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NASA Technical Memorandum 4645
Experimental Surface Pressure Data Obtainedon 65 ° Delta Wing Across Reynolds Numberand Mach Number Ranges
Volume l--Sharp Leading Edge
]ulio Chu and James M. Luckring
February 1996
https://ntrs.nasa.gov/search.jsp?R=19960025648 2020-02-09T03:11:36+00:00Z
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NASA Technical Memorandum 4645
Experimental Surface Pressure Data Obtainedon 65 ° Delta Wing Across Reynolds Numberand Mach Number Ranges
Volume lmSharp Leading Edge
Julio Chu and James M. Luckring
Langley Research Center • Hampton, Virginia
National Aeronautics and Space AdministrationLangley Research Center • Hampton, Virginia 23681-0001
February 1996
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The use of trademarks or names of manufacturers in this report is foraccurate reporting and does not constitute an official endorsement,
either expressed or implied, of such products or manufacturers by the
National Aeronautics and Space Administration.
Available electronically at the following URL address: http://techreports.larc.nasa.gov/ltrs/ltrs.html
Printed copies available from the following:
NASA Center for AeroSpace Information
800 Elkridge Landing Road
Linthicum Heights, MD 21090-2934
(301) 621-0390
National Technical Information Service (NTIS)
5285 Port Royal Road
Springfield, VA 22161-2171
(703) 487-4650
-
Summary
An experimental wind tunnel test of a 65 ° delta wing
model with interchangeable leading edges was conducted
in the Langley National Transonic Facility (NTF). The
objective was to investigate the effects of Reynolds and
Mach numbers on slender-wing leading-edge vortex flow
with four values of wing leading-edge bluntness. The
data presented in volume 1 of this report are for a sharp
leading edge equivalent to 0 percent of the mean aero-
dynamic chord. The data for the small-, medium-, and
large-radius leading edges are presented in volumes 2, 3,
and 4, respectively, of this report. Experimentally
obtained pressure data for the sharp leading edge are pre-
sented without analysis in tabulated and graphical for-mats across a Reynolds number range of 6× 106 to36 x 106 at a Mach number of 0.85 and across a Mach
number range of 0.4 to 0.9 at a Reynolds number of
6 x 10 b. Normal-force and pitching-moment coefficient
plots for these Reynolds number and Mach number
ranges are also presented.
Introduction
Wing leading-edge vortex flow on slender wings has
been a subject of study at aeronautical research laborato-ries (refs. 1-6) for many years. The wing upper surface
pressure loading induced by the leading-edge vortex has
been shown to provide a significant vortex-lift increment
at moderate to high angles of attack for slender wings.
(See ref. 7.) Application of vortical flow benefits has
been primarily directed toward military use for which
designs have been investigated that enhance transonic
maneuverability for tactical supercruisers using vortex
lift (refs. 8 and 9) or that suppress the vortex flow forthose conditions where it is undesirable. (See ref. 10.)
However, commercial application of vortex flow is evi-
dent in the ability of the Concorde to achieve high lift
during takeoff and landing.
The majority of previous leading-edge vortex flowstudies have been conducted on sharp leading-edge
wings, where the primary separation line may beassumed to be located at the leading edge. This assump-
tion permits inviscid vortex sheet approximations in ana-
lytical modeling and should minimize the dependency
of the experimental data on Reynolds number. (See
refs. 3-6 and 8.) However, vortical flow investigations
on blunt leading-edge wings have been less comprehen-
sive. (See refs. 2, 3, and 11 .) The flow around blunt lead-
ing edges is inherently dominated by viscous effects and
presents a significant challenge for empirical, analytical,
or computational analysis. The primary separation line
location and the vortex strength for a blunt leading edge
are known to be dependent on Reynolds number. This
sensitivity to Reynolds number also occurs with flow
reattachments and subsequent development of second-
ary vortices regardless of leading-edge bluntness. (See
refs. 10 and 12.)
Accordingly, the National Aeronautics and Space
Administration (NASA) Langley Research Center
(LaRC) has attempted to augment the existing database
(refs. 11 and 13) for the effects of leading-edge bluntness
across a broad Reynolds number range and to facilitatethe development of suitable scaling techniques in charac-
terizing the complex leading-edge flows. The approach
was to investigate the basic nature of the surface pressure
on a slender wing with various values of the leading-edge
radius. The experiment was conducted on a planar delta
wing with a leading-edge sweep of 65 ° across broad
Reynolds number and Mach number ranges at the
Langley National Transonic Facility (NTF). The model
was fabricated with removable leading edges to permit
testing of four leading-edge sets. The sets were desig-
nated as sharp, small, medium, and large, which corre-
sponded to values of leading-edge radii normalized by
the mean aerodynamic chord of 0, 0.05, 0.15, and
0.30 percent, respectively.
The experimental data for the sharp leading edge are
presented in volume 1 of this report. The data for the
small-, medium-, and large-radius leading edges are pre-
sented in volumes 2, 3, and 4, respectively, of this report.
Wing pressure data are presented along with normal-
force and pitching-moment coefficient data. Note that the
primary objective of the force measurements was to
monitor the safety of the model support system during
the experiment; hence, the accuracy of the force mea-
surements was of secondary importance.
Symbols
a, b, c, d
b
Cm
coefficients in first-blending function
(appendix A)
wing span, 24 in.
pitching-moment coefficient about moment
reference point, Pitching momentq**Sb
CN normal-force coefficient,Normal force
q.oS
P -- Poo
pressure coefficient, --q_o
cR
FN
root chord, 25.734 in.
mean aerodynamic chord, 17.156 in.
normal force, lbf
-
l, m, n coefficients in second-blending function V
(appendix A)
pitching moment, in-lbf
free-stream Mach number
local pressure, psia
free-stream static pressure, psia
free-stream total pressure, psia
free-stream dynamic pressure, psf
Reynolds number
local radius
wing area, 2.145 ft 2
total temperature, °F
uncertainty
distance from apex, positive downstream, in.
initial longitudinal coordinate of blending
function tp, in. (appendix A)
endpoint longitudinal coordinate of blending
function 9, in. (appendix A)
y spanwise distance from apex, positive
right, in.
z distance above X-Y plane, positive upward, in.
¢x angle of attack, deg
7 ratio of specific heats
2y
rl bt
nondimensional distance parameter
¢p first-blending function (appendix A)
second-blending function (appendix A)
Abbreviations:
My
M**
P
P**
PT
q**
R
r
S
tT
U
X
Xo
Xl
ESP electronically scanned pressure
1 lower
L.E., le leading edge
mac mean aerodynamic chord
NTF National Transonic Facility
starb'd starboard
u upper
t local
Facility
The test was conducted in the Langley National
Transonic Facility (NTF). The facility is a fan-driven,
closed-circuit, cryogenic transonic pressure wind tunnel.
2
(See fig. 1.) The test section is 8.2 fi high by 8.2 ft wide
by 25 ft long with a slotted ceiling and floor.
The NTF operating capability has a nominal Mach
number range of 0.2 to 1.2, total pressure range of 15
to 120 psia, and total temperature range of -260°F
to 150°F. The test gas may be dry air or nitrogen. Amaximum unit Reynolds number of 146 x 106 fi-I is
achieved at a Mach number of 1.0. Independent control
of pressure, temperature, fan speed, and inlet guide vaneangle permits Mach number, Reynolds number, and
dynamic pressure to be varied independently within the
wind tunnel operational envelope.
To reduce turbulence, four antiturbulence screens
were installed in the settling chamber, and a 15:1 con-
traction from settling chamber to nozzle throat was
provided. To minimize wall interference, the test sec-
tion floor and ceiling were set at 0 °, model support walls
at -1.76 °, and reentry flaps at 0 °. Acoustic treatment
upstream and downstream of the fan was incorporatedto reduce fan noise. More details of the wind tunnel
physical characteristics and operations can be found inreference 14.
Model Description and Test Apparatus
The basic layout of the delta wing model is shown in
figure 2(a). The wing has a leading-edge sweep of 65 °,no twist or camber, and four sets of interchangeable lead-
ing edges, which attach to the flat plate part of the wing.The four leading-edge streamwise contours are illus-
trated in figure 2(b). The model root chord is 25.734 in.,
the wing span is 24 in., and the maximum wing thickness
is 0.875 in. The wing was fabricated from VascoMaxC-200,1 which is suitable for cryogenic operation, and
had a surface finish specification of 8 microinches.
