AOSR ..TR 8 10 4,0 ,

tkj r)SR TR7

Air Force Office cf Scientific Research

Eglin Air Force Base

Grant *-AFOSR 78-3569-4

0Z(M

0 THE EFFECTS OF WARHEAD-INDUCED DAMAGE ON THE AEROELASTIC

lCHARACTERISTICS OF LIFTING SURFACES

VOLUME II - AERODYNAMIC EFFECTS

by Cj7 .

DEC 19 1980.J.C. Westkaemper

and AR. M. Chandrasekharan

Department of Aerospace-Engineeringand Engineering Mechanics

CENTER FOR AERONAUTICAL RESEARCH

Bureau of Engineering ResearchThe University of Texas at Austin'I

[AJ This da.%Ou.ut boon epp o0"t . " . for puibbc roic,'w,% o d s.1o; ,' .

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SREPOR REPORT DOCUMENTATION PAGE B.REC ' COIPLETINS OR. REOTNME CSINB.3 E IPI'S CA OIE G ORM

AFOSR-TR. 8 0 - I 0 G AC BE

Re TIL. rfd Su i II IIe) S. TYPE OF REPORT & PERIOD COVERED

TJh ffects of Warhead-Induced Damage on the Final cientific ReportAeroelastic Characteristics of Lifting Surfaces 2-1---Zi to 3-1-80Volume II- Aerodynamic Effects 6. PERFOMrIbG ORG. REPORT NUMBER

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(')

J. C. Westkaemper AFOSR 78-3569R. Chandrasekharan

9. PfRFORMINf ORGANIZATIOJ NAMT TO AOOPEPS O. PROGRAM ELEMENT. PROJECT. TASK

Lenter TOr Reronau tica Iesearch AREA a WORK UNIT NUMBERS

Dept. of Aerospace Engr./Engineering M4chanicsThe University of Texas @ Austin/Austin TX 78712 //9Of ,c///96

II. CONTROLLING OFFICE NAME AND ADDRESS Q2. REPORT DATE

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_4

L 18. SUPPLEMEI:TARY NOTES

19. KEY WORDS (Co,.tinue on ,ot'trse side If necessary nnd Identtify by block number) " ,

Damaged Lifting Surfaces. Drag Divergence

r Aeroelasticity & Ballastic Damage

* AV TRACT (Conti n s If neessarX and Identify hy block numbet)-es aerdnmic In a SUbSOnIC Wind tunnel to Determine the effects of damage on

'Ithe aerodynamic characteristics of a T-38 aircraft stabilator half. Six damageconfigurations wre used, one circular and the reaminder trapezoidal in planform,with areas of up to 2 percent of the stabilator area. The damage holes were allahead of the 50 percent chord line, with centers at 43, 60 and 75 percent span.

i ,-FT Surface pressure distributions and lift and drag coeffecients were measured.The 65A004 airfoil used is subject to leading edge separation which strongly in-

A fluenced the results. In the absence of separation, damage effects tended to-:

- _. ... --- 44, _ # t'A #JS,,4 ., __

X- -

WR WITY CLASSIFICATION OF THIS PAGE(Ir7in Daf Enlerod"

be'loalized and aerodynamic degradation was modest. With extensive separa-tion, the damage influence propagated completely across the span, with moresubstantial degradation. There was up to 300 percent ;ncrease on Doh butat moderate lift coefficients t ,e drag increase was generally in- D S

,.l significant. The decrease in was more consistent, ranging up to 10 percent- for the larger damage holes.

t

C *,

[ -I

IMf

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I.-.--- -- --

Air Force Office of Scientific Research

Eglin Air rorce Base

Grant FAAOSR-78-3 569

.THE EFFECTS OF yRHEAD-INDUCED DAMAGE ON THE.AEROELASTIC

CHARACTEr.STICS OF LIFTING SURFACESo

VOLUME I,- AERODYNAMIC EFFECTS

-by-

,--i- / 'I Y/ C J. Weetkaompe~r

R .MChandrasokharan

Department of Aerospace Engineering,and Engineering Mechanics

CENTER F~OR AERONAUTICAL RESEARCH _qT- Gr(A&I.uronu of Engineering Research

The Unive Sity of Texas at Austin t n ---------

T ,niz'Tnn/. __

,Julia 108A' ,t S .o S

ip",

TABLE OF CONTENTS

Page A

.Q

ACKNOLYLEDGEMENT.................. . . .... ... .. .. .. . .....

ABSTRACT .. ............................. a

INTRODUCTION................... . . ... . .. .. .. .. .......

TEST FACILITY. ........................... 2

MODEL .. ............. ................. 2

. . . . . . .

TEST CONDITIONS. .. ......................... 4

RESULTS. ................................

Pressure Measurements .. ................... 6Spanwise Lift Distribution. .. ................ 8

Direct Lift and Drag Measurements .. ............. 9

REFERENCES. ............... ............. 13

~ TABLES .. ............................. 14

.FIGURES. .. ............................17

APPENDIX I -THREE-DIMENSIONAL PLOTS. ............... 47

APPENDIX II -TABULATED DATA. .............. ..... 84

A1IR FORCE OFFICE OF SCIENTIFIC RESEARCH (APSC)

This technical re-oj't h-as been reviewed and isapproved f'or public rel ease IAIN APR .190-12 (7b).Distribution is unlimited.A. D. BLOSEPechnical InIfoematioi Officer

7

-

ACKNOWLEDGEMENT

I. ~This research was sponsored by the Vulnerability Assessments Group

of the Air Force Armament Laboratory, Eglin Air Force Base, through the

Air Force Office of Scientific Research. Mr. J.M. Heard was technical

monitor on the program carried out under Grants -AFOSR 78-3569 and 3569#

during the period February 1, 1978 through January-31.1980.

Austin, Texas

June, 1980

!1N

-iL~ I

MN

Li - ..

ABSTRACT

Tests were made in a subsonic wind tunnel to determine the effects

of damage on the aerodynamic characteristics of a T-38 aircraft stabilator

half. Six damage configurations were used, one circular and the remainder

trapezoidal in planform, with areas of up to 2 percent of the stabilator

area. The damage holes were all ahead of the 50 percent chord line, with

centers at 43, 60 and 75 percent span. Surface pressure distributions and

lift and drag coefficients were measured. The 65A004 airfoil used is sub-

ject to leading edge separation which strongly influenced the results.

In the absence of separation, damage effects tended tn be localized and

aerodynamic degradation was modest. With extensive separation, the damage

influence propagated completely across the span, with more substantial

degradation. There was up to 300 percent increase on CD , but at moderate

0' 1lift coefficients the drag increase was generally insignificant. The de-

crease in CL was more consistent, ranging up to 10 percent for the larger

damage holes.

