LLoouuiissiiaannaa SSttaattee UUnniivveerrssiittyy LLSSUU DDiiggiittaall CCoommmmoonnss LSU Master's Theses Graduate School 7-5-2018 DDeessiiggnn aanndd PPeerrffoorrmmaannccee EEssttiimmaattiioonn ooff aa LLooww--RReeyynnoollddss NNuummbbeerr UUnnmmaannnneedd AAiirrccrraafftt SSyysstteemm Sean Lauderdale King Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Aerodynamics and Fluid Mechanics Commons, Navigation, Guidance, Control and Dynamics Commons, and the Other Engineering Commons RReeccoommmmeennddeedd CCiittaattiioonn King, Sean Lauderdale, "Design and Performance Estimation of a Low-Reynolds Number Unmanned Aircraft System" (2018). LSU Master's Theses. 4773. https://digitalcommons.lsu.edu/gradschool_theses/4773 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. DESIGN AND PERFORMANCE ESTIMATION OF A LOW REYNOLDS NUMBER UNMANNED AIRCRAFT SYSTEM A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science in The Department of Mechanical Engineering by Sean Lauderdale King B.S.M.E., Louisiana State University, 2014 August 2018 i Table of Contents List of Tables ................................................................................................................ iv List of Figures ................................................................................................................ v Abstract ......................................................................................................................... v Chapter 1. Introduction and Design Process ................................................................ 1 1.1 Purpose of the Design ...................................................................................................... 1 1.2 Design Considerations (Mission Parameters) ............................................................ 2 1.3 Design Process and Thesis Structure ........................................................................... 5 Chapter 2. Conceptual Design Phase ........................................................................... 9 2.1 Design Equations .............................................................................................................. 9 2.2 Preliminary Airfoil Selection ........................................................................................ 14 2.3 Analytical Solution to Finite Wing Properties .......................................................... 18 2.4 Initial Plane Design ....................................................................................................... 22 Chapter 3. Preliminary Design Calculations .............................................................. 23 3.1 Flight Mechanics and Aerodynamic Analysis ............................................................23 3.2 Structural Analysis ..........................................................................................................37 3.3 Powerplant Selection ..................................................................................................... 45 3.4 Interim Design Overview ............................................................................................. 48 Chapter 4. Detail Design Calculations ....................................................................... 49 4.1 Fault Tree ......................................................................................................................... 49 4.2 Final Design Weight Buildup ...................................................................................... 50 4.3 Detailed Flight Mechanics ............................................................................................ 51 4.4 Detailed Structural Analysis ........................................................................................ 54 4.5 Final Design Overview .................................................................................................. 59 Chapter 5. Final Iteration Performance Estimation ................................................... 61 5.1 Takeoff ............................................................................................................................... 61 5.2 Climb ................................................................................................................................ 62 5.3 Level Flight ...................................................................................................................... 64 5.3.2 Endurance and Range ................................................................................................ 66 5.4 Landing ............................................................................................................................ 75 5.5 Performance Review ...................................................................................................... 76 Chapter 6. Conclusion ................................................................................................ 77 ii References ................................................................................................................... 79 Appendix A. Market Survey and Differentiation ........................................................ 81 A.1 Review of Market Competition .................................................................................... 81 A.2 Potential Design Modules ........................................................................................... 82 A.3 Manufacturing Cost Estimate ..................................................................................... 83 Appendix B. FAA FAR Part §23 Design ...................................................................... 85 B.1 Maneuvering Loading ................................................................................................... 85 B.2 Gust Loading .................................................................................................................. 