Figure 2(c) is a photograph of three of the leading-edge
sets; one set is attached to the fiat plate part of the model.
With the exception of the seam at the plane of symmetry,
where the left and right side leading edges are joined,
each interchangeable leading-edge set (which includes
part of the outboard trailing edge) was fabricated as onecontinuous piece of hardware. This eliminated the sur-
face discontinuity typically associated with an upper and
lower leading-edge surface parting line.
The wing and sting surfaces are represented by a
fully analytical function with continuity through thesecond derivative and, hence, curvature. However, the
wing-sting intersection line exhibits a discontinuity in
slope across it. The leading- and trailing-edge cross-
sectional shapes are constant spanwise except for a
region near the wingtip where the two shapes intersect. A
lTrademark of Teledyne Vasco.
-
detailedgeometricdescriptionof thevariousregionsof the deltawing and sting(fig. 3) is presentedinappendixA. Unlessotherwisenoted,all quantitieshavebeennormalizedbythewingrootchord.
Themodelwassupported(fig.4(a))attheaftendbythemodelsting,10°-bentsting,andstubsting.Thetotalmodelsupportsystemconfinedthecenterof rotationofthemodelto thecenterof thetestsection.Thebentstingextendedthepositiveangle-of-attackrangeup toapproximately30° .
The model had 183 surface static pressure ports with
each having an inside diameter of 0.010 in. The orifice
size selection was based on prior cryogenic model-
testing experience (ref. 15) at the Langley 0.3-Meter
Transonic Cryogenic Tunnel (0.3-m TCT). The majority
of the ports were located on the upper surface of the rightside (i.e., starboard side) of the model. They were located
at nondimensional longitudinal stations of x/c R = 0.20,0.40, 0.60, 0.80, and 0.95. (See fig. 2(a).) At each chord
station, the orifices were situated at constant fractions of
local semispan so that they were aligned along rays ema-nating from the wing apex. The upper surface orifices
were located every 5 percent of the local semispan out to
one half of the local semispan, beyond which, they were
spaced every 2.5 percent of the local semispan. The
lower surface pressure ports were located on the left side
(i.e., port side) of the model at the same longitudinal sta-tions as on the starboard side. At each chord station, the
lower surface orifices were located at local semispan sta-tions of 0.20, 0.40, 0.60, 0.70, 0.80, 0.85, 0.90, and 0.95.
In addition, orifices were located directly on both the
port and starboard leading edges (except for the sharp
leading-edge set) at every I 0-percent root chord as wellas at the 0.95-chord station. Pressure port locationdimensions are shown in tables 1, 2, 3, and 4. Locations
that did not have pressure ports are indicated by dashed-line entries.
Instrumentation
Surface static pressure measurements were obtained
with four 48-port, 30-psid electronically scanned pres-sure (ESP) modules. Because of limited volume within
the model and its immediate vicinity, the ESP moduleswere secured inside the enclosure of the wind tunnel
pitch system downstream of the stub sting. These mod-
ules were placed in a heated container to ensure opera-
tion in a cryogenic environment. All model pressuretubes were routed downstream through the sting systemand connected to the ESP modules.
Cryogenically rated strain gages configured for twomoment bridges were installed on the model sting. These
gages were used to monitor model support system safety
during the test. One bridge was located at the wing
trailing-edge longitudinal station and the second 4 in.
downstream of the wing trailing edge. In figure 4(b), note
gage locations at the two rings around the sting just aft of
the wing trailing edge. These gages were configured toPoisson ratio full bridges and were shielded from the free
stream by a protective chemical coating. Normal force
and pitching moment were calculated from measure-
ments of these gages and reported as nondimensionalcoefficients.
Model angle of attack was determined from the
wind tunnel arc-sector angles measured during the test
and from sting bending characteristics that were obtained
during pretest loadings. The sting fairing cavity volume
was insufficient for installation of a fully heated onboard
accelerometer package to measure inertial model angles
during cryogenic operation.
Measurement Accuracy
The Beattie-Bridgman gas model (ref. 16) and the
quoted specifications for the instrumentation were
applied to approximate the accuracies of the test parame-
ters and the aerodynamic coefficients. The technique of
Kline and McClintock, as specified by Holman (ref. 17),was used to calculate the coefficient accuracies. The
uncertainties U of the measurements of the normal-force
coefficient CN, pitching-moment coefficient Cm, pressure
coefficient Cp, and free-stream Mach number Moo dependon the uncertainties of their respective primary measure-ments. Estimates of measurement accuracies are pre-
sented in appendix B.
The quoted accuracy of an ESP module is _+0.1 per-
cent of the instrument maximum pressure. Therefore, the
accuracy of the 30-psid ESP modules used in this test is
+0.03 psid.
Data Reduction and Corrections
Data reduction methods used for the pressure data
and wind tunnel parameters were those outlined in refer-ence 16. To obtain force and moment data, the strain
gages on the sting were treated as two-component strain
gage balances in the data reduction procedure. (See
ref. 18.) Because the Reynolds number range was
achieved at only two test temperatures for the various
total pressures, aeroelastic effects (i.e., model deforma-
tion due to pressure) can distort the true Reynolds num-ber effects. However, the aeroelastic effect on the
aerodynamic data is small because of the relatively highstiffness resulting from the model thickness and low-
aspect-ratio planform as well as the support system struc-ture as illustrated in figure 4(a). Measurements for an
inverted model attitude were not taken, and a nominal
-
flow angularity correction of +0.13 ° (upflow) was
applied to the reported angles of attack.
Test Program
Figure 5 shows the combinations of Reynolds num-bers and free-stream Mach numbers used for the test. The
test matrix shows that a Mach number of 0.85 was
selected for the study of the Reynolds number effects andthat a Reynolds number of 6 x 106 was selected for the
study of the Mach number effects. All data were obtained
with free boundary layer transition.
Data Presentation
Pressure data measured on the delta wing are pre-
sented for each data point in tabular and graphical for-
mats in appendixes C and D. Normal-force and pitching-moment data for each angle of attack are presented in
figures 6 and 7. The moment reference point was located
at two thirds of the root chord aft of the wing apex. The
angle of attack ranged nominally from -1 ° to 27 °.
Wing pressure coefficients are tabulated for each
data point and accompanied by a surface pressure distri-
bution plot and a leading-edge pressure plot. The degree
of similarity between the port and starboard leading-edge
pressure plots indicates the extent of flow symmetry.
Note that a coefficient value represented by a seriesof asterisks in tables C1-C3 and D1-D6 is either an
unrecorded or an apparently erroneous pressure portmeasurement.
The pressure coefficient data test matrix is presentedin table 5 for a Reynolds number range of 6 x 106 to
36 x 106 at M** = 0.85 in appendix C and for a Mach
number range of 0.40 to 0.90 at a Reynolds number of6 x 106 in appendix D.
Summary Remarks
Pressure data obtained from a 65 ° delta wing with
the sharp leading edge (i.e., 0 percent of mac) are pre-
sented in the form of surface pressure plots and leading-
edge pressure plots for a Reynolds number range at a
Mach number of 0.85 and a Mach number range at aReynolds number of 6 x 106. Although upper and lower
surface pressures were measured on opposite sides of the
model, model symmetry permitted pressure distribution
plots to be superimposed on a sketch of the half wing.
The plots of leading-edge pressures indicate the extent of
flow symmetry by comparing port and starboard leading-
edge pressures. Normal-force and pitching-moment coef-
ficient plots for Reynolds number and Mach number
ranges are also presented.
NASA Langley Research CenterHampton, VA 23681-0001August 11, 1995
-
Table1.WingUpper Surface Pressure Port Locations on Starboard Side
x/c R of---
0.20 0.40 0.80 0.95
0.050
.100
.150
.200
.250
.300
.350
.400
.450
.500
.525
.550
.575
.600
.625
.650
.675
.700
.725
.750
.775
.800
.825
.850
.875
.900
.925
.950
.975
1.000
r 1 x, in. y, in.
10.294
x, in. y, in.
