Problems of High Speed and Altitude Outrunning Your Own Bullets

Problems of High Speed and Altitude
Outrunning Your Own Bullets
Robert Stengel, Aircraft Flight Dynamics
MAE 331, 2008
• From propellers to jets
• Stability problems due to air
compressibility
• Early flight control systems
• Altitude instability at
supersonic speed
• Effects of wing sweep angle
On Sep 21, 1956, Grumman test pilot Tom Attridge shot himself down,
moments after this picture was taken
Test firing 20mm cannon 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 down from 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
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
Implications of Air Compressibility
for Stability and Control
•
First difficulties with compressibility
– Encountered in high-speed dives from
high altitude, e.g., Lockheed P-38
Lightning
•
Thick wing center section
– Developed compressibility burble,
reducing lift-curve slope and
downwash
•
Reduced downwash
– Increased horizontal stabilizer
effectiveness
– Increased static stability
– Introduced a nose-down pitching
moment
•
Solution
– Auxiliary wing flaps that increased
both lift and drag
Compressibility Problems
•
Similar problems with P-39
Aircobra, P-47 Thunderbolt, and
P-51 Mustang
– Led to flight tests and greater
understanding of
compressibility effects
Birth of the Jet Airplane
The Second Jet Aircraft
Heinkel He.178 (1939), Gloster E28/39 (1941), Gloster Meteor (1943),
Messerschmitt Me-262 (1942), Bell P-59A (1942) shown
•
•
Heinkel He 178
– First flight: 1939
– Turbojet engine
• Burners add energy
to the exhaust flow
• Exhaust drives
turbine, which drives
compressor
•
Campini-Caproni CC-2
– First flight: 1940
– Alternative jet engine
• Reciprocating engine drives
compressor
• Afterburner adds energy to
exhaust flow
From Propellers to Jets
The Early Jets
Douglas XB-43
•
Performance of the first jet
aircraft outstripped stability and
control technology
– Lacked satisfactory actuators,
sensors, and control electronics
– Transistor invented in 1947,
integrated circuit in 1958
•
Douglas XB-42 Mixmaster
Lockheed P-80
Northrop YB-35
Dramatic dynamic variations
over larger flight envelope
– Control mechanisms designed
to lighten pilot loads were
subject to instability
•
North American B-45
Northrop XB-49
Douglas F3D
Reluctance to embrace change,
fearing decreased reliability,
increased cost, and higher
weight
Convair B-36
Convair XF-81
Convair YB-60
Flight Tests Reveal Transonic
Longitudinal Stability Problems
From Straight to Swept Wings
•
•
Straight-wing models were redesigned with swept wings to
reduce compressibility effects on drag
Dramatic change in stability, control, and flying qualities
•
North American FJ-1
and FJ-4 Fury
•
Republic F-84B Thunderbird
and F-84F Thunderstreak
•
Just below Pitch-up
Just above Pitch-up
Mach number
Stick force,
Elevator
Grumman F9F-2 Panther
and F9F-6 Cougar
Normal force,
CN
Pitch rate
Cm
Time, s
Effects of Blunt-Trailing-Edge
Aileron
Mach Tuck
•
•
•
Mach Effect on Control of
Wings-Level Flight
•
Stick force
Low angle of attack phenomenon
– Shock-induced change in wing
downwash effect on horizontal tail
– Pitch-down trim change, Cmo, due to aft
aerodynamic center shift with increasing
Mach number
Effect of Aileron Modification on RollControl Effectiveness and Response
F4D speed record flights (M = 0.98)
– Low altitude, high temperature to
increase the speed of sound
– 1.5 g per degree of angle of attack, M ! 1,
dramatic trim changes with Mach number
– Pilot compensated using nose-up trim
control
Aileron
• 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
Mach number
Mach number
Abzug & Larrabee
Time, s
Pitch-Up
MV Effect on FourthOrder Roots
•
•
High angle of attack phenomenon
Center of pressure moves forward
due to tip stall
F-86 trim change (right)
•
%
(
" Lon (s) = s4 + ' DV + L# V $ M q * s3
&
)
N
+
.
