4 D - 2: Lateral - Directional Stability D - 1

AE317 Aircraft Flight Mechanics & Performance

UNIT D: Stability and Control

ROAD MAP . . .

D-1: Longitudinal Stability & Control

D-2: Lateral-Directional Stability

Brandt, et.al., Introduction to Aeronautics: A Design Perspective

Chapter 6: Stability and Control

6.6 Lateral-Directional Stability6.7 Dynamic Lateral-Directional Stability6.10 Stability and Control Analysis Example: F-16A and F-16C

Unit D-2: List of Subjects

Static Directional Stability

Static Lateral Stability

Dynamic Lateral-Directional Stability

F-16 Stability & Control Analysis

Page 2 of 10 Unit D-2

Lateral (Rolling) and Directional (Yawing) Stability Analysis

• Longitudinal (three DOF) stability analysis: x and z translation and longitudinal rotation (pitching

about y axis) has been done in Unit D-1.

• Another 3DOF stability analysis: lateral rotation (rolling about the x axis) and directional rotation

(yawing about z axis), as well as y translation, needs to be done for complete aircraft stability and

control analysis.

Sideslip Angle

• Instead of angle of attack for longitudinal stability analysis, the sideslip angle plays important

role for lateral & directional stability analysis.

• When an aircraft with good stability yaws, it generates rolling and yawing moments that tend to

return back to equilibrium. These are called, positive lateral (rolling) and directional (yawing)

stability, respectively.

Static Directional (Yawing) Stability

• Positive static directional stability requires that an aircraft, when is positive, generate a right-hand

or positive moment around the z axis to reduce back to zero. This is usually achieved by a

vertical stabilizer. Defining the yawing moment coefficient: ( )NC N q Sb= and slope: N NC C

= ,

the criterion for positive directional stability is: 0NC .

Static Directional Stability


Static Lateral (Rolling) Stability

• The requirement for positive static lateral stability is that an aircraft roll away from a sideslip. In

other words, if an aircraft with positive static lateral stability is sideslipping to the right, so that is

positive, then it will generate a moment that will cause it to roll to the left.

• Because the positive direction for rolling about the x axis is to the right, an aircraft with positive

static lateral stability will produce a negative rolling moment when its sideslip angle is positive.

• Defining the rolling moment coefficient ( )C q Sb=L

L and slope: C C

= L L

, the criterion for

positive static lateral stability is: 0C

L .

Effects of Wing Sweep and Aspect Ratio

• When the aircraft is yawed so that it has a positive sideslip angle (fig. 6.18), its right wing is less

swept (more lift) relative to its velocity vector than its left wing: the aircraft will roll left.

• Another way to look at it, is that the right wing has a higher aspect ratio than the left wing (higher

lift-curve slope, fig. 6.22): the aircraft will roll left.

• Note that the effect of wing sweep on CL

increases as angle of attack and lift on the wings increase.

• Also, the effect goes away when the wing is making zero lift. This is important for an aircraft that

must make vertical climbs, where lift is zero (roll caused by sideslip is undesirable, because if the

aircraft yaws the resulting roll will cause the airplane to make a "corkscrew" type flight path).

Static Lateral Stability (1)

C C

= L L

( )C q Sb=L

L


Wing Placement on the Fuselage

• Fig. 6.23 shows crossflow (sideways component of airflow) around three sideslipping fuselages with

a wing attached at a different vertical position.

(a) High wing: gets an upward crossflow component on its upwind wing and downward component

on its downwind wing (roll "away" from the sideslip: contribute to positive lateral stability)

(b) Mid wing: gets no effect (no net rolling moment and neutral lateral stability)

(c) Low wing: opposite of high wing (roll "toward" the sideslip: contribute to negative stability)

Wing Dihedral Effects

• In fig. 6.24, the wing dihedral angle is the angle in a rear view of the aircraft between its y axis

and a line drawn from the middle of the wing root to the middle of the wing tip.

