directional stability
TRANSCRIPT
-
7/30/2019 Directional Stability
1/14
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.
-
7/30/2019 Directional Stability
2/14
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
-
7/30/2019 Directional Stability
3/14
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)
-
7/30/2019 Directional Stability
4/14
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 =
-
7/30/2019 Directional Stability
5/14
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
-
7/30/2019 Directional Stability
6/14
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:
-
7/30/2019 Directional Stability
7/14
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
=
-
7/30/2019 Directional Stability
8/14
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
-
7/30/2019 Directional Stability
9/14
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
-
7/30/2019 Directional Stability
10/14
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
-
7/30/2019 Directional Stability
11/14
Dihedral Effect
v
v
u
Up-moving wing
Down-moving wing
Approximation for the sideslip
-
7/30/2019 Directional Stability
12/14
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
-
7/30/2019 Directional Stability
13/14
Roll moment due to vertical tail
Roll Control
By differential deflection
of ailerons or by spoilers
-
7/30/2019 Directional Stability
14/14
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