lecture 5 : static lateral stability and controldynlab.mpe.nus.edu.sg/mpelsb/me4241/l5n.pdf · g....

G. Leng, Flight Dynamics, Stability & Control

Lecture 5 : Static Lateral Stability and Control

or how not to move like a crab

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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

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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

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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

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Figure 1.2 : F4 Wind tunnel data - Cn

Question : What happens at high AOA ?

Source : NASA TN D6425

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1.3 Quantifying static lateral stability

cg

Y

X V

lv

The aircraft yawing moment is:

n = ½V2 S b Cn

Lv

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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

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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-)

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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

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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 ?

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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,

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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 ?

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The aircraft is rolled towards theoperative engine

Y

Z

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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 =

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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 =

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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)

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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” ?

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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

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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

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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

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Hence the angle of attack for is effectively

Right wing section

Left wing section

V

Vn

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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

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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)

=

=

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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+)

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Example : Assessing roll static stability

So dihedral is a “good” thing, right ? What about this …