DOCUMENTATION PREOICTI--ETCIU) DTNSRDC/SPD-0927 ...DOCUMENTATION FOR SWATH SHIP RESISTANCE AND PROPULSION PREOICTI--ETCIU) UNCLASSIFIED DTNSRDC/SPD-0927-02 EEEEEEIIIIIEIU)lEllmllhmEEm

DOCUMENTATION FOR SWATH SHIP RESISTANCE AND PROPULSION PREOICTI--ETCIU)

UNCLASSIFIED DTNSRDC/SPD-0927-02

U)lEllmllhmEEm

EEEEEEIIIIIEIEEIIEEEEEEEIIEEEIIIIIIEEIIIEEEIIIEIIEEEEIIIIIIIIIIIIIIIlfflfflf

WIII Q8I L12.

1111112.

11111.25 4UBI6

MII 1?0( OP P ' __ IN f, IIA_

E- DAVID W. TAYLOR NAVAL SHIPC RESEARCH AND DEVELOPMENT CENTERCf) ietheudl, Maryland 20084

DOCUMENTATION FOR SWATH SHIP

0z RESISTANCE AND PROPULSION PREDICTION PROGPAMS0

0(CLOSEFIT AND SYNTHESIS):o

-- MAINTENANCE MANUAL

.,

w" Arthur M. ReedC.-

z0

0 Approved for Public Release: Distribution Unlimiteda.i DTICP U IV JUNO 11981

Ship Performance Departmentr z

0>-U.C)

z-.]. LI..

S APRIL 1981 DTNSRDC/SPD-0927-02

mPD ThSNC 58213 (240) B ~ (1 I "IM.Fo,6 l In

---- Sl L

MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS

DTNSROC

COMMANDER

TECHNICAL DIRECTOR01

OFFICER-IN-CHARGE OFFICE R.I N-CHARGECARDE ROCK ANNAPOLIS05 04

SYSTEMSDEVELOPMENTDEPARTMENT

11

AVIATION ANDSHIP PERFORMANCE SURFACE EFFECTS

DEPARTMENT DEA RTMETSDEPARTMENT

15 16

STRUCTURES 1COMPUTATION,DERTMENT MATHEMATICS AND

DEPARMENTLOGISTICS DEPARTMENT17 18

PROPULSION ANDSHPACOUSTC AUXILIARY SYSTEMSDEPARTMENT DEPARTMENT

19 27

SHIP MATERIALS CENTRALENGINEERING INSTRUMENTATIONDEPARTMENT DEPARTMENT

28 29

NI . tII H M m | ' i~

UNCLASSIFIEDYCAIFICATINO HSPG *ee ieEtrd

READ INSTRUCTIONS

12. GOVT ACCESSION NO. S. RECIPIENT'S CATALOG MUMMER

- -4be-of - -TYP OF REPORT 4 PERIOD COVERED%

SNHS5 ):MAINTENA E MANUA.- N~a~~44-TR UMBER

C 7. AUTOR~a) S. C~o TRACT OR GRANT NUMDER()

L Arthur M.'/Reed /A(

9. PERFORMING ORGANIZATION NAME *.AES9 10. PRO? N E MINT PROJECT, TASKAREA

David W. Taylor Naval Ship Research and Develop- 62543N, ZF43 4T210~ 1ment Center, Bethesda, Maryland 20084 1-1500-103

I. CONTROLLING OFFICE NAME AND ADDRESS C -l," " "j APRA

14. MONITORING AGENCY NAME & AORESS(i1 differert from. Controllin Off11ce) I5. SECURITY CLASS. (of this report)

UNCLASSIFIED

IS&. DECL ASSI FICATION/ DOWNGRADING

F SCHEDULE

IS. DISTRItNI4'IT 4E T fof this Report)

* Approved for Public Release: Distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abstract entered in Black 20, if different from. Report)

Is. SUPPLEMENTARY NOTES

IS. KCEY WORDS (Continue on reverse side if necessary and Idetilfy by block number)

Small-Waterplane-Area Twin-Hull (SWATH) ships, resistance and propulsionprediction

ABSTRACT (Continue on reverse side It necessary and Identify by block number)This report documents two computer programs which determine the wave resistanceand propulsive performance of Small-Waterplane-Area Twin-Hull (SWATH) ships.These programs are SYNTHESIS and CLOSEFIT, and they use as input data themoments and offsets of ship geometry, respectively. While they both employlinearized ship wave theory and thin-ship approximation and share many sub-routines, CLOSEFIT is a more refined program capable of furnishing superiorresults. on the other hand, SYNTHESIS is simpler and includes severaladditional subroutines which cart determine the characteristics and performance

DDIFON 1473 EDITION OF I NOV 65 IS OSSOLETE AUNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (111hen Date EnteredJ)

N, UNCLASSIFIEDt.u~iTv~ CLASSIFICATION OF THI1S PAOE(Whu, D016 Unte00

of a SWATH ship's propulsive system at both design and off-design conditions.

ii UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGt(Whsfl Dala EnterOW)

TABLE OF CONTENTSPage

LIST OF FIGURES .. ................. ......... iv

NOMENCLATURE .... ........................... v

ABSTRACT. ................................

ADMINISTRATIVE INFORMATION .. ......................

BACKGROUND .. ............................. 2

OVERVIEW OF CLOSEFIT .. .. ....................... 7

OVERVIEW OF SYNTHESIS .. ................. ...... 13

PROGRAM DOCUMENTATION OF CLOSEFIT .. ................. 15

COMMON BLOCK DEFINITIONS FOR CLOSEFIT. .. ............ 16

SUBROUTINE DOCUMENTATION FOR CLOSEFIT. .. ............ 27

4PROGRAM DOCUMENTATION OF SYNTHESIS. ................. 61

0COMMON BLOCK DEFINITIONS FOR SYNTHESIS .. ............ 63

SUBROUTINE DOCU1MENTATION FOR SYNTHESIS .. ............ 79

REFERENCES. .. ............... ............ 117

APPENDICES. .. ............... ............ 118

PROGRAM LISTING OF CLOSEFIT .. .. ................ 119

PROGRAM LISTING OF SYNTHESIS. .. ............... 171

LIST OF FIGURESPage

1 -Profile of SWATH Ship with Single Strut. ..... ........ 4

2 - Profile of SWATH Ship with Tandem Struts ..... ........ 5

3 -Tree Diagra of CLOSEFTSWATH Program .. ............ 8

4 - Tree Diagram of SYNTHESIS SWATH Program .. ............ 14

Accesslion For

1Tils GRA&IDTIC TAB

Justif i.cqe ion

Avai~leb.ty Cods

4tli andi/orsp"I al

iv

ii. NOMENCLAJLPAE

Symbol Description

A(x) Body sectional area functlon

A Maximum section area of body0

AhBm Symmetric coefficients of Chebychev sineseries for body

A Sm Symmetric coefficients of Chebychev sine

series for strut

AW Area of the waterplane

b Half of the separation distance of the hulls

BBm Anti-qmmetric coefficients of Chebychev

series for body

B Sm Anti-symmetric coefficients of chebychevsine series for strut

CA Correlation Allowance

CF Frictional resistance coefficient

CFm Form drag coefficient

Cp PBody Prismatic coefficient

C Wp Waterplane coefficient

CI1W Waterplane inertia coefficient

g Acceleration due to gravity

hB Maximum depth of submergence of axis of body

h S Maximum draft of strut

J (a) Bessel functions

LB Maximum length of body

Ls Maximum length of strut

PE Effective power

EV

NOMENCLATURE (CONT

Symbol Description

Rn Reynolds number

R Total ship resistance

% Wave resistance due to one main body

RF Frictional resistance

RFm Eddy resistance

RWS Wave resistance due to one strut

PWS Wave resistance due to the interaction

B of strut and main body

Rw Wave resistance

S Wetted surface

T Thickness of mid length of strut

t(x) Strut half thickness function

T mn Auxilalary function used in calculation ofB

RB

T (Tmax also used) Thickness of mid length of strut

T Auxiliary wave resistance function usedSBmn In calcuation of RSB

T Smn Auxiliary wave resistance function usedin calculation of RS

Um(x) Cheby chev cosine series

V Velocity of ship

Vm(x) Chebychev sin series

W Enn Auxiliary wave resistance function used incalculation of RB

VSmn Auxiliary wave resistance used Incalculation of RS

vi

NONMENCLATURE (CONT)

Symbol Description

W Auxiliary wave resistance function used inSBn calculation of RSB

Variable of Integration

Density of water

-YOB Dimensionlessnumber related to body length

and ship speed, used to remove singularities

YOS Dimensionlessnumber related to strut length

and ship speeds used to remove singularities

Variable of integration.

ENGLISH/SI EQUIVALENTS

I degree (angle) = 0.01745 rad (radians)

I foot = 0.3048 m (meters)

I foot per second (fps) = 0.3048 m/sec (meters per second)

I Inch = 25.40 mm(millimeters)

I knot = 0.5144 m/s (meters per second)

I lb (force) = 4.448 N (Newtons)

I lb (force - Inch Ibs) = 0.1130 Nim (Newton-meter)

I long ton (2240 pounds) = 1.016 metric tons; or 1016 kilograms

I power = 0.746 kW (kilowatts)

V' vii

ABSTRACT

This report documents two computer programs which determine thewave resistance and propulsive performance of Small-Waterplane-AreaTwin-Hull (SWATH) ships. These programs are SYNTHESIS and CLOSEFIT,and they use as input data the moments and offsets of ship geometry,respectively. While they both employ linearized ship wave theory andthin-ship approximation and share many subroutines, CLOSEFIT is a morerefined program capable of furnishing superior results. On the otherhand, SYNTHESIS is simpler and includes several additional subroutineswhich can determine the characteristics and performance of a SWATHship's propulsive system at both design and off-design conditions.

ADMINISTRATIVE INFORMATION

This investigation was authorized under a direct funded block from the Naval

Material Command (NAVMAT 08T23) under Program Element 62543N, Task Area ZF43-421-

001, and funded through the High Performance Vehicles Office of the David W. Taylor

Naval Ship Research and Development Center (DTNSRDC), Work Unit 1-1500-103.

.... ... . " . ... J |||1 ........ [

BACKGROUND

This report (Maintenance Manual) contains documentation for two

computer programs, CLOSEFIT and SYNTHESIS, which have been developed at

the David W. Taylor Naval Ship R&D Center (DTNSRDC) to predict the

effective and delivered power for Small-Waterplane-Area Twin-Hull (SWATH)

ships. This maintenance manual contains documentation for each subroutine

in the programs, definitions of all of the variables in the COMMON BLOCKS,

and a listing of the computer programs. This documentation is intended

for the individual who must modify the computer programs, and must

therefore be able to understand the functioning of the programs, and

should be contrasted with the Users Manual, which serves to define the

input to and output from the programs. The ability to prepare proper

input, and to use the output does not require an understanding of the

workings of the program.

SWATH ships are catamarans which combine a thin strut with a submerged

elongated slender body. Each demi-hull of the SWATH has either one

(single) or two (tandem) struts which support the lower hull. Figures 1

and 2 show schematic diagrams illustrating the geometry of single and

t-...em strut SWATH configurations, respectively.

Programs CLOSEFIT and SYNTHESIS have a similar theoretical foundation

in that they are both based on linearized ship wave theory and the thin

ship approximation in the framework of the potential flow of an incompressible,

inviscid fluid. In general, thin-ship theory can be applied to any

conventional catamaran with arbitrary camber. However, as this theory

has been specialized to SWATH configurations, the ship geometry is

2

restricted to ships with "no-cross flow" cambers. In practice, this

means SWATHS with very small strut thicknesses compared to the transverse

strut separation.

In the theory of ship resistance extrapolation, the resistance of a

ship is typically decomposed into residuary and frictional resistance

components. The frictional resistance component is generally taken as

equal to the resistance of a flat plate with area of the ship, and with

length equal to the length of the ship. The three dimensional viscous

effects are then included in the residuary resistance along with other

resistance components such as wave making resistance. For a SWATH ship,

the calculation of the frictional resistance is not as simple as stated

above, however, the same principle applies if one calculated the

frictional resistance of the bodies and struts separately.

The wave making resistance component of the residuary resistance can

be computed using inviscid fluid flow theory. However, the other

components of the residuary resistance are not easily calculated

theoretically. Because of this, the remainder of the residuary resistance

is computed empirically. The difference between the experimentally

determined residuary resistance and the theoretically determined wave

resistance is calculated for those cases where adequate experimental data

exists. These differences which are denoted as "form drag", are then

plotted as a function of strut speed-length ratio. Under the assumption

that the form drag remains unchanged f or reasonable changes of SWATH

proportions, a curve can be f aired through the individual form drag curves,

and applied to new hull forms.

Ad

3

-4

C,,

4 -J

440

x-4

co 0

-j p

PCa

c 6 4-)

CfU

-1

'4-40

0

I--

u

4.0 42c5

For the wave resistance predictions, the geometries of the body and

strut(s) are represented by modified Chebychev series. The methods used

to determine these series are the principal differences between the

programs CLOSEFIT and SYNTHESIS. The program CLOSEFIT uses an integration

technique, similar to that used to determine the coefficients of a Fourier

series, to determine the coefficients of the Chebychev series based on

the actual hull offsets. The program SNYTHESIS uses statical moments of

the strut waterplane and body to define the coefficients of the Chebychev

series. Typically, the CLOSEFIT program uses a series of 10 to 20 pairs

of terms to represent a body or strut, where each pair of terms contains

an even and an odd Chebychev function, in the same fashion that a Fourier

series consists of pairs of sine and cosine functions. The program

SYNTHESIS uses a series consisting of only three pairs of terms to

represent the body and strut. This reduction in the number of terms

results in savings of ten to forty times in the computation of the wave

resistance in SYNTHESIS as compared to CLOSEFIT.

In addition to the effective power computations, the program SYNTHESIS

also computes the delivered power which would be required to propel the

SWATH ship. The propulsion calculations are performed by a subprogram

SHPCMP and its attendant subprograms. SHPCMP determines the wake and

thrust deduction for the doeign based on empirical relations derived from

earlier SWATH propulsion experiments. The program then calculated the

optimum four bladed Troost series propeller at the design speed, along

with the off design performance of the propeller. This data along with

the effective power computations is used to calculate the delivered power.

6

OVERVIEW OF CLOSEFIT

The CLOSEFIT SWATH program is composed of several modules, each of

which consists of a number of subroutines and performs a specific func-

tion in the SWATH ship resistance calculation. Figure 1 presents a tree

diagram which reflects the relationship among all subroutines.

Subroutine CHEB evaluates the coefficients of the Chebychev series,

which represents the strut half thickness function and the body

sectional area function in wave resistance equations. This is

accomplished by calling READ, SCALE, COMPUT, CHECK and SURFACE. The

offset tables are read in by Subroutine READ, then normalized by

Subroutine SCALE. The driver Subroutine COMPUT calls Subroutine CHEV,

which in turn calls SPLINE and SUMSPL to compute the coefficients of

the Chebychev series. The integrals used to evaluate the strut

Chebychev coefficients are as follows:

Asm - - 1/2 t(sin 0) cos(2m-l)6d6

B n -n/2sm - -- T/2 t(sin 0) sin 2mOdO

where t(sin 0) is a function adopted to describe the offsets of the

strut or the body. The Cubic Spline Function Technique is used to fit an

analytic curve to the discrete offset points. Subroutine SPLINE solves

7

READ

_ SCALE SPLINE

CHEB - COMPUT - CHEV SU?4SPL,

- CHECK EVAL

L SURFACE WTSURFS - EVAL

WTSURFB - EVAL

-ECHO

_PLOTI

_PLOT 2

-PCHEB - PLOT3

_ PLOT4 - QPLOTZ5

-RINIT

-SIMPS-N

-RWAVE RINTEG - BESSJ

-BESSJ

SWATH- RE1FLKT

-PRINT

SUM

-RWOUT - FORMDR YINTP

CF ITTC

Figure 3 -Tree Diagram of CLOSEFIT SWATH Program

8

the set of simultaneous linear algebraic equations, which results from

the spline fitting procedure and obtains the second derivatives of the

analytical functions t(sin 0) at each offset point. Next, Subroutine

SUMSPL uses these second derivatives in a set of integration formulas

based on the Filon Quadrature Technique to evaluate the above trigono-

metric integrals. Subroutine CHECK evaluates the offsets approximated

from the Chebychev series in Subroutine COMPUT and prints out the

predicted offsets along with the true offsets. This permits a check on

the accuracy of the Chebychev series approximations.

Subroutine SURFACE computes the total SWATH ship wetted surface by

calling WTSURFS and WTSURFB. Subroutine ECHO echoes the input data of

the SWATH program on the printer as a check of its accuracy. Subroutine

PCHEB plots the strut half thickness curve and body sectional area

curve on the printer in order to validate the Chebychev series

approximation.

A large amount of the execution time of this program is spent in

the evaluation of the auxiliary functions, T and W, given by:

12 )2 =f d ) D ': h .o

(2n 1)(2n 1) qIW j 1

j~ f 2 2 2

2 J2 . I (0J4. I (aI J, I2,. ()J'n (a)

2m -1)(2n 1) 1 2 2b 7)[_ __ osD

(2m)( 2n)

12 ~ irn (PIJ2 1 )

9

(TSmn(2m -)I( 2n ) d l s D 2

X E SW ) )E j2m (a)j2n )

Due to the highly oscillatory nature of the integrands of these

auxiliary functions, the integration range is divided into three separate

intervals. For each interval, a particular numerical integration method

is used to improve the accuracy of the calculation. To avoid the

singularity in the denominator of the integrand, the integration variable

(ci) is replaced by Z = ci - osin the interval from yos to os+ 1.

The numerical method used in this interval is Simpson's Rule, which

uses 30 points. The central region of the integration process goes

from ci = Yo 1 to ci = max. The choice of %max is based on the require-

ment for accuracy in the numerical integration method used in this region,

where a step size is computed at a given a, and a three-point Simpson's

Rule is used until the upper integration limit of the region, cimax, is

reached.

An analytical integration formula was developed to determine the

effects of the final region, from a = cmax to a = ismax , where a is an

empirical constant which defines the upper limit of the tail region.

Beyond this point, the integration area is assumed to be negligible.

Subroutine PRINT will print the table of the T and W arrays,

provided the flag JTEST is set other than zero.

Subroutine RWOT calls SUM to evaluate the components of the wave

10

resistance, based on Lin and Day's equationsI . Form drag is evaluated

by Subroutine FORMDR, which is based on experimental data. Frictional

drag is estimated by calling Subroutine CFITTC, which is based on the CF

2curve adopted by the International. Towing Tank Conference (ITTC)

For each test speed, a table is printed showing all the components of

total ship resistance and the effective power required to tow the SWATH

ship at a constant speed.

'References are listed on page 112.

! 11

OVERVIEW OF SYNTHESIS

The procedure of the SYNTHESIS SWATH program parallels the CLOSEFIT

program in calculating total ship resistance, except in its approach to

obtaining the coefficients of the Chebychev series. In SYNTHESIS, the

waterplane area coefficients, waterplane moment, waterplane inertia,

body prismatic and body moment are used to evaluate the Chebychev

coefficients. The only other major difference between the two

programs is that SYNTHESIS includes a propeller design and optimization

program.

Figure 2 presents the tree diagram of all subroutines called by the

SYNTHESIS program. The module r4EB is much simpler in SYNTHESIS than

its CLOSEFIT counterpart due to its approach in evaluating the Chebychev

coefficients through geometvic identities as opposed to numerical integrations.

Modules RWAVE and ROUT ave identical for both programs, and in both

require a great deal of execution time.

Module FINDRG evaluates the fin drag of a SWATH ship. It is

directly excerpted from coding documented in reference (3).

Module SHPCMP can determine propeller design and off-design

performance if the propeller diameter is specified. The subroutines

used in this module are excerpted from coding documented in reference (4).

13

1~-nnx

RIN

WSURFB EVAL

_WSURFS EVAL-CHEB

_PCHEB PLOTi

_PLOT 2

_PLOT3

PLOT4 QPLOTZS

-RINIT

_SIMPSN

-RWAVE RINTEG BESSJ

-BESSJ

_REF LKT

SWATH-

-SUMl

-ROUT FORM4D YINTP

_CF ITTC

FRICT

-FINDRG- FOILSC

PRODES TROOST CALC

LBURIL

-SHPC4P- PROPP ERROR

PROPER -POLCOF

I ROOT

FTGIIRF 4 -Tree Diagram of SYNTHESIS SWATH Program

14

PROGRAM DOCUMENTATION OF CLOSEFIT

15

COMMON BLOCK DEFINITIONS FOR CLOSEFIT

16

COMMON/AUX/

PURPOSE: AUX stores the auxiliary function table.

NAME TYPE LENGTH DEFINITION

TS R (10,10) Auxiliary function T for strut

WS R (10,10) Auxiliary function W for strut

TB R (10,10) Auxiliary function T for body

WB R (10,10) Auxiliary function W for body

TSB R (10,10) Auxiliary function T for strut tobody

WSB R (10,10) Auxiliary function W for strut tobody

TS12 R (10,10) Auxiliary function T for strut 1

to strut 2

WS12 R (8,10,10) Auxiliary function W for strut ito strut 2

TB12 R (8,10,10) Auxiliary function T for body 1 tobody 2

WB12 R (8,10,10) Auxiliary function W for body 1 tobody 2

TSB12 R (8,10,10) Auxiliary function T for strut 1 tobody 2

WSB12 R (8,10,10) Auxiliary function W for strut 1 tobody 2

TSBP R (10,10) Auxiliary function T

WSBP R (10,10) Auxiliary function W

TSB12P R (10,10) Auxiliary function T

WSB12P R (10,10) Auxiliary function W

17

COMMON/NAME/

PURPOSE: NAME stores a flag indicating whether the offset data arefor the strut or the body and providing the alphanumericinformation for the strut and the body.


INCHAR I 8 INCHAR (1) = STRUT. Strut offsetdata will follow.

INCHAR (1) = BODY. Body offset datawill follow.

INCHAR (2) to INCHAR (8). Hold thealphanumeric information for the strutor the body.

NAME I 7 Temporary storage location for alpha-numeric strut or body information.

18 4

COMMtON/NORM/

PURPOSE: NORM stores the scaling factors for normalizing X and Y.


YMAX R Maximum value of Y

XDIVER R Divisor for normalizing X

YDIVER R Divisor for normalizing Y

XADDER R Number to be added to normalize X

19

COMMON/OMEGA/

PURPOSE: OMEGA stores the variables used in evaluating the auxiliary function.


