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TECHNICAL NOTE
D-344
EXPERIMENTAL
DETERMINATION
DISTRIBUTION
ON
OSCILLATING
MODE
FOR
i'
IN THE
FIRST
MACH
NUMBERS
0.24
By
Henry
Moffett
]
WASHINGTON
TO
THE
PRESSURE
WING
BENDING
FROM
1.30
C. Lessing,
Jotm L. Troutman,
and Gene P. Menees
Ames
NATIONAL
OF
A RECTANGULAR
AERONAUTICS
Research
Field,
AND
Center
Calif.
SPACE
ADMINISTRATION
December
1960
TN
D-344
lit
¥
NATIOHAL
AERONAUTICS
A}FD SPACE
TECN}TICAL
L_{PERIMEHTAL
NOTE
DETERMINATION
DISTR]mUTIO_
ADMINISTRATION
D-344
OF
TI{E PRESSURE
ON A m_CTm_CULmR
0SCILIATING
HODE FOR
WING
IN THE FIRST BE_{DING
MACH I,YJHBERS FROH
o.24 TO 1.30
By
Henry
C. Lessing,
Jo_m L.
and Gems P. Menses
Troutman_
SUMMARY
The results
of an experimental
investigation
in a _Tind t_unel
to
obtain
the aerodynamic
pressure
distribution
on an uns<_:_pt rectangular
wing oscillating
in its first symmetrical
bending
mode arc pros<ntel.
The- wing _<as of aspect
ratio 3 with 5-percent-thick
biconvex
airfoil
sections.
Data wer_ _ obtain_d
at 0 ° and 5 ° angle
of attack
in th_ _ch
n<_b_r
range from 0.24 to 1.30 at Reynolds
nm_0ers_
depending
om the _[%ch
nmnber_
ranging
also a function
at
H : 1.30.
from 2.2 to 4.6
of _eh
_mm])er_
million
ranged
per
from
The most important
results
presented
of the surface
pressures
generated
by the
data obtained
trader static
conditions
are
foot.
The reduced
fr<'quenci_s_
0.4(i at
H = 0.24 to 0.i0
are the chord<else distributions
bending
oscillations.
Similar
also presented.
The results
sho_,rthat th<o phenomena
causing
irregularities
in the static pressure
such
as three-dimensional
tip effects_
local
shock waves_
and separation
effect<:,
_¢ili also produce
significant
changes
in the oscillatory
pressures.
The
experimental
,data are also compared
with the oscillatory
pressure
distributions
comput<,d by means
of the most complete
linearized
theories
available.
The comparison
shows that subsonic
linearized
theory
is adt,quat_
for predicting
the press-0a_es and associated
phase anglus
at io_,_subsoI_ic
speeds
and io_{ angles
of attack
for this -_ing.
Ko<_ever_ the appearance
of
local
shock _aves
and flow separation
as the Mach number
and anglo of
attack
are increased
causes
significant
change s in the experimental
data
from that pr<_dicted by the theory.
At the low supersonic
speeds
covered
in the experimental
investigation,
linearized
theory
is completely
inadequate,
principally
because
of the detached
bo}_ _ave caused
by the
_ing thickness.
Some indication
of wind-tunnel
resonance
effects
on the experimental
data appear
to be
re sult s.
_as noted;
ho_ever_
the
confined
to the
H : 0.70
INTRODUCTION
Flutter is conventionally defined (e.g._ ref. I) as a self-excit<d
oscillation
resulting from a combination of inertial,
elastic, oscillatory
aerodynamic dmmpins, and temperature forces. In combination_ these forces
can result in Rustable motion (i.e., flutter)
which leads to mild or
extremely severe structural failures.
It is evident, then_ that the subject or flutter
is an extremely complex one and a reliable analysis can
be madeor a specific design only through the use of the most complete
information about the struct_ire, dynamics; and aerodynamics.
The present paper is concerned _,_ith only one of these fields - the
oscillatory
aerodynamics. The basic tool of the flutter analyst as regards
aorodynmnics is theory. Very little
has been done v_ith the application of
<_xperimental data to flutter calc_lations; instead_ exp_:rimental results
haw been used chiefly to evaluat< th< accuracy of the theoretical methods.
Th,_seevaluations have shoT:,a_
that the use of t_ro-dimensional theory applied
iK a strip analysis_ while yielding good r{_sults for w_ngs of high aspect
ratio, lea_ to inaccurate results in the case of lo<r aspect ratio surfaces.
This fa<rt has led to the developmc_utof three-dimensional theories_ t_ro
of the most complete beiug the subsonic ke,"n<,l-fu_ction method of Watkins,
R_uya_ and Woolston (rer. 2)_ and the supersonic linearized theory of
Hi_es (t_<_£.3), an analytically
_ct
tpJatm_nt api_licable only to certain
The expc_rimental
results
used to evaluate
theories
in the past have
teen
!.<,rived chiefly
from rigid wings ex<_cuting flapping_
pitching,
or
pltuK_ing oscillations
at subsonic
sp<_eds (e.g.,
refs. 4.. 5, a_<d 6).
Moll_Christensen
(ref. 7) has obtained
th,_ oscillatory
press<_re amplitudes
at
c_rtain
points
on such vrings at transonic
spot, is.
To date_ only one
experimental
investigation
has b<,,u_ r_norted
:,_ith a, <¢ing perfomning
elastic
defozmlations
(ref. $); this investigation
was conducted
only at low subsonic
speeds,
however_
and
as yet no similar
r{k_sults are avaElal01e for
transonic
and supersonic
speeds.
The pz_loosc _ of the present
investigation
was to develop
a research
t<,cbmique by means of which
the oscillatory
pressures
<_xisting on a
thre_-dimensional
wing perfo_n, ing elastic
deformations
could be obtained
throughout
the subsonic,
transonic_
and supersonic
speed ranges_
and to
compare
the exicerimental
results
with those of the most complete
theories
avai lab !e.
NOTATION
The follo_ing
definitions
are for significant
be found
in the main body of the report.
Notations
appendices
are defined
therein.
A
aspect
ratio
b
semichor£
notations
which will
found only in the
A
3
>
h
Cpu_Cp
Z
static-pressture
coefficient
on
Pu
- Pc,_
q
respectively,
Cp
static
- Poe
P_
q
_
lifting-pressure
complex
amplitude
upper
coefficient_
of
oscillatory
and
lo',,r<_r
Cp%
- Cpu
pressure
surfaces_
coefficient
per
CP_ h
P
unit
q_h
phase angle bet_,,reen oscillatory
lifting-pressure
coefficient
magnitude
and wing-tip
bending
magnitude,
positive
for
pressure
leading
bending
displacement
_ dog
_h
A
3
5
4
_h,
C _@h _Cm<sh
oscillatory
mid-chord
section
per
lift
unit
and
moment
coefficients
about
_h
7h,Thm
phase
angle bet_,_een wing-tip
bending
displacement
magnitu_ie
and magnitude
of oscillatory
lift or moment
coefficient_
positive
for lift or moment
coefficient
leading
bending
displacement,
deg
f
oscillatory
K
turmel
h
displacement
positiw_
)
frequency,
height_
cycles
of mid-chord
do_¢n
line
at
any
imaginary
part of a quantity
- that
phase _rith the wing-tip
velocity
real part of a quantity
- that
with the _.ring-tip displacement
k
reduced
H
Mach
P
static
P
complex
amplitude
_,rin6 surface
q
unit
time
ft
Re( )
p!
per
frequency_
spanwise
component
component
station_
_¢hich
_,rhich is
is
in
in phase
_b/V
number
pressure
at wing
of
surface
oscillatory
complex
_aolitude
of oscillatory
connected
to orifice
at which
free-stream
dynamic
pressure_
pressure
at
pressure
at
P
exists
pV£/2
any
orifice
pressure
on
cell
I,
r
chord_ise
R
Reynolds
t
time
T
m_<imumwing
V
strain-gage
number
chor_{ise
leading
supply
ratio_
or mean
magnitude
o£
bending_
voltage
positive
value
of
oscillatory
phase
between
magnitude
frequency
(')
d( )
dt
Additional
of
subscripts
root
velocity
do_,mstream,
angle
wing
of
angle
of
measured
from
wing
root
attack_
of
deg
attack
ratio_
quantity,
which
P' , positive
oscillation
at wing
tip
due
to
may
association
with
forward
r
association
with
rear
be
for
P
leading
P' , deg
5 2_f
T
_-_
I ( ) 12 =
f
i
free-stream
from
P and
_ring thickness-chord
L
accelerometer
radians
density
circular
to
IP'l
Iml
--_--_
angle
or
measured
free-stremn
tO
mid-chord
ft
distance,
edge
amplitude
static
_ing
thickness
distance
C_
from
per
span<_ise
Y
_h
distance
[Re(
attached
+ [:h(
)]2
to
)]
preceding
2
quantities
accelerometer
accelerometer
component
o£
or resolver
a quantity
rotor
in phase
component
of
or resolver
a quantity
rotor
out
_{ith bending
of phase
with
displacement
bending
displacement
T
value
of
a quantity
at
U
value
of
a quantity
on upper
Z
value
el' a quantity
OO
frec-stresm
on
}rinc ti_
wing
stu_face
lo:_er _Tinc surfac_
condition
FXPERI}4F2FfAL
Test
I]'_ESTIGATION
Facility
A
3
5
4
The experimental
investigations
_ere conducted
in the Ames
by
6-foot
supersonic
:_ind turmel_
_hich
is of the closed-r<,_tumu_
varia]}L pressure
tk-pe capable
of furnishing
a continuous
Hmch nm_?o,:r range
from
0.70 to 2.20 by means
of an asymmetric
sliding-block
throat.
This t<uu_l
can also be o oerated
at
M = 0.24 by halving
the available
coml'_r<sso±_drive po<_Ter. In order to operate
at sonic
sneed and to obtain
more nearly
ur_ifolnn flo_, the test-section
floor and ceiling
_{ere nerforated.
Test
from
Conditions
The pressure
distributions
vTere measured
over
0.24 to 1.30.
The _ing _as oscillated
at its
a }_%ch ntmlb<_r raw,c<_
first bending
fr<_quency.
f -- 26.5 cycles
per second_
at a tip amplitude
of approximately
0.2 inch.
and the resultin_
reduced
frequency
range _ms from 0.i0 to 0.4_ .