85 B.3 Landing Loading ............................................................................................................ 86 Appendix C. Dynamic Thrust Estimation .................................................................. 87 C.1 Theory .............................................................................................................................. 87 C.2 Code Validation ............................................................................................................. 88 C.3 Results ............................................................................................................................. 89 Vita ............................................................................................................................... 92 iii List of Tables Table 1. Qualitative summary of FAA Part 23 design criteria ..................................... 3 Table 2. Qualitative and quantitative design specifications ....................................... 7 Table 3. Summary table of 2D airfoil lift characteristics ............................................ 17 Table 4. Drag minimization constraints on optimization space .............................. 25 Table 5. Delta derivative validation table .................................................................. 32 Table 6. Stress summary table .................................................................................... 43 Table 7. Design weight buildup .................................................................................. 50 Table 8. Eigenvalues of dynamic stability modes ...................................................... 54 Table 9. Landing load maximum principal stress convergence table ...................... 56 Table 10. Maneuvering loading maximum principal stress convergence table ....... 57 Table 11. Full fuel underdamped dynamic stability responses .................................. 68 Table 12. No fuel underdamped dynamic stability responses ................................... 68 Table 13. Design parameters met and summary of the vehicle parameters ............. 78 Table 14. Table of market competitors ....................................................................... 82 Table 15. Common market survey results for modules ............................................. 83 Table 16. Major subsystem cost summary ................................................................. 83 iv List of Figures Figure 1. General plane design process ........................................................................ 6 Figure 2. General objectives of a UAS .......................................................................... 8 Figure 3. Basic flight forces of a tailless, pusher UAS with internal payload body ....11 Figure 4. Fuselage-centered coordinate force resolution diagram ............................ 12 Figure 5. Simplified wing loading analysis.................................................................. 13 Figure 6. S5020, MH 60 and MH 45 airfoil sections ................................................... 15 Figure 7. Lift curve comparison of MH45, MH 60, and S5020 airfoils with respect to airfoil angle of attack............................................................................................ 16 Figure 8. Drag curve comparison of MH45, MH 60, and S5020 airfoils with respect to airfoil angle of attack ....................................................................................... 16 Figure 9. Moment curve comparison of MH45, MH 60, and S5020 airfoils with respect to airfoil angle of attack .......................................................................... 17 Figure 10. Built-up wing cross section for an S5020 wing .......................................... 21 Figure 11. Semi-monocoque wing cross-section for an S5020 and a foam-filled wing. ............................................................................................................................... 21 Figure 12. Foam-filled wing cross section for an S5020 wing ..................................... 21 Figure 13. Preliminary plane design ........................................................................... 22 Figure 14. Effect of wing sweep and aspect ratio of a finite wing on theoretical Oswald efficiency ................................................................................................ 25 Figure 15. Basic planform geometry of Project UAS .................................................. 27 Figure 16. Drag buildup of zero-lift drag and induced drag for an intermediate design iteration.................................................................................................... 28 Figure 17. Swept cord of the aircraft ........................................................................... 30 v Figure 18. 3D VLM lift slope curves for 𝛿= 0,1,2,3 ....................................................... 31 Figure 19. Restoring moment for various planform configurations ......................... 34 Figure 20. xflr visualization of Project UAS directional stability additions ............. 35 Figure 21. Estimated flight envelope at sea level and 10,000 ft ................................. 36 Figure 22. Frame payload section with max stress component highlighted ............ 37 Figure 23. Free body diagram of fuselage frame section with full half-lift load applied ................................................................................................................. 38 Figure 24. Landing load locations on the payload fuselage section ......................... 39 Figure 25. Lift and moment spanwise distribution for an intermediate design iteration ............................................................................................................... 40 Figure 26. Drag spanwise distribution for an intermediate design iteration ............ 41 Figure 27. Pure spar loading deflection curve ........................................................... 