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STABILITY CRITERIAAND
CHANGING STABILITY
Pilot Induced Oscillations (PIO) Videos
F4B Sageburner PIO (May 18, 1961): Pilot J. L. Felson attempted
highspeed, lowaltitude record run Pitch damper failure led to
severe PIO Destroyed airplane and killed pilot
NASA conducted flight research with F8C (1972 1985) 1st digital
flybywire flight control system w/o mechanical back up Smaller,
more reliable In military aircraft, much less vulnerable to battle
damage Aircraft much more responsive to pilot control inputs
Result: More efficient, safer aircraft with improved performance
and design
Problem
A conventional aircraft is in trimmed, level unaccelerated
flight. The wing is generating 40,000 lb of lift and has a moment
around the aerodynamic center of 20,000 ftlb. The aerodynamic
center of the wing is located at 0.25c, the center of gravity is
located at 0.45c, the aircraft has a chord of 5 ft, and the
symmetrical tail aerodynamic center is located 10 ft behind the
center of gravity. What is the lift generated by the tail, and what
is the weight of the aircraft?

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Conventional Airplane
Ltcg
Lw
Ma.c.
xcg
xac
xt
Mcg = 0 = Ma.c + Lw (xcg xac) Lt (xt)
Moments and Forces
Trimmed Flight Mcg = 0
Straight and Level, Unaccelerated Flight (S.L.U.F.) F = 0 L = W
T = D
Problem Solution
Mcg = 0 = Ma.c + Lw (xcg xac) Lt (xt)
0 = 20,000 + 40,000 (0.45c0.25c) Lt (10)
0 = 20,000 + 40,000 (0.20X5) Lt (10)
Lt = 2,000 lbs
W = L = Lw + Lt = 40,000 + 2,000 = 42,000lbs

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x
yz
(LongitudinalAxis)
(Vertical Axis)(Lateral Axis)
m n
l
Aircraft Axis System
Right hand rulePositive moments
RUDDERELEVATORAILERONRotation classically caused by
N(+ NOSE RT)
M(+ PITCH UP)
L(+ RT WING DOWN)
Moment about Axis(+ IAW RT HAND RULE)
WVU
YAWPITCHROLLMotion about Axis
z(+ out belly)
y(+ out right wing)
x(+ out nose)
Axis
Great Summary!!!
x
y
z
xy
z
x
y
z
Note: Longitudinal stability and control can be studied
independently, but Lateral/Directional stability and control is
coupled (yaw causes roll / roll causes yaw).
Longitudinal StabilityOverview
Absolute Angle of AttackTail Incidence Angle and Tail Angle of
AttackRestoring Moments Moment CoefficientLongitudinal Stability:
Wing Effects and Tail Effects Stability and Balance CriteriaNeutral
PointStatic MarginAltering Stability

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Absolute Angle of Attack, a
a L= =0
Absolute Angle of Attack
The angle between the relative wind and an airfoils zero lift
lineAn airfoil positioned at its zero lift angle of attack has an
absolute angle of attack of zero
a L= =0
L=0zero lift line
chord line
V
CL vs. and CL vs. a
Always at the OriginL=0 depends on camber

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Zero Lift Line
Lt
Vitt
Tail Incidence Angle and Tail Angle of Attack
xt
V
+Macwing
Lwxw
Tail incidence angle, it , is the angle betweenChord Line of the
tail and Aircraft ZeroLiftLine.Sometimes fixedsometimes
moveable.
(Tail leading edge down is Positive)t = (a it)
CM
CMo
BIG PICTUREStability and Balance Criteria in SLUF
a
trim(Trim angle of attack)
C
VNE
Stall Steeper Slope = More stable (stronger restoring
moment)
)x ,x( C accgM f=
Cargo, fuel, stores..
Variable wing sweep, Supersonic effects
CM = f (CMac, it)(Moment Coefficient at zero lift)
Flaps Stick, trim
Restoring Moments
Desired Restoring Moment (Mcg )
Disturbance (+ ) a
V

