AD '65 165

THE DESIGN OF AXIAL COMPRESSOR AIRF LSUSING ARBITRARY CHAMBER LINES

George R. Frost, et al

Aerospace Research LaboratoriesWright-Patterson Air Force Base, Ohio

July 19-73

_jI K

DISTRIBUTED BY:

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE5285 Part Royal Road, Springfield Va. 22151

ARL 730107/JULY 1973 I

[ Aerospace Research Laboratories

THE DESIGN OF AXIAL COMPRESSOR,SAIRFOILS USING ARBITRARY CAMBER LINES

GEORGE R. FROST, CAPTAIN, USAF

ARTHUR J.WENNERSTROM

FLUID DYNAMICS FACILITIES RESEARCH LABORA TORY

PROJECT 7065

L IL ,L., L ,UApproved for public release; distribution Unlimited. -..-..

AIR-FORCE SYSTEMS COMMAND

United Stes Air ForceReprodbc.d by,

NATIONAL TECHNICALINFORMATION SERVICE

U I D pormntl of C o.ne.'esp" 'Af, d VA 2211;1

vhen Government drawings, specifications, or other data are used for anypurpose other than in connection with a definitely-related Government procurementoperation, the United States Government thereby incurs no rezponsibility nor anyobligation whatsoever; and the fact that the Government may have formulated,furnished, or in any way supplied the said drawings, specifications, or other data, isnot to be regarded by implication-or otherwise as in any manner licensing the holderor any other person or corporation, or conveying any rights or permission to manu-facture, use, or sell any patented invm-tion that may in-any way be related theretc.

Agencies of the Department of Defense, qualified contractors, and otherGovernment agencies may obtain copies from:

Defense Documentation CenterCameron Station

Alexandria, VA 22314

This document has been released (for sale to the public) to:

NationrA Technical Information ServicesClearinghouse

Springfield, VA 22151

-'i

Copies of ARL Technical Reports should not be returned to the AerospaceResearch Laboratories unless return is required by security considerations, con-tractual obligations, or notices on a specific document.

AIR FORCE/56780I25 July 1973 - 300

!

1

UNCLASSIFIEDSecUulty Cl-salC211i0o .

DOCU AEHT COHTROL DATA. R&Dfse.*h ciao offirJa o1 Ciff.. booy of AbaIrtci &ad i.'dozh.* anotaU.. Ii * b ortlet. whe ft cW). reaj v*". is cla..lll.!

I. ORINATING ACTIVITY (C.p' J.u 542WJ) U. Xr.PORT 2ECURITY CLAR±IfICATICN

Fluid Dynamics Facilities Research LaboratorS .Aerospace Research Laboratories (AFSC) I& CROUPWright-Patterson AFB, Ohio 45433

3. REPORT TITLC

THE DESIGN OF AXIAL COMPRESSOR AIRFOILS USING ARBITRARY CAMBER LINES

4. O$SCRIPTIV9 NOTZI l'pv of *ad ¢lu1alre dte)

Scientific Final

George R. Frort, Captain USAFArvhur J. Wennerstrom

9. RKPQRT DATC 75. TOTAL NO. OF PACK 7b. 4O. or

ftEP

July 1973 -9-1 /725* CONTRACT OR GRANT NO. Ia. ORICINATOWS REPORT NUMBERIS)

In-house ResearchL ,'OCT NO. ARL 73-01077065-04-09

C. 9~b. OThER REPORT N 3 (As7,rod w suboe tsmrbe asgf9 ~dMf. rep")

10. DISTRIBUTION4 STATECKNT

Approved for public release; distribution unlimited.

II. SUPPLC1UENTARY NOTC T2. SPOCNORIN4G UILITARY ACTIVITYTerospace Research Laboratoriec/LF

TECH OTHER hir Force Systems Command4right-Patterson AFB, Ohio 45433

13. A82TRACT

This report describes a technique which has been developed foruse in the design of axial compressor airfoils with camber lines ofarbitrary shape. The slope of the camber line at several points ona streamsurface is determined from the air angles at these points aswell as the incidence and deviation angle 4istributions for the blade.A camber line is pr-oduced by fitting a smooth curve segment througheach pair of points from the leading to the trailing edge. A thicknessdistribution is applied to this camber line to produce the bladeelement. A computer program which uses this technique to produce bladeelements, stack them, and then determine coordinates for planesurfaces through the resultaut blade is also described.

DD Nv1473 /- UNCLASSIFIED/ a., Security Classirication

______________________________________ 1LI4 A LhI4K LIHK C

axial Comliessor

airfoil geometry

turbine enz-iiesI

gas turbines

*UJ.S.Government PrIntng Office. 1973 759-495/634 UNLSSFE

ARL 73-0107

THE DESIGN OF AXIAL COMPRESSOR AIRFOILSUSING ARBITRARY CAMBER LINES

GEORGER. FROST, CAPTAIN, USAF

ARTHUR J. WENNERSTROM

FLUID DYNAMICS FACILITIESRESEARCHLABORATORY

JULY 1973

PROJECT 7055

Approved for public release; distribution unlimited.

AEROSPACE RESEARCH LABORATORIESAIR FORCE SYSTEMS COMMAND

UNITED STATES AIR FORCEWRIGHT-PATTERSON AIR FORCE EASI ,, OHIO

/c

FOREWORD

This report was prepared by Captain George R. Frost andDr. Arthur J. Wenneistrom of the Fluid Dynamics FacilitiesResearch Laboratory, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.

The report presents results from a portion of the effort ofthe Fluid Machinery Regearch Group supervised by Dr. Arthur j.Wennarstrom and was conducted under Work Unit 09 of Project 7065,"Aerospace Simulation Techniques Research" under the overalldirection of Mr. Elmer G. Johnson.

iii

ABSTRACT

This report describes a technique which has been developedfor use in the design of axial compressor airfoils with camberlines of arbitrary shape. The slope of the camber line atseveral points on a streamsurface is determined from the airangles at these points as well as the incidence and deviationangle distributions for the blade. A camber line is produced byfitting a smooth curve segment through each pair of points fromthe leading to the trailing edge. A thickness distribution isapplied to this camber line to produce the blade element. Acomputer program which uses this technique to produce bladeelements: stack them, and then determine coordinates for planesurfaces through the resultant blade is also described.

A

TABLE OF CONTENTS

SECTION PAGE

I INTRODUCTION ................ . 1

II DESCRIPTION OF THE TECHNIQUE ..... ......... 3

1 Technique Overview ....... ............ 3

2. Details of the Technique . . . . . . . .. 3

III THE SECTION CAMBER LINE . . . . . . . . . . . 5

IV OTHER ASPECTS OF THE CALCULATION PROCEDURE . . 11

1- The Section Thickness Distribution .... 11

2. Cartesian Coordinates for the Blade . 11

3. Section Properties . . . . . . . . .... 11

4. Blade Characteristics ... .......... 12

V USE OF THE PROGRAM ....... . ....... 14

1. Definition of Input Data Items . . .... 14

2. Input Data Format. ......... . 19

3. Output Data ........ . . . . . . 19

VI EXAMPLE OF USE OF THE PRGRAM . . . . . . . . 22

1. Input Data . . . . . . . 22

2. Output Data . . . . . . . . . . . 27

VII COMPUTER PROGRAM DETAILSI..... . . . . . 48

1. Implementation of the Computer Program . , 48

2. Deck Setup for CDC 6000 Series Computer . 49

3. FORTRAN Program Listing . . . . . . . . . 50

4. Program Logic . . . . . . . . . . . . . . 88

REFERENCES . . . . . . . . . . . . . . . . . . 96

Precedifl Page blank

ILLUSTRATIONS

FIGURE PAGE

1 Cartesian and Streamsurface Coordinatesof a Point......... . . . . . . . . . 92

2 Locations of Streamsurfaces and ManufacturingPlanes for Example Blade aesign . . . . , . . 93

3 Example Blade Design: StreamsurfaceSections . ................ . . . . 94

4 Example Blade Design: Cartesian Sections . . 95

vi

SECTION I

INTRODUCTION

The traditional approach tc the selection of blades foraxial-flow compressors has been to choose a specific type ofairfoil, subsequently to adjust the parameters defining thatairfoil to suit prevailing aerodynamic conditions. Manysuccessful designs have been accomplished in this manper usingsuch blades as NACA 65-series, double circular arc, multiplecixcular arc, etc. This approach has the virtue of employingairfoil sections about which something is usually known withrespect to losses, deviation angle, and operating limits.Reference 1, an earlier publication of this laboratory, isrepresentative of this approach.

A typical contemporary design will be accomplished using astreamline curvature or matrix through-flow analysis incorporat-ing computing stations internal to blade rows as well as at bladeedges and in free spaces. Some criterion for optimization ofblade shape must be chosen. (The authors of this report chooseto achieve a particular shape of. static pressure distributionalong streamlines.) The spanwise distributions of inlet andoutlet relative flow angles, loss coefficients, etc. will havebeen determined through some preliminary design procedure. Arule for determining deviation angle and distributing it alongstreamlines will have been selected. Subsequently, the aero-dynamic blade design procedure consists of assuming a bladegeometry, performing an aerodynamic analysis using specifiedrelative flow angles as input data, and then repeating thisprocedure as many times as necessary, varying the parametersdescribing the airfoil sections, until the result of the aero-dynamic analysis adequately satisfies the chosen optimizationcriterion.

There are three principal disadvantages to employing thisprocedure for the design of transonic and supersonic blade rows.First, the iteration required is time consuming and, to somedegree, laborious. Many adjustments to the geometry specifiedmay be required before optimization objectives are met.Although the bulk of the calculations are performed by computer,the designer generally must still examine and evaluate theaerodynamic result and decide what to change, and how much, forthe next attempt. Second, when airfoil shape is restricted toany particular class of airfoil, it will rarely be possible toachieve the optimization objectives as closely as might bedesired, everywhere along the span. Some compromise will nearlyalways be necessary. Third, streamline curvature and matrixthrough-flow analyses sometimes experience difficulty in findingsolutions for certain combinations of high relative Mach numberand high absolute Mach number near choking when relative flow

1

angle is specified as input data within blade rows. This is anumerical problem related to the construction of these computerprograms and can vary considerably from one program to another.

A design method which eliminates or appreciably reducesthese problems consists of specifying total temperature (inrotors) or the product of radius and whirl velocity (in stators)as input data to the aerodynamic analysis program and thenfitting airfoils of arbitrary shape to the resulting relativeflow angles. In so doing, one loses the data base which mightbe associated with a-papticular class of airfoil, but the valueof such a geometrically-related data base is questionable fortransonic and supersonic sections. Following this approach,the aerodynamic analysis can be optimized with considerablyfewcr iterations than are usually required with specifiedgeometry. In most cases, optimization objectives can be achievedon nearly every streamsurface. Some interaction is requiredbetween the blade design program and the aerodynamic analysisto insure that the blade lean angles and blockages are keptup-to-date. However, the over-all effort required to achievea satisfactory design using this method has been found to besubstantially less.

The principal difficulty in developing a procedure todefine arbitrary airfoils consists of arriving at a methodwh.ch produces aerodynamically attractive shapes which are inaddition practical from a structural and manufacturing viewpoint.This report describes one such method developed at the AerospaceResearch Laboratories. The method has been incorporated intoa computer program which is an extension of the work reportedin Reference 1. In additio., to determining the shape of theairfoils on aerodynamic surfaces, section properties arecomputed, the blade is stacked, and Cartesian coordinates aredetermined for manufacturing purposes.

The overall design technique is described in Section II.The mathematical details of implementing the technique in acalculation procedure are described in Sections III and IV. Amethod of producing the optimal camber line on a streamsurfaceis treated in Section III; the calculations related to otheraspects of the blade design procedure are discussed briefly inSection IV. Sections V, VI, and VII present the details of anduse of a computer program which incorporates this designtechnique, currently used at the Aerospace Research Laboratoriesin the design of axial compressor airfoils.

2I

SECTION II

DESCRIPTION OF THE TECHNIQUE

1. TECHNIQUE OVERVIEW

The technique described in this report uses an iterativeprocedure to produce an "optimal" camber line'on each stream-surface. A thickness destribution is applied to each camberline, and the resulting blade elements are stacked to producethe desired airfoil. The technique requires the designer tospecify the incidence distribution radially at the blade leadingedge, the location of the stack axis and the stacking offsetsof a.ch streamsurface section centroid therefrom, the pa-.ametersof the thickness distribution, and the chordwise distributionof deviation angle along the span.

The optimization criterion which has been selected for thesection camber line is to maximize the absolute value of theminimum radius of curvature on the camber line. The "optimal"camber line is chosen from a set of camber lines containing theminimum number of inflection points. This original set ofcamber lines is generated by varying the second derivative atthe leading edge.

The starting point of the design technique is output datafrom an aerodynamic analysis of a particular blade row whichhas been generated by specifying a parameter other- than bladegeomctry, such as those suggested in the Introduction, acrossthe blade row. This data is in the form of the meridionalcoordinates of the streamsurfaces and the chordwise distributionof the relatile air angles on each streamsurface. The essentialsteps of the technique itself are described in a qualitativesense in the remainder of this section.

2. DETAILS OF THE TECHNIQUE

The first step of the overall procedure is to determine theoptimal blade section on each streamsurface. This in itselfis a multiple-step process which incorporates an iteration withsolidity to establish a camber line for each of a range of valuesof the second derivative at the leading edge, a search procedureto choose the "optimal" camber line, and the application of athickness distribution to this camber line.

The procedure begins with an initial estimate of solidityon the streamsurface. This estimate is made by applying thestagger angle, assumed equal to the average of the inlet andoutlet relative air angles, to the meridional chord length,obtained by integrating along each streamline from the assumed

3

leading to trailing edge, to get a first estimate of the truechord. The solidity is then computed from this estimate, themean streamsurface radius, and the number of blades in the bladerow.

The total deviation angle is computed from this es-imatein some fashion, such as the modified Carter's Rule withappropriate constants. The deviation angle at each internalpoint is next determined as a designer-specified fraction ofthe total deviation. The required secticn angle at eachinternal point and at the trailing edge is then the difference-between the relative air angle and the deviation angle, whilethe section angle at the leading edge is the difference betweenthe relative air angle and the incidence angle.

Each section camber line is determined by fitting a segmentof a smooth curve, such as a cubic, between each pair of pointsfrom the leading to the trailing edge of the section. The slopeat the endpoint of each segment matches the specified sectionangle there. The true chord length and the associated value ofsolidity can then be determined. If the solidity differs bymore than a prescribed tolerance from the previous estimate,the steps subsequent to and including the total deviationdetermination are repeated for-the revised values of solidityuntil the desired tolerance is achieved.

The entire procedure described thus far is repeated for arange of values of the second derivative at the leading edge.The resultant set of camber lines are inspected first to focusonly on those which contain the minimum number of inflectionpoints, and from these to choose the camber line which is11optimal" in the sense previously described.

A thickness distribution is then applied to this camberline, and the procedure is repeated for each streamsurface.The blade sections are stacked, and the Cartesian coordinatesof the resulting blade determined. In addition, the bladeblockage and lean angle are computed at each appropriate stream-surface-computing station intersection point.

As a final step, the designer inspects the resultingblockages, Cartesian centroid offsets, blade lean angles, andcoincidence of the blade edges with the designated computingstations. If necessary, appropriate changes are made in theinputs to the aerodynamic analysis, and the entire procedurerecycled until adequate overall coin- idence between the bladedesign and the aerodynamic analysis is achieved.

4

SECTION !!I

THE SECTION CAMBER LINE

The first item required in the application of the techniquedescribed in the preceding section is the meridional chord lengthof the blade element, obtained by integrating along the stream-line between the assumed leading and trailing edges. This isaccomplished by passing a spline curve through the meridionalcoordinates (x, r) of the streamsurface. The slope of thestreamsurface is calculated (as the slope of the spline-curve)at 100 points distributed uniformly on the x-axis (axially)between the edges of the blade section. The chord length, Cm,is obtained from the equation

C X 10 n ) 1+ [dr + )-/n 1 2

.4 n nn 1-n=2

An estimate of true chord is obtained by applying thestagger angle, aszumed equal to the average of the inlet andoutlet relative air angles, to the meridional chord so that thetrue chord estimate, Ce, is

CmCe - /S(e+te (2)cos ) )

C 2

The first estimate of solidity may be computed from theequation

NCe-rrk~ (3)

(2 ~te

where N is the number of blades and rke, rte are the radii ofthe streamsurface at the leading and trailing edges,respectively.

5

The calculation of the deviation angle, 6, follows theNASA method (Reference 2, Equations 269 and 271) with anadditional term, y.

6 = 60 K6 K6 + m- ( + Y-

where 60 is the variation from the reference deviation10 for a 10 percent-thick NACA 65-series thickness

distribution

KS5 is a correction factor for a blade shape with athickness distribution different from a 65-seriesblade

K6t is a correction factor for a maximum -hicknessother than 10 percent

m is the slope of the deviation angle variationfrom reference deviation with camber

b is the solidity exponent (variable with airinlet angle)

axe is the relative air ange at the particular edge

i is the incidence angle

y is the arbitrary extra deviation

Solving Eq (W") for 6 yields

6010 K6 (a e-i-te) + Y

6= s t a (5)0] - b

For use in the calculation procedure, K6 , i, and y arespecified by the designer. Several of the ot er quantities areobtained from known quantities and figures of Reference 2:6010 from Figure 161; K6t, Figure 172; m, Figure 166; and b,Figure 164.

6

The blade angle, a, is established at several pointsacross the blade element from the relative air angle, 8,modified by the proper consideration of incidence or deviation.At the leading edge,

'Ie = Ole - (6)

and at the trailing edge,

ate = te -(7)

At the other points, the blade angles are determined bysubtracting a fractitn f of the trailing-edge deviation fromthe relative air angle. At each internal point j,

j -f6 (8)

The fraction fj is determined by radial interpolation from thedeviation distributions specified by the desig-er.

The camber line is constructed by fitting a third orderpolyncmial (cubic) through each pair of points from xhe leadingto the trailing edge of the section. Thus. each segment of thecamber line is defined by equations of the form

y = ax3 + bx2 + cx + d (9)

- I = 3ax 2 + 2bx + c (o)

y" = 6ax + 2b (Il)

As a result, each segment has at most one inflection point(y" = 0) in its useful range, and in most instances has none.

7

The constants a, b, c, and d for any particular segment canbe expressed in terms of the endpoints (denoted by subscripts1 and 2) of that segment as

(Y2 '-Y!') -Y"(x2-xI)

a __1(22X2) -(12)3 [(X22-% 2-xI(X2-X1)]

y," - 6ax 1 (13)2

c =y' - 3ax,2 - 2bxl (14)

d Y1 - ax13 - bxlz - CX1 (15)

For simplicity, the leading edge of the camber line isp1kced at the origin of the coordinate system, resulting inthe following boundary conditions for the first segment:

At x , y 0

y' = tan ate (16)

Y" = Yo"

AtX X ,y' = tan a, (17)

With these boundary conditions, the apprcpriate values ofa, b, c, and d for this segment are completely determined.

The boundary conditions for the second and subseqLentsegments are specified at one endpoint by equating the firstand second derivatives to the values for the preceding segmentat the point of juncture; for example, for the second segment,

At x = X13 Y = Y1~is(first segment)

y' = tan a1

(first segment)

8

and at the other endpoint,

At x = x2 , y' = tan a2 (19)

From these conditions, a distinct set of constants(a, b, c, d) are computed for the second segment. This samerocedure is applied to each pair of points to produce a

camber line with continuous first and second derivatives allalong its length.

Note that the first segment of the camber line requiresthe specification of the second derivative yol" at the leadingedge. This boundary condition affects the constants of thefirst segment and thus the nature of this entire segment, includ-ing the conditions (yl, yj") at the other endpoint. Since theconstants for the second segment are established from theseconditions, and so on for the rest of the segments, the natureof the entire camber line depends on the value of yo" specifiedat the leading edge.

It has been found convenient to specify yo" in terms of anon-dimensional parameter S/Ro, the ratio of blade spacing, S,to the radius of curvature. Ro, at the leading edge. R. is givenby the equation

r, =[ + tan 2 312-3

R = Yo" ae (20)

and S is obtained from

S = (21)N

From Equations (20) and (21),

S 2rr ,e YO

R 0 N l + tan 2 ake] 3/ (22)

9

Solving for yo" gives

{+ tan2 ]T

Y [ tr- (23)2rr.B e Ro

which .ir,dicates that yo"l is the parameter S/Ro multiplied by aconstant.

For a particular value of S/Ro, the true chord length ofthe resulting camber lines may be determined from the endpointof the final segment as

C = (Xte) 2 + (yte12 (24)

This value is used to compute a revised value of solidity, whichis compared to the original estimate. If satisfactorycoincidence has not been achieved, a corrected deviation angleis computed from the revised solidity, and the camber linereconstructed. This iteration is repeated until adequatecoincidence has been obtained.

It is difficult if not impossible to have an intuitivenotion of a "good" value of yo" (hence, S/Ro). For some rangesof S/Ro , each camber line segment may contain an inflectionpoint, while for other ranges, few if any segments may containsuch a point. The authors of this report have assumed that,for aerodynamic as well as mechanical reasons, the mostdesirable airfoil among several matching the same flow angleat each computing station will be one having the minimum numberof inflection point-, betweer leading and trailing edge. Thisis accomplished by calculating the camber line for a broad rangeof values of S/R9 and isolating the range in which the minimumtotal number of inflection points occurs. This range is examinedwith finer S/Ro increments to generate a new set of camber lineson which the minimum absolute radius of curvature is identified.The value of S/Ro which produces the largest such radius isthen made the mid-value of S/Ro for the final search pass,using still finer S/R0 increments. The camber line whichpossesses the largest value of the minimum radius of curvatureat the conclusion of this search procedure is chosen as opt4

10

SECTION I1

OTHER ASPECTS OF THE CALCULATION PROCEDUJRE

Various other aspects of the calculation procedure arediscussed briefly in this section. For greater detail on thesetopics, the reader's attention is directed to Reference 1, wherethese items are treated at some length as elements of thecalculation procedure uv which the subject procedure is amodification.

I. THE SECTION THICKNESS DISTRIBUTION

The thickness distribution which is applied to the cawberline herein described is that referred to as the "StandardThickness Distribution" in Reference 1. The distributicn isdefined by two third-order polynomials, one from the leading edgeto the point of maximum thickness., and another from there to thetrailing edge. At the point of juncture, the thickness and thefirst and second derivatives of thickness are equated. In orderto prevent a reflex curvature from occurring in the thicknessdistribution near the leading edge, the second derivative ofthickness is set equal to zero at the leading edge. The thick-ness of the leading and trailing edges is independently specifiedso that it need not be the same at both edges. At the leadingedge, the blade surface is completed with a circular arc. Atthe trailing edge, the blade surface is truncated by connectingthe two endpoints with a straight line.