The
maximum
available
total _ressure
_,_asmaintained
at each _izch nmnb _r and
provided
Reynolds
angles
of attack
numbers
from 2.2
were 0 ° and 5 ° .
Description
to
4.6
million
per
foot.
The
_ing
of Apparatus
Model.The model consisted
of a semispan
tms<_ept, rectang:ular
_ri:ig
_Tith an effective
asoect
ratio of 3.
(The _<ing _as provided
,,<ith a re<rob !
tip _{hich _as not included
in computins
this aspect
ratio.)
The airL'oil
consisted
of a biconvex
circular-arc
section,
5 percent
thick.
_ith :_har:_
leading
and trailing
edges.
A photograph
of the model
mount<]
in tb
t_ t
section
is sho_n in figure
l(a) and a dra_ing
of the model
giving
]_:rtin _
dimensions
is sho_m in figure
l(b).
The _<ing ,,_asmachined
from forginss
of
SAN 4130 st< :l _;hich '_a_r
heat treated
to approximately
Roc}_;ell C-3i_ hat<[mess.
The u_u_i_' a_
!o';,r
surfaces
_rere machined
separately
and mated
at the chord line to ]<roiuc, _
a monocoque
structure
:<ith integral
spanwisc
stiffening.
Figur: , l(c) [:_
_j
a l)hOtograph
of a representative
the stiffeners
and the resulting
cross
section
showing
interior
partitio_in_.
and
two
of the
screws
l(e) show the interior
sides
halves
_rere held together
by
the location
of
Figum;es l(d)
upper and lo_rer surfaces.
through
the root section,
The
stiff-
eners,
and leading
and trailing
edges.
The shear loads due to _ring deicer marion
were carried
by do_rel pins at the root and tip, together
with the
shear blocks
set in the soan_rise stiffeners,
_Thich ar_ visible
in
figum,_e l(e).
_ing-drive
mechanism.The drive mechanism
oscillate
in the desired
stz_actural
deformation
completely
within
the _ing structure
in
Lances
_<ith un]eno<_ aerodynamic
effects.
to force the _ring to
mode should be contained
order not to create
flow disturA unique
system
satisfying
this
requirement
_,_asdeveloped
for the present
investigation
and consisted
of
two spars extending
the full spanwise
length
of the wing inside
the
channels
sho_s_ in figures
l(d) and l(e).
Each spar consisted
of an upper
and lower half_
riveted
together
at the wing tip as sho_n in sketch
(a)
and constrained
to remain
in contact
over their
length.
Contact
with the
F
Tunnel
wall -__
Sketch
(a)
ring occurred
only at the tip and 50-percent
semispan
station.
The lo_er
half of each spar v_s restricted
from spanwise
movement
by being pinned
at the wing
root support
in the tunnel
wall.
The upper half of each spar
extended
through
the tunnel
wall and was attached
to an electromagnetic
shaker
_hich
applied
a harmonically
varying
force,
F.
The resulting
alternating
tension
and compression
in the upper
spar half,
coupled
with
the alternating
compression
and tension
in the lower spar half_
caused
the
spar to deflect
in a manner
analogous
to that of a bimetallic
strip.
resulting
forces
on the two bearing
points
then forced
the wing to
oscillate
in its first bending
mode, when the frequency
was properly
The
adjusted.
The bearing
points
were chosen
from the results
of an analysis
indicated
that not only first bending
but second
bending
and first
second
torsion
modes
could also be forced by the one drive
system.
practice,
ho_ever:
it was found
driven
with
sufficient
amplitude
The
wing
and
associated
plate
sho_
in figure
l(a),
An inflatable
seal prevented
that these
to obtain
drive
mechanism
additional
data.
were
modes
mounted
which allowed
the angle
leakage
of atmospheric
could
on the
which
and
In
not
be
circular
of attack
to be varied.
air around
the plate
A
1.
q-
into
to
the
test
suction.
seal
the
is,reties
throuF;h
the
use
pressure-c,_ll
sure
at
tight
of
of
root
plugs
by
for
the
The
span
_¢ing
dJstr_but_
at
i along
th
the
<g_r_
fi{%r_
in
sta6g<_r<,@
or'des
%o
sisting
flat,
•,,;as installed_
and
l(e).
prow_:d
and
The
to
Thu
reel
b_
particular
at
=
O.O_s
:u,ritch_
r)r<:ssur<-s
these
each
is
of
a
f:n,d
,_m_
_01astic
or
slut[ '.ts%rl<rou;],ky. ]_h_
c_'a_Lly
avaiiabl<
t}<o< ,.
The
dif;.'_
compl<_t<
to
iut_n:L_ation
of
pro s<,ntiy
.'_',or
that
<rS.t
a_
d_nt
pressurL,
r<:sult£!d
suppl
th_
held
sure
(I.D.
the
to
th_
:
face
interior
or
it
S
limited
th_
rangu
of
of
the
in
to
pr_:v,nt
or
the
in
the
eel!
diaphra_.
,:]-inch
i.u.)
reference-pressure
was
i, nNth
motu_t<_d
outlet
of
in
of
rLm,
a
J
a
each
r
used
%]i{: pr_s-
LLlrh'ac
:rer{
's,
straln-gas,:
bc
th_
fi]u.:
duscrib<_£
Sca_ivalv_
%,,re :Ln:i<_cn-
mod_[ficatlo'n
to
culls
might
coHncr-
requires
to
-D
s[r4:k(
"_fl_onded
b_'
hous,
Scaniva!w.
£toJL
d
in
si]]]u]_-
thu
arran(_:_.mcnt
<_or
striLqli:Nth.
_or,:ssurc
to
For
of
lo?p
_)]'essu_,fL_
{if[_!ai
4
pressure
to
r_:vis:_, th_
l(f)
_quali_L
c<_l!s
_ the
r,u:rnos
this
sta_nlcs_-sto<'l
top
tb
m o:l !
acco_m_o,iat<_
pressure=
necessary
the
nt
a_;'__bn,,_l.
pressur_
to
to
hish-s_sitivity
eL'
the
ful
the
"n
it
a
_;q_
i'.
I(L 0 .
:<:in{;through
ali:i
m_ thod
mo<iiY[
loss
s
£__1 ,_i@2£l..t
: l(a),
of
th_
f'igurc
two
mad_
_:ach
of
_,,rasus_
,'ly_usuni<,dats_
sides
0.OO<%
each
t]Yi
co_i-
i!nch
linc_
oscillatory
in
ill
rn%t_:
ntly
oi' the:
:rhea;
_]
ntation,
]/s
(](:_,,,
[c<s
:b_ order
b,,_- s _cn
diam<t<rs
:L:h or<L_r
or_ both
consisting
all
_ and
manuYacturer
can
ai_t_
!'or thi:_
l.lp]m_sr
c_d_ls
<_omF,ouonts
As
c_lls.
The
Thu
tb_
she<,
electromechanical
pr{:ssur_-s<n_siR
d_%:,rmiriatiou_
L{;_lby
consta_Lt
obtaining
two
ak
manifold
%h(
J_l a_l arraTl(%:9_l<N_t _,Nlich n_:rmitt<_d
taneously
i01ock.
its
(Th
a_s
UlI_iSS ,'re]'{US,<_d ill OrLb:::" t}]at
Of
s_mli-
rurrsc_.
](b).
i_lstrmn,
4_} !;rrssure
pressure
lower
,: -st, _ I t u_J:)in_:
availablu
_ S<OLkciflcatiou
anti
re, _t
o;_ _:ach
o1' fiEw_"
_:_ip_:d :)ut
furnish
-._kug.
pO-p,
set
of
_,,_[n_;(_ith.-r
,_ :._r
:,;,_r_ suL_,,qu
sta[n]_
uxpos[ng
such
r<;.mt'al
eL'f
cells
,:Lcslgn_,l
to
orific
for
and
_]l:_<_J rN;s. fr,9]!! COl'rcspo_l,:]._.ii[<;_'ii'ic::_ on
b:
<.<trek:
This
_ c_lls
orific_
_,To
s
pr,_,ssu_:_,-
mowm..nt
upp_r
and
f;f:R!'>
photographrr
tests
co_mmcrcialiy
_llsi]l[; t_<)vi(:c.
in
th,
r ',_,m<;nt on
r th_
both
nt,
pr_ssur_
_._ th_
s{_qu<nrtialAy
_ rmit
stations
stat_ol_s.
_.;hich _,.;asconnected
This
capal01<
th_'s,_
orific_
uar!y
[nsi(]_
in.)
Scm_lvalv<-.
iu
on
yO-pcrc
s, ction
i_r_-
o_ciilit_.ug
i_str_ncntatlon
pr_s_ur_,
u',n'_lisbl:
pressure
root
visib-L:
rubb
to
d, slgJl<d
th<_
st
lines,
or
ov
m_asured
r_sistanc__
is
l,'a:i-throu_;hs
(I.D.
at
electrical
of
t_-_bulatod
the
system
of
was
shape
of
and
the
orific,_
gask<_ts
-.raLztSS'_,r
t
atmospheric
O.030-i_._ch-dism=t<r
uach
sho-,m
aud
th,
car_
the:
az_,l asexual
rrom
distribution
was
T_n
acco_mnodato
pressur_-measuring
s_ab.d
90-percent.
at
ar_
in
instrumuntation
root.
chord
<;rli'ic{: positions
orific<:s
the
_reat
diaphragm:
prcssuru
distribution
at
that
stream
surfacus
rot
tb,,_ d<_f]_ection
pressure
and
was
rubber
wing
the
approximat_ly
stations
Th,
The
and
matins
conn,<'ctions_
flexiblu
information:
dynamic),
all
h_r{
fr_u
lead-throughs
cl_ctrical
typos
of
on
interior
sold__rud
two
surfacus
the
The
Instrmncntation.-
3
5
4
noted
from
r cement
mating
surfaces;
and
_,rin[,;-driv<,
_ mechanism.
A
b:
wing
rubb_
all
the
or
should
mou1_tii_gs.
the
static
Tt
thu
a bl
h)qx<!,::!m_ic
the'
c___ll motu_ted
t_,:
in
used
_r, s_<i-i'ilt, r
t\fi01n/:
an<l _,_-asconk,
[is
:_d_n
static
block
as
ct::[
to
sho-,nL
in
figure
l(f).
