Problems of High Speed and AltitudeRobert Stengel, Aircraft Flight Dynamics

MAE 331, 2010

• Effects of air compressibility

on flight stability

• Variable sweep-angle wings

• Aero-mechanical stabilityaugmentation

• Altitude/airspeed instability

Copyright 2010 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE331.html

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

Outrunning Your Own Bullets

• On Sep 21, 1956, Grumman test pilot Tom Attridge shothimself down, moments after this picture was taken

• Test firing 20mm cannons of F11F Tiger at M = 1

• The combination of events– Decay in projectile velocity and trajectory drop

– 0.5-G descent of the F11F, due in part to its nose pitching downfrom firing low-mounted guns

– Flight paths of aircraft and bullets in the same vertical plane

– 11 sec after firing, Attridge flew through the bullet cluster, with 3

hits, 1 in engine

• Aircraft crashed 1 mile short of runway; Attridge

survived

Effects of AirCompressibility onFlight Stability

Implications of Air Compressibility

for Stability and Control• Early difficulties with compressibility

– Encountered in high-speed dives fromhigh altitude, e.g., Lockheed P-38Lightning

• Thick wing center section

– Developed compressibility burble,reducing lift-curve slope anddownwash

• Reduced downwash

– Increased horizontal stabilizereffectiveness

– Increased static stability

– Introduced a nose-down pitchingmoment

• Solution

– Auxiliary wing flaps that increasedboth lift and drag

NACA WR-A-66, 1943

P-38 Compressibility Limiton 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

NACA TR-767, 1943

Compressibility Problems

• Similar problems with P-39Aircobra, P-47 Thunderbolt, andP-51 Mustang

– Led to flight tests and greaterunderstanding ofcompressibility effects

Perkins, 1970

Mach Tuck• Low angle of attack phenomenon

– Shock-induced change in wing

downwash effect on horizontal tail

– Pitch-down trim change, , due to aftaerodynamic center shift with increasingMach number

• F4D speed record flights (M = 0.98)

– Low altitude, high temperature toincrease the speed of sound

– High dynamic pressure

– 1.5 g per degree of angle of attack, M ! 1,dramatic trim changes with Mach number

– Pilot used nose-up trim control

• Pull to push for pitch control in turn at end

of each run

• Uncontrollable pitch-up to 9.1 g during

deceleration at end of one run, due to

pilot"s not compensating fast enough

Cmo

Abzug & Larrabee

MV Effect on Fourth-

Order Roots

• Coupling derivative: Largepositive value producesoscillatory phugoid instability

• Large negative value producesreal phugoid divergence

!Lon(s) = s

4+ D

V+L"

VN

# Mq( )s3

+ g # D"( )LV VN

+ DV

L"

VN

# Mq( ) # Mq

L"

VN

# M"

$

%&'

()s2

+ Mq

D" # g( )LV VN

# DV

L"

VN

$%&

'()+ D"MV

# DVM"{ }s

gM"

LV

VN

+ MVD"s + g

L"

VN

( ) = 0

D!

= 0

Short

Period

Phugoid

Pitch-Up• High angle of attack

phenomenon

• Center of pressure movesforward due to tip stall

• F-86 trim change (right)

– At t = 5 s, CN and Az areincreasing (pitch-up),although elevator deflectionand control force aredecreasing

NACA TR-1237

Effects of F-86 Blunt-Trailing-Edge Aileron

• Effect of Aileron Modification on Roll-Control Effectiveness and Response

• Mach Effect on Control ofWings-Level Flight

Stick force

Aileron

Mach number Mach numberNACA RM-A54C31, 1954

Transonic Solutions

• Application of outboard vortex generators to delay tip separation(Gloster Javelin example)