NMAX I Maximum order of Chebychev Series

HSOLS R Ratio of draft of strut to lengthof strut (h /L )

HBOLB R Ratio of depth of submergence tolength of body (hb/Lb)

GAMAOS R Yos = g

R Yob , g Lb/v 2GAMAOB RYo -'19L/2

NOSEPS I Number of different hull separationdistances

SEPDIS R (8) Hull separation distance b (ft)

SEP R (8) 2b/(y os*LS)

CSTRUT R (8) Distance of CL of strut to CL of body

CSTRT2 R (8) Distance of CL of 2nd strut (if present)from CL of body2

GOSQ R Y os

hPHIS R 2(b/ss

hbPHIB R 2(7bb)/Yo

RATIOL R Yob/Yos

20

COMMON/OUT/

PURPOSE: OUT defines and stores physical constants and geometricparameters.

NAME TYPE LENGTH DEFINITION SETVALUES

HS R Draft of strut h (ft)s

HB R Depth of submergence from surface tobody centerline hb (ft)

XLS R Length of strut Ls (ft)

XLB R Length of body Lb (ft)

TSMAX R Maximum thickness of strut t (ft)max

AX R Maximum cross-sectional area of body Ax (ft 2

PI R 3.1415926535897

G R Acceleration due to gravity g (ft/sec ) 32.155

RHO R Density of water p (lb x sec 2/ft ) 1.9367

GNU R kinematic viscosity v (ft 2/sec) 1.2970 x 105

WETS R Wetted surface area of strut S (ft )s

WETB R Wetted surface area of body Sb (ft )

WTSURF R Total wetted surface area St (ft )

VMFPS R Test velocity V (fps)

DELCF R Correction allowance ACF 0.0005

TITLE (8) Array of characters containing the titleof the test

21

COMMON/PLOT/

PURPOSE: PLOT stores the constants and characters for the plotting routine

SETNAME TYPE LENGTH DEFINITION VALUES

NFIRST I Position in the arrays of the first 1ordered pair to be plotted

NLAST I Position in the arrays of the lastordered pair to be plotted 101

NPOINT I NPOINT equals "" each point from 1NFIRST to NLAST is to be plotted, "2"if every other point is to be plotted,etc.

NMAX R Value of abscissa at right-most grid 1.0line

XMIN R Value of abscissa at left-most grid -1.0line

NSCLI L Logical value (Should be false if PLOTIhas not been called and standard grid isdesired)

NCHAR I Number of valid characters in label

NSCALE 1 (4) Printing scale factor of ordinate

PCHAR I (2) Plotting characters

22

COMON/PSI /

PURPOSE: PSI stores the parameters for the integration procedureSET

NAME TYPE LENGTH DEFINITION VALUES

NPTSZ I Number of integration steps from 31y to y+l (odd number)Os Os

PTSAF R Scaling factor of step size in 10.0integrating from qmax to aksmax

EXPN R Empirical constant for intergra- 7.0tion to stop

NALMAX I Maximum number of integration steps 300from y+l to a

OS max

NAL I Counter of integration steps

TAIL R Integration made from a to (Asmax

ALFA R Integrating variable (a)

ALMAX R Upper limit of a for integration

NSTEPS I Number of integration steps froma to amax o smax

23

COMONI PLTPF EG/DEIIIN-

PURPOSE: XRPLOTF stores the values of variables for the plotting routine

XL R Value of abscissa at left-most grid line

XHI R Value of abscissa at right-most grid line

YL Rt Value of ordinate at bottom grid line

YR R Value of ordinate at top grid line

KMOV R Abscissa index increment numberofor array GRAF

YMOV Rt Ordinate index increment number for array GRAF

24

COMMON/XRPLOTG/

PURPOSE: XEPLOTG stores the values and characters of variables for theplotting routein


GR~AF 1 (11,204) Array containing the image to be plotted

25

COMMON/XRPLOTQ/

PURPOSE: XRPLOQ stores the constants and characters for the plotting routineSET

NAME TYPE LENGTH DEFINITION VALUES

II I Ordinate scale factor

JJ I Ordinate scale factor

KK I Ordinate scale factor

LL I Ordinate scale factor

NHL I Number of horizontal grid lines 6

NSBH I Number of spaces between adjacent 10horizontal grid lines

NVL I Number of vertical grid lines 11

NSBV I Number of spaces between adjacent 10vertical grid lines

NCHAR I Plotting character of horizontal grid IH.lines

VCHAR I Plotting character of vertical grid 1H.lines

IY I Number of vertical spaces

Ix I Number of horizontal spaces

V L Logical variable, - . TRUE . when themaximum and minimum values of the oridinateare determined

H L Logical variable, - . TRUE . when themaximum and minimum values of the abscissaare determined

26

SUBROUTINE DOCUMENTATION F~OR CLOSEFIT

27

NAME: PROGRAM SWATH

PURPOSE: Program SWATH is the main program for theCLOSEFIT resistance prediction of Small-Water-plane-Area Twin-Hull Ships

CALLING SERVICE: Program SWATH (INPUT, OUTPUT, TAPE5 - INPUTTAPE6 - OUTPUT, TAPE8)

ARGUMENTS: NONE

COMMON BLOCKS: OUT, AUX, O MEGA, PSI, COEFS

SUBROUTINES CALLED: CHEB, ECHO, PCHEB, PRINT, RWAVE, RWOUT

COMMENTS:

28

NAME: SUBROUTINE BESSJ

PURPOSE: SUBROUTINE BESSJ evaluates the Bessel functionfrom order 0 to order N.

CALLING SEQUENCE: CALL BESSJ (X, N, VJ)

ARGUMENTS: X Argument of the Bessel functionN Maximum order of the Bessel functionVJ Array holding (N+I) values of the Bessel4

function of order zero up to N, where

VJ(o) = Jo(X)

VJ(N) : JN(X)

COMMON BLOCKS: NONE

SUBROUTINE CALLED: NONE

CALLED BY: RINTEG, RWAVE

COMMENTS:

29

NAME: FUNCTION CFITTC

PURPOSE: Function CFITTC determines the ITTCfrictional resistance coefficientC

CALLING SEQUENCE: CF = CFITTC (RN)

ARGUMENT: RN Reynolds number R nat test condition

COMMO0N BLOCKS: NONE


CALLED BY: RWOUT

COMMENTS: C .7

[1og10(Rn) -212

30

NAME: SUBROUTINE CHEB

PURPOSE: Subroutine CHEB computes from offset tablesthe coefficients of the Chebychev Series,which is an approximation of the outline ofthe waterplane area or body cross-sectional

area curve.

CALLING SEQUENCE: CALL CHEB (AMC, BMC, MMAX)

ARGUMENTS: AMC Coefficients of the ChebychevCosine Series

BMC Coefficients of the ChebychevSine Series

MMAX Maximum order of the ChebychevSeries

COMMON BLOCKS: NAVME, OFFSET

SUBROUTINES CALLED: READ, SCALE, COMPUT, CHECK, SURFACE

CALLED BY: SWATH

COMMENTS:

31


PURPOSE: Subroutine CIEB computes from offset tablesthe coefficients of the Chebychev Series,which is an approximation of the outline ofthe waterplane area or body cross-sectionalarea curve.

CALLING SEQUENCE: CALL CHEB (AMC, BHC, NIAX)

ARGUMENTS: AIC Coefficients of the ChebychevCosine Series

B C Coefficients of the ChebychevSine Series

M AX Maximum order of the Chebychev

Series

CO,%1%ON BLOCKS: NAME, OFFSET

SUBROUTINES CALLED: READ, SCALE, COHPUT, CHECK, SURFACE

CALLED BY: SIVTH

COILMENTS:

32

NAME: SUBROUTINE CHECK

PURPOSE: Subroutine CHECK evaluates the Chebychev Seriesfrom the Cheby-hev coefficients obtained fromSubroutine COMPUT and prints out theevaluated offset table for manual checking.

CALLING SEQUENCE: CALL CHECK (AMC, BMC, MMAX, ISBODY)



MMAX Maximum order of the Chebychevpolynomial

ISBODY Logical flag, indicating "Is this

for body?"ISBODY =" jTRUE for body

t FALSE for strut

COMMON BLOCKS: OFFSET, NAME

SUBROUTINE CALLED: EVAL

CALLED BY: CHEB

CONMENTS:

33

NAME: SUBROUTINE CHEV

PURPOSE: Subroutine CHEV uses the offsets to computethe Chebychev coefficients via splineapproximation and numerical integration.

CALLING SEQUENCE: AMC Coefficients of the ChebychevCosine Series


MMAX Maximum order of the Chebychevpolynomial

ISBODY Logical flag, indicating "Is thisfor body?"

I. TRUE for bodyISBODY

FALSE for strut

COMMON BLOCKS: OFFSET, NAME

SUBROUTINES CALLED: SPLINE, FUNCTION SUMPSPL

CALLED BY: COMPUT

COMMENTS:

34

NAME: SUBROUTINE COMPUT

PURPOSE: Subroutine COMPUT initiates the computationof the Chebychev coefficients.

CALLING SEQUENCE: CALL COMPUT (AMC, BMC, MMAX, ISBODY)



MMAX Maximum order of the Chebychevpolynomials

ISBODY Logical flag, indicating "Is thisfor body?"

f. TRUE for bodyISBODY

* FALSE for strut

COMMON BLOCKS: OFFSET, NAME, NORM

SUBROUTINE CALLED: CHEV

CALLED BY: CHEB

COMMENTS:

35

NAME: SUBROUTINE ECHO

PURPOSE: Subroutine ECHO prints a summary of input data andthe Chebychev coefficients

CALLING SEQUENCE: CALL ECHO (NLOC)

ARGUMENT: NLOC Number of strut locations to betested

COMMON BLOCKS: AUX, OMEGA, OUT


CALLED BY: SWATH

COM14ENTS:

36

NAME: SUBROUTINE EVAL

PURPOSE: Subroutine EVAL evaluates the Chebychev Seriesat a given station.

CALLING SEQUENCE: CALL EVAL (XX, MMAX, FFSET, AMC, BMC)

ARGUMENTS: XX Value of X station on a range of-1 to +1

MMAX Maximum order of the Chebychev

polynomial

FFSET Offset approximated by the ChebychevSeries

AMC Coefficients of the Chebychev CosineSeries

BMC Coefficients of the Chebychev SineSeries

COMMON BLOCKS: NONE


CALLED BY: CHECK

COMMENTS:

37

NAME: FUNCTION FORMDR

PURPOSE: Function FORMDR evaluates the formdrag coefficient, based on experimental data

CALLING SEQUENCE: FOR = FORMDR (VL)

ARGUMENT: VL Ratio of ship speed to length ofstrut V//Tj

CO40N BLOCKS: NONE

SUBROUTINE CALLED: FUNCTION YINTP

CALLED BY: ROUT

COMMENTS: Form dra& is assumed to be 0.5 x 10 - 3

for V//LS less than 1.325 and greater than 2.5

1.0.9

L6L

U

0J

4C .4

0.5 1.0 1.5 w 30

38

NAME: SUBROUTINE PCHEB

PURPOSE: Subroutine PCHEB plots by line printer thebody sectional area curve and waterplaneoutline curve from the given Chebychevcoefficients

CALLING SEQUENCE: CALL PCHEB (AS, BS, AB, BB, NN, TITLE)

ARGUMENTS: AS Coefficients of Chebychev SineSeries for strut

BS Coefficients of Chebychev CosineSeries for strut

AB Coefficients of Chebychev SineSeries for body

BB Coefficient of Chebychev CosineSeries for body

NN Maximum order of Chebychev Series

TITLE Array containing the alphanumericcharacters of the title of the experi-ment

COMMON BLOCKS: PL(Y, XRPLOTQ

SUBROUTINES CALLED: PLOTI, PLOT2, PLOT3, PLOT4

CALLED BY: CHEB

COMMENTS:

39

NAME: SUBROUTINE PLOT1

PURPOSE: Subroutine PLOTI sets up spacing anddetermines the values of the axes.

CALLING SEQUENCE: CALL PLOT 1 (NSCALE, A, B, C, D, E, F)

ARGUMENTS: NSCALE Integer array defined asfollows:

NSCALE (1) - I, if printed values of theordinate are 10 ** I timesthe actual value

NSCALE (2) - J, if printed values of theordinate are 10 ** J timesthe actual value

NSCALE (3) - K, if printed values of theabscissa are 10 ** K timesthe actual values

NSCALE (4) - L, if printed values of theabscissa are 10 ** L timesthe actual value

A Integer number ofhorizontal grid lines

B Integer number of spacesbeyond each horizontal gridline to the next grid line

C Integer number of verticalgrid lines

D Integer number of spacesbeyond each vertical gridline to the next grid line

E Horizontal grid character

F Vertical grid character

COMMON BLOCK: XRPLOTQ


CALLED BY PCHEB

COMMENTS:

40


PURPOSE: Subroutine PLOT2 examines the minimum andmaximum values of the abscissa and theordinate and establishes an internalformula for computing location in the imageregion corresponding to the point to beplotted.

CALLING SEQUENCE: CALL PLOT2 (XMAX, XMIN, YMAX, YMIN, NSCLI)

ARGUMENTS: XMAX Value of abscissa at right-mostgrid line

XMIN Value of abscissa at left-mostgrid line

YMAX Value of ordinate at top gridline

YMIN Value of ordinate at bottom gridline

NSCLI Logical flat (should be .FALSE.,

if PLOT1 has not been called andstandard grid is desired)

COMMON BLOCKS: XRPLOTF, SRPLOTQ, XRPLOTG


CALLED BY: PCHEB

COMMENTS:

41


PURPOSE: Subroutine PLOT3 assigns an alpha-characterto each point to be plotted.

CALLING SEQUENCE: CALL PLOT3 (PCHAR, X, Y, SDATA, FDATA, DDATA)

ARGUMENTS: PCHAR Plotting characterX Array containing the X coordinates

to be plottedY Array containing the Y coordinates

to be plottedSDATA Integer position in the arrays of

the first ordered pair to be plottedI if each point from SDATA to DDATAis to be plotted

FDATA 2 if every other point is to beplotted3 if every third point is to beplotted

DDATA Integer position in the array of thelast ordered pair to be plotted

COMON BLOCKS: XRPLOTF, XRPLOTG


CALLED BY: PCHEB

COWENTS:

42


PURPOSE: Subroutine PLOT4 prints the image of thecompleted graph on the printer, includingthe values of the abscissa and the ordinateat the grid lines outside the bottom andleft edge of the graph.

CALLING SEQUENCE: CALL PLOT4 (MCHAR, NCIHAR)

ARGUMENTS: MCHAR Single dimension array containingalpha-characters to be plotted atthe left of the graph

NCHAR Number of valid characters inMCHAR

COMMON BLOCKS: XRPLOTF, XRPLOTG, XRPLOTQ

SUBROUTINE CALLED: QPLOTZ5

CALLED BY: PCHEB

COMMENTS:

43

NAME: SUBROUTINE PRINT

PURPOSE: Subroutine PRINT prints the auxiliaryfunction tables of T and W.

CALLING SEQUENCE: CALL PRINT (I, NLOC2)

ARGUMENTS: I Index indicating strut locationNLOC2 Flag indicating the presence of

a second strutN0 if single strut

2 1 if tandem struts

COMMON BLOCKS: OUT, AUX, OMEGA


CALLED BY: SWATH

COMMENTS:

44

NAME: SUBROUTINE QPLOTZ5

PURPOSE: Subroutine QPLOTZ5 calculates the scalinginformation needed to generate the formatto label the left-hand side of the program.

CALLING SEQUENCE: CALL QPLOTZS (PDQ)

ARGUMENT: PDQ Scaling factor for ordinate plot

COMMON BLOCKS: XRPLOTF, XRPLOTQ

SUBROUTINES CALLED: NONE

COMMENTS:

45

NAME: SUBROUTINE READ

PURPOSE: Subroutine READ reads the offset data ofthe strut or body and checks for error.

CALLING SEQUENCE: CALL READ

ARGUMENTS: NONE



CALLED BY: CHEB

COMMENTS:

46

7I

NAME: SUBROUTINE REFLKT

PURPOSE: Subroutine REFLKT reflects all thesymmetrical matrices of T and W.

CALLING SEQUENCE: CALL REFLKT

ARGUMENTS: NONE

COMMON BLOCKS: AUX, OMEGA


CALLED BY: RWAVE

COMMENTS:

47

-,.- --. , - - --i

NAME: SUBROUTINE RINIT

PURPOSE: Subroutine RINIT initializes the T and Warrays to zero.

CALLING SEQUENCE: CALL RINIT

ARGUMENT: NONE



CALLED BY: RWAVE

COMMENTS:

48

NAME: SUBROUTINE RINTEG

PURPOSE: Subroutine RINTEG evaluates the integrandfor T and W functions.

CALLING SEQUENCE: CALL RINTEG (ALFA, B, D, NLOC2, WTINT,SEPCOS, SQ)

ARGUMENTS: ALFA Integrating variable aB CSTRUT (I) / XLSD CSTRT2 ([)/XLSNLOC2 Flag indicating the presence of

a second strut(O if single strut

NLOC21 if tandem struts

WTINT Reighting constant for theintegrand

SEPCOS Value of the cosine function inthe integrand

SQ Value of part of the integrand

1(a2 _ -2)


SUBROUTINE CALLED: BESSJ

CALLED BY: RWAVE

COMMENTS:

49

=' -2 .. . . ... -I

NAME: SUBROUTINE RWAVE

PURPOSE: Subroutine RWAVE computes the auxiliaryfunction of T and W.

CALLING SEQUENCE: CALL RWAVE (B, D, NLOC2)

ARGUMENTS: B CSTRUT (I)/XLSD CSTRT2 (I)/XLSNLOC2 Flag indicating the presence

of a second strut

=0 if single strut

1 if tandem struts

COMMON BLOCKS: OUT, AUX, OMEGA, PSI

SUBROUTINES CALLED: RINIT, SIMPSN, RINTEG, BESSJ, REFLKT

CALLED BY: SWATH

COMMENTS:

Typical Auxiliary Functions

. T~is.(2m-IX2n-1) I DJ 1(~,J a (a 1-b 7os)xEI(a()WS"0 a- -- o2s O'Ls' S io 2 |, (a) J2. , ,

where

Es .

SI-Sfos (2u' )

50

_ _~~ . . °_, J,. .,. ' . .

NAME: SUBROUTINE RWOUT

PURPOSE: Subroutine RWOUT computes and prints dragcoefficients and total resistance of thetest model.

CALLING SEQUENCE: CALL RWOUT (I, NLOC2)

ARGUMENTS: I Index indicating strut locationNLOC2 Flag indicating the presence of

a second strut0 if single strut

NLOC 21if tandem struts

COMMON BLOCKS: OUT, AUX, OMEGA

SUBROUTINES CALLED: SUM, FUNCTION FORMDR, FUNCTION CFIT'C

CALLED BY: SWATH

COMMENTS:

'P51

NAME: SUBROUTINE SCALE

PURPOSE: Subroutine SCALE ccmputes scaling factorsand scales the input for length between-1.0 and +1.0 maximum beam and sectionalarea to 1.0.

CALLING SEQUENCE: CALL SCALE (ISBODY)

ARGUMENT: ISBODY Logical flag indicating, "Is thisfor body?"

ISBODY= TRUE . for body

FALSE. for strut



CALLED BY: CHEB

COMMENTS:

52

NAME: SUBROUTINE SIMPN

PURPOSE: Subroutine SIMPSN sets up Simpson'smultipliers for numerical integration by

Simpson's rule.

CALLING SEQUENCE: CALL SIMPSN (NPTS, SIMP)

ARGUMENTS: NPTS Number of integration stepsSIMP Array containing Simpson's

multipliers

COMMON BLOCKS: NONE


CALLED BY: RWAVE

COMMENTS:

53

NAME: SUBROUTINE SPLINE

PURPOSE: Subroutine SPLINE fits smooth splinesegments through a given set of discretedata points.

CALLING SEQUENCE: CALL SPLINE (X, Y, D, N, BC, KODE, KKODE,ISBODY)

ARGUMENTS: X Value of abscissas of offset dataY Value of ordinates of offset dataD Value of second derivatives at a

pointN Total number of offset data

pointsBC Value of boundary conditions

0 if user is specifying boundary

conditionsKODE = 1 if user is taking an extra-

polation of second derivativesas boundary conditions

0 if there is no printout fromspline routine

KKOOE = I if spline prints abscissas,ordinates and second derivatives

ISBODY Logical flag indicating, "Is thisfor body?"

SOD TRUE . for bodyISBODY =

K FALSE . for strut

COMMON BLOCKS: NONE


CALLED BY: CHEV

COMMENTS:

54

- - -

NAME: SUBROUTINE SUM

PURPOSE: Subroutine SUM computes sums of the form:

M NE E {Asm Asn Tsmn + Bsm Bsn Wsmn}

m=l n=l

CALLING SEQUENCE: CALL SUM (L, SUM1S, SUM1B, SUMISB, SUM12S,SUM12B, SUM12SB)

ARGUMENTS: L Number of different hullseparation distances

SUMiS Partial sum for strut 1SUM1B Partial sum for body 1SUMlSB Partial sum for interaction

between strut I and body 1SUM12S Partial sum for interaction

between strut 1 and strut 2SUM12B Partial sum for interaction

between body 1 and body 2SUM12SB Partial sum for interactions

between strut 1 and body 2 orstrut 2 and body 1

COMMON BLOCKS: AUX, OMEGA, COEFS


CALLED BY: RWOUT

COMMENTS:

SUMIS

SUM412S IWSJTI ---- M .S1

%. -0

5UM12SBODY I B5ODY

SUM18

55

NAME: FUNCTION SU4SPL

PURPOSE: Function SUMSPL uses the spline coefficientsand integrates the trigonometric integralsF(X)*SIN(AK*X) or F(X)*COS(AK*X).

CALLING SEQUENCE: SUM = SUMSPL (X, Y, S, N, AK, KODE)

ARGUMENTS: X Values of abscissas of offset dataY Values of ordinates of offset dataS Values of second derivativesN Total number of data pointsAK (2m-1) or Oml m = 1,2,3 . ..MMAX

+1 if sine integration desiredKODE

D -1 if cosine integration desired

COMMON BLOCKS: NONE


CALLED BY: CHEV

50j

I

NAME: SUBROUTINE SURFACE

PURPOSE: Subroutine SURFACE finds the wetted surfacearea of the strut or body as well as thewaterplane area or displaced volume.

