Aircraft Flight Dynamics Robert F. Stengel Lecture16 Aircraft Control Devices and Systems

• Elevator/stabilator: pitch control" • Rudder: yaw control" • Ailerons: roll control" • Trailing-edge flaps: low-angle lift control" • Leading-edge flaps/slats: High-angle lift con

Aircraft Control Devices

Robert Stengel, Aircraft Flight Dynamics, MAE 331,

2012"

Copyright 2012 by Robert Stengel All rights reserved For educational use only.!

http://www.princeton.edu/~stengel/MAE331.html ! http://www.princeton.edu/~stengel/FlightDynamics.html !

•   Elevator/stabilator: pitch control"

•   Rudder: yaw control"

•   Ailerons: roll control"

•   Trailing-edge flaps: low-angle lift control"

•   Leading-edge flaps/slats: High-angle lift control"

•   Spoilers: Roll, lift, and drag control"

•   Thrust: speed/altitude control"

Critical Issues for Control"

•  Effect of control surface deflections on aircraft motions"

–  Generation of control forces and rigid-body moments on the aircraft"

–  Rigid-body dynamics of the aircraft"

  δE is an input for longitudinal motion"

 θ = 

Mechanical, Power-Boosted System "

Grumman A-6!

McDonnell Douglas F-15!

Critical Issues for Control"

•  Command and control of the control surfaces"

–  Displacements, forces, and hinge moments of the

control mechanisms"

–  Dynamics of control linkages included in model"

  δE is a state for mechanical dynamics "

and Aerodynamics

Aerodynamic and

Mechanical Moments

on Control Surfaces"

•  Increasing size and speed of aircraft

leads to increased hinge moments"

•  This leads to need for mechanical or

aerodynamic reduction of hinge

moments"

•  Need for aerodynamically balanced

surfaces"

•  Elevator hinge moment "

Helevator = CHelevator 1

2 ρV2Sc

Aerodynamic and Mechanical Moments on Control Surfaces"

CHδ : aerodynamic/mechanical damping moment

CHδ : aerodynamic/mechanical spring moment

CH

α : floating tendency

CH command : pilot or autopilot input

•  Hinge-moment coefficient, C H"

–  Linear model of dynamic effects"

Angle of Attack and Control Surface Deflection"

•  Horizontal tail at

positive angle of attack"

•  Horizontal tail with

elevator control

surface"

•  Horizontal tail with

positive elevator

deflection"

Floating and Restoring Moments on a Control Surface"

•  Positive elevator deflection produces a negative ( restoring ) moment, Hδ, on elevator due to aerodynamic or mechanical spring"

•  Positive angle of attack produces negative moment on the elevator"

•  With stick free , i.e., no opposing torques, elevator floats up due

to negative Hδ"

Dynamic Model of a Control

Surface Mechanism"



δ − Hδδ − Hδδ = Hαα + Hcommand+

mechanism dynamics = external forcing

•  Approximate control

dynamics by a 2 nd

-order LTI system"

•  Bring all torques and inertias to right side"



δ E = Helevator

Ielevator =

CH elevator1

2 ρV2Sc

Ielevator

= C $ % H δEδE + CH δ Eδ E + CHαα + CH command + & '

1

2 ρV2Sc

Ielevator

≡ HδEδE + HδEδ E + Hαα + Hcommand+

Dynamic Model of a Control Surface Mechanism"

Ielevator = effective inertia of surface, linkages, etc.

HδE = ∂ ( Helevator Ielevator)

∂ δ  ; HδE = ∂ ( Helevator Ielevator)

∂δ

Hα = ∂ ( Helevator Ielevator)

∂α

•  Stability and control derivatives of the control mechanism"

Coupling of System Model and Control

Mechanism Dynamics "

•  2 nd -order model of control-deflection dynamics"

–  Command input from cockpit"

–  Forcing by aerodynamic effects"

•   Control surface deflection"

•   Aircraft angle of attack and angular rates"

•  Short period approximation"

•  Coupling with mechanism dynamics"

ΔxSP= FSPΔxSP+ GSPΔuSP= FSPΔxSP+ FδEΔxδE

Δ q

Δ α

$

%

&

&

' (

) )≈

1 − α

V N

$

%

&

&

&

'

(

) ) )

Δq

Δ

$

%

&

&

' (

) )+

− δE

V N

0

$

%

&

&

&

' (

) ) )