This
length
of bleed
tubing
_as
found
to
furnish
an
acceptable
response
time to a representative
step change
in static
pressure •_hile satisfactorily
filtering
out the oscillatory
part of the
pressure
signal.
When the static-pressure
data were obtained,
one less
sensitive
pressure
cell was used in each block_
and it was referenced
to
the static
pressure
at the tunnel
wall.
This provision
is also indicated
diagramatically
in figure
l(f).
Because
of the chordwise
rigidity
of the wing it was assumed
that
any oscillatory
motion
_as completely
determined
by the plunging
and pitching oscillations
of each of its cross sections,
it was further
assumed
that the first symmetrical
bending
and torsion
modes of oscillation
could
be adequately
dete_mined
from a description
of the motion
at four span_ise
stations.
Accordingly_
eight cantilever-beam-type
accelerometers
were
located
in cutouts
along the extreme
fore and aft stiffening
spars at the
95-, 75-, 55-, and 35-percent
semisp_1
stations,
and the oscillating
wing
motion
was determined
from their
i1_ependent
outputs.
All accelerometers
were bolted
to the stiffeners
of the low_r _ing
panel
and are visible
in figure
l(e).
T_o complete
strain-gage
bridges
were bonded
to each tip accelerometer
beam,
permitting
both acceleration
components
to be measured
simultaneously
at that station
while
only one
such bridge
was bonded
to each of the inboard
accelerometer
beams.
Thus_
for the inboard
accelerometers,
the method
for component
determination
descri%ed
below
simply
required
sequential
determination
of one component
and then the other.
The electrical
leads from the accelerometers
were
run
along
the
wing
cavities
to
cannon
plugs
in the
root
section.
All stainless-steel
tubing
and <_iring <{as bonded
to the _{ing interior
_ith PRC 1221 cement
which when dry had a rubber-like
consistency
and thus
could
['lex with the wing without
cracking.
No fatiguing
of either
the
bonding
or the elastic
properties
of the cement
was encountered
dtu_ing the
test.
Electronic
circuitry;
method
for
component
determination.-
The
electronic
circuitry
was designed
to perform
a harmonic
analysis
of the
information
provided
by each element
of instrumentation
(whether
pressure
cells
or accelerometer)
and to respond
only to the components
of the complex amplitude
of the fundamental.
(The term f_damental
as used here
refers
to that harmonic
term which
is of the same frequency
as that of the
gage power.
In the oscillatory
tests this frequency
_as the natural
frequency
for the first bending
mode of the wing while in the static
tests
it was zero.)
A
3
5
4
2¥
9
The
in
essential
sketch
(b)
for
features
the
of the
oscillatory
electronic
test
UUUUUHU
UUv",Uu'
UH--V
circuitry
case.
The
used
principle
%
are
of
Stahc
sho_m
operation
)
deflectiOn
A
3
4
Sketch
of
the
circuit
generator
is
is passed
as
follows:
through
the
(b)
output
a resolver
of
a 5-kilocycle
driven
by
the
square-wave
alternator
supplying
power
to the electromagnetic
shakers
which
force the wing motion.
After
subsequent
demodulation
this produces
two alternating
voltages
at the
wing-drive
frequency
such that one voltage
is in phase
and the other is
out of phase with the angular
position
of the resolver
rotor.
After
amplification,
these voltages
are used to power the strain-gage
bridges
in the various
accelerometers
and pressure
cells in use.
(The voltages
were applied
sequentially
to
the 35-5 55-_ and 75-percent
remaining
gages.)
When
the
wing
the single
bridge
semispan
stations
is oscillating
impose
a time-varyin_
deformation
gage is powered
by an alternating
output
is essentially
proportional
and the resistance
changes
in the
Thus_
if the
gage
the
resulting
of each accelerometer
at
and simultaneously
to the
pressures
(or
accelerations)
on the various
strain
gages.
If each
voltage
at this same frequency,
then its
to the product
of the voltage
signal
bridge
associated
with the deformations.
is undergoing
sinusoidal
B sin (_t + c)
deformations
of
the
form
i0
(where
c
is the phase angle between
the gage
Dosition
of the resolver
rotor)
and is powered
delivered
by the resolver
in the form
then
the
gage
output
Vi : V
sin _t
Vo = V
sin
voltages
vi = K
=K
B
w
T
sin
are,
(_t
£_t
deformation
by the two
and the
voltages
angular
+ 2'
_/
respectively,
+
e) V
sin _t
[cos _ - cos (2_t + c)]
and
Vo
= K B
=K _
sin
(_t
+
e)V
sin £_t
+ 2_
[_in c + sin (2_t+ c)]
Here
K
is a general
bridge
constant
depending
on the type of bridge
in
use, its resistance,
and the choice
of units of
B.
Thus, the output
of
the strain
gage is proportional
to one-half
the amplitude
of the quantity
to be measured,
the frequencies
are twice the frequency
of operation,
and
each of the resultant
voltages
has a time-invariant
component.
As
sh_n
in
sketch
(b),
each
output
voltage
is used
to
drive
a
galvanometer
element
which
has an undamped
natural
frequency
much less
than
2_
so that it is essentially
unable
to respond
to the oscillatory
part of the signal.
However_
the galvanometer
is capable
of responding
_ith a deflection
G
to the component
of the strain-gage
signal
which
is
time-invariant.
The result
is a static
indication
of the in-phase
and
out-of-phase
components
of the harmonically
varying
quantity.
that
This
such
method
is more fully described
in reference
9, where
it is shown
a system
is capable
of filtering
unwanted
harmonics
from the
data.
However,
ration
when the
the strain-gage
tunnel
turbulence
and the occurrence
of leading-edge
sepawing was set to an angle of attack
caused
fluctuations
in
outputs
which
reduced
the accuracy
of the pressure
data.
11
Instrument
Acc_,l<',rom_,_tcrs.:'or
each
acc,_l,_uom_
p<.r
d,zflections
about
the
had
L'a,:,.tors, such
The
mode
snin,:i!.<
tact
s
_h_
betw_
,,;as
small
produced
,.ri_,,i<
c,qttcr::,
]zo
i<.-,
.sf
9N-p:_rcent
the
mi_J_t
rh
as,:.:, i
_:'_:m,:ct %o
%e
xrom<:%_r
rKh
in
that
no
first
mass
the
_z r
apero
s
_.<_re used
mo_%z_s
difference
resonant
than
the
dyp, amic
voltage
to
per
a
static
the
terms
of
th<
_g[_l,
".,r_'th
motion
n_t !:h_
;u:_ro i:_ the
s]so
VNk L" <,;<t,_ :i=-iv<:)
!at<:r
'fout::i
:[;_
h,:;-_,,-
Dru:
cor_si,i_r_:'[k,_
th_
previous!y_
",.,;as
:a!)proxirrlrtt_ly
£r<.quency
a
or
dynamic
pressure
llO
o:"
ceil
cells
maintained
the
effect
c_:lls
?owerin
a
the
6 the
The
value
of
this
root
equal
orders
No
cells
sine,
magni-
constants
with
mean
change_
o£
constants
static
to
so
test.
calibration
from
_¢,.,rc
con_:tants
existo,d
s©vemal
dy_amic
voltage.
at
pr<_:su_"<
sensitivities
<¢as
differed
by
the
calibratio__1
ssure-distribution
The
A
constant
calibration;
of
Th<
the.. static-Dr<
",,r_,;rc
obtai:_ed
was
a]]
out_,ut;_
s:mispnn
mentioned
%<,nt]._'_g
sensitivities
appendix
than
r,_s_;,s
calibration
, xo._¢%,_d,
line
aaRon{tear.
frequency•
in
data
voltage
during
in
test
Ko
i]',
to
or
dia-uN_
of
th
The
frequency
first
to
shat
rx-zj]
or
mOLl,:
,shaft
......
static
of
rather
the
precision
the
the
and
mid-chord
z'_sonant
com_,ared
The
in
the
_oout
,,m:;
cJ rcuit
mo_!-:nt
ord.cr
equal
.,ras
b,_
t,]l,
!in,:
d
<,ri]_;_t th
z'c.su-]t;
:r,q_,s to
th,k
'pS-]',or,cent
sot
prr;s<mt
to
_m_atitudo,
st'sat:ion.
[_his
torsional
directly
Ki
used
_.rLng
o_
as
alternating
voltage
.ql::,,_.
frequency
gr.,at,:r
hating
t,_,::t
c_lls,-
obtain<q/
because
[m:-,ortant
cycles
by
:l<,notod
<,:as
Tiz':_
a_
obtain_!'l
tude
mot[o:_
inv_
an_!.
Con-
t<_'.din6
IX
Kd
uoh_t
torsional
oR
,com!_orzent
consequcnt_ly
the
cil,,,i
ca!iLrat,
th,
that
torsional
mo(t.c.
the
:o_d
Pressure
was
torsio'_a-!
<imate!V
basic
arN.
of
b
_eR
['orc<
w, lt'._
held
th_ _
torsio.'_
kay
t:[p
to
microm_ter.
A p'_zi'e
tl%:
ou:m}oses
which
The
Coupl-_Lg.
to
<or
stan[
",'_'atte±_y-Oow-
st!ss,
axir_
showo,d
a
th,,•
_o_rt:_n< nt
th,, _ _',unt,,,:
tb,
a
tip.
rs
all
d
a
m_hoz_,<_.
accomp:n_};gn6
<taiibrotiou
-i;]_atthe
-,,S.n S
rom_.t
_rat[.on
aft,or
fast_nei
of
or
t]%,. :l<-fl_cti:urz
us,__<i in
o1"
East
cy,::l,,s
the
s,ccel.
of
az:d
,,.rei_Nht's
tirectly
r_c¢'.,;1
that
tips
by
p_.ir
_n,: rtia
galvamom<.t_:.r
t}]U
d,,-termin_
means
,rir_.g
,:lastic
r
det<rmin:iz:F:
_.,rin:i-on
s[,M.nmetry
1%n',lth_,
"bJ
<,quat[on<;
b,):u]i.r_(
J_tLring
no
%h_
f_:rcncek
than
a
the
with
[_r_%ts[ i_].
b_,r_,iinf_ i'ruque_cy_
show_:<t
the
r
r
on
::!_tc,:
-,;as
rather
d.ata-rcduction
-the
s::rJJ
semispan
d':fl_'::tion
i c_".
first
mann,
b,sh,[i:_{i
<[u.antit,
tip
;tat
this
the
occ,,nttric
n_o_.u_ztod,
order
was
by
in£icat:::i
in
"
b_: d._t-i_ninod
_,.rored,_tormin,_d
<'onical
4as
Krj
to
for.
