Download - Mae 331 Lecture 22
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
#
$
%%%
&
'
(((=
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