4

-~ iii

5

V

INTRODUCTION

This report covers the second phase of a study of the effects of

damage on the aerodynamics of lifting surfaces. The work is part of a

larger study of the effect of damage on the aeroelastic characteristics

of lifting surfaces. In Reference 1, the report on the first phase of this

study, it was observed that suitably accurate aeroelastic predictions

could not be made because of the unknown changes in aerodynamic forces

caused by damage. A limited amount of two-dimensional test data and

results for one actual aircraft were found. These produced a very sparse

data base that did not include surface pressure measurements which would

aid in understanding the aerodynamics of damage holes or permit predictions

of the effects of holes other than those tested. In addition, the airfoil

sections were characteristic of subsonic aircraft, in contrast to the

current interest in supersonic aircraft.

As a consequence, a test program was initiated to measure lift

and drag coefficients and surface pressure distributions using a surplus

T-38 horizontal stabilizer with a limited but systematic series of damage

configurations. The phase covered herein is the subsonic, imcompressible

regime; planning is in progress for the next phase which will extend test-

ing to the transonic regime.

43

TEST FACILITY

All aerodynamic tests were made in the University of Texas

5 x 7 ft. subsonic wind tunnel at a Mach Number of 0.186 + .005. The

ti-nnel is an atmospheric-intake, open-circuit type, hence the test

zonditions vary slightly with seasonal variations in the weather. The

turbulence level at the test section was 0.6%. All data were recorded

using a Hewlett Packard 3052 programmable data acquisition system.

The pressure measurements were made using four 48-port Scannivalves,

each with a DRUCK PDCR22, I psid pressure transducer.

MODEL

The models used in all the aerodynamic tests were left-half,

T-38 stabilizers which had been removed from service because of local

delamination of the skin from the honeycomb core. The majority of the

delaminations were small enough in area to ignore aerodynamically, but

in one case a repair was made. The surface conditions on the stabilizers

were thus the same as on the T-38 aircraft; no attempt was made to obtain

an aerodynamically-smooth surface. A small triangular planform section

was added to the root of each stabilizer (Fig. 1) to give a root chord

perpendicular to the torque tube which was then used to mount the stabilizer

in the tunnel. This addition was necessary because the original root chord

was oriented parallel to the boattailed fuselage of the T-38. The torque

tube was supported by two pillow blocks mounted on a stand outside the

tunnel; an angle-of-attack drive was also attAched to the stand.

A-7-

3

Because of the honeycomb construction, the pressure taps were in-

stalled using stainless steel tubing cemeted to the lower-surface skin,

passing through the lower skin and honeycomb to the inner side of the

upper skin which contained the 0.81 mm diameter pressure orifices. Fabri-

. cation details are given in Ref. 1, and the location of the orifices is

listed in Table 1. The stabilizer airfoil section is a symnetrical one,

and the pressure data from the upper skin taps was measured at equal posi-

tive and negative angles of attack; data from the negative angles was used

in place of measurements on the lower skin surface which was distorted by

the pressure tubing. Thus, the data from the upper skin at +8 degrees,

for example, was combined with data from the same orifices at -8 degrees to

tobtain overall lift and pressure coefficients. This method is not com-

pletely rigorous because of the -4 degrees dihedral r the stabilizer,

bv: any error may be expected to be minor compared to the effects of Lhe

damage being studied.

The direct-measurerent forces were obtained from a stabilizer having

four-arm strain gage bridges at two stations on the cantilevered section of

the torque tube, between the tunnel wall and the first pillow block. Two

bridges were located in the axial-force plane and two in the normal-fr..rze

I plane; conversion to lift and drag coefficients was done by the comp-iter

I in the data acquisition system. This stabilizer had no pressure -'nstru-

mentation, hence data were obtained for both positive and negative angles

of attack.

-I

DAMAGE CONFIGURATIONS

One circulamr and five trapezoidal damage holes, as detailed in

Table 2, were tested. In all cases, the openings were perpendicular

to the plane of sywetry of the stabilizer. For -ost pressure distri-

bution measuremei.ts, the honeycomb cells exposed by cutting each hole

were filled with putty to produce a s=ooth-sided openin-. However,

after tests of the effect of filling the honeyco-b showed no difference,

the filling was discontinued. The hole areas ranged from 1/2 to 2

percent of the planform area of the tested stabilizer hal:. The trape-

zoidal ;hape was selected to aid in evaluating computer calculations cf

pressure distributions since curved hole shapes are more complex to model

in computer studies.

TEST CONI1TIONS

As previously noted, the tests were madc at an average Mach Nunber

of 0.186, uhich resulted in an average Reynolds Numvber of 5.29 :million

based on a mean aeredvnaric chord of 1.15- (45.15 in.). Corrections for

tunnel wall effects were =de using the method of Ref. 2. The corrected

angle of attack in degrees was

= + 3.27C.ML

The corrected lift coefficient was

CL =0.937 C_

and the corrected drag coefficient

% - CD + 0.035 Cj

where the subscript m indicates the measured value.

Oil flow visualization was by means of dye in SAE 20 motor oil.

At angles of attack where flow separation was present, model vibrations

4. and unsteady flow resulted in correspondingly unsteady pressure trans-

ducer and strain gage readings. These were recorded continuously on a

strip chart recorder, to determine the mean values. Studies were then

made to determine the number of digital-system readings which when

averaged gave a value equal to the dynamic mean. Although not as

precise a study as that repcrted in Ref. 3, the repeatability of data was

improved by approximately one order of magnitude. For pressure measure-

meats, five readings over a 1.5 second period were averaged, and for

strain gage (force) measurements, 60 readings over 60 seconds were

averaged. The indicated angle of attack range for pressure measurements A

was 0 to +100 in 2C increments, and for force from -12* to +12* in

10 increments.

The stabilizer was supported by a single, hollow steel torque

tube, and as a consequence, substantial vibration was initially observed

at the higher angles of attack where flow separation occurred. This

vibration was a significant factor in the unsteadiness of the data.

A small amount of lead shot was sealed in cavities at several positions

in each stabilizer to supply dynamic damping. This reduced the motion

of the tip to approximately + 0.25 inch, compared to + 0.75 inch without

damping.

4

- -- _ 4- , : '',d o I, I. '''ll A1 1 'l !'