5.147 0.120
.240
.360
.480
5.147 .720
.840
.960
1.080
1.200
5.147 1.320
5.147 1.440
5.147 1.560
5.147 1.680
5.147 1.800
5.147 1.920
5.147 2.040
5.147 2.160
5.147 2.280
q,
10.294
0.240
.480
.720
.960
1.200
1.440
1.680
1.920
2.160
2.400
2.520
2.640
2.760
2.880
3.120
3.240
3.360
3.480
3.600
3.720
3.840
3.960
4.080
4.200
4.320
4.440
4.560
4.680
0.60
x, in. y, in.
15.440 0.360
.720
1.080
1.440
1.800
2.160
2.520
2.880
3.240
3.600
3.780
3.960
4.140
4.320
4.500
4.680
4.860
5.040
5.220
15.440 5.580
5.760
5.940
6.120
6.300
6.480
6.660
] 6.840i
7.020
x, in. y, in. x, in. y, in.
20.587
ip
2.400
2.880
3.360
3.840
4.320
4.800
5.040
5.280
5.520
5.760
6.000
6.240
6.480
6.720
6.960
7.200
7.440
7.680
7.920
8.160
8.400
8.640
8.880
9.120
9.360
24.447
_r
2.280
2.850
3.420
3.990
4.560
5.130
5.700
5.985
6.270
6.550
6.840
7.125
7.410
7.695
7.980
8.265
8.550
8.835
9.120
9.405
9.690
9.975
10.260
10.545
10.830
11.115
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Table2.WingUpperSurfacePressurePortLocationsonPortSide
x/c R of-.-
0.40 0.60 0.80 0.950.20
x, in. y, in.
5.147 -2.160
x, in. y, in.
10.294 -4.560
x, in. y, in.
15.440 -6.840
x, in. y, in.
20.587 -9.120
x, in. y, in.
24.447 -10.830
Table 3. Wing Lower Surface Pressure Port Locations on Port Side
0.20
1] x, in.
-0.200 5.147
-.400
-.600
-.700
-.800
-.850
-.900
-.950
-.975 ......
-1.000 ......
x/c R of---
y, in.
-0.480
-.960
-1.440
-1.680
-1.920
-2.040
-2.160
-2.280
0.40 0.60
x, in.x, in. y, in.
10.294 -0.960
-1.920
i -2.880
-3.360
-3.840
-4.080
-4.320
-4.560
-4.680
15.440
IIi
't
y, in.
-1.440
-2.880
-4.320
-5.040
-5.760
-6.120
-6.480
-6.840
-7.020
0.80 0.95
x, in. y, in.
20.587 -3.840
-5.760
-6.720
-7.680
-8.160[
-8.640
-9.120
-9.360
x, in. y, in.
24.447 -2.280
-4.560
-6.840
-7.980
-9.120
-9.690
-10.260
-10.830
, -11.115
Table 4. Wing Lower Surface Pressure Port Locations on Starboard Side
0.900
.950
x/c R of---
0.20
x, in. y, in.
5.147 2.160
0.40
x, in. y, in.
10.294 4.560
0.60
x, in. y, in.
15.440 6.840
0.80
x, in. y, in.
20.587 9.120
0.95
x, in. y, in.
24.447 10.830
Table 5. Pressure Coefficient Data Test Matrix for Sharp Leading Edge
Appendix table Run Mach Rmac q**, psf t_ °F
C1
C2
C3
DI
D2
D3
D4
D5
D6
88
83
93
84
0.85
.85
.85
.40
6x 106
12
36
6
722
1444
1035
387
85
86
87
89
90
.60
.80
.83
.87
.90
555
692
710
733
750
120
120
-250
120
6
-
Low
-spe
ed
200
Fan
48.6
15:1
cont
ract
ion
Ill Ill Ill
/II
I
Ill
III
III
IIII
Coo
ling
coil
Rap
iddi
ffus
er
Fig
ure
1.
Ant
iturb
ulen
cesc
reen
s
Lan
gley
Nat
iona
lT
rans
onic
Faci
lity
circ
uit.
sect
ion
Plen
um
Lin
ear
dim
ensi
ons
are
infe
et.
Hig
h-sp
eed
diff
user
-
0
/65 °
Y/CR.6
I
.2
Interchangeable leading edge
x/c R
.4
Pressure station (5 places)
Flat plate
.6
Sting fairing
.8
Trailing-edgeclosure region
1.0 ylc R = 0.466
(a) Model configuration.
Figure 2. Delta wing model.
-
SharpSmallradius
MediumradiusLargeradius
(b) Streamwiseleading-edgecontours(nottoscale).
Figure2. Continued.
-
0
(c)
Mod
elw
ithth
ree
lead
ing-
edge
sets
.
Figu
re2.
Con
clud
ed.
-
x/c R
Y/CR0 .2 .4 .6
.6
.8
i.0 _V/cR--- 0 6 .... 0.9797
0 ° taper Region 1
..... 1.175
r/'J-_CR = 1.979 Region 2.................................... 1.253
2.25 ° taper Region 3
0° taper Region 4
1.684
1.758
Figure 3. Delta wing model fore-sting detail.
11
-
to
Stub
stin
gf
Stin
gfa
irin
gcl
osur
e
T_u
nnel
cent
erlin
e...
.--
-__
_10
_/-
(a)
Mod
elan
dst
ing
syst
empr
ofile
.
Figu
re4.
The
65°
delta
win
gm
odel
asse
mbl
yan
dsu
ppor
tsy
stem
.
-
(b)I
nsta
llatio
ninLa
ngle
yNat
iona
lTra
nson
icFac
ility
.
Fig
ure4
.C
oncl
uded
.
L-91
-696
3
-
0 Cr_
i-I o
_rQ
--.I
_.lo
0_
0 ×
_o
w-
-1_
w A v A v
-
_-n.
O0 _Z
o i B"
I0., o t_ 0 o I=1
I0...
,<
I ..p,,
0",
OO
Oo
1,0
O_
t_
I
iii
iii \
¼
!I
II
ii
ii
Ii
ii
L",
_%
\2,
<>
\\
ii
i
b, \ b
b_I
ii
r_ .--,
--,
.,--
.,--
.,-C
__
4_0'
,O
o
> \
[>
_H
PP
IIIIII
IIIIII
_t_O
'_X 0
I
II
I
-
Cm
.55
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05
0
0
0
0
-.05
-.10
-.15
-.20
-.25
-2
_A
v
_z_ z
I
0 2
_o.
I
4
rvx.
I
6
Run Rma cx 10 -6
O 88 6[] 83 12
93 36/X 94 60
X"_ 6,_.Z_
D-_-t _
O--o.
"A-._^
nzr_z._r, c"f3..__
I I I I
8 10 12 14
_, deg
(b) Cra versus _.
Figure 6. Concluded.
"A
o-..
tT, °F
121127
-250-249
I I I i
16 18 20 22
pT_ psia
15.931.822.838.0 --
,£u-o"O
I I
24 26 28
16
-
2.8
2.6 Run M_ tT,°F p_ pslao 84 0.40 120 26.8
2.4 D 85 .60 120 19.586 .80 121 16.4
2.2 A 87 .83 120 16.188 .85 121 15.989 .87 121 15.7
2.0 D 90 .90 120 15.5
1.8
1.6
1.4
CN
. ._A_s,2 A_I
r-_ S ,_0
£3" or-
-.2 i , i i i 1 i i i i I i i i i
-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
_, deg
(a) CNversus o_.
Figure 7. Normal-force and pitching-moment coefficients at angles of attack for wing with sharp leading edge.
Rma c = 6 x 106.
17
-
p==
¢G
O
r_r_
C::
C_
i I'O 0 I'O C_
oo
oo
0 I'o I'o I-O
C_
oo
Ii
_._
0
II
I
,i U_
II
I
6
.I
II
I
r_
I
ii
i
0
II
IIII
IIIIII
IIIIll
IIIIII
IIIIII
IIIIg
lIll
IIIIII
IIIIll
III
f;;?
