Aero Engineering 315
Lesson 37
Longitudinal Static Stability
Lesson 37 Objectives

Draw a stability curve (Cm vs a) for tail and wing
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






Draw a curve for positive, negative and neutral stability
Understand tail and wing contributions to stability
List factors that contribute to longitudinal static stability
State criteria for positive long-stat stability
Identify trim AoA and velocity
Predict changes in stability with changes in tail area,
moment arm, incidence angle, camber, CG, etc.
Define neutral point and static margin
Know criteria for positive long-stat stability WRT CG and
static margin
Moment Contribution from the
Wing
Lw
xw
+Macwing
Recall:
Mac,wing < 0 (for + camber)
and
Lw = CL q S = CLa,wa q S
V
a
C
Zero Lift Line
M cg
(from wing)
Positive slope(+)
Summing the moments and dividing by qSc:
C M = (CLa,w xw/c )a
cg
+ CMac,wing
Form of: y = mx + b
Negative (-)
Intercept for
symmetrical
wing
a
Moment Contribution from the
Tail
at = a - it
xt
Lt
it
at
Symmetric airfoil
St = tail area
V
Zero Lift Line
Summing the moments and dividing by qSc:
CMcg
Lt = CLat a q St
(CLat St xt )
= a
Positive (+)
Sc
intercept
(CLat St xt )
(depending on it)
+
i
t
Sc
Form of: y = mx +b
C
M cg
(from tail)
a
Negative slope (-)
Contributions to Stability Summary
Wing Only Contribution
Result – Wing and Tail
Required Tail Contribution
Total Airplane Moment
Lw
xw
xt
+Macwing
Lt
V
a
V
it
at
Wing
CMcg
Zero Lift Line
Tail
xw
x t St
= (CLaw c - CLat
)a +
c S
CM
a
Wing
Tail
xt St
CMacw+ CLat c S it
CM
0
Effects of configuration changes
Lw
xw
xt
Lt
c.g.
CMcg
xw
x t St
= (CLaw c - CLat
)a +
c S
CM
a
•
•
•
•
•
Move CG Aft
Larger tail (St)
Increased camber
Larger distance to tail
Tail incidence
xt St
CMacw+ CLat c S it
CM
0
Less Stable
More Stable
Decrease CMo
More Stable
Shifts CMo
C. G. Effect on Stability
CM
Center of Gravity moving aft
cg
aa
Bottom Line for stable, trimmed aircraft:
Stable if CMa < 0
Trimmed if sum of moments about CG = 0
Trimmed at usable lift if CM0 >0
Longitudinal Stability—Wing Effects

)
CMcg  CLa ,w xw / c a  CMa c,w
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
Locating wing a.c. farther forward of c.g.
is more destabilizing
To improve stability (lower CMa):



↓ (xcg – xac)
↓ SW
↓ CLaW
Shorter moment arm (wing
back or c.g. forward)
Smaller wing area (hard)
Less efficient wing (do we
really want to?)
Longitudinal Stability—Tail Effects
CM



cg
(CLa,t St xt )
= a
Sc
(CLa,t St xt )
+
it
Sc
Tail aft of cg is stabilizing
Canards are destabilizing
To improve stability (more negative CMa):
o
o
o
 xt Longer moment arm
 St Larger tail
 CLa,t  ARt or
 eot (tail Oswald
factor) or move tail out of downwash
Longitudinal Stability—Tail Effects
it = 0
it > 0
it < 0
Tail incidence angle, it , is the angle between
Chord Line of the tail and Aircraft Zero-Lift-Line
Tail leading edge down is positive
Longitudinal Static Stability Total Aircraft


Most parameters are fixed once the aircraft is
built
C.G. can be moved
 Cargo location
 Fuel location
 Weapons, stores, etc.
 it

changes the trim angle of attack, ae
Variable geometry wings—change cg, CLaW and
moment arm (xcg-xac)
Conventional Tail - Stabilizing
F-22
F-16
Canards - Destabilizing
Su-35
Long-Eze
More Canards - Eurofighter
Neutral Point
The Neutral Point (Xn) represents the c.g.
location such that CMa = 0. It is the center of
pressure for the entire aircraft.
X n
X cg
W
Xcg is the distance from the leading edge of the wing to the CG
Xn is the distance from the leading edge of the wing to the Neutral
Point
Static Margin: Stability Criteria
Non-dimensional difference between Neutral
Point (n.p.) and Center of Gravity (c.g.) where:
xn  xn / c
and xcg  xcg / c
- CM
a
=
n
cg
CL
SM x  x
a

If S.M. > 0 (c.g. ahead of the neutral point) - aircraft is stable

If S.M. = 0 (c.g. at the neutral point)
- aircraft is neutrally stable

If S.M. < 0 (c.g. behind the neutral point)
- aircraft is unstable
Typical Static Margin Values

Transports &
Consumer AC:
0.05 to 0.20

Fighters: 0 to 0.05

Fighters - FBW
Cessna 172
Learjet 35
Boeing 747
0.19
0.13 More Stable
0.27
P-51 Mustang
F-106
0.05 More
0.09 Maneuverable
F-16A (early)
F-16C
X-29
-0.02 Much More
0.01 Maneuverable
-0.33 Stabilized by
AFCS
F-117
Longitudinal
Stability
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NEUTRAL PITCH STABILITY IS EXHIBITED BY THE
AIRCRAFT AT SMALL POSITIVE ANGLES OF ATTACK
THE AIRCRAFT BECOMES INCREASINGLY UNSTABLE
IN PITCH ABOVE 7° AOA
EXCEEDING 14° AOA CAUSES A VIOLENT AND
UNCONTROLLABLE PITCH-UP
7° AOA VORTEX
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VORTEX FORMS AT WING ROOT
ABOVE 14° AOA VORTEX
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VORTEX SHIFTS OUTBOARD AND WING BEGINS TO
STALL AT WING TIPS
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STALL PROGRESSES TOWARDS WING ROOT
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AC cp SHIFTS FORWARD RESULTING IN SIGNIFICANT
NEGATIVE STATIC MARGIN
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STATICALLY UNSTABLE -- OUT OF CONTROL
Longitudinal Static Stability
Summary
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Axes, Moments, Velocities – Definitions
Static vs. Dynamic Stability
Absolute Angle of Attack
Moments and Forces
Static Longitudinal Stability
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Wing Effects
Tail Effects
Static Margin
Next Lesson (38)…
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Prior to class
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Review sections 6.1 - 6.4 and long-stat
stability handout
Complete all homework problems
Read lateral/directional stability handout
In class
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Discuss lateral/directional (roll/yaw)
static stability
Glider Design Project