CALLING SEQUENCE: CALL SURFACE (AMC, BMC, MM1XX, ISBODY)



MMAX Maximum order of the Chebychevpolynomials

ISBODY Logical flag indicating "Is thisfor body?"

rD TRUE for bodyISBODY =

K FALSE for strut

COMMON BLOCKS: OUT, NAME

SUBROUTINES CALLED: WTSURFS, WTSURFB

CALLED BY: CHEB

COMMENTS:

57

NAME: SUBROUTINE WTSURFB

PURPOSE: Subroutine WTSURFB determines the surfacearea of a body of revolution given by theChebychev coefficients.

CALLING SEQUENCE: CALL WTSURFB (AMC, BMC, MMAX)


BMIC Coefficients of the ChebychevSine Series

WMAX Maximum order of the ChebychevSeries

COMMON BLOCK: OUT


CALLED BY: SURFACE

COMMENTS:

58

NAME: SUBROUTINE WTSURFS

PURPOSE: Subroutine WTSURFS determines the wettedsurface area of a strut whose thicknessdistribution is given by the Chebychevcoefficients.

CALLING SEQUENCE: CALL WTSURFS (AMC, BMC, MMAX)

ARGUMENTS: AMC Coefficients of Chebychev CosineSeries

BMC Coefficients of Chebychev SineSeries

MMAX Maximum order of ChebychevSeries

COMMON BLOCK: OUT


CALLED BY: SURFACE

COMMENTS:

59

NAME: FUNCTION YINTP

PURPOSE: Function YINTP interpolates through a set ofdiscrete data.

CALLING SEQUENCE: FR = YINTP (XA, X, Y, N)

ARGUMENTS: XA Point to be interpolatedX Array of ordinate dataY Array of abscissa dataN Number of data points

COMMON BLOCKS: NONE


CALLED BY: FORMDR

COMMENTS: Uses linear interpolation

60

j 4

PROGRAM DOCUMENTATION OF SYNTHESIS

61

COMMON BLOCK DEFINITIONS FOR SYNTHESIS

62

COMON/AUX/

PURPOSE: AUX stores the auxiliary wave resistance function table.


TS R (3,3) Auxiliary function T for strut

WS R (3,3) Auxiliary function W for strut

TB R (3,3) Auxiliary function T for body

WB R (3,3) Auxiliary function W for body

TSB R (3,3) Auxiliary function T for strut tobody

WSB R (3,3) Auxiliary function W for strut tobody

TS12 R (3,3) Auxiliary function T for strut 1to strut 2

WS12 R (3,3) Auxiliary function W for strut Ito strut 2

TBI2 R (3,3) Auxiliary function T for body I tobody 2

WB12 R (3,3) Auxiliary function W for body 1 tobody 2

TSBl2 R (3,3) Auxiliary function T for strut I tobody 2

WSB12 R (3,3) Auxiliary function W for strut 1 tobody 2

TSBP R (3,3) Auxiliary function T

WSBP R (3,3) Auxiliary function W

TSB12P R (3,3) Auxiliary function T

WSB12P R (3,3) Auxiliary function W

63

CO140N/BARCK/IE /

PURPOSE: BARCK stores the variables which define the propulsordesign condition.


IE I Error message pointer

0,if program ran in normal fashion

lO0,if limiting value of P/D has been used

200,if there is an iteration malfunction -- PD(2)used for P/D

SE -- 3,if maximum BAR, 0.95, used -- marine screw

4,if minimum BAR, .4, used -- marine screw

5,if maximum tip speed used -- air screw

6,if blade number is outside program limit --

closest number used

64

COMtON/CDESC/

PURPOSE: CDESC stores the values of constants which define waterproperties.


RHOD R (3) Water density array

ANUD R (3) Kinematic viscosity array

IP I Pointer indicating the particularwater condition used. Set IP Ifor this program to obtain sea watercondition.

65

COM1ON/COEFS/

PURPOSE: COEFS stores the values of the Chebyehev coefficients forthe strut and body.


ASM R (3) Coefficients of Chebychev Sine Series for strut

BSM R (3) Coefficients of Chebychev Cosine Seriesfor strut

ABM R (3) Coefficients of Chebychev Sine Series forbody

BBM R (3) Coefficients of Chebychev Cosine Seriesfor body

M!AX I Maximum order of Chebychev Series

66

- r - - -

COMMON/CPROP/

PURPOSE: CPROP stores the values of the variables and constantsused in the propulsor design routine.


IPTYP I (3) Indicating propeller type

DIAM R (3) Diameter of propeller (ft)

VADES R (3) Speed of advance of propulsor at designcondition (kts)

RPMDES R (3) RPM of propeller at design point

TDES R (3) Thrust of propulsor system (lbs)

QDES R (3) Torque of propulsor system (ft-lbs)

EFFDES R (3) Efficiency of propulsor at designcondition

OMWTD R (3) Thrust wake (1-wT)

CAV R (3) Percent back cavitation allowed on water

screw

Z I (3) Number of blades of propeller

H R (3) Depth of water to centerline ofpropulsor shaft

BAR R (3) Blade area ratio

PD R (3) P/D of propulsor

3 R (3) J of propulsor

IERROR I (3) Error message indicator

KT R (3) Thrust coefficient (1T)

KQ R (3) Torque coefficient (K )

p

67

COWION/INPUT/

PURPOSE: INPUT stores input data.


XLS R Length of strut L (ft)

HS R Draft of strut HS (ft)

TSMAX R Maximum thickness of strut t (ft)maxCWP R Waterplane area coefficient C - AW/(L t

where AW - waterplane are of one strut

CLCF R Waterplane moment coefficientCLCF Mx/(AL)*

CIYY R Waterplane inertia coefficient,C .... I I(A • Ls&)*

XLB R Length of body LS (ft)

HE R Draft of body HS (ft)

AX R Maximum cross-sectional area of body AX (ft 2

CP R Body prismatic coefficient C - h/(A, Lb)where Vb - displaced volume of one boay

CLCB R Body moment coefficientCLCB MxB/(Ve - Le)*

SEPDIS R Separation distance between centerline of thetwo bodies (ft)

CSTRUT R Distance from centerliue of strut tocenterline of body (ft)

CSTRT2 R Distance from centerline of second strut

to centerline of body (ft)

PDIA R Diameter of propeller D (ft)

SPAN R Span of a demi-fin (ft)

CHORD R Chord of a fin (ft)

TFINS R Maximun thickness of a demi-fin (ft)

NLOC I Switch indicating the presence of asecond strut

•All moments and moments of Inertia are taken about the mid-length of the

respective strut or body.

68

COMMON/OFFDES/

PURPOSE: OFFDES stores the variables which define the coefficientsof KT/KQ curves.


PJAY R (4) Coefficients of polynomial representingKT or KQ.

I P

69

COt.ON/OMEGA/

PURPOSE: OMEGA stores the values of variables and constants forevaluation of auxiliary functions and ship resistancecoefficients.


VMFPS R Speed of shipV K (kts)

GAMAOS R - g Ls/V2 where U is speed in fps

GAMAOB R Yob - g Lb/V 2

GOSQ R (Yos) 2

HSOLS R Ratio of draft to length of strut H s/LS

HBOLB R Ratio of draft to length of body Rb/Lb

WETS R Wetted surface area of strut S (ft2 )S

WETB R Wetted surface area of body Sb (ft2)

WETFIN R Wetted surface area of a fin Sf (ft2 )

WTSURF R Total wetted surface area

SEP R 2b/'os" Ls)

PHIS R h2 1 )yos

PHIB R hS

RATIOL R Yob/Yos

CFS R Frictional drag coefficient of strut CF

CFB R Frictional drag coefficient of body CF

APPDRG R Appendage drag (lb)

70

- - -.. .%

COMMON/PCOF/

PURPOSE: PCOF stores coefficients for KQ/KT polynomial

approximation.


CT R (4) Coefficients of the polynomial which

is an approximation of the KT curve

CQ R (4) Coefficients of the polynomial which

is an approximation of the KQ curve

71

COMMON/PHYSCO/

PURPOSE: PHYSCO stores physical constants.


RHO R Density of water

GNU R Kinematic viscosity of water

G R Acceleration due to gravity

PI R Ratio of circumference to diameter of acircle

DELCF R Correction allowance of friction dragfrom ITTC line.

72

--- --

COMMON/PLOT/

PURPOSE: PLOT stores the constants and characters for the plotting

routine.


NFIRST I Position in the arrays of the firstordered pair to be plotted

NLAST I Position in the arrays of the lastordered pair to be plotted

NPOINT I NPOINT equals "1" if each point fromNFIRST to NLAST is to be plotted, "2"if every other point is to be plotted,etc.

XMAX R Value of abscissa at right-most grid line

XMIN R Value of abscissa at left-most grid line

NSCLI L Logical value (Should be false if PLOTI

has not been called and standard grid is

desired)

NCHAR I Number of valid characters in label

NSCALE I (4) Printing scale factor of ordinate

PCHAR I (2) Plotting characters

73

777-

COMMON/PSI/

PURPOSE: PSI stores the values of the variables and constants usedin integration routines.


NPTSZ I Number of integration steps from y to y+l

PTSAF R Scaling fpctor of step size in integratingfrom %max to CtZsmax

EXPN R Empirical constant for integration to stop

NALMAX R Maximum number of integration steps fromy+l to amax

NAL I Counter of integration steps

TAIL R Integration correction made from amax to

tZsmax

ALFA R Integrating variable (a)

ALSMAX R Maxivim of a for integration

NSTEPS I Number of integration steps from amax toa91smax

74

. .. ... . m i .. . . .. .I " l... ' . . .. .

COMMON/ROOTC/

PURPOSE: ROOTC stores the coefficients of a third order polynomialwhich is the approximation of the KT curve of a propeller.


A R 4 Array holding the coefficient of a thirdorder polynomial which is the approximationof the KT curve of a propeller

7 5

C0144N/XRPLOTF/

PURPOSE: XRPLOTF stores the values of variables for the plottingroutine.


XL R Value of abscissa at left-most grid line

XH R Value of abscissa at right-most grid line

YL R Value of ordinate at bottom grid line

YH R Value of ordinate at top grid line

XMOV R Abscissa index increment number for array GRAF

YMOV R Ordinate index increment number for array GRAF

76

COMMON/XRPLOTG/

PURPOSE: XRPLOTG stores the values and characters of variables forthe plotting routine.


GRAF I (11,204) Array containing the image to be plotted

77

COMMON/XRPLOTQ

PURPOSE: XRPLOTQ stores the constants and characters for the plotting

routine.


I I Ordinate scale factor is 10I

J I Number digits following ordinate decimalpoint

K I Abscissa scale factor is 1 0K

L I Number digits following abscissa decimal

point

NHL I Number of horizontal grid lines

NSBH I Number of spaces between adjacenthorizontal grid lines

NVL I Number of vertical grid lines

NSBV I Number of spaces between adjacentvertical grid lines

HCHAR I Plotting character of horizontalgrid lines

ISX I Number of horizontal spaces

ISY I Number of vertical spaces

V L Logical variable, = . TRUE . when themaximum and minimum values of the ordinateare determined

H L Logical variable, = TRUE . when themaximum and minimum values of the abscissaare determined

78

SUBROUTINE DOCUMENTATION FOR SYNTHESIS

79

NAME: PROGRAM SYNTH

PURPOSE: Program SYNTH is the main program forcalculating the propulsor resistance anddesign for SWATH ships.

CALLING SEQUENCE: PROGRAM SYNTH (INPUT, OUTPUT, TAPE 5

INPUT, TAPE 6 =OUTPUT, TAPE 8)

ARGUMENTS: NONE

COMMON BLOCKS: COEFS, INPUT, OMEGA, PHYSCO, PSI

SUBROUTINES CALLED: RIN, CHEB, RWAVE, FINDRG, ROUT, SHPCMP,

Function CFITTC

COMM4ENTS:

80

NAME: SUBROUTINE BESSJ

PURPOSE: Subroutine BESSJ evaluates the Bessel functionfrom order 0 to order N.

CALLING SEQUENCE: CALL BESSJ (X, N, VJ)

ARGUMENTS: X Argument of the Bessel functionN Maximum order of the Bessel functionVJ Array holding (N+I) values of the

Bessel function of order zero up toN, where

VJ(O) = Jo(X)

VJ(N) JN(X)

COMMON BLOCKS: NONE


CALLED BY: RINTEG, RWAVE

COMMENTS:

81

I

NAME: SUBROUTINE BURIL

PURPOSE: SUBROUTINE BURIL uses Burrill's cavitationcriteria to determine if the blade arearatio (BAR) used is sufficient and, if itis not, to estimate what BAR is necessary.

CALLING SEQUENCE: CALL BURIL (T, D, H, VA, N, CAVI, BAR,IERROR, PD, NRET)

ARGUMENTS: T Thrust of propeller (lbs)D Diameter of propeller (ft)H Depth of propeller shaft (ft)VA Speed of advance (fps)N RPM of propellerCAVI Percent back cavitation allowedBAR Blade area ratioIERROR Error message indication as defined

in Common Block BARCKPD P/D of propellerNRET Internal flag indicating BAR

optimization

rO if not optimizedNRET

1 if optimized

COION BLOCK: BARCK


CALLED BY: PRODES

COMMENTS:

82

- i&A

NAME: FUNCTION CALC

PURPOSE: FUNCTION CALC calculates "KT" or "KQ" fortwo to seven-bladed propellers, given J,BAR, P/D, Z, and an indicator for "K'T" or

~"KQ ."

CALLING SEQUENCE: TQ : CALC (J, BAR, PD, Z, ITQ)

ARGUMENTS: J Advance coefficient of propellerBAR Blade area ratioPD P/D of propellerZ Number of bladesITQ Index defined by

I if thrust is inputITQif power is input

COMMON BLOCK: OFFDES


CALLED BY: TROOST, ROOT, POLCOF

COMMENTS:

83

NAME: FUNCTION CFITTC

PURPOSE: Function CFITTC determines the ITTCfrictional resistance coefficient C7

CALLING SEQUENCE: CF = CFITTC (RN)

ARGUMENT: RN Reynolds number at R at test conditions

COMMON BLOCKS: NONE


CALLED BY: SYNTH

COMMENTS: 0.075

C[logl 0(Rn) -2]

84


PURPOSE: Subroutine CHEB determines the Chebychevcoefficients and wetted surface area ofthe strut and body. It also plots thestrut waterline and the body areadistribution.

CALLING SEQUENCE: CALL CHEB (TITLE)

ARGUMENT: TITLE Array containing the 9lphanumeric char-acters of the title of the experiment

COMMON BLOCKS: COEFS, INPUT, OMEGA, PHYSCO

SUBROUTINES CALLED: WSURFB, WSURFS, PCHEB

CALLED BY: SYNTH

COMM.ENTS:

85

I-NAME: SUBROUTINE ERROR

PURPOSE: Subroutine ERROR prints the error message of

the propulsor design.

CALLING SEQUENCE- CALL ERROR (IE)

ARGUMENT: IE Error message pointer as defined

in Common Block BARCK

COMMON BLOCKS: NONE


CALLED BY: PROPP

COMMENTS:

86

NAME: FUNCTION EVAL

PURPOSE: Function EVAL evaluates the Chebychev Series:

WMAXF(X) = Z A(M) * U(M,X) + B(M) * V(M,X)

M= 1

CALLING SEQUENCE: EV =EVAL (X,A,BJIMKAX)

ARGUMENTS: X Arguments of the Chebychev SeriesA Coefficients of the Chebychev

Cosine SeriesB Coefficients of the Chebychev Sine

SeriesMMAX Maximum order of the Chebychev Series

COMMON BLOCKS: NONE


CALLED BY: WSIJRFS, WSURFB

COMMON BLOCKS: NONE


CALLED BY: WSURFS, WSURFB

COMMENTS: UM(X) = Cos((2M-l)(6)]

VM(X) = Sin 2M 0

0 = Sin 1 (X)

87

NAME: SUBROUTINE FINDRG

PURPOSE: Subroutine FINDRG determines the fin drag.

CALLING SEQUENCE: CALL FINDRG (RHOS, XNUS, VSFW, SFINS,TFINS, CFINS, TBFINS, SBFINS, DS)

ARGUMENTS: RHOS Density of waterXNUS Kinematic viscosity of waterVSFW Ship speed (fps)SFINS Chord * spanTFINS Thickness of a fin (ft)CFINS Chord of a fin (ft)TBFINS 0.01 * TFINSSBFINS TBFINS * spanDS Total fin drag

COMMON BLOCKS: NONE

SUBROUTINES CALLED: FRICT, FOILSC

CALLED BY: SYNTH

COMMENTS:

88

AD-A099 533 DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/6 20/4DOCUMENTATION FOR SWATH SHIP RESISTANCE AND PROPULSION PREDICTI--ETC(U)

UNCLASSIFIED DTNSRDC/SPD-0927-0223IIIIIIfIIIII

EEEEEEEEIIIIEEIIIIIIIIIIIIII~hIIIEEEIIIIIIEEEEEEIIIIIIEEEEEIIEEEEEEEIIEEEIIEEEEEEIIIIIE

lI25 I 41.01 1 3,

NAME: SUBROUTINE FOILSC

PURPOSE: Subroutine FOILSC calculates the dragcomponents for a symmetrical foil section.

CALLING SEQUENCE: CALL FOILSC (XS, CFS, TOC, TOC2, TOC4, SS,TS2, SBS, CLOTB, RFS, RFVAS, RPS, RINTS,RBS)

ARGUMENTS: XS Ship constant = *p* SFINSVSFW ** 2

CFS Flat plate friction coefficientTOC Thickness/chord ratioTOC2 T/C**2TOC4 T/C**4SS Chord * span = area of foilTS2 (SS) ** 2 area squaredSBS TBFINS * spanCLOTB Chord/O.01 * TFINSRFS Frictional resistance of a flat

plateRFUAS Resistance due to velocity

argumentationRPS Resistance due to pressure and

separationRINTS Resistance due to intersection

with hullRBS Base drag due to bluntness of

trailing edge

COMMON BLOCKS: NONE


CALLED BY: FINDRG

COMMENTS:

89

-- kv -2

NAME: FUNCTION FORMDR

PURPOSE: Function FORMDR evaluates the form dragcoefficient.

CALLING SEQUENCE: FDR = FORMDR (VL)

ARGUMENT: VL Ratio of ship speed to square root oflength of strut V/AL-S

COMMON BLOCKS: NONE

SUBROUTINE CALLED: FUNCTION YINTP

CALLED BY: RWOUT

COMMENTS:

1.0

.9

I

09

NAME: SUBROUTINE FRICT

PURPOSE: Subroutine FRICT calculates the flat platefriction coefficient based on the localReynolds number.

CALLING SEQUENCE: CALL FRICT (CF, VF, XLEN, XNU)

ARGUMENTS: CF Flat plate friction coefficientVF Speed of ship (fps)XLEN Chord of fin (ft)XNU Kinematic viscosity

COMMON BLOCKS: NONE


CALLED BY: FINDRG

COMMENTS:

91

NAME: SUBROUTINE PCHEB

PURPOSE: Subroutine PCHEB plots by line printer thebody sectional area curve and waterplaneoutline curve from the given Chebychevcoefficients.

CALLING SEQUENCE: CALL PCHEB (AS, BS, AB, BB, NN, TITLE)

ARGUMENTS: AS Coefficients of Chebychev SineSeries for strut

BS Coefficients of Chebychev CosineSeries for strut

AB Coefficients of Chebychev SineSeries for body

BB Coefficients of Chebychev CosineSeries for body

NN Maximum order of Chebychev SeriesTITLE Array containing the alphanumeric char-

acters of the title of the experiment

COMMON BLOCKS: PLOT, XRPLOTQ

SUBROUTINES CALLED: PLOT1, PLOT2, PLOT3, PLOT4

CALLED BY: CHEB

COMMENTS:

92


PURPOSE: Subroutine PLOT1 sets up spacing anddetermines the values of the axes.

CALLING SEQUENCE: CALL PLOT 1 (NSCALE, A, B, C, D, E, F)

ARGUMENTS: NSCALE Integer array defined asfollows:

NSCALE (1) = I, if printed values of theordinate are 10 ** I timesthe actual value

NSCALE (2) = J, if printed values of theordinate are 10 ** J timesthe actual value

NSCALE (3) = K, if printed values of theabscissa are 10 ** K timesthe actual values

NSCALE (4) = L, if printed values of theabscissa are 10 ** L timesthe actual value

A Integer number ofhorizontal grid lines

B Integer number of spacesbeyond each horizontal grid

line to the next grid lineC Integer number of vertical

grid lines

D Integer number of spacesbeyond each vertical gridline to the next grid line

E Horizontal grid characterF Vertical grid character

COMMON BLOCK: XRPLOTQ


CALLED BY: PCHEB

COMMENTS:

93

. . .. .- --- l,' l . ,


PURPOSE: Subroutine PLOT2 examines the minimum andmaximum values of the abscissa and theordinate and establishes an internalformula for computing location in the imageregion corresponding to the point to beplotted.

CALLING SEQUENCE: CALL PLOT2 (XMAX, XMIN, YMAX, YMIN, NSCLI)

ARGUMENTS: XMAX Value of abscissa at right-mostgrid line

XMIN Value of abscissa at left-mostgrid line

YMAX Value of ordinate at top gridline

YMIN Value of ordinate at bottom gridline

NSCLI Logical flag (should be false,if PLOT1 has not been called andstandard grid is desired)

COMMON BLOCKS: XRPLOTF, XRPLOTQ, XRPLOTG


CALLED BY: PCHEB

COMMENTS:

94


PURPOSE: Subroutine PLOT3 assigns an alpha-characterto each point to be plotted.

CALLING SEQUENCE: CALL PLOT3 (PCHAR, X, Y, SDATA, FDATA, DDATA)

ARGUMENTS: PCHAR Plotting characterX Array containing the X coordinates

to be plottedY Array containing the Y coordinates

to be plottedSDATA Integer position in the arrays of

the first ordered pair to be plottedI if each point from SDATA to DDATAis to be plotted

FDATA =2 if every other point is to beplotted

3 if every third point is to beplotted

DDATA Integer position in the array of thelast ordered pair to be plotted

COMMON BLOCKS: XRPLOTF, XRPLOTG


CALLED BY: PCHEB

COMMENTS:

95

, !.


PURPOSE: Subroutine PLOT4 prints the image of thecompleted graph on the printer, includingthe values of the abscissa and the ordinateat the grid lines outside the bottom andleft edge of the graph.