2. CARTESIAN COORDINATES FOR THE BLADE

The preceding material has described the methods used todesign individual blade sections. When located as desiredrelative to the blade stacking axis, the section coordinates arethe coordinates of the streamsurface blade section. A seriesof sections on all streamsurfaces specifies the envelope of theblade, but the surface coordinates are not in a form convenientfor manufacturing purposes. The calculation procedure uses aspline-curve to interpolate (or extrapolate) the coordinates ofthe blade surfaces for manufacturing purposes.

3. SECTION PROPERTIES

The sta.:king axis of the blade is passed through eachstreamsurface section either at one of the edges or at a pointspecified relative to the centroid of the section. Because thestreamsurface sections are in general non-planar, the centroidsof the manufacturing sections will not generally lie precisely

ii

on the stacking axis when the streamsurface sections are stackedon their centroids. By determining the locations of thecentroids of the manufacturing sections so obtai 3d, it ispossible to estimate the offsets that must be applied whenrestacking the streamsurface sections to locate the manufacturingcentroids as desired relative to the stacking axis.

To assist further in the mechanical analysis of the blade,the areas, second moments of area, principal axes, and principalsecond moments of area for both the streamsurface and manu-facturing sections are also determired in the calculationprocedure.

4. BLADE CHARACTERISTICS

A calculation of the volume enclosed by the blade betweenthe innermost and outermost streamsurfaces is made. In addition,quantities which describe the blade on cylindrical surfaces andwhich may be required in an aerodynamic analysis of the bladeare computed as an option. The calculations are presented herebecause a typographical error undetected during editing ofReference 1 has impaired their usefulness in that Reference.

First, the angular position of the camber line with respectto the stack axis at a streamsurface-computing stationintersection is specified in terms of P, defined in Figure 1.

The physical passage blockage (B) due to the presence ofthe blades is determined as a percentage of the passagecircumference in terms of the number of blades in the bladerow and T, the angle subtended on the cylindrical surface byeach blade:

B (25)27r

The blade lean angle, C , with respect to the radialdirection at a given point is obtained from the slope of aspline-curve fit through the y-z Cartesian coordinates of thestreamsurface section camber lines at the particular axiallocation.

Thus

Arctan (26)

12

Two other quantities are needed to produce the propermean-camber line angle on the cylindrical surface: The localcomputing station inclination, P, obtained from the specifiedstation description; and the local streamsurface inclination, y,obtained from the specified x-r streamsurface description.*Together with the camber line angle on the streamsurface, a*,these quantities are employed in the following equation tocalculate the proper cylindrical-surface section angle, ag:

tan y tan C + tan a*/cos ytan tan an tany (27)

t

I13f

-SECTION V

USE OF THE PROGRAM

Basic information required by the user to run the ARLcomputer program which incorporates the calculation proceduredescribed in this report is given in this section. The variousinput data items are defined first, and the input data formatis then specified. A description of the output data that maybe expected is given. (Implementation of the program on acomputing system is not discussed here- but in the sectionentitled "Computer Program Details".)

1. DEFINITION OF INPUT DATA ITEMS

TITLE An alphanumeric title of 72 characters that may beused to identify a run.

NL:NES The number of streamsurfaces which are defined andon which blade sections will be designed. Mustsatisfy 2 NLINES <15.

NSTNS The number of computing stations at which thestreamsurface radii are specified. Must satisfy3 _ NSTNS 10.

NZ The number of constant-z planes on which manu-facturing (Cartesian) coordinates for the bladeare required. Must satisfy 3<NZ<15.

NSPEC The number of radially-disposed points at whichthe parameters of the blade sections are specified.Must satisfy l< NSPEC_<15.

ISEGPT The number of points to be used to define eachsegment of the camber line. 2<ISEGPT<Integer( 80

-IRTE-IRLE

NBLADE The number of blades in the blade row.

ISTAK If ISTAK = 0, the blade will be stacked at theleading edge.

If ISTAK = 1, the blade will be stacked at thetrailing edge.

If ISTAK = 2, the blade will be stacked at, oroffset from, the section centroid.

14

IPUNCH If IPUNCH = 0, the quantities necessary for aero-dynamic analysis of the resulting blade are notproduced on punched cards.

If IPUNCH = 1, these quantities are produced onpunched cards.

IFPLOT Where CALCOMP software is incorporated into thecomputing system, IFPLOT specifies the creation ofprecision plots. (Further information regarding therequirements for this are given in -the sectionentitled "Computer Program Details.") -

If IFPLOT = 0, no plots will be produced.

If IFPLOT = 1, a plot of the streamsurface sectionswill be produced. All NLINES secticns are shownsuperimposed. The origin for each section plot isoffset from the centroid of the section by distancesspecified by DELX and DFLY. If IFPLOT = 2, a plotof the manufacturing sections will be produced. Theorigin is the blade stacking axis, and all NZsections are shown superimposed.

If IFPLOT = 3, both of the plots described forIFPLOT = 1 and 2 will be produced.

If IFPLOT = 4, individual plots of each of themanufacturing sections will be produced. The axesare rotated clockwise by the section stagger anglefor each plot.

IPRINT The input data is always listed by the program.Details of the streamsurface and manufacturingsections are printed as prescribed by IPRINT.

If IPRINT = 0, details of streamsurface andmanufacturing sections are printed.

If IPRINT = 1, details of streamsurface sectionsare printed.

If IPRINT = 2, details of the manufacturingsections are printed.

ZINNER, The NZ manufacturing sections are equispaced betweenZOUTER z equals ZINNER and ZOUTER.

SCALE When precision plots are produced, SCALE is the scalefactor employed.

15

STACKX The axial coordinate of the stacking axis for theblade, relative to the same origin as used for thestation locations, XSTA.

PLTSE The size (inches) of the plotter to be used in thecreation of precision plots.

IRLE The number of the computing station designated asthe blade leading edge.

IRTE The number of the computing station designated asthe blade trailing edge.

NRADEV The numbe of radii at which the non-dimensionaldeviation distribution is specified. I NRADEV 5.

NINC The number of points which describe the incidenceangle distribution. 1: NINC515.

NSIGN An integer which specifies the sign convention ofthe particular blade. Conventionally positiverotors and stators have NSIGH values of -! and +1,respectively.

IFCA If IFCA = 1, the factor m in the deviation anglerule is that of the NACA-65-series mean line(Figure 195, Reference 2).

If IFCA = 2, the factor m in the deviation anglerule is that of the circular-arc mean line.

IPASS The number of initial values of S/Ro which are tobe used in the procedure to find the optimalcamber line. 20SIPASS 550.

XKSHPE The shape factor (Ks) in the deviation equation.

SOLTOL The solidity tolerance used in the iterativeprocedure to produce a consistent camber line.

NPTS The number of points defining a particular chord-wise deviation distribution. 15NPTS 10.

RADEV Radius at which a particular deviation distributionapplies.

SM An array of NPTS meridional chord fractions which,together with DEVCRV, specify a particulardeviation distribution.

DEVCRV An array of NPTS normalized deviation fractions which,together with SM, specify a particular deviationdistribution.

16

RINC An array of UINC radii which, together with XINC,specify the incidence distribution at the leadingedge.

XINC An array of NINC incidence angles which, togetherwith RINC, specify the incidence distribution.Input positive for cQnventionally positive rotorsand stators (see USIGN).

DELDEV An array of NINC angles which, together with RINC,specify the distribution of the "arbitrary extradeviation" term in the deviation determination.Input positive for conventionally positive rotorsand stators (see NSYlN).

KPTS The number of points provided to specify the shapeof a computing station.

If KPTS = 1, the computing station is upright andlinear.

If KPTS = 2, the computing station is linear andeither upright or inclined.

If KPTS > 2, a spline curve is fitted through thepoints provided to specify the shape of the station.

IFANGS If I1'ANGS = 0, the calculations of the quantitiesrequired for aerodynamic analysis will be omittedat a particular computing station.

If IFANGS = 1, these calculations will be performedat that station.

XSTA An array of KPTS axial coordinates (relative to anarbitrary origin) which, together with RSTA, specifythe shape of a particular computing station.

RSTA An array of KPTS radii which, together with XSTA,specify the shape of a particular computing station.

R The streamsurface radii at NLINES locations at eachof the NSTNS stations.

AIRANG The relative air angles at NLINES locations at eachof the NSTNS stations.

17

ZR The variation of properties of the streamsurfaceblade sections is specified as a function ofstreamsurface number. The various quantities arethen interptlated (or extrapolated) at each stream-surface. The streamsurfaces are numberedconsecutively from the innermost outward, startingwith 1.0. ZR must increase monotonically, therebeing NSPEC values in ill.

YA The fraction of meridional chord used as the leadingedge in the calculation of the section chord forthe solidity iteration on a particular streamsurface.If YA = 0., the true chord length is calculated.O.0YA5I.0.

YB The increment in S;R0 which, with SDIVR and IPASS,establishes the initial range of S/Ro which isinspected in the determination of the optimalcamber line on a particular streamsurface. May bepositive or negative.

YC If YC = 0., the radius of curvature at the leadingedge of each camber line will be considered in theprocedure to identify the camber line whichmaximizes the minimum radius of curvature.

If YC = 1.0, the Tadius of curvature at the leadingedge will not be considered in this procedure.

YE The maximum number of inflection points expected ona particular camber line. If the calculatedminimum number is greater than YE, an informationaldiagnostic is printed.

RLE The ratio of section leading edge radius to chord.

TC The ratio of section maximum thickness to .hord.

TE The ratio of section trailing edge half-thicknessto chord.

Z The location of the section maximum thickness, as,afraction of camber line length.

SDIVR The initial value of S/Ro .

DELX, The stacking axis passes through the streamsurfaceDELY blade sections, offset from the centroid, leading,

or trailing edge by DELX and DELY in the x and ydirections, respectively.

18

2. 11PUT DATA FORMAT

Data input is by punched card, and three formats are used.The first card only is alphanumeric, using the first 72 columnsof the card. Integers are placed in three-column fields, whichstart with Column 1. No decimal points are used, and theinteger should be right-justified. Real numbers are placed in12-column fields, which also start with Column 1. Decimalpoints should be included, and the numbers may be placedanywhere in the field.

In the following chart, one line corresDonds to one card.

TITLE

NLINES NSThS NZ NSPEC ISEGPT NBLADE ISTAK IPUNCH IFPLOT iPRINT

ZINNER ZOUTER SCALE STACKX PLTSZE

IRLE IRTE NRADEV NlINC NSIGN IFCA IPASS

XKSHPE SOLTOL

NPTS

RADEV repeated NRADEV times

SM DEVCRV I repeated NPTS times

RINC XINC DELDEV ) repeated NINC times

KPTS IFANGS

XSTA RSTA I repeated KPTS times repeated NSTNS times

R AIRANG I repeated NLINES times

ZR YA YB YC YE RLErepeated NSPEC times

TC TE Z SDIVR DELX DELY

Listing of a sample input data deck is included under"Example of Use of the Program."

3. OUTPUT DATA

Printed output from the program may be considered toconsist of four sections: a printout of the input data, detailsof the camber line and blade section on each streamsurface, a

19

listing of quantities required for aerodynamic analysis, anddetails of the manufacturing sections determined on theconstant-z planes. These are briefly described below.

The input data printout includes all quantities read in,and is self-explanatory.

Details of the streamsurface blade sections are printed ifIPRINT = 0 or 1. Listed first are the results of theinvestigations of the S/Ro parameter. The initial table presentsthe results of the first iteration which is used to idenzifythe range of S/R o in which the minimum number of infleciionpoints oc'cur on the camber line. This range is in tur-ainvestigated with finer increments of S/Ro to determine themaximum value of the minimum radius of curvature. Then followthe details of the optimal camber line which has been identifiedby a third investigation of S/Ro with still finer parameterincrements. These details include the deviation and soliditywhich have been calculated for this optimal S/Ro, ani adescription of the camber line in terms of coordinates, firstand second derivatives, and the radii of curvature. Listed nextare the parameters defining the blade section, some of whichare computed and some of which are interpolated al the stream-surface from the tables read in. Then follow details of theblade section in "normalized" form. The blade section geometryis given for the particular section, except that the meridionalprojection of the chord is unity. For this section of theoutput, the coordinate origin is the blade leading edge. Thefollowing quantities are given: blade chord, stagger angle,camber angle, section area, location of centroid of the section,second moments of area of the section about the centroid,orientation of the principal axes, and the principal secondmoments of area of the section about the cenLxvoid. Then arelisted the coordinates of the camber line, the camber line angle,the section thickness, and the coordinates of the blade surfaces.A line-printer plot of the normalized section follows. Thescales for tha plot are arranged so that tlhe section just fillsthe page. Thus, the scales will generally differ from one plotto another. "Dimensional" details of the blade section aregiven next. The normalized data given previously is scaled togive the proper blade section. For this section of the output,the coordinates are with respect to the blade stacking axis.The following quantities are given: blade chord, radius andlocation of center of the leading edge, section area, thesecond moments of area of the section about the centroid, andthe principal second moments of area of -the section about thecentroid. The coordinates of points on the blade surfaces arethen listed, followed by the coordinates of 31 points distributedat six degree intervals around the leading edge. Finally, thecoordinates of the blade surfaces and points around the leadingedge are shown in Cartesian form.

20

The quantities required for aerodynamic analysis areprinted at all computing stations specified by the !FANGSparameter. The radius, section angle, blade lean angle, bladeblockage, and relative angular location of the camber line areprinted at each streamsurface intersection with the particularcomputing station.

Details of the manufacturing sections are printed ifIPRINT = 0 or 2. At each value of z specified by ZINNER,ZOUTER and NZ, section properties and coordinates are given.The origin for the coordinates is the blade stacking axis. Thefollowing quantities are given: section area, the location ofthe centroid of the section, the second moments of area ofthe section about the centroid, the principal second moments ofarea of the section about the centroid, the orientation of theprincipal axes, and the section torsional constant. Then thecoordinates of points on the blade section surfaces are listed,followed by 31 points around the leading edge.

Precision plots are produced if IFPLOT = 1, 2, 3 or 4 asdescribed under the definition of IFPLOT given previously.

If IPUNCH = 1, the program punches the quantities requiredfor aerodynamic analysis, together with identifying indicesdenoting station number and streamsurface number, on cards inthe following format: 5 fields each of 12 locations for thequantities themselves, followed by 2 fields each of 3 locationsfor the indices.

21

SECTION VI

EXAMPLE OF USE OF THE PROGRAM

This section shows the use of the program to generate acompressor rotor with an inlet hub-to-tip ratio of 0.31, a rathersteep hub ramp angle (32.50), and a constant outer radius. Theblade is defined by six computing stations, one at either edgeand four internal. This results in a camber line composed-offive segments. Six streamlines have been used to define theflow and hence the blade by means of the streamsurface bladesections. The computing-stations and streamsurfaces whichdefine the blade are depicted in a stack-axis projection inFigure 2.

I. INPUT DATA

The input data deck used for this example is listed below.Some roints of interest are noted in the order in which theyoccur in the input.

As mentioned above, six streamsurface blade sections areused to define the blade. The streamsurface radii are specifiedat eight computing stations, the first and last of which areoutside of the rotor. This ensures that the boundary conditionsimposed on the spline-curve (zero curvature at the endpoints)have little influence on the shape of the curve representingthe streamsurface within the blade. The useful relative airangles are specified at the six computing stations defining theblade. The computing stations within the blade are curved inan attempt to make the meridional projections of the camber linesegments approximately equal. The parameters which define thestreamsurface blade sections are given at six locations; thatis, at every streamsurface. Twelve points are used to defineeach segment, which results in a camber line defined by a totalof fifty-six points. (This number serves the purposes of thisexample well, but it would be advantageous to use more pointsif the precision-plot output is to be incorporated directly inthe manufacturing procedure.) There are twenty blades in theparticular blade row, stacked approximately on their stream-surface centroids. No punched output is requested. Alloptional sections of the printed output are to be printed, andsuperimposed section plots are to be produced on a plotter(with an 11-inch useful range) at two and one-half times fullsize.

Stations 2 and 7 are the leading and trailing edges of theblade, respectively. The deviation distribution is the sameat all radii, since it is specified only at one radius. Theincidence angles and the arbitrary extra deviation are specified

22

at six points for this rotor blade. The factor m in the deviationcalculation is to be thax of a circular-arc camber line. Thirtycamber lines will initially be investigated in the effort toidentify the optimal camber line, representing a broad range ofthe S/R o parameter. The shape factor in the deviationcalculation is unity, and the tolerance on solidity in theiteration for each camber line is 0.005.

The streamaurface radii and relative air angles have beenleterrined from an aerodynamic analysis of the flow through theblade row. The leading edge of the blade has been establishedas the point from which the chord length, and thus the solidity,will be computed.

The increment in the S/Ro parameter has been initially setequal to + 0.04 in the investigation to find the optimal camberline. This increment will automatically be reduced twic-subsequently as the most favorable range of S/Ro is noreclosely scrutinized. It is anticipated that no inflect-.onpoints will be required near the hub, while a single "nflectionpoint wil. probably be required in the mid and tip re ions ofthe blade. The blade thickness distribution is deterinined byaerodynamic and mechanical factors. The leading edge radiusand trailing edge half-thickness are set to approximately 0.005inch, probably a practical minimum. Maximum thickness/chordratios vary from 6 percent at the hub to 2.5 percent at thecasing. The maximum thickness is placed in the rearward portionof the camber line, which helps to maintain a small leadingedge wedge angle.

23

EXAMFLE - LCh PUE/TIF RATIC COPPRESSCR RCTCR OESIGf-6 8 7 6 12 20 2 0 3 C.

2.5 a.50 235 -7.05 11°62 7 1 6 -1 2 30

is .0056

3.3

C.2 ,110.4 .15

OE s22.8 .38

, 1°.002.68 5.37 2.3,84 5.57 2,560 4.85 2o6.42 4.2 2.7.7S 3.92 2.8.5 3.65 2610 -

-. 2.352.353.E4544.9893

6*3E177 .77238.5

5 0-805" 2*6514-eo5926 5906E3-8.531 6.398c

-e°.3115 7.7861-8e16i 8.5

2,6514 -40.9E9530801 -47s23705.07a6 -50.80396*4169 -53*63787s7902 -57o2S648*5000 -59.7859

4 1-7,.05 3,0363

CIO 0 5.07-7.S6 6,48-79725 8.5

3.03E3 -30,0198406S6 -37*29065.2456 -44*51166s4975 -51*04047*8091 -578i788o5000 -61,3719

24

4 17-7,35 3°- ....

-7,395 5,385

-7.=15 E,565-7.311 8,5

3,38S3 -20003934o 344 -28.O2825,4154 -38.6E816.5824 -47705 A7.8307 -56.27068.5600 -60.2293

4 1-6.801 3.7385-6,801 5,49-Eoe7 6.6E5-6,94. 8.5

3.7385 -12,2E984.57S8 -21,26185.5662 -33o33346.6591 -44*21267.8459 -54.08328.o50CO -58°9884

4 1-::251 4.0884-E18 5.7-E., 6.725-Eo56 8.5

4.0884 -5,4 5i4.8259 -13o81075.7147 -27.67986.7242 -40,6S667,-8575 -51,64658,5000 -57.5196

5 1-5r.65 4,4612-5-,846 5,896-5,7208 6,7945-5.9C516 7.8E61-E,134 8.5

4*4612 11,58815.07S5 -7.09805,8623 -25e62226.7858 -40,07517,8716 -51,33518.50C0 -56o5798

4 0-5,52 4,5534-5.35 5,2-5.3 5.80-5,7 8,5

25

4 .5534

5 9412

7,88778.5

1.0 a. 0.04 O. 0. .0D015t6 .00155 .56 -0.2 .01

2.0 0. .04 O 0. .00149050011 39 -0.15 -"018

3.0 0 .04 10. 1e .00143•0423 .*0143 .E2 -063 o0354. 0.0 ,C4 0.0 1.0 .00137• G325 300137 .E5 -1# 3 0025.0 000 .O4 Do 1.0 .00131e 02E5 .00131 *E8 -2.0 016. .0 0.04 0• 10 00125•C25 .00125 .70 -2.3 -*001

26

2. OUTPUT DATA

The input data specified all optional output data, and asample of each segment of the output is presented in thissection. A brief description of some aspects of the output ispresented below.

Shown first is the printout oil the input data. This isfollowed by details of the first streamsurface blade section.The tables presenting the results of the S/R0 investigations arefollowed by a description of the camber line which has beenselected. Then appear the details of, and a line-printer plotof, the normalized blade section, followed by the specificationsof the section scaled tn the proper dimensions. Printed firstare the 56 points specified for each blade surface. Nextappear the 31 points cLescribing the leading edge radius. Thefihal data for the strea silrface section are the equivalentCartesian coordinates for these same points.

The format is repeated for each of the remaining stream-surface blade sections, but these results are not reproducedhere. Subsequent to the streamsurface data are printed thequantities required for aerodynamic analysis at those stationswhere requested by the IFANGS parameter.

Details for the seven manufacturing sections defining theblade follow. Reproduced below is the output relating to thefirst (innermost) section. Properties of the section arefollowed Ly coordinates of 56 points on each surface and 31points around the leading edge. It will be noted that thesection centroid is not calculated to be exactly on the stackingaxis. If it were desired to have the centroids of the manu-facturing sections lie more nearly precisel-, on the stackingaxis, the program would be rerun with either DELX and DELYoffsets specified so that they would counteract the mislocationof the centroids previously determined, or with a slightlyshifted location of the stack axis. However, the user must bearin mind that the final step in the design procedure is to obtainsatisfactory coincidence of the blade with the stations definingits leading and trailing edges in the meridional plane. It ispossible that a blade which had all manufacturing sectionsstacked precisely on their centroids at a particular stacking-axis location would have quite an undesirable meridional profile.There are tradeoffs, then, between the stacking preciseness andthe coincidence ol the calculated blade's edges with its assumedprofile on the one hand, and the number of iterations it wouldrequire to find the truly optimal stack location and centroidoffsets, on the other.

The input data specified superimposed precision plots ofboth the streamsurface sections and the manufacturing sections.These plots are reproduced (at reduced size) as Figures 3 and 4,

27

respectively. It'is of interest to refer also to Figure 2. Theinnermost manufacturing plane is well below the lowest point onthe hub streamsurface section in the plane of the stacking axis.The Cartesian coordinates of this streamsurface section showthat the lowest point on the section (the 14th point on theleading edge) is at Z = 2.57224. The streamsurface radius atthis point is 2.6514, and the innermost manufacturing plane isat Z = 2.5. Thus, at the leading edge, The extrapolationrequi- l' to define the manufacturing section is somewhat smallerthan might first appear. At the trailing edge, extrapolationis required for the first three manufacturing sections. Thestreamsurface radius at the casing and the Z-coordinate forthe outermost ma,,ufacturing plane both equal 8.5; however, theZ-coordinates of the blade section are all actually below 8.5.Thus, the outermost section too is defined completely by extrap-olation. Of course, portions of the blade that are defined byextrapolation do not appear on the final blade, but facilitatemanufacture.

