Stability, Control, and Power

Effects on Configuration DesignRobert Stengel, Aircraft Flight Dynamics

MAE 331, 2008

• Preliminary layout of the plane

– Mission

– Payload requirements

– Propulsion system

– Wing design

– Tail shape and sizing

– Balance and neutral point

– Stability and trim

• Aerodynamic coefficientestimates

Copyright 2008 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE331.html

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

• Control surfaces

• Avionics and feedbackcontrol requirements

Goals for Design• Shape of the airplane

determined by its purpose

• Handling, performance,functioning, and comfort

• Agility vs. sedateness

• Control surfaces adequate toproduce needed moments

• Center of mass location

– too far forward increasesunpowered control-stick forces

– too far aft degrades staticstability

Airplane Balance• Conventional aft-tail configuration

– c.m. near wing's aerodynamic center (point at which wing'spitching moment coefficient is invariant with angle of attack~25% mac)

• Tailless airplane: c.m. ahead of the neutral point

Douglas DC-3

Northrop N-9M

Airplane Balance• Canard configuration:

– Neutral point moved forward by canard surfaces

– Center of mass may be behind the neutral point, requiringclosed-loop stabilization

• Fly-by-wire feedback control can expand c.m.envelope

Grumman X-29

McDonnell-Douglas X-36

Wing Design Parameters• Planform

– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Chord section– Airfoils

– Twist

• Movable surfaces– Leading- and trailing-edge devices

– Ailerons

– Spoilers

• Interfaces– Fuselage

– Powerplants

Wing Design Effects

• Planform– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Inertial and aerodynamiceffects– Performance

– Short period damping

– Phugoid damping

– Roll damping

North American F-100

Short Period Transient Response

Roll Mode Transient Response

• Variable sweep

– High aspect ratio for low-speed flight

• Landing and takeoff

• Loiter

– Low aspect ratio for high-speed flight

• Reduction of transonicand supersonic drag

• Variable incidence– Improve pilot!s line of

sight for carrier landing

Wing Design EffectsGeneral Dynamics F-111

LTV F-8

Sweep Effect on

Thickness Ratio

Grumman F-14

from Asselin

Sweep Effect on Wing Subsonic

Lift Distribution

• Planform

– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Sweep moves subsoniclift distribution toward thewing tips

• Sweep also increases thedihedral effect of the wing(TBD)

Sweep Effect on Wing

Center of Pressure

• Planform

– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Sweep moves subsonic liftdistribution toward the wing tips

• Center of pressure of straightwing moves aft with increasing !

• Swept outboard wing stallsbefore inboard wing (“tip stall”)

– Center of pressure movedforward

– Static margin is reduced asangle of attack increases

CL(!) vs. Cm(!)

• 30° swept wing exhibitspitch-up instability

Pitch Up• Crossplot CL vs. Cm to obtain plots such as those shown on previous slide

• Positive break in Cm is due to forward movement of net center of pressure,decreasing static margin

F-100 crashes due to tip stallhttp://www.youtube.com/watch?v=rMLynu5YoPM

http://www.youtube.com/watch?v=NyJkKcXYqSU&feature=related

http://en.wikipedia.org/wiki/F-100_Super_Sabre

Shortal-Maggin

Longitudinal

Stability Boundary

for Swept Wings

• Stable or unstable pitchbreak at the stall

• Stability boundary isexpressed as a function of– Aspect ratio

– Sweep angle of thequarter chord

– Taper ratio

• Straight Wing– Subsonic center of

pressure (c.p.) at~1/4 meanaerodynamicchord (m.a.c.)

– Transonic-supersonic c.p. at~1/2 m.a.c.

• Delta Wing– Subsonic-

supersonic c.p. at~2/3 m.a.c.

Mach Number Effect on

Wing Center of Pressure

• Mach number– increases the static margin of conventional

configurations

– Has less effect on delta wing static margin

P-38 Compressibility Limit

on Allowable Airspeed

• Pilots warned to stay well below speed of sound in steep dive

Cm(!) vs. CL(!)

• Static margin increase withMach number– increases control stick

force required to maintainpitch trim

– produces pitch down

from P-38 Pilot!s Manual

• Strakes or leading edge extensions

– Maintain lift at high !