CALLING SEQUENCE: CALL PLOT4 (MCHAR, NCHAR)

ARGUMENTS: MCHAR Single dimension array containingalpha characters to be plotted atthe left of the graph

NCHAR Number of valid characters inMCHAR

COMMON BLOCKS: XRPLOTF, XRPLOTG, XRPLOTQ

SUBROUTINE CALLED: QPLOTZ5

CALLED BY: PCHEB

COMMENTS:

96

NAME: SUBROUTINE POLCOF

PURPOSE: Subroutine POLCOF determines thecoefficients of the polynomials whichapproximate the KT and KQ curves.

CALLING SEQUENCE: CALL POLCOF ( PD, BAR, Z)

ARGUMENTS: PD P/D of propellerBAR Blade area ratioZ Number of blades

COMMON BLOCKS: OFFDES, PCOF

SUBROUTINE CALLED: Function CALC

CALLED BY: PROPER

COMMENTS:

97

NAME: SUBROUTINE PRODES

PURPOSE: Subroutine PRODES is used in the designof a propulsion system to determinecharacteristics and performance at thedesign condition.

CALLING SEQUENCE: CALL PRODES (IS)

ARGU1ENT: IS Type of propulsor (in thisprogram set equal to 1 toindicate conventional fixedblade propellers)

COMMtON BLOCKS: BARCK, CDESC, CPROP

SUBROUTINES CALLED: TROOST, BURIL

CALLED BY: SHPCMP

COMMENTS:

98

NAME: SUBROUTINE PROPER

PURPOSE: Subroutine PROPER calculates the open watercurves' table and off-design performance ofpropulsor system "IS."

CALLING SEQUENCE: CALL PROPER (IS, VOF, TOF, PWR, TITLE)

ARGUMENTS: IS Type of propulsor system (in thisprogram, set to I to indicateconventional fixed blade propellers)

VOF Off design speed (ft)TOF Off design thrust (lbs)PWR SHP at off design conditionTITLE Array containing the alphanumeric

characters of the title of theexperiment

COMMON BLOCKS: CDESC, CPROPR, PCOF, ROOTC

SUBROUTINES CALLED: POLCOF, ROOTP

CALLED BY: SHPCMP

COMMENTS:

99

NAME: SUBROUTINE PROPP

PURPOSE: Subroutine PROPP prints all data incommon block "CPROP"

CALLING SEQUENCE: CALL PROPP (IS, TITLE)

ARGUMENTS: IS Type of propulsor system (in thisprogram, set to 1 to indicateconventional fixed blade propellers)

TITLE Array containing the alphanumeric

characters of the title of the

experiment

COMMON BLOCK: CPROP

SUBROUTINE CALLED: ERROR

CALLED BY: SHPCMP

COMMENTS:

100

NAME: SUBROUTINE QPLOTZ5

PURPOSE: Subroutine QPLOTZS calculates the scalinginformation needed to generate the formatto label the left-hand side of the program.

CALLING SEQUENCE: CALL QPLOTZ5 (PDQ)

ARGUMENT: PDQ Scaling factor for ordinate plot

COMMON BLOCKS: XRPLOTF, XRPLOTQ

SUBROUTINES CALLED: NONE

COMMENTS:

101

NAME: SUBROUTINE REFLKT

PURPOSE: Subroutine REFLKT reflects the symmetricalmatrices to T and W.

CALLING SEQUENCE: CALL REFLKT

ARGUMENTS: NONE

COMMONG BLOCKS: AUX, COEFS


CALLED BY: RWAVE

COMMENTS:

102

NAME: SUBROUTINE RIN

PURPOSE: Subroutine RIN reads input data for theprogram.

CALLING SEQUENCE: CALL RIN (TITLE)

ARGUMENT: TITLE Array containing the alphanumeric char-acters of the title of the experiment

COMMON BLOCK: INPUT


CALLED BY: SYNTH

COMMENTS:

103

NAME: SUBROUTINE RINIT

PURPOSE: Subroutine RINIT initializes the T and Warrays.

CALLING SEQUENCE: CALL RINIT

ARGUMENTS: NONE

r.Of'ON BLOCKS: AUX, COEFS


CALLED BY: RWAVE

COMMENTS:

104

NAME: SUBROUTINE RINTEG

PURPOSE: Subroutine RINTEG provides numericalintegration for the auxiliary functionof T and W.

CALLING SEQUENCE: CALL RINTEG (ALFA, B, D, NLOC2, WTINT,SEPCOS, SQ)

ARGUMENTS: ALFA Integrating variable (a)B Ratio of distance between

centerlines of strut and bodyto the length of strut

D Ratio of distance betweencenterlines of second strutand body to the length ofstrut

0 if single strutNLOC2

1 if tandem strutsWTINT Weighting constant for numerical

integration.A SEPCOS Value of the Cosine function in

the integrand1

SQ Value of (,2_ .2)- in the integrand

COMMON BLOCKS: AUX, COEFS, INPUT, OMEGA

SUBROUTINE CALLED: BESSJ

CALLED BY: RWAVE

COMMENTS:

105

NAME: SUBROUTINE ROOT

PURPOSE: Subroutine ROOT uses the 'egula Falsimethod to find the intersection of the"K" curve and the "IK/J**2"I curve.

CALLING SEQUENCE: CALL ROOT (PD, Z, BAR, COEFF, IPJ, ITQ,KT, KQ, EFFIN, J2)

ARGUMENTS: PD P/D of propellerZ Number of bladesBAR Blade area ratioCOEFF Optimization coefficients as

defined !t; TROOSTIPJ Optimization index defined by:

1, no optimization2, optimize N with KT/J**2

IPJ 3, optimize N with KQ/J**34, optimize D with KT/J**4

L 5, optimize D with KQ/J**5ITQ Index indicating the following:

1, if thrust is inputITQ =

L 2 , if power is inputKT Thrust coefficientKQ Torque coefficientEFFIN Open water efficiencyJ2 Advance coefficient

COMMON BLOCK: ROOTC

SUBROUTINE CALLED: FUNCTION CALC

CALLED BY: TROOST

COMMENTS:

106

NAME: SUBROUTINE ROUT

PURPOSE: Subroutine ROUT outputs the computed resultsfor all components of drag coefficients andeffective horsepower.

CALLING SEQUENCE: CALL ROUT (TITLE,EHP)

ARGUMENTS: TITLE Array containing the alphanumeric char-acters of the title of the experiment

EHP Effective horsepower of the ship

COMMON BLOCKS: INPUT, OMEGA, PHYSCO

SUBROUTINES CALLED: SUM, Function FORMDR

CALLED BY: SYNTH

COMMENTS:

107

NAME: SUBROUTINE RWAVE

PURPOSE: Subroutine RWAVE evaluates the auxiliaryfunctions of T and W.

CALLING SEQUENCE: CALL RWAVE (B, D, NLOC2)

ARGUMENTS: B Ratio of distance between center-lines of strut and body to thelength of strut

D Ratio of distance between center-lines of second strut and body tothe length of strut

NLOC2 Switch indicating the presence ofa second strut

NLOC2 = if single strut

Ij if tandem struts

COMMON BLOCKS: AUX, COEFS, INPUT, OMEGA, PHYSCO, PSI

SUBROUTINES CALLED: RINIT, SIMPSN, RINTEG, BESSJ, REFLKT

CALLED BY: SWATH

COMMENTS:

Typical Auxiliary Functions

2 *-a D (, 2 o ) S )( 2 m -Ia ' [ L S X ! (al). 2 (((MX.n)

where

3Ls(2U)2

108

NAME: SUBROUTINE SHPCMP

PURPOSE: Subroutine SHPCMP determines a propeller'sdesign and off-design performance and usesthis to determine shaft horsepower.

CALLING SEQUENCE: CALL SHPCMP (VDES, EHPDES, PDIA, BDIA, HB,VOFF, EHP, SHP, NV, TITLE)

ARGUMENTS: VDES Ship speed at design point (fps)EHPDES Effective horsepower at design

pointPDIA Diameter of propeller (ft)BDIA Diameter of hull body (ft)HB Draft of body (ft)VOFF Off-design speed of ship (fps)EHP Effec -'ve horsepower at off

design speedsSHP Shaft horsepower at off design

speedsNV Numb'r of test speedsTITLE Array containing the alphanumeric char-

,..,'ers of the title of the experiment

COMMON BLOCKS: CDESC, CPROP

SUBROUTINES CALLED: PRDES, PROPP, PROPER, PROPERO

CALLED BY: SYNT

COMMENTS:

109

NAME: SUBROUTINE SIMPSN

PURPOSE: Subroutine SIMPSN sets up Simpson'smultiplier table for numerical integrationusing Simpson's rule.

CALLING SEQUENCE: CALL SIMPSN (NPTS, SIMP)

ARGUMENTS: NPTS Number of integration steps (oddand greater than one)

SIMP Array containing Simpson'scoefficients

COMMON BLOCKS: NONE


CALLED BY: RWAVE

COMMENTS:

110

NAME: SUBROUTINE SUM

PURPOSE: Subroutine SUM computes the matrix productsas follows:

n mSUM = E E Asm As T + Bsm Bsn Wsmn }

m=l n=l

CALLING SEQUENCE: CALL SUM (SUM1S, SUM1B, SUM1SB, SUM12S,SUM12B, SUM12SB)

ARGUMENTS: SUMiS Partial sum for strut 1SUMIB Partial sum for body 1SUM1SB Partial sum for interaction between

strut l and body ISUBM12S Partial sum for interaction between

strut 1 and strut 2SUMI2B Partial sum for interaction between

body I and body 2SUM12SB Partial sum for interactions between

body 1 and strut 2 or body 2 andstrut 1

COMMON BLOCKS: AUX, COEFS


CALLED BY: ROUT

COMMENTS:

SUM12STI SU1S ____ RJ

%y I~ T I;

7n " I

SUM1B

-11-

NAME: SUBROUTINE TROOST

PURPOSE: Subroutine TROOST is used with SubroutineROOT and Function CALC. Either rpm ordiameter can be optimized given the other.

CALLING SEQUENCE: CALL TROOST (VA1, P, T, Ni, D, Z, PDNEW,BAR, KT, KQ, EFFNEW, J, ITQ, IPJ, RHO,IERROR)

ARGUMENTS: VAl Waked ship velocity (kts)P Torque per shaft (ft-lb)T Propeller thrust (lbs per shaft)N1 Propeller rpmD Propeller diameter (ft)Z Number of blades of propellerPDNEW P/D of propellerBAR Blade area ratioKT Thrust coefficientKQ Torque coefficientEFFNEW Open water efficiencyJ Advance coefficientITQ Index defined by:

1 if thrust is inputITQ i

2 if power is inputIPJ Optimization index defined by:

1 - no optimization, J known,I calculates KT, KQ, EFFNEW onlyi 2 - optimize N with KT/J**2

IPJ = 3 - optimize N with KQ/J**34 - optimize D with KT/J**4

.-5 -optimize D with KQ/J**5RHO Water densityIERROR Error message indicator

COMMON BLOCKS: NONE

SUBROUTINES CALLED: ROOT, TROST2, FUNCTION CALC

CALLED BY: PRODES

COMMENTS:

112

NAME: SUBROUTINE TROST2

PURPOSE: Subroutine TROST2 is used to calculatea single KT, KQ and efficiency value fora given propeller.

CALLING SEQUENCE: CALL TROST2 (KT, KQ, J, PDTR2, BAR, Z,EFFTR2)

ARGUMENTS: KT Thrust coefficientKQ Torque coefficientJ Advance coefficientPDTR2 Pitch to diameter ratioBAR Blade area ratioZ Number of bladesEFFTR2 Open water efficiency

COMMON BLOCKS: NONE

SUBROUTINE CALLED: Function CALC

CALLED BY: TROOST

COMMENTS:

A, 113

NAME: SUBROUTINE WSURFB

PURPOSE: Subroutine WSURFB determines the surfacearea of a body of revolution given byChebyehev coefficients.

CALLING SEQUENCE: CALL WFSURFB (AREA)

ARGUMENT: AREA Surface area of a body (ft2)

COMMON BLOCKS: COEFS, INPUT, PHYSCO

SUBROUTINE CALLED: FUNCTION EVAL

CALLED BY: CHEB

COMMENTS:

114

NAME: SUBROUTINE WSURFS

PURPOSE: Subroutine WSURFS determines the wettedsurface area of a strut.

CALLING SEQUENCE: CALL WSURFS (AREA)

ARGUMENT: AREA Wetted surface area of a strut (ft2)

COMMON BLOCKS: COEFS, INPUT

SUBROUTINE CALLED: FUNCTION EVAL

CALLED BY: CHEB

COMMENTS:

115

NAME: FUNCTION YINTP

PURPOSE: Function YINTP interpolates through a setof discrete data.

CALLING SEQUENCE: YTP =YINTP (XA, X, Y, N)

ARGUMENTS: XA Point to be interpolatedX Array of ordinate dataY Array of abscissa dataN Number of data points

COMMON BLOCKS: NONE


CALLED BY: FORMDR

COMMENTS:

116

REFERENCES

(1) Lin, L.W. and W.G Day, "The Still-Water Resistance and PropulsionCharacteristics of Small-Waterplane-Area Twin-Hull (SWATH) Ships."AIAA/SNAME Advanced Marine Vehicles Conference. San Diego,California, 1974.

(2) Proceedings of the 10th International Towing Tank Conference,London, England, 1963. Published by the National PhysicalLaboratory, England.

(3) Lasky, M.P., "An Investigation of Appendage Drag." NSRDC/SPDReport 458-H-01.

(4) Roddy, R.F. and J. Strom-Tejsen, "Study of Air Cushion VehiclePropulsion System - Propulsor Design and Performance." NSRDC/SPD

Report 378-09.

117

APPENDICES

118

PROGR~AM LISTING OF CLOSEFIT

119

C9 0oD IM . .

CD UAI wu .

1.- 0 W CA I--

(D w0J ca -0 0N a or 0 InV CL x - 1- -- - 0. 0. l - J U. -. 1

to t- ;f) 0- C 3 (- o ta V) m 1-. cw - oo 0- - .0 U -j La 0L0 w o C (

x 3 I*.- - 0- In U) -- - W 1--o o m "S W 0- 0. L 21 0t - -tow > OI- t- w u 0 -0 C. - - a. W t tn w 10 w co w

:) of-- - z 1C . - * L 0 Z U. .4U 0- In w-

CD ZZ "- .9 3 0)-0) n U .1 - -- zl- U) a. O

11 (A I.- z5 U)1 *1L wt -0 IX LL I I .- I. >- -U)D I; ; In 0 - U)- 1CLt 4 1.-U1 0-0

1- D- _j 00 (a -0- lO 4o -. aw In LI.A 0n Ia -M V (A d -i IZ 0 ~ U)M. U 0 - i -- < LIL. 0 Zz Wu>U t- z 00 ZZ c.4t n 0-- TO!CI L -1 - a- 1- W 10 0 w Z

II .- U)I 2K -C4 Of mwc '- I- cc U.1 L.U a 11 - 2xD I.3 U) (S LAI-. -a. . W a.z t-~a 0

I- (A 0 4- 0. 0 -.1 ( 0 0 D (iU1 <. U. (A ta.q~.U 0 .- 0) -. 0 1- Z) U.U. 0Z -

0 m- A 0- - 4- *) 0 1- 04 u - .1 w 130U.1 4 .O) LJ .1-I 4 D L II )2 0 Ln 3 wO9 I 004DI . -C I.- C..- <0 2 f- Z (A 04 i .- 0 LC 0n1- U. -Z.

Zm 1-4wC0.20 0. --- . 0 u - 0 4- w C -UZ 0W-Z#-- .4X) t I ECI- 4ULuW l-- -0. -0 -Wa Wz 4u W 0 0 0 >.1.fl -0 I.- aW.0 UJW

4 0I 3 3 z.~ 31/ ?. a;I 1- 41 a.- **A I1U 4-)> U) U)4:a W * o I 0- U) 312/ I- 1 0 U u w m co1 - DIX ) 0W 44

a. ~ ~ ~ - za aJ 3 x o I u0 - W 0 U)1 -ZfU.. .- U)f a:1t1- a. w.) U. .1 .- On.d 0- 4 (A IL - IWn00 CA (33 a 1-3UU4)

4t t -O 4- # 0 -l f- 0- 2a U-CUoW J Ww W~f.. u ~ z z1) m 0 AJo Wa. 1 z -Z owl .- 00 -40 - 3n 1-0OIOW-0W W w w IN, W WU..-

* ~ ~ 0 < WWWLI IA-I --- /Ia 00 =a U) U.1 U.lZI.-.-OOfhdm1- 1II.- 1- oa U) 1 0C- d0 0a. a 0 Z L.) W - U. U 0 Z AZm 1- 1 W :3

0 0 w aW- --r I -- 0 L DU 0W 0 u W.Cl U4-.I < .141 _j j , 0w 4 fwwz a. . ai u 01 tu)- -U) Wd 0. I- w0U. a.rw .- 0 u u CNU-1 04 0u)

0 1 U-JU.Z -. UJ 0- I - 1- UI C;- 17 ZA... 0 Z- .. al D a DIa.< X0 -- 0a--0 , 4 0 - 1UZ mnw 00 0 u Dcral1,

0.- 0. 1 0.) w 10 co x0- 0-. - U jl.Ol, -'0.U..-U)ML *2 D- mC. cr 0~ 1-0 ca 0 i) 0---- <4CL1- N1 -- 01 0_0(1) 070-1-0wwl-<L)0 WI ()C/IW..JW0 0 Cflzw X Ia 4 -( a 2 W4 U) 2 :2 2: :D UI)4 U U IL3 Z 2 A 40D

- i U.: -IX .. W 0-0 m Ua 1 r l- U1) f- f-1- I1-1- n-13 crzz--aca-O .:)Do 2zI 0 -. 1 I (A U)3 U))oU (A a. U. 11 C.4-.E>-)-4W44 ()1- 2 3aCd I> 1-3391-- 4 Z Ia 3 Z . m Z0.3O naml0-- LI0C ,1 -6--4 1.-

1 C 3 .4 U. - I- L Ia - 0 39 u r I IJ3 ) )- LJ 030 w 2 A (A .. Ou C I.-wI- .

N. 1I(1-1.- - 3 2 U) ZOOM-ZU.-j-j333mf-I100 0 2 )A3 0 .4 0 Co . 11 of If ii 11 of 11 11 I 01 I I 1. 1 I 0 2 2 * If 11 416.

4 &a .)-0 0 Z 2 2 z z 0 - (A f))t- C4 U.La. uIll : w 0 0 0 0 0 X~ C---L =) b- cmN aw I03 za or C -(3 m 2 2 2 n 4 4-- - -Ua.mo uu x( 00 3U) IL00 -aMUMaoa. 2 2 In 3 3 1- U) 3330 3 1- 1.- 00 4-C -U) a.IA 9 C

a. 3CIZL 0 0 0 0 0 0 31 -4 3 44 U) O 22 333311 -CL - .-CI' C4-a u uu u u0(xNW X < 0 Q z m3 1 9(

M C

000 0n U InI 0 n 0 in)O O O O O O OO O O O O O O C

44C T 7I

a.2

Sal

- - - - - - -

p4

a.z

0.w

0L

ohI 0 - .x ( _ * I- U -

+ ..-

I- -U I.0

C. 03

ZL u C4 4 ? 'iiI- 0 I - 4

In 0U t"I-L c $-401 0s .9 z I-U -W-CU

W 0 (A 1. Ii. 44Uj Z Z 0& r 4

0; -4 34 4 3u I L0 D a

I- -C I. -- j n(a .3 W >.- 4 )C NU j '

. -C m -I I- -J z0 2J - -A n -A - 0

oj ' : 0 - C (n 0 ~ 0 (

0 x D ~ u 0.- 3'- C4 0 7 k jz ta. ~ M Z (ZMC WC UJ 6- 4f 39 0 01--U

I-. 0 4 (A In 0In ~ u In tAm( 0J U 01k.4 4 - A- 0*1.- inU+ >i 2 j i.zu > 0

(A- PC 4 n - ( Z Z-&i. -j u -M xxX0- 1 0 (A4 IA 0C -C I. 2 WU * W - 1 > 0 -( !

*- C! z 4n 4 0-- 0 o n00 - o xx 0003 01 0co InC 0 3 -A C4 C4 >W ) I N c

TZi U w t i ' 1 C4c 4C ? x al it I- -'l - I 4 *n -a 0n. LAr- In x u .*1 U 2 : . I.JN 1 J in

0 n u- u o- w k -In in 4n 0 4o -c-I La to u 1 .- . m-. ct) t2 4n > r 0 0 -n-- *w ~

0L a-I a~ I- 6t- 0 J _j :- M I 4.U, j- , InL I n - 3 1--0wI z j n - f u

z -1 - -j w -j i -2 A OOXU-- 0- a- -1 a-0- 9x WI . nZoI T0w 4c0 - .- wn iU W mL -, .9 Z -j-0 -J in 'm Z I W 0 - -04(

0-zc ) c uu u u 3 M~ : 0(0 4r 4j 5- Z L ul - c '' > In-r -0i C0I- Q- -- II . I I --- W l nI~~ .- (W-*

V s c-a inn 0 In 0( 0 2 u - 0 a In in- 0-03 ~ O*e~ ~~~ ~~~~ 0w I w I - C-~- ~ 0 - C I -I2 I~

V il * W W (4 u.. W I cd-(I.Cdl 0 0 I I oi a 0Is * 5

is If IU I * 10 Sa "* 00 0 ~ 05- 011 (0121

-- - - - - -- - - - -

U. IC0

0 33 3 33 3 3 33 3 33 3 3

00

II.N

I...-

9 .- N .- - U.

a.~ 0 0i

-JZU 0-n01 # * 4 ."

94l0Im I.- IL=2C. I- 2117

W N 0 Z j * EC i -j it ZZxc rl

CI -1 N 04 0

£0 in - i4f M-t M

o 3 Ifl ~ 122

cl.

1

q- "MV 4 44 44 44 44 44 444WOO4 44 44:,.0! N "-N " NN--I -"II- - -I I -NI-I I I- -1 * -1 * -l - -l - -I -I I I- - I- - I- -

-j A 4-j i j j j 4 - - -4 i4 i-j-444 j 4 i i -4 -4 4 i4 i-j-j-j i 4 4 A - - , 4 4

in

U. uJ-

(a a 404I.- -j Z In 4C

v En LL X 4I.- -jI U

I- 3 2U. * - .

o 1 a-n X - N1 -z 0- U

a 4Z > 4ix

*0 OrCI IX

<, -1I In >I 1 --9W 4 >2I-

IX *- I.- x u hA 4.

