Directional Stability

7/30/2019 Directional Stability

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Directional Stability

AE 430 - Stability and Control ofAerospace Vehicles

In an equilibrium condition (figure (a)),

an airplane flies so that the yaw angleis zero. To have static directionalstability, the appropriate positive ornegative yawing moment should begenerated to compensate for anegative or positive sideslip angleexcursion

Static directional stability

Static directional stability is ameasure of the aircraft'sresistance to slipping. The greaterthe static directional stability thequicker the aircraft will turn into arelative wind which is not alignedwith the longitudinal axis.


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Directional (Weathercock) stability

The main contributor to the static directional stabilityis the fin. Both the size and arm of the findetermine the directional stability of the aircraft.The further the vertical fin is behind the center ofgravity the more static directional stability the aircraftwill have. (This is often called the weather veiningeffect, because it works the same way as a weathervein.)

As mentioned previously all rotational motions of the

aircraft occur around the center of gravity.Directional stability refers to motions around thenormal axis.

Stable/unstable aircraft


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This figure shows the variation of yawing-moment coefficient

with sideslip angle. This positively sloping line indicates a

directionally stable case.

Wing contribution to directionalstability

A wing produces two effects that give a yawing moment with

sideslip. The important one is due to sweep-back angle, andthe other minor effect is due to geometric dihedral.

Directional and lateral effects of wingsweep due to sideslip

The second effect,

due to dihedral,results from a tilt of

the lift vectorwith sideslip.

(Both effects are stabilizing)


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Lateral Effects

Wing Dihedral

Dihedral effectsdue to sideslip

Sideslip producestwo importanteffects other thanthose mentioneddirectionaleffects:

rollingmoment

side force

Wing Sweep

Fuselage

Contribution to directional stability

Fuselage and enginenacelles (in general aredestabilizing)

wf

fs f

n n RL

w

S l

C k k S b =


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Contribution todirectional stability

Wing-body interference factor

Reynolds numbercorrection factor

Vertical tail contribution

vv L v v vY C Q S =

v = +

Sidewash due towing vortices

v

Y

v


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Moment produced by a side force

( )v v

v v v v L v v v v L v vN l Y l C Q S l C Q S = = = +

( ) ( )v v

v v vn v L v v L

w w

N Q SC l C V C

Q Sb Q Sb = = + = +

v vv

S lV

Sb=

vv

w

Q

Q =

Vertical tail volume ratio

Dynamic pressure ratio

Contribution vertical tail to directionalstability

1v v

n v v L

dC V C

d

= +

4

1 0.724 3.06 0.4 0.009

1 cos w

v wv w

c

S S zdAR

d d

+ = + + +

+

USAF Stability and Control Datcom:


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Some comments The moment associated with yawing and rolling are cross-coupled,

i.e., the angular velocity in yaw produces rolling moments and viceversa. If a pilot steps on a rudder pedal causing the aircraft to yawone wing will advance and the other will retreat. The faster movingwing produce more lift than the other which will cause a roll in thesame direction as the yaw. This will be exaggerated by wingdihedral.

At a normal flight, i.e., steady rectilinear symmetric motion, all thelateral motion and force variables are zeroes.

There is no fundamental trimming problem: control surfaces(ailerons and rudder) would normally undeflected.

Lateral control provides secondary trimming functions in the caseof asymmetry.

Effects of CG movement are negligible on lateral and directionalstability

Due to cross-coupling effect, (e.g., the rolling motion will causesideslip), we investigate the directional and lateral effects ofsideslip.

Directional Control

Rudder

(+)

Positive rudder

deflection, producesa positive side force, that

will produce a negativeyawing moment

v vN l Y=

vv L v vY C Q S =

vLv vn v r

w w r

dCQ SNC l

Q Sb Q Sb d

= =

vL

n v v r

r

dCC V

d

=


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Requirements for Directional Control

Table from R. Nelson book Adverse yaw

Crosswind landings

Asymmetric power condition

Spin recovery

Rudder control effectiveness

v

r r

Ln n r n v v

r

dCC C C V d

= =

v v

v

L L vL

r v r

dC dC dC

d d d

= =

A 747 lands in a very strongcross-wind


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Adverse Yaw

Roll-Yaw Coupling

Asymmetric aileron deployment produces asymmetric dragAsymmetric drag produces adverse yaw

Rudders required for coordinated turn

Static Roll Stability

The roll moment created

on an airplane when itstart to slip depend on:

Wing dihedral angle

Wing sweep

Position of wing on the

fuselage

Vertical tail


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Figure (a) shows a head-onview of an airplane that has

dihedral where the wingsare turned up at somedihedral angle to thehorizontal. If a disturbancecauses one wing to droprelative to the other (figure(b)), the lift vector rotatesand there is a component ofthe weight acting inwardwhich causes the airplane tomove sideways in thisdirection. When wings havedihedral, the wing towardthe free-stream velocity,hence the lower wing, willexperience a greater angle

of attack than the raisedwing and hence greater lift.There results a net forceand moment tending toreduce the bank angle(figure (c)).

nv

u = sinnv v=

Dihedral Effect


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Dihedral Effect

v

v

u

Up-moving wing

Down-moving wing

Approximation for the sideslip


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Effect of wing placement on lateral stability -Fuselage contribution to dihedral effect

Wing sweep effect on roll stability

The windward wing (less

effective sweep) willexperience more lift than

the trailing wing. The resultis that the sweepbackadds to the dihedral effect

On the other hand, sweepforward will decrease theeffective dihedral effect


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Roll moment due to vertical tail

Roll Control

By differential deflection

of ailerons or by spoilers


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Roll Control

By differential deflection of

ailerons or by spoilers

( )LiftL y =

Ll

C Qcydy C cydyC

QSb QSb Sb

= = =

a aa

dC C C

d

= =

2

1

2w

yL a

ly

CC cydy

Sb

= 21

2w

a

yL

ly

CC cydy

Sb

=

Control

power

11

2rc c y

b

= +

Tapered wing

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Directional Stability