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    Unmanned Aircraft Design,Modeling and Control

    Rotorcraft

    Lecture 1: Introduction

    Konrad Rudin

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 2

    Course section contents

    Lecture 1: Introduction to rotorcraft (today)

    Lecture 2: Dynamic modeling of rotorcraft (exercises)

    Lecture 3: Case Study: Modeling of a coax

    Lecturer: Christoph Hrzeler

    Lecture 4: Control of rotorcraft (exercises)

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 3

    ROTORCRAFT OVERVIEW

    Part 1

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 4

    Introduction

    Unfortunately, the use of helicopters is restricted to applications where other

    concepts are not suitable!

    High maintenance costs

    High power required for flying

    However, the helicopter ability to hover, allows it to land almost everywhere

    Ideal for rescue missions (in mountains, in oceans, ...)

    A helicopter is a collection of vibrations held together by differential equations John Watkinson

    The helicopter is probably the most complex flying machine

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 5

    A short history

    DaVincis helical airscrew (1490)

    First manned helicopter Gyroplan Nr. 1 by Breguet & Richet (1907)

    A flying... dreamer

    First practical helicopter FW61 (1936)

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 6

    Types of rotorcraft

    - Power driven main rotor

    - The thrust (T) is to the tip path plane

    -The air flows from TOP to BOTTOM

    - Tilts its main rotor to fly forward

    Helicopter

    T

    - Un-driven main rotor, tilted away

    - Forward propeller for propulsion

    -The air flows from BOTTOM to TOP

    - No tail rotor required

    -Not capable of hovering

    except in:

    Gyroplane (Autogyro)

    wind

    - Power driven main rotor

    - Additional propeller for propulsion

    -Main rotor remains // to dir. of flight

    -The air flows from TOP to BOTTOM

    Gyrodyne

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 7

    Rotor configurations

    Contra-rotating, no need for tail rotor

    Total disk-area

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 9

    Helicopters at the UAV-MAV size

    - 4 rotors in cross configuration

    - Direct drive (no gearbox)

    - Very good torque compensation

    - Hi agility

    Quadrotor

    - Passively stable

    - Compact

    - Suitable for miniaturization

    Coaxial Std. Helicopter

    - Very agile

    - Complex to control

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 10

    Fixed rotor

    Moment produced by control

    surfaces

    Heavier

    Coaxial configurations

    Ducted fan Coaxial

    Lower rotor with swash-plate

    Complex mechanics

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 11

    Helicopters at the UAV-MAV size

    Helicopter:

    Large rotor

    High inertia

    Slow motor dynamics

    => Keep a constant rotor speed

    Change thrust by adjusting angle of attack

    MAV-UAV

    Smaller rotors

    High dynamic brushless DC motors

    => Keep collective pitch constant

    Change thrust by adjusting rotor speeds

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 12

    Airfoil theory in 2D (see lecture #1)

    Pressure distribution on the surface can

    be reduced to 2 forces and one moment:

    Lift force

    Drag force

    Moment cvdycCdM m 2

    2

    2

    2

    vdycCdD d

    2

    2vdycCdL l

    with

    : Density of fluid (air)

    c : Chord length

    v : Relative flight speed

    Cl : Lift coefficient

    Cd : Drag coefficient

    Cm : Moment coefficient

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    Basics forces and moments on rotor

    On each part of the blade lift and dragis generated

    Represent aerodynamic force by dFz

    and dFx

    Integrate dFzand dFxover the blade

    Sum of forces Fzcreates thrust T and

    rolling moment R

    Sum of forces Fxcreate drag moment Qand hub force H

    r

    Vindv

    f

    dL

    dD

    dFz

    dFx

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 14

    Force distribution over a blade

    Rotational velocity increases linearly

    with radius

    Most of the thrust is generated in

    the outer section of the blade

    T ~V2

    Increase the thrust in the inner

    section by twisting the blade

    Blade pitch angle decreases with

    the radius

    Used for propellers

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 15

    Autorotation

    Vertical autorotation

    Forward autorotation

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 16

    Rotor vs. Propeller

    Thrust direction is

    constant

    Blades fix to shaft

    Chambered profil

    Twisted blade

    Increase efficiency for a

    specific operation point

    Thrust is perpendicular to

    tip path plane

    Blades elastic

    Symmetrical profile

    Constant blade pitch

    angle

    Nice aerodynamics over

    whole AoA range

    Propeller Rotor

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    Forces on the rotor head

    gF

    LiftF

    gF

    LiftF

    gF

    =0 >0

    >0

    Blades are affected by centrifugal force due to rotation and lifting force (leadsto rotor coning)

