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8/9/2019 Introduction Rotorcraft
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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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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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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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Rotor configurations
Contra-rotating, no need for tail rotor
Total disk-area
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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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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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Autorotation
Vertical autorotation
Forward autorotation
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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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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.mpg8/9/2019 Introduction Rotorcraft
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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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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.wmv8/9/2019 Introduction Rotorcraft
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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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ROTOR PERFORMANCE ANALYSIS
Part 2
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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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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)