ΔδE

Δ 

$

%

& ' ( )

ΔxδE= FδEΔxδE+ GδEΔuδE+ FSP

δE

ΔxSP

Δ 

Δ δE

#

$

%

%

&

'

(

(≈

HδE HδE

#

$

%

%

&

'

( (

ΔδE

Δ 

#

$

% &

'

−HδE

#

$

%

%

&

'

( (ΔδEcommand+

H q Hα

#

$

%

%

&

'

( (

Δq

Δα

#

$

%

%

&

'

( (

Short Period Model Augmented by Control Mechanism Dynamics "

•   Augmented dynamic equation"

•   Augmented stability and control matrices"

FSP/δE= FSP FδE

SP

FSP δE FδE

"

#

$

$

%

&

' '=

V N − δE V N 0

"

#

$

$

$

$

$

$

%

&

' ' ' ' ' '

ΔxSP '=

Δq

Δ

Δ δE

Δ  δE

$

%

&

&

& '

(

) ) )

ΔxSP /δ E = FSP /δ EΔxSP /δ E + GSP /δ EΔδ Ecommand

State Vector!

GSP /δ E =

0 0 0

Hδ E

"

#

$

$

$

$

%

&

' ' ' '

Roots of the Augmented Short

Period Model "

•  Characteristic equation for short-period/elevator dynamics"

ΔSP/δE( ) s = sIn− FSP/δE =

s − Mq

−1 s + Lα

VN

VN 0

= 0

Short Period" Control Mechanism"

Roots of the Augmented Short

Period Model "

•   Coupling of the modes depends on design parameters"

Mδ E, Lδ E

VN, Hq, and Hα

•  Desirable for mechanical natural frequency > short-period natural frequency"

•  Coupling dynamics can be evaluated by root locus analysis"

Horn Balance"

CH ≈ CHαα + CH δ Eδ E + CH pilot input

•  Stick-free case "

–  Control surface free to float "

CH ≈ CH

αα + CH δ Eδ E

•  Normally "

C H

α < 0 :reduces short-period stability

C H δ E < 0 :required for mechanical stability

NACA TR-927, 1948!

Horn Balance "

•  Inertial and aerodynamic effects"

•  Control surface in front of hinge line"

–  Increasing elevator improves pitch stability, to a point "

•  Too much horn area"

–  Degrades restoring moment "

–  Increases possibility of mechanical instability"

–  Increases possibility of destabilizing coupling to short-period mode"

€

CH

α

Overhang or

Leading-Edge

Balance"

•   Area in front of the

hinge line"

•   Effect is similar to

that of horn balance"

•   Varying gap and

protrusion into

airstream with

deflection angle"

CH ≈ CHαα + CHδδ + CH pilot input

All-Moving Control Surfaces"

•  Particularly effective at supersonic speed (Boeing Bomarc wing tips, North American X-15 horizontal

and vertical tails, Grumman F-14 horizontal tail)"

•   SB.4 s aero-isoclinic wing"

•  Sometimes used for trim only (e.g., Lockheed L-1011

horizontal tail)"

•  Hinge moment variations with flight condition"

Shorts SB.4!

Boeing ! Bomarc!

North American X-15!

Grumman F-14!

Lockheed L-1011!

Control Surface Types

Elevator"

•   Horizontal tail and elevator

in wing wake at selected angles of attack"

•   Effectiveness of low mounting is unaffected by wing wake at high angle of attack"

•   Effectiveness of high-mounted elevator is unaffected by wing wake at low to moderate angle

of attack"

Ailerons"

•   When one aileron goes up, the other goes down"

–  Average hinge moment affects stick force "

Compensating Ailerons"

•  Frise aileron"

–  Asymmetric contour, with hinge line at or below lower aerodynamic surface"

–  Reduces hinge moment "

•  Cross-coupling effects can be adverse or favorable, e.g yaw rate with roll"

–  Up travel of one > down travel of other to control yaw effect "

Abzug & Larrabee, 2002!

•  Spoiler reduces lift, increases drag"

–  Speed control "

•  Differential spoilers"

–  Roll control "

–  Avoid twist produced by outboard

ailerons on long, slender wings"

–  free trailing edge for larger high-lift

flaps "

•  Plug-slot spoiler on P-61 Black

Widow: low control force"

•  Hinged flap has high hinge moment"

North American P-61!

