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G. Leng, Flight Dynamics, Stability & Control
Lecture 5 : Static Lateral Stability and Control
or how not to move like a crab
G. Leng, Flight Dynamics, Stability & Control
1.0 Lateral static stability
Lateral static stability refers to the ability of the aircraft to generatea yawing moment to cancel disturbances in sideslip
V Question : Which direction should theyawing moment act to align the aircraft withthe velocity vector ?
positive sideslip
G. Leng, Flight Dynamics, Stability & Control
1.1 Yawing moment variation with sideslip
Cn
1. Cn should be an anti symmetric function of
2. Cn / ( denoted as Cn ) must be > 0 for lateral staticstability
G. Leng, Flight Dynamics, Stability & Control
Figure 1.1 : F4 Wind tunnel data - yawing moment ( = 0o )
Observe
1. Positive slope
Source : NASA TN D6425
2. Quasi linear variation
3. Effect of rudder
G. Leng, Flight Dynamics, Stability & Control
Figure 1.2 : F4 Wind tunnel data - Cn
Question : What happens at high AOA ?
Source : NASA TN D6425
G. Leng, Flight Dynamics, Stability & Control
1.3 Quantifying static lateral stability
cg
Y
X V
lv
The aircraft yawing moment is:
n = ½V2 S b Cn
Lv
G. Leng, Flight Dynamics, Stability & Control
The dominant contribution to the aircraft yawing moment comesfrom the vertical tail …
ntail = ½ V2 Sv CLv lv
= ½ V2 Sv lv av [(1-) + r ]
Where
av : vertical tail lift curve slope
: vertical tail sidewash factor
G. Leng, Flight Dynamics, Stability & Control
Hence the aircraft yawing moment coefficient is approximately :
Cn = ntail / (1/2 V2 S b)
= [(Sv lv)/ (Sb) ] av [(1-) + r ]
The yawing moment curve slope is
Cn = Vv av (1-)
G. Leng, Flight Dynamics, Stability & Control
1.4 : Interpreting the vertical tail volume ratio
Sv lv
Vv = -------Sw b
Similarly the effectiveness of the vertical tail is related to thevertical tail volume ratio
lv : distance from aerodynamic center of vertical tail to cg
G. Leng, Flight Dynamics, Stability & Control
0.16 0.20 0.17 0.18 0.17 0.13 0.30 0.14 0.26 0.23 0.19
Comments ?
Question : What are typical values for Vv ?
G. Leng, Flight Dynamics, Stability & Control
2.0 FAR Part 23.147 – Directional and lateral control
(a) For each multiengine airplane, it must be possible, while holding the wings levelwithin five degrees, to make sudden changes in heading safely in bothdirections. …with the
(1) Critical engine inoperative and its propeller in the minimum drag position;(2) ….
(b) For each multiengine airplane, it must be possible to regain full control ofthe airplane without exceeding a bank angle of 45 degrees, reaching a dangerousattitude or encountering dangerous characteristics, in the event of a sudden andcomplete failure of the critical engine,
G. Leng, Flight Dynamics, Stability & Control
2.1 Directional stability - One Engine Inoperative (OEI) flight
For OEI flight, the rudder has todeflect to cancel the torque from theasymmetric thrust from the operativeengine.
Is the aircraft now trimmed ?
G. Leng, Flight Dynamics, Stability & Control
The aircraft is rolled towards theoperative engine
Y
Z
G. Leng, Flight Dynamics, Stability & Control
2.2 Coupled rudder-aileron controls for OEI
Torque from operative engine = -T le T
le
Y
X
Fr
lv
D
Rudder Torque = ½ V2 Sv av (r) lv
Assume steady flight T = D
Hence
or rtrim =
G. Leng, Flight Dynamics, Stability & Control
How much should you roll to maintain directional stability ?
Force balance in the Y direction Fr = W sin
The trim rudder force is
Fr = ½ V2 Sv av (rtrim )
Force balance in the Z direction L = W cos
Equating Fr =
tan =
G. Leng, Flight Dynamics, Stability & Control
2.3 FAR Part 25.147 – Directional and Lateral Control
(d) Lateral control; airplanes with four or more engines. Airplaneswith four or more engines must be able to make 20° banked turns,with and against the inoperative engines, from steady flight at aspeed equal to 1.3 VSR1, with maximum continuous power, andwith the airplane in the configuration prescribed by paragraph (b)*
of this section.
Notes
* Two critical engines inoperative
VSR1 : reference stall speed for the specific configuration in paragraph (b)
G. Leng, Flight Dynamics, Stability & Control
3.0 FAR Part 23. 177 - Static directional and lateral stability
(b) The static lateral stability, as shown by the tendency toraise the low wing in a sideslip, must be positive for alllanding gear and flap positions. …
Question ? What’s “raise the low wing in a sideslip” ?
G. Leng, Flight Dynamics, Stability & Control
3.1 Roll static stability – the dihedral effect
In the OEI example, a sideslip disturbance was countered byrolling the aircraft.
Now we are concerned with a roll disturbance and how tocounter it by using the resulting sideslip. ( ! ? )
Z
Y
L
Z Y
L is vectored off
+ve rolldisturbance
G. Leng, Flight Dynamics, Stability & Control
Define Cl = (Cl )/ as the rate of change of rolling momentwith respect to sideslip
Question : For the aircraft to be statically stable in roll, i.e.have a self correcting tendency, what should the sign of Clbe ?
Z Y
Need a –ve rollingmoment to counterdisturbance
Z
Y
Wings returnto levelpoisiton
G. Leng, Flight Dynamics, Stability & Control
3.2 Estimating the dihedral effect
Z
Y
Vb
Vs
Resolve the sideward velocity Vs into components parallel Vb
and normal Vn to the wing.
Consider a +ve sideslip
G. Leng, Flight Dynamics, Stability & Control
Hence the angle of attack for is effectively
Right wing section
Left wing section
V
Vn
G. Leng, Flight Dynamics, Stability & Control
Y
X
For small sideslip, the sidewardvelocity is:
Vs =
For small wing dihedral angle, the normal component of Vs
is :
Vn =
The change in angle of attackis:
V
G. Leng, Flight Dynamics, Stability & Control
Now consider the wing section at location y of chord c(y) andwith dy.
Y
X
yThe incremental rolling moment dl due tothis section and the corresponding one onthe left wing is :
dy
dl = -(½V2 dS CL) x (2y)
=
=
G. Leng, Flight Dynamics, Stability & Control
Hence the total rolling moment due to the dihedral effect is:
l = dl = -V2 a y c(y)dyb/2
0
The dihedral effect is measured by :
Cl = - a 2 y c(y)dy
S b
b/2
0
For a linearly tapered wing, this works out to
Cl = - (a/6) (1+2)/(1+)
G. Leng, Flight Dynamics, Stability & Control
Example : Assessing roll static stability
So dihedral is a “good” thing, right ? What about this …