6

RESULTS

Pressure Measurements

The results of all the pressure tests are presented in the Appen-

dices in two forms. Appendix 1 consists of plots in three-dimensional

form of AC for all six configurations for which data were taken. Asp

noted previously, pressure taps were installed on the upper skin surfaceonly, thus ACp was obtained by combining data for runs made at equal

positive and negative angles of attack, e.g. + 2, + 4, etc. Although

equal positive and negative geometric angles of attack were used, the

tunnel corrections produced some minor deviations in actual angles of

attack; this may be seen in Appendix II which is a tabulation of all

pressure data. For example, for the undamaged case, + 80 geometric

- angle resulted in + 9.80 and - 10.10 after wall corrections were applied.

The variation is primarily the result of uncertainty in setting zero

angle of attack. For the pressure model, this was done by aligning the

tip chord with the tunnel axis. Subsequent testing with the force model

f. disclosed some misalignment.

The sharp leading edge of the thin 65A004 airfoil causes a

leading edge separation bubble to form at approximately 40 angle of

attack (Ref. 4) and the length of the bubble increases with increasing

angle of attack. As a consequence the data obtained without separation

were generally of better quality than when separation and reverse flow

were present. Separation also influenced the effects of damage on

pressure distributions. Without separation, as in Fig. 2, there was

little spanwise flow, and pressure changes were concentrated ahead of

and aft of the damage. Separation produced both spanwise and reverse

A- --.-.- --

7777A-

7

flow (Fig. 3), and the strongest damage influence was observed outboard

and forward of the hole for this case. The damage also substantially

reduced the spanwise and reverse flow in some cases, as shown in Figures

3 to 5. The regions of perturbed pressures were small for the attached

flow case, and generally were limited to a distance ahead of and behind

the hole approximately equal to the hole chordwise dimension. For holes

centered at 75% span with separated flow, the influence was concentrated

at the leading edge and extended approximately to the stabilizer tip.

The hole centered at 44% span caused less change .n pressure than did the

same area hole at 75% span, and influenced a smaller region of the skin.

Figure 6 shows the chordwise pressure distribution at 75% span

for the undamaged stabilizer and the 1% area trapezoidal hole, for an

angle of attack of 2.40. The undamaged-case data are consistent with

the two-dimensional results of Reference 4. For the 1% hole which had a

length of 20% chord, the influence is concentrated in a region of 10%

chord ahead of and behind the hole. Immediately aft of the hole, the

pressure is reduced on both the top and bottom surfaces. A reduction is

I also observed ahead of the hole on the lower surface. These are all com-

patible with the expected flow into and out of the cavity formed by the

damage. (The data points at 20% chord are the "base" pressure at the

center of the forward face of the cavity.) Figure 7 shows similar data

for a hole of 2% area, with similar trends but a larger change on the

lower ,urface. Again, the pressure plotted at 10% chord is the base

pressure within the cavity.

Ar

8

Figure 8 shows the influence of the 1% hole at 83.5% span; com-

parison with Figure 6 indicates only minor changes at this location,

primarily on the upper surface. Inboard of the same hole, at 67% span,

the perturbations are also small, as seen in Figure 9. This is consis-

tent with the earlier observation that there is limited spa-iwise propa-

gation of damage effects at lower angles of attac', where the flow is

not separated.

Figures 10, 11 and 12 show the pressure distribution for the 1%

hole, at 83.5, 75 and 67% span, and 9.80 angle of attack. The influence

of separation is evident since the damage-induced disturbances are

stronger at the outboard position than at the damage station or the

inboard location. However the local lift from integration of the pressures

is diminished inboard of the damage as will be shown in detail later.

SPANiSE LIFT DISTRIBUTION

The surface pressure distributions were integrated for several

representative cases in order to show the spanwise lift distribution.

The local lift coefficient C is shown in Figures 13 through 16 in the

$ 1

same form as used in References 1, i.e. referred to the mean geometric

chord, c, and to the angle of attack in radians. The data for the un-

damaged case is included for comparison.

Figures 13 and 14 present the results for the 1% and 2% trapezoidal

holes at 75% span, based on pressure data at 2.40 angle of attack. The

localized nature of the disturbance is again evident at this angle, for

which the flow is attached. The 1% hole reduced the total lift by 2.1%,

32

r9

whereas the theoretical prediction of Reference 1 was approximately 5% for

a very similar planform. Figure 15 presents the results obtained at an

angle of attack of 9.80, at which substantial flow separation exists. The

damage effect is seen to propagate to the row of pressure taps nearest the

root and thus is substantially stronger than at the lower angle of attack.

Data for the 1.96% hole located at 43% span, with a = 2.4' is shown in

Figure 16. This hole was between pressure-tAp rows 8 and 9, so the lift

at the hole centerline was obtained by spanvzise interpolation of pressures

prior to integration for lift. The loss .n lift of 2.6% is only slightly

higher than for the 1% hole at 75% span.

DIRECT LIFT AND DRAG MEASUREIENTS

As noted in Reference 1, investigation of the aeroelastic effects

indicated that damage-induced drag is a possible source of sLructural11 failure. For this reason, a second T-38 stabilator half was instrumented

with strain gages to directly measure normal and chordwise forces which

were then coverted to lift and drag coefficients by the data system com-

puter. No pressure instrumentation was installed in this stabilator. For

both pressure and force tests, the angle of attack was varied with a lever

arm bolted to the stabilator torque tube using pre-existing holes in the

tube. The zero angle of attack position was initially determined with the

pressure model by aligning the symmetrical airfoil with the tunnel axis.

This same setting was used for the force tests; however, it was found during V

these tests that zero lift did not correspond to the zero angle of attack

setting. Consequently there is a slight offset in the results, as shown

it. Table 3 which gives the results of the force tests, in equation form.

. I -,

- 10

These equations and the test data are shown in Figures 17 through 28 as C1

vs a and C vs C.D. L*

For all d.amage configurations, Table 3 shows an increase in zero-

tslift drag, C although the relationship as shown in Figure 29 is sensitive

I to the orientation of the damage as well as the size. The four cases

indicated by the circular symbols all had the same spanwise dimension; the

area was progressively increased by increasing the chordwise dimension of

the damage hole. The approximate ratios vf chordwise to spanwise dimen-

sion were 1, 1.5, 2.0 and 2.7 for the 0.5% to 2% area holes. The results

indicate that C decreases as this hole "fineness ratio" exceeds 2. By

contrast, the 2% spanwise damage which had a fineness ratio of 0.8, i.e.

1 its long dimension was oriented spanwise, resulted in a C which was

nearly twice as large as for the 2% chordwise hole, even though the actual

dimensions were nearly the same. This characteristic is evident in Figure

30 for small lift coefficients as well.