F
F 7_
I2
F S
_oe
oe
0
'-Z ,4F
I1
Ii
-
Appendix A
Delta Wing and Near-Field Sting Analytical
Definition
General equations were used to define the leading-
edge semithickness, the flat plate semithickness, the
trailing-edge closure semithickness, and the transverse
radius of the sting fairing. The equation tp defines the
particular shape of interest (e.g., the leading-edge con-tour) and the equation _t defines the boundary conditions
(at _ = 1) for tp. Details are as follows:
= (X-Xo)/X 1 (A1)
tp(_) = ++_xl(a.T_+b_+c_2+d_ 3) (0
-
Trailing-Edge Closure Region
The streamwise trailing-edge closure is designed to
produce a sharp trailing edge and to match the flat plate
wing at the 90-percent root chord station with continuity
through the second derivative. The closure is described
by equation (A2), the coefficients in table A2, and the
following definitions:
x0= 1
x 1 = 0.10
Sting Fairing
The sting is a body of revolution and the sting fairing
is designed to emerge from the wing slightly aft of the
60-percent root chord station and to match the constant-
radius part of the sting slightly ahead of the wing trailing
edge. The transverse radius of the sting fairing is
descfibedbyequation(A2), the coefficientsin table A3,
and the following definitions:
x 0 = 0.61057051
x I = 0.36916023
Fore-Sting
As shown in figure 3, the downstream continuation
of the sting in the near field of the wing is referred to as
the fore-sting. It can be subdivided into the four regions
listed in table A4 for the purpose of defining the sting
transverse radius q). In region 2, the sting transverseradius increases by the radius of curvature equal to 1.979
from x/c R = 1.175. (See fig. 3.) Beyond region 4, theactual sting geometry becomes more complex. For com-
putational purposes, the sting could be either extended asis or closed out in a convenient fashion.
Table A1. Leading-EdgeCoefficientsforEquation(A2)
r/_, percent a b c d
0 0 3d -b 0.1133386669
.05 0.06666666666667 0.21501600073802 --0.25668266740469 .08833866691267
.15 .11547005383792 .12350964979191 -.19567843344062 .07003739672345
.30 .16329931618554 .03382978289013 -.13589185550609 .05210142334309
Table A2. Trailing-Edge Coefficients for Equation (A2)
r/_, percent / a b / c d
0 r 0 3d T -b 0.17000800036901
r/_, percent0.27910261994295
Table A3. Sting Fairing Coefficients for Equation (A2)
O. 10040234847327 0.33279822819157 -0.39554969598736 O.13603332984884
Table A4. Fore-Sting Transverse Radius q_
Region Taper, deg x/cR q)
From 0.9797 0.06412
2.25
To 1.175
From 1.175
To 1.253
From 1.253
To 1.684
From 1.684
!To 1.758
0.06412
0.06412
0.06564
0.06564
0.08258
0.08258
0.08258
2O
-
Z
_=0
_=1
(_)
---_
J
l/
'I\
,la/"
/
I_r
le//
=(X
-xo)
lx1
I I I I I
x0
=X
le
xI
_m,.I
i i
Figu
reA
1.D
elta
win
gse
mith
ickn
ess
func
tions
.
rX
-
Appendix B
Data Uncertainty
The uncertainties U of the measurements of the
normal-force coefficient CN, pitching-moment coeffi-
cient C m, pressure coefficient Cm and free-stream Machnumber M** depend on the uncertainties of their respec-
tive primary measurements.
The coefficients C N, Cm, and Cp (Mach number isdiscussed separately) are derived by
F N
C N = _ (B1)
My
Cm - q**Sc (B2)
P -- Poo
Cp - (B3)q_,
The primary measurements used to define these
coefficients are the normal force F N, pitching moment
My, surface local static pressure p, free-stream static
pressure p**, and free-stream total pressure PT. The free-stream static pressure and the free-stream total pressure
are used to compute the free-stream Mach number,
which, in turn, is used to compute the free-stream
dynamic pressure q.,.
The free-stream dynamic pressure that accounts for
the compressibility effect in high-speed flow is definedas
1 M 2q., = _TP** ,, (B4)
where T denotes the ratio of specific heats. Substitutions
for the dynamic pressure in the normal-force, pitching-
moment, and pressure coefficient equations (B1), (B2),
and (B3), respectively, give
F N
CN - 1 M z S (B5)_Tpoo .0
My
Cm- 1 2 - (B6)
_7Po, M.. Sc
P -- Poo
Cp- 1 M 2 (B7)_TP** **
The Mach number, which is not a primary measurement,
is derived from the free-stream static and total pressures
and the ratio of specific heats. Thus,
r/..1 l}= --1 (B8)The coefficients are then functions of the following
measured variables: the normal force, the pitching
moment, the local pressure, the free-stream static pres-sure, and the free-stream Mach number; the Mach num-
ber is a function of the free-stream static pressure and the
free-stream total pressure (i.e., stagnation pressure). The
uncertainties U( ) of these primary measured variables
are presented in table B 1.
Table B1. Data Uncertainties
Variable Uncertainty
U(FN), lbf ...............
-
Equations (B5)-(B8) are used to obtain the sensitivity of
the derived quantity with respect to each of the primary
measurements. The uncertainty in Mach number is first
determined with the nominal wind tunnel static and total
pressures for representative Reynolds and Mach num-
bers. The sensitivity factors (i.e., quantities in partial
derivatives) change as the values of the primary measure-
ments change based on test Reynolds and Mach num-
bers. The contributions of the static pressure and total
pressure measurement to the calculated uncertainty in
Mach number, normal-force coefficient, pitching-
moment coefficient, and pressure coefficient are listed in
tables B2-B5.
Table B2. Contribution of Primary Measurements to Mach Number Uncertainty
M_
0.40
.60
.85
.90
emac
6× 106
6
120
6
Pr, psia
66
19.5
76
15.5
tT, °F
120
120
-250
120
-0.0004
-.0003
-.0002
-.0003
0.0002
.0002
.0001
.0001
U (M_)
0.0005
.0003
.0003
.0003
Table B3. Contribution of Primary Measurements to Normal-Force Coefficient Uncertainty
M_
0.40
0.60
0.85
0.90
gmac
6 x 106
6x 106
120 x 106
6 x 106
PT, psia
66.0
19.5
76.0
15.5
tT, °F
120
120
-250
or, deg
4.84
3C N
bF N U(FN)
0.01187 -0.00003 0.00037
U (CN)
0.0119
9.95 0.01189 -0.00008 -0.00080 0.0119
20.17 0.01189 -0.00019 -0.00202 0.0121
0.02020 -0.00019-0.000044.99 0.0202
10. !4 0.02020 -0.00009 -0.00045 0.0202
20.26 0.02021 -0.00022 -0.00106 0.0202
-0.000120.003234.95 -0.00005 0.0032
10.34 0.00322 -0.00012 -0.00030 0.0032
14.57 0.00323 -0.00017 -0.00044 0.0033
0.01501 -0.000075.06 -0.00015 0.0150
120 10.20 0.01500 -0.00016 -0.00034 0.0150
20.33 0.01503 -0.00034 -0.00074 0.0150
23
-
TableB4.Contributionof Primary Measurements to Pitching-Moment Coefficient Uncertainty
M_
0.40
0.60
0.85
0.90
gmac
6x 106
6x 106
120 × 106
6x 106
PT_ psia
66.0
19.5
76.0
15.5
t_ °F
120
120
-250
120
cz, deg
4.84
OCm
OM r U(Mr)
0.00000 0.00000 0.00005
u (c,,,)
O.O0(X)
9.95 0.00000 0.00001 0.00012 0.0001
20.17 0.00000 0.00003 0.00027 0.0003
0.00000 0.000030.00_14.99 0.0000
10.14 0.00000 0.00001 0.00007 0.0001
20.26 0.00000 0.00003 0.00014 0.0001
0.000020.000004.95 0.00001 0.0000
10.34 0.00000 0.00002 0.00005 0.0001
14.57 0.00000 0.00003 0.00006 0.0001
0.00000 0.000015.06 0.00003 0.0000
10.20 0.00000 0.00003 0.00007 0.0001
20.33 0.00000 0.00007 0.00015 0.0002
Table B5. Contribution of Primary Measurements to Pressure Coefficient Uncertainty
Moo
0.40
0.60
0.85
0.90
Rma c
6xlO 6
6x106
120 x 106
6x 106
Pr, psia
66.0
19.5
76.0
15.5
tT, °F
120
120
-250
120
Or,deg
4.84 0.00458 0.00001
BCp
_M U(M )
0.01_6
u(%)
0.0116
9.95 0.00459 0.00002 0.01077 0.0 ! 17
20.17 0.00459 0.00007 0.01101 0.0119
0.00780 0.002310.000024.99 0.0081
10.14 0.00780 0.00005 0.00238 0.0082
20.26 0.00780 0.00010 0.00249 0.0082
0.000620.001254.95 0.00000 0.0014
10.34 0.00124 0.00001 0.00062 0.0014
14.57 0.00125 0.00001 0.00063 0.0014
0.000640.00580 0.000025.06 0.0058
10.20 0.00579 0.00006 0.00068 0.0058
20.33 0.00580 0.00007 0.00070 0.0058
24
-
Appendix C
Experimental Surface Pressure Data for 65 ° Delta Wing, Moo = 0.85
The experimental surface pressure data for the 65° delta wing at constant M_ = 0.85 are summarized in tables C1-C3. Because of the extensive data contained in these tables, they have not been included in the printed copy of the paperbut are available electronically from the Langley Technical Report Server (LTRS). Open the files with the followingUniform Resource Locator (URL):
ftp://techreports.larc.nasa.gov/pub/techreports/larc/96/NASA-96-tm4645vol 1appC.ps.Z
25
-
Appendix D
Experimental Surface Pressure Data for 65 ° Delta Wing, Rma c = 6 x 106
The experimental surface pressure data for the 65° delta wing at constant Rmac = 6 x 106 are summarized in
tables D1-D6. Because of the extensive data contained in these tables, they have not been included in the printed copyof the paper but are available electronically from the Langley Technical Report Server (LTRS). Open the files with thefollowing Uniform Resource Locator (URL):
ftp://techreports.larc.nasa.gov/pub/techreports/larc/96/NASA-96-tm4645vol IappD.ps.Z
26
-
References
1. Winter, H.: Flow Phenomena on Plates and Airfoils of Short
Span. NACA TM-798, 1936.