• Mach number feedback to elevator on F-100 to counteract transonictrim change

Supersonic Directional Instability

• Reduced vertical stabilizereffectiveness with increasing Machnumber

• Loss of X-2 on speed run

• F-100 solution: increased fin size

• X-15 solution: wedge-shaped tail

• XB-70: fold-down wing tips

– Improved supersonic lift

– Reduced excess longitudinal staticstability

Hypersonic Stability and Control• Turbojet/rocket for launch/takeoff

• Ramjet/scramjet powerplant for cruise

• High degree of coupling, not only of phugoid andshort period but of structural and propulsive modes

• Poor lateral-directional characteristics

• Extreme sensitivity to angular perturbations

• Low-speed problems for high-speed configurations,e.g., takeoff/landing

NASA X-43

Boeing X-51A

B-3 Concept

DARPA HTV-2

Variable-Sweep/Incidence

Wings

Searching for the Right Design:The Many Shapes of the XF-91Thunderceptor

• Variable-incidence wing

• Tip chord > Root chord

• Vee tail, large tip chord• Full nose inlet

• Modified nose and tail• Radome above inlet

Early Swing-Wing Designs• Translation as well as rotation of the wing

(Messerschmitt P.1101, Bell X-5, andGrumman XF10F, below)

• Complicated, only partially successful

• Barnes Wallis"s Swallow (right), solutionadopted by Polhamus and Toll at NACALangley

Boeing 2707-200

Supersonic Transport Concept• Length = 318 ft; 300 passengers; larger than the B-747

• M = 2.7 (faster than Concorde)

• Cancelled before construction

Boeing 2707-300

• Variable sweep

– High aspect ratio for low-speed flight

• Landing and takeoff

• Loiter

– Low aspect ratio for high-speed flight

• Reduction of transonic andsupersonic drag

• Variable incidence

– Improve pilot"s line of sight

for carrier landing

Variable Sweep and IncidenceGeneral Dynamics F-111

LTV F-8

Advanced Variable-Sweep Designs• Fairing of wing trailing edge to

stabilizer leading edge at high

sweep

– reduces downwash at the tail andcorresponding pitch stability

– effectively forms a delta wing

• Wing glove/leading-edgeextension and outboard rotation

point

– provides greater percentage of liftat high Mach number and angle ofattack

Grumman F-14 Tomcat

BAE Tornado

Swing-Wing Solutions• Fuel shift to move center of mass aft as wing sweeps aft

• Forward wing surface that extends as wing sweeps aft

• Advanced stability augmentation systems

Rockwell B-1

Grumman F-14 Tomcat

Dassault Mirage G8

Oblique Wing Concepts• High-speed benefits of wing sweep

without the heavy structure andcomplex mechanism required forsymmetric sweep

• Blohm und Voss, R. T. Jones ,Handley-Page concepts

• Improved supersonic L/D byreduction of shock-waveinterference and elimination of thefuselage in flying-wing version

NASA Oblique Wing Test Vehicles• Stability and control issues

abound: The fact that birds andinsects are symmetric should giveus a clue (though they use hugeasymmetry for control)

– Strong aerodynamic and inertiallongitudinal-lateral-directionalcoupling

– High side force at zero sideslipangle

– Torsional divergence of theleading wing

• Test vehicles: Various modelairplanes, NASA AD-1, and NASADFBW F-8 (below, not built)

Aero-MechanicalStability Augmentation

B-52 Control Compromises to

Minimize Required Control Power

• Limited-authority rudder, allowedby

– Low maneuvering requirement

– Reduced engine-out requirement(1 of 8 engines)

– Crosswind landing gear

• Limited-authority elevator, allowedby

– Low maneuvering requirement

– Movable stabilator for trim

– Fuel pumping to shift center ofgravity

• Small manually controlled "feeler"

ailerons with spring tabs

– Primary roll control from poweredspoilers, minimizing wing twist

Internally BalancedControl Surface

• B-52 application

– Control-surface finwith flexible sealmoves within aninternal cavity in themain surface

– Differentialpressures reducecontrol hingemoment

CH ! CH"" + CH#

# + CHpilot input

Boeing B-52

B-52 Mechanical

Yaw Damper

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

• Advantages

– Requires no power, sensors, actuators, or computers

– May involve simple mechanical components

• Problems

– Misalignment, need for high precision

– Friction and wear over time

– Jamming, galling, and fouling

– High sensitivity to operating conditions, design difficulty

Boeing B-47 Yaw Damper• Yaw rate gyro drives rudder to increase

Dutch roll damping

• Comment: “The plane wouldn"t need thiscontraption if it had been designed rightin the first place.”

