rotorcraft introduction

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151-0851-00 V

Marco Hutter, Roland Siegwart and Thomas Stastny

27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 1

Robot DynamicsRotary Wing UAS: Introduction Design and Aerodynamics

||Autonomous Systems Lab 27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 2

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

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IntroductionRotary Wing UAS: Introduction Design and Aerodynamics

27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 3

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Rotorcraft: Aircraft which produces lift from a rotary wing turning in a plane close to horizontal

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Rotorcraft: Definition

“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

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Helicopter Autogyro Gyrodyne

Power driven main rotor Un-driven main rotor, tilted away

Power driven main propeller

The air flows from TOP to BOTTOM

The air flows from BOTTOM to TOP

The air flows from TOP to BOTTOM

Tilts its main rotor to fly forward

Forward propeller for propulsion

Main propeller cannot tilt

No tail rotor required Additional propeller for propulsion

Not capable of hovering

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Rotorcraft | Overview on Types of Rotorcraft

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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

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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

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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

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Mechanical DesignRotary Wing UAS: Introduction Design and Aerodynamics

27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 9

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Tip path plane (TPP) Plane spanned by blade tip

within one full rotation Thrust perpendicular to TPP Control UAS by controlling TPP

Blade flapping angle βFl(ξ) Tilt angle of the blade Blade flapping video

Blade azimuth angle ξ Azimuth position of the blade

Blade pitch angle θR(ξ) Tilt angle of chord line Used to control TPP motion

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Rotorcraft | Rotor Definitions

TPP

βFl(ξ)

θR(ξ)

T

ξ

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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!

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Rotorcraft | Steering a Helicopter

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AerodynamicsRotary Wing UAS: Introduction Design and Aerodynamics

27.10.2015Robot Dynamics - Rotary Wing UAS: Propeller Analysis and Dynamic Modeling 12

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2D flow around an airfoil creates aerodynamic force due to change in momentum of fluid.

Lift force

Drag force

Moment

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Aerodynamics | 2D

22

2dyVcCdM m

2

2cdyVCdD d

2

2cdyVCdL l

with

: Density of fluid (air)c : Chord lengthV : Relative flight speedCl : Lift coefficientCd : Drag coefficientCm : Moment coefficient

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Hover Speed increases linearly with

radius Axisymmetric

Forward flight Dissymmetric speed

distribution Lower speed at retreating

blade Reverse flow region

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Aerodynamics | Rotor/Propeller Speeds across the Blades

ωR ωR

V

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Example: Rectangular infinitely long blade in hover Lift and induced velocity distribution along radius (const. θR) Neglecting 3D boundaries!

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 radius07.11.2016Robot Dynamics: Rotary Wing UAS 15

Aerodynamics | 2.5D Lift/Force Distribution along Blade

Lift

Induced velocityBlade radius r

dL/dvi

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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

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Aerodynamics | Blade-tip Vortex at Hover and Axial Climb

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Lift distribution considering tip vortices Rectangular blade with constant θR

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

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Aerodynamics | 2.5D Lift Distribution with Accounting for Blade Vortex

Lift

Induced velocityBlade radius r

dL/dvi

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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

(rotor)/Rolling moment (propeller)

Drag torque Q is integration of dQ distribution over blade In forward flight asymmetric

distribution over blade Additional hub force

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Aerodynamics | Forces/Moments on a Rotor/Propeller

ωR

V

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Absorb energy from the air to rotate the rotor blades Principle of the Autogiro. Used by

helicopter in case of engine failure Consider pure vertical

autorotation Relative airflow has Horizontal component from rotation Upward component from descent

Resulting aerodynamics force can have forwards or rearward component

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Aerodynamics | Autorotation

Driven region:

Driving region:

Stall region:

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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.

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Aerodynamics | References