDO Problems Ideally, the experiments should be conducted in a wind tunnel since Low Reynolds number and low aspect ratio aerodynamics are notoriously difficult to accurately model using traditional estimators. However, the traditional estimators are all that is available due to lack of low Re knowledge and the unavailability of an ultra-sensitive wind tunnel balance. These estimators are not necessarily inadequate for this application, and they can provide valuable insight into low Re and aspect ratio design. One of the most important aspects of research is understanding how different assumptions affect the results. One set of assumptions leads to the traditional estimators. 2.3.5 MDO Procedure To compute the endurance of the vehicle, the energy in the batteries needs to be known. Multiplying the amp-hour rating by the battery voltage and number of batteries yields the total energy available in Joules. The battery energy is divided by the total power required (aerodynamic + avionics) yields the endurance. The aerodynamic power required is simply the product of the vehicle drag and the flight speed divided by the propeller and motor efficiencies. The Vehicle drag is the product of the dynamic pressure, wing area, and drag coefficient. The drag estimators are typical estimators used in conceptual aircraft design. The drag can be decomposed into three parts- parasitic not varying with angle-of-attack, parasitic varying with angle-of-attack, and induced drag. The constant parasitic drag term is estimated using a flat plate turbulent skin friction coefficient. This coefficient depends on Reynolds number. To simplify the analysis, the Reynolds number was based on a flight speed of 35 ft/s. The skin friction does not vary too much when the Reynolds number is varied a small amount. The reference length used to compute Re is the mean aerodynamic chord. Calculating the parasitic drag in this manner ignores the complex flow fields that are generated by low aspect ratio, low Reynolds number wings, which are dominated by large upper surface vortices. The parasitic term varying with lift coefficient is based on an empirical estimator for large aircraft and 3

depends on the wing sweep and the constant parasitic drag term. The induced drag is calculated using the vortex lattice method. Like the parasitic term, it can not model the vortex-dominated flow of the real wing. Assuming that the Reynolds number doesn t vary and assuming that the propeller and motor efficiencies are constants, the optimal point can be found by C 3/ 2 L maximizing with respect to the lift coefficient. C D Once this optimal lift coefficient is found, the optimal speed can be determined using the lift coefficient and wing loading. This speed is not currently used in the analysis, but it is the speed at which the vehicle should ideally be flown. Given the fundamental limitations of estimating the vehicle drag in this manner, the results should not be heavily relied upon unless verified with wind tunnel or flight test data. 2.3.6 Design of Experiments (DoE) To reduce the complexity of the MDO problem, a simple wing was used initially that can be described by a trapezoidal geometry on either side of the vehicle symmetry plane. This shall be referred to as the one panel geometry. After the one panel analysis has concluded, a two-panel wing will be analyzed that is composed of two trapezoidal sections. The optimized two-panel configuration will then be incorporated into the Phase 3a MAV configuration. For a trapezoidal geometry, the free parameters are the root chord, tip chord, leading edge sweep, and semi span. In terms of typical aircraft design variables, the free parameters are aspect ratio, sweep, and taper ratio. The independent parameters for the one-panel geometry are wing area, aspect ratio, wing sweep, and wing taper. The two-panel geometry incorporated three more parameters: sweep 2, taper 2, and semi-span location along the x axis. The following equations show how the trapezoidal geometry is defined. 