• However, mode characteristics --especially damping -- vary greatly withaltitude, and most jet aircraft have yawdampers

• Yaw rate washout to reduce opposition tosteady turns

Northrop YB-49 Yaw Damper

• Minimal directional stability due to small vertical surfacesand short moment arm

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

• The first stealth aircraft, though that was not intended

• Edwards AFB named after test pilot, Glen Edwards,Princeton MSE, killed testing the aircraft

• B-49s were chopped up after decision not to go intoproduction

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

Northrop YB-49

Northrop/Grumman B-2

Northrop N-9M

Altitude/AirspeedInstability

High-Altitude Stall-Mach Buffet

• Increased angle of attack and liftcoefficient leads to “Stall buffet”

• Intermittent flow separation at transonicspeed and “Mach buffet”

• The place where they meet = “CoffinCorner”

• Can induce an upset (loss of control)

• U-2 operates in Coffin Corner

• Citation X (M = 0.92) has wide buffetmargin

Citation XU-2

Supersonic Altitude/Airspeed Instability• Inability of XB-70, Concorde, and YF-12A/SR-71 to hold both altitude and airspeed

at high speed cruise

– Phugoid mode is lightly damped

– Height mode brought about by altitude-gradient effects

– Exacerbated by temperature/density gradients of the atmosphere

• Engine unstart

– Oblique engine-inlet shock is "spit out," decreasing thrust and increasing drag

– Can trigger large longitudinal or lateral-directional oscillations

• Need for closed-loop, integrated control of altitude and airspeed

Effect of Supersonic MachNumber on Altitude/AirspeedStability

• Characteristic polynomial for 2nd-order approximation

!(s) = s2 + DVs + gLV /VN = s2+ 2"#ns +#n

2( )Ph

• In supersonic flight (M > 1)

DV= 2!"

nPh#

M2

M2 $1

%&'

()*

• DV decreases as M increases

• Phugoid stability is reduced in supersonic flight

Effect of AtmosphereVariation on Aerodynamics

• Air density and sound speed vary with altitude, –z

Dz!

! CT M( ) " CD M( )#$ %&1

2m'V 2

S()*

+,-

./0

123

!z; L

z=

! CL M( )1

2m'V 2

S()*

+,-

#$4

%&5

!z;

Mz=

! Cm M( )1

2Iyy'V 2

Sc(

)*+

,-#

$44

%

&55

!z

! z( ) = !SLe"z

#! z( )

#z= "!

SLe"z

a z( ) = a zref( ) +!a

!zz " zref( )

!a z( )

!z=!a

!z

M =V

a

• These introduce altitude effects on lift, drag, and pitching moment

Third-Order ModelIncluding Altitude Effects

• 3rd-degree characteristic polynomial

!!xheight (t) = Fheight!xheight (t) +Gheight!"T (t)

! !V! !"

!!z

#

$

%%%

&

'

(((=

)DV

)g )Dz

LV

VN

0Lz

VN

0 )VN

0

#

$

%%%%%

&

'

(((((

!V!"