% L#
(
L
V
+ -( g $ D# ) V + DV ' V $ M q * $ M q L# V $ M# 0s2
&
)
,
/
N
N
N
1 +
4
.
+ 2 M q -( D# $ g) LV V $ DV L# V 0 + D# MV $ DV M# 5 s
3 ,
6
N
N/
–
Short
Period
At t = 5 s, CN and Az are increasing
(pitch-up), although elevator
deflection and control force are
decreasing
Phugoid
%
(
gM# LV V + MV ' D# s + g L# V * = 0
&
N
N)
D" = 0
• Coupling derivative: Large
positive value produces
oscillatory phugoid instability
• Large negative value produces
real phugoid divergence
!
!
NACA TR-1237
Mach number feedback to elevator on F-100 to counteract trim change
•
Transonic Pitchup Problem
•
High-Altitude Stall-Mach Buffet
Sign reversal of Cm! with
increasing angle of attack
•
– Combined effect of Mach number
and changing downwash effects
on horizontal tail
•
•
F-86 Sabre wind-up turn
•
– Turn at high bank angle, constant
load factor, decreasing velocity,
and increasing angle of attack
•
Application of outboard vortex
generators to delay tip separation
(Gloster Javelin example)
•
NACA TR-1237
•
•
Increased angle of attack and lift
coefficient leads and “Stall buffet”
Intermittent flow separation at
transonic speed and “Mach buffet”
The place where they meet = “Coffin
Corner”
Can induce an upset (loss of
control)
U-2 operates in Coffin Corner
Citation X has wide buffet margin
U-2
Citation X
Supersonic Altitude/Airspeed Instability
Supersonic Directional Instability
•
Reduced vertical stabilizer
effectiveness with increasing Mach
number
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
•
•
•
•
•
Inability of XB-70, Concorde, and YF-12A/SR-71 to hold both altitude and airspeed
at high speed cruise
–
–
–
•
Engine unstart
–
–
– Improved supersonic lift
– Reduced excess longitudinal static
stability
•
Phugoid mode is lightly damped
Height mode brought about by altitude-gradient effects
Exacerbated by temperature/density gradients of the atmosphere
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
F-18: vertical stabilizer toe-in
•
Effect of Air Density
Gradient on Lift and Drag
Effect of Supersonic Mach Number
on Altitude/Airspeed Stability
•
Characteristic polynomial for 2nd-order approximation
(
"(s) = s2 + DV s + gLV /VN = s2 + 2#$ n s + $ n
•
2
)
"(z) = " SL e #z , z negative
$"
= #" (z)
$z
Ph
With nominal thrust = nominal drag
#C " C &
#
g
M2 &
DV
(( = "
DV = "g%% TV
%) "
(
VN ( L /D) $ 1" M 2 '
$ CL N '
# M2
&
g
="
+ )( = 2*+ n Ph
%
VN ( L /D) $ M 2 "1 '
!
• Air density variation and gradient
where
CTV = "
CDV =
CTN
, " = #2 for constant thrust
Vn
CDN M
, a = speed of sound
a(1# M 2 )
• Lift and drag sensitivity to altitude variation
#$ 2
VN S /2m = %CLN $(z)VN 2 S /2m
#z
= %LN /m = %W /m = %g
Lz " C L N
!
!
•
!
Phugoid stability is reduced in supersonic flight
#$ 2
2
VN S /2m = %CDN $(z)VN S /2m
#z
%W
%g
= %DN /m =
=
m( L /D) ( L /D)
Dz " CDN
!
!
Effect of Air Density
Gradient on Altitude Stability
•
2nd-order approximation
$"V˙ ' $ *DV
& ) = &LV
% "#˙ ( &% VN
•
•
*g'$"V ' $ T+T '
)
)"+T
+&
0 )&% "# )( &L+T V )
(
%
N(
•
(
"(s) = s + DV s + gLV /VN = s + 2#$ n s + $ n
•
!
•
!