28

28

0: V

0*

IZ -

Us* m0I

44m)9x:f/

m* (n 0 wC3aC. 30* C29 34 21

-* 0.0VIi j o%

111 usI04 T40 n

xu C3 C2CC )0U D z> C 3m

44 r4 4~ w4U

2 IX UH

4- (0 0l00 0014* W0 dc w Ix ooo

to* xU = x- = 0

U)~~ I. zCI-M- H I.

-a 00)0 (1) 0M L7 0AaK* HC 0I-0 ILI w. 1 - 00000H=0w: P- 000 1 U0 U US P4"01-Ur0cc00a99 4X* Z* 4Z H Zw2 1 M I 4H

001-11-1001.4 70 3>

a IL a Qwew .I.I LL 0. I..Q 3-.L lW =U. 0z 30 3C 2

o-U I ) U) H Lt -= % c - r"iCNCCC~ ~ (z. 1% LA Ltc -H-M xw x" 0 9 Mc TNU

w WUlIlIL ULU W0u0m u wwicN 1- 9 4 : 0 XU 0 * 0

0-; = .O4 mZ-U1 LU xUC x0 00 x I- =0000=00c - 4 00=zwx <i 0 - q~

H== === mwm H a - -H 94O 3-= LU H 0 z ziz0220HH NN M -'4: on Ill. 03HU

204: 412Q 4:243tQ..J: 2 11

uCHS-S~-W3-(0 ZH~H 4:29

z X, .4 ;c

.4 C3 1= O- 7% P U . l ?wU 2s pik lt lw

z 2cm C C C2 1%=11 (t1

1- 4 4 t n[th 14 o)V 7ULn% F4 m uNV TM%aL 4t 'a I x61 I

CL . C6 - ul. w

0 w0 00 T Na w 44 =: w: wNIG WO NM 0: 0NY a T M~ CUCY C)14u P U4 N- Sw wt Il *4 N4 I" 6 U . (.t 14 -1 4)t . D f La n4 14 CJrV4 w NoL 04 %D trt n t4 %D CD 4 N.11 0 3c oI P 4 1 A1161;

to a. 0** a 0 . 0 a e 0 L. 0 ** 0.L

o w~ InD C13m4 X Z 2c 7;0 Z) -j :2

P4 cc 4 Ix H I14 -0 UU A: 0:- wiI.0 at =~ a)x0omx14 -4 . n v a XO o.tO Py mn * 4T %n U)I 4x Z:C~fl4 %M VlQ*.t4%I% 4 N K W%

LL 4 WC N = cm WI" 0 m w 2CN 0 47 tn4fZtP19 : 2: w zz k

m 0 a 0 0

0- a) w0 %D 4w% D% )c *0 fto CD Cn( D C 0c D toCD 3 c%

I*J U: a) H: = c: w *: 0 =a0a

Of mI fm w uJ -. IW w - 0 fi %wc P s%

C3 w4 LU2 W) 11 V4 WC i nC nV

CO 2: CD 2: CO Zn CO P) COU P c % )m2: 0 0 x a0

M 14 40 a4 cocoG

a) 6- - 6-30

V4 .42.

(n

4 4cIt LL LL. U.H 1-4

-T w .T U in LUJ .7 us

4f 1 4 * 40 4tiD~u so vi T~~2Z Ui V4 AAV0 0 Ax *0 V4r 00y l*N z C 100 0 2 0 200 20Zm CU W.4) CUC2 s 1 4 Z7 90 i IN so IDin 4 %n U 2s MC zC

3.44 V V) .4 t.?I U H M "qWWii 3.4 I-I CD(i~n f 1-m 1-3 CD UP4z In MSgg V4 I O3 4 4 l Lt Ml H

H HH H

o U U CLif 40 in 01 %D..4~ 0% LfsC Jfl4 LUW4 D 0P

HL t-C3iDl =- 40 N t.1-~Q S*a Hf o nL 40 oo .C) *ooo 00 LL. 0 0 0000 .*9 L.L 0 00 0 0 b 0 0 00 04 ULiD to0.c 4 . U D N~ cc 4 0 4

wLU U) LU

2 U 2r U LU U)

x aw ) = cu c~~*. en~qTal .2 iW'.7 in ; W 012 11 I. n W W2 M~ .7 14%Win u)j p w' )

4 ox 44U)Ln c TfO C U2 C032M U) N~l4 )4 0Co C* C3,~ Ci0*D 3UV4C U 4CD 0

r'oui aUC3c o lo C3 to -4 CD.Tus% 4W2 O1.Nm 71.0' zAx- DLnU %E- M~ 0X 3.4 xC M@o 3. at * o H 2C 0 0*0

P- U t'3flw H: aI usIIU W 9% 41& N Q ITU sI-~~1 0.-0 HQ 4

2 0. IL 0.. I--

y M Moo C2 C3 000 C, () C3~,~ o, toc(to410 C2 M TO C3704 C2 cmC0I030aC3cC3) t* ~4 U)coc % toCq M) D LN A 0 U) Ntw oc c P)L - vi ft4()I tn w (P T.O'4 US A0 1)POX 000 0 Ox 00*00 *K 00000 DX 00

31.

3-- U.

w Q. ca f. c;ci461 si.RLA -,

0w LL -1 " N J

U10 . C .4 c

P- Ia

-I

(/3 1- U) i C a 2

wo s, IV Ut a,I.-II

I'DCL .

LI

.a LI C3*. I. iL

we'

ID

41;L ;00.4c;

Xi W '4CI )4,.

.u

LI I i i D 4 .. li

-j

Vi L

fi ~~L~0..iL L )C%'w O 3 w

23

La

.7c I S ' i0 x ~ . L -0 ' ~ I - ' I ~ I iU L I.

t i. V) tJ.SJj~.~77...77 ~ 1JUi%7. 7777J."rp

Ui-

ca L)

c~z

V) V)E wwwww"

w- IQ-

U Z

I-- z

C.

-33

wutm2:

4L

L)

U.

V4 i U

C2 --

Q: z. 1-4

0

U.

Zr

LU V)

C) Z:

14

-i -

2: -Li0

z01-4 I-I I

ittv,

0H* - CZ Ca

U. a.

f.- <

w

II * 34

m r I m w ria~I wo nC .4o* '3)Inl 3 W u% oW UI' %0I r "I 0% %D w. Cut9. to a IA' C3 t w . a.-7 7" 1-1vs .p.~ 3.3~ fIlIl( 3 4~.13(i. 0 'J...1-~ 3 '3~Pll04*~ jll('U.(3 U JI. 3'U t

luc . .1 Im t E l W(.CY b('JU c C CS Cu Cj TV N -4. c . v44 IV r444 2 . U't. w '('. .4, t

C3.4 a .334 ID % t Dcm- C3' 0.4 c c (3).7 O'C .4f in " m o iC 32 0 D Ta. , -.43 a .7 CP a U% 4 -' iU% 14 r- M a, N. CU

CIO 0% U'.. C3 1'P2,CJ. CD40'' NWU' 3t't' 0,. NN t,1 0' Vf.0- 's0-,I'

4.4 43

00 u.-w)( iL

N LL CL U M r Iw4 .. .r lT T% aU vC3% D u -CAMr

U.- . iw=0? lt mc

-O'D 3Z

z z -jwt~Q-l- Q UP-H -4 P4 .1 C5 Ofr %a o0. zM 3NC %c aI oc %% Dr DTC 4c 0T n 0 F2'w)J TN 7 -. 4 4 co 4.3 UN T Gt-"P a ej ir u - r t % P-.w 5W )UPU(.U.l'N. %VU wI r -St 4- "JU (3 .1 W " T '.43Wi J a).43r-;F3 a .7 -72.7 rJ<3 z " 0 N o m m m 10CSP1) 0 W w00 N""- 40 % %04 % 3N ot o o ( n PO' ,

a uif uWI-AmV ~ mt V v"%l , uI:. ,..................a.. .... ..... ... . .. .. .Vi UJ 6Ca 1'gaa8m911 11 gseaaaalsaa aa

I-.0

004

IIJU Au-I-a a-

a g

tn 0) IL10 0

CD 4j 4L)

z - W. 4,.j A.

Z4 t5

-J v) Ha

L -4 P- ai

35

ww M%- "Pftw=

m" V4 molt *

%m f co T C2 Ul c .1

n NT -&i cu Ull lqp c

ul us ol US t2 t%=

o~~~U ii, l1%JWr)P* . 0560@5

D~Dt-36

ILI*

0.4 *~ &

us 0 L =w w== 9

us. 0*= ' i

16 0r_ 4=== ? ~ 3C" o ~f.

00-g at -W O0t we cyC LS0% . M at4C~

1~- 0 9 P7 4r. U%~ No 1 r w~ 0% D t

0 0 " 1" 0 ~~0. V 0C2C20 3 CD 4.2 3 D 2 v q v

=5 0 U)N00NL2C r.2a

U(J U. C002U0 W14141

it W~~. L; Lt. tn t-NP iPINI"I p41 F) vi

JL,~W-4 .8* 2; - 2 C Y 7w4 2flT 7Cv4

-C ~ W V) V2 C C2CD C V4 Iq o C P2

V)~2 1,- z- 0 00114

M. IA. 1 31--11M

-O ft 00000041..li - & CSIS. LI IIcS#

S. Z M 04 1- 1- 31 C3 -.1 0o T4 00 0 a .l r v i O *Fr

S1* 0 24 0 H4 H@44 =x M * v 0 0 **440

z~~~ ~ ~ ~ = z4 cz= I*1%i"~~~~~~~~ H 0.0 I.P -w N 0P 24102as4.-0In?

ILI 2-4 U.1 UP U11- 0 ccdO[ 0 nP

Lr-~~~~U w f C 1 :.C

I-IW U3 2.- w 1.u go02 4 4 P -I

0-- IL CL 24* at -a 1-4 M 0 oV4-wN4 T

U)r V4 w M.3 M- tD W vt W

CA-1-aN C3 0~ cc) (2 ( .0 - 0.

0%~~~~ r*naL z0 1 )N a 4i oN n- 214C i M UN P ? u .W C D L I- rC3 w C rs d .% * T c 3C

%o cw N-V tv w & Ln oc 2 "C3 x o3A

Q4 vo %DC30 In N2 C%0 4V P 4v2 C P 40 Ut m' M' U% vi so0 to #A0.4 MN P200 0n P 0 C 3'S 40 42 = N . C2 N 2

Axx 0 2 a4 0n 0 0 In 0 0 a 40 In 0 0 aU P2 02 0 0 0 0 In 0 o 0 0 0 4 2 0 a0

0 M00Z0 C) 0 4r " 0% .7 N CU 00 0 V4 "7 NO .94 IA C 0 CU 40 N -T rAI 4 P21 4 V4 C2

IL - - 04 0 MT Nv U % 7 7 T V4 W N v V4N CU"' CU NDIJNP M22P 4?QP t-2P 4TP222P CU% Wo M W =I.M .M7UWW 3t =t .. cv Cec cc cc* vl.:. toe 0*** * e @5@ * -%a* 6CC *Cg* ot

le a a05 .7 0i 0 0 N 15 3 0 .70 0 N In 0 IU U) .7 5 e 4 P2 d 0 0 a 0 0 0 A P2 N 0

gy- CP rIN 30MP)2 N OTNv4 00U% M M -TO 51 4 0-0 4 t2*0W00 N z CI,- 4 C NIUI N W W4 CD.?WCO

vi %1C oO 2C 3MU OI 140 0 M M0. 4P2OCMM W M 0 2 C ,t 0 4 0 CN OI CN . w44M.

pMC. w.7 w SA Cy WT ulJw06fit D iV L JA U~yN 4n ' W r-Ul %%1154 01 T V n 4 .I UsU - OW CO P.

Qom C00 20 P 0 0 0 W P N P N 4 1 * 7% 1 N C7 In CD w Q w w 0Inw0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ O P27. In aV% CU a011151 a'P 023..I aAI WD It-N N N 1wNWt3

co wMc0 o0wNviwwM4W1 qU . Tt 2F 2" vii 1 W V4 %o to1 WT4 M 47 4= NNNN NNWN NNCU4 ITUw- U% e~ ee .. .e c4c C3c .. CO0ee )w 4fV l 2C 000 Dc N .C2 Mec U% N **C % ?-r)rV4m

1±1 w 6 1 1 6* 6 8 16 18m1 1 1 6 16 11 61 r,63*w' lr qC ococ r nC oo 7CiGaf.r -c qC swci o-lwg oc i"tw0 * # a* a a &ISat a 0

tnW 0 I 1 =v MIJU P2322W M " 4. n U% In W WIAUD N N fNCO cNC 0 1 0 000CO 0 NWz . V qT4w 4T ~ WNccNNCjNWmNNNC Nsee seccWe(e. cc. Ne... e e i Ne c ce c W YWNwN CAIm

tot De0t o0 0 000 000 0t

w Pc ar N0t n% Nt Dc sWC C3n0 P P2 'g 0 0 0 in7 -Ti0 N 'O 4nP N 4n 5 0 0 coV .7(u%150 -T4C Dfl.U t lWCO%

I- U

1-.4 X .n% c o l 2 v4 w P) t u% W N co a% c3 vi N m -z t o - c 0 c3 w to 4 n 0 N co w C2 cy m T Sn S

0 4V4T 41 q(jC 0NI .P W 400%J .7rNIV CUto 99to ) 00U ) o 0 N 4) to V) T dDO14Pin n (AUCLZ NNN N111 . 1YyY 11 6 444

6615 6I66 66I ,611 338

pa

I U

us a

I-

I a%

a Pl1 ..

ap v

1) I

a I a

U I %al 0) Sa

li I ala I 39

4 .,4..4.. .4W P %.444 .4 .4 .4 .44 . 4.1.

U. m=W'NN 14,0.7 4W"WO,0 -NN 0-'&1 0 In3'.tr0 CIX'0V .40C'Um5'm ,40'm.0N'WC2P'.4a-ZI,2 >%my mVm W. 4 0=

0,w w "1,4 1 OP41%)U O N0 r3 Q Clr7 300P)43:FI)r.

U" Iu I a as I t 1 a 2 1s I I

IM .4p 0 .4 1. . .4 .1 %IJ.5.l.11... .41 0 0.Lu~ ~~~~~ 00 0 0 0 wJ00 0 0 00 '0 00 0

0.C UiOR.nw3,W0C -4'P,' N. 1 WP m N w SI N m S

asawm"4 sstall a

1- , qpU N. =4.7 at ,4.111W4M4. ,* " I'. I- 5*) Lu 1 W 7 'a III 4 4,US4-4.4.4,0. 00- w 4 0 n0 " t 414 00000 0 0000000m0000I o6%a10

L. 2- 0'O co %O. S.1S" -- - - -%V w-4 - - C) 11U14' ' C7 0%'A

v* C-* 1 * I. . . . . . . . . . p +

IJ is2s sit m)U UU ,J . U m.jUuL311 +0 24 .NC.a %( nr 7C OQ . nU 1r 7r rU

< x S t . 5jx u 7 % n l . 4 U p ' U I 7 I U %

cz1 1' 0 CJ OS 2C 0WW W WCIA O CDW .7ID43 C1 U T SO. JC CSJUW Z 0CO .W3M UJS

.j * W0- - -

(n* II vL , I Lt t SI tSt1. UN UN U.14

*i I

It' I- I0

w ~ , 1. 1 I.3 . . 1 . 11 m-.4,i W. . UJJ1.r) . % 1-4m v I % ,N V . 4cu4NINS m" mu w00 0 00 0 0 C3, M000, w 00

0.1 IS0 47. SOW") WWWWW # I.-uMWWWWWWWWWm Um WW17

I- U.- --In M I S)c .1 43 U34 N N ~~. 53'5 .43i V Jt 1 vI' U5 ' VU J . " -H14 - 1

U3 11 11 itL.i 13 1 1 L) 11 I

x'I >-x II .U

x0 .U MO uS (1. Ve r>Nj- gj IX " s II 0i 35% Sit U%** ** 1315 USl 15 25 I ~.2 S

* 0C (jt, US2 .7 0j US N.5. P)t US. Dl M 04 ',P 0. W N a v-4 US ZP) io N CU fN 'r )<.i 0' C) U) 5.14, "1 .7. N/I a ? OD r CU Z 1 ") Z US .5%U M .7 0 'P 7.)70U'D - II S

431 9- S4 03 z3 z'-5 u" 5.43 1, 1.*' 04390 .4 1; 4 .u3U5V4 U' 1 9'U IJ U

3-4 . V) 3 0 1I9 ( C2 19 94 to 45 1 -112 4 4 NJ 4 . 4 UIC J q5 4IV O UW ,44 ID'Ir .2

U, IJ U, SII It .. Il 1111~,. JI11, 1 IV It .7. %m S11, NI G.. "I II IIwM S 7 jQ ,

01.7 %D jc Caro W).~ 0). =CLXmS))nC

14 S 1 ))( L LU. .55115 It I 1lil 1 111613Li U) Lu 1 U) -~l U)SUN U)UUUU ZWPP - f.U Ph "U(VJ 0 9 I W 10 UIr-.W.UO

,f' I-) U. N0S' ANU - nN0 1e lN(N"r nNa IU"I V4 4 0. 111 43m 4%1 &%1 r) m r) 0) 1") -r43L 4T 4 r .7159S

Z . 3 43U. 599~,JW J.3sJ.r5. 2 0.441 9' '0 3901401

CD C31 ) C3= C3C3 C CD 4 1 -4 4 .44 .

13 C2 =) CD CD F3 n3.7 2 = .CD In 3 C3 C2)

ILP tu U.1 L U.1 . ILI III 0 UP 1. us1 I F ) 1. InU'.4T .7 %D r, 0 N* In N N 10 r- 11 =4

U. S U 1SC -44 C .7%InNU A wILI 40co -7INq

LiI C'U In I. I7 Si F) v: C) v:) I) 1. 11 1 ;

1. L'. . 1.~~~~ ~ ~ I .1 IL1 111. 1 1 1.I I ,. I n i In I I In # In IUL

-4~~~~~ ~ ~ ~ ~ "7 C) mn NO C2. w C2 In w N.4: I N .7 "In oC To4 t N F)0w ~ ~ ~ ~ ~ ~ ~ ~ ~ C 4)' "~ U% -1 " -.7 ILI I'. C: wn Uw N co IS U CUJV0 .*%IwU . S

Q I, CO C 111 % CD = vq t cu u M . r U UN % %D % t r N 1'. Inr. NJIO0 %Ina CDCD0C3 N2 CDC2NCInC3 C = 4C)C3 C)4m CEn U. . + . + * .0.f. + U . 4.nU l +

US I 3 34. I. U. Ii I It It I 3 3t It It I II It t it 34 1t 3 3L W w w 3 I '. .- . CI 1. U U iJ )Nu )

Ins, WW~WWW CAI nEU WWWW WWW nWU WEJ~nW UWj 3v w 11 -4 14 U% w 3n I. I 3I

U) Fl 4EU CD C1. ) C) F2 C-1 C2 EU C3 0 2 co %3 C2 Us*J 3 .4 U C3 Q C. C3 SI) I'.D

-. NNOO0044UC5).. .7 n n n ) NN NNw ~ 00000000000000000wwwWIS t w www

m ~ ~ ~ ~ ~ ~ ~ ~ ~ U rS. NI 1-m4 N N N OF) CID U) m F) W% 10v U-1)4: or u

.7).I.. UI I ) N In In . I I' I) IF InIw- 0. W U 134. 0.7W CU).U.US WW . .

