1. Lesson 37 Longitudinal Static Stability
Aero Engineering 315
Lesson 37 Longitudinal Static Stability

2. Lesson 37 Objectives
Draw a stability curve (Cm vs a) for tail and wing
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

3. Moment Contribution from the Wing
+Macwing Lw
Recall:
Mac,wing < 0 (for + camber)
and
Lw = CL q S = CLa,wa q S
Zero Lift Line xw V a
C (from wing) M cg
Positive slope(+)
Summing the moments and dividing by qSc:
C = (CLa,w xw/c )a
+ CMac,wing M cg a
Negative (-) Intercept for symmetrical wing
Form of: y = mx + b

4. Moment Contribution from the Tail
Zero Lift Line xt
at = a - it Lt
Lt = CLat a q St it at
Symmetric airfoil
St = tail area V
C (from tail) M cg
Summing the moments and dividing by qSc:
CMcg = a it
(CLat St xt )
S c
Positive (+) intercept (depending on it) a
Negative slope (-)
Form of: y = mx +b

5. Contributions to Stability - Summary
Wing Only Contribution
Required Tail Contribution
Result – Wing and Tail

6. Total Airplane Moment C C xt xw xt StV a
+Macwing Lw xw
Zero Lift Line xt Lt it at V
Wing
Tail
Wing
Tail
C = (CLaw CLat )a CMacw+ CLat it M cg xt c St S xw C M a C M

7. Effects of configuration changesLt xt Lw xw
c.g.
C = (CLaw CLat )a CMacw+ CLat it M cg xt c St S xw C M a C M
Move CG Aft Less Stable
Larger tail (St) More Stable
Increased camber Decrease CMo
Larger distance to tail More Stable
Tail incidence Shifts CMo

8. C. G. Effect on Stability C a Center of Gravity moving aft
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

9. Longitudinal Stability—Wing Effects
Locating wing a.c. farther forward of c.g. is more destabilizing
To improve stability (lower CMa):
↓ (xcg – xac) Shorter moment arm (wing back or c.g. forward)
↓ SW Smaller wing area (hard)
↓ CLaW Less efficient wing (do we really want to?)

10. Longitudinal Stability—Tail Effects
(CLa,t St xt )
S c
(CLa,t St xt )
S c
C = a it M cg
Tail aft of cg is stabilizing
Canards are destabilizing
To improve stability (more negative CMa):
 xt Longer moment arm
 St Larger tail
 CLa,t  ARt or  eot (tail Oswald factor) or move tail out of downwash

11. Longitudinal Stability—Tail Effects
Tail incidence angle, it , is the angle between
Chord Line of the tail and Aircraft Zero-Lift-Line
Tail leading edge down is positive

12. 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)

13. Conventional Tail - Stabilizing
F-22
F-16

14. Canards - Destabilizing
Su-35
Long-Eze

15. More Canards - Eurofighter

16. 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

17. Static Margin: Stability Criteria
Non-dimensional difference between Neutral Point (n.p.) and Center of Gravity (c.g.) where:
- C M a C L =
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

18. Typical Static Margin Values
Transports & Consumer AC: to 0.20
Cessna 172
Learjet 35
Boeing 747
P-51 Mustang
F-106
F-16A (early)
F-16C
X-29
0.19
0.13
0.27
0.05
0.09
-0.02
0.01
-0.33
More Stable
More Maneuverable
Fighters: 0 to 0.05
Fighters - FBW
Much More Maneuverable Stabilized by AFCS

19. F-117 Longitudinal Stability
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
THE FIRST AXIS OF MOVEMENT COVERED WILL BE PITCH.
AT SMALL POSITIVE ANGLES OF ATTACK, THE AIRCRAFT EXHIBITS NEUTRAL PITCH STABILITY.
THE AIRCRAFT BECOMES INCREASINGLY UNSTABLE IN PITCH ABOVE 7 AOA.
ABOVE 14 AOA RESULTS IN AN UNCONTROLLABLE PITCH-UP, HENCE THE FLIGHT CONTROL COMPUTER HAS A POSITIVE AOA LIMITER.

20. 7° AOA VORTEX VORTEX FORMS AT WING ROOT
AT ROUGHLY 7 AOA, A VORTEX ATTACHES ITSELF TO THE WING ROOT. THIS PRODUCES AN INCREASE IN LIFT FORWARD OF THE CG AND DRIVES PITCH STABILITY SLIGHTLY NEGATIVE, MAKING THE AIRCRAFT UNSTABLE.
REMEMBER: 7 AOA IS THE ABORT FLIGHT ENVELOPE MAXIMUM.
VORTEX FORMS AT WING ROOT

21. ABOVE 14° AOA VORTEX
VORTEX SHIFTS OUTBOARD AND WING BEGINS TO STALL AT WING TIPS
STALL PROGRESSES TOWARDS WING ROOT
AC cp SHIFTS FORWARD RESULTING IN SIGNIFICANT NEGATIVE STATIC MARGIN
STATICALLY UNSTABLE -- OUT OF CONTROL
AS AOA IS INCREASED, THE VORTEX PROPAGATES ALONG THE WING’S LEADING EDGE, EVENTUALLY REACHING THE WING TIP NEAR 14 AOA.
AS AOA CONTINUES TO INCREASE, THE VORTEX DETACHES FROM THE SURFACE OF THE WING (DESTROYING LIFT FROM ITS POSITION OUTBOARD TO WINGTIP), AND MOVES INBOARD.
INCREASING AOA MEANS INCREASED PITCH INSTABILITY. THE RESULT IS AN UNCONTROLLABLE PITCH-UP ABOVE 14 AOA.
REMEMBER THE AOA LIMITER FUNCTION OF THE FLCC.

22. Longitudinal Static Stability Summary
Axes, Moments, Velocities – Definitions
Static vs. Dynamic Stability
Absolute Angle of Attack
Moments and Forces
Static Longitudinal Stability
Wing Effects
Tail Effects
Static Margin

23. Next Lesson (38)… Prior to class In class Glider Design Project
Review sections and long-stat stability handout
Complete all homework problems
Read lateral/directional stability handout
In class
Discuss lateral/directional (roll/yaw) static stability
Glider Design Project