It is likely that increased C is partially the result of reduced

pressure on the cavity forward face, i.e. base pressure, and of increased

pressure on the aft Lace. In several instances these two pressures were

measured. As seen in Figures 6 and 7, a negative base pressure coefficient

was observed. The pressure on the rear face was found to be essentially

the free-stream dynamic pressure. By this rationale, spanwise holes would

increase CD by more than equal chordwise holes, which is the trend in0

Figures 29 and 30. However, the uncertainty in the data at these low drag

levels does not justify drawing more exact conclusions.

•A

=M t __ -

Reference 5 reports the results of measurements of the effect of

circular holes on drag, using a two-dimensional model having a NACA

65 -012 airfoil section; these results are discussed in some detail in1

Reference 1. There were three configurations tested which were circular

holes at 25% chord. For these, the C based on hole area was -0.1,D 0

+0.1 and +1.1. The results from the present tests was +0.38 for the

circular hole, and +0.40 for the 1% area trapezoidal hole (which had a

fineness ratio of 1.5). These two most nearly correspond to the damage

of Reference 5, and the results fall close to the center of the range

reported in that reference.

The influence of damage on drag is summarized in Figure 30 which

shows the effect of orientation of 2% holes, and in Figure 31 which shows

the effect of chordwise holes of 1 and 2%. Both figures demonstrate that

at higher lift coefficients, the increases in drag diminish to the point

where they are obscured by the uncertainty in the data. In general, the

increase was less than 10%, with only the 2% spanwise hole showing a

consistent increase. This is contrary to the results of Reference 5, in

which both CD and K of the parabolic drag polar equation were found to

increase.

Figure 32 shows typical effects of damage on lift coefficients,

at angles of attack below and above the separation angle; both force and

pressure data are included. Generally, the reduction in CL was small and

approximately constant up to a = 50, beyond which the reduction increased

markedly to a peak at 100 or 11, followed by a decrease. There was

substantial scatter in the force data, particularly for the smaller damage

i - -- -I - "-" - "

12

cases, because the magnitude of the changes was small compared to the full-

scale capability of the strain-gage measuring system. This was parti-

cularly true at smaller angles of attack. At a = 2.40, for example, the

lift force of the undamaged stabilator was about 30 kg and the damage

effect was about 4 kg, whereas the maximum lift force was approximately

275kg. As seen in Figure 32, the integrated pressure distribution gave a

more consistent result than did the force data; at a = 2.40 the change in

the lift curve slope of Table 3 was also a good indicatoi, although it

under-predicts the effect in the presence of separated flow as at a 9.80.

I.I

43b:79_d3I

SI

= --- r ~ - ~ = ~ ~ S V - - ' v--- if

--------

t. A

13

REFERENCES

a • 1. Scott, D.S., et al., "The influence of Ballistic Damage on the Aero-elastic Characteristics of Lifting Surfaces:, AFOSR TR 80-0220,May, 1979.

2. Pope, A., and Harper, J.J., Low Speed Wind Tunnel Testing, JohnWiley & Sons, New York, 1966.

3. Muhlstein, L. Jr. and Coe, C.F., "Integration Time Required to ExtractS4 Accurate Data from Transonic Wind-Tunnel Tests," J. Aircraft,Vol. 16, Sept. 1979, pp. 620-625.

4. Gray, V.H., and von Glahn, U.H., "Aerodynamic Effects Caused by Icingof an Unswept NACA 65A004 Airfoil," NACA Technical Note 4155,Feb., 1958.

5. Shatz, R.E., "Aerodynamic Vulnerability of Aircraft", Final ReportNo. Gl-634-G-14, Cornell Aeronautical Laboratory Inc., Mar.31, 1952.

-

14

TABLE 1

PRESSURE TAP LOCATIONS

ROW # % SEMISPAN

91.7

2 83.5

3 79.3

4 75.2

5 71.1

6 66.9

7 58.7

8 50.4

9 35.8

10 17.4

In each row, chordwise tap locations, numbered from the

leading edge, were at the following positions in percent of

the local chord: 0, 1.25, 2.5, 5.0, 10, 15, 20, 30, 40, 50,

60, 70, 80, 90, 95.

L

- - - - - - -t£. r

15

TABLE 2

DAMAGE CONFIGURATIONS AND DIMENSIONS

SHAPE AREA HOLE CENTER LOCATION ORIENTATION, TYPE DATA% % Span % Chord Long Axis

Circle 0.5 75 25 --- Pr., F

Trapezoidal 1.0 75 27.2 Chordwise Pr., F

Trapezoidal 1.5 75 22.5 Chordwise Pr., F

Trapezoidal 2.0 75 27.1 Chordwise Pr., F

Trapezoidal 1.96 43.4 19.9 Spanwise Pressure

Trapezoidal 2.0 58.9 16.5 Spanwise Force

HOLE HOLE EDGE LOCATIONSAREA Percent Span Percent Chord

1.0 71.6 78.6 17.4 37.01.5 8.0

iI2.0 46.2

II 1.96 36,9I 49.8 12.8 27.0

2.0 47.8 69.9 11.5 21.4

2. _ __ _ _ __ _ _ _ _ _ _ _

7: ______ _______ ________ _______

:1 16

00 0 0 0 0 -

0 - n Lnc

0 0. 0r ~ 0 C)

0 0 n 0 0 0

* .1

'0~ LA ~ ( N ."q

0 a~( *~. 2 2 Iej p to C 0 cEU 0a U - 4 ( ( V

~-~ -- -Eto c N* "! UI* 6*.e

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~~0 0- 0

-4 = * o* -

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ca_:I I I I I I I I II-

,.=1W "0 u. u j *,

cj E 0 i ra

0 -H a

18

FIUE2

I I

19

.. .I

~ FIGURE 4.