1 b b AR span = = 2 2 2 root chord = span 2 (1 + b taper ratio) tip chord = taper ratio root chord where b = wing area, and AR = aspect ratio. Figure 2 depicts the seven independent parameters used in the optimization and how they represent the MAV geometry. Note that this is the two panel geometry, and the one panel geometry is represented similarly with the exception that there is not a span fraction, sweep 2, or taper 2. Figure 2: Representation of MAV Geometry using 7 Independent Parameters A fully quadratic model will be used for the DoE. This implies that 3 levels (different values) for each design will be needed. A full factorial design would yield 3 4 = 81 total designs. In the case of the two-panel geometry, the full factorial design would yield 3 7 = 2187 total designs. To reduce the computational time required, a reduced number of designs will be analyzed. A coordinate exchange method will be used to generate D-optimal designs. Wing area will be limited from 0.05 to 0.25 square feet, aspect ratio from 0.5 to 1.8, sweep from 0 to 60 degrees, and taper ratio from 0.1 to 1. Endurance (minutes) (Dimensionless) Chord 32 28 26 24 22 20 18 Sweep 2 Trend line Wing Area Sweep 1 Span WIng Area (S) Span Fraction Aspect Ratio Root Chord Sweep (rad) Confidence intervals for X # designs Taper Ratio 0.15 0.2 1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Figure 3: Explanation of DoE results (applicable to all DoE graphs) Where the Trend line shows the mean trend relative to the number of designs run and the confidence interval represents the upper and lower endurance values for all geometries. The dashed horizontal and vertical lines are of no significance. The trend lines indicate that increasing wing area and aspect ratio increases endurance. The taper ratio seems to have very little effect on the endurance compared to the wing area and aspect ratio. If the wing area is further increased, then the maximum linear dimension constraint is violated. The same holds true if aspect ratio is increased. Sweep appears to have a moderate effect on endurance. The number of design was increased from 27 to 40. Taper 2 Taper 1 4

32 28 26 24 22 20 The results show that wing area and aspect ratio still have a large effect, but wing sweep is now important. If the aspect ratio is set as 1 for the current data set, the results shown in figure four illustrates that the sweep angle is not as important at lower aspect ratios. This agrees with the previous analysis. Taper still demonstrates little effect on endurance. 18 32.5 0.15 0.2 1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Figure 4: Trends for the Optimal Design, Max AR = 1.5, N = 40 This resulted in the confidence intervals tightening around the trend lines. This means that the fit to the quadratic response surface is better with 40 designs rather than 27. Running the analysis with the lower bounds raised and the upper bounds lowered should tighten the confidence intervals. The upper and lower bounds were set at 0.12 to.2 square feet for the area, 1.2 to 1.8 for the aspect ratio, 0 to degrees for the sweep, and 0.1 to 0.5 for the taper ratio. This resulted in the confidence intervals being fairly tight. Notice that with higher allowable aspect ratios, higher aspect ratios can be used, but with lower wing area (effect of the maximum dimension constraint). Area and aspect ratio remain the dominant parameters. 45 40 35 25 Once the DoE of the 1 panel geometry was completed, the code was modified to represent a twopanel geometry. Since there were now seven independent variables, the code took longer to run, and therefore the full factorial could not be covered due to time constraints and computational limitations. Instead, a coordinate exchange method was used to produce D- optimal designs for analysis. The results from the preliminary two panel analysis are shown in figure 7. 