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Restoring Moments
Desired Restoring Moment (+Mcg )
Displacement ( )aV
NonRestoring Moment and Loss of Control
JAS39 Grippen, Stockholm Airshow 8 Aug 1993 Manufacturer and
customer knew large and rapid stick movements could
cause divergent Pilot Induced Oscillations Considered likelihood
of it actually happening insignificant, so all pilots
weren't informed Red warning light too late in telling pilot
control system saturated for him to
do anything about it
JAS39 Grippen on Landing
Moment Coefficient
Recall how we summed moments about the center of gravity:
M M L x x c L lcg ac ac t t= + ( )We can define this moment in
terms of a coefficient:
C CMqScM M
cgcg
=
The variation of this coefficient with changes in absolute
angleof attack is the key to longitudinal static stability

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Longitudinal StabilityOverview
Absolute Angle of AttackTail Incidence Angle and Tail Angle of
AttackRestoring Moments Moment CoefficientLongitudinal Stability:
Wing Effects and Tail Effects Stability and Balance CriteriaNeutral
PointStatic MarginAltering Stability
Zero Lift Line
V
+Macwing
Lw
Moment Contribution from Wing
xwRecall:
Macwing < 0 (for + camber)and
Lw = CL q S = CL q S
Summing the moments and dividing by qSc:
C = (CL xw/c )+ CMacwing
Mcg Positive slope(+)
Negative ()
C (from wing)M cg
Zero Lift Line
Lt
t =  it
Vitt
Contribution from the Tail
C = 
+ it
Mcg(CLt St xt )
S c(CLt St xt )
S c
Negative slope ()
Positive (+)
C (from tail)M cgSumming the moments and dividing by qSc:
xt
Lt = CLt q StSymmetric airfoilSt = tail area

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Contributions to stability Summary
Required Tail Contribution
Wing Only Contribution
Result Wing and Tail
Longitudinal StabilityTail Effects
it > 0it = 0
it < 0Tail incidence angle, it , is the angle betweenChord
Line of the tail and Aircraft ZeroLiftLine.Sometimes
fixedsometimes moveable.
Tail leading edge down is Positive
Stability Criteria
We want the change in moment coefficient to be opposite the
change in angle of attackLeads to criteria for longitudinal static
stability:
C
NoteC
CMa
M
aM
cg cg< =0 ( : )

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Balance Criteria
We want the aircraft to trim at a positive angle of attackThis
gives the balance criteria:
CMo > 0
In summary, the stability curve must have a negative slopeand a
positive intercept if the aircraft is to havelongitudinal balance
and static stability
Neutral Point
The Neutral Point (n.p.) represents the c.g. location such that
CM = 0. It is analogous to the aerodynamic center for the wing
alone (CMcg = constant as changes).
Xcg is the distance from the leading edge of the wing to the
Center of GravityXn is the distance from the leading edge of the
wing to the Neutral Point
Xcg W
X n
C. G. Effect on Stability
Neutral Point Where CM = 0
CMcg
a
Center of Gravity moving aft and retrim

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Static Margin: Stability Criteria
Nondimensional difference between Neutral Point (n.p.) and
Center of Gravity (c.g.) where:
cgn xxSM =cxxandcxx cgcgnn // ==
If S.M. > 0 (c.g. ahead of the neutral point)  aircraft is
stableIf S.M. = 0 (c.g. at the neutral point)If S.M. < 0 (c.g.
behind the neutral point)
 aircraft is neutral aircraft is unstable
 CMCL
=
Other examples
Badminton shuttlecockArrow
Stability vs.Maneuverability (Control)
Stable Aircraftnot very easy to move Not very maneuverable C5,
C17, B52, Passenger airplanes
Maneuverable Aircraftvery easy to move Not very stable (unstable
in many cases) Require Flight Control Systems
Stability Augmentation System (SAS) Flybywire FCS
F16, F22