:zing
both
sidnal
_d
po:_itio:_n_t
to
had
re-Lit angular
the: ,,7i:,<iiR
acc02rate
opposed
motor
in
in
microm(_ter
__tL b_nt:1]ng,
constant:,
constants
Rs£,_age
of
Kh
p<;r
_,,rer,_
_ account,x!
orovi,:._,:[
moans
A,
spring-supported
of
which
and
oscillating
au_tib].c
<]::-ctric
the
-the
and
an
by
';,_s
of
<rith
wing
excited
instaiffe,i
accelerome%_r
imps
cn
apo<.n,lix
Th, se
fixity,
danger
_>roduc,:,£
from
constants
acceleration
root.
root
rs
th<_
_;,rhich
eel,re,
b,,_n
the
calibration
lin_:ar
shape
microme%
minim-z,_'A
a
as
calculating
l.<th
,,,_-r
unit
acceleromet<:r
accelorometers
of
Th_
Calibration
au
alt.:r-
square
the
of
constant
coupled
_¢ith
12
the factor
1/2 noted
in the
d_amic
calibration
constant
expressed
The
in the
data
units
of
presented
section
on Instrumentation_
resulted
in
equal to
_
times the static
constant
Ki
for
and
Ko
given
Test
Procedure
each
test
in appendix
condition
were
a
when
A.
obtained
in three
distinct
stages;
the static
test, the oscillatory
test, and the orificetube calibration.
Data from each of these phases
were automatically
entered
on punched
cards and the results
appropriate
to each phase were
computed
electronically.
A
Static
test.The static-pressure
distribution
_as obtained
by
po_ering
one of the cells in each Seanivalve
r_uit _ith a constant
voltage.
Each cell was referenced
to th . static
pressure
at the _¢all of the test
section,
so that its output
for each orifice
_as directly
proportional
the static-pressure
difference
between
the _ing orifice
and the tunnel
wall.
Adjustments
co_d_ficients.
Oscillatory
to
test.-
free-stream
The
_in_
b_ding
frequency
in order to
,of motion
(approximately
0.2
coW.ks in the" Scanivalves
_ere
section
on instrumentation
so
s,_ction_
combined
yielded
in the
_Tas driven
yielded
in
the
resonance
cell
were
outputs,
recorded
at
its
first
corresponding
to the
for each orifice.
Simul-
the acc_lerometer
outputs
were also
_ith the data obtai_ed
as described
the mode
equations
static-pressure
obtain
the maximum
available
tip amplitude
inch for all test conditions).
The pressure
connected
to the bleeds
as described
in the
that no static-pressure
difference
existed
acro. s the cell diaphragm.
The
oscillatory-pressure
amplitude,
tan_:,ous r:_adinss of
thes,_ data, together
conditions
to
shape and oscillatory-pressure
of appendix
A.
recorded,
and
in the next
distribution
when
Orifice-tube
calibration.The calibration
was performed
by means
of
the fixture
shown in figure
l(g) which
clamped
to the wing and simultaneously
covered
all orifices
at a given span station.
A similar
fixture
_¢as used in the calibration
of the root orifices.
At most test conditions
the oscillating
pressures
experienced
by the pressure
cells in the Scanivalves
were not representative
of either
the magnitude
or phase
angle of
the pressures
existing
on the wing
surface
because
of the attenuation
and
phase
characteristics
of the tubing
which
transmitted
the pressures
to the
cells.
It was experimentally
determined
that the tube characteristics
were functions
primarily
of the frequency
and static
pressure
existing
in
the tube_
and essentially
independent
of the amplitude
of oscillating
pressure
for the values
experienced
during
the investigation.
The tube characteristics
could also be affected
by the introduction
of foreign
particles
into the wing orifice
and by necessary
maintenance
_ork on the Scanivalve.
To minimize
the possibility
of such occurrences
affecting
the data, a calibration
was made immediately
after each
3
5
4
lj
o_ci!latory
test.
In th,:>calibration
the absolute
static
prcssur<,
as
dcte_nin_d
from the
static
t_st, and the frequency,
as detel_nined
from
the oscillatory
test, _ere matched
for each orifice
location
and an average value of osciilating-prc.ssure
s_mplitude was applied
at the orific
.
A
3
5
4
Th<_ calibration
fixture
consisted
of a chamber
which appli<d
the smn,
conditions
to all orifices
on the upper or lo_,¢er surfaces
of the _¢ing.
S<_al_ng arotu_d each oriL'ice <{as accomplished
by clamping
on the rubber
grommets
visible
in the photograph.
The static pressure
was s_t to tb:
value
corresponding
to the particular
orifice
beinL_ calibrat<d.
Tb_,
oscillatinc-pr:ssur_,
amplitude,
supplied
by a piston-cy!in_
r arran(_ mo_it
mo_mt_ d on an electromagnetic
shaker,
'_as indicated
by the two pressur_
cells mourLted in each half of the fixtui_e as sho_,n_. It was experimentally
detelmlined
that there was no attenuation
or phase
shift introduced
%y th,c
calibration
fixture,
so that the pressure
cells in the fixture
gave a tru<
indication
The
o2
data
th<_ oscillating
obtained
pressure
L'rom the
existing
calib!'ation
were
at
each
reduced
orifice.
to
the
fol_
of
amplitude
ratio_
Z, and phase
angle,
8_ and were used in the data-reduction
equations
of appendix
A.
A plot shovnLng the variation
of th_s_ quantities
with
static pressure,
typical
of the orifices
at the 90-percent
semis,pan
station,
is presented
in figure
2.
Aithouch
the investigation
was conducted
at the ms_cimum turmel
pressure
available,
the decreas<
in static
pressure
with incr_asing
Hach number
caused
an increasing
loss of syst-m
acc_macy
because
the ma_:imum Math
_,ras 1.30.
of the
number
resulting
at which
RESULTS
attenuation.
Because
of this
reasonably
accurate
data could
A}_
Static
_,_fLk
ct
bc o%taim>£
DISCUSSION
Data
The pressure
distributions
obtained
Lmder
static
conditions
are
present_d
in fi_ure
3 for s_Igles of attack
of 0 ° and 5 ° .
(These
angle of
attack
values
are nominal
in that the ttmnel
stream
angle varied
across
the span,
generally
%ecominc
more neEative
toward
the root as can be s< m
from the zero angle of attack
data.)
The data are given in the form of
th_ chord<<i.s_ distributions
of the s_rrface pressure
coeffici<_nts
(upper
and lower)
and the lifting
pressure
coefficient
at the four instrumented
_ao=omo.
In {>eneral,
airfoil
and rectangular
little
comment.
the static
data agree with
wing studies
(e.g.,
refs.
those of other
i0 and ii) and
biconvex
require
For the transonic
soeed ran{p
(H = 0.9 - l.lO)_
the local surface
Hath ntunb :rs w_rc com_uted
from equation
11.4 of reference
12 and the
result:', are presented
in figum_e 4.
These data sho-_ that for Hach numb,:r_
l.O and i.l, th_: _L%ch number
frcczc
condition
(see, o._._ ref. 9) exist,:_l
14
over the entire
surfaces
at both angles
of attack,
while
number
a significant
freeze
occurred
only at _o angle of
was confined
to the leading
edge of the upper surface.
at 0.9
attack
Mach
and then
Unsteady
static pressures
occurred
at the root station
over both
surfaces
and were most
significant
near the leading
edge.
These were
attributed
to the effects
of a turbulent
wall boundary
layer.
In addition,
certain
unsteady
pressure
phenomena
which were encountered
during
the oscillatory
tests are believed
to have their
origin
in the static
environment
of the wing_
and the relevant
features
will be pointed
out
here.
First,
at Mach number
0.9, the presence
and location
of the shock
wave terminating
the region
of local supersonic
flow should be noted as
seen
in figures
3(g)
and
3(h).
Although
it
is not
sho_cn
in figures
4(e)
through
4(h)_ there were also shock waves terminating
a small region
of
supersonic
flow near the leading
edge of the upper
surface
for
_ = 9 °.
Small changes
in the location
of these
shock
constantly
occurring
as
a result
of
slight
changes
in the
at
H = 0.7
waves were
flow
conditions.
Second,
although
the effective
semiwedge
angle of the airfoil
at the
leading
edge was approximately
7°_ and thus the upper
surface
of the _ing
leading
edge was at approximately
a 2 ° negative
angle of attack
_¢ith
respect
to the free stream_
the
_ = 5°
data of figure
3 indicate
that
the induced
upwash
raised
the effective
flow angle
sufficiently
to require
the flow to expand
over the upper
leading-edge
surface.
Because
of the
sha_pness
of the leading
edge, a small region
of separated
flow probably
existed
for most test
the possible
separated
5-percent
chord under
conditions.
However_
region
to be confined
static
conditions.
the
to
data of figure
3 indicate
the region
ahead of the
Finally,
at 5 ° , for Mach numbers
0.9_ 1.0, and i.i, the local Mach
number
plots
(fig. 4(e) through
4(h))
sho_¢ that the flo_¢ over the uoper
surface
of the wing _ras almost
entirely
supersonic_
therefore,
the wing
tip may be expected
to have a domain
of influence
on the upper surface
similar
to that of a purely
supersonic
wing, and the associated
abrupt
changes
in the pressure
at the boundary
of this region.
The approximate
location
of this cu_ed
boundary
line for
M = i.i
was computed
from the
local Mach number
data of figure
4, and is shown in figure
5; as a result
of the transonic
Mach number
freeze
over the
surface,
this boundary-line
position
is also
and 1.0.
The correspondence
of its location
slight
peaks nearest
the leading
edge in the
of figures
3(h), 3(k), and 3(n) at the three
tip portion
of the upper
applicable
for
M = 0.9
with the position
of the
static-pressture
distributions
outboard
stations
shows that
the peaks
mark the boundary
of the tip domain
of influence.