39.5 0.15 0.2 1 1.5 2 2.5 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Figure 7: Sweep is not as Important with AR=1.0 32 31.5 39 31.5 38.5 29.5 38 0.14 0.16 0.18 1.4 1.6 0.1 0.2 0.3 0.4 0.2 0.3 0.4 50 45 40 35 25 Figure 5: After the DoE was run on a large design space, it was narrowed down abound an optimal point, and rerun. Analyzing over this smaller design space improved confidence in the results and will probably change the optimum point. Letting the maximum aspect ratio be 3.0 allows higher endurance as seen in figure 3, again, it appears that going with a higher aspect ratio is better than increasing the wing area. 37.5 37 0.15 1.6 0.1 0.2 0.3 0.5 1 0.6 0.2 0.4 0.6 Figure 8: Two-Panel Trends for the Optimal Design Max. AR=1.8, N=200 Notice that the wing area is now more sensitive than the aspect ratio, although the aspect ratio is still sensitive. Sweep 1 is not significant, while sweep 2 is significant. Taper 1 and taper 2 are moderately sensitive, and the span factor is not so sensitive. This contradicts the previous analysis. The number of designs was increased to 400 and the upper and lower bounds were tightened about the optimal point (suggested by the previous analysis). This yielded the following results, depicted in figure 9. 0.15 0.2 1 1.5 2 2.5 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Figure 6: Trends for the Optimal Design Max. AR= 3.0, N=40 5

37.4 37.3 37.2 most optimal out of the ten. This configuration is shown below in figure 10. 0.1 37.1 37 0 36.9 36.8 36.7 36.6 36.5 0.12 1.6 0.1 0.2 0.3 0.2 0.4 0.6 0.4 0.6 Figure 9: Trends for the Optimal Design with Constraints Tightened. Note that the AR Confidence Interval is Low The results of the two panel geometry with the bounds tightened indicate that the progression of flight duration vs. aspect ratio is very smooth, due to the low confidence interval compared to the other independent parameters. Again, the aspect ratio seems to be the most sensitive. The taper ratios also seem to be rather sensitive. This contradicts the one panel DoE, but it is very possible that this is true for the two panel geometry. These results also oppose the two panel DoE without the tightened bounds, since these results show that wing sweep of the outer panel should be higher than shown. However, this does not mean that negative sweep is favorable; just that in this regimen, the taper should be farther back than the preliminary D-optimal design started with. 2.3.7 Optimization Shortly after the one panel DoE was conducted, the optimization of the one panel geometry was conducted. A gradient based approach was implemented, due to the inherently large computational time required when using genetic algorithms, and since the design space was predicted to be fairly smooth. The optimizer generates ten initial designs, and optimizes each. The results of the one panel optimization produced ten optimal designs, each of which varied slightly from the other. This suggested that the design space was fairly smooth, with some relatively flat planes dominating the low points (highest duration). The optimization was run several times, in order to debug it as well as to see if differing starting points would alter the point of optimality. Changing the starting point did not seem to affect the optimum point. The final one panel optimization was run, and the two geometries that violated the maximum dimension constraint were disregarded. The configuration that produced the largest flight duration was selected and deemed as the (Dimensionless) -0.1-0.2-0.3-0.4-0.5-0.3-0.2-0.1 0 0.1 0.2 0.3 Figure 10: Optimum One-Panel Configuration The optimization code was modified to represent two panel geometry. This code was debugged, and was run. This two panel code took inherently longer to operate since the design space was much larger due to the increased number of independent variables. Therefore, the code was only run twice, since the optimum designs for both instances were very similar. There were three designs that exceeded the maximum linear dimension constraint, and these were disregarded. The configuration that was predicted to produce the longest flight duration was selected as the optimal design from the remaining seven geometries. This was considered to be the optimal design for the Phase 3a Micro Air Vehicle. The optimal MAV configuration is shown along with it s specifications in figure 10. 6