– Reduce c.p. shift at high Mach number

Wing Design Effects

McDonnell Douglas F-18General Dynamics F-16

• Vortex generators, fences, vortilons,notched or dog-toothed wing leading edges– Boundary layer control

– Maintain attached flow with increasing !

– Avoid tip stall

Wing Design Effects

McDonnell-Douglas F-4

Sukhoi Su-22

LTV F-8

• Planform– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Chord section– Airfoils

– Twist

• Elliptical lift distribution

• Tip stall

• Bending stress Republic XF-91

Wing Design Effects Wing Design Effects

• Planform

– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Chord section– Airfoils

– Twist

• Camber increases zero-! lift coefficient

• Thickness increases transonic drag

• Planform– Aspect ratio

– Sweep

– Taper

– Complex geometries

– Shape at root

– Shape at tip

• Chord section– Airfoils

– Twist

• Washout twist– reduces tip angle of

attack

– reduces likelihood of tipstall

Wing Design Effects Wing Design Effects

• Vertical location of the wing,dihedral angle, and sweep– Sideslip induces yawing motion

– Unequal lift on left and rightwings induces rolling motion

• Lateral-directional (spiral mode)stability effect

• Wing tips

– Winglets and rake reduce induced drag

– Chamfer produces favorable roll w/ sideslip (spiral mode)

Wing Design Effects

Yankee AA-1B-747-400

Boeing P-8A

• Longitudinal stability– Horizontal stabilizer

– Short period naturalfrequency and damping

• Directional stability– Vertical stabilizer (fin)

• Ventral fins

• Strakes

• Leading-edge extensions

• Multiple surfaces

• Butterfly (V) tail

– Dutch roll naturalfrequency and damping

• Stall or spin prevention/recovery

• Avoid rudder lock (TBD)

Tail Design

Effects

North American P-51

• Ventral fins

– Increase directional stability at high Mach Number

– Increase directional stability due to design change

LTV F8U-3

Tail Design Effects

North American X-15

Learjet 60Beechcraft 1900D

Horizontal Tail

Location and Size• 15-30% of wing area~ wing semi-span behind the c.m.

• Requirement to trim neutrally stable airplane at maximum lift inground effect

• Effect on short period mode

• Horizontal Tail Volume: Average value = 0.48

!

VH

=S

ht

S

lht

c

!

"Cmtail= "CLtail

Sht

S

lht

c = "CLtail

VH

where "CLtailis referenced to horizontal tail area

Curtiss SB2C North American F-86

• Analogous to horizontal tail volume

• Effect on Dutch roll mode

• Powerful rudder for spin recovery

– Full-length rudder located behind the elevator

– High horizontal tail so as not to block the flow over the rudder

• Vertical Tail Volume: Average value = 0.18

VV=Svt

S

lvt

b

Vertical Tail

Location and Size

!

"Cntail= "CLtail

Svt

S

lvt

c = "CLtail

VV

where "CLtailis referenced to vertical tail area

Curtiss SB2C Piper Tomahawk

Tail Location and Size

!

VH

=S

ht

S

lht

c

VV

=S

vt

S

lvt

b

McDonnell Douglas XF-85

• “Short-coupled” designs havestability problems

• Increased tail area with no increase in vertical height

• End-plate effect for horizontal tail improves effectiveness

• Proximity to propeller slipstream

Twin and Triple

Vertical Tails

North American B-25

Lockheed C-69

Consolidated B-24

Fairchild-Republic A-10

Handbook Approach to

Aerodynamic Estimation• Build estimates from component effects

– USAF Stability and Control DATCOM (download from Course Blackboard)

– USAF Digital DATCOM (see Wikipedia page)

– ESDU Data Sheets (see Wikipedia page)

• Ilan Kroo!s web page (http://adg.stanford.edu/aa241/AircraftDesign.html)

• UIUC Applied Aerodynamics Group(http://www.ae.uiuc.edu/m-selig/)

• NASA 30! x 60! Tunnel

– Full-scale aircraft on balance

– Sub-scale aircraft on sting

– Sub-scale aircraft in free flight

– Maximum airspeed = 118 mph

– Constructed in 1931 for $37M(~$500M in today!s dollars)

– Two 4000-hp electric motors

Wind Tunnel Data

Tested virtually every USairplane used in World War II,when it was operating 24/7