2
)
•
Ph
3rd-order model including altitude variation and density-gradient effects
$"V˙ ' $ *DV
& ) &LV
& "#˙ ) = & VN
&% "˙z )( & 0
%
*g
0
*VN
(
= ( s $ +z ) s2 + 2,- n s + - n
"˙z = #VN "$
2
!
*Dz '$"V ' $T+T '
Lz )& ) & )
"# + 0 "+T
VN )& ) & )
0 )(&% "z )( &% 0 )(
•
!
2
)
)
Ph
Assume that the modes of the characteristic
polynomial are widely separated
Phugoid approximation (“fast”)
(
2
= s s + 2%& n s + & n
"(s) = s3 + DV s2 + ( gLV /VN + VN Lz /VN ) s + VN ( DV Lz /VN # Dz LV /VN )
(
2
" n Ph # gLV /VN + $g
"(s) # s[ s2 + DV s + ( gLV /VN + $g)]
•
Characteristic polynomial reveals a real height mode
= ( s # $z ) s2 + 2%& n s + & n
Substitution for Dz and Lz
%
L (
"(s) = s3 + DV s2 + ( gLV /VN + #g) s + #g' DV $ V *
&
L /D )
Altitude dynamics
Characteristic polynomial
2
!
Approximate Factorization of
the 3rd-Order Model
2
)
% Ph #
Ph
DV
2 gLV /VN + $g
Height mode approximation (“slow”)
&
L )
"(s) # ( gLV /VN + $g) s + $g( DV % V +
'
L /D *
!
Ph
!
&
L )
%g( DV " V +
'
L /D *
(s " #z ) $ s + gL /V + %g
( V N
)
!
!
!
B-52 Mechanical
Yaw Damper
Equilibrium Response of
the Models "x* = #F #1G"u *
• 2nd-order model
$
VN '
$"V * ' & 0
LV )$T+T '
)& )"+T *
& * ) = *&*1 V D
N V )% 0 (
% "# ( &
&% g
gLV )(
!
"V * = 0
"# * =
T$T
"$T *
g
• 3rd-order model
!
!
$ Lz
'
& VN )
& 0 )T
& LV ) +T
$"V *'
&* VN )
&
)
%
(
"+T *
& "# * ) = * LV
L
Dz V * DV z V
&% "z * )(
N
N
!
!
• Combined stable rudder tab, low-friction bearings,
small bobweight, and eddy-current damper for B-52
• Advantages
– Requires no power, sensors, actuators, or computers
– May involve simple mechanical components
• Problems
T#T
T#T
"V =
"#T * =
"#T *
L
DV $ Dz LV /Lz
DV $ V
L /D
"% * = 0
T#T
T#T
"z* =
"#T * =
"#T *
Dz $ DV Lz /LV
&g( D /L $ DV /LV )
*
–
–
–
–
Misalignment, need for high precision
Friction and wear over time
Jamming, galling, and fouling
High sensitivity to operating conditions, design difficulty
B-52 Control Compromises to
Minimize Required Control Power
B-52 Rudder Control Linkages
•
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
gravity
•
Small manually controlled "feeler"
ailerons with spring tabs
– Primary roll control from powered
spoilers, minimizing wing twist
Boeing B-47 Yaw Damper
The Unpowered F4D Rudder
•
Rudder not a problem under normal flight conditions
– Single-engine, delta-wing aircraft requiring small rudder inputs
•
Not a factor for upright spin
•
•
– Rudder was ineffectual, shielded from flow by the large delta wing
•
However, in an inverted spin
– rudder effectiveness was high
– floating tendency deflected rudder in a pro-spin direction
– 300 lb of pedal force to neutralize the rudder
•
Fortunately, the test aircraft had a spin chute
•
•
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
Yaw rate washout to reduce opposition to
steady turns
Stability
Augmentation Systems
Powered Flight Control Systems
•
Early powered systems had a single
powered channel, with mechanical
backup
A4D
Reversion typically could not be
undone
– Gearing change between control stick
and control to produce acceptable pilot
load
– Flying qualities changed during a highstress event
•
Hydraulic system failure was common
•
Alternative to eject in military aircraft
Modification of stability characteristics by feeding back motions to
control surfaces
Inner-loop function downstream of pilot inputs
•
– Pilot-initiated reversion to
"conventional" manual controls
– Flying qualities with manual control
often unacceptable
•
•
McDonnell F-101 Voodoo
A3D
B-47
– Redundancy was needed
Stability Augmentation and
Equivalent Stability Derivatives
•
•
Control with full-state feedback
Open-loop system
•
Feedback(SAS)-plus-pilot control
•
Closed-loop system
"x˙ = F"x + G"u
!