0.1 0-0.1-0.2-0.3 Aspect ratios of 1.0, 1.25, and 1.5 were incorporated into each planform/airfoil combination. The three airfoils optimized by XFOIL were used for these articles. Three planforms were also chosen to be part of the wind tunnel analysis: Black Widow, Elliptical, and Zimmerman. These planforms are shown in figure 12 (shown with an AR of 1.25) Black Widow Elliptical Zimmerman -0.4-0.5-0.3-0.2-0.1 0 0.1 0.2 0.3 Figure 11: Optimum Two-Panel MAV Configuration Specifications: Wing Area (in.): 19.8842 Aspect Ratio: 1.7829 Sweep 1 (Radians): 0.0000 Sweep 2 (Radians): 0.1552 Taper 1 (Radians): 0.7583 Taper 2 (Radians): 0.1995 Span Factor: 0.5274% Predicted Endurance: 38 min 48 seconds 2.4 Wind Tunnel Analysis Since the validity of the MDO is not known, wind tunnel data is needed to corroborate the results. Three airfoils, aspect ratios, and planforms were selected for analysis. However, the access to wind tunnels that can measure the extremely small forces generated by MAVs is very limited since there are very few tunnels capable of giving such precise readings. An ultrasensitive balance (designed for MAVs) at the University of Dayton is in the progress of being constructed, and the predicted date of completion was early January. Unfortunately, the balance was unable to be completed by this date, and is now predicted to be set up by early April. Eighteen wind tunnel test articles are currently being fabricated, and will be placed into the wind tunnel for analysis when the tunnel is complete. 2.4.1 Test Article Selection A total of 27 test articles (3 planforms x 3 aspect ratios x 3 airfoils = 27 test articles) were rendered using Design CAD 3D MAX Plus. This was an essential portion of the project as a whole, since inaccurate building plans lead to an inaccurate physical model. Figure 12: Three Wing Planforms to be Analyzed in the Wind Tunnel Analysis These aspect ratio and planforms used were selected due to their success in past MAVs. Each planform/aspect ratio combination was scaled in such a way that the maximum linear dimension was 6, including the allowance for the propeller (3/16 wide). The width of the leading edge and trailing edge was proportional to the aspect ratio. The thickness of these the components was determined by the airfoil. The positioning of the wing spar was determined by finding the optimal position of the spar (maximum airfoil thickness at cruise angle of attack). The airfoils were plotted according to the coordinates produced by XFOIL. 2.4.2 Test Article Fabrication It was determined that a built up airframe would be used to fabricate the wind tunnel test articles. This was a significant decision, affecting the entire scope of the project. Fundamental research has suggested that a wing with spars that slightly protrude from the nominal wing geometry may produce a wing that is as efficient, if not more efficient than a perfectly shaped wing. Such geometry is thought to promote premature transition from laminar to turbulent flow. Since composite structures such as carbon fiber and fiberglass are costly and require vast amounts of time to accurately mold, a balsa wood airframe with Mylar covering was used in the test article construction. This structure will also have qualities similar to that of an adaptive washout wing, if constructed correctly. Such a configuration would allow this year s research to be very applicable to the adaptive washout configurations that will be developed in upcoming years. Precautions were taken that would help eliminate unwanted deviations such as weight, density, and thickness among the test articles. The weight and density of each wing rib was calculated, as to establish uniform weight and density throughout the test articles. The densities of the leading edges and trailing edges, as well as their dimensions were recorded. Once the balsa 7

wing ribs had been completed a standard of ± 0.010 throughout them was established. The same was true for the leading edge and trailing edge. The test articles varied in weight from one gram to three grams, but their geometry was kept to within about ± 0.010. Modifications to the articles were made so that they could adequately fit onto the University of Dayton s sting balance, specifically designed for MAV research. The test articles were sanded, and covered with 0.0025 mil clear Mylar (to aid in the adaptive washout phenomena). 