44 Figure 28. Power required at sea level and 10,000 ft ................................................. 46 Figure 29. Power budget curves for all physical and legal flight regimes ................ 47 Figure 30. Simplified project vehicle fault tree .......................................................... 49 Figure 31. Elevon deflection required for trim as a function of level flight speed ... 52 Figure 32. Root locus plot for underdamped modes ................................................. 53 Figure 33. Converged FEA results for landing loading on frame .............................. 55 Figure 34. Wing maneuvering loading ....................................................................... 56 Figure 35. Isometric view of wing skin deflection ..................................................... 58 Figure 36. Bottom view of wing skin deflection ........................................................ 59 Figure 37. CG speed with respect to the distance travelled in hand-launch............ 62 Figure 38. Wide open throttle vertical climb speed .................................................. 63 vi Figure 39. Steady, level turn bank angle .................................................................... 64 Figure 40. Minimum turning radius of vehicle for two limiting cases ..................... 65 Figure 41. Short period chord-wise velocity response ............................................... 70 Figure 42. Phugoid chord-wise velocity response ...................................................... 71 Figure 43. Dutch roll span-wise velocity response .................................................... 72 Figure 44. Short period position estimation .............................................................. 73 Figure 45. Phugoid mode position response ............................................................. 74 Figure 46. Dutch roll position response .................................................................... 75 Figure 47. Simplified views of the project UAS ......................................................... 78 Figure 48. Power consumption and max speed of various UAS ................................ 81 Figure 49. Section view of a typical propeller airfoil with force and velocity diagrams .............................................................................................................. 87 Figure 50. Static thrust estimation curves ................................................................. 88 Figure 51. Dynamic thrust estimation curves ............................................................ 89 Figure 52. 10x6-4 Propeller thrust force estimate and comparison to APC data ..... 90 Figure 53. 10x6-4 propeller normal force estimate and comparison to APC data .... 91 vii Abstract The purpose of this thesis is to conceptually design a fixed-wing unmanned aircraft systems (UAS) with a higher flight-time and top stable speed than comparable systems. The vehicle adheres to specifications derived from the client, the market, and the Federal Aviation Administration (FAA). To broadly meet these requirements, the vehicle must fly for a minimum of three hours, return to the original flight path quickly if perturbed, and must be hand-launched. The vehicle designed must also have a large potential center of gravity movement to allow for customization of the planform and client customization. An iterative design process was used to quickly perform tradeoff analysis and to refine the overall design. Analysis is split into two categories: flight mechanics, and structural analysis. Flight mechanics determines the flight regimes in which the vehicle is assumed to fly and the aerodynamic load factors used in structural analysis (up to 3.8 times the level flight loading. The change in lift due to skin deflection is determined to be negligible under maximum gust conditions. The vehicle itself is stable in all flight conditions, except the spiral mode; however, the addition of a stability augmentation system (SAS) can allow for corrections and autonomous flight in future iterations. The vehicle can operate between sea-level and a maximum flight altitude of 10,400 ft as required by the FAA in 14 CFR Part 107. The final flight time of 24 hours comparable to high-end UAS sold in the U.S. Further, the vehicle is stable in speeds up to 100 mph, allowing for the maximum legal speeds of travel. viii Chapter 1. Introduction and Design Process The unmanned aircraft system (UAS) design addressed in this thesis operates in the low Reynolds number flight regime (Re<1,500,000) – characterized by small wing cross-section, and/or low speed flight. An initial configuration was determined using basic aerodynamic relations to allow for quicker iteration of internal structures, and wing geometry. Iterations of the design were performed using standard analytical solutions to planform wing geometry, flight forces, and structural considerations from references [4], [5], and [6]. To mitigate the main failure modes identified by a fault tree analysis, closed-form solutions are refined through numerical analysis. The final design for this thesis is comparable in flight time to high-end internal combustion vehicles, with better gust and maneuvering performance while maintaining an estimated initial purchase price of $10,000. 1.1 Purpose of the Design The current market of low Reynolds number unmanned aircraft systems (UAS) is focused on multi-rotor vehicles – the most common being a quadcoptor. A market exists, however, for longer flight times and more gust-stable flight. This necessitates the design of a fixed-wing craft. A market also exists for a single, modular planform that allows users to customize their experience without the undue burden of purchasing multiple UAS packages (Appendix A). The purpose, therefore, of this thesis is to design a long-endurance UAS that is stable with many 1