!z

#

$

%%%

&

'

(((+

T*T

0

0

#

$

%%%

&

'

(((!*T

sI ! Fheight = " s( ) = s3 + DVs2+ g

LVVN

+ Lz( )s +VN DV

LzVN

! Dz

LVVN

#$

%& = 0

= s ! 'h( ) s2 + 2(P)nPs +)nP

2( ) = 0

• Oscillatory phugoid mode

• Real height mode

• Neglecting Mz and short-period dynamics

!P,"

nP( )

#h

Approximate Roots of the

3rd-Order Equation• Assume phugoid response is fast compared to height mode response

sI ! Fheight = " s( ) = s3 + DVs2+ g

LVVN

+ Lz( )s +VN DV

LzVN

! Dz

LVVN

#$

%& = 0

Phugoid Mode Height Mode

Phugoid Mode

Height Mode

!nP" g

LV

VN

+ Lz; #

P"

DV

2 gLV

VN

+ Lz

!h " #VN DV

LzVN

# Dz

LVVN

$%

&'

gLVVN

+ Lz( )

3rd-Order Steady-State Response

• From Flight Dynamics, pp. 476-480, with negligible Dz

!xSS = "Fheight"1Gheight!#TSS

!VSS!$ SS

!zSS

%

&

'''

(

)

***= "

"DV "g "Dz

LVVN

0LzVN

0 "VN 0

%

&

'''''

(

)

*****

"1

T#T

0

0

%

&

'''

(

)

***!#TSS

!VSS

!"SS

!zSS

#

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&

'

(((=

T)T

DV

0

*T)T

DV

+

,-.

/0

LV

VN

Lz

VN

#

$

%%%%%%%%

&

'

((((((((

!)TSS

• Steady-state response to constant thrust increase

– Bounded airspeed increase

– Horizontal flight path

– Bounded altitude increase

2nd - order Approximation

!VSS = 0

!" SS =T#T

g!#TSS

Phugoid and Height Modes of5th-Order Longitudinal Model*

Stengel, 1970

Altitude = 70,000 ftM = 3

* Short-period, phugoid, andheight modes

PhugoidPeriod, s

PhugoidDampingRatio

PhugoidWavelength,

ft x 10-6

HeightMode TimeConstant, s

!xT = !V !" !q !# !z[ ]

Altitude Response of 5th-OrderLongitudinal Model

Stengel, 1970

Control Effects Disturbance Effects

ThrustControl

LiftControl

MomentControl

VerticalWindStep

HorizontalWind Step

RandomVertical

Wind

Next Time:Maneuvering andAeroelasticity

!"##$%&%'()$

*)(%+,)$

Transonic Pitchup Problem

• Sign reversal of withincreasing angle of attack

– Combined effect of Mach number

and changing downwash effectson horizontal tail

• F-86 Sabre wind-up turn

– Turn at high bank angle, constantload factor, decreasing velocity,and increasing angle of attack

Cm!

NACA TR-1237

F-86 Flight Test: Attempt to Hold LoadFactor at 3 in Transonic Windup Turn

Just above Pitch-upJust below Pitch-up

Mach number

Stick force, FE

Elevator deflection, "E

Normal forcecoefficient, CN

Normal load factor,Az

Pitch rate

Pitch momentcoefficient, Cm

Time, s Time, sNACA RM-A54C31, 1954

Flying Tail of theXF10F

• Variable-sweep successor to the F9F-6Cougar and precursor to the F-14Tomcat

• T-tail assembly with controllable canardand no powered control

– Like a small airplane affixed to the fin

– Pitching moment was inadequate duringlanding

Handley-Page Oblique Wing Concepts• Advantages

– 10-20% higher L/D @ supersonicspeed (compared to delta planform)

– Flying wing: no fuselage

• Issues– Which way do the passengers

face?

– Where is the cockpit?

– How are the engines and verticalsurfaces swiveled?

– What does asymmetry do tostability and control?

Boeing 2707-300

Supersonic Transport• Variable-sweep wing dropped in favor of more

conventional design

• Final configuration had weight and aeroelasticproblems

• Project cancelled in 1971 due to sonic boom, takeoffsideline noise and cost problems

B-52 Rudder Control Linkages