Abzug & Larrabee, 2002!

Elevons"

•  Combined pitch and roll control using symmetric and

asymmetric surface deflection"

•  Principally used on"

–  Delta-wing configurations"

–  Swing-wing aircraft "

Grumman F-14!

General Dynamics F-106!

Canards"

•   Pitch control "

–  Ahead of wing downwash"

–  High angle of attack

effectiveness"

–  Desirable flying qualities

effect (TBD)"

Dassault Rafale!

SAAB Gripen!

Yaw Control of Tailless Configurations"

•  Typically unstable in pitch and yaw"

•  Dependent on flight control system for stability"

•  Split ailerons or differential drag flaps produce yawing moment"

McDonnell Douglas X-36 !

Northrop Grumman B-2 !

•  Rudder provides yaw control"

–   Turn coordination"

–   Countering adverse yaw"

–   Crosswind correction"

–   Countering yaw due to engine loss "

•  Strong rolling effect, particularly at high α"

•  Only control surface whose nominal

aerodynamic angle is zero"

•  Possible nonlinear effect at low deflection

angle"

•  Insensitivity at high supersonic speed"

–   Wedge shape, all-moving surface on North

American X-15 "

Martin B-57!

Bell X-2!

Rudder Has Mechanical As Well as

Aerodynamic Effects "

!  American Airlines 587 takeoff behind Japan Air 47, Nov 12, 2001"

!  Excessive periodic commands to rudder caused vertical tail failure"

Japan B-747!

American A-300!

http://www.usatoday.com/story/travel/flights/2012/11/19/airbus-rudder/1707421/!

NTSB Simulation of American

Flight 587 "

!  Flight simulation derived from digital flight data recorder (DFDR) tape"

Control Mechanization

Effects

•   Fabric-covered control surfaces (e.g., DC-3, Spitfire) subject to distortion under air loads, changing stability and control characteristics"

•   Control cable stretching "

•   Elasticity of the airframe

changes cable/pushrod geometry"

•   Nonlinear control effects "

–  friction"

–  backlash "

Douglas DC-3!

Supermarine ! Spitfire!

•   Friction"

•   Deadzone"

Control Mechanization Effects "

•   Breakout force"

•   Force threshold"

B-52 Control Compromises to

Minimize Required Control Power "

•  Limited-authority rudder, allowed by "

–   Low maneuvering requirement "

–   Reduced engine-out requirement (1 of

8 engines) "

–   Crosswind landing gear"

•  Limited-authority elevator, allowed by "

–   Low maneuvering requirement "

–   Movable stabilator for trim"

–   Fuel pumping to shift center of mass"

•  Small manually controlled "feeler"

ailerons with spring tabs "

–   Primary roll control from powered

spoilers, minimizing wing twist"

Internally Balanced

!   B-52 application"

!  Control-surface fin

moves within an internal cavity in the main surface"

control hinge moment "

CH ≈ CHαα + CHδδ + CH pilot input

Boeing B-52!

B-52 Rudder Control Linkages"

B-52 Mechanical

•  Combined stable rudder tab, low-friction bearings, small bobweight, and eddy-current damper for B-52"

•  Advantages"

•  Problems"

Boeing B-47 Yaw Damper "

•  Yaw rate gyro drives rudder to increase

Dutch roll damping"

•  Comment : The plane wouldn t need this

contraption if it had been designed right

in the first place "

•  However, mode characteristics

especially damping vary greatly with

altitude, and most jet aircraft have yaw

dampers"

steady turns"

Northrop YB-49 Yaw Damper !

•  Minimal directional stability due to small vertical surfaces and short moment arm"

•   Clamshell rudders, like drag flaps on the B-2 Spirit"

•  The first stealth aircraft, though that was not intended"

Princeton MSE , killed testing the aircraft"

•   B-49s were chopped up after decision not to go into production"

•  Northrop had the last word: it built the B-2 !

Northrop YB-49!

Northrop/Grumman B-2!

Instabilities Due To

•  Aileron buzz (aero-mechanical instability; P-80)"

•  Rudder snaking (Dutch roll/mechanical coupling; Meteor, He-162)"

•  Aeroelastic coupling (B-47, Boeing 707 yaw dampers)"

Rudder Snaking"

•   Control-free dynamics"

–  Nominally symmetric control position"

–  Internal friction"

–  Aerodynamic imbalance "

Douglas DC-2!