    Coning effects generates large moments at blade roots

    Use of articulated rotorheads

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 18

    Forward flight

    Hover

    Thrust (T) balances exactly the weight (W)

    The forces on the blades do NOTvary as they turn

    T

    W

    Forward flight

    e.g. forward speed = 130mph

    e.g. propeller speed at tip (linear) = 420mph

    Relative airspeed unbalance

    Maximum speed at =90 (min. at =270)

    Lift force changes during one revolution

    Leads to great cyclic stress at rotor roots

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    Types of rotorheads

    Hingeless

    Teetering

    Fully articulated

    Controlled feathering axis

    Stiff mounting to rotor shaft

    Tip path plane change through blade flapping of

    flexible rotors

    Controlled feathering axis

    Blades are connected through teetering hinge

    Tip path plane change through teetering hinge

    Controlled feathering hinge

    Blade attached to series of hinges

    Tip path plane change through blade flapping at

    flapping hinge

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 20

    Fully articulated rotorhead

    Reduction of stress at blade root

    Rotor blades are not rigidly attached to

    head, but hinge-supported

    Three hinges: Feathering, lagging and

    flapping

    Flapping(up & down)

    Reduces stress due to rolling moments

    But, allows large Coriolis moments in the plane of

    rotation (due to CoG displacement)

    Flapping

    Lagging

    Feathering

    Lagging(forward & backward)

    Releases the rotor from these Coriolis moments

    Feathering

    Enables the blade pitch angle to be changed

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 23

    Rotor control: the swashplate

    Swashplate converts steering signal into

    blade pitch change

    (rotation about feathering axis)

    Collective pitch for altitude control

    Cyclic pitch for roll and pitch control

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 24

    Describe position of the

    blade by angle x

    Blade pitch per revolution

    Rotor control: the swashplate

    x

    x []

    Pit

    ch

    []

    Changed bycollective pitch

    Changed byCyclic pitch

    http://localhost/var/www/apps/conversion/tmp/scratch_5/teaching/lecture/movies/heli-swash-collective.mpg
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    Stability augmentation: the flybar

    Gyroscopic behavior

    Acts on the feathering axis

    Slows the rate of the rotor change-of-attitude

    The flybar tilt is proportional to the roll (or

    pitch) rate of turn

    the angle between the flybar & the mast is a

    measure of roll (or pitch) rate

    E.g. The Bell bar system

    With sensor-based control, the flybar became

    obsolete for full-scale helicopters

    On some model helicopters, the flybar is still used

    (because of the high dynamics)

    On some coaxial helicopters, the flybar act on the

    upper rotor

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 26

    Stability augmentation: the flybar

    Bell system Hiller system

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 27

    The tail rotor

    The tail rotor provides a torque to balance the

    main rotor counter-torque

    Variable blade pitch enables yaw control

    (Blade pitch variation by Swashplate mechanism)

    (collective pitch only)

    Fail Tail

    Is there a possibility to get rid of the tail rotor?

    Tip Jet Helicopters

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 28

    Tail rotor alternative concepts

    Works like a ducted fan

    (tips enclosed, large # of blades)

    More quiet and safer

    Tail boom behaves like a wing in the main

    rotor downwash

    (effected by airstream from Coanda* slots)

    Higher ground clearance

    More quiet and safer

    (*See Coanda effect)

    Fenestron NOTAR (NO TAil Rotor)

    http://localhost/var/www/apps/conversion/tmp/scratch_5/video/Tail%20Rotor%20Failure.wmvhttp://localhost/var/www/apps/conversion/tmp/scratch_5/video/Tail%20Rotor%20Failure.wmvhttp://localhost/var/www/apps/conversion/tmp/scratch_5/teaching/lecture/movies/Tail%20Rotor%20Failure.wmv
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    NOTAR

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 30

    Ground effect

    It is due to:

    The interferenceof the ground with the airflow pattern of the rotor system

    ... Which causes reduction of the velocity of the induced airflow

    ... Which causes less induced drag and a more vertical lift

    Flying in GE tends to reduce the rotor tip vortex

    ... Which causes higher rotor blade efficiency

    up to ~one rotor diameter.