(a) Positive dihedral: positive sideslip angle results in a negative (roll "away") rolling moment

(contribute to positive lateral stability)

(b) Negative dihedral: opposite (roll "toward") rolling: contribute to negative lateral stability)

Tall Vertical Tail Contributions

• In fig. 6.25, it shows that a tall vertical tail contributes to positive lateral stability. Because its

aerodynamic center is above the aircraft's center of gravity, it generates a negative rolling moment

when the aircraft has a positive sideslip angle. This is a positive contribution to lateral stability.

• In addition, placing an aircraft's horizontal tail on top of its vertical tail (T-tail) will create an effect

of an end-plate on the vertical tail. This will increase the effective aspect ratio of the vertical tail,

and therefore increase its lift curve slope. This will also make the aircraft's rolling moment (due to

sideslip) more negative (contribute to positive lateral stability).

Static Lateral Stability (2)


Three Modes of Dynamic Lateral & Directional Stability

• Most aircraft exhibit three distinctive dynamic lateral-directional modes: spiral, Dutch roll, and roll

modes. Each mode has unique characteristics, and each is influenced in different ways by the same

aircraft features that contribute to static lateral and directional stability.

Spiral Mode

• The spiral mode typically involves a gradual increase in bank angle, causing the aircraft to make a

descending turn. As bank angle increases, the aircraft's node drops father below the horizon, and its

speed increases (death spiral).

• The requirement for positive spiral mode stability is that an aircraft, when disturbed (rolling) from

wings-level flight, should generate a moment that tends to return it to wings level.

• If 2 3NC C

L , the aircraft's static directional stability turns it into the direction it is slipping,

reducing the yaw and preventing its lateral stability from rolling it out of the turn. In this situation,

the aircraft often has a very dangerous (divergent) spiral mode.

• To correct this situation: increase dihedral and/or sweep, or mount the wing higher on the fuselage to

increase CL

. Alternatively: reduce the size (but not the height) of the vertical tail, or move it closer

to the aircraft's center of gravity to reduce NC

.

Dynamic Lateral-Directional Stability


Dutch Roll Mode

• If 1 3NC C

L

, an aircraft's lateral stability is out of balance with and overpowers its directional

stability. When a disturbance causes aircraft to yaw, its powerful lateral stability causes it to roll

away from the yaw before its directional stability can turn it into the sideslip. This triggers an

oscillating rolling and yawing maneuver (side-to-side rolling motion). Because of its motion, the

name came from a famous Dutch ice skater of the time.

• The period of Dutch roll can be shorter than the pilot's reaction time (difficult to correct).

• To correct this situation: decrease dihedral and/or sweep, or mount the wing lower on the fuselage to

decrease CL

. Alternatively: increase the size (and reduce the height) of the vertical tail, or move it

farther away from the aircraft's center of gravity to increase NC

.

Roll Mode

• The roll mode is the aircraft's response to aileron inputs. When the pilot deflects ailerons, the

resulting rolling moment causes the aircraft to begin to roll. As the roll rate increases, the motion of

the wings causes an additional relative wind component that increases the angle of attack on the

down-going wing and decreases it on the up-going wing. This, in turn, creates a moment opposite

the rolling moment created by the ailerons, which gradually builds until the aircraft reaches a steady

roll rate.

• The roll rate (sensitivity) can be adjusted by changing the size of control surfaces (control authority)

and/or software changes of fly-by-wire flight control system.

Adverse Yaw and Spins

• Part of the roll mode is a yaw response that is caused by differential drag on the two wings. The

wing with the aileron deflected trailing-edge-down creates more lift than the one with the aileron

deflected up. This, in turn, creates more drag on the wing with the greater lift. If the wings are long

(i.e., sailplane), this differential drag can create a powerful yawing moment away from the direction

of the roll. This is called an adverse yaw.

• At best, the adverse yaw can delay the turn; at worst (if at high angle of attack near stall), it can push

the aircraft into a rotating stalled condition, called a spin.

• To reduce adverse yaw: use differential ailerons that deflect trailing edge up much more than they

deflect trailing edge down. This works because the trailing-edge-up deflection is so extreme that it

causes flow separation and additional drag to balance the additional drag due to lift of the opposite

trailing-edge-down aileron.

Dynamic Lateral-Directional Stability (Continued)


F-16 Subsonic Flight Analysis

The stability analysis begins by estimating the location of the aerodynamic center of the

wing/strake/fuselage combination, which will be the same for both aircraft.

