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

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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National Aeronautics and Space Administration.

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Printed copies available from the following:

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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

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