OIL FLOW PATTERN, 1.5% HOLE, a =9.80

I m__; M-

FIGURE 5.OIL FLOW PATTERN, 1.96% HOLE, a 9.80

~S

uAM,

20

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C4-

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00L w

CO *~J 00a

~ 00 CO

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00 Rx1 0

C,

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23

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2- ,, Ar- A , 4q 3 ... n _ _ " .. I ,I n" . -73 0 .' " .153

' . 377 . 2 ). -1 ..3 X) 0 . 2 0 . A.2 0- .133

22 e% n,30 ?.7 1.1 0 2.21 1 ) '1.-) . 3 9 -97 r" '7n1-. 2 0. .- 07 ?4e 10 .. 0!')1 0.1 n . '.51 .32 "1 . ,0.252

_ f7 0S -00 15-9 P ~ 2'' 1.11 1 7V~ ' 1 *.1 3 Iq!, 2.f) In -01,- 0 I 1 1 -1 0'1 010 5 ) ')i7 0 ..1 133

10;; -0.033c -I12 A~.'2 -200 n02 -162 Of.IO 0.075 f! .029

-- C..,o , n, 1 4s~~~ .,,1 1)) . 9.3 ";,'

l -1 .-132

2 n ,. 4 1Pi 0 3 3

7.. 1 11 , -, , 1 2 i75 -3 .21 -a .S -0 31 3' 0.: P ?7, 0. 1"' ?' 10.01 -f Y 0-r 5 0 .095

Tnci ,--nce: -7.1 , 5 . .,- oe iati n:1.0 Ww-- .. , row I Po,,,? c . . r .,". [ow -.%w , o 7, , ,,. , q -'-o 9 ow M

] nwci C': ." (.5. .f ,v75%iro25..,3

2 - '5 , - f i. 1 0. 1 -1 - P72 5 O n %n g , - = '55 - 1 '71 fl. , 6 4 ' A% 0 "5

4 .' , 0 ~ 0. % 0 "l * 22' 1 ' q "'* g "-1 " " ' C ) A4

-0.035 O.Of] - .03V -0.1~1 rj.075 I 'g r'g2 ' 0. )2 fl12 0.04 0. , . V1 , ..2t-1 ") . n7, _ j;1;) , v.

61 0. 5 0.0?1 -r.,i 1 - .99% -- 0 3 fl.137 0 .0c; oo 0 .800*flI.~~~~~~ C,/; 11 ." -- O7' r,73 .- 2~

H. 3P.5 -0.1 -. 07 .93-.0 -300 0129 7 0 -11) 900712 -0.042 -0.02;' -0.026 -. ),3 -0.019 -r.I11 0.00, 0.103 -S.0l1 0 016

3.3 -0.037 -0.031 -. 0 25 -0.9'I -0.017 -0.01 1 -0.009 -9. 03 0.009 0 .01I4 -0.043 -0.034 -0.016 -C.003 -0.018 -0.005 0.003 -0.005 9.015 0 .02115 -0.019 -0.002 0.007 0.018 0.0 8 -0.000 0.00S 0.002 0.010 0 .030

Incidence: -2.5 d!ec. R'mq .Deviation: 0.040Tan Row 1 Row 2 Row 3 Pcw 4 Row 5 Pow 5 Row 7 Pow 8 Pow 9 Powl0

1 -0.448 -0.976 -0.339 -0.966 -0.799 -1.336 -1.500 -1.210 -0.5652 0.455 0.452 0.407 0.392 0.3R7 0.346 0.419 0.425 0.381 0.3793 0.248 0.259 0.259 0.264 0.260 0.230 0.297 0.285 0.2604 0.143 0.178 0.159 0.161 0.190 0.135 0.193 0.205 0.217 0.18395 0.061 0.092 0.050 0.037 0.075 0.073 0.098 0.0qg 0.100 0.12216 0.025 0.050 -0.00q -0.082 -0.005 0.041 0.051 0.055 0.069 0.0617 -0.007 0.028 0.030 -- -0.108 0.013 0.032 0.028 0.036 --8 -0.039 -0.00-0.00t 0.001 0.0009 -0.066 -0.046 -. 121 -0.309 -0.075 -0.020 -0.02 -0 0 2 -0.01) -0.0221

10 -0.071 -0.061 -0.045 -0.053 -0.053 -0.039 -0.043 -0.046 -0.022 -0.033111 -0.073 -0.960 -0.047 -0.04? -0.042 -0.941 -0.041 -0.031 -0.032 -0.042l12 -0.058 -0.037 -0.041 -0.039 -0.037 -0.031 -0.027 -0.016 -0.027 -0.020-13 -0.042 -0.033 -f.031 -0.022 -0.026 -). 021 -0.018 -0.015 -0.006 -0 .00414 -0.027 -0.021 -0. 903 -0.001 -n.Oll -f.002 0.012 -0. 001 0.013 0 .01415 -0. 005 0.01! 0.021 0.0?4 1.03.3 3.00t 0.-107 0.001 0.013 3. 0211

1 ncide ce: , ? , "1ei t o 0.033a' 3 "e-; , , ,; " "o 7 Pow " "o q Pow;A07I .. 53 0..3 0.3P2 0i 41 0 .7 10.i5r 0.S% 9.S14 0.622 -2 0.O'6 0.SE 0.0- -51.'?7 -1.0:5 -0.112 - L.hl 0.07; 0 .11. 0 .02,3 0.024 0.013 -0.013 '1.052 0. 1 " 0.311 0.053 0.03 3.06A --4 -0. 1 0.030 - .033 0.011 . 005 - 32 -0.)00 .. 0913 0 0215 -9. 53.9 - .. -.. 07 ) V 1 57 - 1, Q 5 0. - 3 0 - .,) A - 15 - .0 -5070 -0.4 - ..086 -0. 1; -3 .01 -,).)7- -0.070 -0.05') -0.052 - 35-f,

7 -0.076 -0.041 -0.001 -- -3.155 -0.076 -0.074 -0.66 -0.076S -0.093 -0.068 0.53 -- 0.146 -0.075 -0.0 035 -0.05 -0.086 -0 056

-0.093 -0.105 -0.231 -92. 1 -0 -0.09! :)0;0 -0.00? -0.093 -90 1310 -0 .3Z -0.102 -0 .101 -3.120 - .113 -0 1.0 -0. 0, -0.9 7 -0.09i -0 032111 -0.035 -0.)4 -. 306 - 0.,1 -1.177 -0.33 -n.0P6 -0.071 -0.08 9 .67412 -0. 64 -0.05q -6..06G -0.03,. .070 -0 '1 -0.03 -0 r.1C7 -0.071 -0 0413 -0 .37 -0.042 -.. ,37 -n. 37- 0 0,A4 -0.3 - -0.045 -. 94 -0. 02 -0. 0214 -0.023 -0. r1 -(r.00-% .011 -0. f1.7 -0.011 -009 -0.023 -0 .(0G 3 0015 0.007 C.022 0.0!1 0.019 0.038 0.004 -0.003 -0.005 -0.004 0.017

!n i ren e -

' - "' ;.v - i n '

2 -,,.-,7,3, 0.33 . - .I' -. :I1 i., .- .,. "-K ; ".~-, " ).3" :;.] -- .