I- 8( z. 4A .- I. II4- IC.- In I.-

z MW LA 2 I.- M co I .*I- f-0 (A* I-- (A N

x I-I LL- .9 Zj z2n 0 z M-cO ..- '1 0 M 1. 2 IX 2. 2

I. 01! InI Z1 t- O 0 00 Z n .CL to* II * Iq 0 IX (D In- 0 -C -

o ICL £1. x J 2 Ifl )O N. 0 ; 0 2m C4 wu. - L0 .- 0 n - 0 i 4L N. IA - -J 4c x z

(fl NZ-1 0 In 0n N.x 0oawIn. I0N 1 I N. N . - J. * In l

4 0 1-1-. -J z ' WI I- . 0a 0 IX >- . -! 2.1- , 11 C-nI -* .4 O1-NO 2 x 0N.0w 2 n (Ao z a-C L CN. & -0110 a i- -l Z *U -C z z

In 2 01 - -2 -N I- 000N-A .- N 0 -J 0 0. N 0C N.. 4 I- C N

0. N. u 11 -J u 00 000 a1 M40 N ) 0 a a- w

u-4 I 0. 0. In u N N U U - 44 u In u IX -

N.44X 2 W N I 4 N X 14 . C Z 0.- II0-Jn 2 .J

in 2 n 0 i444 0 in 4

4- -V t

12

__ I I

to N-r oU c vc0 NMVL 0 ,C 7 nt -O

NN N N NMmom mm

to -wC

ox01

03 0 - 4 U

Z - W. o a). -C00

0 0 0 C; *IDI ZZXD-* J t

C20 :3 -f(.-) u Ix~fo3 a M. l a! OL X I fl I(r :43

ID - 1.- a. !! w. 00 wu - o4 M ix a )CN. 00Cw -fW

4E OC1- 0 K 0S W 4 z uu-N.f-- C1.I A 9V U) 3. - *2 )N x'--aU' t-z0-3 0 .*j Z >.) * N .-

I-N4 MC- OZ~ zI Ll W -- W t00U>-"in0- 4d. - - 22 Wxxx W

In 0 0 2. 2s, a 2 O;--- 2u *IiPO. w-0 900. $. -* flfl O2 - Ixa0 M ->

.- C.(A xW.- tI c .UJ:d)O I-n4 W WW -

=P0(1- CU 1 0 CAx - u UZ U -- LL..0 3 D 40 I - 4-lzJ ZII

0---. 4- _: _0 0~lUU0.'- Co0 ;flO J - W ( - r0 I..ZV 00Cl0 0 0 CL 6-- t.-Z

0 0 2- W 9 a 0-fl - - JL AIOIL - -002ML ix a -l 411 M- 2 l~ 02 L 9 - 01004 -.xxW- I-X31-d 4 x( > cn ) )CxM m-~n ZZqW- WWr >

N. -00- -J 0W L * __ 2m m- r000 IT11024n* *-)0 0- IA..Jm 0l m~ m2 MI mI >-U. *"->2000 C;

Ai OC3O 00 -- . . . . .. W~0 . x T x 0

2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ O -I-- -11 -I "i iI - 2r 10)W-o -.3- -J -(U -~ I-. - -- - - - - - - 40

x 2 --- -- z( I--) $.-0I - I6- - I.- C~

Ix 1- 0--- 402 2/ xI2~4~4IL) 1~f a a a . a w

m Cr C,- 211C -U- cr rr cc

0. 0 10 us- OW 0s) 1 0 000 000 0(A Q 2 AA A A 3 0..............................111W111W1W10

V ~ ~ ~ ~ 0 (1 CV WIIWIWWI - O - I - - .

0n 0 InaI C0~~~~~~rrrr~ C Cin 00 0

0~4 0 0I)U 0mb 101)

I -. IN 1MV qn~fl124f

'III

aI.

to to QYQ4q$

0 .0

4

.1 W

U ~ ~ ~ - a- I.-t - _ _: _ -

4 o.-I. co0 Z Ln t iL

ix un 00 a4 -9 4 .4

2 4- 0-- - MIV

z -w v 6n'-I 03 a10 44 3 I- - n u, (z .o; -o -3 0 on:3 C) -U, O fI-- V) -- - -0

0 1 I.A own- 1fl 1 32r 3: WD .~ .O.Ir.

U. . C, o0 Iflw 4 M 4n 4n 1: 4 4n 4n 4n o A t A (.4 C 0 - O D4- X1 3l I.3 xX j t . - t 1 , t 3 1- -a t3 -a 3

M . o (A - V) - 4 3 3: Co. w 7-- a7 <' a t- : 4 4~~ I .3 2 49 1- 4 4 20 3 Z Z Z Z

1. - -- 0..I 3

C uj >W -3.- 09 #- - -1 n Z 1 Z o Z z 4 4 n 4 4 4 4tot .0 0*1- I- . 0 0II00 0 00 0 0 000 00 00 * 3 30 3 0 O 30

r UIn 0- .1 - . - mm Z0 Zm m' - m 3 mo 3r Mo 'm m m (Aa o

- - 0 4- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

O I C In t- 1-0 1-- 1 1- - 1- 1- 0. 4- t 1- 1

:31 0 0 0.C4 a U U Oft3

in- U-I oclnm a O- 0- I I I 3 3 3 3

4.01 4. U l0- In 0 -1 0 -. 0aA..oo~CI .iI ell mU q.- o4n on ~ r 2 Z 3 3 3a

a. 2 a. * --- 0 O -W~-- . -. c- ~ 125r

IV

maZz

q0

40 ~O-N(uifo IflD40(00404

N. ZZZZZZ

u

0

-W

40 ZI 0d cd

z

I.-

0 02

. ..............

(3

0) 00'd 00000000 0 0O( (000000-C 0(01-0)00.-NM ocjc000)00 MD)L4

o. In In

0 .

z z L 0 0 a (&L - I

:3 0 .0 ON

U) 0:Mv : c N

1.j (A 0-)0

0A 0. a]O 0 co 0)

Co Z)U V). -oI to 3 -It

0. I -0 -- (0 _j )0 -0 )UI- 0ca- - .-N - ) -44 U J-

0 4- .00- n) 0) In In-~ 0.o

or ;) ?-- 0011-0 0)0 3 t III -U) I.

~ 0* ~ .. U)-.3 .U *C)13 U)0 'CU _j _ '

o~~~ 0o - cl 4A *-- J- )0. Z I * ) U 3IF x 0 +U--- 0 - 1.- 0- (C N -U 2 (A f )U

:3 0j u 0 _-0 I.C .- 0-) c', U) -) 40 U)3m) UC

0. _j 0 0u) 0-- IN.1 U) (AU .*. 01.U--( ) U(3 )4 ~ ~ 0io (30 10. , 0I -W 0. 2; (of W ' 0. WLL V)-0 M *4 .- 5 ;~

Q. 0'- I> -3:3w- w 0 I- U) 0- 0 *3- .i (A U)0.U) A).0 If-) N .0fV U) 0-- I- In (3 In _j a. * UJ 0 0 - x* (A- InO- U)-- 0)-

:3 W W- x- 0. U. -A 4 <4 +10 Z - 4 U.0 -. 104 U04; .- QW 0 4j 4 CL ZI c3 U) U) !!::~N1 -I 4(I431 U

0 0 0 0 0 ) 00) 0n ;1.41 U) 3 I- - rTI. 0 l' x > 1- U) .4 -i- Z a t)1- 0. .- - . - l,~i U .

4 - Un U, U- 0 U n 0)0- (AM 0 .- L4444 U 0r. w0. 133) 01- C - '0 _j1 u D x )

0 0 0 0 to 00 01 000 0-t of of (A 0) ilxUc A _ j j z z Mv L n( i'

IM_ tom2uo ~.1I-u z 4444;

6-I0 v() u e ) i co q< L

0.u 0u u Q u LL~

- In 0 o01 0 III 0 tC)U-- 1 01(0 0. 0 m

127

fr

ow

C, 000 0(0000 0000000000000000000000000000000 00000000 oco 3 335:A3 A 3393333A 333333 3 A3 33 3 3v3333.3333 3 3 3-a 3 3 A 3

0.

0

to

+~

-i -j

00 01 -

+ + 0 0

W~~~U x FI C1 aC1- (A - to mu In -j -0 I. I-

-~~ ~ 0 *00J V In -" 0n 0. 'A-

0 OC 4 0nono lf 0, 0cn Un ULA (4 a-U 224; 4 x 1.

C5 (A ( If.-.t in .01 a 4.0 -0- - .o In L a- 39 0 - C- CD m (nA L L UJL tiV o (na-- I. -U.L A m3 ! a- M;:=O 0.- -to 0 -j1 -. m 00. (5 -j CS *-*.:-41 I *.QA- 3 x - + cyia-0> -. 4 , U oUU 1- i,- 4 <- I" Oc; C3 .xI U I0. 4C 2 cr-9CI In A MUl0 N - U r- r Z 2 * 330. in LA E)A to a a (- in a

0 49 I Lf* 1 - NON.ON . cr ;i ( 0 0 > > 4 co 0 0.aLj . w (A (A ->.! c a]dtt UlA T AU1Ul 0 M a I- w-.5 4 a 0. L U. - x t( f-0 03 0mo in -L3 0.: C..0. * LL. 003 LL UOd 0 i .4 2 001 w CL N U w w 0 U. -4 0 -M0UIIU x m . 4 u-. UJ > ------ I- - a

- o 4A + to202 2 i WU< .- $. - w a + a6- U i 0 In U)0 0(DU) a P1- (0>- n >2(C 2> > X 0 IZ -I~ + w 0 Mi 4 - 1qLl~ N fvN z0 inInCVN0 -0 0 0 1'- U.+ * U. LL.-an& u.L~.. ++ I-- mm n .q

rI 1 3.. U. LL Mi of~i M i MO OU LAI M0 LL. w I 0. m N . Coooooot 04ttl.tC14 C10 U Wuin Mo LA a 0 1,- U" ' a- Ir1 1 2 - -------- o- -c4 -t.- Od o t$a- n tofi It w ueua 0j LL) Uj UJJW WJ ODw w wW(A mont 11 of z 0. Irt li 0. 11001 0. M f a t it 0 a. azza a- - -cc it)N in 0Oino om * 0 2 (A w (A o CAnto P. 0.A 2X3C'jM a M "M J2 0 1& x c 0 w W 1, 1U.W-t.U-U. 0 1.- 1.- x D n r mcum m m0 U000 U.U.%>U.>> U 000. 0 000.0.000 0 0SX wL 0 A33AZ33-3(53s33

031

a 00f 00 0 0 0U 0 0

0It

o A0 ain 0 in 0 in A n0w £ to r- wo co010 0 0

128

S.

(34

Co j

t- OO0oO0c00000000c00000000000000000OOOOOOOOO00000c00000000c)

0

IOD

+ a 11 C M 0; mQ> m on mw mw .4J-) -J .2L~ ; -; 00, 00 00d 0;0 .00 0. 01-

M(aC or U.J 7l) *Q- fJ l- 0-( Ii) ID I- - -(D IL.I(Dx 1 Qon *L .*I- co C', UIZ - C 4 0 0 91) :j0 J 1 0 jC ) L )

(D o '. - .. J a 0 1t; 1)7 -f) : " .

z9 tri.. L,_ It IZ I0 CO~ )04 4 -T - -7._;

I-4 a to(-0 01()0i d, 0 41 41c (11)

co; C4CI 4LI Iu4II 44. *41 , a.o toC L.,4 JO ct(9

I- (D a C) T -Lii 0 9 1- *UAJ to9 0l d _o *C > 4- 44i- .J I- 1,-~ 1 D t J-.01'-il- 1)9 C'IZ 00 . . .~ 00Gon4.J49n I-43

0 ~ ~~~~ (1 to _1 U D00 < f ~ .w- Li I 0 Cr .l LAi Al44 Lit In1 ) -. 1 to ~- .w 001o4) 't x x9 ail 41) CDU9-C9- CO :5- -A CV)1)1,

Z U )u -Z 41) LiZ Cr--.C 0144 J -1 (A -Iia9 I4.i0 1 -0 ~ ~~~~ *il)9n. fl0> a0- 0 (7 -U-l- 1. -J 0i~ 0 cl Ili)9 (A .4 C,9 L.)-()

to I.--- a 0 (A U- 1 i.4- a-. - . a >m.~ Ci-Cc > -cc >- 401- C4a C4 4-I -.1- 4 l - I-_ C 0 -* 11 l-~ Dl CV X 0 > -. Ina 0a>-00

0 O a - -C'C~~ 39 2 CD-Cr I- I- oI-I-r - .1> >- . o *- M .I o at.. TO0 -iu(f0 nca0ODEc C4'4 Li. M4. W4 r1L I -X_ 4 4 0Z> TI-)a0MUt r( -ZI I D -. 4;

1. 3 *0 3C-C 3l c rr.. 0 x- - M3 31 4 o r :)o -aoz __3 uD -a u0C. CD U 1)4)C -l- iIlilIWO D - Cr ~ W i ? D -.-C Cr -3a - V' " V()-.-() z ~ nw

0 L! 2~ U0 M9 LAi ui- 1714 1a -- a 0 n O A Mu- -.o.a-1- 3 o - w'- < .- -~ -i--mu f on-40 0 0 on c4C.-D ( - 0 1- )l l--0 A a _1 _.4a- M 39 *9349 > CNj 9<- 9<>4.1 39j

4r toi iO-'C) IX -- U - 0 , :): L -1 -C - 1 1r- r -11Ma n Cr- M -44C OCr - r.0wsqiiWfllfi 0 4: 0 91) Li. M 0 * 1 *0IM 0 0N 0 -0 0j C T 0 -(0:

--. ~ ~ ~ ~ ~ -4q 4 - >0 > -j I I. 0 -I 0 0U *I-I NI 'I l)ZI1I9 IIIIIChi C DICIDJ -- a- a -* '0 -- T T_ <(9 * -C4 i-d0-C4 Ne C3 -

-xiiiWWJr -1 L9) 4h (A 44 < 4 3 M > 0 T 0 'r T MT 4

ff)a - (23Cr I.: aDWOC 0: 0 0a 0 0 0r L0 0 :0 _ I CC 0 0 0 a0 za0 0

2n 0 2- 0 Qi 0 m A _j 0n a a orI0 U ~ u. 4L~ 4) 4 ;n CD ::) 1)9 ;' 1 4 DM ) x nx D I

;O3 (9) (9)3 xD (9 ) () .. 4 44 4~c4 441

Cr0 41) U- in~l M LIt (9 09 1(9)1w3 1 rMrwutoOx2z x~ x

a U aao M) rM0 0 an 0 0 0 in 0 a 0 0n 0

- IT4 4)3n (9) 44 M41 in in CD D-

1129

C%

LD mvm t-0O

C' 0000000

0 i

o x a m

U. (A 1.

z 0.0.I- ~ c -fl ')

4z ( Z '1

cr .M, acrU.

wo 1. 1$-4

Ix or1 In r 05

a4 0 00

%L LI LIXIOC u.UJII

o IXl

us 0UI--

0 130

O !C

Szzzzzzzzzzzzzzzz2z

o

0 (

U. .

Ir in

ED w

or 0 0

q a

0

C w -Jf/

of- 2 -

01- z o

C - w

CA 001t -

r- I-z Ena. 0IOO O 2m

in co 0I. 0nz ( )2- 0n 2J in Co t

o u .- c z a0a. - .-C a -a Ent t 1-o

M. 2 . (- a..a. V in ao zw 0 in i 2IA

4A OI0( A Uuf CUP U * u M M I-

a. m--+ m a

0- w z. Cd~ Iacw z.m-~n. *E

In nn m *. I- 4nIA . -mE~-a m m

2~~ in 131-~(~ZfOUE~L

IL

0 -; C

o coIxC

-( 0

-0 0 m ) 0( 1V,. #A a z

oO .- .. .( 0 -w .-

co Z -- 0 .- 0

I- ( to- 0-0 Ma 0

IL--NO In.w 0- 1.- 393; + - Oti - 1-

ol -4- -ao co ca 7 z

it 0 .0 0- O 3 0

- -n 0-- 4- -0Zc 0 -0 - +; 0Z Z 3

,l0 0. . . .

(n 'A U0-- -0. q ZZZ 33J-- Ii tD D 4-cmxc(A 11 306 dc- LA- .1c -34 c o. o 4

0. j M300000 0

+ 0 0-3-4 13-**. 0 us 1- 0- -JO C;C ;C 3C 1 t"1 f$ 1U) f

4A u U _ UL *' A( L nk lL n000( Wn LfA- 0 0n (A 0 LaO n L A n, n )I V 000:L0C1 zl n 3 *- -- -4 4 4 - -

0. - --- 00 4*I * * * ** *3 0. 0- CV- 3- ('V~flo ~ n 0-- 1W- in3~~ZZ23 3ZZ -('000

ii ' Z - -0 -- '0 4 -. --- ---- --.1-u 4 0u ta 3 3 33 3 3

0. - 0. 0---- 4.1- N. 0~O~ 3 ~fl~l~uo d- -''0. 2 44 4 4 40 0 0 WI++

W 4A00 3I. I (+ ++ + + + + +I~~l~ ili~il C 4 IV I~~VLlt~(D '' 4

Ill II 1-334- 4 ma 13 4 4 4 4 4 4 ~ 4 3 3

(321

w I 0-:2! 4m t ovq v q-- 0 0 0

9 w w w w w w w w w w w w w w w w w w w w w w w w w w w w

>>>->>>> >>>>>- > >>>> >>>> >>>> >>> >>>> >>>> >>>> >>>

0. . .c4 4 4 I f<. 444400444.

0 WWWWWWWWWWaJUJWWWWWWWWWU.WWWWWWWWW~hWWWWWWUJUJUJaJWWWWU

Nui#. 4 444 444 4444 444 444 444 4444 444 444 4444 444 444 444

39 -I - (1- (3 -1 (A Z

CO -; -C a .+. Cf 0 N CD a U 4 0 c N

In. .- 0) (n (Ac L j.o 03- - 0 fIn-:

o N. It 0D Or 24 0 0In 3r 0n C- w 3 4

+~3 (A. (A MC.--0 0 4OW I-LL0 /.( (A 3 ( in-a 0.W4

z w -TC 0 C (V > 4 (A o- z> 43 (A in- - 0 -i - l 40 cr0y in -. 0- >A 4 0 0 -..

-!_ a-- 00 o-- a- -10 WU 4f - - -X:) 0 wl 3 .- N .- J (A F a .-

U.. in 0--I0 2A :L qD Iin -2W9 0 0 - -CO0 O -j -C> 4 In- uj4 zC>! Z &OC4 01-- Z. 4U 40 Si0 Za.

- l 0 :3 CL (n X -> 44N)-n3 0 -0 (Dn- (A: I -.- I c

04z In m 30 n (An - -4 c 4A in-i-0zaaz wr I *-u 40 41 zu 0

ef w - 10 aA- -CwC 3. in -w z- 0n.-I.-O In 9z 0.-. 4<! - . I-U N kn w 4;-

aC C 02-n 0( M-J Z a? Z~u4in>-.i- OD CC -- I - 4 XZ 00. 0r -J--uaU~ a1 a-. Ln fl T 4.-. 4- - jLI

1 5 0 'A4 'A0 Of .(In 0 CL L w4N

0 !:Z tl< 1- -0 3', a - 0 ix3 o C -9 u -4 0 LLUjw4 -Cu - CIO In-W 4In '11 3 ) c u a a N I -

-j -D >0- 00 in OD W Lw InC ED 4 In.0l~ 0 : 30 -.- _3 - i l .. 4 j 0Ji N .n ZIn i- -. J

43 0A 4- 'If. m- al 0M -f- 04U4- u 120 z3 - - w - 0 -10 C; 0 In (nl tn-0.floa ; 4m

*~u -A da (A- -- In 0-1N -In 0.j0 - 3 - 0-- -In P.3 - to a n a 3- I.

to M in - - (0- - - - In l zz 004 Xi >- ZU - CaN)'..P (7) fl> (A- 0i Inn O ( - .0 w 4 (0 Ca (AS C- f" N4-

C cc 0W3. X4- .J3 Li. n kA COn IZ Zi3i -0 In > " 0 in

L 21( w0 2-0 Cl a f.- Oi -140 a L 4W4 a2W -0 w. imT tiCLX-0

03 00 >A- 1-00- nc zn In 3Z x3 Z (A 3 (40f -; - N>n 11 - - 24, *(.. 30 *C 0 ~ Xi t. 3 A 4 A 7n z z (A0

a. w 0- 4 IOA 0 -I.-- N In .000 (A w I. 4 -C-- .1 u - . -0 .0 0. I -4-'0 0W (A M N.- (z-S N IS 4 WnU i-nZ'N

4 z - "1 -U- -W- XIn in .4I9 1-3 v000 4 4.3-i U I ~ .. -U uoL 4 In znn~ N. 0. (A 49 4~(5 _ Cc _j In.- 1- 1 .- zZw -. 0-

9 c3 N N w N. z - 0m 44 fon z~ Jnai(A ?- Z (coU i-nC i. (U 1- ( .0000 (U i-.1 44.- wA If I4

3 - 0N 0 0 0 a 3CiCm 5-- 2C 0 N w 4z me i-IA in- a- -- N. N. 0. N.1 -4 -m (U IIn 04 .-. U. f 0.-

A 0 InU 0 In 0d.. In~ oC .rInwm m .-c*Itn(*n .P

13

40

o w wwww owwn LOLDIDIOL 00000000 -~0O0O0

Is 4444444444444444 444444<444444444444C44444444444444 44 C4

0004

I.-J

I.-

'0 0

Off 0. C0 = C - 0 (A

5-0 4 3 0- 0 *

Or 4 0Y C49

0- -J 4

ULA 4r -Jin Z

0 0 it- 1- 41,1wt

00 -1 0 0 c j UZZ j .-. 1 a + cc z ait

Iili 4 00 .1a 30 w 2 30 I.- -0 0 UCL?

4-9 'i -. -- I, C3L) 4 W -11 a -w .. 40. U) CE N - .