Fm)l In1 wmz)D Utc N4 V) a, SIP 4)3 In C 7UtS 4I N r) z) U-%L In 0o F: No V) 1o -)T

~~~ .C .U~IU. -. T U U U U C S .. F W )I III.l .1 11 iUINS Ev r,

b-.4 .4.4-4.%v4.4. .4.4.4.400 0:%J ILINN N N NN N NN N N N1.0 NNNN % AT . lr % I

In i I I it In tin InLI) I It tIn I I InI InI ILI

FI)) N U CD LIII Fw Fms N U mIN U I wS NU L

I-S x- -44; " v 1 oIII w ai\ ' I

ILI LIw 43. - 1

ILI + + 4. * . . . . .

In!L II L La133 jW IiiLI UIC)I II ILI) I I ILI nwcuvi i\ v L -IN r-) V) .7 4T "EN 1'U U% M U.]I - O V W A C (0T4 1 W ZU1I.S . 1 U .7

.7 UN N\ In - \1 I 0 " F II() P. ) aU)1 r

3- a4 vi.. . . . . . Aa. . .C/) I-I 444-144 '')C N W L~

< k.,3 33 31 3

41.

0 - 0 0 0 00 0 000= =0=C. 0= C1 3 Cj =.I 3C 00 0 0 0 000

.44 =~ Nl CuN wu r. .7 ' l w P3W us %U' "' VI U' 10 1' Cu F) F) 0o ID 0V "' up. W I" osn " C2 atP.40 M~ Mn CMU NJ 0 7-T 0%. f C C2 134.T UI O-F ) Cu 4 =. "Is NM T "W P211)41 C 2.W UsfI x4 M0V).CLl2 -u I 0F)P2Cu1140N4 . " 0 r%%aCu4-o In0t. i -4 Is 04Prin 440t =U COW N Tt wu

C3 C3 CuC3 C)l NU*..D.43..3 C2 C2. C3 CD C2 C2 4 CI2 CD C3 ID CD C3 C2p C3F FD C) C3 C C3 cx Cuc 3.

13111 3311 1133 111 IIIt JlJUj w jj & wtuuu O jUJJJ L "u ILI tutu13 3

x o "' 1 "n F .40 ID m4 m Ua N c I) 43s UI .7 a.? C's N2a U% CD F).40 FD 04 U3 U .4 7 C, -A I- l N

..... . .4u.44.... .. . ........ uC JP.4I W4 uU ...... 4. ...

C)PG C 0 i C) co L II 000 I= 000 00 LI C. CZ, 00 0 .1 0 %20 C2 0000 Up Q 'iC I D : 3 Ic

* . +' -V .. . ** * + ... 4. - . 4.4 4. . -.4 *. 4 * 4 ' 4. + 4ui Li L US tu Li w U, Liw CLI Li U, wLiw w ww w Li L iL iLiiLiiLiiL iL i0LI LI i Li (i i Li Li wi.0 Mu OF NJ C-I I Us C2 MU' N f. N N N- W Cu" 14) 0 IU% 0.140 0 Cu W0 WL WU N. WP27 W W M)2 UN Ul CIA I U' 030( U' N .74 1 Cu V ' In .4.W "l = Us C, u W14 Cu N. 01 1 In -0. P8I).7 P9 Us ,l U-

In '4 W) -A O C3, .7 W W 0 IV F) In% UYN U' W. " F) In UP I" .4 F) 0040" M C Cu :0 "2 0 MPt NM CuIC. " UNco 44co 47NO.N C2r s 2CD" D 7%w %09% V U4LJ In 004q.7 co I I COCU U% wCY0 CP2Wr*4 WIV )FINJ . 7r. -7.1 U.1IlU.'1 I'00 NN 00 I UOOC .4C uUJFli )P2F)1,1 I. 4

............... I.4 *4...a79 AZI F) F) F) F) In MP UI W) F) t, wI F, F. M, F) F) F) F) 4) M' ") FW M~ M77. r-77... IV r l 4M" L sI 7- sC

14 - - - - :w-N I.TP-wUI -z0r .J. . . . . . . . " 's W w w w so4W W W w %4CW W 4 'J. W U W W W

C*c, C3C 02 C)IglLIN u 40W' .C 0 O u C In C CD C2 0I 2 CD a I CD = uS =0 0 4C cP = 7~ = Q= NC

J, us Wl In 4.1 t 4 ILI " U w ' III II)t 4 1 w .4 I4 It .4 1. 1. .1 I. 11 L, ELI W4 W #.) I WJ tu) I.)LI U! W. W. At WI LU LI I Ia LI 1A LI LI LI LU LI 1.Is 0 0 00 0 0 00 0 0 00 0 0 sp00000000000 s s1- 21 s sW " V %P O .NC ) 711U U .1 7 l-J . %W 0 04 "Us000 0UP 00U .

In1 W.O N 0 u) ,4n00 3 .~n.~ 4 Nn'J0 C N N )F0 .7 7.7 X .7 T7.T 7.t .. 7.7.T7.7X) I 0Ul 41 UL)Ul.".1 IIt r: IF) W It CN 11: "W.40.W1 W . lIMJJP "s. .7r.J...J.7777

.~~~~~~~~~~~~~~~~~~4 .... +..........++++ .. .. .4.. 4. I.4. . . . . . . .LUuJ WU..JUW JUJWW uIluJWWSW'IJWLU J W WtLJ UJIhJUu&IA3 W W t LuJUWWu LA QwwwUw "OwU..00 w wjJU Ul

W' I.uP) 1 .77. l~ulI %w wrlr a W.V. UIU UsLLL.l44 u'I ())~ x7 1s Us 1Us UsUI "ut uIU UI I Us 1% "ulQ

Is) 0t q ;

o 442

CD CDC) I= C3 C31 C2 D

r- ' r- r-. , fl r- r N~ w .* r- N P

6 0 40*S S S *

LU Lu U Wi to KU Lu LU U LU LU LU W Lu Lu"I1 %\j ul UW -7 ci -T fr- Us T T-- '- 6Oj us cu

3~ 0500566 0 OS 00 0

TI ~ ~ C TI U) CT IViT1 r

Ui q= Cl Q: (. U J i r-) c.i Qj 10 C) C). .4 . . . .--44 . It. + + +uJ uu U Ww LU L W 1~W Ld i W LU Lw W

N N N N N r- S N r- N N N

W~ WV tn~j LJ %N I'S Al W' W' LM1 W~ I'S) LD .I %\I

43

"). - , Oj , . m I5. 4. 1 4, % U, co 4. C4 D0 3 C .2. C r. i

.1*J Ill w5

± L

* ~ ~ C CD 'Dz ' U ) I N ajw .4 rU..r wn U.? Q cu 5.11 UJ,1 j-2 ac Ul 7- u~t.In7. ga 4p u % ut.7 LI 1 3 I Li 4x XLri D C'U'rU Li -

-j .0 4 c C C 4 -jt 4. 1-~4 0~ 4 a .3 -% -0 .4 ~ 0 14 MJ (I m34 ooIIVw4* IL a u .. .0 IL. CUt X U)L ... . L 0 CU. S . 13 IS. w0* 00

0U. LU

wJ'.1U

u lU 2. IV. vIIrU S lr,-v l1

re 4.14 4~~u1 1

N. V)14 Vlr~ qU N 4 .~ J.Mgt5 4 .1U . O.U.

W15%C I . Tuw w .wow L Tc pVS . . . . J1 . 0 nN 1

V) tD L Uur..i vi .4~ ~ g . q .i .4 .'~ t u ... < . c4 q V N

4 0 1- O I e c 4 1-4 N0 -i 1- U % t~ fn-4 L n ..1*j t't.SV..r. i . I~ t.ng.r -j z. Ztt r~ , in 4.J Uer~r

u* .L W vi w- r. a4 1-0 C, w z M II % 4 1- P1%,- J 4

z CI! 1- Li. 1.4 . . . . . .It ) u Q4 .7 u'm..N C ) L I Wl W4 0

4 0i t IV ci IV) "I5 ( J i iw .l U.4

wA mr)~ U~ 'fl WP)i~f t ui' -Z Ii Cn 11 4 %L)

"l PSW1u.-p '1) a) U. s.u %D UliaJZnr%

0z Q Pl

U, D fl InIL~~~~~7 .7u ug .L aL NUO

N L CO IL . U n~..

444

4 *D T DcO c=%D

ul t CP 7 I- r- LfVJr- C2 W V wl V

.Li1Y

9% -0 C DC C )1:

-iU- w0

LU

.. JZ * U m)r- &

t e . .4 L U I" ) w - IN

* t- a 0 S 0 * *-j W4 cVq m F)M%rV4

V)LI) co H . mr-Ut'IA

LI) LJuto %UL1=

a * 0 a 0

45

xx

USU

1.2 L2

C3 0

OUO0%V IV IM P~41. 1 5US

U ;uvi:~~~~~~~~~~~~~~~4 I, C 3 4-4)W TW . zWu 3mC0 0f C P - SC L 2t 7 c nciCW - nto( mex 7 , %ac g L a m qr!)20,-

i -t .% a.i u e 1 nU e 0"W1 27" m4 31,1"1 -1 r

* ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ :C S 4..-.. . . .. . . TJV 4IWSC' 4... .4444..

0. C:I W II I I4 I II II I I I I I I4 I 3 I II II I 1

LU* C25 WWU IIIW L.8L ?U IO) I5W .. , 4L.4W I.I . I OO I . I . 1 1

Lt. In. InI. zW r- C. IS *% *2 " W *0v S 07="% OI OIIIW0 ql)t "W sV)0L * W4 .40 m4UU z415 z4 V4 LUUIO..7?I4) See6Jm 4 W " U W to1Wi r.7 r- a le) or r40 0 (P 44 .N

upS III x.U .494 LLL 9w494 s 14 ?% e . ZC I %" "1 4 p N I

4-4*~ ~~~~~ * I Ii I I I tI II Ie 1 54 O aaa ooo ooo1 1oo1a 1 1ao1

LbI 0- L4 7 "1 UP W C) W00 Q0W C4z; =q ( ZP W C404) C3 0 C 0 '1150.44 LU 0000C0~ =1 . C :1t 2 2

4.fl* W x* J-0 ow em to 3 rdo42 W.40 co C j N N oO 'o co U n 11. .14 = r) C'S %D -t .* co41Se.4?.) N .. 2

er. U US U L SLX v

AL L* U .1

-- I I* LX P. W U SL U u I11 I11 UUJ Let U, Us11 U, 111, llW I US-I* t-., al III* WU UUL W W W. LUW WUJ CMW UJ 01U4LU UWWUJW LIruW .1

t-l Z* Y 0 0 LA OO W -TN NMU0 0 1.0 Se J '4 m OLU UIO ' 4 . 10 m o 00 7010,'l C3 m I

Lv) -j m4 I/C I- IV t U- UW.7 4 . ri w -. ' - IV . -W " U.4 "..00x'0'0r4 . 4.NWN00Ifl0_x W WU -- CD.5 C2C D 4 4S e - C 7 3% OW e lV

.J "I* N w. a, 4a5 N54 r) aU U% 4.14 S, 11144. 0, w4 I. tw 1.1 4.) 44U N4 co U, C7 Li 4.14 I444 0 T44V, dJI vi 4-4- 04 T4l 0V IV (M IV t-1 tw (w 61%V V11-,3r?1r)

4.4 ~ ~ ~ ~ ~ ~ ~ ~~~p I-. I 41 - LUL WJ4ULLLUIWU LLL WUUUL WJ W 4IJ.L

LU *In4~...,.0'0O NL U115 7744)4)N' 44 0I U 4

* 11 5111 441 4114 648 6634146

WIL Li CJ C31 M %no C Li 000 UP C3 CA LI IMP L

Wt In M) Ut .NU 0 M~ w13 -T0 vj v4 Ut <., 0' r;4

0.1 'D N .2 M.? =' " M. W% = N %D 4 m 0 1, t I 0%

L U.1 1 11, . W .U II p.

M4 -T4. N - 4 .4 =' W v4 4 W4 M M W M~ 4 Ul Lu N.

J- ; liii fl nta Di 11 1 11

40 Ui Mi a, C) L.7 10 LU ; C2 C3 %.I C2 Lu C3 L2 112 4= 10 C3 to 0 C3 C 24LUC i4 2 243C2 41 D

,OLIN -40=0 ?.-N O"N" W w i c N .2 40C N 0 M N N7 Ml 0I N- I- %D Mi 0'0NWI N 4i W. "4 .7o 0" 03. ). CU co.4 U Utt VN CU co0 ci 4() 2 I 47c n"CUJ- 2. ZNJ l ot 4f C lwUtCa NIf -Z %D m7 C.A M3 10 (n m V1co 13 t TIN -M 0 liN 1. .1 t. 7 tC A 'NVio. P. tV , D Dr nC PG lL

w. .N U JJrF) amP-U 7m 1UI 0 C MnUUIJ O J W%.7In f- Il a yiyr 7mv LI 0c 'L"c - l- mit # uw lc vC mt

*~~ . . . . . . .... . .. . .

0 L CiLI0 CI Li l iL IL 0L IL 000L I LIL I0L 0 0 MI -) -4 .4 LI M t 0 V) cl I LI CP In 0 I %D LI LI LI N rp co LI 0to11 C - M1 a la l ,T1 l% 4MC D- 0 ~ 1 u 9 DD1 %DP ught-D D% a %I TI ill .711 fl)l 1 08W1N1111 = lIE

VA , u ILu LU Lu wu Lu ll u wu us ul d i el u L u Lu Lu Lu ) -ZLu - .7 -r Lu Lu -J Lu di 1 7 Zu Lu -1 Qu Lu Lu Lu . 0 4T Lu -J Tu L .3 QJ Lu T u .33..4ociDC I 'N4I CtoID 0% LINSIM.toS)N 0 vr QN N 4 T 7 Z 4Z LI 4 4 0 1 N 4 -TL 0.7 74 -NI''.7 -7.7 -T Z 7J -

I. l LNNWiiT0 ' TN M .7 W CO , J v4 W VL.7 n I. a jzUd I- 4 N w 0'.. k M W4n m . (DUC2 q %atLI 0. UF0%U to L Z.VN4.' r) W) 'A 7 7T .7LI 'D Z T ZIn m 'anI t 4n 4- - f4 9 Wn tv w-4~t' 0'0 N S)4'0F N l)D COau a N ttMIWM

Ut O'iFNINIWN..U N-'0 UtI~U.D7IlP U L3FN~N~44tUUN.NLI0~ULIT.4VW'3WW4J~tJNt3

13. ELtL4'tI4 4 u'~ N I t4 .3 F .it~l~UU~ttZ.tf ~~~. ~ .3 W 4L W DD .

* ** * t *P ~ * ** * * ** P* ** ** ** *** PP *P 47.~

SECTION VII

COMPUTER PROGRAM DETAILS

1. IMPLEMENTATION OF THE COMPUTER PROGRAM

The program is written in FORTRAN IV and was developed ona CDC 6000 Series System, incorporating the version 3.3 SCOPEOperating System. When loaded into core, the program (andresident system) occupies about 32K of storage, so that theprogram will probably not be usable without modification on arelatively small computer. Apart from this limitation, theprogram should be compatible with the majority of moderncomputing systems. The program consists ofa main program, andSubroutines BQ, CQ, Dl, EQ, and FQ. The six decks have beengiven the identifiers A, B, C, D, E, and F, respectively.Listings of the decks are shown below, and the deck set-uprequired for the CDC 6000 Series System is also presented.

The program uses three numerical system units for itsinput and output routines. Input is drawn from the card unitvia READ statements referring to Unit LOG 1; output is sent tothe line printer by WRITE statements referring to Unit LOG 2;and punched output is produced via WRITE statements referencedto Unit LOG 3. Units LOG 1, L'OG 2, and LOG 3 are set equal to5, 6, and 7, respectively, on cards A130-140 in the FORTRANprogramming. On the CDC 6000 Series System, the "PROGRAM" cardmust also establish the input and output linkages. On othercomputing systems, the "PROGRAM" card may not be required, andthe input-output files may be established via control cards.

The program as presented herein utilizes an on-lineprecision plotting capability available at the programdevelopment site. Calls to four subroutines not included inthe deck are included in the program. These calls are executedonly if precision plots are specified in the input data, andthe entry points expressed are part of standard CALCOMP softwarenormally supplied to users of CALCOMP precision plottingequipment. The various call statements used in the program areexplained below, to facilitate modification should the need arise.

CALL PLOT (XPLOT, YPLOT, N)

The majority of plotting is done using this form of call. Theparameters XPLOT and YPLOT are the "x" and "y" coordinates (ininches) on the paper to which the pen is being directed. Theparameter N indicates pen up or down, INt = 3 or INI = 2,respectively, and will cause XPLOT or YPLOT to be assignedas the origin for further coordinates if N is negative.

48

CALL SYMBOL (X, Y, H, TEXT, THETA, N)

This call is used to title the plots. The parameters X and Yare the coordir.ates (in inches) of the lower left hand cornerof the first character, H is the character height (in inches),TEXT is the character to be printed, THETA is the angle of thelettering with respect to the "x" axis and N is the totalnumber of characters to be printed.

CALL NUMBER (X, Y, H, F, THETA, 11)

This call causes tne printing of the number F. The parametersX, Y, H, and THETA are used as for CALL SYMBOL. The parameterN indicates the number of digits following the decimal pointif positive, or truncation to an integer if equal to -1.

CALL PLOTE

This call terminates the tape.

In the event the program is used on a computing systemwhich does not include CALCOMP software, and the operatingsystem will not execute a program with unsatisfied externalreferences, dummy entry points may be supplied by adding to-the deck a subroutine such as the following:

SUBROUTINE PLOT

A = A

ENTRY SYMBOL

ENTRY NUMBER

ENTRY PLOTE

RETURN

EN D

2. DECK SETUP FOR CDC 6000 SERIES SYSTEM

The deck setup required to run the program on a CDC 6000Series System incorporating the SCOPE 3.3 Operating System isshown below. Production runs of the program would usuallyemploy relocatable binary forms of the routines produced fromthe source decks to avoid having to compile the FORTRAN foreach run and the waste of associated computer resources.

49

JOB Identification, etc.

FTN.

LGO.

718/9 End of Record

SOURCE DECK A

SOURCE DECIN B

SOURCE DECK C

SOURCE DECK D

SOURCE DECK E

SOURCE DECK F

7/8/9 End of Record

DATA DECK

6/7/8/9 End of Job

3. FORTRAN PROGRAM LISTING

A listing of the FORTRAN program appears on the followingpages with each subroutine started on a new page.

50

in ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - V4 " T4 04 "f 0r T4i 0 I i'I0 'I0 'i0 'i n0 W ir0'i 0 i V4 Tl V4 V-4 " "n V4 "n T4 - N

C2 4k WCM4 Y4( CD Chi444 I-444...444444' 4..4

V4) 'w %ft U) " 4% 9J) g- .3 s % 14 9

0 0 00 % 4 i4 0 r. (P Z

LL C)' 9%i 9%O nO .4, C;) "% LX a, LL C.,a t t-ri a-La - H=.t) . W4n q4 er-a.' iU). m 11.

I2 -0 W 0 I~ 9S 00 *: " t JrfWM " C C L r

.) n oC L - 9% (D M% 0 "W a, InM .

o UJ v4 Y4 2:= LL 0 v4 Z OM C2 W 4 92 'Si CL 14. 9

%D 2 U U I- x Z1"I)- V4 03-r4 a Wq * Ox

Luj -c ft"-4ncf 0, 9 *q 1 0 Lo 4 I-a. wIX -- IX. MnC 41 Z t- V4 WW - r LL L L11 of "% LL W0Z 1-0o t C us" V) F-I

innn-~rI.- I.- t - )L M 03 % f. a, N -1 1-4 Ob

a. V9 T% '4 -0 %X3-NO C) a) 0' 'T a. (7 0I- .. 'V) %W L- -% 0% %4 Xn N. % 0 D a Lx LI C3

T4 L-4n r%.V) M= 0 . %. <% 03 CD4 9%f 03 02 t 0 CX

CL CO-HV t~r - 4w% .. n = 94 3 0 o0 . 0%1... co <Z - - C W 0 rV q7- CD -i n- 7 w 'd N .Jm - aI-I ul LLZ Q0 W 9%0 1 e r- *-. 901 U % ~ ft tCDc D z

U)~- fXiMn IX < "% ("JO. 0 0 Cd N 3~ P.~ "0 Zft rI9. % ".,LU " I- 0 C2 N V4 9k. % r'2 0 0 9%, 3

w tX -ok-t% L%)C 0. V() VI 0 0 * 0 g.C\ %NJ cm 4 )2, V4

LI. - j r- oftI# "UJ~ 9% X0 a,1- ZW 9.C C., =% V4~i 0 XW L (

cm CdJ4h- %'.# rf CD = = .lk M Va C) 9%DD = 00 .4% 3 0f- w 0%9 001U WXT - qt C 9, ft LII & (r- ftU CO(

LnN9 % / L-n % 00 Ln = C2 %D %-b CO 4 3- CD(1) H-

rf3q o 6L 3td V ;-~ i )( " U3 >c * 0 ~ ' 09% 14II O9% 't- 4 O

o CO-vl-&ZI) ftWC.%" 1-4 C 3 0 N-0. (fla4Tco-c 9, (3.j WU ~41- H % 10 ::- 94 us 9%C a. eP) V, m m. wX N C. u

a. 4k Z LL. 0 -1LL W J 0 vZ C 0CV *A C0 * 2 4 -W CP. ...I- Co .4 1-- . j -N 'T 04 30 ZP0' ObO e p1CL cn

X - Ix 9% T4 - I- C3 - )C a 004o * 01 v.L co .- C Z

C3 co in U .p 4%4 oft 0-40 02 C2 P =J' %D1 mL4 a9Wq%-vizf

Z - 0,-H v I- IA C W. &%, 4k a. T4 0, V414 caN _j I% C%

0. U- WN N X " r4 2%-.)- t.0,*3ft0 0, coH W C28gi t9W%%

CL >- a.C..W M%9%tLaX TI4 6% 0.020033 W (7019. P ftco z.2 > jT P ,a 6J 4 4cLl M. g % V , 0 Ak r-t' % -rI D W.4

a. OW U. L i-rL IWWI-4Hin X a .- N Ozqq4 v .C4P) m..J-- COI- a. -L U 9rf o vi I-L.L -H" 2 I = 4 4' 3. a tm f 9%) t-C V) zD - % 9 0.z tv, 0 9. ELL 9.0 aa0 flN * =i a*n a U.-3 H . 0

o in ft..* M M M .9Z > = J000Y4 C 90- C3 3 - o. COft9%oT4-i- 1:tA1r x a0H ~ II 4 .'W 0 " 0 9 ) .0. ' v.(% WCOC LU)3:U

D 0inH~C0C~- vqa % )% w j 90, D 3c 9.0 v4~ v4r- C3 W LU I-Z X Z P-4

CL .. X4 9 'N- X 9 )N C\0 W > *~ CO*ODN 0 ON1, ww4 .. )-4 4x H 4Z C '-10 I -. 4%(L:c Q .0L.0 .0 * -VA 2 * In a C3. 3- -. z

Q- V31I _.j U 01M -% Z x "10 -1-q4 = @,= o ft 4-0 9 9W Ga- . %r

~ Z ~ r4# 9%H1IrwCr40C 9%96%9% V. 4~ N3v fC l.0 al % 0. 9 % ) 9

Or <Z 4% LL. n 0co ) I-) - ">- 0D 9Ta %N "-i00 .0 3' . CO.

(X-. V =~~- - 04 ft N. ok -Cc .)( x . 0 UN & oO 2 0 LA vvr4P%M ~CJ"-1-.I.0= V- V~u% 02 tH z 3C2 to %0 4=D L#51w0 % 0% 4%I ri r) 4%I

(D . gm- i ota) H- qvtin U n1H @,,-. % 0 U3 N. CU " I IJ1- W4^V. 0.1- NZ

Ix Q w %0yN %0 % *r T4H %W>1 ) 1-- 0 V m C m<0 = 0C.43* T4zwo -4

< 11 -n o%(~' -- A % X 0, n -4ULLLL ,r- U.N LLOL. UU#3N r4 =i 4- -1Ja 4

Q W W 0, 0 '71 O c I- Ln % % a m c Z 4444 <(Z% CE T 404HC J M ) H 0 3t- X ph .- :

o a. 1: C3 T4 4% U-i-4 VI) of cz 4- I- F- I- "-4 0 V.P3- 9.3-I-W o 133( 11 <II : M4O 34 X < 0 M H ..JCx ta H ri4 4%L>OWILnW 0%"%0 - 0W444am4<CZ <In 3 I < A C CO0 0 0HOCLLJ0 cz 0 CP JOIj 0:.

-H ~ ~ ~ ~ ~ ~ ~ ~ ~ i V4 .o444CYr)4 nwvqcirr r 14 T

51

U,% = mI C7 mI =- mI =o mn = m Co- ca CO CD Wi 4= UlI -2 LIN C2 ULn ) % C3 £z 1 4= U% = i C2 Ul C; LII C2 U4 C n=o i-4 ". wu SA P3 19 .7 .7 U% iul w %D 11. r%- co qD us C c C2 "I II 04 CII m." -W .3 In MI wL w~ f%. f%. co Ou QN (P 4