2 -0..24 -0.22, - -C.4 -C.";i -3.237 -3.%: --22:;; -0.1 -3 3 3 -0.293 -9 .2017 -..- 0 -t:.13. -0).221 -').2-'2 -K .U -". 2.01 -. .'> -V.9.5 -- 246-0.179 _n ,'- _..2l 3 3 -3*?,0 -? "-" -e V9- -n "-,. -O - 57 - 01 -9.l3 0 C .1)1 -- ;9 -0.2" -1* -7; ̂ 9r -.... V-K~ -

T.lQ A

-0.147 -0.I. -..- 2 - . ' . .' -3..' .'. - .. 0. ).( -0.0".7-3 "

3;- 0~ .. 31 2-J -713 -02 _,.0 -'K>4 -4- -4.0!7 -C- -. 2 2"% 0 2 ' =- -.3152

5 0 0u.i -192 C 1' -1 -7, 2314.10 .1

" 'p rv "P - ' " : - . - '' -0. 3

7- -. . ...

-- 122O -1.!2131 - 1 ",- .- 17 -'. o",1 -. s -"h "'' --- : "" -3.-'12

3! -0.37: -¢.!27 -0.120 -'.! -. 172 -7 'K- -- 01 ..

4 '~ 'Y -. ~ -. .7. - -- 7- -. , . -o~!2 -0.303 -0.3",7 -0-1 -, " A. o. ." ', - -' - e

13 -0.951 -P.2 -r.9 4 -0A'! -3 _.31' _.3. -333 " -. -3.053

-0.25 - .222 -2 0- -525 n R .2 0O2 027-.i -0.2 -.214 32-0.137 -- ? -3.934, -0.2 :.-. --. ?U- 0.223,, -0.0!4 i

.2 -2.13-0.12? -0.113 -,.'2, -0..2. -.. 2" -,.11 -9.115 -0.122 -0 .523 -0.5 _..9P. -0.07 -. *31 -0.,75 -0.0-! -,.- , -.. 2 -0.073 -1 .32

5 -314,-0.053 -0. t -3 7 - ,.0 ] - -. 4 _.0. -_. 3t - .9 "" - '.0'" - ' .- ',

13 _0.0.2', _-,.2,l' -0.2 % -3. t. -',0., I , -).03 -(,.01 , -0].010, -0.." ) 0< - 0. _

1 0_9-.2-.~ l07-.7 -0. " -i .2i' -01 -1.2-% -

--0.0252 - -.3 -2. 2 . 0 . - 7 0 -1 5

-0.220 --. .4, -(..1-' -G- - . - . 5 - 1 .0.23. -0.-0.235 0.5 7 " -0. -7 -7 .... -07.5 - '. 0_- .0 -

10 -0. 173 -0.1. -. 277 - :024 -j32 -0.V- -0.317 -0.593 -0.1 7 -0.194i 7 -0.12 -0.176 -. -. -. 17- -7.4 -. 77 -0. 57 -3.153 -0.1671.2 -0. ! -0.1 . -0.15 -,,. i5 - 2.7 -4. 121 -0.1 -. !5 -0.156 -0 .11513 -0.,9 6 - C.07 -C7.l -0.1. 70 -0. -3.31 -0. 2S -0 on C .73 -0 0 714 3 . -0.053 -. 07- -0.031 -7 2 -"."O7 -0.072 -0. 31 , 0(31-0 02 '415 - . - W.03 -0 P. r - 002 -* -0."40 -0 1,lc -0 007 0 004-

1 nci:: e r.. c?-: r".'e ti n 0.16 7

', ].9 n -0.- ' - .1' C - ,: -1 . 71 2' . "3 -1 -" -2 -0.133. -1 . ... - -..

I., --7. 0 -4 -0, 3 - r)57. .3-, q I.:,3 1.q ,! - i 1. -r c - 1 4

r. - .q2 -0 7"' n 0 ' - -- 13 -. qO - 1" -: n . 2 -0. ' - F. 51 -0 .49123-O G7'. - . 71 -0G~ - .,. 5% - 6.. 14. 5n. 2 - 17 - . G 0 , -0.459 - o.34"1

"7 -0 .- 2 5 6 51 -2. , . -- 7' ,q -: .. 4 0 0. 3-q - 1]9 -- {; q -0.353 -0.35" 61 ="3 -- -3 2 9 -)2 ' 9 132 (.1 7-1.. qt - . :

11 -0,.216 t.3.. .. .. ... -,.9 2 22 22"-1iel

12 1o"', -o 6 -0. 157 - 1. 6 -0 . 1 "7 -,'1. 1'' -0.1s; C.1 -0.].-3-6 -0O.i1-A.513 -0. 1 ,2 "2 -C. ' 6 -0 . 12 0 -0 .121 - -.. 13 - 12 1 1 0" - . 1,03 - 'O3{

14 -0.13]7 -0.08.3 - 0. 071 -n 07'i - C-. rn7 2 -(1. C7 , -" .07 - 0. 0 31 0049C15 -0. 086 -0.043 - 0.f,4 5 -G.0,15 -0.023 -,.9 - O 0.O04 - (.n-331 . 0- 2.,.- - 0. 0!0

*i.. . = I7 -- ' 0 T! S - .. .--. ' n -- -1 1 . e o o

7 '. , -'-1 7 - . - -

7- -7 .0 3 -I "''- -f.l'1 --l -34 " - J' -.a ._ . .:_' 3 - . l ----

0.1 3S ;1 -7--0. 4 In

I ".

-' - 27 o,

". 3 2 - 0 -

72 -0.3 3- -0.3' -¢..73 -3' -. - - . 3 33 1-

11 - 0.75 -- 2"57 - 0 7 C - _ -- - : r 2 55 - 0. 1 t - 0 .2 -. 1 47

14 -0.42" -0.3 . - 0.. , .. --1 -. 11 -. 3';.7 -0.-17-12 -0.2 .-0 .. 1 -0. -O.3! -(. 1'9 C.. -. 3 -2 1 _ - .2 -n 3

1.7 270 - 3... . - . .... -2.14 -0. 2.5 -0.217 -0.213 -1.21 -. 7' - ' -. 1" -0.121 -1.075 -0.077

' 1 -0. 22 -3., :q -O.-J]1 -07.'33" -9.7&7 -0.* V' -1.002 _]l-.,7 1 -1.007 --

, -G.P21 ~~o~os~ ~P. , '77. n I -N7 ~*''-C iM 1.0' I2 -- 7. 03 -0.71n - .7 "'e -n.. ' -'. - ': 1 - 0.-5" -2.2'-