•   Solutions"

–  Trailing-edge bevel"

–  Flat-sided surfaces"

–  Fully powered controls "

Roll/Spiral Limit Cycle

Due to Aileron Imbalance"

oscillation grows until it reaches a steady state"

limit cycle"

Lockheed P-38! Control Surface Buzz"

may occur on control surface"

differentially "

nonlinear oscillation (limit cycle)"

ARC R&M 3364!

•  Solutions "

–   Splitter-plate rudder

fixes shock location for small deflections"

–   Blunt trailing edge"

–   Fully powered controls with

actuators at the surfaces"

Rudder Lock"

sideslip due to stalling of fin"

moment-due-to-sideslip at high sideslip

(e.g., B-26)!

unpowered and requires high

foot-pedal force ( rudder float of

large WWII aircraft)"

•  Solutions"

stability by adding a dorsal fin

(e.g., B-737-100 (before),

B-737-400 (after))"

Martin B-26!

Boeing 737-100!

Boeing 737-400!

Control Systems

SAS = Stability Augmentation System!

Downsprings and Bobweights "

•  Adjustment of "

–  Stick-free pitch trim moment"

–  Stick-force sensitivity to

airspeed* "

•  Downspring"

–  Mechanical spring with low spring

constant"

–  Exerts a ~constant trailing-edge

down moment on the elevator!

•  Bobweight"

–  Similar effect to that of the

downspring"

–  Weight on control column that

affects feel or basic stability"

–  Mechanical stability augmentation

(weight is sensitive to aircraft’s

angular rotation)"

Beechcraft B-18!

* See pp 541-545, Section 5.5, Flight Dynamics!

Effect of Scalar Feedback Control

on Roots of the System "

Δy(s) = H (s) Δu(s) = kn(s)

kn(s) d(s) KΔε(s)

•   Block diagram algebra "

H (s) = kn(s) d(s)

= KH (s) [ Δyc(s) − Δy(s) ]

K

Closed-Loop Transfer Function "

1+ KH (s)

Δy(s)

Δyc(s) =

KH (s)

1+ KH (s)

Roots of the Closed-Loop System "

•   Closed-loop roots are solutions to"

Δ closed

loop

(s) = d(s) + Kkn(s) = 0

Δy(s)

Δyc(s) =

K kn(s) d(s)

1+ K kn(s)

d(s)

"

#

&

'

= K kn(s)

d(s) + K kn(s)

K kn(s)

Δclosed loop s

( )

Root Locus Analysis of Pitch Rate Feedback to

kq( s − zq)

s2+ 2ζSPωn SPs +ωn SP

2 = −1

!  # of roots = 2"

!  # of zeros = 1!

!  Destinations of roots (for k =

±∞ ):"

!  1 root goes to zero of n(s)"

!  1 root goes to infinite radius"

!  Angles of asymptotes, θ, for the roots going to ∞"

!  K -> +∞: –180 deg "

!  K -> –∞: 0 deg "

Root Locus Analysis of Pitch Rate Feedback to Elevator

matter"

•  Locus on real axis"

–  K > 0: Segment to the left of

the zero"

–  K < 0: Segment to the right of

the zero"

Feedback effect is analogous

Root Locus Analysis of Angular

* p 524, Flight Dynamics"

Root Locus Analysis of Angular

Direct Lift and Propulsion Control

Direct-Lift Control-Approach Power Compensation"

•  F-8 Crusader "

–  Variable-incidence wing,

better pilot visibility"

–  Flight path control at low approach speeds "

•   requires throttle use "

•   could not be accomplished with pitch control alone "

–  Engine response time is slow "

–  Flight test of direct lift control

(DLC), using ailerons as flaps"

II and direct lift control studied

using Princeton’s Variable-Response Research Aircraft"

Princeton VRA!

Vought A-7!

Vought F-8!

•  Direct-lift control on S-3A

Viking"

–  Implemented with spoilers "

–  Rigged up during landing

to allow ± lift."

•  Speed brakes on T-45A

spool-up time of jet engine"

–  BAE Hawk's speed brake

moved to sides for carrier

landing"

–  Idle speed increased from

55% to 78% to allow more

effective modulation via

speed brakes"

Lockheed S-3A!

Boeing T-45!

Next Time:

Flight Testing for Stability and Control

Reading