The boundaryline location
for
M = 1.3
was computed
in a similar
manner
and is also
shown in figure
5However,
for this Mach number,
the tip effect,
in
terms
of peaks in the pressure
distribution_
was so small that it was
negligible
statically
and unnoticeable
dynamically.
A
3
5
4
15
Dynamic
Data
Mode shape.The mode shape,
normalized
with r_spect
to th_ tip
amplitude_
is shown in figure
6 for both wind-off
and _¢ind-on conditions.
The wind-off
curve was obtained
by means
of depth micrometers
as described
previously.
The wind-on
data were obtained
through
use of the acceierometer
equation
(A4) of appendix
A.
Data are missing
from the 35-pc_reentstation
accelerometers
because
of an electrical
failure
at this station
in
A
3
5
4
the
early
stages
of
the
investigation.
Chordwise
pressure
distributions;
_ : 0°.- Figure
7 presents
the
result
of applying
equations
(All) to the data for
M = 0.24
to give the_
components
of the chor_rise
surface
pressure
distributions
her unit tip
angle
of attack,
in phase and out of phase with the wing bending
deflection.
Application
of equations
(AI2) to these data yields
the in-phase
and out-of-phase
components
of the chef,rise
distribution
of liftingpressure
coefficient
as sho<m in figure
$.
Finally_
equations
(AI3) yield
the chordwise
distribution
of the lifting-pressure
coefficient
amplitude
and phase
angle shown in figure
9, the form in which most of the d_u_uic
results
of this investigation
are presented.
The
pressure
distribution
for
M = 0.24
(fig.
9(a))
appears
smooth_
but as the Mach number
increases,
various
irregularities
in th<_ data occur_
as is evident
in the succeeding
parts of figure
9.
The general
deterioration in smoothness
can be attributed
to the inherent
loss in system
accuracy
with increasing
Mach number
discussed
previously.
However_
certain of these
irregularities
are isolated
enough
to demand
an explanation
based
on the physical
characteristics
of the flow.
The first of the isolated
irregularities
is the sharp break
in the
phase-amgle
distribution
at
M = 0.70 (fig. 9(b)),
particularly
at the
two outboard
stations.
Because
of the associated
small pressure
amplitudes,
these
jumps of nearly
180 ° are probably
partially
accounted
for by the
inherent
inaccuracies
in the phase-angle
computations
amplitudes,
but their
consistent
nature
may be due to
resonance
effects
which will be considered
later.
for small pressu1_e
possible
tm_lel
In the
M = 0.9
data (fig. 9(c))_
this jump is still present
and is
accompanied
by sharp peaks
in the pressure
amnlitude
distr!bution
over
the aft portion
of the chord.
The static-pressure
data show that the terminating
shock wave is also in this vicinity,
and the pressure
peaks
are
attributed
to the movement
of the shock with the wing motion.
The amplitude of the peak is roughly
a measure
of the harmonic
content
of the
oscillations
in static pressure
associated
_ith this shock motion_
which
is s_nerposed
on that arising
from the oscillatory
angle of attack.
T_o
sets of data are also shown for this Mach number_
and the poor repeatability
in the neighborhood
of the shock is further
evidence
of the
sensitivity
of the shock location
to slight
changes
in the flow conditions.
16
Chord_¢ise _ressure
distribution_
_ = 5o. - The components
of the
chord_,_ise pressure
distribution
on the upper and lower
surfaces
are shown
in figure
i0 for
H = 0.24; also sho_n for comparison
are the correspondim6 data for
_ = 0°
from figure
7The radical
change
in the pressttre
distribution
at the leading
edge of the upper
surface
is apparently
the
r_,_sult of th_ ttnsteady pressures
associated
with the changing
chordwise
extent
of the leading-edge
separation
mentioned
previously,
caused
by
the additional
increment
in angle of attack
furnished
by the wing oscillations.
As shown in figure
ll(a),
the phase
angles
were relatively
_uuaffected
At
by
a Hach
the
separation.
number
of
0.70
(fig.
ll(b)),
both
the
amplitude
and
phase
anglc_ of the pressure
coefficient
exhibit
leading-edge
irregularities_
but th__'s,_,
may not result
entirely
from flo_ separation.
As mentioned
previous! K. local
supersonic
flow occurred
over the leading
edge at
}4 = 0.70
_rhen at angle of attack,
and movement
of the shock terminating
this region
could
have caused
increased
pressui_e amplitudes
in the same manner
as that
,described
for
H = 0.90
at 0 o.
Because
of the reduced
angle of attack
associated
with bending
oscillations
(as compared
with that for
M = 0.24)
sild also the increased
l_ading-edEe
separation
to be the case for the
Reynolds
number_
it is doubtful
if significant
occurred
except
perhaps
near the tip.
This appears
data of Hach numbers
0.90_ 1.0, and l.l (figs. ll(c),
(i), and (e)) which
show a large pressure-amplitude
peak at the 90-percent
s_mispan
station.
The data also show pressure
amplitude
peaks
at the
three-tenths
and mid-chord
points
of the 70 - and 50-percent
semispan
stations,
respectively.
The similarity
of the data for these three Bach numbers is evidence
of the Mach number
freeze
sho_n in figure
_.
As discussed
_,r_viously,
the freeze
held only over the for_rard portion
of the chord at
H = 0.90.
Altho_h
not presented
herein_
the sel_arate surface
data show
that the peaks
occ_rrcd
on the upper
surface
only; the coincidence
of their
locations
_ith those
of the abrupt
changes
in static pressure
which were
previously
sho_m to define
the boundaries
of the tip domain
of influence
suggests
that the peaks are the result
of the movement
of this boundary
line with the wing motion.
As can be seen_ relatively
small (but well
defined)
changes
in static pressure
at the boundary
may produce
a surprisinEly
large pressure-amplitude
peak in the immediate
neighborhood
of the
botu_dary.
However,
the diminishing
of the peak at the 50-percent
station
_hen the flo_¢ is accelerated
from
H = 1.0 to H = i.i, attests
that this
neighborhood
is extremely
small_
and the peak might not be detected
unless
there
_ere an orifice
located
there.
Section
lift and moment
distributions;
_ = 0°.- The oscillatory
aerodynamic
section
lift and moment
coefficients
were obtained
by numerically
integrating
the lifting
pressure
coefficient
distributions
for each
l_ch number
corresponding
to those of figures
8(a) through
8(d) for
M = 0.24.
It -_as assumed
that these pressure
distributions
varied
linearly
bet_een
adjacent
chord points,
and the necessary
leadingand trailing<d[]_::
values
were selected
by inspection
for each spanwise
station.
A
trapezoidal
scheme
of integration,
consistent
with these assumptions;
was
th_n utilized
to obtain
the in-phase
and out-of-phase
components
of both
A
3
5
4
8¥
17
the section
lift and the section
moment
coefficients
per unit effective
tip angle
of attack.
From this information,
the magnitude
and phase
angle
of the oscillatory
section
coefficients
were computed
and the results
are
show_
in figure
12.
Of particular
interest
are the rerun results
of
figures
12(c) and 12(f) which
show remarkable
agreement
considering
the
approximate
nature
of the integrations
of the original
pressure
distributions.
A
3
5
4
and
the
general
erratic
character
Although
there is some question
as to the qu_utitative
accuracy
of
the results,
definite
trends
with increasing
Hach number
are in evidence.
Among
these are the decrease
in the section
lift phase
angle from approximately
120 ° at
H = 0.24 to 55 ° at H = 1.3, although
at each Hach number
this phase
angle is relatively
constant
across
the span.
One of the most
remarkable
features
of these data is the gradual
flattening
of th_ distribution
of the section
lift coefficient
amplitude,
until at
H = 1.3
(fig. 12(f))
it is almost
elliptical.
It might be expected
that at least
the
and
out-of-phase
component
_,_ould retain
some evideuee
have its m_ximum
somewhere
in the vicinity
of the
theoretically
sonic flow at
for a parabo!ically
twisted
M = 1.3; but figure
12(f)
wing
shows
of the mo_e
wing tip as
in st_a:ly linearizod
superthat the m_im<_
oscillatory
lift is produced
at the root section
where the wing deflection
is
Similarly,
for the section
moment
distribution,
the most
striking
of compressibility
is the decreasing
of the root phase
_gle
from
M = 0.24 to -_15° at M = 1.3_ _hile the phase
m_gles
for the thre<
stations
are relatively
unaffected.
Because
of the general
irregularity
: 5 ° , no attempt
_as made to integrate
section
lift and moment
coefficients.
Comparison
years
With
shape
it _ou.l!
of the pressure
them and obtain
zero.
effect
75 ° at
outboar<{
distributions
the associated
for
Theory
Of the many oscillating
wing theories
developed
during
tb:_ last ten
(see ref. 13 for a fairly
complete
survey)
only two furnish
the
lifting-pressure
distribution
and both of these assume
the
flow,
there is the approximate
14, and 19 which
has recently
on a defonning
conditions
for
wing of moderate
linearized
flow.
aspect
ratio_
For subsonic
kernel
function
approach
of references
culminated
in a usable
program
for the
2_
IBM
electronic
computer_
and for pure supersonic
flow there
is the analytically
exact potential
obtained
%y Miles
(ref. 3).
The latter
has also been
developed
into a usable
program
for this report
(appendix
B).
MolljChristensen
(ref. 7) and Miles
(ref. 16) have investigated
the necessary
conditions
under which
unsteady
linearized
flow theory
is valid,
and
reduced
them to the following:
704
18
_¢here
A
From
1.
A_
2.
A-_
>>SmJs
3.
I}_
- iI
4.
k
is
the
the
MA_ kA,
>>
k_
1
/
>>a213
any one or mor,_:
of these
A 2/3
thickness
values
<<
of the
ratio
of the
appropriate
wing.
test
parameters,
it
is
seen
that
although
condition
i was a_¢ays
met, conditions
2 and 4 were never met,
while
condition
3 would
require
either
M >> 1.O65,
or
M << 0.930.
Therefore,
in general,
it }_ould not be expected
that the results
of these
linearized theories
should
agree well with those obtained
experimentally,
except
possibly
at
H = 0.24, 0.70, and i.30.
With the reservations
dictated
by
these
considerations,
the comparison
between
experimental
results
and those
of the above linearized
theories
_ill be examined
in more detail.