3 -0.774 -0. - . -.. _ -A' - 73 -P..g3 -].l52 - -30

11 -0.015 _0.A 7 0.604-,i _ 0l -. '. -O.$17 -0, -.- 57 -0 .7 ._ 32

12-3.47 -3.50. _..,57 -053. . -2.-. -- -.. 5 -.. 2 -1.3"' -.. 2.7

17 0, . qT0 51 7n ,,V- .7 -r., I 1 1 7 0. -,f- ,.- f- 7 1: 7 1o 4

0] . 7 1"). " - 0. -6 0. ,-', .n e .- -f'j;. A0 'I .. "7 n 1 4 .oj7 _n,. CV). -0 . 2 3 ,-'

12 -0.674 - 0. 506 - 0. 5 A 2 - 0. 5 - ' , -5i - ." - . I - -0.452 -0. 309 - 0.- 2-57

13 -0.432 -0.449 -0.49 -0.17 -C - .4 ,, 0 --. 4.. -0.371 -0.209 -O.132

14 -0.357 -0.401 -0.415 -0.404 -0.419 -0.407 -0.345 -0.212 -0.149 -. 104

15 -0.366 -0.37A -0.380 -0.382 -0.388 -0.390 -0.304 -0.254 -0.115 -0.06!

I'C

7 7

t

- - - L -,

1.5% TVDEZOIDAL IiOT,3 e75%5S,25%C

Incidence:-12.4 dec. r'iq neviF ion: 0.007,Pr Roa 1. Pow 2 ow 3 P-w .. Pow 5 i'ow 6 Row 7 -cw 3 Dow !z oW,:

-1.551 -1.950 08 -. 007 -0.q12 -0..F05 -0.901 -1.057 -1.44. -

2 0.655 0.682 0.610 0.524 0.577 -0.623 0.670 0.616 0.720 3.7523 0.609 0.613 0.459 0.376 0. '69 0.549 0.599 0.620 0.6584 0.492 0.503 0.252 0.096 0.307 0.436 0.499 0.529 0.555 0.569

5 0.347 0.387 0.043 -0.991 -0.143 0.215 0.372 0.306 0.419 0.4306 0.255 0.331 0.115 -- -0.297 0.173 0.290 0.314 0.336 0. 364

7 0.138 0.298 0.156 -- -0.2,4 0.132 0.233 0.259 0.281 --

8 0.0q6 0.244 A.364 0.457 -0.065 0.130 0.119 0-1'30 0.197 0.210

9 0.031 0.150 0.282 0.453 0.319 0.15- 0.112 0.118 0.129 0.143

10 -0.019 0.062 0.110 0.140 0.144 0.112 0.071 0.070 0.085 0.094

11 -0.067 -0.002 0.023 0.036 0.055 0.052 0.032 0.045 0.049 0.054

12 -0.00-8 -0.039 -0.027 -0.020 -0.015 -0.003 -0.001 0.015 0.020 0.049

13 -0.104 -0.084 -0.080 -0.070 -0.064 -0.059 -0.048 -0.025 0.011 0.0314 -0.143 -0.144 -0.137 -0.13R -0.139 -0.124 -0.111 -O.O6 -0.016 0.013

15 -0.147 -0.161 -0.173 -0. 166 -0.146 -0.1(0 -0.163 -(.1 3- -0.054 0.002

Incidence: -9.9 deg. D-3 Deviations: 0.019

Tao Pow I Row 2 Pow 3 Pow I c, 5 Pc-, 6 'vow 7 Pow Z qow q rowlF 1 -1.487 -2.341 0.911 -0.q28 -0.79q -0.735 -0.-2q -1.097 -1.5032 0.673 0.6R3 0.596 0.94 0.564 0.+ ,O n.657 0.490 0.702 0.717

3 0.582 0.500 0.434 0.134 0.441 0.51 0.5;4 0.5c! 01.4-.40.454 0 262 0.233 0.0 8i 2n 0.2 lA ' f) 0 :350 0. -. . ... 5 A. .0 . 66+ , 3. O:q .. ..- 5

5 0.309 0.345 0.077 c -,"1 l 2.. 3.- 2"- -1 .. 1 1 3 - 3.155

6 0. 22 l"'.21 0. 12.4 -0 n1i 0. 5 .1. I'l . -1 7 1 .3. 01 0 3. 1)7 0.163 0.25 3.1 3 -- -0.230 .l " 3.1) 0.123 0.237

0.052 3.211 0.333 0.553 -0.033 .) 1 7 9.122 0 .II 0.1 3 0.1J

= 0.327 .130 0.2..2 0.3' -0.2-":0.i "0 0'7 0 .0' 0.I05 3 .1n10 -0.005 0.057 10.100 0.3 ) . - e A i P. 0 5 n 07 7 011 -0.041 0. f0) 0.033 0.053 0.15, ').* -' "3.012 ,. 3 3.41 .

12 -0.051 -0.91 -0.00- 0..00P 0.032 1.fl 5 0.)21 .? 0.f22 2-113 -C.0 , -,-.12" _-.02. -, -'3 -.. . 0.. 2 . 11,...14 - 2. . -0. 3 c3 -G.076 -- . 7 -0. -1.047 -0.031 .01A .G,215 -0.0.2 -0. Wl -0.0F2 -0.'q.1 -1 .c; 0. ...

I ncilence: -7. -ei. fl'3D':i~t'): 0.010e, 1 2 7 -0 - . " - N

1 -1.133 -I.035; ] .q3 -0. 'l1 -'0.'01 -'.1'15 -i .90 -i. n" -1 .343 -

2 . 7 0.77. .5Iq 0. :8 0.:33 1. " n .. ,. 6- 1 .-"5 13 0.521 0.537 0.-11 '.310 0. 105 31 . .52 0- 1 54 0.3Pn. 0.413 0.220 0.067 0.251 1.360 0.414 0.43 -1 42 9 0.1 3.5 0.252 0.2(3 0.106 -0.7.! -0.10 q 9.214 0.2R02 0.2 n 0.301 1?6 0.175 0.237 0.12'3-0.177 1" c2 0 .210 0.225 0 .234 0 . i67 0.122 0.107 0.138 -- -3.l'1 14 .8)7 0.;- . .I ; 0.I :7 -

! ,.051 0. iI6 0.7")2 .0(I I " .1 , 3 0.091) 02. 7 0 123 0 .1!.( 0.017 0.398 0.l~fl 3.9L' 0.2 12 7.12 1.076 , f) 17 G.97 3.)k " 10 -0.008 0.04? 0.090 0.10 a .14 ... 8 k .. .0" .84 0t.1 - 0 ) .1" 0 _4- 1 . , . n 8 001 0 .8 5 : 0 0 . 4 0 . ".3

