AAE556Lecture 7Control effectiveness

AAE 556
Aeroelasticity
Lecture 7-Control effectiveness

1
Purdue Aeroelasticity


Reading

i

Sections 2.15-2.18

– These sections are painfully worked example problems – read through
them to understand principles discussed in class

– Section 2.18.2 has a virtual work example – wait to read this until next
week

i

Skip 2.19 for now (will do next week)

i

Read 2.20, 2.20.1 and 2.20.2

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Our next goal
learn about control effectiveness
i

Demonstrate the aeroelastic effect of
deflecting aileron surfaces to increase lift or
rolling moment

i

Examine the ability of an aileron or elevator to
produce a change in lift, pitching moment or
rolling moment

i

Reading – Sections 2.20-2.20.2

3
Purdue Aeroelasticity


Ailerons are required for lateral stability
They become increasingly ineffective at high speeds

i

Many of the uncertified minimum
ultralights, and perhaps some of the

certificated aircraft, have low torsional
wing rigidity. This will not only make
the ailerons increasingly ineffective
with speed (and prone to flutter), but
will also place very low limits on g
loads.

–

/>lutter.html#flutter

4
Purdue Aeroelasticity


The ability of an aileron or elevator to produce a change in lift, pitching moment or rolling moment is
changed by aeroelastic interaction

L = qSCLδ δ o + qSCLα θ
no α o
M AC = qScCMACδ
Lift
α0 + θ

V

MAC torsion spring KT
shear center
δ0

e
6-5
Purdue Aeroelasticity

aileron
deflection


Herman Glauert’s estimators for CLd and CMACd

The flap-to-chord ratio is

C Lδ =

C Lα

π

(cos

CMACδ = −

−1

E=

(1 − 2 E ) + 2

CLα

π

cf
c
E (1 − E )

( 1− E ) ( 1− E ) E
6

Purdue Aeroelasticity

)


1 DOF idealized model – no camber Sum moments about the shear
center

L
Linear problem (what does that mean?)

e

∑M

sc

= 0 = Le + M AC − KTθ
Remember

αo = 0

7

Purdue Aeroelasticity


Solve for the twist angle
due only to aileron deflection d

c

qSe C Lδ + CMACδ
e

θ=
KT − qSeC Lα
Lift



δ

o

L = qSC L δ o + qSC Lα θ
δ

8
Purdue Aeroelasticity

The aeroelastic lift due to deflection


CMACδ
q
c


1 +
 

qD  e  C Lδ
L = qSC Lδ δ o 
q
1−
qD
Compare answer to the lift computed
ignoring aeroelastic interaction

Lrigid = qSC L δ o
δ

9
Purdue Aeroelasticity






The aileron deflection required to generate a fixed increases as q increases

 1− q 

qR 
Lo = qSC L δ o 

δ
 1 − q

qD 

The required control input is …

Aileron deflection increases as q
approaches reversal

Lo
δo =
qSC L

δ

1− q


qD 



 1 − q 
qR 


Is aileron reversal an instability?
7-10
Purdue Aeroelasticity


The most common definition for
the reversal condition

L flex = 0
Is it possible that I deflect and aileron and get no lift?

We usually use an aileron to produce a rolling moment, not just lift. What is the
dynamic pressure to make the lift or rolling moment zero even if we move the
aileron?

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Purdue Aeroelasticity


How do I make the numerator term in the lift expression equal to
zero?


q  c  CMACδ
L=0, reversal
1 +  ÷

 qD  e  C L
δ

L = qSCLδ δ o
q
1−
qD
L=infinity, divergence
12
Purdue Aeroelasticity


÷
÷
 =0


Solve for the q at the reversal condition

qR
1+
qD

 c  CMACδ
=0
 ÷
 e  CLδ

numerator=0

q = q reversal = q R
e C Lδ
qR = −qD
c CMACδ

or

KT
qR = −
ScC Lα

 CL
δ

 CMAC
δ


Why the minus sign?
13
Purdue Aeroelasticity







Understanding what the aileron does
Two different ways to compute pressure distribution resultants due to aileron

deflection

aerodynamic
center

aileron lift = qSC L δ δo

aileron lift = qSCL δδo

d

MAC = qScC MAC δ δo

δ0

e

(a) aerodynamic center
representation

δ0

e

(b) aileron center of
pressure

14
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Force equivalence
the same moment at the AC with 2 different models

+

− Lδ d = qScCMACδ δ o

Solve for the distance d to find the CP distance from

=

d

the AC
A lift force at d produces the
same result at the AC as a lift
force and moment at the AC

CM δ
d
=−
c
CLδ

e

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Purdue Aeroelasticity

Lδ

δ0


Aileron center of pressure depends on the aileron chord

mid-chord

midchord position

Dist ance f rom aileron ce nt e r of pre ssure
t o airf oil ae rodynamic ce nt e r
(Glaue rt pre dict ion)

Distance
distance
ngths
aftinofchord
1/4 le
chord

0.20

AC

e xample
she ar
ce nte r
location

All-movable surface

0.10

quarte r chord location
0.00
0.0

0.2

0.4

0.6

0.8

1.0

f lap to chord ratio

Aileron flap to chord ratio, E

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Purdue Aeroelasticity


Summary

i

Control surfaces generate less lift because the control deflection creates a
nose-down pitching moment as it generates lift.

i

At a special dynamic pressure (a combination of airspeed and altitude) the
deflection of an aileron creates more downward lift due to nose-down deflection
than upward lift

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Purdue Aeroelasticity