For the subsonic
speeds,
the computing
of control
ooints
on the plan form at _¢hich
the mode
shape)
is to be specified.
9_elve
the 1/4-, 1/2-, and 3/4-chord
points
at the
s_m_ span stations.
progrs_n r_quires
the selection
the dowY_wash (as determined
by
control
points
were chosen;
20-, LO-, 60-, and SO-percent
At
H = 0.24_ c_ = O, the agreemen±
bet_,¢een the theoretical
and
_xperimental
pressure
distributions
is good (figs.
7, 8, and 9(a)).
The
data were obtained
at the greatest
static
pressure
of any data of the
inv,sstigation,
so that the phase lag and attenuation
of the, orifice
tubes
were at their minimum
values.
There ',¢asalso no evidence
of stream
fluctuation,
so that these data are the most reliable
of all that were obtain,_d
in the oscillatory
testing.
ment _,ho_¢s that linearizecl
The good agreement
bet_¢een theory
and experitheory
is adequat_
to d_scrib_
__,hc
- flo,,r at this
blach humbler.
The comparison
bet_,r,;_,en
th,_ory an i oxperfmeT_t
in tht_ fo_n of
section
lift and moment
coefficierlts
(fig. l,_(a)) sho_¢s considerably
.Ynore
discrepancy
than would be expected
on the basis
of the pressure
distribution comparison.
The primary
cause of the discrepmncy
has been traced
to
the oressures
assumed
to exist at the leading
edge; _¢hereas the exp<_rimental data were extrapolated
to pressures
considered
reasonable
on a physical
basis,
the theory,
of course,
assumes
the usual
subsonic
singularity.
Therefore,
if a more realistic
handling
of the leading-edge
pressures
could
b(_ incorporated
into the theory_
better
agreement
with the experimental
values
of lift and moment
would
undoubtedly
result.
At
H = 0.70, _ = 0 (figs. 9(b) and 12(b)),
although
the pressure
_aplitudes
are in fair agreement,
the phase angles
are not, particularly
near the three-quarter
chord line_ while
the lift amplitudes
show a
noticeable
decrease
from their values
at
H = 0.24.
The latter
circumstance
suggests
the possibility
of wind-tunnel
resonance
rather
than
violation
of
the
limits
for
application
of
linearized
theory.
If
the
19
resonance
induced
by
a bending
wing
in a rectangular
considered
to be primarily
a two-dimensional
erence
16 is applicable
for predicting
the
reduced
frequency
at which
resonance
could
test
section
is
problem_
the theory
of refcombination
of Mach number
and
occur.
The slotted
floor and
ceiling
construction
of the test facility
necessitate
considering
an
effective
tunnel
height
somewhere
between
6 and 18 feet.
A plot of the
appropriate
test parameters
is given
in figure
13, with critical
resonance
curves
from reference
17, based
on tunnel
heights
of 6, 12, and 18 feet.
As can be seen from the figure,
resonance
at
for an effective
t_el
height
of approximately
believed
to furnish
a partial
explanation
for
discrepancies.
H = 0.7 could indeed
occur,
13 feet_ and this is
the above-mentioned
At
H = 0.9 (fig. 9(c)),the
agreement
is poor_ particularly
vicinity
of the shock waves over the afterportion
of the chord.
to be expected,
since linearized
theory
is unable
to account
for
pr_sence
or the effects
of these shock waves.
The poor agreement
evident
in the lift and moment
plots
of fig_re
12(c).
For
H =
H
0.99
= 1.0,
have
been
the
theoretical
used
for
subsonic
comparison.
coefficients
Although
the
in the
This is
the
is also
evaluated
amplitudes
at
of
the
pressure
coefficients
are in better
agreement
than they were at
M = 0.90,
the corresponding
phase angles
are not (fig. 9(d)),
nor are the sectionlift and section-moment
coefficients
(fig. 12(d)).
The requirement
for
the application
of linearized
theory
is clearly
invalidated
at this Hach
number
and good agreement
could not be expected.
For
H = 1.10
and
1.30
(figs.
9(e),
9(f),
12(e),
and
12(f)),
there
little
or no resemblance
between
the
results
of the
experiment
and
those
predicted
by Hiles
linearized
theory
for
parabolic
bending_
even
in the
plan-form
regimes
in which
the
latter
is
formally
applicable
(see
appendix
B).
The discrepancies
here
are
primarily
accounted
for
by the
nonlinear
effects
(detached
bow wave) associated
with the thickness
of the
wing_
and partially
by the
earlier
in the text.
For
over-all
loss in system
M = 1.30_ it is evident
accuracy
that the
discussed
condition
is
for
linearized
flow theory
(M >> 1.065)
remains
unsatisfied,
while
the general
r_peatability
evidenced
in the rerun data provides
a measure
of the
reliability
of these data.
CONCLUSIONS
An
experimental
distributions
in its first
range 0.24
conclusions
investigation
was
made
in which
the
pressure
on an unswept
rectangular
wing of aspect
ratio
symmetrical
bending
mode were obtained
over the
to 1.30.
From
can be made:
the
results
of
the
investigation,
3 oscillating
Hach number
the
following
2O
i. Large effects on the oscillatory
pressure distribution
can be
caused by the presence of static phenomena_such as local shock waves,
flo_ separation, and finite span effects.
2. The results of linearized theory comparedfavorably with those
obtained experimentally for M = 0.24 at _ = 0° where the flow was essentially
incompressible and inviscid.
However, the agreement deteriorated
at transonic speeds and at angle of attack where the important effects of
thickness_ local shock waves, and separation could not be adequately
described by linearized theory.
3- The comparison of the experimental and theoretical results tends
to confirm the Miles and Moll_-Christensen criteria
for the application of
linearized flo_ theory.
4. Someevidence of _ind-tumnel resonance _as noted; however, the
effects on the experimental data appeared to be confined to the M = 0.70
results.
_. The experimental method for obtaining the oscillatory pressure
distributions
developed in this investigation in general gave satisfactory results.
The upper range of Mach numbers_as limited by the
increasingly poor frequency response characteristics
of the pressuremeasuring equipment.
AmesResearch Center
National Aeronautics and SpaceAdministration
Moffett Field, Calif._ July 26, 1960
A
3
5
4
21
APPF_'@ IX
OSCILLATORY
TEST
DATA
Acceleromet
In the
follo_ing
equations,
A
REDUCTION
EQUATIONS
er Equations
the
outputs
of
the
accelerometer
strain-
gage bridges,
which
in reality
are alternating
voltages,
are given the
symbol
G
which,
from the section
on Instr_aentation,
indicates
a static
galvanometer
deflection.
No confusion
should be caused,
however,
since
it was sho_
that the static
deflection
is directly
proportional
to the
A
3
5
4
amplitude
constants.
and
of
the alternating
quantity,
after scaling
by the appropriate
All constants
are taken to be included
in the factors
Kh
K@.
8
h
Sketch
Consider
harmonic
wing
wise rigidity,
by
the
accelerometer
(c)
geometry
shown
in
sketch
(c).
motion
of bending
and torsion.
As a result
of
the motion
of each cross section
is completely
For each of these motions,
accelerometers,
the total
proportional
to the
to be in phase with
h :
lhl
sin
et
@ =
I@I
sin
(tot + N)
by virtue
output
of
amplitude
it.
of
the
Assume
the chordspecified
of the high natural
frequency
of the
the strain-gage
bridges
is directly
motion
in question
and
may
be
taken
22
These outputs are as follows:
a. due to bending
forward accelerometer
Khfl
rear
Khrl h l_2
accelerometer
h 1_o2
b. due to torsion
(rKhf
+ Kgf) lel_2
(rKh r + Ker )l@lw 2
_here
Khf
fo_ard
accelerometer
acceleration
Kh r
rear accelerometer
acceleration
galvanometer
galvanometer
deflection
deflection
per
per
K_f
forward
accelerometer
acceleration
about
K@ r
rear accelerometer
galvanometer
deflection
per
acceleration
about rear accelerometer
root
For
fo_ard
unit
galvanometer
deflection
per
forward
accelerometer
root
the combined
motion_
and rear accelerometers
the rotating
are shown
Forward
accelerometer
unit
A
linear
unit
unit
linear
angular
angular
vector
diagrams
for the
in sketches
(d) and (e):
/
L'/_
..._flh
I
Khflhlw=
%f I
--./_-7-L_-_
_-_'(rKhf
+
I_
L
"G if
--
KSf)181 '_z I
•
Sketch
(d.)
rotor
3
5
4
23
Rear
accelerometer
G°r F
A
/
K
h---r+iOr]ol
_Jt
_
/
S_
_,h
\
lIj
tr__
__
i__
_iResolve
rotor
3
5
Sketch
For
the
foz_¢ard
Oil
I
r
(e)
accelerometer_
= Khfl
hle%os
;_h -
(rKhf
+ K@E)
@ leacos
F_6
(AZ)
Gof
For
the
= Khfl hleasin
rear
+ K@f)
2h -
(rKhf
nh
(rKh r + K_ r)
_ i_2sin
f_a
accelerometer_
Oi r = Khrl hl_2cos
+
(A2)
Go r
:
Khrlhlm2sin
2h
+
(rKh r
+ K_ r)
0 le2sin
N0
_h,:,r<: G i and G O
are the galvanometer
deflections
proportional
to the
strain-6age
signals
in phase and out of phase _,¢ith the resolver
rotor.
In actual
practice
in-phase
and out-of-phase
components
were indicated
by a separate
strain-cage
bridge
or else the t_¢o components
_ere read
consecutively;
with either
procedure
there _as the possibility
of diff,_rent sensitivities
K h and K e
for the t_o components.
To indicate
the
_possioility
of different
sensitivities
for the in-phase
and out-of-phase
eom_)orle_ts_
eq-,ations
(A1)
and_ (A2)
are
rewritten
as
24
Gif
= Khfilhl
_ac°s
Gof
= Khfo hhl wasin
g_h - (rKhfi
+ K_=i
_' )l@Iw 2cos
f_@
_h
+ _±,o )l@l_2sin
g@
-
(rKhfo
(A3)
Gi r = Khri Ihlw2c°s
_h
+
(rKhri
+ K@ri) l@l_2c°s
g@
Go r = Khrolhl
gh
+
(rKhro
+ Kero) l@l_2sin
_@
_2sin
Equations
(A3) can be solved
four accelerometer
stations:
(a)
Bending
for
the
following
quantities
at
m(rKhr
l hl : _
the
angle
+ K8 r )Gif
+ (rKhf
+ Kggf )Girt
I __i___i
.....