• For the F-16 wing alone:

Wing taper ratio: tip root 3.5 ft 16.5 ft 0.212c c = = =

Mean Aerodynamic Chord: 2

root

2 1MAC 11.4 ft

3 1c

+ += =

+ and

( )

( )MAC

1 25.875 ft

6 1

by

+= =

+

Wing ac: ( ) ( )o

ac MAC LEtan 0.25 MAC 5.875 ft tan 40 0.25 11.4 ft 7.8 ftx y= + = + =

• Adding the effect of the strake to the wing:

Starke taper ratio: strake tip root 0 ft 9.6 ft 0c c = = =


root

2 1MAC 6.4 ft

3 1c

+ += =

+ and

( )

( )MAC

1 20.33 ft

6 1

by

+= =

+

Strake ac: ( ) ( )o

ac MAC LEtan 0.25 MAC 0.33 ft tan80 0.25 6.4 ft 3.5 ftx y= + = + =

=> These are defined relative to the leading edge of the strake root chord, not the wing root (the strake

root is 8 ft forward of the wing root): strakeac 4.5 ftx = − (relative to the wing)

F-16 Stability & Control Analysis (1)

Stability & Control Analysis Example: F-16A & F-16C

Fig. 6.27 illustrates F-16A (early model) and F-16C (later model): the difference is the stabilator. The increase in stabilator area was made for F-16 to increase pitch control authority. Table 6.3 lists descriptive data for each aircraft. Determine the effect of this change on the F-16's neutral point location and SM, for both subsonic and supersonic flight.


( )wing strake wing

wing+strake

ac ac ac strake

ac

strake

6.5 ftx S x x S

xS S

+ −= =

+

Recall, Unit B-3 F-16 Whole Aircraft Analysis:

Eq(4.32) ( ) ( ) ( )strake

with strake without strake

300 200.0543 deg 0.0579 deg

300L L

S SC C

S

+ += = =

Eq(4.37) ( ) ( ) ( ) ( )whole aircraft wing+body+strake horizontal surfaces with strake1

t

tLL L L L

SC C C C C

S

= + = + − =

( )( )0.0579 deg 0.0543 deg 1 0.82 108 300 0.0616 deg= + − =

Also, the wing-root leading edge is 20 ft aft of the fuselage nose, then: wing+strake wing+strakeac ac20 ftl x= +

( )

wing+strake

wing+strake+fuselage wing+strake

2

ac2

ac ac

whole aircraft

0.005 0.111f f

f

L

ll w

lx x

SC

+ = − =

( )

( )( )

22

2

26.5 ft48.5 ft 5 ft 0.005 0.111

48.5 ft6.5 ft 6.4 ft

300 ft 0.0616 deg 57.3 deg rad

+

= − =

• For the F-16A stabilator aerodynamic center:

Stabilator taper ratio: stabilator tip root 2 ft 10 ft 0.2c c = = =


root

2 1MAC 6.9 ft

3 1c

+ += =

+ and

( )

( )MAC

1 23.5 ft

6 1

by

+= =

+

Stabilator ac: ( ) ( )stab stab stab

o

ac MAC LE stabtan 0.25 MAC 3.5 ft tan 40 0.25 6.9 ft 4.7 ftx y= + = + =

=> These are defined relative to the leading edge of the stabilator root chord, not the wing root (the

stabilator root is 17.5 ft aft of the wing root): ( )stabac 22.2 ft relative to the wingx =

• Center of gravity and distance from stabilator ac to the center of gravity:

( ) ( )o

cg MAC LEtan 0.35 MAC 5.875 ft tan 40 0.35 11.4 ft 8.9 ftx y= + = + =

stabac cg 22.2 ft 8.9 ft 13.3 fttl x x= − = − =

Tail volume ratio: ( )

( )

2

2

108 ft 13.3 ft0.42

300 ft 11.4 ft

t tH

S lV

Sc= = =

• Since the F-16's cgx is specified relative to the leading edge of the MAC, it is convenient (and

common) to express wing+strake+fuselageacx and nx relative to the same reference.