cm cu Qj cu Ema wuC cu r C% w cv cq w Cu cu CII Cui &M P3 "m rg In 29 " In to "9 V9 "9 IV. 29 m9 m9 m9 m9 2929

W 0 T'l aI-N 1-4 N. U. cof M.J UPI- m 4nc .-. 1]t C l OC)

w V4a S % 1- w=0x= xX~ WCico -X a U3l - -j I-zIIC2 Q 4 Iii t9% N .

x .03 toYI EL :r C3 _j jm2~~- cz "L co cz Cu *

Z V.J V. U.i %aJ N U)M Uc)u l'- %DX VJ1; vo a) It. 2. 4 .L.co2 Z m X x x1-1 3 06z n >-1 I t

". D i-4o3 C: C= ;1- 11 04-. 1-- 0 )CV-1 4V4 1-U. x -( 4 cm n I

X.JD, 7( . ". f.-. F-I t-(LV4V)-Tx cn N. c mixc 0.-- Z CD

W-. X ".ZU * <CL .I- E .W~ w w 0.. 7( 0,I-4-23 V)JU o CL 44 U. W0 ". -C I C3

to z1-Dz#. w wi WLL. if H U.4= Y) co 1. 0. rf Z 1-31- 'X : W 1 4 1- *- u~X I- Z r- a- -0 .J-41- z

l- 1-U..OV-N 4 )D11 amI-LW~. U. vi~% C3 w0.1tS 4/i L 0 1--4 -V)/ I- u3 : C) L. U.m C) -4% M W4. .:czi = 1 ZII-i -1 M4 LLHXM"4(4- CD 11 O0~ i-i JT1 U ).LE W X.J U .L 0% "- V1I III " o 11 -:0.~I U. Iw-c;75j Q.'.4Q. -. W7( X Z ,%-ZV4'- U 7 1'- 4koZ z ) V

X. M ) I fiW a% x.7 9.. .-TL'Z- C ~ U, U. '.IJn W- I.

%0LL - XX C N. LDHVW7i M a. z H3-4 -,V.u )=)4 -Z .c 0~ = a 14 7C) CfZCtD). 11 '.4 tzI-

t) w1-H 1U.--C-in % c.) 0, 0Z. -W Lt. be 1 -4 IL 0C.- CE)U 29.o X V - V.~ 4x uZ N L W,. a, P . 0 EX 0 C)tLZQ-U.0-H" -WLL 44- ZHZ .- HZW 11 -.1 - W- wM= X s11w4j f4/i H-47umovtU -. e N)w 0~z 4mC=tt L .1 < co x z a4-W 6.: T Y-I ~CM I~-I- H , a

m . r-u LI % '.i- '.U7( cc -pi - -. 1a M .Eu:N<f 0.U0. >LU < 11 ) V)Z >U 4%' O<

< C% . UiWlj) 11x .0 . x5 0,: CC) :: 2N

1- C2 a-HN = 1.o t- 4% V. WZWX01,- a 0 1-u I > U.Zx Z I-IV) " C 4 "I-3; % 7(k vi UILIj CL4% ) -23 u ._- tjJ oftXCZ) t4 A

ft _j y~ V. = 0 4%U .. WO -MC.)= A4 a(U 0 y cvj'V4 x( aU. I.Wl ~~N. u4 wI. o- w mJ. -4 v iVi( W. X aj l. 9.

0 l )- . U. 4 f 1-*' L %'.L U. L) N 4x % - 7 - C3 -329 IL I--flW m-(fo O :"L *C1j Z U.WU.4 LL V0 U, 'X( -x c" -0 z H " 4wIL WwLXH- U.ZZ a.-" W L X V .--- H . =MIO 0

U) . o.~ U C. Z~-* w 0 U P" -. j A 1-j 9A. LUJiI W - U.t- 'j V.1 V..J.. Li .m w x m ll z = z1 I =ICJ4ZZ- rfo. V)L Z4 - -1s-.o z -EZXWL.Da.ZI-I HX in-) (r< r, 0 0 V) le %, 4-0U.IN E ZZ X -H~= -4oMW X .- 4I-4 H N " . M 1-4 WZ H..5 ItIfxEm CL < N ' -. Hn -4LIn Oc4- U.3LV)~ U2.N X U14 ..j u ?1- L x( /) z WK 'i 1% U.w

x4) - -.. W7 U. %D1- XH ft4 x4 .t.w 0 9. CL -a.4NZ% Xft4 .% C3 C2 W. Ul 7- ) - t )1,- 0% P%%C *OoftUI.L4T .OCD =CO Co

C-'viXW%NJLI2 *XN e.WI 4Cu<HOX U -*-H CO < trIIIT*t0 Mo *t~o uC In .5.hV) W tv. U.- a cu Vq %4~ LA. -4 U. O ) I f~it Cu U. VIXy4' U.fZ 9 %cm q U. .-H cmC ui V

CD W V)H V9 4 (DU.v4~. LL 0J7( 0) II U XL. X TI W C3 1Z . .N V4 X -- : q U. W = % viy.LC1J0 x U.Ci)4W40'LIN N U4Xi U.4W II X v w 0u " V'4i U. o M t 4 Dcm0 U.4 z Q) m U

-H=,& 1 V-wj ri..L)J-( If~X a. o44d U)... Q - -I- " = j T - xw U.4 WC,1. ) _j _.j W-C III ICZ -- -j i~L - J

I--l 4M -U-414% x, - U.0% W L V) "CU 0 l- x IQ- II %,, -7 0 I-

WO. U. L Lo U.XLLMT-1C\ re)4U InT- 1N t o2 4T I -I N. 4~

Co U%( wI 0l LII Ulc - lI

Nl Ne') m ~ 4 ULIC '.0 t

52

.7 444T 74 . .7.47 -4..7 4.4 7 :r -"I rn -T ii i MIA mn IA mm MIA 1A i MIA mn IA 11% IA wn'

cn 04 - k- 4x

ch W -m 1- W,

-u x Z I-I 1-4 -

cof C.) W- xs-s U.. D z %-4I- 0~0 ft .

1,-X 1-4 19x HV) -- MI- T4 tfl V) W.

ItC -I WUU. .4 X ;K wLL . a) i-1P-4 rX~ E E

Z W 0 xQ in C3 in00 tI ZV) Vq COp T1. a. Zrw ft) iS V4I V

I. zin '-COO C3 X 1f p.t

0: cNZ01cy C~i W Cuj .

P- LU OL VI t1 w .~ vi I vi:: 4- Xi'S 0 0 Q co

UjU 5-. LL P4In " . -J.0 ..j U..OZ1- LU ..J fX 'i-

In Zt m ID 9.T. I 0 T ol Ht 1-% U LU LU

SWur *I I.. ftmU ?- I- I-I- xc -Zf t 1i qI H -H

(.DCO1 W t 1- 0l2 MLWf LU 0 ft1-H 4f

Lu ci .1 1-1 V l-ftLu Ul.00 CE ft ft LD0I. a. ~zz LL (~f ~ -. D V) vi Vl)#aw C2 QMS (AI 3) .I zZ LUJ LU LU 0

0WII C EL cmJ' z z z ft ;13 H I-I f v) l' I-D N O - - 0

z z9% z 4 -.1%IH 41- .J .J z. -4% LLU I-.iILI 4- LX d-r. t ft Zm A t

0.. Ix~ LL (3 H 110 U.t- wI- lI 1-4 u o' U- V) 0% j -1 3u

L) aft. 4k 0-0 C3o W. DJ1 = Q 0X90 0 -

HlU 5- v4 1-4 .1 i0<- t 0C

rvj. -f CXu + N - CI)OI. Lt.4~ T4 0j %: 042 .C ~~~~ ~ l-j' En 6% U0 GoCO %H N"- z z %4

x=4 Hin (D ft HZ Vv X or m L

=t- CL 00 X .% . ..O4 N D0..J c

In" am 0% 0.Z-Il - + -.. <X m ZI-I - 1-I T7 U

u.t U % 1- 0%, LU 4 ex a U'sn 2. In TOO DA a: Z 0 cm'~r- '44.4 0 M C3D - J- C 1,-i n LA 0Cf0-i Dc .x on cl) 0 CDCI-

-5. ftfZi T- ul 0 I/) fU 0%w 0 ftk. 0 W. rI'On I- I- I- t.- U- L. ftb9.WUs M IV T4 3% f0. oft0% a: 0."- *WJCV-H I- C\j I.-I "t 0t. .0LL U. ft 0. x

X _ a W: LDE 4 r4 W H1. lf 11 go - V j D + WX OX ".% xH9 xx(

W. W QT 1 VJ0 J- . V)~ UJ UI T... W -It (m U -1 In 11 0.- * I)(

" 4 %1.iu V U-' ) -$1 -~ HCZj 00Act:..Z HJIV xu r L . IX LL %0OW-.W L0.fl)WJC.U.O ZL I-- w J L9.L&15W4Z) M

I'..~ CE Ix 0' 0

53

4. '.4a1-1C.0 ' )_~ ~ -, I14 9 40

LU 9-. EL2 o..C cuz. 4 I >- ft LU

-2 _j =-1. IX. % 0i-, '.d .~ rL C O 14b. 0. lo

9-. co -4 . Vf) *14 I0

t. - C2 11 "qU . 4. 0

V) le 4.OI 4h C3 C2-

- 'ft U 4% Q X 4 0 4D

-L .11-- QO C3/) I% ILI N.LU .64mV L03 -1'"- Vq I-

0 0e CX XLL.144 14 4

111 1-14 I f.itZ C2 t- ZU.)Lw )- U.X'N34V) LU

21- "4 . ft CO .. r" H4- 3.L Q-. .00 .- >v44 o I ~ CD 0xx

ftoU. u/V V)) O = W 6.o 1 4 U.. +. 4C.) O) Z ZfC.s COO 4e 4. ILI..-3

>.7- -. o ~0 %% o - I-I- 04141-

ft4k T- 4 0 4d 0 WX 4i _-r%4 ~I1-= - a1' M .M 0 CD

-- ) a% =. ft LIfN 4. I 1- 1-1 T4 CD

In M4 >.-0xIoft * o W". a. w O 0 91 1

tv-- - Z0 4r 4.T % (D mn L 0c 0. EL - TX4.-) f (M . UN 1% '. Z0 M-40 P. 4.) LU IX 9 V,

-0i z) I4WZ- co x- -IINw1 4 z4m 4 (W.LiU .0 L-- C 0 W 0 Ok -. 1 41 ;0 ftu

4w >-OH-40 x N" 01-- z- or C) I.- -

EL 4.4 Ix.(J- j44 tL4 X4 4) -. 1

n 1 V0 0. H L w.. fX 4Xn% ) -wvw CjDttl% . 41 .. CU) 02 9- (3 - .

MXI ^Q OL3.1 sk1 4.1 1. 0.4- x I-U *r UJLu (x x N j =xI'Hx = - oz .0 #0 4 71 111 0 CL WII0.. N. -1 -111MAZIA01 0 w Irl w LU P% 0v 1 (4)2 V00.L.m(/n W 1.1W 0 - - I-- a % C/ 0 Ck0 (1) 1- H- w% + Z(.V0C0z .+ 4 ci 4 L = . 0% 0 LU * jE W . .'-% - 6.1-1 ~,TIAU WoCP WC3 J,- U) ft 4U e 0 cc 0 0 -*r x- E. 1.1.1a C7 .0. -40WU% c CL M 2 e14 4.H - - XX =WD00 1-40 C5-W M (P < CX C o- LIXl.

* tV)- 4. (01'.# .W. N on M ': to 0u W %.f'W Z4 -1W4 SW X41 9%+Iu r H 0W vI Z 4 oz " W :) 4 :c u .4..tCD0 9 W a 0 6M ( 0'(nC( S V.0%WX ^I EX EX I-jL0 + vl=Xt1k4XIIH ~x-l1-I- Z I- 4"HI M.W W#INJT4S- X 'u 1-1 MNN0 Q i,-ua1"W.u0ca 4.ZtLcrZ.0 CE C ' 0% 11 .1I w 0 C Z It I X -0 It %

i-4 j U uE3 1 -.1 ) %Wx t- . 04. j .1 ( '..1 Ck1 - 1-1 V) W)( O1H91- 1-1 1-54 V)

0. LU 61 V) N LU x~ W~ E1 MV C2 0-1-4 (A. 0 L . - -H =9 11 %W U 1 1 C:3 V) T4Vl

HQU<3-XNMH 11. toLL U. 0 H I-4 V-41 1 11 H-404 J "1144Ju~e Z j ojN )j)9 0 -- ~c t

4:E440j.zNl.J.3c1 V4 V1 (M t) - .11 0 14

In 02 In 0D I U%04a m4 3") .7 . 14% u%

54

~. ~ ~ ~ - ~ __________________v-

"" WM 4TnT mo inr- co Win~ C3 Vf 0 i 0i 0L 0 oinoino Inoi 0 in o in o o wvn or ino a; 0 in

U1-

x*

H+

w Ull

t 14 rVT o - TT4 W1-4 U.U 4 9

x HUUzo% %Wj

V. j P C D -

4k~C U" V. P. 0.1-O ^ -. P.2: T-

V* 1'- vi) ixP W4' UZZ-jWt )C i4p, 0, 1 "~ P.L P_ , . 1-P. - v

1. CL .UW- ft* 1ftaWWMHDO W Lo-4 In t '4-Wi- ) < IP.Ct

-, L)J~ -- ) )W (cW UX 0 P-u -) H *ix -- 40 -j- 0 P. 0H *v 0(1 -~w0 CO(f < . 0- Z .

P.'4 .P.Pc.P. H - Ny4 J *CK I.40. CD-I Xr X H-

W W 0 % -ft 04 HD% *H nWi CO he L.,0 '..0

wwJzL2 U Cc1/ V1)- 0- JW 0 x %. P.1V.1' (X^U nL -( =Z L .- L LCL) % '-xMr00H 00 ON IDi0.b4Oi P. P. P.I- WM

P. ( P. -PV Wcn L V)7 En PY -. iL WCH N O .( - wl T4 4 U W.c 'x~~~ ~ ~ ~ P. zZ .J- C2aC -0 Ze z 'a ( 4f )1- ju L.LL. e-CX HJ; V

P. P. P% . P. P '4f *, ~ a% P..'% -- % X 0 z t ft P P.C * L P. *. V

P. -( .> -Z J 3 w0C)c N.~ Q~ N~ l' N vi N a

ft ft "W ( ft0.ftczM o K W- N Z~ H %In .q.) P )~ . - C Hf

____-4 *(M1 Cr z I C) -. < 1 1-LL i t4 (.W(VV) P. %-' P.w F4 P.- - 40 O.ZC O .V4 U.P. P0*- Lo '11* -

rl T4 V4 V4 T4 -HV cV 1 1DV 0 4 d 2) V4-H- 4 T4 4 T4 U 1 v.-

LL c I W u itLi -4 taLL C twig1r-. 11 etx x .j .J4..-I.j..j j jII I -0 T --. .1zV)- P.H 2:131 -. f 0~. j Iz11

-iijj-3jj- If Z 7-H' z w 0 i -J..J..Jt- i- .. j -j .1.J.j..- 11 If _.j X bx m 0 .U 1-Ewwac 1 MC -< wv

T-1 q-4 v-t i-4T

55

02 C2 C) CL n0i ) W~ = ) M = Cf ) = =) in "S ml v4 v4 Y4 v4 "n " V4 T4 " " w4 V4 vi in " 4vi'4' (gq iJ1 V4 V4 V4 " ",V %I. r. . .) .~ .' . . .- .4 .' V4 . .. U. .n . .D . . .) .) .' . W4

-0

-j

0 L I I

HWe. * , n" !

rn uj CL a.n

I-

-H +

ZU . 4 . .

i. W, ,. 0.0 ,.4 g .3

I- ' 1 4 %W I- x -U

"m 7 HW 4 * -tr 0 , *f - ,

v 4 0. Q.~ 0 z

C ,-. I - LI ,? t.. a

1' H - r Ice Wo

5- 51 1-t t"tr '

VZO il 0L n AI.3I- I'4- T1 w c 0 0 -0 4 0 W

" a L- 0.. "- J. =Pu CL- - -iL

CL CK - in in Xa~ oft. UlC 4a

WI' C C3C co ) 4%W C= ID 0.. H I

0 ZZ. i V) ~ 0 4.Z *- = >. J

4 C2 (x I- ca= 9 VC) c 7 P 4 I- 1- 0 +a -4 +1-H V) W ( V) M 74IW W e II V4 L 40 e3 atzwM9 e. 0% z Z C 2 ~1-4 T- LL U.L 00 C2 x

_x j 1 t0 Ot 0f b OZ.- CZl N- V- *LL LU v t.-

r)9 H-. A I .4 _j + ",' HI - CD. *W .%. 11 *Ui& 11 II NX~- aL eH WW -Hlz .W Y4 %- v*o 4 0 W - 4-Iu4,W wl W !)c 'V)

V. 4T 111 0 Hi j ni in V4' ~g.4 w C2 04 . ' -' VqM-0 3 z 0)I3- o I-1-I11 In IL rI C 2 Q MI I--J-Z~ Il-Il UJ11 11 in%0Q.Wu . IVZ 1 ca -s If %0 Cnj

I-IL 1% I 0 f C-4 "^ 2 w .4@- r-0% l.*If 0- xUt4M"C . - - )

Wi 11ZWVI0L. L10%V 0 < U 0 in .= 0 )W L( LC QC( 4v#J0U \

LA C) In In L1uIN

u-I -lu -1 N IN N N

56

TI ~ -VT uvw I ~I3. ~W~a ~ D% V =W 4== "W TIT WJ M ' 9 ?47 Lfl IZ U) U) N. f6N cc 010%=

1- 0

on -jVC)

TI aU usL

E~ - in

-L I a

fta C/) 0 N~

*0 H

_~L WU- T~

%-1 ( >. 1 0

#-ba 0 0 C3 o -_ I-

NA C3 + 11. C SZ 0 -

cy _j 0o CL _4 CfO z

C/) vi in V) Cl) C) f -1

ch 11 , L * ;0- %

TI _j EN -. LXta Z..0 -. (

I--a' ~-Ci.I4 MU N 01--1 -4 N .-

a TW a) 4xx: EC> - N0f EnH ) z

V)a +E .4W 1-4 .- * /Lf * V. aL

T4 T4 0 i-4 0- *.0 J x + of 4K * 0 z C

Vl) (A 1 -4* W)-LoD' - C/) I.- -I-N l'- H )

I * out- I- u .A P4 II - - -. N 0 Ixo

S * CM J9 m5L V1 u a. If HH j 0 (L

C)%*C0 TIo U..fl* u- .via -C so) 0000 C/) H-9

- G* _4 f 1-4 + % 0 c Mof > CLs a .CJ) v4 o

* a) 0U. 1,- OC14 Q -A4 ;j 6A. 1 H " w.- C; u

1 -4i % U. V) V'C) 0 O)U a 5-o.n 0, .o-4 _-4 (LD

U. V CM14 " W)+* D* WW+tufl aC3 :; 0

Q* vT-1 V1a~l T- a^cc a ox - Z o >-)% 0 Wa

CE V) V) Il i C/) .T4 _j+ * s-s-TriCa. o0 2.W - O ~ v m~-Sl T 95)

** * it Cfln 4 vt "0io * j -i- CLW 0, 1-3-cz I LL 0 a

vs- < (V 11 + + Id _j It U)-

- 99 >(D -w TrI X VU)9- 0 0 41-4 0 0

9L.W*V % TI91.- 11 /) - 11 W W" of a9 i 0 1 0-CE =1-4 0 -JC=W

>.ov * j *VUZ4+ j % = x )W www va cL YW (n 00.,-'0L) a*

I q* -H-4 U)0'o-4o L'm coc00.N4j i m9 1-0 cm .- ) 11 THifl) itu V) v4 x

cu Ui. tI4 i a U .Ugin sXW iti L /La-C 4a -(/It i jt z14L Tq0 1JL ) I 3 I J -13

>- (L41.--H N .j 4 H W mx> T T4 If I 11 4~eU.l 1-41-J

< U'o 0 )x 40

57

KX .4 4 ccI m 4z Im 4 GM <~ <L <. 09 42 CZ 0% cc le1 c1 < 4x 14x <% < -a 4z IM %x < f 4 aO I % ax 4m 4z at 4m

%D (fl T4%N 4% U

Q z wc

C2 at.L2

,-t (J In.£ ~ ~ a 3-4 InU. C

wV j. 01.- 221CU 0 I. H = 4 z

It Z a I-- 4 J CU

Oft~W Ixo X 4

Z - U .li1 U Ift". N. H6 H z

'-u CDC V%D tA e.

owJ (TO N ) MID 0I + z 4a~)Z a. Z

1,-~u- )-- 1-4 t.- U..- of -7 W fw otI

.2 oo fD 4r -4 T- HU.0. 2: rI1.U --W

"1- G2 C .CLI- P" V) Q U. .4 a

X:0 0 0 a H ft H4 oOZ 4 z1 a H oa

w X 09- In 4, 0 * * - I 4.. +- X tfU)3 f ix CC op Z *I )xe do a 0 N... *0 H4~ H ifl- CW N WZZ tof

(#20 I0.-2 be0 mo 0Z WO zz HJ9- %%*o N L.zZ3-g f- 4I- -IM -3 C ki .4 a L A 0 U. A:Ub " .L a a-2.:a.

Wt 6.J "I I- X: X0 0 x94 *L3 C3 L' -<.)L ) ggj Jvi_jW111U W40 00 ZJ *W 0 Z 6 - II 1 II (jLD x V.

1-- : 0 P% 0 C 0*iD t tC .(c5.w Of HI 2U% -J co I- I-x E j zW L. c _ W UU-1Z I U.10"~ I- '- X 0j V C

C21-1 0 < 0 ( (LZ22 L U U 00 U o% t- V)In In H In W 4k IOUCJZ

0 XC c U "otI " U Us tuzz~. - N H.%

V) (A0 CD IL Z X -) -) C" D 0 IZ Z ll OD z 0 N S' H a4 W H U. Z 0Z

T- :07-1 XIj u w = IW - N 0 LI -V) 0oN4 =

A j~ I m.. U) III- c05z r 4Z! )m-01- - Xo # C

=(.8w~ C Z ~ - O ZLV N t- (ZI If 1NL .- 1 Dc

-. 0&1 m0 4 - 4 "j 2 - 0 Z l a W 6 x58c

IA = m1 0l Ul = mI0i in = In oIn 3 In q= In 1= In 3 In 02 U. i n 2 In C3 % o 2 In = oin = In co 11% 3

0P -4 il km WU m' r~i 4T .T i% in %D lU r' . .1 U) ul 4' C2 = vB "- WU INS MM -77 M4 Ill W1 U) 41 -t. - 0.) 0J M ' 0PC

W )Q V% U D% )o % 0% DWWW -r t' -Ir- -?- -r P- % 1 -P.N

-j-

H- 1 I-X 4 V-1

W1-4 .. )-0: -

t-I u 4m tu

0: V)~ V-4 CD:-7 w0 1/) --)C LL

C/) Ix 0 tn c. x

-.j U) zo Will -.1 C. I< U) dm 0'

V) 1-4 CD = =0:O 4U.. U.. 9

l' - -- IXr*-z 0 :-o~-

< 0 ZZ z (D 0= ) N --I cx

1-4 u -Z B- I jW

. 0 w% WW x) U).1z: * Ill Il . I- ) 0 U =O' 03 .

&4 U) I- U 0 ILI N- 9.0 CL

-LX X b - B~ W '- x r- ft in T4

L! ) - U-U ILL ~ ZW i-I :x Dwx ftot

ItV -,.L W4U 0- _.-J* z QJ 9L U)

V)-Z W 1.- * IC e * uW XU I J z.I- lW )

(x T4 (LLV)~ 0: 00C Z a = 0 Z i (1).J - %

". Il44-4CL1 I LiX-e 1- 24- .- L i -) 14 P V)

1-U4-1- 4.f H 0 . Z 1-4X " 4Z tDW 0.C. U int n1 -T ~ I-- I.-

0:~ Z -I C/) x >x HWCC0WOi-40 H 9X9 11IU) H1-Hf, A. a. L . L z-Lu -i- vi 0 S -%.. U. L. W

(n .L )0 1- V) m (1 ) 00 a.1- " )I 001 0 0 Z; C. NCO H.. 3:

ix H UnZCU)/ i-4'n'H H %-a 0- *W I-- 0 ( Z 1-4 W

H- ax 0 (X tz to 1 1- Er w 0 XZZIXZ M )%. qm ozw Of

U-~~ ~ ~ 0*C L-' )"V L.1a f- ll m ~ w I m. H P- ()1'0 U'1

H (=H Z L J B-i'i cro:I- z 4 V ClL W -. C3:.A x.1 j 4I.4.-r -

0 04a "-l EXb- " ) C i .4 V)/ *ve V4 ol Z aV 0

Clao 0 e ...-. EX = 0 0 0 H<_ '±11' .'V- Wm Wil

= ww 4"Ca a m-4Tl <.% -H'' 4 C= P)?)m m j w Z C.XWJLJ) 0 C._

o q 0 e*WiW 0 oL t.... -i *i410 H- 0 a 0 vi oV 0~ .111 C2 a)m

01-10-0 o *o3owc .j 0~'% 42 a a* 1-U0 -1 x0 aft

UjV )W - -.U)U) J) EX .o *J11 r o tu ) *U *U * W Ex 1-X0 4OHQ

m 00 i i 0 Z~ EL T-4 C3 0 (L L C

w-i C2uI Hlm m.JV)z l) U l~.-J0Lb0 bI/LL U Ill4 i 4 LLb Ill l-H

EX0~ 0x Z C3. (0 m .. Jz H(XBI 1-4H

HHHIHH-H0(/)U)jo o" c~1.I.QHLWHHH -. 1 OHM W. H.014

in 03 UN a in 0z

0.2 0l j 0.-

59

0 m4 14~ UP I Iin w wD t*- r. w =n (P 0" m 1-1 w4tJii8)1)44i w N r- co * U, (P C3

vi v141 Tq "4 "4 1414 "1 " 14o1T4 I r 14 " " iinr i ""% "44 4 lr 4 14 V444444111111 1 v. -I1 " M

st9

4% O

V4 0

-~I ..

*z a)LXt0C P0 wCL. W'

U. 0 Z?. ;011 4xI0. t P. a, . I-

-7 0- 111 -W ~ * 0H- ' I-- Q'

P.~~4 czc H eLM 9. U. P.L)H..7 x-

o %I4EL - 0'j~ 0e cx

Li M. H f0w 0

'Lp 2; 10-4~

4' ~~~ W-0 ~ b4.. . 0* ~~ 0. XW a-Vi.1

0± m. )-v4.Oeft 0

- x Ile v~i.. ft ( 0C V4ObV *14o X o >-. 4

1-I * I.- ~ ( V)4 '-'00 -M 0.. 8-

0- l' 01 %., '-0) 0.- "tt O V to Cw)o 0na C

e. X 14- V)0Ob V44 to4.X)P.W. >J- 0,f i- - - .1 >- I- .. J.J07% IT F-4 Z% ' * ca ft s, cfO3 -04 C-44 < .<.Z CZ4IT1 V)3 L) " 1,- M. E xC2C I00.- V) = ( x V " 0 UU I.J- 0 -- 4 Q)LuIt 9. cr) Z H -I lke- 4h -91 4 ;-- q m z -% c.1 cn v)tbto -4 inic.)0 6 U).j cm "% I Z T4 XWLUW 0D4. A U% X%.) W.C0 A 8-W 0 * * _jC~ U .. J0 C

ft"1-14 V) o% --. (4X 4i+W W C3 o% )W o4l~W - n C 4X.DV) E-4PL . CL Z v4.Jx t-4ci-4 ft.''to I 44 x~ s.'* . s~%IILs ix @% n 4% . a% %., P.'- " . *.

w- vi 11 EL=V -i 1 t I I 1 . . V 1i 4 1 11co U)4O 1--4 1 t-4x-. I zx-2:%0640 ll W x C3 C HI V) It X~00 I- I t Ins .Wi Hi -. II W "L" I M

ILL4~z*...L zi irI -.1~,. w 's-i t L -7 11 % .7uJ -- t- Iii-) Ul ut-Il-

In00- to1'411 In'- 's-2J 9. ~ in CD.4 ... J Z.J.

60

LI~~~~~~~~~~~~~~~ C* In = n~Il~Il ~ i n-i i n-i t0~ ~ U%= WMt u01m4n rz In m w o r%. r- co 4a cp a% c ) O0 01v J-wc~i m In .W4Utm Inw % - v- w cOOus'C

CD0 0200000020=c~ 3 m 2C24 C C3 4v q iW - r v i 4v 4v V4 4 .14 V4

-4k

CD 14 -0 C0E

t. = . AftI-a o

2- - IJx - 6%2;-

W : = . )0 V

o LU L :"c)c .8-4.%0 00. 012..

^<A P D . C ' lo-4 - =W ZW14 1.

.. -wJ _j I- a.. LL 1- L- i

a.. a.. CL X )=2 L Ha a x M t4HC

I--I ut- W - l- It, x 1-a-1~ 1 a (flU 11 E XX E1I a s XX

LLc i 1LLi t .1 C)U .. 3 i In C J. I1 In-C3: E H" 1-1~ 0J % IL - "~ HH(P

-ja0- m" - m 0.i "0.W O =- X ZI f m a 1 - X) -mxI-8- - jz -1 a.< .J)-- 1f Wa LD&* %-4 %'l - Cn Z

< *00 < a. CL 4zn0 L U ac 0 U 0 - cz a i 014 (f) V) V) 01--a4 aC ( L 3o ... a .* (1 3 . -4 *j H 0a4.0L1 - 0 0 c a aWJ C.. - x xU i a Dwj C.. -

Lr% 1 14 -g m aZUN.Z C W Z.ULZ cm In 1=-~r'UN w14-' a r.. e. W )a--I l cu j~l aco)0 us U) aXO