I. 5--' 4I ! - XW X (4 1-04L ia4 0 NiC I n - C t. n - LO Z WjU .z 4z

0 T i- 0 OA M 4Cl: +( ul 0I I 7*Ut 0. 0. *0 -i~ 0i z -j a. ; .'I 0 a(' 4~ -1-1- mO + L* 0 1 C C3 tz Cm -1 - C-L N9 . il

-C S64 0 - .. *0'1 m iL Ix ClW 04 I.C 0 WO -. C'Ea I -dO U -- -tA .iC a.l 0 V N Jit*-JC -C - t L - .6

2 _j Z-.J 0 013%.D444 tn I 00 t0 0 0 Z- -C lnc-o2 1 1 ,N *Z 2; Zci i-c- a. If If.. LL Jz VZ ( f#-NMO VI tD i - ; t 1

If o l Z 1- 1 .0 41 , 4A .0 Ut CYO -Z c, 10 0A -.1c;

o 4 4 : 0 -4 a*wo t ,p. 0. -La-wm 41 a Is $AJdc -CI uJ m. * - - 1-f- N 0-z Z 4 W - 1- N 1- 1t--. 0

.- L N CL 0 - 1,0E- 5() *Cl 0-ZL -At U . U - -- MO1) 00. Nj -.1 i0t4 IA.4 -j 44 -. 0 m .-40 3 A 41 0-0 j Y0 4 1 LLa / -j I5Z -1,0z00 Z 2 .

0 +l0.ItJ + AA+ u3 u- 0. .9 a LC - - -'4 t- in 444

39 0LiU 0 i ) 4' C~- in 3 141)4 0 a-n(d . N 0 ' *r .. t- IN - -r r- i0-..n ' n I

n i4n0 - I ~ 4bn I ZOO lIm i 0 ldtJ 0.n LtI * 0N~jt4 -. Zn II f ( 04W i L t i0t,- i -O0 04W.J I'sf

13

ri

0 C

CD4.111

C d

461,

go z

4j ZC-W2 -. 1 UII. L, OU

1- 0.I .

+ 0. >Z > U. 3cbI i (A -9 -C 0IN C! I4N4z 4 -i LU4l - UIL co U-, -

-j - A N It -I- 4-U0- 0 4; 44 In w. - n(

<n 4 -0-. 4 LC 4 x 3a. C) ....-. U. 0-

* O1 . ,F -J 0-.1 +n 44 2i3c xI+ t

02 0- C; X -3'j a- < 4 4n x -I 4 00 -4 20 20* C-.U nE

Z -W -j m2:jI 0I c0 V 4 -J I- 1 2 In

o 0-~~ II LUL -- -n + I VON 13.- 2: 4;0.~' *fl 01 -J n1- 3 U nI~ .

o 1,4 * -J-J++LU 30 . 0. i In -AW 2 -c I. I.- 44 + Z 31 1- 1- 1-3 & -l 4C J- M 1-

r- 03 In *1 11 z z LA -aAC f-n U IC NJ ~ IN0. U4 z0 .Cd m 3>> Z, -. u.V -j a 44+2 0A 0o uh an1 - 0*3 . o. z-I .- a" :4 .. JNil z . 4 4Aasa :) m .. j c-

U W.X.-- - 0 " V Z IN 11 0 (4 1-I N _ -. u -2 3 1- 4000,0 *In (D ( 3 co.I~ Z I - -. 1 Now n~ cc

it r Nf W-1- 11L IN 03- 11 4 - U n 0 to- oil 1- a) 3 )--. o INAnO CM N4 Z4 "- 2 II .-C . W -3.J0 . .. tII

- ~ ~ ~ ~ ~ ~ ~ ~ C 0WN-n U)3 01H 3 30 "',ea -a

U. > 1 4nW-U i20 Z ZA0.- 3 1.-I. 31.I s- Oo 3n- A---ZN NA

I-II-0 10

00.

%n 0In 0in 0 In 0 in

135

0

0. .

z

I

o;" -

00

-0 0 :)LAJ 1. .c

u co0- .0 M.

it )1 - 114 -- N

+ I 'I- 0

-0- 0

0 *0za o-.- a-

'-00- 2n1-0 -00 01-

0. 0-. 4-; 9Wj 0000 0

Co x oi* .0 o

0U. 2- -0 2-C co4l In 1--0 ccWPCKw it1

I- #. x - . 4 C C ; o 00- - -

11 0 . - --J .PC 4 -- ma. 0.-;O.z zz j i~3:oci- 444a.imi

it I, -- -I - Z :

o 2 -. - - -

-00' In0-a o- ON- m o 0 0

(A (A (n. (A A-(.C 0000 0 0 00 wL) I- 0 0--- A01 P..' A- 0.1-3A339a A A3 3 Z

La .- l I- InCi0 0W in 0 In Ou110

£ N 1-31 444 000 0-0 0*m m V2-

4 - * 053 1.0 I 001362

r~z 7- ------ ~-.u -

IN

o ---- -- -- -- --- -- -- -- -- --- -- -- -- --- -- -- -- --

a.a~ a~~a~~a~aa~aua~~a~aa~aa~aa~a~~a~~a~aa~aa~aa~a~~a~~a~~a~aa~aa~a~~a~rrrra~aaoaa rV;391

+ 0 0:1 on a(D z I0- In 0w_

1-0- 0

a. .3-IA CL (44. a.l W Al-~0 - 0 - C

0 1- -01- -4 L C4 im >0 4(A 44l

0. UJ *0- 00 -9 0 1. '-Cd U- Cl I-( 0" 0 " 'u z (

or- 0 -100- "!0 a. 0I 1.0

*s 0 . :'- 00. S) kn c- 4C 3oi - _O_ -A -W o0 I- 4 u

0~4 z -i> *U ,a'a'lWJCa

G* 0 (A- ' A 0 .1I_o of I.-- J a.I.Ila.A u. I 0 OW * -

-A 4 40 0 uA (A x3.4z n - 0 -- ' -1 r 4 0 4 4 0~j( -

a . 2 1- n 0'--- 4.1- 4" .- , 1 :to of wC, 0'I..~ ca0-004W~

O I- Z on~a -W (A. I. (A 4 .- I x *..-Cora NNw a -9 .0- cfl0 ..J *C' IL. U. K1 K 4 0 4 W.1 K

of (JIh j 0- 0 *i *l ::1 O0!. wZ 4nC(3 .1I 1-331- 4 13 - ~ W. l' 000 4 41 4W ;P ~ 1.

C4 4) 0. -. O - 4 a1, -9 4-.4 1- t- IC *,Ii 0n01 A U 1- 3I- z- U a! m a Ikh 4 4 '( - o It J *.

(n- (A 4 n 0A 09 *a. 10 +0 UI :D on w U'0 C, *-. .J 0 IAl U -.0 1- A K- X to ull L . U e- 0 a. - IMW q. A-K .m 1-NCO 2w Z xA Iil -C .4. uj 3- 00 ..-. 0

z3~ m-0L 0..0 44NI n I- n0 1 .-- rg -

(2 IA Uo x 0 04 .1t1(0-. 0(0 00 tolJ'..W aU 0 j- ) >>00 l- o02 ~ -( 4 ' -CXd- 3 - i

0- 0 -4 -M O t(Azu0 2 nq U0(, u u .

IA0 In 00 on 0(2 000 (IO 04. n 0 00in

113

00 wowow

a 03a( o 0 0 C0 7 00 00co0Oo===m aa m mamma

to-

z

00 IVu

+ i- 0 -IDM 4 w 4-U U -.-

CC4'~~z zzO O

00 . W w 0 ( . a * M *A X00 0O *j 40 44 0 .1.4 -0 w C

--- 4 0 4 4 0 4 -M- U 4.. 0

u2 ZZ444444144-3-3-3n 7 0. -041 0 . to *-3IA .IL (141 (141 * * 0. * !.0T.* f n444 --- 4 ~ . J0 LJ.J- +0.W

W ~ ~ ~ ~ ~ ~ ~ ~ . -9U 0-44 44 4 -4. 30141:4 414w -, <J 4.. wI Il kA CA w ~~ . 0 + z + 1+ +10*

4 4 w 0.,~. > 4mwwz z 9L4111 IxUL1L0uo 3

-z - -- - - 6-1-40 p/41 -C2+ (f+C2An+42 L L3 440 < WW W W 4022 2222 wo. . .4- 4 3--U 0 4 0LL 1 - 4- Il 0 - ++)Z + 22+on+on+M2

cc 0 W W 3-3-j-3- 4 4 -3 - - -- 3- 44 -C .I- -C4 - -4 -CNI- -f444-00>>~ >>>>00 Z +Z + 2+2 m ~ j .-1 (AJNC~ N

6-* *nA1(1~~1- .*. - *t-t *- :t - I- 0-f44~ 41 /33Co. 4/14/1 O WWWWWWWWZZ20.20.02Z 0. ZZV)V)O.flL11-004- v

O WWJW WLIJ * *** Co M-- 4 - - I0- 0 - X 4 I.- IIIx t 0 M0 *4444444420/ 0 co C041 22u a Ill 44 11 11 4

w~1 0-a P- I...444---- - to it 4 ItI.4 -- M- Z * 2 .9- + * +4- I-- 33 3 33 m 44i6 ;I IIi *Z Z - -- -2 -

% 1 2 Z33 33 of' - '- -- t -

9.V IC4zC1 C1 1 1 t 1itof6 2* 2LIi a i Z Z* 22Li '2 22 2-J - .a7 0 -J

IftoInIfo I I II I a I 24 SI zI SI 442 -2 *2 UZ ;2 2 C.. NuJ0-. 4.0SI~~~ wI Ifl 2; II 44 N45 N4 W. N. N. -. - -2~ -2Z -- -. 1 - - -CC4U *'C

I-

In) 0 o 0 n 0

00

138

oN N N N mm m m m v q q q o m o

w- w II UII w WLLWL .ww .i L LW w wwi , ,W.L ,.

00

z 0- 0 CL

I. 0.3 -0 0N

00 *'0 c' 0.a

in 0 ' to L!(03 J - f Ifl0 Of.-~ 0

w .1-. a z a:

I.- -0 Cc- > -0

It-i L C )U. *-D . :)

9z I.-fl DO3 3 L, : :

-C'd 3.S Y "r-. 4 vN I nt

o Co M z LI1,to #A .1- Ux Ox ' . ;i ;z

O0 :2 -o .. o4 r 39 330- -9t(fn4A(A a 0 Z '0.e Q

. ; 6. 3 11' it i . A 3 ZZC_- u I- ('i w . > O 0

N. 4 It- I - -uz :2:o2 z z_j z KJ Z Z 0 it 0NU. .- fO -3 - U

N .; CNI 00 Z Z Z 30j 0 m- *j _j -- - -- - -- .N 04 .N( 0

0 nuuaw- ,D0 x 0. 1- A~l. 3. A. 3c - 1t 2 - AAua 1.. - 1-xa -1.A

40 IA uiums 0. 4 .In5Ns~I ( N i-N- 1-331 04 V -3 InNN I W O 1- 3 r/O /

4 N. * U 313.W1-1-331-~139 I IN 1U3 Z- 2 2

us

13

m oow

to "

00

9L

0-

z z

o ..

. uo

C9 -

0.2

r 140

06

CV.

of M MO:

+ 0

0

LL a

0 C;.

0 a

0 0U-4 z

(3~~ _j(10l 2) I -x

o *0 I _9 0. _j

w~~c IN II _jl JO-W ~ ~ 0 *_

55 in C 4 0 + z- -j

I (coJOD4ITLL--I1fX ID (zl:3 x a) OD :3 (L 44 z a

0 > Q) 04 J 5 1 o j+* .

oO ~ II v)IIjulX xj1 U7+-.1~~0 I' .- j 2 -3* LO 4o c :4-

L, 4 -5 - n.~ .- 0s ;z z 4 _j4-0) 44 - 501 -1I "7- ;::~fI a..- .-j

IIII0 Z 0. -- .-. z u) 1r ~ zw+ 0-

co 0u 0 03 0 A(6 +N7-:u .. 1 0 0 o 0 1

0- .- z CcI D C 7 -1*"(1 70 i- ttQ L0 C0

- D IDwI- j c 0 ID 01 11 0 a I _ 0 4 If

0" 733 15zu 9 0 1(Lu : 1a 1 1.

Ix - 141 - :, - . ,, 1 LA z

IiIi

C4x

a 01

> - - " n Z n - n

VA. 00m 0 0 00 2a0 000

0Iom

+ n 0iI14

'I!

0

(I)

ccu

E *x a 9

*L 2 0Z >0 )>0 4 0a

Z4 InI ULa. Z 4 0 U UI-t -J(7I -LCL a , n11 IL-i (A .- 3 Uar 0 l- 0f.- -J -iI.4 -.Ill Z 2 CID C0 -q-1 - in In7 4. >l -

LU 4 1- ! r I~ Z! z-4 3 00 u OL a tl)1.- 41 2 2-U

I- OI- OI.> -J 0 4x

cc > L, >IL 1- ) >1- 0 0 0 Z J 00In (17 uJ IJO CD co 03 zD Z -

z z z a3C 4 i ,D 4: -.q 0w 0 l'-> l'-> In L) U0

4 CD 4i .2 52 I4 I.-- ---

co xD >0 > 2 *- - Z- a 4 IL4l(CD- I .1 .>- -J> Z Z -I T I- 10 *-. I7CD

* > ('O 'J In u C13 -l 0 I-ILJ+ +cDa >w >LJ w (nl 0- 0 Z C. . mI2 M4E - .1

Z 4 ) X-. x CO - Ix ax 4' a3 Z -.- ~Zz0~ , 05 0 2uJ-* . U- Q --

z Cl) 4 L) W. . AZ 2 t- > 1- 0000 z>7 >ZI co wJ a- 7 -CL 4 0 C) c > - I (I ) u000 40 ca (lA (n LU. Y z> ZU U Z Zz

.~~~- 4 ..-1.t1L 7J( -> z 7U) awi CCw 0 -1 Z ~ tn) -J 4.-3CLfC

0 12 LJ00 *C(a C 41 0;- -- 44 .

1- z cr > >- 0-4 a- = (naCl <o c'. * - >aL to 0 n m~l an 4a a4 - - -'- -0;. - 0o w - .4- .2 1>;q0 4 -I I. 2- 6- 0Oi1 0l..-1 .

X I.- t- t- 2 - U> ('-0 U1 4 -0-- 0 u-1.1.In co 0 001 ---u u knZ 02w w 2 x ZaiL- :- U- jZ 2 0- ->. w " 0 -4J0

IL 7 -1J Ilo 41 -o U9 -Zl 0 (C l) 1 IfW M- a)t- U OL OttILwI CL' InU 0l I l) a M-0 00)- ) x )z z

Z 2 - 20 Z 0 X4 IN - -1 r 2 Z Z 0 *- it 11 10~(--- it 2 w m T n <- 0 4 41 42 L-. aL ) 00 -4--o 2 " co- z I4+ 22 W

a- a- 03 0 0 22 -41 N -1 - - Lu 0 .- - - - Z> >1-n - 0>:3 G VD)IZ (A Z 2 40 to Z 4 C/x U 0 l- 04<W -- 22 2 z I 0t .1 --0 1-4 4 4. Z - 0 0 0 ZZ 41 O6- MODO o- It 0I.LILIm 1. :3 - IW ir r CAU ;t->> 01 LU ~z III -1co 00 U). P2 < ;0 22 LU2z:3 a....I 0 0 0 z 4.01 7 0In a 0 L QQu

Mi 00 0x 00 0

0 0 0

IXi

I-

0 in In 0 I 0 In7 0 70 A-c'd CIA m ~ m ~ q1 -9 I In

143

us

Itsi

0

Clw4z

+ 00 000000m 00c) 00 0 0 000 000 00

o 0n C M

I.- w w i LIcLLZ .4 4 1c n 0LI

x w 1- 0 0 0 zu .- " 3( wo o-

S 0 4 L#-zuW r m/ Z; z~ Ir z z c

-s x~ 24lI 0 (A 0 2 U.00 L z1:U. -Z < <- 0 LI.I. -I

CI - - I I UJA

* >l z 2- 2 13 21 )-) -A (A< In .4 - - - 4 931 ' -,X c

a. 1 -^ -I- 03 2r I-I I InI (A x

0. 2 n 01- -- LI G- LA. 0 aor - -J 2 L 1.- 2 I CL C' 0Z - 1- Lfl

0-J 22 u-3 Ii .- 1 0- *I.

0 0. 4 ' C LIJ ' 4 I n 44 0 i0 .4 Inio h in 0 I.-Of 4 0. II - .,

0A 0 ta 2U 00 0 -i t.f 4 x LA.

oj z; 0 2 C 0.0 .- 4 0 . ODLJ 4C0 ( -. 1 -0 - (A I.-0 -- xI 0 - LI .4 >.

CL L.-2I 0 In". 1 1 14- ~0-1a I- LL,- 1 0I CON I

11 0 l 0 4 .1. 0 0.. 00 I 00 0-6-- - 1 -%EJ -JC2 I - I 'J3 z4. w. -a-

0. us 9 0 x A wZ 0. . 0.0 -C -9 zr 0 .1 to I-0 u ' 0 1 C3 :3 LIJ 1 0 to 42

In ~J .0 cr2 . i .4 .-. 2) L) -JZ v) -CX

0 0 a4L.- 0 03l 00 0. 3 00.1- w a. N.

m 0

V 0 0 ( 00R000 030 00( 00I; ( 30 0 JOIa- 402 ( i - _ j I jg ; _2 L C L C .M0 L z U

u i 6- c .

0

144

* -- *_ _ ,-I.N, **4-N

C!

r- 0 0 0 0 0 0 0 0 0 0 0 04j _ I j_ j _ 3_ j_ j_~ j_~

0 .

_j >.C

1

>~ I

U!,

aa

I-4

It _j

z . 192

(n UA

I.-I

V In I

t - CL 0

:a .- Z I 11 I AQnVlo VP _ZzzzZ u

n 0 Wo 145

CIO

to NMVME4-C h0 C D 0 NMV00t

wa Ua -- - -- - .

04+ IL

-iI -j

zzI.--

U. 00 .IA Z.J

*4 W g

2 0)- z

CA '- ;

w 0.0.>"U:, 0 0W

2 j . I- ;E

u~ U

X I.LZ - I U--~ )( I.-o _jmt

9 2 4 U9 9-

0 . 40a: 0 xC 0: 0 I-.C C 020 -J -. l* 0 m. 0 0f

x 3 Z!X In u- 1- U-

L U- f.- x- 0:, -J x 4t _- a) +0I zC D-.O w 4 >- z U) ~po 0 1--

-A w 0 (Y *I 0 -I0. -J3 1- I + U - -I0 9 ; ::. '-'2 l'- I- l'-0 0 0 D 11 - 3 "- A -Iti :

0 U- u4 0 1 - 1 1 0> .- N-- u OW 0 -j U) I-9- -UXi u LI 0. N I o -IL0 0: -: Z- :~ 19W 2 0-

I- CcIJ >- Z -'9 & I-r 0 - f- *-o - 2- ? 0-1-0 4 11 *-. C, 000 0-11XX X--. IW 'U I 0 0 u -'1ZZ9- Za

I.- W 1-I - 1 - -j0I 0 m 11ifI <. 0 -1 0 m 11x - - It111- > - 09- >J > 1-1 -x:) Z IA 0) Il .9 I Z U 11 ;1 11 - 0) in M I z-X 0 (A - --- I- Z- Z 09-- 2

o i-wI 00 2 000 U) - 1f-11> -niflU U -. itZ LL--j 0 00-1.0. I 9- -i W-Z W Z~ Z CJZ Z 7X>>9-l 1 -> >0 00>-m 4C0 ,9- 1. ~- 209:Ez --U) W4z 0.--J 000 - 01100 - ID 0 11 0 )Uu x

to 0 %-IT

000000 0 u U

Z

P.-

- n0 to 0 In 0 In 0 ini a inN4 C4 12 m -T int

146

(4T

(0 a o mm 0

T

o 77

0

0It

I.

00

r- - 0 ZxII w

O U C,0 '

Z I I I I I i0 0 ir a

NN

4 C4m

II

o. i

0

0U. I

o147

1!to

0.

4 -i

z -i

> 0WD -J 00

CDZ W

% CL

ft u0 0 0cz -J. q 0 a -

e- U - X -

4 x r. . 0 -i a C0 4 l : I Lo

0 3 uT

a: Z C 3:

u L. . 'r 0q 0r cz -i

0o C 4 X Ico oo - ?0

CL m- .1 -1 LL 0 3 D

I-0 0 US - 0--(J

-i -l t < CJL .-0 U .0CL - 00 a H- -.-0 -- 04

He 3 C - x * I- (A. -q -*0L LL 01.-.L9- )( 0. 4L 4 >0Q u- *40.00

Z z uJ 0 z4it I Z o 0 0x M. >J 0--- 00---

0 0 00 >- 4).-c 0-J' C L 0r -

, I- p. ?- !- 9> 2E zI-0UJ

0 LL, 4 I- 00U a0C t-- *-0.

o I- 43 0 -4 u' a.IL J- - U oZI

o0 0 UC -I'-J-U -J .4 Z. 1-- 4J- * '0 U-

V ~ ~ ~ ~ C 41 34f"-.. ~ -WU 1U

I- US00 00. .. II0OH-.148

IL.

toi

4 ~ ~ ~ y~~~v~~m~m m mn o r ma ni

to -- C --. - - -q 4 q qq m I n n

ITz-+. 0- I -- b IAAi - -4 A

i- U00 0 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 r )o .4444444444444J4................4 J444444444.J .. x .4

0

o0 0CDL 8a 0 c M-

I .- c Ca. W -

z 0I 0 - -xl

z >. GO -3- I

20 1.- 0 c0-CL0 U. z c

w-x o. x 2 2.

-x Ou. > II *.-.- 0Ix2 0 -j >- 3 4 -xNI

0w -C (A IA u IUIZx -. 04-

It 2x - 0 Vn -- 4D u 1.- 0 >- Z xz4 0

0x 2r u0u -J -5- - Or

Mx 2n -0 0 IT M M44

0 U 0- xx x0 U1, 2 3 w u -3 > 0 - ---)L U r r

0 cx WO Un in -i t-, CD 0 oI- C--.In _xM. 4 I I a. -n ao0-rcc

0 - w: 1-ClI I- 0 .LL Z0 444 +-.0 0 a * ,U. 0 -C. -1 -III w +,IA .0 . jDW l' .- 1- -~ 0 -0 .U XN I ~ - Ui

CL x x-a 0 n M n z 0 0 - 10 > I 1-C It2 00 -A -Jo X- W-J -- J- N't; -. + IA.: I--~ cx , 1 -x0rC I- W o C IaC M ~ 0 -J -J47 *

LM 4W5 tfl W 1--1 -> -' c* or M 0 Ijaz>>+ II c 1z z. w1 w ac - ,.L. it 00 P<- 01 CN W I -c~Ixo O 00 Z :ru1-) 0 )

4- 1-c M-1 *-i - -ii-. NC4 .0 > : ." 3 nz 4 - DOOO D - T 2;i I:) 2 i u In 1 Lt z xa0 .1- Wwzwn--J'4 0 uT 0* - U Z I Z. 7 " A O I

2 iwG w WOW InU Z tD - CI> Z )Kz - 1 . - WW Z- '0 I) 2' U4 - (3 C3 i

:3 0.4 WW In ZZ Z 0.00 4 W 0 4 ZLL 0 U AA Z>I-W I ZU CJ 00-u0u1 02 .