( )wing+strake+fuselage

wing+strake+fuselage

oac

ac

6.4 ft 5.875 ft tan 400.13

11.4 ft

xx

c

−= = =

F-16 Stability & Control Analysis (1) (Continued)


Recall, Unit B-3 F-16 Whole Aircraft Analysis: 0.82 = , then:

( )wing+strake+fuselageac

0.05361 0.13 0.42 1 0.82 0.27

0.0572

tL

n H

L

Cx x V

C

= + − = + − =

• F-16A's SM is, therefore: SM 0.27 0.35nx x= − = − = 0.08−

• Repeating the similar calculation for F-16C yields: SM 0.36 0.35nx x= − = − = 0.01+

F-16 Supersonic Flight Analysis

• Wing: ( ) ( )o

ac MAC LEtan 0.50 MAC 5.875 ft tan 40 0.50 11.4 ft 10.6 ftx y= + = + =

• Adding strake: ( ) ( )strake strake strake

o

ac MAC LE straketan 0.50 MAC 0.33 ft tan80 0.50 6.4 ft 5.1 ftx y= + = + =

• The strake root is 8 ft forward of the wing root: strakeac 2.9 ftx = − (relative to the wing)

• Hence: ( )

wing strake wing

wing+strake

ac ac ac strake

ac

strake

9.1 ftx S x x S

xS S

+ −= =

+

• Supersonic lift curve slope (based on M = 1.5): 2

40.051 deg

1LC

M

= =−

( )

wing+strake

wing+strake+fuselage wing+strake

2

ac2

ac ac

whole aircraft

0.005 0.111f f

f

L

ll w

lx x

SC

+ = − =

( )

( )( )

22

2

29.1 ft48.5 ft 5 ft 0.005 0.111

48.5 ft9.1 ft 9.0 ft

300 ft 0.051 deg 57.3 deg rad

+

= − =

F-16 Stability & Control Analysis (2)


F-16 Supersonic Flight Analysis (Continued)

• F-16A stabilator ac:

Stabilator taper ratio: stabilator tip root 2 ft 10 ft 0.2c c = = =


root

2 1MAC 6.9 ft

3 1c

+ += =

+ and

( )

( )MAC

1 23.5 ft

6 1

by

+= =

+

Stabilator ac: ( ) ( )stab stab stab

o

ac MAC LE stabtan 0.5 MAC 3.5 ft tan 40 0.5 6.9 ft 6.4 ftx y= + = + =

=> These are defined relative to the leading edge of the stabilator root chord, not the wing root (the

stabilator root is 17.5 ft aft of the wing root): ( )stabac 23.9 ft relative to the wingx =

• Center of gravity and distance from stabilator ac to the center of gravity:

( ) ( )o

cg MAC LEtan 0.35 MAC 5.875 ft tan 40 0.35 11.4 ft 8.9 ftx y= + = + =

stabac cg 23.9 ft 8.9 ft 15 fttl x x= − = − =

Tail volume ratio: ( )

( )

2

2

108 ft 15 ft0.47

300 ft 11.4 ft

t tH

S lV

Sc= = =

• Since the F-16's cgx is specified relative to the leading edge of the MAC, it is convenient (and

common) to express wing+strake+fuselageacx and nx relative to the same reference.

( )wing+strake+fuselage

wing+strake+fuselage

oac

ac

9 ft 5.875 ft tan 400.36

11.4 ft

xx

c

−= = =

Recall, Unit B-3 F-16 Whole Aircraft Analysis: 0.82 = , then:

( )wing+strake+fuselageac

0.0511 0.36 0.47 1 0.82 0.52

0.0544

tL

n H

L

Cx x V

C

= + − = + − =

• F-16A's SM is, therefore: SM 0.52 0.35nx x= − = − = 0.17+

• Repeating the similar calculation for F-16C yields: SM 0.61 0.35nx x= − = − = 0.26+

• Fig. 6.28 plots neutral point locations calculated for the F-16C v.s. Mach number and compares them

with actual values. Note that, despite the F-16's relatively complex aerodynamics, the method

produced reasonable good estimates.

F-16 Stability & Control Analysis (2) (Continued)

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4 D - 2: Lateral - Directional Stability D - 1