2. Wilson, Herbert A.; and Lovell, J. Calvin: Full-Scale Investi-
gation of the Maximum Lift and Flow Characteristics of
an Airplane Having Approximately Triangular Plan Form.
NACA RM L6K20, 1947.
3. Ornberg, Torsten: A Note On the Flow Around Delta Wings.
KTH-Aero TN 38, Div. of Aeronautics, R. Inst. of Technology
(Stockholm), 1954.
4. Lawford, J. A.: Low-Speed Wind Tunnel Experiments on a
Series of Sharp-Edged Delta Wings--Part IL Surface Flow
Patterns and Boundary Layer Transition Measurements. Tech.
Note Aero. 2954, R. Aircr. Establ., Mar. 1964.
5. Hummel, Ing. Dietrich: On the Vortex Formation Over a Slen-
der Wing at Large Angles of Incidence. High Angle of Attack
Aerodynamics, AGARD-CP-247, Jan. 1979, pp. 15-1-15-17.
6. Vorropoulos, G.; and Wendt, J. F.: Laser Velocimetry Study of
Compressibility Effects on the Flow Field of a Delta Wing.
Aerodynamics of Vortical Type Flows in Three Dimensions,
AGARD-CP-342, July 1983, pp. 9-1-9-13. (Available from
DTIC as AD A135 157.)
7. Poisson-Quinton, P.: Slender Wings for Civil and Military Air-
craft. Israel J. Technol., vol. 16, no. 3, 1978, pp. 97-131.
8. Skow, A. M.; and Erickson, G. E.: Modern Fighter Air-
craft Design for High-Angle-of-Attack Maneuvering. High
Angle-of-Attack Aerodynamics, AGARD-LS- 121, Dec. 1982,
pp. 4-1--4-59.
9. Polhamus, E. C.: Applying Slender Wing Benefits to Military
Aircraft. J. Aircr., vol. 21, no. 8, Aug. 1984, pp. 545-559.
10. Polhamus, E. C.; and Gloss, B. B.: Configuration Aerodynam-
ics. High Reynolds Number Research, NASA CP-2183, 1980,
pp. 217-234.
11. Henderson, William P.: Effects of Wing Leading-Edge Radius
and Reynolds Number on Longitudinal Aerodynamic Charac-
teristics of Highly Swept Wing-Body Configurations at Sub-
sonic Speeds. NASA TN D-8361, 1976.
12. Howe, J. T.: Some Fluid Mechanical Problems Related to Sub-
sonic and Supersonic Aircraft. NASA SP- 183, 1969.
13. Henderson, William P.: Studies of Various Factors Affecting
Drag Due to Lift at Subsonic Speeds. NASA TN D-3584,
1966.
14. Fuller, Dennis E.: Guide for Users of the National Transonic
Facility. NASA TM-83124, 1981.
15. Plentovich, E. B.: The Application to Airfoils of a Technique
for Reducing Orifice-Induced Pressure Error at High Reynolds
Numbers. NASA TP-2537, 1986.
16. Hall, Robert M.; and Adcock, Jerry B.: Simulation of Ideal-
Gas Flow by Nitrogen and Other Selected Gases at Cryogenic
Temperatures. NASA TP-1901, 1981.
17. Holman, Jack Philip: Experimental Methods for Engineers.
4th ed., McGraw-Hill Book Co., 1984, pp. 46-99.
18. Foster, Jean M.; and Adcock, Jerry B.: User's Guide for the
National Transonic Facility Data System. NASA TM-100511,
1987.
27
-
REPORT DOCUMENTATION PAGE OMBNo.ozo4_las
Publicreportingburdenfor this collectiono_informationis estimatedto gwerageI hourper response,Including the timefor ravlev_nginsb'uct|ons,searchingexistingdatasources,gatheringandmaintainingthe dataneeded, andcompletingandreviewingthe collec'_onof information,Send commentsregardingthis burdenestimateor any otheraspectof thiscollectionof information,indudlng suggestionsfor reducingthisburden, to WashingtonHeadquartersServices,Directoratefor InformationOpera,oneand Reports,1215JeffersonDavis Highway,Suite 1204, Arlington,VA22202-4302, andto the Officeof ManagementandBudget,F_k ReductionProject(0704-0188),Washington,DC 20503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
February 1996 Technical Memorandum
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Experimental Surface Pressure Data Obtained on 65 ° Delta Wing AcrossReynolds Number and Mach Number Ranges WU 505-59-54-01Volume l--Sharp Leading Edge
6. AUTHOR(S)
Julio Chu and James M. Luckring
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
NASA Langley Research Center
Hampton, VA 23681-0001
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, DC 20546-0001
8. PERFORMING ORGANIZATIONREPORT NUMBER
L-17411A
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
NASA TM-4645, Vol. 1
11. SUPPLEMENTARY NOTES
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified-Unlimited
Subject Category 02Availability: NASA CASI (301) 621-0390
!13. ABSTRACT (Maximum 200 words)
12b. DISTRIBUTION CODE
An experimental wind tunnel test of a 65 ° delta wing model with interchangeable leading edges was conducted inthe Langley National Transonic Facility (NTF). The objective was to investigate the effects of Reynolds and Machnumbers on slender-wing leading-edge vortex flows with four values of wing leading-edge bluntness. Experimen-tally obtained pressure data are presented without analysis in tabulated and graphical formats across a Reynolds
6 6number range of 6 x 10 to 36 x 10 at a Mach number of 0.85 and across a Mach number range of 0.4 to 0.9 at aReynolds number of 6 x 106. Normal-force and pitching-moment coefficient plots for these Reynolds number andMach number ranges are also presented.
114. SUBJECT TERMS
Aerodynamics; Delta wing; Reynolds number; Leading-edge bluntness; Vortex flow;Cryogenic testing
17. SECURITY CLASSIFICATIONOF REPORT
Unclassified
NSN 7540-01-28(_5500
15. NUMBER OF PAGES
2816. PRICE CODE
A03
18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATIONOF THIS PAGE OF ABSTRACT OF ABSTRACT
Unclassified Unclassified
Standard Form 298 (Rev. 249)PrescribedbyANSI Std. Z39-1a298-102
-
1
Appendix C
Experimental Surface Pressure Data for 65° Delta Wing, M∞ = 0.85
The experimental surface pressure data for the 65° delta wing at constant M∞ = 0.85 are summarized in tables C1–C3. Because of the extensive data contained in these tables, they have not been included in the printed copy of the paperbut are available electronically from the Langley Technical Report Server (LTRS). Open the files with the followingUniform Resource Locator (URL):
ftp://techreports.larc.nasa.gov/pub/techreports/larc/96/NASA-96-tm4645vol1appC.ps.Z
-
2
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. T
abul
atio
ns a
nd P
lots
of S
urfa
ce P
ress
ure
Coe
ffici
ents
.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
1C
N =
-0.