S____L
I
b
+ KhfiK@ri
+ KhriKSfi
]
between
2rKhfiKhri
resolver
rotor
and
bending
}i/2
(A4)
amplitude
i (rK___
hr_O i O)______
KS r
GO 7
_o_ro +_o_ro+_hro_o
J
I rKhf____o_
O i K@fO)f or
_h
(AS)
= tan'm
+
2rKhfiKhri
(c)
Torsion
_+ +_
+ KhfiKSri
+ KhriK@fi
J
amplitude
I m
KhfiGir
_ r-_m
KhriGi+ f_KhriKSfi
18' = _-_
b_ { 2rKhfi Khr_"
+ K--hfiKo
)2
(A6)
+_2rKhfoKhrN
A
3
5
4
+ [ (rKhf
2rK----hf
O o-Khr--_
+ KOfo +)GOr
K_fo--K_r_
+ (rKhr+ O"Kh%o-KOf%
+ Kero )GOf._2
j
Phase
of
amplitude
l
(b)
each
+ K hfoK8 r----_
+ K hroK8 fo
4¥
25
(d)
Phase
angle
_?
between
= tan
-1
resolver
L2rKhfoKhro
__
(e)
Phase
angle
be%¢een
rotor
and
+ KhfoK0ro
KhfiGir
bending
torsion
and
amplitude
+ KhroK0
f
(AT)
- KhriGif
torsion
A
fi : f18 - 2h
3
5
Pressure-Measurement
(A_%)
Equations
Consider
the harmonic
pressure
variation
of amplitude
IPI
and ohase
angle
hh
occurring
on the surface
of the wing at a particular
orifice_
where
hh
is measured
with respect
to the wing-tip
position.
Because
of
the attenuation
and phase characteristics
of the pressure
line conmectin_
the orifice
at the wing
surface
with the pressure
cells outside
the tmunei_
the pressure
cells
experience
a pressure
of amplitude
IP'l
which
lags
the pressure
at the orifice
by the phase
angle
5.
As mentioned
previously
in the text_ all aerodynamic
quantities
are made dimensionless
_rith
respect
to the wing-tip
angle of attack
amplitude.
The necessary
is indicated
in the rotating-vector
diagram
of sketch
(f).
geometry
Resolver
rotor
Sketch
The amplitude
subscript
T.
and
phase
angle
of
the
(f)
tip
motion
are
indicated
by
the
_6
Demote
experienced
on the wing
by the symbol
by the pressure
surface.
Then
Z
the
cells
ratio of the pressure
amplitude
to the pressure
amplitude
IPI
IPI
IP'I
exi st ing
IP'I
Z
=
and
hh
= A
+ _ - _hT
Now
A
Pi
=
IPlcos
3
5
3
hh
= IPloos(A+ _ - _hT)
I P' I
Pi'
= T
IP'l
Pi
Pi'
cos
(_
-
_)) +-
Po'
IP'l
sin(_hT
- _)]
or
and
= _
c°s(_h T - b)
+ Po'
sin(_h T - _)
similarly,
Po:_
Po' cos(a_-_)
-Pi' si_(_-_)
Now
Pi'
= KiGi
Po'
= KoGo
where
Ki
in-phase
component
deflection
}[o
out-of-phase
deflection
of pressure
component
amplitude
of pressure
per
amplitude
unit
per
galvanometer
unit
galvanometer
27
T]lerl
Pi =
Po
The amplitude
=
of the wing-tip
angle
lil
_h -
A
3
4
}
[XiGicos(_h
T _) + Xo_osin(_,_ _)_
J
of attack
T
V
(A9)
is given by
eb hi T
-
(ilO)
V
Dividing
equations
(Ag) by (AIO) and by the dynamic
pressure
q
gives the component of the surface pressure coefficient
in phase and out
of phase (hereafter denoted by Re( ) and Im())
_rith the bending
amp iitude.
}_e( cp_ h) -
V
IKiGicos (ShT (All)
m(cp_h) - z_qlhLT
V
where
Z and _
[KoGocos (_hT _ 8)
are found as indicated
- KiGisin(i'_hT
-
3)
in the text.
Equations (All) were developed for a general orifice on either the
upper or lo_¢er _ing surface.
The data for
M = 0.24 obtained by means of
these
equations
are
show_
in
figure
7
as
Re
Cp_
Im
p_lu,
lower wing
Im
, the subscripts
] , Re
'
and
h/u
\
u and Z
denoting
upper
and
surface.
The real and imaginary
are given by
Re
components
p_h/l = Re
of the lifting-pressure
- Re
p_
amplitude
u
(AI2)
Im
P_nl
and are shown for
P_
_ -
M = 0.24 in figure 8.
Im
C
p@_ u
28
the
The magnitude
lifting-pressure
and phase angle with respect
coefficient
are given by
to bending
_nplitude
of
icp_ht: {[Re(Cp%)]_ + [I_(Cp%)]_}
_j_
(A13)
{h
: tan-l
Re(Cp%)
The
data
are
presented
Integration
of
coordinates
gives
in this
form
for
(AI2)
with
respect
equations
SO
all
Mach
to
numbers
in
dimensionless
9-
A
chordwise
3
5
4
figure
I
I_(Cp%) a{
(AI_)
_(Cr_h)
where
= x/2b
and
[
:
is the
I_(Cmh) (_' - _)a_
center
of moments
([ = 0.5)
I c_%L : {IRe(Or%)] _ + [I_(Ct%)_}
7h
from
_,rhich
_j_
= tan-i
(AIS)
Ic_l
7hm
: {[Re(C_)]
= tan -l
_ + [m(C_p]_}
Re(C_h)
_j_
29
Figure
12 giv<-s tho r,:sults for all Hach numbers
at
attack
in this form comouted
from numerical
integrations
to <quations
(AI4).
A
3
4
zero angle of
correspon:ling
3O
APPENDIX
APPLICATION
OF MILES'
RECTANG_
B
THEORY
FOR
OSCILLATING
SUPERSONIC
WINGS
In reference
3 Miles
considers
the linearized
problem
of an infinitesimally
thin quarter-infinite
lifting
surface
having
one straight
edge parallel
and another
normal
to
_--Y,Y, the stream_
undergoing
harmonic
oscillations
of frequency
_.
For
ease of reference,
the surface
and
an appropriate
coordinate
system
is
shown in sketch
(g).
By use of the laplace
transformation,
he obtained
the exact
linearized
expression
for the complex amplitude
of the perturbation
velocity
potential
on this surface.
With suitable
identifications,
and
with the signs of exponentials
reversed
for more conventional
X,p
Sketch
phase
interpretation_
sion is as follows:
XI
this
expres-
(g)
k
kiZ _o xl
\_
VA
Xle-iMk]_u
_
(BI)
where
2kM
k I = -_a
_a
= Ma
x
XI =
Yl = i
9 = i - yl
2b
- i
J1
=
first-order
Bessel
function
$ = _e -i_t
ml
=
2
A
3
5
4
31
and where Z and 2b are reference lengths in the span_ise and streaaT_ise
directions, respectively; _(xl,yl,k)
is the downwashamplitude resulting
from a wing deformation prescribed by
H(x,y,t)
and
related
to
= ZH(xm,Yl)
it through
_(xl'y!_k)
the
=
(postive do_)
e i_°t
(B3)
equation
- VA2 [_
(x1'Yl)+
2ikH(x1'Yl)l
(m_)
A
3
5
4
The superposition
and lift cancellation
techniques
of supersonic
steady
flow can be used to obtain
from (BI) the potential
at all points
on a
finite
rectangular
plan-form
lifting
surface
performing
either
symmetrical
or antisymmetric
oscillations,
such as that indicated
by the dashed
lines
in sketch
(g)_ providing
the Mach line from one wing tip does not intersect
the side edge of the opposite
wing panel
(i.e.,
_A _ i).
From
this
potential,
with
Z_p =_peiWt
defining
section
some
the lifting
pressure_
lift, and the section
integration
by
parts)
as
= 2p
_-_ + V _)
the expressions
for
moment
distributions
that pressure_
the
are obtained
(after
follows:
(Bs)
_(y_k)
=
- _ [#
VT (1,y_)
+ 2ik _o I _
(_l,yl k)_xl]
(B6)
D_
_ma_ (Y_,k)
= •
VZ
4qb 2
_,1
¥ (xl,yz
x_ v-£
- 4iki
"-
where
the
used,
and
vanishing
xl
= al
,k) 4xz
(B7)
O
of
the
potential
is
the
moment
at
the
wing
leading
edge
has
been
axis.
A
Even for elementary
deformation
modes,
the
of equations
(BI) and (BS) through
(BT) has not
and in order to facilitate
numerical
evaluation,
consider
For
the
following
s_mmetric
classes
of
mode
shapes.
modes:
H(xm,yl)
= Hn(S)(xm,yl)
= +
lymln(Anxl
for
For
analytical
integration
been accomplished
as yet,
it is convenient
to
antisymmetric
(rolling)
H(xl,yl)
all
+ Bn)
Yl,
It
is
seen
the
to
= Hn(A)(xl,y!)
spanwise
that
wings
this
=
choice
undergoing
variation
is
i,
2
modes:
+ lylln-l(Anxl
+ Bn)yl
n
application
n = O,
of mode
shapes
chordwise
rigid
expressible
:
1,
limits
subsequent
deformations
in a power
series
(BS)
2
in
for
Yl
which
= }-
Upon substitution
of equations
(B$) and (BI) into equations
(BS)
through
(BT) it is possible
(after
some interchanging
of the orders
of
integration)
to carry out all except
the final two integrations
exactly,
but numerical
methods
are necessary
in order to complete
these.
Series
methods
are applicable
to the inner integrals
since their integrands
consist of certain
products
of Bessel,
trigonometric,
and algebraic
functions,
and as the resulting
integrated
functions
are well behaved,
Gauss'
method
is employed
to effect
the outer integration.