~~~~~~~~~ " -U j)4( 1~V) 1a~.1-4~l 4'~

0I-Il~ftJUJ )LJ 1-4 W..) 4-4 P.61-4.ll ig I1I.'1~I II

-1 T Av lU Li9 In -) -7 I Ut %D i r- r- co co a,, cr. cD =) vq 'i y cJ 1) In %T . Ini ati wD w r%. .N OD co 0' c CD

< M4 4 X<-MC MNX4 M4X4LCE4 X41o MIM4 N 4 M4 C MGMM M44 3 Z x4 x z<d

T- C

%.W 2z %.W

F'). ILH N >. $4

0,T wl . x

9. 9.1

-,x x

7 LL I.

V) X)0

W9 H H .

I.-Z -4 )CLI 3cmi a. cii x x

w. O)) V. >. I

TI ~~LL ft . '-

to U). Zr ~MH C%I -- NY ~Li

* U. 0 ii re) V) x Wu

I.- CAI % 0. Ci xC IM 0.) ZX U)X 9 4T .

IL fi)l 1-1W cu 1-I 0 V. W

')I (LU. 4 T4 %-.ti eJ 4T C'j ia 47I .TCL X Wil -T TiT 44 7 2 LTqx . %.0 0 U9. 0 1-4 11WW

0 C3 U)2 W- M1/ l'O 10 Z 0 0 ItIJ1 - .LI4 r*4 L1 1- 4,4 r4 U JLL

9.o X.I~. 0 0 4%.TH -9T *3 MHD wtO 0-. CDO M. 0o H 9

93 %0 s LD x (.D 9. X

H , U C t#. In~~-. C4CW C)1 19 -- W x..~ - C) C C) Lnvqw

W 0 . r LX.%LXIXXW e @%9. Z 9. a. UJ * 9. 0%U 0 ft W. a% fV) V) x 6 1 11 0.I HS cmI~ It W * CMJ x TILLWLNTIV ;. W6U W fryIi cv t xX V) x T4 94 (3OtI J D +WxI- LD CD + z -3(DX :r iL± +(D (D LoC)it~ t1-l-ItlI e.0 I3-t'i 0 C'-H 1.- . v wO . I .0 U I- VPh OT4

H V4 V-1 N n - ') M ' Z~ 0 - Z4.20'- X 4.0T Q W %~00 =M - M T 0 C4J % 1.- _j a 'e I- C~ji N IH .- ) P- l'-

x.J.F U)WWTIf Wx -%W 1--10- X2:c 9.j l'T4- 2:+ -4 l'-U. = t .')W0'4I- -- TIMI--c x-+

w0~ W )- 0-24. wJLC w2. wL24H- z1 z.J3I4 Ix0xN JIxQ1 .LL( L Kzz .3- 11U.I-4;

In C) In UN WIO WN M) W )UCcm 1 9 IJ I)ff) -Z . Ul U10 U

4T 4.4 .r..4 4 4 :r 414

62

4 4 -1- A 4 _ .7.7 4M dM C 4C4 M. ItZ .7 <7 4 W .7 4%' <' U'. U4Z <' CC AM U'. 4'. I_- WU' 4% <' uCZ 4X a1.U CZ

,c- Cl) I>->-1 I N1 V4 X I -'I T4 a

43-3 I 1 A%:'- I P

-4 W. >*.- - IJ41

Vq * 1 -1 M LL Cl)

06 * I- L + I-4 .>--3 * L X-0 EN -7 v. LLUc

NO. H-C/V.-*C) n-H 1 41+ ' * a~-,.-% (r (a*t4. + )F. S I-1(fH-4C

U)~I Z-- ~ LnwC

&CL r4L ) 1--Xs-.0I r4 V)s

I 1 1,- 1 1-1 + -. L LU-s. V) -IO- W/ aC\J 0<

>--. - .1-l11 * GMaN - -) ILI) I 1*- -.1w

-3 + a+vq CD 0D

onl ;I )N -7 L ) -4- CL.)-- 1*11 x* S X a. 0 Cl)~~ -4 -.. * (fl I I -INt~

0%,.. .~ ~ X s-I + LUkNi-I I-1 -H 77. 1-4

* .- 14S lI- - U'A* .7a a-1-1-4.L.a4. Lm

-30 .1 UNC2 'LL L3±. 0 " I. i-ly0l

7-+ Ia~ ~ + *. N U. C

U.0 ' 4 1- + 0- I)-4.- 0 0too- 0.4 a . -X X 0. -1 M 0 x 0

-7---) '* I 1.'U i- I Nt.- .J- C- - lu0 %040 *1H * %01 H r. 04 M 0%

00 on 'a) II) -- 1-)-3 ,%0 - 0 <0C0 T1- I-"N - X -3 M M * -> TI N. 0 -. 1 0

-% W %V fr.,J .- (~a j C. 9 I aj V QC3 Z -7 4~ CDfX~l. - X inatl X z w0 110'U'n --- 14cl14. vb+'-s-- faW. U). coN I go m o,- 0

In CD4 0 lJ()+O.QOM a * +-4U' co 04 af~.4w~ ~~~~ C3N .Vb.''a- ft a% a 0aaaz1

+ ) 3 o D - CU* a %0 CL* )* C3 v- J (.D + 0X 0CL r W mvV)e- * 00 U'. 1 T Z0 lls l X* S V) -3 E I LI UC 10 041Q

-. -4 LflWI'-4 -3 + 4% 1-4 + I'asa + *N1N 4j 4 . . 1 -

_j 0 Z z7 CLO C 00 % C3 OQ 4 1-4 1 (v N ;c J t--.4 'a) IV'ar P3U'.LIt ".- A LA' ItW I -I C)4 4 f. -P 4-7 r- = I ft"v4 -4* I-I -J 11tU LU C 3P4L UJQ. CMW~ 11 WI W1-

Iw'- - - -5 - 11 411 1 %-0 T11 H -7 06a I Ob *- *- t- - - 1 - ' . n") I-1- Z _4 '3 C _ 4 7 TI QH U1-1~ w vq H Hw V-1 M

Z U U. (XCe C)00. 0 0 0''00 )l-' Is' 13 Z ZZM010L-MC-Q% -0Ua =4X 4 HU rf of -)H o. -. :cX 45 W 4Z4 H.1 01-1 101-1

T4 ~~ ~ 4 Hc o TI DNc

63

in =mmo =m =mn =un-i n n~i.=L n n c2in = In o~ in ~ n - u.= =m in n i oin m n=" t wwi m- =w CV== vi3 mm . in in L3' ) '00w ,1C l 2P r- n iii Dr. N N o ol us C3*Jwwww ~ il~ Dil'0il' ~ ~l' Ot ~ ww 0 OSN wo Nw wo 4D N~~ N N N NN N IN N N N N soLU fli cN cu 4cm LV e t M Ci cu wl tv El li W NI CVj tv V w N~ m. cu CV tv IN Nu cu Wcu N1 ENS cuw Cli W cu

H U j~Z

~ .4 9.

* ~ ix 1-1 1

a. 0.I

0 IL +-'

M Mm 04 tel- ob 1-4 %

CC) 4- 4z 4% - 9

i-I 7Li f In P- - .4P, 9. 0 lex W 06 11 I

Er. mi Z0 qm

-7- C2 c. nL in - 1-.Hl 1-4 V4. W* cz LA+u

Gl. V) CL0 - -

T49 >. N Ill CY 16% .4 .- - 0>- .r C-. ft (n EL CL~ 1

9.1 T4 ft4 q-i O- Uf 0(3d) 049 -% .4 04 C- a. wD1-I-~~u U.V -i 2i t-11

-V-4-). T-1 0 9... CD U% V) 0.m4 .V zI. -X..) 4h - 0L .7 CIJZ .8 V. w l w% U

f-- 14 9I4 V- Lu 0. M. X < 0 nM

9.9 CA z k - V _j J < to.J. he03--4 .

44 C) CL V) IU Z -)Z O cx He %c* cY'nI-% -a. * w 0 w %, Pin IxL 9. T -

ZC C, -Hl 9.I .4 1- a)' En< N .

P-II.J e x ft x. T4 1)v W ktp - 9.4 0 -4.*P CMtv a .9.9 00H U) " WZ X wUaZ - W 10 Z +M C H 0 .M-D.l- N P.

" -o * 3 . C- W + X CD to ZU 4%1-10 1-1 . u LZ 1,-l1-- ZM 0 0- - 0 U- 9. C3 9. 1-3 vs ca W Q.= P.z 14 ^1- 0.1.I-

