Robot Dynamics Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling 151-0851-00 V Marco Hutter, Roland Siegwart, and Thomas Stastny Autonomous Systems Lab Autonomous Systems Lab Robot Dynamics - Fixed Wing UAS: Basics of Aerodynamics | 20.12.2016 | 1 Contents | Fixed Wing UAS 1. Introduction/(brief) Historical Overivew 2. Basics of Aerodynamic 3. Aircraft Dynamic Modeling 4. Aircraft Performance (wrap-up) 5. Aircraft Stability 6. Simulation 7. Modeling for Control 8. Fixed-wing Control Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 2 Historical Overview Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 3 http://en.wikipedia.org/wiki/Montgolfier Historical Overview . First Flight: Montgolfier Brothers 1783 . Ballon filled with hot air . First unmanned demonstrations . Later with animals . Finally manned Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 4 Historical Overview . Otto Lilienthal . First person to make repeated successful short flights . Used a fixed wing glider . Died after a crash in 1896, saying “Sacrifices must be made” http://en.wikipedia.org/wiki/Otto_Lilienthal Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 5 Historical overview . Wright brothers . Started as glider engineers and pilots . First engine powered flight in 1903 . First to actively manipulate the plane by control surfaces http://en.wikipedia.org/wiki/Wright_Brothers Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 6 Historical Overview | Small fixed-wing UAVs Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 7 Basics of Aerodynamics Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 8 Basics of Aerodynamics | Basic Principles Analysis on differential volumes: . With viscosity: Navier-Stokes Equation . Without viscosity: Euler Equation . Incompressible along streamline: Bernoulli Equation v2 p gh const 2 www.speedace.info/pito t_tube.htm as on 29th July 2009 Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 10 Basics of Aerodynamics | Basic Principles V=FASTER P=LOWER LIFT! V=SLOWER P=HIGHER https://commons.wikimedia.org/wiki/File:Streamlines_around_a_NACA_0012.svg Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 11 Basics of Aerodynamics | Basic Principles . But…Bernoulli isn’t the whole story! . Watch out for common misconceptions of lift . E.g. the “distance traveled” argument for speed difference . What is really going on? –streamline curvature induced pressure gradients. p fluid particle out centripetal force: p > p v out in pin Nice lecture by Dr. Holger Babinsky, University of Cambridge streamline https://www.youtube.com/watch?v=XWdNEGr53Gw Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 12 Basics of Aerodynamics | Basic Principles . pupper < patm patm . plower > patm . Therefore: pupper < plower LIFT! pupper plower patm https://commons.wikimedia.org/wiki/File:Streamlines_around_a_NACA_0012.svg Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 13 Basics of Aerodynamics | Wing Geometry Wing Geometry x b: Wingspan y c: Chord c0: Root Chord c 0 ct: Tip Chord c A t A: Reference Area c AR: Aspect Ratio b b2 AR A Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 14 Basics of Aerodynamics | Wing Geometry Wing Geometry x b: Wingspan y Mean geometric chord c: Chord 푐 c0: Root Chord c 0 ct: Tip Chord c A t A: Reference Area c AR: Aspect Ratio b b2 AR A Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 15 Wing Geometry . Various types of wing . Biplanes & vertical composition of wing . Lift not proportional to the number of wings. Biplane: factor ~ 1.5 . Drag also increased . Advantage of higher stiffness and less Inertia around x-axis (Aerobatics) Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 16 Basics of Aerodynamics | Airfoils 2-Dimensional Flow Analysis . Flow field (pressure distribution, laminar/turbulent) highly dependant on angle of attack, Reynolds number and Mach number Transition point Turbulent Separated Laminar boundary layer boundary boundary layer layer Suction Overpressure Stagnation point www.thuro.at/aerodynamik2.htm http://www.thuro.at/anims/abloesung.gif Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 