Ain C -(3 0 UUU ooolC(nJW-U- U Z Y.-. CU ) u>z- U t 0

1-4 l)in t Go0

-

0

In

- noI 0 In 0 i. 0 In

149

z 'i u.U

C;

C1

a.3

r- 00 00%000 00 00 00 00 00; 0

0

at -*-(

z M

10 z I.+ '

I > 0 -

on of Up4A 1,1 - . - 2C'

- I, z * D > z

C 0uX- u 2Z - m Z :

-. #-- -o 0 i z - m"X

0 L)- I-- it 2

IM w 02 04 42 6 .0-O 4 1.* 2 1.9L a -. -

to co

0 2- -~l+('4 + 2 l 150

Ito clr qt t

t- A _j JJ _j -- ~J j

00

%n -.N La 0.-

0 C;

0 +

09 --411 X -n5

:3I . ZZ.0 9:.- iW Z

03

o In

co - M M~-WON TOt M NVMt M ,NqMr

Mmi M MM M 0W M MM MW 3 (nDC)DCC d)m CO 10M MCOa3 11 a3(3in M aC CO ) f D CO C illCOM O M M 0 a) CM~f M a) M 13M Ma)M CO~

0

o zCD in Z (

+. Z

U-

0 0

0 C

> 02 4co

(n o (A w (Aw 0-I 0 Q

x lu4l 0 .11 ca (x L-4 CL 0 C3 0u0 I

CE. )I0- U >- 0 JI- 3 >LL CO Q 0 tn 0 D .

'( L 0' (00 I' 0D L- 0 cA 0.I--.- 4 CUl $.- co %1n 0 0 -.

* 2 0> .4A 4-. A 4 co 0II 2 CU u 0.- I- - UJ t. - D

0 w W 0) x (AU 4 w .- C-z e m. . I- >-' ~ 4 T A

D I.-u :3 Z 0 1-4 ~0 co 41 09 i- 0- 4r CE EU- 4 2 L C

Ct~ ~~~ ~~ pC- uj 0 - IC 4 ~ 2U 0 0to 0 CDJ L) 0 >~ -0 U 4A A

C) 0 x 14 U- U S Li n U C. z0 0 .4 Z41 0-fE L 0 I'- :F CY C) 0- I3 TE I

$.- 4 - 4. >- 41 (n WCE Q -1 U4 UaL CO .1 0 2: LU toO 0 u U LAW - L 2 ft a, - Z zCEo In cE - U 0( LA Uw CA C 0 2 U-AU 4 Lu 71- 7 C

u C :: - Z . LL 03 u 4 L, 2 - Wf *-:). I-X CU U u I-0 w- --- 0 A~ Ji Lu > C0.0 D) - -- CE

U U 4 *--- WO U 0 (a - u C- Lu - I- LuJ -3 Z0 0 LuP. U' D) 2 w-LA I- -CfC Ux Lu 2: :3 ~u x u 4 (.421 - (.4 . m

--. Z r Cul z 4C U- D) -x4 -f .14 -. cU C- >- U IL U- m m4 - I-T 0 Z 0-, C XX a9 -I, 4C 4 m w( Lu a: U. * l 24 fk Lu

r- I- C -- - -.- -I 4lU Lu Luu U Lu C Lu w Lu 2) u Lf2) LA z 4 - 2 C: P.- 0 1.- u x U I- (A x - -I0 , f 7 0 00 .-.. D) 2) xU 2) U) 2Z CE, Lu 1C44

Cf 2)0 Lu 2 . 0 0'a . -J L) -. CE -J a 4 a. D. :70. 1; XU3D C .j a a 202 4C 4 -1 Mw -j -j WW u - 2 .4 42 CL -D z - Cr r n':3 Z T - 0 00 Lu" LUL t 4 0 41 C 4i II m 0 4 LuU CE CE--.OcurJzLAm C 0 U U-j CE CEZ"- u u u U) u U. - u u u c UC V) CE?-. Lu 4LL.-C.W

(0 0) (O

Lu

0.-

0

215

uJ

010

Ir

InIn

0 3

+ 0.

inI-3

00(00

InI>-

2J W aL) xn xq. x LL

c. 0.

:00

m I

0 ca - aI

0. L4 W> ca 004(

I-. a In -AW U 0c3 ) 4W l 4_. Z r

to tA ;4 -! c.1 U U - -J 9C0 c w 42 0 ) (A 0. 0:

0. X u0u - X-u -JM C;o IIn4 *4 . I

IIn +n (fUx - . 039 U. :3 a M3 1 0 ca *

Z. 0. WZ 0 eU In t11 Io U -j >D - -0 +-- - 0 Il -4I

:) I-- I- *U O N~ 0 0. -J~JL O

C- 11 It _n3 0.'- . . 4 i )(3r WD 3 Z> '--. 0 m a O'- xn CL* )-

1. W -. 1- 4 (A 0 1.- Z--+-J 4w. D 3>o 2 .1 -. 0 - L 0w U.10. wLL (A 0 0 0 4-0 a OI A a -0.0. 3144

In in 0 toInI-Z--

In D . C 0,~4n 0 U.153J

IT

('(A

(D (A z caAC

)c 333 3333333 333

00

x .J

C;

+f U- LI

LD no

I. I-

I- 0 3(x . Lo

02 Z

a w 2

U 1 00m- I - ! U

4> Z 0.4X> X -

x I- UT 0- 1- Ar4 )C 02 -4 x ( w P.IX 4i La - 0L. *J . . iI

v ~ us 4> toW Er- La 1- 4- ln 3 C-- 1 1:3I

w (A 4 111. 00 t0 - .1-Z oCC 3 3 zf I-0 0 ItIo2- ,- - "

a o 0D 'A- - F 0 n 022 z O11 (A 0-Z I

.002 0 4Z -- w z'Uo (A u. ... )U a- 03A0-0u3

:3 0.L-* -0.I C ODA *- X 0C.

I.U-. C 3 -iI3309>~ 0 4i C

4uu - u . 4 0 - (l

0 o 0n 00 *CCOOJC4-CX~~cl Lam C154lC001CA

CD 3 CCC I- 2 -I-------

40N a.M ) CIMT q q 1vq O I)11

0 .i4 jwu jLJWu jw" . juju . . . . iU;wLiU1U0U &CD :c xc :o ta rc c xac rmi rC I rC ma r0 ro ro ro rc r rc Ka0 r0 :ac !o

q

0

0

+ w. -0

0 za.

w 0 0

xl 0 -

0 to

>. I.- LI 0

w 0 or ED1:0 0 40 -

0 - r in Ci

1.- . CdO- C- Z 0 -. 4 0 0*x 011 0 z 0 wa

a. OUJO0 Z . -0 L O

Z3 Cl 00. .5 4 np0 zL > :3 x 0 0 Z X~

a. 0 *> 0. 0 0 Z 4 I

It otrI a. ). fLO 0 I Z4 z-5-. 4* 4 . 0 00<1-1 -. jw in fz

a.0 09 -x u. 0 U., - c<a U; 2-4

Ul 1- -z~' t z in 0 a. 0-00 in L- x ji 4 - 0 0a. ul i- >-4 C- -j - ul C 0 01 0 4 - i-4fltfl) --- j z - 0

In W- W.L 4 on CD - . --C4 - 04-T 1.1. IL CA w2 m C14 11 L Or 2c 1- -- C ICL5 l' + I U- IL x 1, I

I~ Z IL 1 I2#X *r w _C u I-- w :*-..-. >IL.. - 0 IL1 4 0 a. to I Z 4 N .*C t --C iJ (N

4 - O0 z L-O-C3 -c0.. z0'()-IILI wl WCD MlC. 1- 0 -. -. Ii 0. M L( ( ' -- Z Z -z q : D D 3 D - -.):

0 41 z .II .-- LIL *,,U! .- -LjuI-> Z, - -- Z z z -I -a. LI 0000 r-- -4 Ilo z a. - - 'I0--C<-.Z 110 4Lot -Z0- M .a44 <C1 a. >2 X-IVqW 4 .. 0 - - --- n --- Lz 1- 1w - .:3onl 0000204IZ09to ILLIIU.U.0U-ol.U-U-U,>ZO- L~.--0>COa,-OLIO00Z

a y if) cc.t 4 4w (T

(r r- m(7t m' 0 C4wt000 It 000 mml(I --

Ml

Izt-

155

W

Co3

to c!o 11 -C "00 NC)4 rlU C - 1 3L DI-O 7C!-a-CIC4C4 l :4C N 1 m ()m o

V) (JUULI(JUUul t v UCJLItOOIOO .100 0 o ULI OOOOU00UUUO000U0

or

0 z to

to i z to.I to 0 >-+ z- 4! IM cr

z 0 l- z>1, uU w - La

U. La Z; 0r toino.- n 00 0

CL at o mn o LJ II wujZO 0 < cO 2OIC

wa x In I- --kx W I- a )-21,- 0 uj j ocr - :

wLJ -S w -1 A c

LI U- 0 4f ixi- 00 Z) (A0 n( 0 2 - -1 La -.1 U

C!4 0. > 4

2 -L - ...- 0 4 I 4x40 In r at 0 Z :o- >2 2 0

z - . LU W - T I ):0. >:(A 4 ouwn >- 1-i to z II X

o a (0 >- a-- w, w (2 . 00 4* U- - *J- n (1n 0(

:2~ ~~ ~ 0o --z -(i-. 0 - C -U. 13o 0 L ) 1 - ., 0... wr u-or in 4+ .> ~ .l - UOJ Lo. x 00 *.

In . (0- N C -e In IO - --0 0--- 2 10- -- L-

Co (O-Zu, , Z Oa-) .-- .- > LLW :~:.~l1~I-24 - 4 n--L . > llz~ f

4 "40 -Z .1 XI-0 V) In X (- I . 4Z4LI -) 4 - ,! c-> C3 xz 3 0- .- w o 0 c.r a 4 X

In ing 2--. in V) -3. w(It L L 2o (AW~ ;o- -I -47 4Lan '0 -- *(O ,

I.- ~ ~ ~ ~ U of WZ.07-,I--.2f() c~O 0; I O ( O I-W -La -x .0 - 0 * 04(N U 0* N> C~i-4n~ 1- 0. 0 z.N-- er0(0 .(U .~CL fW _ZZ (rc a- Z- - 0.. W0Z--cc * (-I

0 Owa- C0OU WwW ~ .WWW 9- . af44444 4an L) -- 0 >-- >u a :V---a 2i-c Xcr

:2 0000 004-Ua--a U.1 uWWOOOOOO 02In (UI.-J 9(9(..A3 3 s - c-- 31 .UJ c -- uU uwu

LIu non u u u N '!

z

IM

0 0n In a l in ati-I .)('

156

w

CL

otmm -MT w m

0- 00)00000000000000000000000000000.'00000~

0

0 2(D 4A 2

z >J+ 4U- 0.

0j * 3im 0

>2 )- ZL Co

0i 0 m m LLIi

0~~I U .-- A

0 0 4010 I0 -: 0-

cr - 0InI.- 4Cw :C

2 0 I- 1--0 0 t

o n It 1.- 0 o- Lo 0 930 w 2o

a) w 0 04#

0 I 00 4) 0W If4

o. wC C xI-j 4- L; - . :0>- *-

2 0 0-uJ 9w- 0 - wUJ 3 _

0 2. -1-> 0 0 > - 0 u2 w In - 2- . C)9- X l: 4 0 U.U. CiIi,0 o- OCu C0 xi Cx t- 9- Xf ;<U :)

o 2 Z =0 > 0 00 * .i .- ' O0

S .9 ---- a20. -' - 4 - - C>- 9- :f 00-(

0- w L. 2 0 1 > ;4 :: >-:: 0 1 2 0 )Z U. -a- 0 - 3 - (S .- Cl-

R- 9- 0 0 4 *W I--( W 0 22-I--A-4-wo

a:2 .W - m2>- - ! f (- - .- 4 -- 0 0 ZZn n -Eto I- 2-.-O Z; < - -- 4 0 - 4 **wI'

m -~00 0~ 4O((----L0. wa CiiV)9- 0 c~u - Q D In(L 0-fl (0(0 I M --

0 0 0 0 4 0Z W J 0 0444

I- I0 00 0- to''( - 0- - 3 0 .0....

0n

too

in 0n0 inC 0 L000I N m~. 0m -

15

Ill

00

+ 04LA 3

o. 0LL0

0

WO 0

o o (A1. 0CAO 1 z L(D -O

.1 00 'Al0 A W

ii In : 3XO . a3 L c n w U

a M2 4 a 0w0-f 1- AD w 10

En -- ' W% - u r (

U< >0 3 10' U AD 0 '

0 ft U 1 0 m c ) i ( :3w 97

Al (z LA -jc O 0 Z R 4 30 xC n -

04 0 -J U(A V A C w q :-J 2i :3 0-. >U~ 1-0 0. ,l <*aI o C - 0 u< U wwa

C -% ~ Z 0- CD tw3 n 0- w c L - LL -0 )0 0. )- 1- T-.--AD1 l39 C LJL 4 o0 1-0 QW (A 0 4ui 4Z) 3lA CL I- 1J I. w I I( n 09 L 3 0.4 co .0 .n *- I

f, U) LLZ -0 V) 0- LU.) I.0 x - w _ m ~ az z 0 D 4 - a L D I- D AL I.- WA 0-AD'

4 Ar 0C 2~ 4 0 0, 4 --0 D L)-jt 1-AD(A3 ) 1(39 - M. 4 X1 '- 0 :3 0.. $.- CL 1

0 0 4 AL 0. 41 0. 0. 0d L0f >-LAa2 0.0 2-- X.u 0 * LA CL : A3 fA0 -9

*2 2* 2WA Z. (n -'- .- 'WLA4Inft 0 00-C 1&.l.- * 4 a 4r0 4 LA .- 0 LA 20 -'

40~~ 001- CA04-- U ~ - > C..f4cx 0 IL -J Z 0 4 2 - 4PC .ZZACL

0uu u 0.4 -'(A -u IA A Auf l > - Wr-0Z

I-~~ 0 LAin-4 O 0 n 0 in 4 4 ''-- I0..A O0.~~ N -2i mO n Mf - L . 4 A 2. .J aA f--(-f-0-

0 AL -4 20. - I 4 Al 3 I- 43 . * WA/44158(

WU

N N N NN M m mm m m

- UUUUUUUU)UUUUUUUUUUUQUUUUUUUUUUUUUUUUUULUUUUUUUUUCuj~uuujuuU

00

o w

to zT z

+ 4

x w

z > 2 I

0n CL I

CU 0 a. u :3 0:4 00ocr

C- CO CI--a. Z 4 i r (ACC/zi0 1.- W C- u0 WJ z 0 W

- U- w -C 0 C

o 02 LA -- U -/C-CU 0 0.--- 1+ z 00- CW

c CD <C h n. &L wUcc - - gr -I- uU CU W- -

(A C/C0 0 J4 Uu.

* 2 u- _: t . C/ (A U 22 r- C 22 w U.-T4

2 0 Z 02 w - I.- C! C 0 *

z2 L) I.- --- ;D ;J a. C 2> 0 2--- u. .' lxo D : -C x -- COD U- 4r W CA N~C> > 4a. CO x . ('C 0 0- 0 -J 44J 0 CU (W C. 0

U n U/ 0-C C/C C/C -'a itC-.~ M- -I- ----- UC 2 (A4 O tD U. CU X CUCQ( CUL) D -

4 4D -a) (N to LL- W 0- 0 w- -'i - .--- OD> 2 44 rL- C' 4 x~ L4 0- x- C m 0: -M000 >- 4 -C

0. O-Z inC I- i--2 - -- U WC-2m s-C wU mWO. CC0 >' 2 (n > 0: W- 2 a - CU 0 xC , -J -JCN-- 0 -2 4 X 4C a. a. Uc - --

x cr2 UCI.-.C 2 b-C+ .9 - 0~DD-. Cr02 -0 m (-O -- CU ow 2C-O CU "0 5/ 4 2 * 2 U CC 30- .* D 0

It 0- 4CDW' >' - -W -1 -- O:3 :)-2 2 C-Cd'4--0 0 '-C-~ CU Cr0 UZ~n aZ > -I ZZ2 0 A2 U- *ODDCID C I4/C0>f / -1U9. W 0..- ZUL -2 - 0 H-.- Z CD U XSCN W - >'NNNCCdCD - f-CClN-

T a OOZ U IC -Z -4h ofJ 5---cN115 5 C- 0......... 0r- U-I~. -. -j - - > a. - 0 .4 -4 C -1 0C-DCC( D CDC to toto-

D L -C IZ40 2L I- Z 11 0 - > 2 C" -5~- -" OC- -- ssn-Z - C-S-C-C--C0 XC 00 a.U0 C2 4 L(C- 03 :2A CZUUCC i..Ur X -f4 14<4 44(k I.. U CU 2 2 i In .. 4 CC I n Z D >- ->- - - - U -i 7- :-C -C -C -02'2 '2 2to (50C C- C- Q-JC5 U U C OU UUU -j.. . . . .acrccrca

2 -. 0004 00AD DZ CL 4C 0 4 O:2Crmr22'2 C Uu-CrcrMrMrWrMru-CWOOWOOCCCCC(AC DUO-JO 0 -0ZZ'-.Z 4 2 04444m4CD u -. 324-Crru-a ---- U

CU N Cd('

x 0U 0in/ 0 CPOOOO0

u00 UUU In 000000 u u -000 CID4NN 4(CU2

C-0 : o0 2t

0 l Nt

a.5

'A

C,

C4

Int o~,(D

U. u u uO

0uu

0

o 0co

'A .M

w I _*)1m

dt 0of

-a.U wJ

ww

.40

. 2

00 Io4 to

0 ~Jc .-

o 4160

Lola-.

us(2IL

0 v YNNC 4C 4NN n( )Mm.

P;4

z XV - - - - . -

+ UUJUU)UOa:.UULJ a.>-'JUK'JUUr-0 ct a xi~~Wd iii~1.~~~ii U~ WIi~~~~u~iii.~u

I.- z wX 0 -.0L w I~-

Mi 0 -4w

oo T LZa

+~~ 0 cr.

z usMi.1

I- L 0 0 OMix 0 ML ait

ix r, In IU (3 ro

I. x I - - Z jZ * 13V -

lp 2A Mi 0 4 03c -. -e4

a - 0 i > - X. to zA C

X Z U. .. >4 3& -U0 000 U- 0to0

4 -' 0. 03 - 00....0. 0 Gn - MA - 01-3*I w

CL x c- - x< U U9 3L uW C

0. Q xll u1' o ~ ('4 02 1-U 1 -X0

xI U. z W U- U U C- 3901V

U M4 0)- 002- z- z 4 -+4. 3

0cc! > -CI-4n w 3 * 3

:) UA 2CD Z CO-" a x- 3- -N 00O z 4 0 0- .- U --I 4 3 c 40

-T Mi~ 0I 0 )0 3 .4 0- 4 3r- Zn(A - -4 X-. ca 3 4D (-wx > ( - mj.0.

0 3 U - L, L zzx :31U( 0W0 )- - - >. .1- .Mi x0 --- 2 Or ~ 2 3- U)

rz oi U1 .- L"r3 0- (w 34 c1)

2;*. i 00 0 A 0.- .o 4 0- 4 *Om.W DO o

0A 1U. Z U A *MiA0 U - W - OW.-.cr444 4.3c iC W2. 3--11. 4 -I .4 111-~ 2

u 00 -- 0 0(jIUUu u'J Q U U U - - (.4 ('4

Miz

in0in0I-0I2 4C

16

cl.

o >>>>>>>>>>>>>>>>>>>>I I W w w U.1wW LWJwUwAwUJ sW LaWWWJ L

z

I.-

+

z

:3.1

>4 1U) >

to Wf3.-

P- w IZo

IL ++

z 1- C 0

04( 4 X- I& u

I.- aw 4 4 w!S U) ) 0U -W)

1- _j z 0J- 044L ZW0 0 L

0 2j >) 41U +0. w z0 ) - 1 U.- Z

v. di I. U.o r4

0I Ip 0a * iIt 4 00." 0 - 0

0 CLi ) 0i - 3 -3 111 +I4 i Zl'- 4 '-c

00(A Ifx. jUJ W l - If 1 2 W:

CD4-2I W 0 1--M in

D - X U2 0 - -'C~wm3>w- In 0. a 4 U. 44 0L1-if c .

0 n 0. In4 -

:2 ~ ~ ~ N 162.. -. X 0~U w

WlIto04 4i DI DC ~m

vv qTv. 0 0 0

IDC!qq ~ ~ n~e~

- ju jwwwwIlwwIlwwwwwwwwwIlwwwwwwwwwwwwu iu WWUJWWWWWWWWWWIll JWWWWWWWWIllWWW WWWWIUWWWLIIWWWWWaJWUJWWWWI4JWWW j

_1 jZ _ _6Z j _1 1 j _6_1 1 _Z _6_1Z _ _J_1_0 1 _ _1_6_1 Z1 - Z Z_1 Z 0Z _ Z Z Z_1_0 Z - Z_1_1 Z1 _ _1_1_1 Z AZ _

t ~ ~~4~ 44.J~ 444 444JJJJ44ujo j

LA4I,

0 4jD i0

10 D 0 ~z z a.

n 0 kl. u 0I

4, 0 (A w

I- O1 0 ) 0

aU 0 Z 0~ or01- 4 - -C 0 -

x . C - o - I- D U)I0n C)qe --. 0 0U 1.-.x447- 00 Z0.. c- a.

0 004a 40 e--00-1-1-04j x L -> L-4 0x 0' I a

0- 0 0~ to0W -- to 1z D r (

I, a :! - Z O co -4 ~ 0 Zo 0- 0 27 0L)0 %.J Za -. 4 n- 0

Z4 : Ze. ta) -- 00 WZ 1 :0> i a- 4a. ul 3 41 w 0l 0 1-:-M &

0 Q~l 0 m rz< :r4 0- (A InU I-.- 0L I" -n

.1 Ill Z- qf4-1 0- 0 ~ .41 -- .oL > 1-4- -Z-. 0 0. L0 I.