This
final
work
answers
and
was
the
subsequent
programmed
for
combinations
the
IBM
704,
necessary
and
this
to
obtain
programwas
the
used
3
5
4
33
in
The
the
obtaining
input
true
the
supersonic
information
reduced
theoretical
required
frequency
is
the
results
presented
specification
eb
k = -_- _ the
aspect
of
in this
the
Mach
Z
A : _
ratio
,
reoort.
number
the
H,
moment
axis
al, and the mode shape as reflected
in its general
classification
(symmetric
or antisymmetric)_
the choice
of
n_ and the coefficients
An
and B n.
In its present
form_ the program
is only applicable
to the
aerodynamic
situations
for _<hich
_A k 2_ i.e._ those
for which
each tip
}hch line is entirely
contained
on its wing panel.
The
program
furnishes
the
pressure
distribution
at
any
specified
points
on the plan form_ and the section
lift and pitching
moment
for any
designated
spanwise
stations.
Since the various
integrands
are essentially
nonsingular_
the required
series
expressions
and integrations
are straightfo_£ard
and it is believed
that the final answers
are in error by no more
than i percent.
34
REFERENCES
i.
o
,
,
I,_ACA Subcommittee
on Vibration
and Flutter:
of Flutter
Research
and Engineering.
NACA
A Survey
and Evaluation
RM 56112,
1956.
Watkins,
Charles
E., Runyan,
Harry L., and Woolston,
Donald
S.:
the Ker_lel Fuslction of the Integral
Equation
Relating
the Lift
Dovrnwash Distributions
of Oscillating
Finite
Wings
in Subsonic
NACA Rep. 1234, 1955.
(Supersedes
NACA _
3131)
Miles,
John
Supersonic
W. : A
Flow.
General
Quart.
Solution
for
Appl. Hath.,
the Rectangular
Airfoil
vol. ii, no. i, 1953.
Edward,
Jr., Clevenson,
Sherman
A.,
A.:
Some Measurements
of Aerodynamic
and Leadbetter,
Forces
and Moments
at S_sonic
Speeds
on a Rectangular
Wing
of Aspect
lating
About
the _dchord.
NACA TN 4_40, 1958.
Laidlaw,
W. R.:
Theoretical
and Experimental
om Lov_-Aspect-Ratio
Wings Oscillating
in an
M.I.T.
Aeroelastic
and Structures
Res. Lab.
HO a(s) )2-5_6-6),
Sept. 1954.
Moll_-Christensen,
Erik L.:
An
tigation
of Unsteady
Transonic
ril.
in
Woolsto1_,
Donald
S., Clevenson,
Sherman
A., and Leadbetter,
Sumner
A.:
Analytical
and Experimental
Investigation
of Aerodynamic
Forces
and
Moments
on Low-Aspect-Ratio
Wings Undergoing
Flapping
Oscillations.
I_ACA T}_ 4302. 1955.
Wilmeyer,
S_mner
f
On
and
Flow.
Ratio
2 Oscil-
Pressure
Distributions
Incompressible
Flow.
Rep. 51-2 (Contract
Experimental
and Theoretical
Flo_.
Sc.D. Thesis,
M.I.T.,
Inves1954.
Epperson_
Thomas
B.. Pengelley,
C. Desmond_
Ransleben_
Guido E., Jr.,
a_d Younger_
Dewey G.. Jr.:
(Unclassified
Title)
Nonstationary
Air!oad
Distributions
on a Straight
Flexible
Wing Oscillating
in
a Subsonic
Wind Stream.
WADC TR 5_-_23,
Jan. 1956 (Confidential
Report)
•
i0.
Lessihg_
Henry C., Fryer,
Thomas
B., and Head, Merrill
H.:
A System
for Measuring
the Dynamic
Lateral
Stability
Derivatives
in HighSpeed Wind T_inels.
NACA TN 3345, Dec. 1954.
Knochtel,
Earl D.:
Experimental
Investigation
at Transonic
Speeds
of Pressure
Distributions
Over Wedge and Circular-Arc
Airfoil
S_ctions
and Evaluation
of Perforated-Wall
Interference.
NASA
TN
ii.
.
D-15,
1959.
Croom,
Delwin
R.:
Low-Subsonic
Investigation
to Determine
the
Chordwise
Pressure
Distribution
and Effectiveness
of Spoilers
on
a Thin, Lo_-Aspect-Ratio,
Unswept,
Untapered_
Semispan
Wing and on
the Wing With Leadingand Trailing-Edge
Flaps.
NACA RHL58B05,
1958.
3_
12.
Liepmann_
H. W. and Roshko_
A.:
Elements
and Sons, Inc., 1957_ Pp.342-346.
13.
Garner,
H. C._ and Acum, W. E. A.:
Note
Oscillating
Wings.
British
ARC 18952,
Unclassified_
Contents
Confidential.
14.
Runyan,
Harry L._and
Woolston_
Donald
S.:
the Aerodynamic
Loading
on an Oscillating
and Sonic Flow.
NACA Rep. 1322, 1957.
15.
Watkins,
Charles
E._ Woolston,
Donald
S._ and Curmingham,
Herbert
J.:
A Systematic
Kernel
Function
Procedure
for Determining
Aerodynamic
Forces
on Oscillating
or Steady
Finite
Wings
at Subsonic
Speeds.
NASA TR R-48_ 1959.
Miles,
John
Cambridge
17.
W.:
The Potential
University
Press_
Runyan_
Harry L.,and
Watkins_
Effect
of Wind-Tunnel
Walls
Dimensional
(Supersedes
Subsonic
NACA TN
Theory
1959.
of
of
Gasdynamics.
on Some
January,
Recent
1957.
Flow.
P_ers
Title
Wiley
on
Method
for Calculating
Finite
Wing in Subsonic
(Supersedes
NACA TN 3694)
Unsteady
Supersonic
Charles
E.:
Considerations
on Oscillating
Air Forces
Compressible
2552)
John
NACA
Rep.
Flo_.
on the
for Two-
1150,
1953.
36
A
3
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Figure
lower
i.- Continued.
6¥
41
ToP.
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Bleed filter
j
A
3
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cell
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fJ
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Sconivolve manifold
(stator)
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L
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Scanivalve body
(f)
Details
of
Figure
Scanivalve
i.-
modification.
Continued.
42
L_
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-.2
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0
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or
3
5
4
+-2
CPt
0
-+.2
,2
0
.2
.4
.6
.8
1.0
xl2b
(a)
Pressures
Figure
on
upper
3.-
and
lower
Static-pressure
surfaces;
M
=
distributions.
0.24,
_
=
0 °.
45
-.5
Y/Ab=90
0
+.5
Y/Ab=2'0
0
Cpu
or
±.5
CPl
Y/Ab=.50
0
+-.5
Y/Ab:0
.5
0
.2
.4
.6
.8
1.0
x/2b
(b)
Pressures
on
upper
and
Figure
lower
3--
surfaces;
Continued.
M
= 0.24_
_
=
5 °.
46
R=2.1x I06
o
Y/Ab=.90
0
Y/Ab=.70
o
Y/Ab-50
0
Y/Ab=O
Cp
.2
.4
.6
.8
x/2b
(c)
Lifting
pressures;
Figure
3.-
M
= 0.24,
Continued.
_
= _o.
47
-2
Y/Ab--.90
0
-+.2
0
Y/Ab :.70
Gpu
or
+-.2
Cpz
Y/Ab=.50
+--.2
:Y/Ab=O
0
.2
0
,2
.4
,6
.8
1.0
x/2b
(d)
Pressures
on
upper
a_d
Figure
lower
3.-
surfaces;
Continued.
M
= 0.70_
o_ = 0 °.
48
-I.O,
-.5
Y/Ab=.90
0
+--.5
0
Y/A b=.70
0
Y/Ab=.50
0
Y/Ab=O
Cpu
or
.5
0
.2
.4
.6
.8
1.0
xl2b
(e)
Pressures
on
upper
and
Figure
lower
3.-
surfaces;
Continued.
M
= 0.70,
_
=
_o.
'¥
49
15
I0
5
Y/Ab =.90
¥5
Cp
Y/Ab=.70
0
_.5
Y/Ab=.50
0
¥-5
0
-.5 0
Y/Ab=O
.2
.4
.6
.8
1.0
x/2b
(f) Lifting
pressures;
Figure
M = 0.70,
3.- Continued.
_ = _o.
I
5o
Y/Ab =.90
A
3
5
4
Y/Ab=.70
.2
0
.2
.4
.6
.8
1.0
x/?_b
(g)
Pressures
on
upper
and
Figure
lower
3.-
suI_faces;
Continued.
M
= 0.90_
_
= 0 °.
51
--I0
--5
O
YlAb=.90
+-.5
A
3
B
4
Y/Ab =.70
0
CPu
or
cpt
±.5
Y/Ab=.50
0
---.5
0
Y/Ab: 0
'50
.2
.4
.6
.8
I.O
x/P_b
(h)
Pressures
on
upper
and
Figure
lower
3.-
surfaces;
Continued.
M
=
0.90_
_
=
5 °.
52
1.5
Cp
0
Y/Ab=.90
0
Y/Ab-70
0
Y/Ab=.50
0
Y/Ab=O
•2
.4
.6
.8
x/2b
(i) Lifting
pressures;
Figure
M = 0.90_
3.- Continued.
_ = 5°.
1.0
53
O
Y/Ab=.90
0
Y/Ab=.70
0
Y/Ab=.50
0
Y/Ab=O
A
3
5
4
Cpu
or
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40
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.6
.8
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on
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and
Figure
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Continued.
M
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54
- 1.0
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A
3
5
4
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Y/Ab=.70
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Y/Ab=.50
0
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Y/Ab=O
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0
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.4
.6
.8
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(k)
Pressures
on
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and
Figure
lower
3.-
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Continued.
M
=
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55
5
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A
3
5
4
O
Y/Ab=.70
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Y/Ab=.50
O
Y/Ab=0
Cp
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.4
.6
.8
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x/2b
(2)
Lifting
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Figure
3--
M
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Continued.
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56
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A
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3
5
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0
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0
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.6
.8
1.0
x/2b
(m) Pressures
on upper
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3.-
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M = i.i0,
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57
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mud
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Continued.
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58
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A
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5
4
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59
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3
5
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0
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0
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on
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and
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M
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e
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61
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4
t
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4
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Y/Ab=O
0
L
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NASA
- Langley
Field,
V_..
_-354
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