2.5 Phase 3a MAV Fabrication The phase 3a MAV configuration that was defined by the MDO analysis was assumed to be the final, optimum design, and the MH 46 airfoil was incorporated into its geometry. Two vertical stabilizers with an area of 2 sq. in. each provided roll and yaw stability, essential to MAV success. The final Phase 3a Micro Air Vehicle configuration and its specifications are shown in figures 13, 14, 15, and 16. Phase 3a Configuration Specifications Wing Area: 19.8842 in 3 Aspect Ratio: 1.7829/1 Airfoil: MH 46 Weight Breakdown Weight (g) Receiver: JMP Micro Receiver 2.80 Cells: (2) E-Tech 250 mah Li-Poly 10.98 Actuators: (2)E-Flight Mega Actuator 4.20 Motor: AstroFlight Firefly 10.23 Propeller: Union-80 0.66 Structure: 10.0 Gross Weight: 38.87 g Figure 13: Optimum MAV Specifications Wing Ribs: Roacell (foam) laminated with.007 unidirectional carbon fiber Trailing Edge:.0 >015 unidirectional carbon fiber Leading Edge: 0.25 x0.125 balsa laminated with.007 unidirectional carbon fiber Rudders: 0.03125 balsa laminated with 0.56 g/sq. ft. fiberglass Component Hatch and Elevator- laminated balsa and 2.6 g/sq. ft. woven carbon fiber fabric Motor Encasement: 0.56 g/cu. ft. fiberglass laminated balsa Battery Compartment: 0.007 unidirectional carbon fiber Figure 14: MAV Structural Specifications Figure 15: CAD Rendering of Final Phase 3a MAV Configuration Figure 16: Underside of the Phase 3a MAV. Note the Removable Panel Used to Access Avionics 3.0 Conclusions 1. XFOIL can be used to generate optimal airfoil geometry at the Reynolds numbers pertaining to Micro Air Vehicles. Although the Lift coefficient is most likely smaller than predicted, the CFD analysis produced the correct trends. 2. A Design of Experiments can be run in order to avoid running the full factorial of experiments, without degrading the validity of the results. 3. A Multidisciplinary Design Optimization methodology can be implemented to generate an optimal Micro Air Vehicle design with a feasible result. 5. Unsatisfactory stability characteristics on both the roll and pitch axes are currently hindering the desired flight duration of thirty minutes. Flight testing will continue until the stability factors are overcome, and a stable platform is obtained. Experimental data suggests 8

that the flight duration of the stabilized configuration will be thirty-one minutes. 4.0 Acknowledgements This project would not have been possible to conduct in its entirety without the help of those who assisted in various aspects of this project. Special thanks to John and Cynthia Moore (parents) for their numerous areas of support. Thanks to Mr. Dale Whitford for providing excellent advice as an adult sponsor. The MDO analysis would not have been feasible without the help of Mr. Jason Bowman of the Air Force Research Laboratories. The wind tunnel analysis will not be capable without the support of Dr. Aaron Altman of the University of Dayton [10] Simons, M. Model Aircraft Aerodynamics- Fourth Edition, Special Interest Model Books Ltd., 1999 [11] Torres, Gabriel, and Mueller, Thomas J., Micro Aerial Vehicle Development: Design, Components, Fabrication, and Flight-Testing, University of Notre Dame, 2001 5.0 Resources [1] Drela, Mark, (MIT Aero and Astro) XFOIL v6.91, Oct. 2000 [2] Harrison, Kyle M., and Bowman, Dr. Jerry W., Aerodynamic Performance of Thin Curved Plate Airfoils with Different Maximum Camber Locations at Reynolds Numbers of 20,000; 40, 000; and 60,000 National Free Flight Society, 2003 pp 16-21 [3] Keenon, Matthew T,, Grasmeyer, Joel M. Development of the Black Widow Micro Air Vehicle, AeroVironment, Inc., 2001 [4] Keenon, Matthew T., Grasmeyer, Joel M. Development of the Black Widow and Microbat MAVs and a Vision of the Future of MAV Design, American Institute of Aeronautics and Astronautics, 2003 [5] Lyon, Christopher A., Broeren, Andy P., Qiguère, Philippe; Gopalarathnam, Ashok; Selig, Michael S., Summary of Low-Speed Airfoil Data, Volume 3, SoarTech Publications, 1997 [6] Math Works, MATLAB v6.5, 2002 [7] Morris, Dr. Stephen J., Holden, Dr. Michael, Design of Micro Air Vehicles and Flight Test Validation, MLB Company, 2000 [8] Raney, David L., Slominski, Eric C. Mechanization and Control Concepts for Biologically inspired Micro Aerial Vehicles, American Institute of Aeronautics and Astronautics, 2003 [9] Selig, Michael S., Donovan, John F., Fraser, David B., Airfoils at Low Speeds, H. A. Stokely, 1989 9