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7/21/2019 AAE556 Lecture 12
1/19
AAE 556
Aeroelasticity
Lecture 12
Swept wing aeroelasticity
The flexural axis concept
12-1Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
2/19
Purdue Aeroelasticity 12-2
Swept wing static aeroelasticity
Reading Sections 3.1 through 3.6
i Goals Compute changes in aeroelastic loa on swept
wings ! lift effecti"eness
Explain effects using the flexural axis concept
A
#$
C
%
1
1
1
%section
1&1
sin
2
7/21/2019 AAE556 Lecture 12
3/19
Notes on Homework
handed back today
1' (ou must raw accurate) meaningful)
eciphera*le +ree #oy $iagrams ,+#$s-
2' (ou must ma.e your /0 neat an
organie
' (ou must clearly ientify your answers
3' (ou must chec. for imensional
compati*ility5' 4rering euations
Purdue Aeroelasticity 12-3
7/21/2019 AAE556 Lecture 12
4/19
Fridays Homework
roblem 3.3
Purdue Aeroelasticity 12-4
( ) ( ) tan0.75
tan2 2
K Q d e Q d ed c e
WQb QbbK
+ + = +
7/21/2019 AAE556 Lecture 12
5/19
7eminer & 0ing structure iealiation with
aeroynamic loas
82
81
f
%% cos
*
oC
C
springs resist upwar
an ownwar motion
12-5Purdue Aeroelasticity
tancos
on oLift L q cba
= = +
2cosnq q=
7/21/2019 AAE556 Lecture 12
6/19
Static e!uilibrium e!uations
= tant
( ) ( )
=
+
e
bQ
QeKQte
QbQtbK o
2cos
22
n lQ q Sc =
12-6Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
7/19
"e#lections
+
=
eK
Kb
QK
Qb o
2
tan
1
cos2bending
slope
+
=
eb
K
KQK
Qe o
2
tan
1
cos
twistangle
12-7Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
8/19
$i#t e##ecti%eness
+
== tancos
o
on SaqLLift
+
=
2tan1
cos
QbKeQKSaqL oon
Substitute for the angles and
12-8Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
9/19
Fle&ible wing li#t
intermediate result
+= eKbK
KK
QqSaL oo
2
tan1
1
cos
2
tan
=bK
eK
KKQD
n lQ q Sc =
12-9Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
10/19
Final result
cos
1
l o
D
qSc
L QQ
=
Lift on rigid surface
1
cos 1l oD
LqqSc
q
= lift effecti"eness
efinition
12-10Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
11/19
'n e&le wing
=
2
tan1cos
2
0
K
K
e
c
c
b
qqD
2/250 ftlbqo=
let
o
30=
6=c
b1.0=
c
e3=
K
K
12-11Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
12/19
59992592991591995999'9
9'5
1'9
1'5
2'9
lift effecti"eness "s'ynamic pressure
ynamic pressure ,psf-
lifteffecti"eness unswept wing
i"ergence
9 egrees sweep
15 egrees sweep
unswept wing
$i#t e##ecti%eness %s. !
So what(
)hat are the
conse!uences(
12-12Purdue Aeroelasticity
7/21/2019 AAE556 Lecture 12
13/19
Purdue Aeroelasticity 12-13
Fle&ural a&is concept
an attempt to e&plain aeroelastic e##ects
Definition - the line along which the streamwise (or
chordwise) angle of attack does not change when a discrete
load is applied there.
xo
yo
0tan == E
upwar loa
7/21/2019 AAE556 Lecture 12
14/19
Purdue Aeroelasticity 12-14
Fle&ural a&is de#inition
)hy the con#using de#initions(
)hat is the di##erence between #le&ural a&is and elastic a&is(
flexuralaxis
xy
upwar
loa
The air is off
0tan == E
7/21/2019 AAE556 Lecture 12
15/19
Purdue Aeroelasticity 12-15
Fle&ural a&is concept
an attempt to e&plain aeroelastic e##ects
xo
yo
=
o
o
y
x1tan
0tan == E
=
M
M
K
K
0
0
=
o
o
Px
Py
M
M
7/21/2019 AAE556 Lecture 12
16/19
Purdue Aeroelasticity 12-16
Step *1
+ompute angular displacements
=
o
o
Px
Py
K
K
0
01
=
=
K
x
K
y
PxK
yK
KK
P
o
o
oo
o
7/21/2019 AAE556 Lecture 12
17/19
Purdue Aeroelasticity 12-17
,se #le&ural a&is de#inition
0tan! ==
K
y
K
xP ooE
0tan == E
tantan =
=
K
K
y
x
o
o
This result always gi"es us a flexural axis location forwar of
the usual elastic axis' :ncrease wing sweep*ac. rotates the
flexural axis further forwar an opens up the istance
*etween aero loas an the hypothetical flexural axis
=
=
K
x
K
y
PxK
yK
KK
P
o
o
oo
o
7/21/2019 AAE556 Lecture 12
18/19
Purdue Aeroelasticity 12-18
e&le
2=
K
K
1=
K
K
3=
K
K
tantan =
=
K
K
y
x
o
o
K
K
7/21/2019 AAE556 Lecture 12
19/19
Purdue Aeroelasticity 12-19
Summary
i A loa place at the flexural axis creates no
streamwise angle of attac. at that section
i the flexural axis position epens on the
stiffness ratio an the sweep angle
i the flexural axis an the elastic axis coincie
when there is no wing sweep
i the flexural axis is upstream for a swept *ac.wing an ownstream for a swept forwar
wing