041,
Cm
= 0
.012
5α
= -
0.4
°,M
∞ =
0.8
50R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
033
0.00
740.
1321
****
***
****
***
-0.0
007
0.00
690.
1203
****
***
****
***
-0.0
005
0.00
630.
1072
****
***
****
***
-0.0
078
0.00
510.
0959
****
***
-0.3
202
****
***
0.00
440.
0839
-0.1
308
-0.3
361
-0.0
244
0.00
610.
0712
-0.1
134
-0.3
537
-0.0
349
0.00
070.
0634
-0.1
047
-0.3
959
-0.0
419
0.00
350.
0546
-0.0
942
-0.4
471
-0.0
532
-0.0
027
0.05
18-0
.088
1-0
.486
6-0
.057
9-0
.003
50.
0393
-0.0
852
-0.5
063
****
***
-0.0
084
0.03
07-0
.077
9-0
.521
0-0
.055
7-0
.007
90.
0312
-0.0
770
-0.5
327
****
***
-0.0
138
0.02
83-0
.075
8-0
.549
2-0
.041
7-0
.016
00.
0234
-0.0
746
-0.5
723
****
***
****
***
0.01
97-0
.071
5-0
.597
0-0
.030
9-0
.018
90.
0163
-0.0
681
-0.6
269
****
***
-0.0
269
0.01
11-0
.072
4-0
.653
9-0
.022
6-0
.040
10.
0087
-0.0
723
-0.6
898
****
***
-0.0
501
****
***
-0.0
741
-0.7
115
-0.0
089
-0.0
560
****
***
-0.0
706
-0.7
251
****
***
-0.0
620
-0.0
103
-0.0
763
-0.7
215
0.01
03-0
.063
8-0
.029
8-0
.080
7**
****
***
****
*-0
.055
3-0
.040
8-0
.081
2-0
.743
70.
0377
-0.0
425
-0.0
490
-0.1
001
-0.6
006
****
***
-0.0
277
-0.0
471
-0.1
154
-0.6
350
0.07
78-0
.003
4-0
.029
6-0
.115
5**
****
***
****
*0.
0287
-0.0
089
-0.0
888
-0.5
934
0.12
170.
0704
0.03
47-0
.050
3-0
.322
7**
****
*0.
1173
0.09
650.
0248
-0.1
450
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
-0.0
492
-0.0
077
0.07
74**
****
*-0
.300
4-0
.072
3-0
.013
40.
0375
-0.1
066
-0.4
096
****
***
-0.0
217
0.00
43-0
.090
9-0
.522
3**
****
*-0
.074
7-0
.010
5-0
.093
2-0
.705
7-0
.043
6-0
.108
0-0
.076
8-0
.096
6-0
.744
0-0
.011
1-0
.089
0-0
.100
1-0
.149
7-0
.635
00.
0264
-0.0
621
-0.1
013
-0.1
748
-0.8
556
****
***
****
***
-0.0
335
-0.1
274
-0.3
685
****
***
0.06
100.
0237
-0.0
541
-0.2
124
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
0.07
780.
0797
0.03
130.
0264
0.07
040.
0759
0.02
27**
****
*0.
0347
0.03
74-0
.028
8-0
.033
5-0
.050
3-0
.043
8-0
.116
6-0
.127
4-0
.322
7-0
.339
3-0
.375
3-0
.368
5
-
3
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
2C
N =
-0.
022,
Cm
= 0
.010
2α
= 0
.0 °
,M
∞ =
0.8
50R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
140
-0.0
032
0.12
72**
****
***
****
*-0
.009
6-0
.002
80.
1137
****
***
****
***
-0.0
157
-0.0
026
0.10
18**
****
***
****
*-0
.020
9-0
.000
70.
0893
****
***
-0.3
203
****
***
-0.0
035
0.07
71-0
.136
3-0
.329
8-0
.040
8-0
.002
70.
0637
-0.1
189
-0.3
444
-0.0
504
-0.0
059
0.05
79-0
.110
8-0
.383
7-0
.057
9-0
.007
30.
0456
-0.0
980
-0.4
304
-0.0
678
-0.0
099
0.04
47-0
.094
4-0
.473
6-0
.070
8-0
.014
70.
0306
-0.0
906
-0.4
957
****
***
-0.0
165
0.02
48-0
.084
8-0
.518
5-0
.073
3-0
.017
00.
0236
-0.0
828
-0.5
247
****
***
-0.0
225
0.02
08-0
.082
7-0
.538
8-0
.057
3-0
.024
00.
0147
-0.0
796
-0.5
617
****
***
****
***
0.01
14-0
.081
0-0
.586
7-0
.048
0-0
.028
00.
0082
-0.0
777
-0.6
234
****
***
-0.0
369
0.00
09-0
.081
3-0
.657
7-0
.038
7-0
.059
40.
0003
-0.0
794
-0.6
952
****
***
-0.0
728
****
***
-0.0
810
-0.7
214
-0.0
254
-0.0
805
****
***
-0.0
801
-0.7
344
****
***
-0.0
864
-0.0
194
-0.0
867
-0.7
306
-0.0
067
-0.0
825
-0.0
472
-0.0
920
****
***
****
***
-0.0
787
-0.0
649
-0.0
879
-0.7
379
0.02
15-0
.066
5-0
.069
2-0
.119
4-0
.589
8**
****
*-0
.049
7-0
.067
9-0
.142
8-0
.584
80.
0603
-0.0
282
-0.0
550
-0.1
383
****
***
****
***
0.00
75-0
.031
9-0
.111
7-0
.584
80.
1057
0.04
540.
0096
-0.0
751
-0.3
380
****
***
0.09
610.
0714
0.00
22-0
.166
2
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
-0.0
408
-0.0
026
0.08
74**
****
*-0
.312
2-0
.055
4-0
.003
60.
0432
-0.1
001
-0.4
275
****
***
-0.0
180
0.01
13-0
.085
9-0
.540
5**
****
*-0
.056
1-0
.003
3-0
.087
1-0
.702
4-0
.026
9-0
.086
6-0
.057
4-0
.094
3-0
.739
20.
0057
-0.0
694
-0.0
786
-0.1
338
-0.6
663
0.04
38-0
.038
5-0
.076
8-0
.154
9-0
.880
8**
****
***
****
*-0
.006
2-0
.100
5-0
.351
2**
****
*0.
0849
0.05
18-0
.024
0-0
.189
3
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
0.06
030.
0626
0.04
910.
0438
0.04
540.
0535
0.04
51**
****
*0.
0096
0.01
50-0
.002
8-0
.006
2-0
.075
1-0
.069
7-0
.089
0-0
.100
5-0
.338
0-0
.355
3-0
.365
2-0
.351
2
-
4
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
3C
N =
0.0
23,
Cm
= -
0.00
09α
= 1
.1 °
,M
∞ =
0.8
51R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
314
-0.0
183
0.11
17**
****
***
****
*-0
.031
8-0
.021
30.
1018
****
***
****
***
-0.0
360
-0.0
170
0.08
72**
****
***
****
*-0
.046
1-0
.022
80.
0758
****
***
-0.3
090
****
***
-0.0
214
0.06
31-0
.149
4-0
.308
2-0
.066
0-0
.022
20.
0500
-0.1
314
-0.3
243
-0.0
747
-0.0
242
0.04
33-0
.124
9-0
.362
7-0
.080
6-0
.027
10.
0300
-0.1
126
-0.4
036
-0.0
898
-0.0
304
0.02
72-0
.108
7-0
.434
7-0
.096
7-0
.036
60.
0125
-0.1
057
-0.4
345
****
***
-0.0
387
0.00
70-0
.101
5-0
.444
2-0
.100
8-0
.041
50.