Interpreting Wind Tunnel Data

• Wall corrections, uniformity of theflow, turbulence, flow recirculation,temperature, external winds (opencircuit)

• Open-throat tunnel equilibratespressure

• Tunnel mounts and balances: struts,wires, stings, magnetic support

• Simulating power effects, flow-through effects, aeroelasticdeformation, surface distortions

• Artifices to improve reduced/full-scale correlation, e.g., boundary layertrips and vortex generators

Computational Fluid Dynamics

• Strip theory– Sum or integrate 2-D airfoil force

and moment estimates over wingand tail spans

• 3-D calculations at grid points– Finite-element or finite-difference

modeling

– Pressures and flow velocities (orvorticity) at points or over panels ofaircraft surface

– Euler equations neglect viscosity

– Navier-Stokes equations do not

Design for Control

• Elevator/stabilator: pitch control

• Rudder: yaw control

• Ailerons: roll control

• Trailing-edge flaps: low-angle lift control

• Leading-edge flaps: 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

– "E is an input

• Command and control of the control surfaces

– Displacements, forces, and hinge moments within the control mechanisms

– Dynamics of control linkages

– "E is a state

!

˙ ̇ " =L

!

" ˙ ̇ E =L

Control Flap Carryover Effect on

Lift Produced By Total Surface

from Schlichting & Truckenbrodt

!

CL"E

CL#

vs.c f

x f + c f

!

CL"E

CL#

!

c f x f + c f( )

Aerodynamic Moments

on Control Surfaces• Increasing size and speed of aircraft leads to

increased hinge moments

• This leads to need for mechanical oraerodynamic reduction of hinge moments

• Need for aerodynamically balanced surfaces

• Control surface hinge moment

!

Helevator

= CHelevator

1

2"V

2Sc

!

V

"

!

CH = CH ˙ "

˙ " + CH"" + CH#

# + CHpilot input+ ...

!

CH ˙ " : aerodynamic damping moment

CH": aerodynamic spring moment

CH#: floating tendency

CHpilot input: pilot input

• Hinge-moment coefficient, CH

– Linear model of dynamic effects

Dynamic Model of a

Control Surface

!

˙ ̇ " =Helevator

Ielevator

=CHelevator

1

2#V

2Sc

Ielevator

= CH ˙ "

˙ " + CH"" + CH$

$ + CH pilot input+ ...[ ]

1

2#V

2Sc

Ielevator

% H ˙ " ˙ " + H"" + H$$ + Hpilot input + ...

!

˙ ̇ " #H ˙ " ˙ " #H"" = H$$ + Hpilot input + ...

mechanism dynamics = external forcing

!

Ielevator = effective inertia of surface, linkages, etc.

H ˙ " =# Helevator Ielevator( )

# ˙ " ; H" =

# Helevator Ielevator( )#"

H$ =# Helevator Ielevator( )

#$

• Second-order model of control-deflection dynamics

• Control mechanism dynamics

Horn Balance

• Inertial and aerodynamic effects

• Control surface in front of hinge line

– Increasing improves pitch stability,to a point

• Too much area

– Degrades restoring moment

– Increases possibility of mechanicalinstability

– Increases possibility of destabilizingcoupling to short-period mode

!

CH " CH## + CH$

$ + CHpilot input

• Stick-free case– Control surface free to “float”

!

CH" C

H## + C

H$$

• Normally

!

CH"< 0 : reduces short # period stability

CH$< 0 : required for mechanical stability

!

CH"

Overhang or

Leading-Edge

Balance• Effect is similar to

that of horn balance

• Varying gap andprotrusion intoairstream withdeflection angle

!

CH " CH## + CH$

$ + CHpilot input

Trailing-Edge

Bevel Balance

• See discussion inAbzug and Larrabee

!

CH " CH## + CH$

$ + CHpilot input

Internally Balanced

Control Surface

• B-52 application– Control-surface fin

with flexible sealmoves within aninternal cavity in themain surface

– Differentialpressures reducecontrol hingemoment

!