UJ EX -7 X )' X 1-4H - 4K8 w: T.-1W 4S x H CD* Q ClLL. I--%""", I V 11 C 9.X Z-Va) %- +i X Y Z -- 40..- 00 IV) l. UI

1 ):- -'. U r. tz .(1) 4. If 1-W--i349. 3 4 OC. 2-

MOO= It -%o - o~l 1 I Zo z ( ~'~l' .4 En3" ax DUV 1 < m I--. I.-x

2:3-I-. x 9. -3 . 1. 1 1-0 1-1001-M0 w- WEL:'11C 9 W 9. 9.tl --

~~~~- T- 1H CY~. I t- . ~ o T-0 t.

7 ~ ~ ~ I UN~CZ CD. Q.4n( W.D LA.4Z4W CW.

0 i n 0 l tn UN UIeiNo

64

=" wWm)-z m wUr ino wanC ==" -TIM L In 0 ~ in VL utr

A -M <*i IM lic n n' r- 4C 91 4M 4C 4Z~ 4Z 41 OM 91 < .91 CZ 4M an <n 4M fa < < UT CZ <' IC

fn )C 0 0 0 0 0 0 0 ~0 '0 0 i '0 '0 'a 'a 'a '0

Q +m I>

0 1, t . -

u-4 It LL C3 0

Nm itc C 0% ** w f

31P9% k i -m 4=C2 tl)* N N a% 0 .a

U-u -3 to 00 -t.l-

0~r o* U) Nh. N.1 .~ 0 . 1T*% itN IJD C2 = C3~ LLLLx*=3M V

4c. W P- .) - - WW I4H--11 0' ft oL 9UW (

Lr%~)U "Ity4 - >-

I--* --- I ±W * U -' w Il I- W

= x *0I W z . -nOf 03 U)3v4OL0 -T* t- 1.-CJ 1 .1- T- iI IV) z

to~~~~U CD 0 11"0 cn ;v -CZN N N N (n.1)U -j - 1e ('.0 .

4m o0* o * LLLW V- ) w icli *U. N * IlZZZZ H H + )- *% 3

j J-3.J- T *j -M -4

In LU w .1 -- I s 2= ) -,,-)P00 U..* 0. I--4 H H LU W V4

0 41 0 *LL N t ft LO' tn c. ~U) n C5-- H 1- N 0 VIH T q W4 x )- )>- )(U))clr

Wv. 0 x~ -t- P.~ + +. 6 ;P-o W*o 0 w (n al.0 .- m'. 0. -U) 4~* -M z N >-- 1.- >-) )C CUI -44 1-4 +-

r- -. 1e. 4m. w Q 10. 4l eC'J T444 % 0X 0 tu T- cu.- 1-T TI3l *~ I

V4 0zx -- - 4 Zr 'CH H-H1-4 H 3-7C U. %.0 CI ~ t,- ---0 -7 P- * 0 z EX I.-ll 1 %V C. %0 x~ X- 0 .. .') ELt- CL o U 0.00 V)

*~ zl~Il4 $- N w 91". V.) V) LU LL 2-= : V) V) 114 44 V)f* I V)1.- ~ (HP *I t tM'IN 4NNNN 4WWLUW vl4NN~otI....'rXOe-4* 3l1- .1I-")-

Z UM 1-4* Z LUN It-% I t 1 s It 11--II s- It H-4-41 -'X~cX Odc 11 n: @-.%1.-I _j0 - Q 4 I-It - 4's4 0 Ht 11 11 11 H -7 - 0.-)'o* 1.- - W H -7 +

EX ' W* Cr -M - I N TI 4 V t - H V4-1 -7- P) 1- 1-0'ce V ( Ml

11LUL MV)WJ 10 1 .1- Ul Il- U U. f L5 it " x 11 U0 w tU.*3

lk-1- * Z I'-1-UN I-- in -JJ- JI 1 - r JM2 DV t4 1 1--1-Ul In <

Li.. x 0 qa 11 ii.. N N 0 00C)0 0 < <± C' 0 (/1 U) M. 0. U 0 C ) U ) 0 0 EX WU -H " H Q LU T4 -1-4 -J X . * HiONONNC3(uo~>X-(u~>CWc f ex>.c3o s

TIN~r 4Ili

0n co UN IA Dto) 4 4T' ID lIf% It% IA U% iIn

65

C3 " V14 v 01' m V) viT In In to? WU Nl r. o ID a% Ok C2 4 V11 -A CU cm ) ti' " 4 11T tZn LrD U) 1%. g'. CD co L' cp =

lei " V) If) If) lW vi 1 9 1v ' 9 41 I') "9 91) 9 9 9" #9r 1') " v to i M v m v " v m rlv lV P7 1 9 m vi' I v) m v m v m i M 1 " v Mv 1 2

%. -.) z

In 5

(N CY on cu

92 C +' 14U

4 x

W. >. H * -,

-x >- V. Ob HNA-4 %U+ - +' -, - 1. V-4 C3 D

%08- 9* 5-2 1 -

>- >- L n 0%-7-, Es o% ,.,- e. -

V)4 V) 14 01- V)*E 1-i 2

xs__5 :I- * - I as C) x.-* -+L Ii. * H 1-1 C.7'ca 4-40%9 0% H r* M ;I 5- .-

0.0 1-1 1- W N .O W -4 - s-

E - 4.

sb4 4- +4 .. )- 1* 0~ 0

-. %0 .0.s O- 5- N~ - 0 * *, 0-.H) loft W) (n U.H vi-.9 x- x~S H*- i I+N +^II :P- I- 1 *% *0. U- I-- -4" f

(-M4-4 oft -.3 -C e- -* N, Ns 1-Z1C

H-5 *- * 0 '4 I1-'% M- 44* 0 3* - f

EM EsX cc 4. CL U -EI 7H- 0 00 )-J 4 Es EsWX> 2 -Cj -n4 C') 10 )- - * *. 4- 0 C3I

EsW WM + 04 z + x +)- 4. 5-7 V) T-1 14a Q )5-v 2 G

0 mootV 0. V)~5

0% E 05 tJ #k 5 X. tI - X L w 1 %- - 5,

I.. 5-5 V1~O. 0. Esl s X H H Xu06 * * %-0 W) 4lH-H Il

Es I lfl zz z"I X-2 -4 Es Tl m.4H8I C'iC I+EsL Q=6 e

Es 1-1- H) 1-1 . 1-- a.S~ -i tl. ;2p*EsN<.d'.4Es Xs 0 1-424a x :;- >- E xE ) w 0 m w w % <Z 1-4* C,0C , 4W1111(

1* 11 t oi * i;K;-1 u tt*NIt w- -

- C215 - - * .. 1-) x.E ;s-0 A 4% 1 4 -I - i

o% 4 4440.0.- .- w U )% v.0 1 C'+ ) + (JI-1 n%4-2 %0 1 1 4 5 5

111 tI

Es.JJJW X Ill> 8.. (9 0.511 1C 3 1 I fj- pw 1 1 fO 1I A - If - 0 * * D fi Z.6 Z :0I of H H" rC VA 4. 11110 v +4c w 11-a1 V...1 4 0x) x00I x5 )IM = -Cfl0I0L)

H .> > - -X -- 4 M E* 0 v.4 N5C. -4 * , 5-In HI-4 HW115-~- r4-* X s a-10 4. z

0014-In I-551 C2I ~ £~sX-* EsI ) Lw~/VV W - ZO P-0.01rL 14- O

I 111111tt))-~ pL2')-~c.~g-N~'JJ **~-Vi~Vi )4 5.~5-5II

Es~'1--55(f *oui-5~+94)~---OO~tl-,-StilII4661Z

Z V4 i- V 9.-4-*9X -9, .I0

X. * 4 vX' N%4vix. 1- 14V-" 4S

CL4 f'IJLJ *. a, ftJ... 4. "9 9W1-4C o It .'w - u

0. W -I cr U :c rT --0,U)

z C 0l'- w -w 0-4z -4OM U'%[Xf-Z .. ) *LIJ) ELUC. 9W, U -4 1-Ttvci 4 x (

CX %0W 0 Z v4 -H> -0-f *LX 01 W.( X W. 9.

. *LLUL. . x -4 11 C3 x0' OP0V) UZC X -4 C4)

1-1-X LL a H- vm%94cQ yZZ 1-11 -OZXX ~ -e. I--

1-4-4CD ID 11 "U<HX)(4 V4EUz - -- 4 X ) *WV) Ill X

1t I f4' 1-4 w w %v 1 - sk Q w V- .0= ca W 9x0 . -X4 < -U. T-

P* - O-ri = 4Z 4, X. 014z XX F-4 C r.r4 N C/) Cl) c

3 " P-4-1 ) - W.i GO -f S Il. 9. 2 0l ;U1-1- + ". c)NX x 9. *.XN N~ l-

obf 1% 1-4 In;2 L1)W LI - . 4z cm(( Z T 9. 1-4 0 X1- 4- l- z P.z- z% 9.- 9.. z 14 0x

(L. <4 <x W %, < V) 9LLJN.% P. 4 0 N9. LU 9-.J-X 9CC. t- c

+ + VI) V) Z* .Wztn0-'.L CA) 0 9%00 Lu D * 4T xx U X:V 'C= x 0 WfH -- W04 Z*.oz:=- H-490 0xf.9ft * w w a t'WO-4 u x1 u

C.0. Z-N 40J Cl rC 1-1* (XO -0-. < WI 1-4 x 03>-( x X N% uj -o I-* )t U~ X 4ax. xxd 0% 1- U%+.4 +s- Xi I- * 9.tur%1/)' - z 0 In u oft %D

H>'.Z 14->- 0 m W* 11 -04 vq 601-4 LU0-4vz:rZsI.H 1- 0 Ef u* =.. w .j 0 4 0 En 0 Vl) z 0

I I K . J- a I t- 1 14 J&f. w " w.. ( i - OLC P-. t-1-43-H** >.- 4 X 0) 9.4 * o% 4 4 -4CL woo 0' t--

v. tz z* H 1-1 4110 C) t *X a W 0H VT4 -t- 0 4 C 0m EZ4 % (D -* ID CICVN00w W 0 39 1-4 1- W3x 3( j >- I o-XAfW7 .-. t--* NTI LWU LL % .

Vcnlf* * LLxOO y4.j. WI 02* -UWXZ-t0rIc304 A% c3 mInI.. m -2-x -4 ex0 -4 0 *-H UI u) O UI * 4).I .UIXI Vo ft 9.C 0Ul =C%IZ?,X0 03

+ - - J ) + * C W 0 *W VT CD N -.* u i 1 ,I)- LW. 1 A X f CCJ * Q O W~% 9.%D c C . 0

O 994+ x (%j I-. *-JLo +43 x~ 0 o N x 9.4(m o. + J(D + W x to- T4 +.4)O1-'-4NZ* l'- u %J N1,Z w.lviX 0 -4~%3- 0 a1- U N 0 I) 11 1--

u VI) ) H ")- 4xX Wtce 0' Z %. * "-4 * om .4In Z L)~ Z .o =~ ft .

II ~)- 4 ICX-4 w -j 11 wL 4*tQC 4'-- %T 0LLW4 a 1jf I t W va U) w 4Z44 If .. Jcm11 It H-41l 1 11i 11i 1.~- 1- l'-1- m* wW 4%.i%.1-N3xI-.- - -I-9-- x 1- t1- DI-. ZI z 1 1 >. kx )-( 1-403 H ~ u .)H nX 4% - LL XH C.) " a H W0H~ (3WX X1xmm w z Q* :c it X 4%~~xZ.zz~)x0L

0 )P X( H- H4 H 4M H- gc4 H4 H- -J4 -i J X Q3 U.L N .T X W *0 9.%A J . .JtLC.ZL.0 .1-H ~N m r %oN c

In z irN C0 1A 0) U3%.o v 0' 0l w 0

tl [ Wi UN In %o kD

67

441 -T -T -x~ t'x 47 47 -T m In mf VW 0 '0 a 'I m. In In m1 m* m IIA IA mD C m w 0 0

H H

CLU

a. In

_ aP

x n9a 0

W, In 1)O a

inde n C)C

&~a 0DC 3t. Ur CV r9. Din ~ I ~

" w %D vi 0% @' 0 .-. A~- ~WH W WO Ill 0- I- Ill- I-

U) (M O 0 0 l'l'3- 0 00 .J..JO 0

H "c) 0 0 H aLD (D _jj >- _.j t _ _j>- (n f>- J j>

-Inn -.- In V4 ~ -In LANin1)V flot-)4 0 0 OV)Cn f -4 H OV) V) 0tac i nL C-610 min C2 g) cm M n * w .1 C. * i CL * * i .1 a .. * **.

0 W %0 In co % H Dc %D~r W.0' 'H 1,-0.0.ZH .M M0MM%JJX a'p3~ a. 0.-4 U.3 t%.) e . a .a.,g * a . .- .

0001" 0 tS- C.3II IV 11- a00 0 m Qu f-II- H+ ' - I; WWI- -

j1 -.1 I. -1.4 -H1.J 4J .JJ wahIfww 01-I1-11 lua~wIu WOWU

UHI-H 0H0f V -H H ... J... .J.J.1 Z..J-J-j J. ..IJ.I cz ix Ex U6 Zu m z ix 0o= t. ix cx z cz 0 . tL a3. ml < o m. m < o it 5.. ~ <c) 0EL m. < a. 6. c

C.,In C3 tA n LAn in 0InT43 "' %V134 W' re I YUlUtoDIO to ok t tot %0tOt

68

wi w wr wow0i 0ii IDi 0 WID wo w i w ww 0 iii 0,- iN o*- r* N 11- 0~-r Nn ?*- NN N in0 n i 0

< Z4 MXC XI iii iva iM ini0W NE04XOIMI00y <44W 4Mftj 4tntii I-N AX X4Z.) 4V

fDWNt

lvi E) 1) p Lv W 91 9W)3)4 94 91 ' v v v 9l)l)()f I)1 91 9lif3f w4 5

Wi V)

* -

V) -7 :

W- - -1Wk.%

N - - I% N D (Df.lD DU ) U) (f W i)

0. H (n D I l- EnU ) l- C (00(Ci) q4ZL e3 0 * )0 00 0 0N w* * * * *M

W I40D * LL IIv I W% j - 90u-1 - % 9% _j oft af, f

U%0.4 Xin 0%.N 0 U)> P* - > . 9 . &.4 1t- f9 1

W )0>1 . ZC - j J H ZJ -1A> .0 )-- L x>

LIUW )i w Ci )0 11.xl-F 0 X-- 5-

4 o) Mi )" 11w M j 11 11 oi4 ) U .1 1 1 .. j N I 7 . 1- )V)- ) )-6 )

On ztO in (Y-( ( W z- u. p. v; Pti si ti Li 1()i tL 1I i i. in 11S it Z m i*x 1- 1- 1 . - 1- 4J 1- 1-1 .- L m .- t- - 0. t - m1 -

_j11_ CUJ)~ Z V) j --.1 - .1 .. 1 - -1-. 1 j ~ -. J ~- .L -4z -.0 C << 4 '~'- - C'i-1 H C L ( U C L)0 . L< _ CLt LLC L< Lt aQ.Q a00LC. ) LL

w x0u ) ('5) ) u x:0 -. * 0 H )(-HC * 0 x )( 9.-4 :1*

.4 ~* .4 O~O~ o.in~.~0o wu~w P.W~j. WUO) WO-Z ZUUInL . Jj 0 *.i 4. .. J CJ.JJ I 4.

ow 0)1- P..)5..5-4ON)( *'J1-0C~t- ('3)-*N5-t 0t''I

QIZ LZ~~L C/ 0 0*~'JLUN .t OX -OO OO HS69.

C2 N, CVW LiIf tiW .7 tf n CO0t~3

zzH1-"V) W

in v).z,7-7 "2U"cpiv

*> x

V)I V)f+VI

- pq1- 0 C.)-.- a * a 'VC~i9 . -

"3 .-1 -j 0% #"%o ~**Lf o4

x 3 -DJ1-4ij .J .

X 1- 0 0 C .0 41i0flk o W M " N O

x to , * tvwtf-W w iu W(v

cm i**X** j tD =

4 444) O y 4Q

x. :IC - u. x( Lo 0- 5 1- I ) )W

o2 CDi nCvi~W Uttp C2C2Vto toI N N .

70

11 ~ ~ ~ ~ ~ ~ ~ % r4NNI~1 ~4W l D~ *. N~ w~ o oil Ul P C2 V4 W4 tv( 1) ri M 4 47 Wi til %U U) 1%w lr. c co ' 0C

I.- 'r 0- .. ) H. e..-(fL 0*LJ X .~4 T-14-Jt. = Z CZ j

C1 ."viC -Ln M.0i -ell-~it (.Ln o% IY-X "I-t U14=1. o_ 06

CIULJ *2. -4 wJ 4a J ~i = I-- IL UPIl V

coe Me 42 o) o.O O u9.j.4 Zt- a,~ 4M ZJ e.LL N-403 LL.Z

M ft v, =WW OOJ j0 1-V4 L& (. ftI .. X 13 v.L .W 4 %'%l~L

£L) V) V1 o-Z = o cm

*y. c 'X U; .(0 a- Up WO U41 L ZI

z cn 10 XW03 MX fto. <~ 1-4x

In Y c I --0 -- 0 H z.N0 ex -e -V

VI CO.z 9.j -L W0 :?4QJ Lii- %, e NJ V) ~ C)_ 2C XV -4 00

Oex 2 t 10'.-w Lt0C/ L 42* 0X-4 X V4 'u) .4 o. :j j 0iu -' X. 94

r, %. 11x wc 11 9.Lxf)0W% > 1%*x x ~ W Up v jJ V I% %

T4X ..- 1-4uj eve-z c I,._zn 44 to o w.w1,-0 41 =X-VgX- x Wi

_j Z JII -- ui~ H T1XLt0q%% H 6 "X

0 - 4>- .'41%.SW v. 0 4 2: 4% -* 0o.~fl- 0 -". e.NOX U. 2:~~ zW

CLZ &.0 o- c cz ~ v~qD W co7 1-1 r 00 34H

4% eOjb O W4P M 0o U W . i 9.O x c X %o V1

x W." L U1 C ~ V) i':& J. IA. kv qt W 0 V)vWIX q qtAq4 = - U. T4 - tLi..i-I 4% v0 * C0

LL'.~ U.Z cmH- -F O %w w % N V)U V. 4+ *i A-.x * 6 C

e)- >.~ EnO 0WMX=IfiUAoWZN wx~ EX >_ 3.J Z(0 / 40 CL . &-D-v - vq- *ZOv-1 WW 0 chc3Z 0%.=PJ eH "X 4Wu f r4: r4 v%~ +~,,~- %; t'. _j 0 o

vWX I~oco 00 toj =H L S X nI-c01-0 5- 0. x ot4 .% V) (\j.10 X =..0 ) o tmi - xaH<LyZ IO 0* T4 U. S * 0 0VL2-I H.I- v. v. ftI . w. u~. t.3-0 0 o+1 zLr %~

UJWX r 'W .o I N - X W COX I .jZ a4l x -% f. - LO 0 0 C 0Z s. > .~(. I Xo% ) a Q _r 4M CU. U. C C3 N'~4~ 2c CI "Mtx. j 4 L

aO )'- 0 WI=U\ C n'44 e% -- - eN 0 j . 3: cm OZ ) 0OC) N~jWa) '- a) H V1) 40-'C W 0 u 1 t (P X C.0 u- OD X* U0 r4

W .I- e)- -0- ly4(I- (MIi4 Ix~.I l CD e* ..- I x cz*% x %1% 1-?1zW-%a. -4 a i C3 < H in 4L) Z1i M .v.N Lxt, wx0 o o 1 )( ~ f0x %~ 11-I 3 uC"OV %X.Y04I I .0Y1I~ X.-2-W T1 0 P X C* 11 X,.J INJZW00

I- -- 4 O Ut-I~ 0L. z x" 14 . .7 C. ko -IU II it CPM 110 H *404X I>0 *WMN

M >_ V)L 14.1V X)LL0.0I3LL%.---NU. .JII4ZoIAxj.0000(00cfl0-)-I-V3

N V w1- X ft "v1U.Ix0 _TWI%14ft 0 X iH0"-M11 1 - -1

TI~ 4 N4 N1 ~

71

0 rIr4 N ~) 7 . 4. ~ WU) -. .. QI i 00 r ~1%~JlU ) 5W 4.4. J~ l U U) . 1. U U)9)'0'j

us wN~ NJ..

ix 2- c4

IIw0 LL0 M

X (L (ZC - f r

CL +Z+Z >

o+ 0.so~ M

* .U2f w2 U) i U I -v

C) ~0000 W0 U.v0

-. 2: CZ ) Z a0 1-4 H 0

X x. + ** '0% -~b Oft rjJWZ - tIL x 4 viof ) *V- 0 -2 n -3n V 4xInWC * 0 %'. 1- 0

W 4'- 4z ,IN CU ..h .. ) W~ E) m rg-A Z* ZN I' N) X) .-

Ob Ito - t1 111x 1 0 &0 +W N 4+4 M ) +

M Z.7 a-4-301-.% e*N - all~ 92 2. . ... .5 1- - O

@0AW - z- N S-r W z 0- J JU) 1-I J 11X ItI 1 )1 . I K:-x:I4ti 0

11C -* 4.4 It flu It It.Z5 ZO1t I-. of of '1V H

L.7 U C2 U N ) U W0 i % .

OS ~ ~ ~~ V**ti)* 2 4 4

.0 - -~'~Z~Z+ .H )U>1- * 5-.i--IW 72O

tnC n4 I 3I 311 3U nCMI =U KM I nMM l = = = =WOW0U 0~0 f C;U ' 0 L U ' U ' 1 0UMWWr r'WWWO

H to

p z -U.

c,%D -,

0 .1-4 u >-(x11c -, l'- w94~

C3 CD z cz4 0Z LD

(I))C Z . 3-M1- .3 EMc t- S.

* - *.-C ** =' "Ja)3f, 4 * )- V) x

o % -% I - C, % -j 04 J

~V) I J LUW-ot. P 1-1 1Z L u1 3 x7 I-- 3+n

02 1)f 00 CDU D1-C

~~~~~Z V)s Li I" '* ~L) ..

C= X D. Ul 00o C) LU Ix i

0( OC?-.v4 'It-. .D~ L -' 7 T- v4 U .C9 V.) ft

M. wl 4%. U f- ZI 1.3 I- it~ * .s'x u. L'*)4h=)O , < < * -3%4 4.) ) (/D T4 w LI v

r*4 ~ ~ W--..' C-4Z) Z( 0 o% #%V)V;a-IDVc v-# x0C m H-H Z00 Zy4:~ 11-1- on <% H cz

Z 0 T4< M -4Q0- -Il W 4(X I-4X) >- - 0 0 4 0V'y4-4 e 'MA.h N Z3 H v4 .-- ) MX* 1-4 1-1 0. lyL 0

V) p x+3= c - >- >- S i1'.. ;P.I I a- Lr.' w L"u

ZQ=.L V'..X 0- (3 4M- 1-4 oISa 0( e. ix

- XLH( T4 C= C\""0 (.DWW x%,. W

V) -3 - V) T, I= + ~--Z 1,- -7 X I-1-) >- I. +I I ~ 4 I.- ' Cp XiC d r. -r4 + + - 3- 1-I Ill > cl +)3 w-- Z EE cm. ID-WO

2:r-* H(>-.,J.J4t +I) 10(3Z ) 1 t .1 + (9xN L) >- 1 (33- tozx o

I.D~~~~~~~. W ay) c XU'U w - wZ

eI 0~ sY- C314"- xl uc :- +< L

y)onc mm 3 XV)1,4 -4 + +X M -. (D3o

'- *- u,* -. - u~ + . 1- 11Z U L 4

*-%COO Il£If 0111 0)f~I 0~ U0~llL1Ll01 L0 1LlIl~f0 1

K= Z4 %0 H~ a) x x

It1Q mom U (12=c U)0.

0. x tz H 21- 0.

u P3 -.j j4m C'4JW-4 0e 0.4 _...J

w.1US )%o4 NI. CL Om0 x

qm 0 40.8 )C 03 LL v 4

WWOZO -M V) W

0ID0 0 Ou CK )I- T4 C.1-4Z t..-3 4- H. ..- .

QOo -Uw fl4U~ 1

wctz W= H J CID Z* () W 7 ZLU XL -U.3 W ULA

X .1 U)-l a . m4 H M

vyi0V) x 010 We U) In 0-1, -Z W ~ Lq( U)a

x( N 6O0 N Z iD Cl)z::&4- CDZ v-:C1- Xu I. . LL

.-4 X N 0V)I-I.- X- 0 4% 0% - .3CD 4 H H j -l' N~ In

ot .. j o f<4% m ZX0. co0 0

C~.Oin~~ _jWC. U *H 00=LA.-D4A 0 W 2:'- W -W WUN 0. ou i*-

o .U. e . @.-Z ". 4%I-IDo.- f-L-

wwO11HWM X -. o-..D u. _) x3=9:~-4 0.4L 01= r- = L)0 1; w .I.0

LL. 4..X U. -ZXZ - 0 u. 0Z 0%IQ r-- 0.C -)tv1N x (L C2 4 0.

_j 0 0 ' Z D . 0.11 0- ,1 t h: U. .. cm0£014 x .1' 0. 00 CX N- 0. - O.. ((I '

e-, (M %; eCZ2 J.4-I ft-If IV- A; 1 ulI II- 0Z

qI DUI M s1% U II CI-- 0.n. 000 t~ Y 4

x0N 0 N U1-40 . X x - --4Zu - C4J - x i z I a) CI.- W - H T4 0 X(0.#I-I'.jC W.LU4 *I(.8-U. 4'JLD .W "ZO + -(D- 0- Ht- 1 ( Z r-'TW4 YAJ~H 64 - oTIxL 1 1 1 Wf-w II O0 4Q X 0I- P-- 0 -1 W N )-Z444IH- 4 -C. 44 aM-% oXCUV)- 11 1-C~~( H-j i u )4 1 'mH ~ .I 11 V)i V) (L4 . V4 l#-

X . C I- e.j z ' - .

C~ U c III H H - 0 U 11 H 4%I 0 11 11 -x 4

Nn N U2 UN L

74

.4* ft4o==,~O OU r D* 11 -N mt )OI1-4 U) #')

z~4 T,4 1' toi4Z * 4)~.%U)~?' 3 X

X- I- .74C' f4 - 1 1 3

CL r W*% OL -0 n .- m~.I 0

V.l XW"bwQU OK~gL V. m 0.W WJ DIXW -11.a4--ZV

x -W * UJT I '.-LC Lf

1-4 = < X G C_ C' -Z 11 =

x ix3p 114 .. '0.*- o

C. * w0 xW' % .tD -cm x ')

1- * v4 j o X 4,CL-H.

W.J* -~lO os> X U q4 00

D* *3GW -4-0%.O. S %0

H- -' vq4 X ItLL 4

t-- %.*(ZW -Ti V) M 3-1-1-3-04 .* fvio~-jo> IOZ v. 3

- W .O (X .. * 1-0 W C' (4) 0C)

u< -~%* U)'J '. .% W). C3 a ('4 xxAE4x4 .. Wl x. P' '4 1-i) u) .l 4z~a 4m o

III 00=0~-4* w N CDO>( >_ a I-o

0 t'U O Zo* .Lr30<%.4 .8 1.) l'-2O

a) ( 0 0 U) m 0* _j ' i... x = KU Q-1 -1 .4- xO *n Zr' Ll N 0.- o -1 44. -1 j_ j LDw 34 c I6 W- "( 2 OvqLL. 6W LU -.. W3 113 to

_j HU m-n I43'UXw* w4WOWM CD - U% Ox -41-HHJ CD OItTa4 4 x XJ4D =Oi "M c.LL vi c XV) v zi' 1,4 *eWOC -1

X1 ' .v - OC2 % - U LL H XC .Z N . 0.> . Joo of .

o * (X * <4W xLL 1-IL f X W ft a ,Q .-C H 11 1I 3 (D440 CD .+

X 0 II t4 CO * Z *4E '% xZ-f itb-I- 4 C.3-i4I04"-:1-b-4 '. e -t-I.- 1-WOW (XX LLXIlt H -ic1w )* N = u -III- 4 >Q0_j-C3 v, - 1-)' 3H( _ _ j_