0016
-0.0
992
-0.4
464
****
***
-0.0
479
0.00
21-0
.100
6-0
.457
3-0
.089
6-0
.052
2-0
.006
4-0
.099
9-0
.467
6**
****
***
****
*-0
.008
1-0
.098
3-0
.485
2-0
.079
4-0
.059
2-0
.015
2-0
.098
1-0
.519
5**
****
*-0
.070
0-0
.022
9-0
.101
1-0
.563
4-0
.072
6-0
.085
0-0
.028
4-0
.103
2-0
.628
1**
****
*-0
.100
7**
****
*-0
.105
6-0
.692
1-0
.061
8-0
.107
7**
****
*-0
.106
1-0
.728
5**
****
*-0
.121
4-0
.056
1-0
.112
6-0
.726
8-0
.045
3-0
.123
0-0
.082
4-0
.123
6**
****
***
****
*-0
.119
9-0
.101
0-0
.125
0-0
.685
5-0
.018
7-0
.112
2-0
.115
5-0
.155
7-0
.563
0**
****
*-0
.101
9-0
.114
2-0
.186
9-0
.554
10.
0213
-0.0
789
-0.1
060
-0.1
904
****
***
****
***
-0.0
470
-0.0
879
-0.1
678
-0.5
426
0.06
31-0
.006
8-0
.047
7-0
.140
6-0
.369
3**
****
*0.
0397
0.01
29-0
.067
9-0
.214
0
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
-0.0
135
0.01
480.
0963
****
***
-0.3
311
-0.0
268
0.01
280.
0563
-0.0
869
-0.4
742
****
***
0.00
110.
0271
-0.0
706
-0.5
994
****
***
-0.0
292
0.01
80-0
.069
9-0
.708
00.
0111
-0.0
469
-0.0
212
-0.0
719
-0.7
200
0.04
26-0
.028
2-0
.039
3-0
.092
7-0
.733
00.
0809
0.01
12-0
.025
9-0
.104
8-0
.884
5**
****
***
****
*0.
0478
-0.0
413
-0.3
153
****
***
0.13
080.
1043
0.03
26-0
.146
5
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
0.02
130.
0225
0.08
540.
0809
-0.0
068
0.00
010.
0926
****
***
-0.0
477
-0.0
468
0.05
020.
0478
-0.1
406
-0.1
330
-0.0
332
-0.0
413
-0.3
693
-0.3
949
-0.3
390
-0.3
153
-
5
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
4C
N =
0.0
62,
Cm
= -
0.00
61α
= 2
.1 °
,M
∞ =
0.8
51R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
477
-0.0
325
0.10
08**
****
***
****
*-0
.045
6-0
.036
40.
0882
****
***
****
***
-0.0
483
-0.0
377
0.07
44**
****
***
****
*-0
.054
4-0
.037
30.
0633
****
***
-0.2
984
****
***
-0.0
419
0.04
86-0
.160
5-0
.305
7-0
.071
2-0
.041
50.
0373
-0.1
463
-0.3
144
-0.0
826
-0.0
457
0.02
54-0
.134
7-0
.338
4-0
.092
0-0
.045
60.
0169
-0.1
276
-0.3
690
-0.1
081
-0.0
532
0.01
08-0
.121
2-0
.395
4-0
.114
9-0
.058
7-0
.000
9-0
.121
4-0
.400
9**
****
*-0
.061
7-0
.011
0-0
.113
0-0
.408
0-0
.122
9-0
.064
7-0
.013
6-0
.116
2-0
.412
5**
****
*-0
.072
5-0
.019
5-0
.116
1-0
.419
5-0
.121
9-0
.079
0-0
.025
9-0
.114
3-0
.423
7**
****
***
****
*-0
.031
2-0
.117
1-0
.425
5-0
.114
2-0
.087
9-0
.036
9-0
.114
6-0
.435
6**
****
*-0
.097
6-0
.046
6-0
.119
2-0
.443
8-0
.105
8-0
.118
3-0
.051
3-0
.124
1-0
.459
6**
****
*-0
.135
4**
****
*-0
.127
6-0
.480
8-0
.095
5-0
.144
5**
****
*-0
.129
7-0
.521
5**
****
*-0
.156
4-0
.086
0-0
.138
5-0
.534
3-0
.080
4-0
.161
8-0
.115
7-0
.151
3**
****
***
****
*-0
.160
2-0
.139
1-0
.158
3-0
.503
5-0
.054
6-0
.155
3-0
.159
7-0
.191
5-0
.512
1**
****
*-0
.149
0-0
.161
0-0
.223
8-0
.524
9-0
.018
1-0
.128
3-0
.159
2-0
.235
6**
****
***
****
*-0
.099
8-0
.146
6-0
.227
6-0
.746
60.
0216
-0.0
617
-0.1
135
-0.2
033
-0.4
293
****
***
-0.0
156
-0.0
550
-0.1
372
-0.2
793
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
0.01
700.
0338
0.11
12**
****
*-0
.351
70.
0004
0.03
250.
0718
-0.0
735
-0.4
964
****
***
0.02
480.
0474
-0.0
548
-0.6
372
****
***
-0.0
015
0.03
84-0
.048
7-0
.725
60.
0470
-0.0
046
0.00
99-0
.047
7-0
.704
70.
0788
0.01
130.
0041
-0.0
611
-0.7
123
0.11
460.
0546
0.02
00-0
.058
9-0
.853
1**
****
***
****
*0.
0924
0.00
69-0
.286
7**
****
*0.
1655
0.14
350.
0765
-0.1
139
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
-0.0
181
-0.0
138
0.11
940.
1146
-0.0
617
-0.0
520
0.13
07**
****
*-0
.113
5-0
.107
40.
0956
0.09
24-0
.203
3-0
.194
30.
0153
0.00
69-0
.429
3-0
.442
8-0
.309
9-0
.286
7
-
6
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
5C
N =
0.1
03,
Cm
= -
0.01
29α
= 3
.2 °
,M
∞ =
0.8
51R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
674
-0.0
517
0.08
68**
****
***
****
*-0
.073
7-0
.056
60.
0774
****
***
****
***
-0.0
793
-0.0
527
0.06
21**
****
***
****
*-0
.089
2-0
.057
70.
0506
****
***
-0.2
815
****
***
-0.0
558
0.03
51-0
.172
9-0
.298
0-0
.097
7-0
.062
10.
0227
-0.1
566
-0.3
078
-0.1
083
-0.0
603
0.01
23-0
.146
1-0
.333
5-0
.117
9-0
.069
00.
0001
-0.1
395
-0.3
593
-0.1
337
-0.0
721
-0.0
030
-0.1
346
-0.3
815
-0.1
420
-0.0
830
-0.0
223
-0.1
366
-0.3
948
****
***
-0.0
849
-0.0
249
-0.1
291
-0.3
936
-0.1
519
-0.0
880
-0.0
363
-0.1
329
-0.3
904
****
***
-0.0
984
-0.0
345
-0.1
271
-0.3
924
-0.1
531
-0.1
027
-0.0
490
-0.1
351
-0.3
966
****
***
****
***
-0.0
507
-0.1
362
-0.4
030
-0.1
505
-0.1
151
-0.0
611
-0.1
353
-0.4
114
****
***
-0.1
277
-0.0
688
-0.1
375
-0.4
147
-0.1
419
-0.1
479
-0.0
781
-0.1
473
-0.4
204
****
***
-0.1
670
****
***
-0.1
479
-0.4
293
-0.1
336
-0.1
793
****
***
-0.1
581
-0.4
351
****
***
-0.1
970
-0.1
197
-0.1
658
-0.4
385
-0.1
208
-0.2
047
-0.1
515
-0.1
836
****
***
****
***
-0.2
085
-0.1
780
-0.1
893
-0.4
276
-0.0
978
-0.2
070
-0.2
013
-0.2
252
-0.4
478
****
***
-0.2
013
-0.2
107
-0.2
642
-0.4
861
-0.0
614
-0.1
831
-0.2
114
-0.2
855
****
***
****
***
-0.1
507
-0.2
031
-0.2
825
-0.7
603
-0.0
288
-0.1
084
-0.1
578
-0.2
688
-0.4
732
****
***
-0.1
744
-0.2
016
-0.2
109
-0.3
325
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
0.03
960.
0506
0.12
62**
****
*-0
.373
30.
0225
0.05
250.
0870
-0.0
615
-0.5
311
****
***
0.04
470.
0682
-0.0
380
-0.6
711
****
***
0.02
680.