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Static Margin: Stability Criteria (2)
Typical values: Transports &
Consumer AC: 0.05 to 0.20
Cessna 172Learjet 3 5Boeing 747
P51 MustangF106
F16A (early)F16CX29
Fighters: 0 to 0.05
Fighters  FBW
.19
.13
.27
.05
.09
.02.01
.33
More Stable
More Maneuverable
Maneuverable with other benefits
Altering Longitudinal, Static Stability
Most parameters are fixed once the aircraft is builtC.G. can be
moved Cargo location Fuel location Weapons, Stores, etc.
it changes the trim angle of attack, eVariable Geometry
wingschange cg, CLW and moment arm (xcgxac)
Longitudinal StabilityRecap
Absolute Angle of AttackTail Incidence Angle and Tail Angle of
AttackRestoring Moments Moment CoefficientLongitudinal Stability:
Wing Effects and Tail Effects Stability and Balance CriteriaNeutral
PointStatic MarginAltering Stability

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Back up slides
Zero Lift Line
Lt
Vitt
Total Airplane Moment
xt
V
+Macwing
Lwxw
C = (CLw  CLt ) + CMacw+ CLt itMcgxtc
StS
xwc
xtc
StS
Wing WingTail Tail
CM CM0
Changing the CG Location
C = (CLw  CLt ) + CMacw+ CLt itMcgxtc
StS
xwc
xtc
StS
CM CM0
LtxtLw xw
Move cg Aft
xw xt
increasesdecreases
CM
CM0
Increases (slope rotates CCW)
depends on trim
c.g.

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Benefits of Canard Trim
Lw
Lw
Lw
Lw
Lt
Lt
Lc
Lc
np
np
np
np
Conventional Fighter X29
Subsonic Subsonic
Supersonic Supersonic
SM > 0 (small)
SM > 0 (large)
SM < 0
SM > 0 (small)
cgn xxSM = Requires > wing lift
Longitudinal Stability:Wing Effects
Mcgwing = Mac + Lw (xcg xacW) = Lw xW + Mac
Note: This is an unstable situation(Positive slope)
CMcg
a trim
Wing Only CM > 0 cg
Lw
Ma.c.
xcg
xac
Mcgwing = (CLw q S xw) a + MacCMcgwing = (CLw xw /c) a +
CMac
xw
Longitudinal StabilityWing Effects
Wing a.c. forward of c.g. is unstable
Decrease instability (lower CM) (xcg xac) Shorter Moment Arm or
move
c.g. forward SW Smaller Wing Area (hard) CLW Less Efficient Wing
(hard)

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Longitudinal StabilityTail Effects
Ltcg
Lw
Ma.c.
xcg
xacxt
Mcg = Lt (xt) = (CLt q St xt)t
CMcg
aPositive Stability
Mcg = (CLt q St xt) (a it)Mcg = (CLt q St xt) a + CLt q St xt
itCMcg = (CLt St /S xt /c) a + CLt St /S xt/c it
Longitudinal StabilityTail Effects
it > 0it = 0
it < 0Tail incidence angle, it , is the angle betweenChord
Line of the tail and Aircraft ZeroLiftLine.Sometimes
fixedsometimes moveable.
Tail leading edge down is Positive
Longitudinal StabilityTail Effects
Tail aft of cg is stablizingCanards are destabilizingIncrease
stability (more negative CM) by xt Longer moment arm St Larger tail
CLt ARt or et
or move tail out of downwash

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Contributions to stability Summary
Required Tail Contribution
Wing Only Contribution
Result Wing and Tail
Quiz
Which of the following diagrams indicates an aircraft that has
met the longitudinal static stability requirement for conventional
("upright") flight but is NOT currently trimmed for balanced,
straight, level, unaccelerated flight? What should you do to trim
the aircraft?
it > 0
Changing Variables*
C M cg
C M cg
CMo _____CM _____trim _____Vtrim _____
CMo _____CM _____trim _____Vtrim _____
Slow Down (c. g. constant) Move c. g. Aft
* In Handout Package
No change