CH " CH## + CH$

$ + CHpilot input

All-Moving Control Surfaces

• Particularly effective at supersonic speed (BoeingBomarc wing tips, North American X-15 horizontaland vertical tails, Grumman F-14 horizontal tail)

• SB.4!s “aero-isoclinic” wing

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

• Hinge moment variations with flight condition

Shorts SB.4

Bomarc

X-15

F-14

L-1011

Aft Flap vs. All-Moving

Control Surface

• Carryover effect

– Aft-flap deflection can be almost as effective asfull surface deflection at subsonic speeds

– Negligible at supersonic speed

• Aft flap

– Mass and inertia lower, reducing likelihood ofmechanical instability

– Aerodynamic hinge moment is lower

– Can be mounted on structurally rigid mainsurface

Ailerons• When one aileron goes up, the

other goes down

– Average hinge moment affectsstick force

• Frise aileron

– Asymmetric contour, with hingeline at or below loweraerodynamic surface

– Reduces hinge moment

• Cross-coupling effects can beadverse or favorable, e.g. yawrate with roll

– Up travel of one > down travel ofother to control yaw effect

Spoilers• Spoiler reduces lift, increases drag

– Speed control

• Differential spoilers– Roll control

– Avoid twist produced by outboardailerons on long, slender wings

– free trailing edge for larger high-liftflaps

• Plug-slot spoiler on P-61 BlackWidow: low control force

• Hinged flap has high hinge moment

North American P-61

Rudder• Rudder provides yaw control

– Turn coordination

– Countering adverse yaw

– Crosswind correction

– Countering yaw due to engine loss

• Strong rolling effect, particularly at high !

• Only control surface whose nominalaerodynamic angle is zero

• Possible nonlinear effect at low deflectionangle

• Insensitivity at high supersonic speed– Wedge shape, all-moving surface on X-15

Martin B-57

Bell X-2

Control Tabs• Balancing or geared tabs

– Tab is linked to the main surface inopposition to control motion, reducingthe hinge moment with little change incontrol effect

• Flying tabs– Pilot's controls affect only the tab,

whose hinge moment moves thecontrol surface [BAC 1-11 deep stallflight test accident]

• Linked tabs– divide pilot's input between tab and

main surface

• Spring tabs– put a spring in the link to the main

surface

BAC 1-11

Control Mechanization Effects

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

• Control cable stretching

• Elasticity of the airframe changes cable/pushrodgeometry

• Nonlinear control effects– friction

– breakout forces

– backlash

Instabilities Due To

Control Mechanization• Aileron buzz (aero-mechanical instability; P-80 test, Avro CF-105)

• Rudder snaking (Dutch roll/mechanical coupling; Meteor, He-162, X-1)

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

Downsprings and Bobweights• Downspring

– Long mechanical spring withlow spring constant

– Exerts a trailing-edge downmoment on the elevator

• Bobweight

– Weight on control column thataffects feel or basic stability

– Mechanical stabilityaugmentation

Beechcraft B-18

Mechanical and Augmented

Control Systems• Mechanical system

– Push rods, bellcranks, cables, pulleys

– On almost all aircraft currently flying

• Power boost– Pilot's input augmented by hydraulic servo that

lowers manual force

• Fully powered (irreversible) system– No direct mechanical path from pilot to

controls

– Mechanical linkages from cockpit controls toservo actuators

Mechanical, Power-Boosted Systems

McDonnell Douglas F-15

Grumman A-6

Advanced Control Systems

• Artificial-feel systems

– Restores the pilot's controlforces to those of an "honest"airplane

– "q-feel" modifies force gradient

– Variation with trim stabilizerangle

– Bobweight responds to gravityand to normal acceleration

• Fly-by-wire/light systems

– Minimal mechanical runsthrough the airplane

– Command input and feedbacksignals drive servo actuators

– Fully powered systems

– Move toward electric rather thanhydraulic power

Boeing 767 Elevator Control System Boeing 777 Fly-By-Wire Control System

Control-Configured Vehicles

• Command/stability augmentation

• Lateral-directional response

– Bank without turn

– Turn without bank

– Yaw without lateral translation

– Lateral translation without yaw

– Velocity-axis roll (i.e., bank)

• Longitudinal response

– Pitch without heave

– Heave without pitch

– Normal load factor

– Pitch-command/attitude-hold

– Flight path angle

USAF F-15 IFCS

Princeton Variable-Response Research AircraftUSAF AFTI/F-16

Power Effects on Stability and Control

• Gee Bee R1 Racer: an enginewith wings and almost no tail

• During W.W.II, the size offighters remained about thesame, but installed horsepowerdoubled (F4F vs. F8F)