0613
-0.0
316
-0.7
253
0.07
990.
0311
0.03
91-0
.022
8-0
.690
00.
1085
0.04
660.
0388
-0.0
345
-0.6
923
0.14
450.
0915
0.05
97-0
.020
7-0
.799
4**
****
***
****
*0.
1277
0.04
71-0
.260
6**
****
*0.
1872
0.17
060.
1066
-0.0
883
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
-0.0
614
-0.0
568
0.14
840.
1445
-0.1
084
-0.1
068
0.16
30**
****
*-0
.157
8-0
.164
70.
1323
0.12
77-0
.268
8-0
.254
30.
0555
0.04
71-0
.473
2-0
.475
9-0
.282
9-0
.260
6
-
7
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
6C
N =
0.1
53,
Cm
= -
0.02
43α
= 4
.2 °
,M
∞ =
0.8
51R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.0
948
-0.0
666
0.07
59**
****
***
****
*-0
.099
9-0
.072
80.
0643
****
***
****
***
-0.1
009
-0.0
698
0.05
14**
****
***
****
*-0
.110
4-0
.076
10.
0358
****
***
-0.2
999
****
***
-0.0
788
0.02
42-0
.184
9-0
.287
6-0
.118
2-0
.077
40.
0067
-0.1
721
-0.2
833
-0.1
317
-0.0
821
0.00
14-0
.160
4-0
.313
5-0
.141
5-0
.086
5-0
.014
7-0
.153
1-0
.350
7-0
.159
2-0
.096
0-0
.018
4-0
.150
0-0
.369
9-0
.170
3-0
.104
9-0
.041
8-0
.152
0-0
.390
6**
****
*-0
.108
8-0
.043
8-0
.146
6-0
.398
0-0
.181
1-0
.113
2-0
.054
7-0
.144
8-0
.396
3**
****
*-0
.122
2-0
.055
6-0
.149
3-0
.397
0-0
.184
5-0
.128
9-0
.069
6-0
.149
9-0
.393
3**
****
***
****
*-0
.076
0-0
.157
4-0
.406
0-0
.181
8-0
.144
0-0
.083
2-0
.156
9-0
.423
8**
****
*-0
.159
9-0
.095
2-0
.163
1-0
.439
8-0
.177
8-0
.179
9-0
.101
0-0
.170
1-0
.453
6**
****
*-0
.202
9**
****
*-0
.174
8-0
.477
6-0
.173
4-0
.216
2**
****
*-0
.183
0-0
.497
6**
****
*-0
.234
5-0
.147
4-0
.193
3-0
.520
5-0
.162
3-0
.248
8-0
.184
6-0
.211
0**
****
***
****
*-0
.255
1-0
.213
9-0
.220
9-0
.525
5-0
.139
3-0
.251
5-0
.241
1-0
.265
3-0
.440
7**
****
*-0
.245
7-0
.247
2-0
.301
2-0
.472
7-0
.101
7-0
.217
4-0
.250
6-0
.325
6**
****
***
****
*-0
.191
2-0
.232
9-0
.325
4-0
.747
1-0
.082
5-0
.275
4-0
.311
4-0
.332
5-0
.506
2**
****
*-0
.399
9-0
.462
5-0
.499
0-0
.486
4
0.05
00.
100
0.15
00.
200
0.25
00.
300
0.35
00.
400
0.45
00.
500
0.52
50.
550
0.57
50.
600
0.62
50.
650
0.67
50.
700
0.72
50.
750
0.77
50.
800
0.82
50.
850
0.87
50.
900
0.92
50.
950
0.97
5
0.06
050.
0709
0.13
99**
****
*-0
.400
60.
0480
0.07
210.
1048
-0.0
468
-0.5
745
****
***
0.07
160.
0830
-0.0
216
-0.6
861
****
***
0.05
470.
0845
-0.0
169
-0.7
201
0.11
140.
0650
0.06
68-0
.000
1-0
.671
30.
1389
0.07
930.
0717
-0.0
067
-0.6
701
0.17
070.
1265
0.09
570.
0117
-0.7
459
****
***
****
***
0.15
840.
0794
-0.2
384
****
***
0.20
080.
1874
0.12
78-0
.069
2
-0.2
00-0
.400
-0.6
00-0
.700
-0.8
00-0
.850
-0.9
00-0
.950
-0.9
75
0.20
0.40
0.60
0.80
0.95
0.90
0.95
0.95
0.95
0.95
-0.1
017
-0.0
947
0.17
440.
1707
-0.2
754
-0.2
221
0.18
93**
****
*-0
.311
4-0
.239
00.
1600
0.15
84-0
.332
5-0
.304
60.
0888
0.07
94-0
.506
2-0
.511
1-0
.257
1-0
.238
4
-
8
1.0.8.6.4.20
x/c R
ηC
p,u
Cp,
uC
p,u
Cp,
uC
p,u
Cp,
lC
p,l
Cp,
lC
p,l
Cp,
l
0.2
.4.6
.81.
0 x
/cR
.80-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
x/c R
η
Cp,
uC
p,l
star
b’d
port
star
b’d
port
/ /
Sur
face
Pre
ssur
es N
ear
Lead
ing
Edg
e
uppe
r, s
tarb
oard
/por
t
low
er, s
tarb
oard
/por
t
.51.
0 η
0-.8
-1.6
-2.4
-3.2
-4.0
-4.8
-5.6
Cp
.2.4
.6.8
1.0
η
Cp
0
η
Cp
0
η
Cp
0
η
Cp
0
uppe
r, s
tarb
oard
low
er,
port
Sur
face
Pre
ssur
es
Tab
le C
1. C
ontin
ued.
Sha
rp R
adiu
s L.
E.
Run
No.
= 8
8 ,
Poi
nt N
o. =
193
7C
N =
0.1
99,
Cm
= -
0.03
35α
= 5
.2 °
,M
∞ =
0.8
51R
mac
=
6.0
× 10
6
x/c R
x/c R
x/c R
x/c R
x/c R
.2.4
.6.8
.95
-0.1
118
-0.0
867
0.06
31**
****
***
****
*-0
.114
4-0
.083
50.
0503
****
***
****
***
-0.1
237
-0.0
920
0.04
29**
****
***
****
*-0
.127
9-0
.088
80.
0247
****
***
-0.2
616
****
***
-0.0
985
0.01
16-0
.200
8-0
.280
3-0
.139
8-0
.095
2-0
.008
8-0
.182
3-0
.292
2-0
.153
1-0
.102
7-0
.018
3-0
.175
8-0
.317
9-0
.165
7-0
.108
7-0
.027
9-0
.165
1-0
.336
9-0
.182
1-0
.117
8-0
.038
7-0
.165
1-0
.345
6-0
.194
6-0
.127
3-0
.054
5-0
.165
8-0
.347
2**
****
*-0
.131
3-0
.066
6-0
.162
3-0
.362
7-0
.208
5-0
.137
5-0
.069
1-0
.159
7-0
.361
0**
****
*-0
.142
6-0
.077
4-0
.165
0-0
.373
2-0
.214
0-0
.156
1-0
.087
7-0
.165
8-0
.383
4**
****
***
****
*-0
.098
0-0
.168
5-0
.420
3-0
.215
4-0
.170
3-0
.102
1-0
.170
7-0
.482
2**
****
*-0
.188
3-0
.116
9-0
.180
5-0
.537
0-0
.214
2-0
.212
0-0
.123
9-0
.182
6-0
.588
6**
****
*-0
.236
2**
****
*-0
.191
6-0
.658
9-0
.206
9-0
.253
9**
****
*-0
.197
3-0
.697
6**
****
*-0
.271
1-0
.174
9-0
.225
0-0
.726
8-0
.195
9-0
.283
4-0
.210
7-0
.243
5**
****
***
****
*-0
.284
0-0
.238
4-0
.251
0-0
.761
9-0
.166
0-0
.278
6-0
.259
5-0
.296
9-0
.558
0**
****
*-0
.259
1-0
.258
8-0
.337
3-0
.795
3-0
.159
1-0
.273
3-0
.323
8-0
.365
8**
****
***
****
*-0
.397
5-0
.451
8-0
.476
1-0
.852
1-0
.137
3-0
.520
5-0
.577
5-0
.584
0-0
.569
8**
****
*-0
.508
2-0
.565