11 -0.031 0.002 .07 0.0 1 0.052 1.0-2 1.137 . ' 7.... . 312 -0.033 -0.002 0.012 0 P:17 .011 0.033 .27 1 ,2" - 0-.02-- 0.03-

13 -0.,31 -0.0l3 -0.005 002 0.000 0.11 3.013 3.117 0.032 G .03714 -0.04- -0.)34 -. 3.0110 -0.13 -0.020 -1.005 0.005 0.0 o i.02l 9.03613 -0.035 -0.017 -0.011 -0.007 0.009 -0.^17 -0.003 1.10 , "..n3 0 t33

Sa M

1~~~-* .5% --! 7 I - T 251

-0.035io 0..2 013 *'

. : T I -' ~ ~ ~ ~ ~ ~~ 1(-- re '' >:° <= .... ::, T ,: f%-,: L: : :

5 25 1" ' Z T '[ 20,.,: t- 5 121'1 -

13r,..027.-0.0 -. .0020.0' -03 0."O .... 0.01i4 0.01

35 0.OCS0.01 0.2 7 .3 3.A -- 1' 0.1 -171 7.1

3 . .o 1 2 r 3 c, 4 !;o, S ,. . 7 '-,A ( 2 1 1I7 1 1

1 -_.3, - ? 271 -7 - -07 ---1.37--_ -1 -0 " --

2 19.427 0. 13- . 3 .5 0'00351.5 .7 i l37

3 0.51 0.S43 0.07A 0.177 .71" .' ,.n ".C. 4 1. 1. ,

1 0.0 3 0.1 0.003 ,.0n. ,.11 '.... , 2 0. 7 7 0.0)-

12- 0. 3 -,*, 0 . * 0 - .0 . 219' 0 .01 ,1 . I .1 0 )7 f .')I -0

13 -0.0270 0 *3 n 0 .002 0 .001 ,1! 1. 0. 0 03 MI74 -(0.02 -0.0S 0.001 - -3 .. 01 . 0 10 . C; I . 7- 0.2.7

3 -0.037 0.017 0.-2 3. 0.. '0.. 02. 0 __

ln ia*ct, -2 , l6

Ta Po. I' Po "l c-.- 4 o .c.. 7- . - ,, ow ,91 Pc'.zl762 -0.9-n 1 7 -. 1. "?.7 -0 .06 3 1 < f : - . 0. 7 0 1 '1--, .

20 -. 49 - 0 . 0.40-0.33 -. 17 n.020 15 5 371 e -. -- 0 .0 3332 -0.251 0.04' -0.037 -0.'71 0.7P1 0 ", 7.13-'027 -0.004~ -001 0.002~ -'.007 " zf0.89 -O.00-q 77- O. -,0 1 0 .1

I. I 33~ l')3 1).% 17 (1 ~ -' 93* '3 r)~ ~ r) .1 - C -. 1- 1.( 1 *-T! -, .1 0. _57

14 -0.030 -0.009 0.00!7 0.00 ).00 0.010 o.01y (0. !] 0..5 0.02

15 0 .02. 0.17 . .3 .a, q 0 2 0 07 8.9 - .! .

Inci -e.ce: - *1 ¢'). ";. " Uv-i 'to - " 0-.3''Tao POw; 1 POW 2 owz 3 "O- NV U w - mow' 7 T IO ,n'- O-I

7 02 0 P O."e .5 l> "- 5 7 -0 0 37

3i% .I p,

4 . 0.0 C... 37 -0.Q."1 Q. -. 7 043-

L7 -0.07 -0.03" 0r .2 -- -0.02 -,.0S -0.077" -Cl .37 .... 7 -

21 -. 011 0 - .. '- . 0,-- , - . 03'3 -". 0 2 -0.. 0-".. -- "S'

-0.0 oo 0.0" _ .2" . 1P -1* 1• .- (33., -f.3 -. ii -l0

! ~~10 -0.O5l -0.0.'30 -0."090 -0).1 -".10--0-."3 -(o.:"- -r'.-i" -'"o ' 0011-OO -0.0 ';7~ -0. 03 -. 0q7 -0.90%1 -_ ... -.P, ....n -r ^1V. -3.351 -',. 0,3

. 2-00:." -. O,:-0.073 -0.0% -0.02 -3.3;-~ _0.5 _13.0-r 43 --.7 g13 -0.01' -4.'3-1 -3.033 _n.1 0 , '". 3'. 3. 0 ,.3$ _- .. . .. _,. 0 f3 _3 -~ -3.'17

14- -0.005 -0.01] -0.30- 0..001 -0.012" -:.01-0 ".Ce' -0.9' 0 00n3 " 0!01" .Q] g. " " C'.'It7 n~n- , 9.9'.: o.oo] , r. ,' q ': n.')r 1. 0')7 0.1

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T----O I O::-I _____.,_no .9 ". :_' O: (W "

n• , nc? 0. 3" , 01O

-0.025 -0,00q 1 0.144 -0. 3 r 0 rn.' - _, --0 " -5.5! 06 -l 0.-n 0,0 3 . 02

3 0 S -0.1027 - f0 . - .0 f. -10. 7 7n -~ Cn. 6 0.0 1 -.. 0. 3 .0

_ _ _- - 0 ;5 6) 01 -. 0.1

0 5 0 2 0 01? 7.l -0751 -0.0502 0. 05 _n00 -3.0420- 005 0. -36 0 . n17 -- -0.0 - 0 t-0 0 ' - n.05 0; 0 4 -

7 -0.074 -0. 0 1P 0.023 -- -0.025 - 0. 0 55 -0077 V A 7 i -0.0-' -- .'I -. ".. £ - S0 6 0n. Or%: 0.7 r7 0 .1n-, -3 .~ -01.qo _,0 l S -0. -S5 I),.I 'D 4

Q • 4 0 P. -21 , n. r 3 -

I0 - . l - .. 3 0. 095; -0.!1]1 -f) lI J -n.]3in -o.0" -s. Zn O 0 3 - .} qtl! - c,. (7£ -0.7; - A S -0..070 -0 .07 n - q. ". -1..q ..7 p-.93n -3007 -

12 - 0. 057 - 0. 0 T: - (1.05;2 -P).056 -0.0 " -- 3 a n.0"):-" -r) 731 -0.0467 -3.,14

13 -00 1 -C,0 1 -0 0 0 1 1 0 -G 0310 . .147.0 0 z

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