• Use of flaps means high powerat low speed, increasingrelative significance of thrusteffects (AD)

Douglas AD-1 Grumman F8F

Grumman F4F

GB R1

Multi-Engine Aircraft of World War II

• Large W.W.II aircraft (e.g., B-17,B-24, and B-29) had unpoweredcontrols:

– High foot-pedal force

– Rudder stability problemsarising from balancing to reducepedal force

• Severe engine-out problem fortwin-engine aircraft, e.g., A-26,B-25, and B-26

Loss of Engine• Loss of engine produces large yawing

(and sometimes rolling) moment(s),requiring major application of controls

• Engine-out training can be ashazardous, especially during takeoff, forboth propeller and jet aircraft

• Acute problem for general-aviationpilots graduating from single-engineaircraft

Solutions to the

Engine-Out Problem

• Engines on the centerline (Cessna337 Skymaster)

• More engines (B-36)

• Cross-shafting of engines (V-22)

• Large vertical tail (Boeing 737)

NASA TCV (Boeing 737)

Cessna 337

Convair B-36

Boeing/Bell V-22

Direct Thrust Effect

on Speed Stability• In powered, steady, level flight, nominal thrust balances

nominal drag

!T

!V=

< 0, for propeller aircraft

" 0, for turbojet aircraft

> 0, for ramjet aircraft

#

$ %

& %

!

"D

"V> 0 for most flight regimes

!T

!V"!D

!V> 0

!

TN"D

N= C

TN

1

2#V

N

2

S "CDN

1

2#V

N

2

S = 0

• Effect of velocity change

• Small velocity perturbation grows if

• Therefore, propeller is stabilizing for velocity change,turbojet has neutral effect, and ramjet is destabilizing

Pitching Moment Due to Thrust• Thrust line above or below center of mass induces a pitching moment

• XB-51, PBY, MD-11, A-10

Martin XB-51

McDonnell Douglas MD-11

Consolidated PBY

Fairchild-Republic A-10

Velocity-Dependent Thrust-

Induced Pitching Moment

• Negative "M/"V (Pitch-down effect) tends to increase velocity

• Positive "M/"V (Pitch-up effect) tends to decrease velocity

• With propeller thrust line above the c.m., increased velocity decreasesthrust, producing a pitch-up moment

• Tilting the propeller thrust line can have benefits (Lake Amphibian, F6FHellcat, F8F Bearcat, and AD Skyraider)

!

"Mthrust

"V#"T

"V$Moment Arm

Douglas AD-1

Lake Amphibian

Grumman F6F

Grumman F8F

Propeller Effects

• Slipstream washing over wing, tail,and fuselage

– Increased dynamic pressure

– Swirl of flow

– Downwash and sidewash at the tail

• DH-2 unstable with engine out

• Difference between single- andmulti-engine effects

• Design factors: fin offset (correct atone airspeed only), c.m. offset

• Propeller fin effect: Visualizelateral/horizontal projections of thepropeller as forward surfaces

• Counter-rotating propellers tominimize torque and swirl

Westland Wyvern

DeHavilland DH-2

Jet Effects on Rigid-Body Motion• Normal force at intake (analogous to propeller fin effect) (F-86)

• Deflection of airflow past tail due to entrainment in exhaust (F/A-18)

• Pitch and yaw damping due to internal exhaust flow

• Angular momentum of rotating machinery

North American F-86

McDonnell Douglas F/A-18

United Flight 232, DC-10, Sioux City, IA, 1989

• Uncontained engine failure damaged allthree flight control hydraulic systems(http://en.wikipedia.org/wiki/United_Airlines_Flight_232)

• Crew resource management(http://en.wikipedia.org/wiki/Crew_Resource_Management)

• 296 people onboard

• 185 survived due to pilot!s differentialcontrol of engines

Propulsion Controlled Aircraft• Proposed backup attitude control in event of flight control system failure

• Differential throttling of engines to produce control moments

• Requires feedback control for satisfactory flying qualities

NASA MD-11 PCA Flight Test

NASA F-15 PCA Flight Test

• Proposed retrofit to McDonnell-Douglas (Boeing) C-17

Next Time:Linearized Equations and

Modes of Motion