H Wil 0 11_ -W ZU* *ML L _MX JU14 L Xi 01 M Wa l ] _ 1 J111 LZ <i mI I' I- x%, *

1-I 1-4 T- 4 T4 1-4

7S

T 4" W v W"i "' T 7 mn MID 0D Fr- to w Ot 0M V'~~ 4 W W "f Mf .7 -T MM In u I,* ". co- Go 0 0'

~~~T 0C4 000 .0 . 0 . 4 . 4 . 4 . 4 . 4 Vq 4 Ti V4 - 4 4 4 4l .4 .4 .4'

-jca

co -T

iL.

H 0s

E C

V4

-1-4 -11-

a. - x iixii'

v. U v. 14 4 % 9

9.01- w % Enf) a -1v 'ai 4. x 4r3W.4a .U D i- tV

-In00 - 3Il %D mw I

X~- - LI w M w+ V

-.91 4 J. P) w. A % t aH4 o. 0 0 r-. T4 --.u -i I LI) mc

(A cu(f 3t -.1 x ma. 4 x < =- < -4XQ~ I N)* a x 4 +I

4. o -T> 4Tw DT 0. r^LI> l I jC I - JL )C HU-1 0~b- W H f D H1 1 04 0 < *- 0rm l-I>

H LU 0 N %D4 ZL0 V)- e. L. J " a 3*X> (3-.jW)W 0wLv r N OS4 x0 OW cm W+ 00"V - + ) NV

v . N -- 0 io 0 0 1iX -1 XOJf t. e- 1- 'T "ri- .. H4 I- L 34 _j . < -)( )l mi I H.J -1 0. WW- w *mc oC z V) H 1 V)1

Inff H~ H V) XXi-I le .iI~4 D ' -X OOqmfl4 I *1 "v1X>-a -jHv9.9 l- EL ZI. * z *i .- I )9.- W . LL _j t- Z 4- If ~ X. In--'b 9.(). - 111X1

Ox" ifL~L'*~ *+ 4 x It e 1-- Ix ~If r" j I(fX 0 W )C3 41 I- -II x-4 c C Z Z 0 @I-4 IX 0V III 4W V) 1- Q I-4X Z ) 9 41 %4 m - .flw

IX- .1 LUU C LQ UV 1 L U. W Z 0- 0 V) V) L) V) c% v% M )3 CCDJV)C%) 0 1) V)

mU IA 0 In a) InO C3 M0

Y4

YT-1 4 v4 -H T44 wl 4 T4

76

V4,

V)V)

V)

V4 V4

Q) EmU)WI

ILI V. ,of X %.%W I.- -I 74 T- IL- -i m~ T-

5.4 <Iii S.S W9. 4.% .,W.*CL

1. (3 =)D = =po . c 0 u Oj +

C. V. W. P. Ex T4 4% ..U e co .L. U tiV)"%. 9.. U) 'V .

V-1 a l'-Z.M DI. c1-1X W. V V ) V) (J) V.I V)- x

t. 4 +OOO . 1 V V

04 3 LL C O..D j + .1 1

5%. T4U -H' -H C i OfT4

'- 4r TIX X W-1 N

CD C V4 z ")

!Z x <77pq u Z: 9

41P 4T TI.To mm nmtmt

' V )

V) /V) L

LL LL Ul)

* w - 4

Ioft - a)

It EZ X C3< 4.

xx .1 Oft

(30% H V- TI-1*

X C2,8i4- of 0'.J I U) 9

w LE + VA T4 V-144 00 C f0 000i) '- X) z U) ( coX x x V)vi Z4 11 H- - z , 44+ H- .0 9 Z0 Z V,<.- .-. 4C . x

CD W -~ -j A=.. x x:2 _j: -. 1 JIll V)" C4fO~- <C OX z-49-lX z rq

9. 4TI4 vi vi C~l 11 *. (D x .j %0 _ 10 - -% L

-0 -%-~ ci, H * I-4I4= AlII-4W X

1110 V)lI C) (29 U o. IX IX -4 W (1) i. V) (n . V) 0, o 4V

x x X===04110C/ 9- a 00 tI CMi W111It10, C) %= CDO0 - =~ "Z T~I~lT It a) mC)

C= -r4 qH T4 T4 Z *1Z (L. CL .X XX AMC c ( W++ + T4 4.4T+ C% A. T G C2X 2 Oft z LL z>>- >- cxIx 9z 4mL1 X-I a

LD V-1 v zwcvto)cUxxx 0 * *T40TI4Z!Acm O Z CC %V1-s 2% -4 All)U V) AV) A A V-1 0 a C0 O.9- 9 H ft Ao- Ax tu .S-W s.X

V) Z- I%0111 C3is r4 L u11 if 111 11 V) VV) * 11 1 11IX)>-11 oof *o ae . .01 X -J 0 0

.j V) ~1V)CC < " .4i W -IT) 4v, 4Z "4X -4 Z.ILJS -4UJ UJ WJ SW E0.. S ZUlw If iw a3 A . 9 9 9 ft4 TAi I.- 6440 11)- l 4 ..%

0 ~' n :0:00 ) fU)U~If - ~. fl~2:2::22::2 C2 Ic) Lo02:zz7

41- 4Y fI 4ZiL xmzc 4 .A T x2 t . ;-" L

u 0 C uV 0 in W

MI LA 90 UN' C= InG3L

Nu cuN N NN N~ NCj

78

'0 4

14 4 ~14c%0 %% I- T

x

x - V* 4"

( 4 m

Z~ ~ 0 x- '

0 x 4 z

~% +4-4 .

4x 5- 4%

f.- 4 I-I 01- w

o ~ 5 44 C2

t4 .- k 4 0 4-.

1A4 U r% 4 1.x - T-am Wl i= Ik- 4l K -c m 4+r

1, %0 4%q I N0 0 - + -

0 4 to 5- t' I 0 1 I c

v. -. IV ofUt zOU

4 W 4 vi T'l I_ I-- I.- I -1- X vi C) l' , d 4 4 X 00

X V I - Ile %w N C2-44 x4 Sr-0 2 . 4 - 5-5- Ut z 4c qcam

UP >-~ ut I-- I-- C3i5- vi CM1 41 CN 0 z 01 It 0 1 1 14 H. t 4

0 1,-. CU 0u CD 0 OoI I

Z* V qC -3 -. ' 4= T I4 =0- w4 l'-4 t- I-- P.. +-

1-. T.44 .. 4 -4 T4-

caU '05- -i>- UN- C24 U- 00 C2 00 4A*~I v4 5-4- c N) m- U% LIN %0 0

4U~-.r~) rZ Z 4 4 W 0- 55-9 79

W ~ u~j cm (N W Nr i 0 li N mv 0v Wi 0~ vc N 3mw )fi

Z-4 -

K I-4X 'x0

C3 a-C L x31, CJ0 IV

#%a * 0 N.. "1-4 C3 +

' 0 *. -

H Xi

%-a.0 -3 ,. 2-1 a-Z1- H'J 11% 1$.- = i -

ZC D I x O -

x X-7- yl H I--. Ic cv-4C lT4 I-l C C ..

0~ ~~~~~ +ZS4 ~ 5 iI''

0 o )( X S N- . 0 In4x4

Zi I.- . 'X4' ZX *n+ H0 C - Hal-

-1 z % l". c c I4 0*1

c c'- * p - I-- 4=%Wftt) x1

. X < V4 P.. t.- ^% o-% ~-H*~d I ZI- (a* CZZW ' =-0-40>0

x 0 P.-- P. H 3 I- It I-

-.4 w A. 4 x wT4 .' p-ft 4 z d 2:A I';.Z --

11 4% M14 IE S4 C9 * H cz 0

LL. X UW 0 ^- " W. M~ 11 WIL. 0 X W. 0 U. Q. 0 0 + WL 0 U. W Z:b -4 %0 1-4 0-4bI)-. H H> I-4 H- =- H. >D> - . "- X~ W

T-4 -v4 .

0 U% 0 A C)C 0 LII u0 UII 0 0l v.3 w W

Ill Go ~ 0' vCi rl vc -H

80

14~ ~ ~ ~ ~ ~ ~ ~~~~~~~~r T-s VIj V4 vi gvq 44 -A vn -WI V.9 T4 rv. -ri vi~ Vq wsg 4iitJN~1 *.~LIUsW '0

14 ji4 114114144144 14141441441411#

0~~~ ~~ 0 0000 0C

z m

CL 0

.7 tl a-14 q* 4z < 4

F- U

I0

CD 4m 1i4

C3 En 1D4 a < 0 1

.4 -l tv T4 - 4z ft4

1% 4% 0, 0 0p

x - toI-

%% VI Ul L 4 9z CZ

0~~ 4' % L

L' 0% CD <6 44c <0

0% -LII 0r '- Z4C5-

4 n U. 0V 42 4z C0a0TT 0

Tq >.. 4 0 0 ex I -

La %' 9 .0 -% )-1 I- ..- co

. oft 0% &4i M4 0 _C

o 1.-1111 CL.W . 0 ' 0 C21 I 1 \1 C = c 14 a c

t- f-4 tD <, "u ..- >- z 47 -N N e

= Sa()v 3 H1 - H. t H 4z H s-I I 5-4- mu~~~~~~~- X *

W Ar 7leul f

03 ect5 x 42 Tq MI )0 H 1HT 4 -

tL U. LL LL 11 UII 11 4 04 5- 1K0 0 .1 U W1

4 11 ~Ut .SI aj Z.~

C2 I in w ...4=0l C.+s (. us 4)(W 0I LAol i

4n v4 14 ciN (\ J.7. In m U% LA o

0 Na -- U + 4 4*81

[l= = M M= = = =I D =MPM6i2L(U-

P- 4-Z

I. .- 44a -LL

46 4- - %

04- ta v4Y T 0

06 IX0 1- 0.10

LL 4-- 14N

0.4~~ GjT1

1.4 of -a ft V-

XXz C;L + 0%C L qq. lC 4V01- H o-%C3+ 0. 1---

0%- !Z4 -) T4 Z+..I- TX2, 1-z 4%. a. 1- w uc r %01 -

-a CZ W-4- 41X 4- m e If a 41 + -oft

0t- H3 1-. 4q01- 4 Q.4 0L 400 .am4 4- H4. M M. 6- m iM L

0 0 +-4 N ~ . -- 0 i <~4

x4 <4 CZ-z- T4 1 X 4 -H - - t Z Xzt-H-2x 42 4

4 -L4

I -1f H ~ H- m- H I -" *a C21 cM s 4 00 414 x (4 00 4L W X4% A." 2 0. o

of o O 0 ^ % - xH m~ I.4- - t- I-- l'- - I.- + j--44 Z~Jl4 H V4 444 -H it 11 : =) n +n-1,-4,1vi--O~, i o ti . .mt .mo 70-0 o .o p '-, L . 1-L1 C 0 0-0 9-4--U.110LZ

0 1 M 0" M' X- ILD Y. 20-4 3t - 0 >' HH ' ( L > U >-)-HV -"fH4

CD4

=4)-

r---640 M 4 6 614 H 4 -H40 z

4-1-4-Oi 4-) II QI UN 0..00.0 3-000 II ILN II UN 0U)MU I C wm

C2 w 0y1 4 -T T .tLo uil %U w r..r.wON1 'r44w- 11 T414 T4 T4'~4 Ti V- 1 4 T4 1-4 4444 7

82

'-' -i W W' "' P~) .7 IT In ul %D U. f. 9* m at op = '-' " -" 'j C- " In) %T In In WV OZ 14 %.1 W m ' a' aCv.~i "TqT - T4 q 4 v YfT 4 1 4 '

wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwUwwzwwwwww

(4) Nr-H

zI-H

4+'.4vi

LU 4- -lzJ cio

-. 1 00 0

+ IV) 0

- '4\: C;

)4 4K0 X: x >- 00 C

;o- p,%0 . o0 In rtn In ZZ zV. W V-1 T4 JU Iv) "A W NC ci .- 1,x

?I X 14 x* >--~ - x . r). 0 0: cm cx ~ ~ ~ I II Ifit 11 1 zC SD MI MI Q0-G0i IV W )

H4 1-41-X4 InflinCO O x x UII0 L l =.4. 2:: : :: r :-N NIn(D -1 .1 -. < < x

x :3:3:3 .... 4-XX::' P.4 40Ko t-I . x A% <9 .4 X .: 'CCC X x 3II :IXX

; 4.I- I- --- *4 4%x.C x~ 0 x I0 - xXx(3 'C4LD.JU0, L9 * L3:3:--X43: > x3 >-0CDIm

Wj T % s - 9- I. I- t0 0 W C cl c: N N X ZX 6 %w %o * v I14.,03 - -$j -4x -4 0 -. 1 W'+=x o- - + + t-4 t-4 C23=CI.-Xt-

D~~f >- ()()).'>- )C -4W WNWJ ('1iJ '-I'IZ =:4 l-f< 4 1:- >-"- I 4 443 :443 :3

m4W 4zz Z'CXX--o-'-X'-X)X'CZ.xZ'C'C'C- I0 < = -#-414 4 < IIIII11f 411 11'm11 11 4%H 1-141 44 1

in

83

Ln c LnM~t = n t C3 % C LnCa n =Ln C U- C2Ln 2 L in n L C3Ln 2 L 4= l C UC2 n C

LA- LA: W

oZ L7 C

Z~~U P-I -ttt

e d0 0) .j~ OF

I-Ix uW 0 0

C3 0

0V Ws- 4r X

wo C., C. a

H-4 U% 40 H- N wo

Z t w N t-H a-~ zr

3:. I- LJc 24 .

(I) -0 zPH 40 LA.. H LC HW UN 4

iba 0 Ni- r-i4 q5

xU WO + > +o ~0 * o LX 0 LrL * o0

w)L LU I%- =~ O c LU .0

94- ~ ~w zw ff) (\I a CJ

A. *U oP- u )*

Y- 0z C2 Oil w% z~- zX.J.).. I *U.'v4W X4 Ln *C) 0 +0,m *%0 .%0 *4LA.

W m L)C C) IUN) 3:V).I 0. -.LijLD.S X U -j evi o

09..J I ZZCHWUCOW ox% ot 0. 0 o% %I) X I~ H - V) -% V S J 01 W ZO0X i X K .. L Z 11 11 Z -r4 1;v l " C311 4 l It 11lll1 11 W11 H - 11 ). IW Z o 1-4 _j 3

% 1- 1 w'IJ J .. J *y4 r4 v-i- .-jTI .. w *-4ri JZ .JCa J 5-N

I; (X zzdz z ozz zz zzz z -z -zz uWOHW

-4 V-I C%

U%0 nC U.' up u U%'i-M N Q NI) V), ?. L

84

I 2In C2 sri C2 LIN cm .1 4= U.

IJJ LU LU U U U LULU U LU WU WW LU LU Lu

Ui)

I.,

'C.

LU

toLULi

zz

%0

a.

W) 4-1 z

T4 U4 InC) Il4 1 o% t&.O -.

o tou. .v. 01) N~ ONft *X " ) Vo 4%~? 9D.

iSQr4ZX i JZ(D.'to %

~ l-S~S~ I-- -Z i

w WW o oC

85

Lfl ~ ~ ~ ~ ~ ~ ~ ~ C U% in C= usl = n0Ii0I n0I n0t 0U il C2 in 03 in I= U, 03 in 0a n C3 10 = I% 3 U% 02

""W ~~~ w-mm IT. ljq i-Bw P 4 4 WWO =w4 w w4 m4 4T .7 MID w4 f- =4 a% M=

o 0

M I

UU

I- rH -J

w w*L LC Irw

a. wLw w AU

W 0 -vi ViI-V u -- j ""

j .1 0 10 -. 1 U I - I

. . w L i WW *)W U. 11** IINBl . L 2

W w INB- B-4B N 0= 3N 8-CBN- NV < a. 040ie qu )zC )V ~ 0 N4 w.J *411- us-4I-0jI== U

*- 1W IN - W 1-- -. . U -. 1N1 1-s _NO .- _V) +CI + 0 V). J 0Z _ x NII.- - I- -jW I LL>. ( V U ( 0tCU4 Cf LL 1-CP UU4 U t-WLV)"III*- W %W1 %0W%

-D C 4* * 9 .o* * 0 # * * * D _j* LE 4* 04C

Z Z LD !Z0. * WJ n a H O .Dt 40m 4 V a iNc V004 %O2:C. C3 " CLUI L01-5-1-H-40 C4=.* B).CU I1 1 M 4i 0. 1 =~ C2 W vw4r N I I M* in a Lt)* r4 spW I >-OUU4J1

t- H -Bf *)( *i " Bil &x a1 11 cU- 0.1 1 oili * 0~ Oil *IU Bly C o f- 1B 11i -J._.J-J J

wn x 1- -.1ww IIWW4 111 ) <4 ZWW4< 4W.1 wt .1W1W11z -jj -.D H4..J J40i J.W0U.4. j -.1 mo O44 L 44Oi.MW 1.0 44-jo MM< <<*

H MH D XX - ;- X HX XX H0 U XXXXH -> 0 M ->-0>->

86

ft-c3 Ln c2 in i at cL

ZL w - U-L . U. WI IL.L M L

C2 V

2: 0C) q42

9.4

2: 0

H Q.

U vi

w CD

U j

ICW ) . f

Z Z "V4 Vq0lC2w w ao n 1

+~ x

I-- I- C c W m

(1) 0.L V 4V)V

CcJ x< c coHt z L

va n C3

r- I87

4. PROGRAM LOGIC

The calculation procedure which has been described inthis report is performed primarily in the main program andSubroutine BQ. The calculations regarding the construction ofthe camber line, the stacking of the streamsurface bladesections, and the determination of manufacturing sections areperformed in the main program. Subroutine BQ applies thethickness distribution to the camber line and determinesquantities necessary to obtain the Cartesian coordinates ofthe section from the streamsurface coordinates. Subroutine Dlis the curve-fitting routine, and CQ is used to determineslopes of various spline curves at particular points, EQproduces the line-printer section plot in the printed portionof the output, and FQ produces axes on the section plots forIFPLOT = l 2, or 3.

A description of the calculation procedure employed inthe main program and in Subroutine BQ is described below.Each step is keyed to its location in the program by theparenthetical deck serialization.

1. The input data is read and printed. (A155-A680)

2. If precision plotting is specified, the plot is initialized,and axes produced if IFPLOT = 1 or 3. (A695-A710)

3. A loop which creates a section on each streamsurface iscommenced. (A715)

4. The axial locations of the intersections of a particularstreamsurface with the computing stations describing the bladeare determined. The meridional streamsurface length isobtained as described in Equation (1). (A720-A780)

5. The parameters relating to the streamsurface blade sectionare interpolated (or extrapolated) from the input tables. IfNSPEC = 1, they are taken to be radially uniform. If NSPEC = 2,linear interpolation is used; if NSPEC = 3, spline-curveinterpolation is employed. (A785-A840)

6. The loop to determine the optimal camber line is initiated.(A855)

7. The first estimate of true chord is calculated per£quation (2), and the solidity as in Equation (3). (A870-A910)

8. The incidence angle and extra deviation applicable to theparticular section are obtained by interpolation of the radiusat the leading edge of the streamsurface in the input tables.(A915-A920)

88

9. The section angle at the leading edge is determined as inEquation (6). (A925)

10. The quantities required for the deviation angle calculationare obtained by interpolation from various figures ofReference 2. (A935-A960)

11. The deviation angle is calculated using Equation (5).(A995-AlO00)

12. The section angle at the trailing edge is calculated usingEquation (7), and at internal points using Equation (8), withfractions of deviation obtained by radial interpolation fromthe input distributions based on the streamsurface radius atthe trailing edge of the blade. (A1020-A1085)

13. A camber line is constructed of cubic segments followingthe analysis of Equations (9) - (15) for the initial value ofS/Ro . The number of inflection points is determined. (A1090-A1350)

14. The iteration on solidity is performed until the toleranceis within the prescribed limit. (A1355-A1395)

15. Steps 13 and 14 are repeated for IPASS-l values of theS/Ro parameter. (Al40G-A1450)

16. The range of S/Ro with the minimum number of inflectionpoints is established., (A1480-A1600)

17. Steps 13, 14 and 15 are repeated for finer increments ofthe S/Ro parameter in the range determined in 16. The maximumvalue of the minimum radius of curvature in this range isdetermined. (A1645-A1690)

18. Still finer increments of S/Ro on either side of the S/Rovalue which produced the maximum value of the minimum radius ofcurvature in 17 are examined to find the optimal S/Ro value.(A1730-A1745)

19. The details of the optimal camber line are printed ifIPRINT = 0 or 1. (A1755-A1810)

20. The normalized chord length of the optimal camber line is

computed. (A1820)

21. The total streamsurface length is calculated. (A1830-A1890)

22. If IPRINT = 0 or 1, the parameters defining the sectionare printed. (B65-B115)

89

23. The coefficients of the two thickness equations arecomputed. (B175-B220)

214. At each point of the camber line, the correspondingcoordinates on each blade surface are obtained from thecoordinates and slope of the camber line, and the appropriatethickness, scaled for an overall section meridional chord ofunity. (B225-B310)

25. The section area and centroid location are determined.(B315-B365)

26. The camber line is redefined in terms of 100 points toassure sufficient points for accurate linear interpolation inthe determination of 0 (Figure 1), needed for the eventualCartesian coordinate determination. (B380-B440)

27. The various streamsurface section properties aredetermined. (B445-B560)

28. If IPRINT = 0 or 1, details of the normalized bladesection and a line-printer plot are produced. (B575-B750)

29. Sectional properties are scaled to produce the "dimensional"results. (B755-B830)

30. If IPRINT = 0 or 1, the section information is printed.(B840-B1095)

31. The coordinates of 31 points describing the leading edgeare determined. (B1070-BI080)

32. The origin of the coordinate system is shifted to thestack axis, and the relative 0 values for the blade surfacesare determined. (B1120-B1595)

33. If IFPLOT 1 or 3, the streamsurface section plot isproduced. (AI950-A2040)

34. if the calculations for aerodynamic analysis are required,various items related to the camber line are stored. (A2045-A2095)

35. The Cartesian coordinates for each point on the sectionsurface are computed, and printed if IPRINT = 0 or 1. (A2100-A2435)

36. The loop initiated in 3 is repeated for each streamsurface.(A2440)

37. Unless IPRINT = 1, the volume of the blade is computed andprinted. (A2445-A2555)

90

38. If specified, the calculations for aerodynamic analysisare performed and printed, and punched if IPUNCH = 1. (A2560-A2790)

39. If IFPLQT = 2 or 3, the axes are drawn and titled for thesuperimposed plot of the manufacturing sections. (A2800)

40. If no output relating to manufacturing sections is specifiedby either IFPLOT or IPRINT, the remainder of the program isbypassed. Alternatively, if printed details of the manufactur-ing sections are specified, a heading is printed. (A2805-A2835)

41. 'he location of each of the manufacturing planes isdetermined. (A2840-A2865)

42. The (Cartesian) coordinates of each point on the bladesurface are obtained by spline-curve interpolation at each ofthe manufacturing sections. (A2870-A2945)

43. A loop that is performed for each manufacturing section isinitiated. This loop contains the determination of sectionproperties and the output of results for the section. IfIPRINT = 0 or 2, section properties and coordinates are Drinted.(A2950-A3495)

44. If IFPLOT = 2 or 3, a plot of the manufacturing sectionsis produced. (A3510-A3605)

45. If IFPLOT = 4, an individual plot of the manufacturingsections is made. The axes are rotated clockwise until thechord line is horizontal. The angle of rotation is indicatedas the stagger angle. (A3610-A3845)

46. The loop initiated in Step 43 for each manufacturingsection is terminated. (A3850)

47. if precision plots have been made, the plotting isterminated. (A3855)

91

3' z

x

/1.Typical Point

Figure 1. Cartesian and StreamsurfaceCoordinates of a Point

92

7

6

54

STREAMSIJRFACES MANUFACTURINGP LANES

4

_ _ _ _ 3

2j2

LEADING EDGE OF BLADE\ TRAILING EDGE OF BLADE

Figure 2. Locations of Streamsurfaces and ManufacturingPlanes for Example Blade Design

93

Figure 3, Example Blade Design:Sti'eamsurface Sections

94

Figure 4. Example Blade Design:Cartesian Sections

95

REFERENCES

1. Frost, G.R., Hearsey, R.M., and Wennerstrom, A.J.= "A ComputerProgram for the Specification of Axial Compressor Airfoils,"Aerospace Research Laboratories, Wright-Pattenson AFB, Ohio,ARL 72-0171, AD 756879, December 1972.

2. Johnsen, I.A., Bullock, R.O., et al, "Aerodynamic Design ofAxial Flow Compressors," Lewis Research Center, Cleveland, Ohio,NASA SP-36, 1965,

96.

96