!
"u = "upilot # C"x
"x˙ = F"x + G("u pilot # C"x )
= (F # GC)"x + G"upilot
= F'"x + G"u pilot
!
Early Swing-Wing Designs
•
•
•
Translation as well as rotation of the wing
(Messerschmitt P.1101, Bell X-5, and Grumman
XF10F, below)
Complicated, only partially successful
Barnes Wallis"s Swallow (right), solution adopted
by Polhamus and Toll at NACA Langley
Flying Tail of the
XF10F
Practical Problems of
Variable Sweep
Variable-sweep successor to the F9F-6
Cougar and precursor to the F-14 Tomcat
T-tail assembly with controllable canard and
no powered control
•
•
–
–
•
Principal problems
– Aft shift of the aerodynamic center as
the wing sweep is increased
Like a small airplane affixed to the fin
Pitching moment was inadequate during
landing
• Leading-edge extension ameliorates the
problem
– Complex and heavy structure and
mechanism for sweeping the wing
•
Control issues
– Inability to use ailerons and spoilers at
high sweep
• Solution: all-moving, differential
stabilator
General Dynamics F-111
– Coordination of fuel shift with sweep
– Coordination of sweep with Mach
number
Advanced Designs
•
Fairing of wing trailing edge to
stabilizer leading edge at high sweep
–
–
•
Solutions
General Dynamics F-111
reduces downwash at the tail and
corresponding pitch stability
effectively forms a delta wing
•
•
•
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
Wing glove/leading-edge extension and
outboard rotation point
–
provides greater percentage of lift at
high Mach number and angle of attack
Rockwell B-1
Grumman F-14 Tomcat
Grumman F-14 Tomcat
BAE Tornado
Dassault Mirage G8
Northrop
Switchblade
Boeing 2707-200
Supersonic Transport Concept
•
•
Boeing 2707-300
Supersonic Transport
•
Length = 318 ft; 300 passengers; larger than the B-747
M = 2.7 (faster than Concorde)
•
•
Oblique Wing Concepts
•
•
•
High-speed benefits of wing sweep
without the heavy structure and
complex mechanism required for
symmetric sweep
Blohm und Voss, R. T. Jones ,
Handley-Page concepts
Improved supersonic L/D by
reduction of shock-wave
interference and elimination of the
fuselage in flying-wing version
Variable-sweep wing dropped in favor of more
conventional design
Final configuration had weight and aeroelastic
problems
Project cancelled in 1971 due to sonic boom, takeoff
sideline noise and cost problems
Handley-Page Oblique Wing Concepts
•
Advantages
–
–
•
10-20% higher L/D @ supersonic
speed (compared to delta planform)
Flying wing: no fuselage
Issues
–
–
–
–
Which way do the passengers
face?
Where is the cockpit?
How are the engines and vertical
surfaces swiveled?
What does asymmetry do to
stability and control?
NASA Oblique Wing Test Vehicles
•
Stability and control issues
abound: The fact that birds and
insects are symmetric should give
us a clue (though they use huge
asymmetry for control)
– Strong aerodynamic and inertial
longitudinal-lateral-directional
coupling
– High side force at zero sideslip
angle
– Torsional divergence of the
leading wing
•
Test vehicles: Various model
airplanes, NASA AD-1, and NASA
DFBW F-8 (below, not built)
Next Time:
Second-Half Exam
We Have a Lot to Learn About
Variable Wing Geometry