Robot Dynamics Rotary Wing UAS: Introduction Design and Aerodynamics 151-0851-00 V Marco Hutter, Roland Siegwart and Thomas Stastny Autonomous Systems Lab Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling| 27.10.2015 | 1 Contents | Rotary Wing UAS 1. Introduction - Design and Propeller Aerodynamics 2. Propeller Analysis and Dynamic Modeling 3. Control of a Quadrotor 4. Rotor Craft Case Study Autonomous Systems Lab Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling| 27.10.2015 | 2 Introduction Rotary Wing UAS: Introduction Design and Aerodynamics Autonomous Systems Lab Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling| 27.10.2015 | 3 Rotorcraft: Definition . Rotorcraft: Aircraft which produces lift from a rotary wing turning in a plane close to horizontal “A helicopter is a collection of vibrations held together by differential equations” John Watkinson Advantage Disadvantage Ability to hover High maintenance costs Power efficiency during hover Poor efficiency in forward flight “If you are in trouble anywhere, an airplane can fly over and drop flowers, but a helicopter can land and save your life” Igor Sikorsky Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 4 Rotorcraft | Overview on Types of Rotorcraft Helicopter Autogyro Gyrodyne Power driven main rotor Un-driven main rotor, tilted Power driven main propeller away The air flows from TOP to The air flows from BOTTOM The air flows from TOP to BOTTOM to TOP BOTTOM Tilts its main rotor to fly Forward propeller for Main propeller cannot tilt forward propulsion No tail rotor required Additional propeller for propulsion Not capable of hovering Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 5 Rotorcraft | Rotor Configuration 1 Single rotor Multi rotor Most efficient Reduced efficiency due to multiple rotors and downwash interference Mass constraint Able to lift more payload Need to balance counter-torque Even numbered rotors can balance counter- torque Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 6 Rotorcraft | at UAS-MAV Size 1 Quadrotor Std. helicopter Four propellers in cross configuration Very agile Direct drive (no gearbox) Most efficient design Very good torque compensation Complex to control High maneuverability Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 7 Rotorcraft | at UAS-MAV Size 2 Ducted fan Coaxial Fix propeller Complex mechanics Torques produced by control surfaces Passively stable Heavy Compact Compact Suitable for miniaturization Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 8 Mechanical Design Rotary Wing UAS: Introduction Design and Aerodynamics Autonomous Systems Lab Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling| 27.10.2015 | 9 Rotorcraft | Rotor Definitions T . Tip path plane (TPP) TPP . Plane spanned by blade tip within one full rotation βFl(ξ) . Thrust perpendicular to TPP . Control UAS by controlling TPP . Blade flapping angle βFl(ξ) . Tilt angle of the blade ξ . Blade flapping video . Blade azimuth angle ξ . Azimuth position of the blade . Blade pitch angle θR(ξ) . Tilt angle of chord line θR(ξ) . Used to control TPP motion Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 10 Rotorcraft | Steering a Helicopter . Helicopter has six DoF (position and attitude) . Pilot has four control input . Vertical, with collective pitch (up and down) . Directional, with tail rotor pitch (yaw) . Longitudinal and lateral, with cyclic pitch (forward/pitch or sideward/roll) . Tilts TPP to desired direction . Controls are coupled! . Different for other configuration! Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 11 Aerodynamics Rotary Wing UAS: Introduction Design and Aerodynamics Autonomous Systems Lab Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling| 27.10.2015 | 12 Aerodynamics | 2D . 2D flow around an airfoil creates aerodynamic force due to change in momentum of fluid. 2 with . Lift force dL Cl cdyV 2 : Density of fluid (air) c : Chord length 2 V : Relative flight speed . Drag force dD Cd cdyV 2 Cl : Lift coefficient Cd : Drag coefficient 2 2 C : Moment coefficient . Moment dM C c dyV m m 2 Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 13 Aerodynamics | Rotor/Propeller Speeds across the Blades . Hover . Forward flight . Speed increases linearly with . Dissymmetric speed radius distribution . Axisymmetric . Lower speed at retreating blade . Reverse flow region V ωR ωR Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 14 Aerodynamics | 2.5D Lift/Force Distribution along Blade . Example: Rectangular infinitely long blade in hover . Lift and induced velocity distribution along radius (const. θR) . Neglecting 3D boundaries! dL/dvi Lift Induced velocity Blade radius r . Lift proportional to relative speed squared . But angle of attack decreases at outer radius . Lift increases less than squared with respect to blade radius . Most of the lift is produced at outer blade radius Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 15 Aerodynamics | Blade-tip Vortex at Hover and Axial Climb . Change in momentum of fluid creates pressure difference . High pressure below the blade . Low pressure above the blade . High pressure difference at outer blade . Boundary condition: No pressure difference at blade tip . Generation of strong vortices trail at blade tip . Trail downstream with induced velocity . Aerodynamic interference when moving vertically downwards Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 16 Aerodynamics | 2.5D Lift Distribution with Accounting for Blade Vortex . Lift distribution considering tip vortices . Rectangular blade with constant θR dL/dvi Lift Blade radius r Induced velocity . Loss of lift due to the vortices . Due to vortex induced velocity, angle of attack decreases over blade . Effect decreases at inner radius . Use blade twist and tapering to reduce tip vortex . Twist: decrease θR with blade radius . Taper: Decrease chord length with blade radius Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 17 Aerodynamics | Forces/Moments on a Rotor/Propeller . Represent aerodynamic force in tip path plane coordinates . Total thrust T is integration of dT over blades . In forward flight asymmetric distribution over blade . Additional blade flapping V (rotor)/Rolling moment (propeller) . Drag torque Q is integration of dQ distribution over blade . In forward flight asymmetric ωR distribution over blade . Additional hub force Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 18 Aerodynamics | Autorotation . Absorb energy from the air to Driven region: rotate the rotor blades . Principle of the Autogiro. Used by helicopter in case of engine failure Driving region: . Consider pure vertical autorotation . Relative airflow has . Horizontal component from rotation . Upward component from descent . Resulting aerodynamics force can Stall region: have forwards or rearward component Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 19 Aerodynamics | References . Books . [1] Leishman J. Gordon: Principles of Helicopter Aerodynamics, 2nd Ed. Cambridge University Press, 2006. [2] Bramwell Anthony R.S. et al.: Bramwell‘s Helicopter Dynamics, 2nd Ed. Butterworth-Heinemann, 2001. [3] Padfield Fareth D.: Helicopter Flight Dynamics. Wiley, 2008. Autonomous Systems Lab Robot Dynamics: Rotary Wing UAS| 07.11.2016 | 20.