17 Basics of Aerodynamics | Airfoils Leading edge dL c Angle of attack a dM dD Trailing edge Chord v 25 % Chord Thickness Pressure distribution can be reduced to two forces and one moment per unit length: 2 : Density of fluid (air) [kg/m3] Lift force dL C cdy V l 2 c : Chord length [m] V : Flight speed (w.r.t. air) [m/s] 2 Drag force dD C cdy V C : Airfoil lift coefficient [-] d 2 l Cd : Airfoil drag coefficient [-] C : Airfoil moment coefficient [-] Moment dM C c2 dy V 2 m m 2 Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 18 Basics of Aerodynamics | Airfoils Coefficients Cl, Cd and Cm depend on angle of attack a . As long as flow is attached: Separation point dC . C – linear: l 2 l da . Cm – almost constant . At stall: flow separation . Cl – stops to increase Flow field highly depending on Re (and Ma), . Cd – increases dramatically in particular: . Location of laminar/turbulent transition point . Separation point . Stall angle Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 19 Basics of Aerodynamics | Airfoils Reynolds' number influence Polars of Airfoil we3.55-9.3 W. Engel and A. Noth 2005 Re V c Cl Re Inertial Forces Viscous Forces at low speed, Re and Cd McMasters, J. H. and M. L. Henderson (1980). "Low Speed Single C a Element Airfoil Synthesis." Technical Soaring 6(2): 1-21 d Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 20 Symmetric Airfoils Airfoils . The choice of an airfoil depends on: Reflexed Airfoils . Flying speed . Wing loading . Construction method Flat-Bottom Airfoils . Kind of flight (acrobatic, glide,…) . Placement on the airplane . Standard airfoils (some examples) Semi-Symmetrical Airfoils . Goettingen . Eppler . Wortmann Under-Cambered Airfoils . NACA Example: NACA 2412 Thickness (% of chord) Position of maximum camber deflection (tenths of chord) Maximum camber deflection (% of chord) Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 21 Airfoil Lift, Drag and Moment Methods to determine airfoil lift, drag and moment coefficients: . Theoretically using 2D-CFD software . Javafoil Javafoil http://www.mh-aerotools.de/ . Xfoil http://raphael.mit.edu/xfoil/ . … . Experimentally in a wind tunnel . Extruded airfoil mounted on a measurement system . Laminar flow produced by fans www.uwal.org/publicdata/photos Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 22 Induced Drag aerospaceweb.org From 2D to 3D: the wing is not infinite… . Vortices are created at wing extremities . Tip vortices induce NASA Dryden Flight Research Center downward flow (w) dDi and thus reduce the effective angle of attack dL V (free stream) w . Approx. induced drag: 2 CL . e: Oswald Factor < 1 for C Di non-elliptic lift distribution e AR Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 23 Blended Winglets: Less Induced Drag Modern Glider Designs www.aviationpartners.com Spiroids http://airpigz.com/blog/2010/8/27/poll-spiroids-funky-circular- winglets-love-em-or-hate-em.html Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 24 How to Reduce Induced Drag: Winglets . Ideally, winglets… stream) V (free . … reduce induced drag at low speeds . … reduce spanwise flow . … increase the Reynolds Bound number near wing tip vortex Upward v . … do not increase the Wing winglet parasite drag too much (relevant for high speed Top view performance) vortex Tip Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 25 Parasite Drag . Wing: integrate Cd along the wing . Fuselage: highly Re number and geometry depending… Drag total . Friction drag . Form drag . Interference drag Speed . e.g. at the transition between fuselage and wing . Can also be negative Autonomous Systems Lab Robot Dynamics – Fixed Wing UAS: Basics of Aerodynamics & Dynamic Modeling | 20.12.2016 | 26 Control surfaces . For small airplanes, the standard control surfaces are: . Ailerons (rolling) . Elevator (pitching) . Rudder (yawing) . For larger airplanes, they can be more complex… Ailerons: 2. Low-Speed Aileron 3. High-Speed Aileron Lift increasing flaps and slats: 4. Flap track fairing 5. Krüger flaps 6. Slats 7. Three