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 31

    ROTOR PERFORMANCE ANALYSIS

    Part 2

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 32

    Blade momentum theory

    Ideal propeller

    Infinitely thin disc area A, no resistance to air

    1-D analysis

    Thrust and induced velocity distribution is uniform over disc

    Far upstream/downstream the pressure is static pressure

    No viscous effects

    Incompressible

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    Blade momentum theory

    Consider streamline going from 0 through1, 2 to 3

    atmospheric pressure on far field at 0

    and 3

    Conservation of mass

    v2= v1=vind (1)

    Bernoullis equation

    From 0-1

    P0+1/2V2= P1+1/2 (V+v1)

    2 (2)

    From 2-3

    P0+1/2 (V+v3)2= P2+1/2 (V+v2)

    2 (3)

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 34

    Blade momentum theory

    Thrust force

    T = A(P2P1)

    From eq.1-3

    T = 1/2 A ((V+v3)2V2) (4)

    Change in momentum

    T= A(V+v1)((V+v3)-V) (5)

    From (4) and (5)

    V+v1=1/2(2V+v3)

    v1= v3/2

    T= 2A(V+v1)v1 (6)

    If V=0

    T = 2Av2ind (7)

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    Blade momentum theory

    Ideal power to produce rotor thrust

    P=T(V+vind) (8)

    In hover

    P= (9)

    Increasing disc area reduces power

    Mechanical constraint: Tip mach

    number

    More profile/structural drag

    Longer tail

    A2/T 2/3

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 36

    Ideal propeller efficiency

    Propeller efficiency

    = TV/P

    = 0 in hover

    Efficiency with respect to velocity

    V = (P/2A(1- ))1/3

    Real propeller are approximately

    10-15 % less efficient

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    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 37

    BEMT

    Combined blade elemental and momentum theory

    Include blade profile

    Divide rotor into different blade elements

    Calculate forces for each element and sum them up

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 38

    BEMT

    Force at a blade element

    With the relative air flow Ve can

    determine angle of attack and

    reynolds number

    Corresponding lift and drag

    coefficient are found on polarcurves for blade shape

    Problem: What is the induced

    velocity w?

    Use momentum theory at the

    blade annulus

    q

    if

    r

    V

    w

    dL

    dD

    dT

    rdQ /

    RV

    eV

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    BEMT

    Momentum theory at blade annulus

    Induced velocity

    Lift at blade annulus

    Propeller with B blades

    Approximation:

    Lift:

    Thin airfoil theory:

    Empirical value:

    Or deduce from polars directly

    Angle of attack:

    ff cos)cos(22 iRiRmt VVVrdrdT

    iRVw

    2

    2 elcdrVCBdL

    Re

    be

    VV

    dLdT

    fcos

    ll CC

    ifq

    ffq

    cos)(2

    2

    Rilbe cdrVCBdT

    2lC

    7.5lC

    Unmanned Aircraft Design, Modeling and Control - Rotorcraft 40

    BEMT

    Equate momentum theory with lift

    equation

    Calculate lift with the estimated

    angle of attack

    0)(8

    )8

    (22

    2

    fq

    T

    Rl

    T

    Rlii

    bemt

    Vx

    VC

    Vx

    VC

    x

    dTdT

    ifq

    xR

    BcVxVRV

    R

    V

    R

    rx TRT

    f

    122 tan,,,,,

    2

    2 el VdrcCdL

    2

    2 ed VdrcCdD

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    References

    BOOKS

    J. Watkinson: The Art of the Helicopter

    Bramwells Helicopter Dynamics

    R.W. Prouty: Helicopter Performance, Stability, and Control

    WEBSITES

    http://www.cybercom.net/~copters/helo_aero.html (helicopter)

    http://www.grc.nasa.gov/WWW/K-12/airplane/short.html (general)

    http://www.helis.com/pioneers/ (History)