Aero Engineering 315
Lesson 38
Lateral/Directional Static Stability
Important Safety Tip…
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Glider project due next lesson!
Turn in paper copies of
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Cover sheet (name and documentation)
Glider Design Project questions
Spreadsheet (color version – or highlight which, if
any, blocks are RED)
 Design AND chart pages
Keep the rest of the info stuff for the fly off portion
Remember it is INDIVIDUAL EFFORT ONLY
Glider need not be constructed until flyoffs
(beginning Monday, 10 May)
Glider Design Spreadsheet
My Glider Design
B-2—Lat/Dir Stability Challenge
Lat/Dir Stability Objectives
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Define CNb and recognize directional stability
Understand the contributions of the vertical
tail, wing and fuselage to directional stability
Define CLb and recognize lateral stability
Understand the contributions of the vertical
tail, geometric dihedral, wing sweep, and wing
placement to lateral stability
Understand coupling effects of directional and
lateral stability
Sideslip Angle (b)
V
b
Positive b occurs when
the aircraft is flying with
“wind in the right ear”
b is the angle between V
and the aircraft’s x-axis.
Directional Static Stability
(Weathercock Stability)
x
Yaw Moment Coefficient:
+b
C N ,cg 
V
+ Ncg
N cg
q S b
y
Dir.-Stat. Stability Derivative:
slope of CN,cg vs. b curve

C N ,cg
b
For a stable system what sign
should this have?
(+) positive
Directional Static Stability
(Weathercock Stability)
Positive slope indicates DIRECTIONAL STATIC STABILITY
- a positive b generates a positive (restoring) moment
- a negative b generates a negative (restoring) moment
CN,cg
C N ,cg
b
b
ZERO YAW MOMENT
AT ZERO b
0
Vertical Tail Contribution to
Directional Static Stability
+b
x
V Design Considerations (main contributor)
 Vertical tail aft of c.g. is stabilizing
 To increase directional stability
y
+ Ncg
Lv
Top View
Vertical tail further aft
Vertical tail bigger (or add
another)
 Increase tail lift curve slope
(increase ARvt and/or increase evt)
 Ventral fin


Wing/Body Contribution to
Directional Static Stability
x
+b
Lw/b
V
y
- Ncg
- Ncg
Top View
Design Considerations
- Fuselage area forward of the cg
is directionally destabilizing
- That’s why aircraft have tails!
Individual Component Contributions
to Directional Static Stability
CN,cg
Tail
Aircraft
b
Wing/body
Directional Static Stability
at High Mach
TAIL LESS EFFECTIVE
WITH INCREASING
SUPERSONIC MACH
CN,cg
Tail
Aircraft
b
TOTAL ACFT CAN BECOME
UNSTABLE AT HIGH MACH
(EX.: F-15 & F-16, XB-70)
Wing/body
THE YAW AXIS. . .
IS WEAK
IN DIRECTIONAL
STABILITY
 THE
THEF-117A
F-117A
IS WEAK
IN NEUTRAL
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DIRECTIONAL STABILITY
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HIGH PEAKED CANOPY
SMALL RELATIVE VERTICAL STABILIZATION
WEAK YAW STABILITY TO 0.6 MACH (300 KNOTS)
ABOVE
0.6 MACH - UNSTABLE, AND INSTABILITY
 HIGH PEAKED CANOPY
INCREASES AS MACH INCREASES
 SMALL RELATIVE VERTICAL STABILIZATION
AT
WEAPONS EMPLOYMENT MACH, AIRCRAFT IS VERY
UNSTABLE
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YAW INSTABILITY EXAGGERATED BY WEAPON BAY DOORS
Lateral Static Stability
(Dihedral Effect)
Rolling Moment Coefficient:
C L ',cg 
L'cg
q S b
Lat.-Stat. Stability Derivative: slope of CL’,cg vs. b curve 
V
C L ',cg
b
V
y
y
+L’cg
z
Rear View
Top View
Lateral Static Stability
(Dihedral Effect)
Negative slope indicates lateral static stability
- Positive b generates a negative (restoring) moment
- Negative b generates a positive (restoring) moment
C L' ,cg
b
CL’,cg
<0
Zero roll moment at zero b
b
Vertical Tail Contribution to
Lateral Static Stability
V
-L
z
Rear View
y
Design Considerations
- Vertical tail above c.g. is stabilizing
- To increase lateral stability:
 Vertical tail taller
 Vertical tail bigger
 Increase tail lift curve slope
(increase ARvt and/or
increase evt)
Wing Sweep Contribution to
Lateral Static Stability
x
+b
V
V
y
z
y
Rear View
Less lift
More lift
Positive wing sweep is
stabilizing
Top View
Wing Position Contribution to
Lateral Static Stability
Rear Views
High wing placement is laterally
High Wing
V
stabilizing
Mid wing placement is
Mid Wing
neutral
V
Low wing placement is laterally
destabilizing
Low Wing
V
Geometric Dihedral Contribution to
Lateral Static Stability
V
Rear Views
Positive dihedral is stabilizing
Anhedral is destabilizing
-L
Paper airplane example…
+L
Coupling of Directional and
Lateral Static Stability Modes
Directional Static Stability:
Lateral Static Stability:
C N ,cg
C L' ,cg b
b
0
<0
Good aircraft design provides enough stability for both as
well as a reasonable balance between the two:
 C N ,cg

 b

1/ 3 
2/3

C
L' ,cg 


b 
• Too much directional static stability
(compared to lateral)
= bad “spiral mode” (>2/3)
• Too much lateral static stability
(compared to directional)
= bad “dutch roll” (<1/3)
Summary
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Sideslip
Directional Static Stability
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Lateral Static Stability
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Vertical Tail
Wing/Body
Vertical Tail
Geometric Dihedral
Wing Sweep
Wing Position (high/low)
Lateral/Directional Coupling
Next Lesson (39)…
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Prior to class
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Read dynamic modes of motion handout
In class
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Discuss dynamic modes and glider
construction