CL *10 u-. z 2 1x1 t IW W - 0- a. 0 0

o A Ix- 0- 0 41 Il ~ -1-0- 14 In

0 .1- 0 ZZ0 D -- W(.- 2)( 0

0.O.0 z4 II! Ito ItW 0 a00 a - z x- - -Iena~n-- It-0- to L5 111-Z11 - 4 .- ~)(I-

C,- 9( 1H I o. to -I_ 1-1 It~4 0Z 41 1.0 4 -- of n *It7----

D __OU 4z 4 0 0.-a. x -011 v>>> ~ CL 000 0 -N-D(I00j V 0_ ).-4) -4 1 14. 4A -. 1 nee xC %l1 N h w111 1-. IM nD 1- u

0-'. CX 00 00 2 -clC0. - - - 0 .

0

0 In In 0 in('% i00~CN Noo o o u o o m' in -A1.

116

to M0 NMV0Wt -WM0 MV0W -WM0 NMV0WC Ti -C 7

w! Oa0 0 W O t ~-----rr- w w w w M M M M 0 0 0 0

I, W W W W W UW UW ~ w w wj uw w w w w ww w w w w w w w w w

-. . j - . 1 -1 - . . . . . . j -1 - 1 -1 - . . 1 -1 1 -1 -1 -1 - . 1 - 1 -1 - 1 -1 - 1 - I - j - 1 - 1 - j -M LC LCLC .a .C .a0 LC La .C .0 .a f c Lc .c.c a La i .o f .aC La ai

V)II A IV IC t s4 A0i C A Ai Ai 014 A0i 0L AO0000000000000 0000

+ 31. ~ ~ ~ ~ m C ~ IfCt0~-OO( 4f

o ~ C W W W W C D W W ~ O~ 0 oo~ o ~ ooo

+ W W W W W W A W W J W W W W I W W .W W A W WJ W W W W W W W J U W

o~~ 0 . d0 ~ 0 a ~ a ~ ~.

0 1

CD - z c

a. ele(tN(

0 0 0 I I t

c-z u XQ 7 0 N.O -z z;: 0 000 -

-, 0 -' I - u o -

0 0 90 0- 1 -z

r- - O w oo- -o 19 Z OO-zz 0 -0:IT C - W0 U - ~ IA It~ IfZzt

im ONg 0 -(0- +

* T l- -N. t: 1- U I- Z- CD.1 -*ux, W LIU 0U aC 0 0a 0 0

oJ i - In -030 -C C) -- C CI a 0 6zaa aa i 00 i's. W* .Uaa ; O a

W) 0 0 N~. t I (-- N -

I UU 0V IM v-N). D ~ . C 0 w ItU0 - -at

o In 0 to. 0- In ~ N. 0n N. inO*.IW (a( CI cc- (f m2- - w- 0-

1- + 0 - (N N-- CD Z~f IZ O- IC.2 Z 164C

0

Cl

o - - - q 4 c r q q L A t A f l n llM

W WJ LU W US US LU WS W US WS WS W LU W U) USJ LU WS U LU US US US UJ US US LU US USJ WS UI US W US US IUS uJ us W US UJ UJ WS WS W

0 Z ZZZ Z Z Z Z Z Z Z Z Z Z Z 7 Z Z Z7ZZ Z Z Z

j -

w I.

0 (A0-

CD 1N . - I-

+ 0

: .-. 44>0o

('4 L5400

0- 1 1 -.x I

0.0 Of.- I

N 14 t0cD.- c-U Z X 0.n' US 0 -US-ZI Z

US0 -(Z -- U, .-1U2U. D~0 0t- 03 0 w-O 0..Z S- 4-

a C 0 (x 0 0 W1 EOLA 4S-j

i- - - C CA. -, t"~ C, V) 40 0 r 0US-0-(4 )- 0u ui *w - z- uacc -- * ~ AS I -

-~~ - - -(. - 07 XC- 3

* ~~ 0 C) CL * .) O- 0O 0 0 0-M00--U O ZII - -. a). S O--O O c. L a Z .j:-u Z t Du U-.0 .0 ZC0 - ca 0 )(a 40 OD- 0CAZ

.7 -3 1 (D CDDto 0 w- 4 (r. L.-. a.-.L23 0 1 D .-. c( o--- x u 4 x- 0n-0 .- C 0 -OUSUSUS 0i CDZ ~> >- .7W 0.tz u I C) - I .- -I- CL *- *cx- Xnz r- z I.-(A

02 -! 0O- U * (01 %. 4 ? tDf fl 4, 4~ .-. 2 ;01 Z co -3 1 - .3~ US W3n USZw u iz7 Z- 07zI.- a* 00 w mU m CL(~UZ~U~4 0.C. (3 0-00 US 4:t~ .---- !O0 0--

-e (4-Or M23 *c0al-u.-a9 -

-- I- Z f-.. -n w C uSW wU U- r 1

43 0- 2 It :,- x 7-I -' 4-' I4 p- -

r. 3wC :3 z0-~0 0 WOZ 0 0'-4N 0--. 0 00.

Z l-0 1- -, -2 0 x ~az Z (z A-0.-l-7 Z -. I-0-.

z 1 0z z 0713Z - -A Jc a-0 i. Dc cccx - crro0 -5CL 0U0 a 0 -jW 0 0 0 <a a0 4 a -j 0 0

z -4 N"c' - ' - M - N" M V

-J 000. 00 - 0 -(41

In 6' C C00 0 0 o

US

0

q) ini 0C 0 in) 0 In 0- ('4('4 A) C) 4 CD T)I

165

N q0t - 0 0 -0: NO &N T-W-Wm

I"'

00

WP z

J, 7.0.0 aO.a ..- 0. .0 0 0. .0 0

I.. x l +1

.9 0 u

tW z

Q oo > - co N0o

00 +4

4A (9 Wm 0 -

>- 40. + 0 a 0u

a (f u . 0 + -00 o u

4(3 01 wN WU0 NKl.0 1w "i) z za Au-0.l 0.q 1- -JdU- 0L: u00-o

( u1 ( - or + +

on A -'x.Ul,.>c . - 01 on >- 47 *0. j+ _W w _j- 0 (a IL -c qql,

0 ~( (0 4 o0 0aL .. JO 0 -

-KI- - c 4 cc44 1 J l It, 'N 42U 1 N A 9N0 0 * 0~0 " 1, n *c .. Z* 2.

0 ) irl-(00 Z 0 (A m- *'-1(d .L..~wx>o 0 i i, 0.-.- 430I.. a.W OO 1.J-4<.- 00 (A Q0 IW0l *- -j . 0+j. -_

_j t U b.- .- x* -- :)- cc L~ -(1( (A IU)1 U -I - n0C a0 It.- I. -9 0o U It *((1 24 -0-N- 4-r

I. * 0 ""! N-- 0X M Z- . -~ 4T 1 * L ,44 I ) Ci 443A g(AN 3 0 w I

_j cc I.- I.- (3D 011N .9 c or.A >--( . *-...uZA* u(V u .9/I

w uin.-. In I -20 L.40 4 0 U0 2ll . 02>0 020.-..--.Z(IV 02 ) 00 1-. N m-4 ~ U 00 >-U m( W dd).W

016

C1

£0

40

T

II

to xCL

+ +

LA.

z z +I- > i +

U- 0

It F + 0(n I

o~ +-Z toI>. U f f

CLC~

o J x -f

4 -J Z

I.- I it Z0 I-- 0 t1

mt C3 4 j - -t -j 0:1to to 11i-W

mm 0n .- .- 1> +0-iO

I.-n

o, to. 4 0n CD 167-tf~

I-

4C

to1

Iq

00

Ccn

o tIn C

L&

In

0 cc o

0 0)x

In

U, *4;a"

z -C(> - 44.IflC4

0 *0~0o- 168M

UI.9L

"m otm4M M C

NNN.N

2 '

0

CD(0- a ~ - I -

.- 2>-I.-

CD0 4

CL D

C-C.

'I-. o i z2ILuC

Z 1. 2 I-O z-

OIwI 4z 0 oi Ww

o u- u - 0 0CL0 Of .-W O- a 4N ~ Lnt

I- C, - N0 . 4-

in 0. In -(N inZ 2 f IC-- X Z~ I2 I.- 0'-. dO~C .- aIX

Z I- U i.II I 269 0 0169

C- nt -CD (Aso

- uuuuuouo

0

vLAJ

zIi.

a:

Lis

0

L- in

z t-

1--0

0

-Z Za n a

U. La Z

I.-- V)0z za -. 0D- X 9- CL uO

u U 0ru

zr- 0

1-4. U

I-. 99170

PROGRAM LISTING OF SYNTHESIS

I

171

r- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I Millzz z zz z z z z z z zz z z z z z z z z z z z

o C:

C'-a()wl'

ot ~>-J! 0 U-- >) -

-T 1.-0 o- i 0.) na

U) 40Z . 0.uXmc1- o 2 Z 0 -C V) LUo L0 u- 0 -A- $.0 l' 0 .1

i0 _j 00 0 2jLo o. U ) mo . 00 ZU4

4 or I. in-. o I-toN0

I -0 "' - ;.;) 4fU 0 0 U)'- a

U, -. 6-- a- 00 (A -C2 Q x4- oo0 20 (A0 U) 1- L. LU

U. o-Z o0 41 x *r'. u. 11 z w o0U D 0.0 co -1 -4 -L u C11 0J14Z)

w 9. !: 3 1 - - - 01 -U X u I- VI a ILIO -.. M- 0-JL zIn. = 0 U)4 -A C DOU

0. i .- Ul. 3 a ~ _. 04 - 0. l') w0 m.4 14 E NI C-30 4L 0. Z d (Cn ( 0 0 -j C

0- '% $. u0 *- 4 U00a- 0. in 0U) w m -A 4- 00 U)4 Ir ( r ! !

41 LU(> q m - 0- 4L =; U) 4-.L -zo A-o 0.4 a a 0 0 .. X1 U. .9 4.1 w 00 Z.;

Z 0 0 1)C3 10 ) u4 (A z I .. < P.- x T.A MfJ..U3U'- 4 0. LL o- x 0n - LA %

0 m0 w1. V0 m Lo:4 0 (A .- I 00 2 t-4:> IA 0 - - Co Lo.U 0 -C > >- CL IIIA -0o w

0. WLCO 7> j AD 1 M X (A 0 z A.L 0 1; xcI- 0-L M ~ Ir -C: - >1 -l Co 0L -a WU in i

Co. L. W -w 1() 0F. le 2 '4 UU o--A

0* * 2 ).. IX(30 U) i-0 w (3 2u w (SI 0 m in m -~ -U 00j 1 20I -L.A1 4 C AL 40. L - 0. -.1 X- Zi I- U.U >i 0 z x0 .o 0. 00. to ) D u 0 in -o u x U) X1 LALU. 4

0. 00 >. z) U) m LU: U. 4" 0 :zI U.,00 4.- 4 a. -u II x3 U. A- I- 4u)4"t 40 0 WU Z' a U) 1' U.It- 0 1-- z (3'- I t 1-

9- 3 0 Z4 U fl (0. I U) 0 -9 X X 22: i.I0 wL ; 0IA A0. 9L LU( ( U) 40 20 0. x-U :) 0 In 0 f)44 1-) a.

-.1 0 00 0. 0 43 (I to o 0.0 it it0 0n M U)I or- a z ww U) I- a. aw u .- LU 0.1 U)- w j

0 ! -Z200. 0 Z) ) L L K. -LA .1LA - z i mm I I6- )A .- l4'L Z 2100 U. 0U w 3 U) 0. A- L 0 z Ij- 4 LUA-()('1.-'--.-4 II I-

LU2 m .E u mC l' 3EI no - j_ -LU N..N) 22 Uo'- WUI -. aU

1 0. 2 -. -j - a. dc 02 -4LLAi --0 L ( -0. -4. -tz 0. N.U '- a . 0.- a 0 w110 0 in W-i UL M . LU -C -JIL 12 u. -u u 0.00O.I L U -

0. 0 00 0 00 2 UJ L u. 4 (1000 U)Z J-Zu uJ u Luv

0. 0 t0o 0 In00-U4--)) 0 0 .kAIM

17

ul

CL

0

SnU0 -1

I- z~nf0. (AII I I I I I Z II I I I I I I I ~ II I I I I I I I

Nz ZZ Z Z Z Z Z Z Z Z Z Z Z ZZZ Z Z Z Z Z Z Z Z Z Z Z Z Z

LU~S I za0

0 aa

+ 0 5

CD a D . z 0

0 > 0j z Ln LA 0. V

I2 U. (A( 0 a C

5- r- LL u uIi0 -DL 5- >n 2 L -. C In 0-

0- co >- D D C<- IC ) XU

o. -Ju c,.T -- , Lw (0L co + i' C :CLDCI.-~C Z. OD Z . La 0 -0 0. 1 C-4-L - -

LL t9 W %0Mo2r a 0 1- 1 0 A-

0 2 CL 0 2 X .X & n) 0 Ir C >zUJ C

11 >a W a ZLLa L2 LI -Ta IN IX J - i 4 0 C4 -% m 1 c CWI 2:3 z w7L X - L4 - .9 M. 4 a.XLLXU a. -j 0 0L.Wa #.. > t

ax +- #- U - e4 0 CDC co 0 fc A- XZ - c - 1 >. -u- 4j --s -. f (2 0 0S

if a U 1.. *9 aa :) w t 11.3 :11 Zi LL 2t (Al C4A CO 0 In (A 45-ziZA Z

.0* L IL 0 0a c. 4 s- M w ~ - -j11 z- 01 C4 >. CLru cu CL 0 su - 0 0 0 a. Q T>'559#- L -C

> z -J IL -j -J C- Z 0 -a -2> 0 * X- .9 o. 2 0 5- 0 La1.- C

o >Z uD >W A. 0 tr 4 3 0-4. . * J L

3.09 O .Z 4 00 .. - -0A IC CD 0..- I.5 a a

5- ~ uu 20 2 - az a -u). 0 I-u -1 _* j cmJ a. -r- a

0 0 In *SsS s-s 02 L -n 0- 0n ZIZ 25 ns0 -f2 LL0- La a- L a -CN -

4 '.-C' a ..-.. JL . 5C55dC54 a. 0La.W 5-~ CLa. I -C~173CC

I,

'h

0

M0 ( 0 t Le (A (A

0

c- zxzzx0 > >-.-> > >

I.-

0 4

I,o o

+

z VI-.

U

W l(AN 0

I- Z

> 0

CL CD0 -0

LU - 44 - = -

• " -

I-

,(l

Z v

W cc

0 0O

cc

o -0 ow

L a~

C47

v 4 -......- s I -.-

Cf l q at cr a00 1- 00Z

I

17b2 0- 0t

0- -- -j*1 *!,I, -i -i- jA - i- i

4

a.4

CC.)

-~ ~~~~~~ 44(A44 4 4 44 4 4 4 4 4 4 4 44 4 4 4 4 4 4CD ~-~~- ico

0

to CA4 i-i(-

oA Ui x -

u *l -C CmD CL .9 *U

4V 2 4 to 4:> U

xi x 3. .9m zz. z J ..i P. a))- co U)D 4 h UA An Zo m k

M C; U. 4 I 0 -j z .

.x -j * 0 " Ux 4 Z;, u .-. 4 U

0 0 x 1- 0 . U. CDtoL t - 0.

C.) -C a ( C) -2 0i 41 1 -

CLNf--r4c of Zn - - ot2 0- 2A 0 - XC 2j m a,- 4(A U) *_; t& -J 0 M- 0) -4t A

4i x 0 X - - 0 0 6: xDCD -4 -1 I 4 0 z

41 2 IL -2 0 Ix U a ) M U L N. 0. . C jI. (A (A 2 cc z x -w- u 0iW- . r x .

Ix _3 a 0- z 0:3 Uj Z 0 91 0 : - :- -

"I -C " 1 - Z w -2 D C- " ~ x- 0 - 0

o z. * U- 4 J w m (3 0 &L aZL 0. u L

ca u u .0 o C u- 1 0 0 Q~ C 0 C- a 0 0 .a - 2 a U

LIn An) . 0 .4 0 I - 0 N 0 U). a4 ~ ~ ~ ~ ~ ~ ~ c m -4 C J U N . IC ~ U NCC -L

1'. 4 U 0. 2 0 0. ) *N.NC.) U- U- 4 L CA-175-

o a:

I. ( . coc

w. 0 D0

D xi U0 -CT 4n c 1 L 00

-O 3 . .- V- wX 00 a

a 0 uI U> . 0w I. 00 In ;

M -0 Oh. a. 2 - . o c 00U - O - m- L -V

ID LA I-.- w 4 0-(

u -EU 0 In -C .*u U-J. a 3 (I.- C.)n - -- .l .

u 9L 00 hi 0 - ) - 33(A ca )-O 1.- I. 0 C

0- z )c I Lfl 33r L - .9 .w 4u 4+ D ai f0:

3.4 *0 3 3 -10 x wwwLu U O 0 a. CnIIu) 0

x U.. 04 :) ZZ x u02 L.2. 4 0n Z- -C >u >

2N 0J 3L 0L 0- ' 4f- Z3 XX-12: wN 0P. In UJ 0 & -f44<U 0 Ju xco 1. mm >- I- 3 23 39 Wi -.- EUO O M

LA 0 41 U. J CA In + w I-.c ~u uj a (

z LA 0. XLI L- z x-h 00 -3 z u. mI w W

x 0. In 0 m )0 u x0 L4 . . U. In 4 + A >>cxc w c

cr 4. 1%I -. W 3-o CD .- 0L ---- 30- 4 0G. 0. 0t an~ :) c I..- 23 1- 0 II 2 wuj3A 2 CLr

3 - I.i- >4AU O * 394 -0 W j U. -4444U. - L 00 I6.-n in~ 0. 01 (A 0.3 a: l U. m 3 3 _ ;, >> 00L i aM , In U 2 3 M -4 Un O-l uUI 0U a---.3 -j CD kn LAc omm):; . .*

u2 0 1.- -C 2 j I- I 2- b. 3G. w- - II .x %L 3 0 I n - -x I XCDZ L 2n -aI l r) . 3 9 0 m m

0 = A Cr U) L >- - 2 0-0 -00 0 LU 4l-+L >O-Z -33~ - -D - u-ommqT0 g x8 i-u z . *.3 .- . .UG .- .U .- .*-.zc.A jc ni - L-a

I- w IL2 .- 9L LU 0-In ~ -c - U.. fl30. 3 qTmm It in-- 4 ca o -0 I.- ai -Ja s2 56: II . - 4O UU I- ml "I~ M3 ~ M M m.G 00

Ln 13 ' 1I 0i of- In " 11D3 of CC 3 *0 11 0 - .J - -. .... T - -I.- 0.- In I- w U-U LL t. _j -- I z. U) to33 I to -4 10u (D

M0. *- Z I- -- - - -0 -. - -J -l - O C- -J X3l~ me 2 LZ-t0~~u 93 0L 1.- 0. -1 zI N. 2. V; a--( 1 -CDCu

LU U -. 4 0 -J I- m a0 wi a - LW * - - - . A X -OTu O AL 0( M- 3UD 0a In 03 -C .9 33LU*C InJ P- ;; - 1 20(9a

4 0 ZA 0U In 8- Z * * *. * . U2 . W 0f00-

In in 0A~ In1 0l In aJDD.1 inC4 N3 z U Z------------- G m*-IV--In

'~ : $ ~ LU.-G. a. WUJULLUJ -17644

ChIn

In (D to to (D

C;

o 3 do c1ca

u. UUU Q

tD *U *

LJ 1- 1- U.

z r uj UWU'u.1

z z

u U

4 0:

us 0 WW WOOI.

Li I.-1-W

-jI -C

i0 0t.- (A CO L .-a.

N. 0

x t-

i

0 17to- NU

0

u A

o9 -jL D-

0L

0.. 4 WO

-- ow a

u 2( LL zA u 0

ind 2. UJWU NW tz Z; U3 z9 af zo3 a - in3 w

CL - x~J cc(IA. C, If 0- -~ UI 4 M-o =1 V uI - W * m . ZU..'

0? a. 7- 20 1 a.. L

a.. 1, I- - o wi. r', I4 L. N m - w uix0Z U -0 Z I , C13 w 0 0 a

0 1 0 Um 49 CN )-z WO. 'a - a; z m a --C4 LA I-j 1 4-. W 00 N OZ - -. JC.I (A z Iw~

I. I - -- _. _flOZ * N O.1l- 0 w nI0.* 0 NA <I -. W)( ..MM 0 a 0-0 w

3 4 9- IS >N' -L . .. O .- ' *- ;; ZWz 0- 4 AUuu .. L.JiL w -04( . - 0 L-I-

CA01 r " ,Z 0 0 - u'IAJ u 2. a~ .0 Ln t . ..- U

In n - 2 -0. c -0 -mW A0f I-z Z

0 l2VE II wL 9-- -q -0 0 w0 z i(N0 0 00 xn-.m -Z V*r - . 0-I. W4-ZI -i Co nnr 0 II 4w. 0 a-'--x I n L.) x u I

-j *UI ccfl ---- J 1 j -0 4 -.-. U 0 1-4~J 'Iz U U - U

OL 0. CfI L~I m -A 4 w 0 a 0Iz 4 OL z 0 (r0 =j .. ZL. 4 -,In :-- u. MI ~ Z 0 204t 0 ZWO 0 X9- IJ.IU 0 C

V;4o L u 10 2 -J Ja 0. 3t- -49 cl- X~r9 ~ J I U U . 0 -J -I u. *U -U09 9 2 x).~ 4JAI0 of l0.z0 .3 ifI -)Dn0 qo I r (n x w m I'n. U uLI

a- a if 6 9..~C '1A, s 1t 11 L t w 1 it I& Ii w P QJJ- IiuO US " of 02 9.-0 *I- --0. 9- CsO -L w U- 0. is W '.9-.-. U 45C.'>- 0 Z r- *- -0-0- 0(Z4?

o 23 - + " 6Z~-L w '9-Z 4 L W~ l 0 -j -jO O 9-I3m4-9.0) 0u2 I- * -j zWr4-- z4 -L J 4O0 In...~-0 CrL4 *-JLJ.l~

0- I/ - .- 1 02 4.o3 J0 m 40D fla mUr lrLAU 'a 4UA;.I C!1 9- CZ 0.- - (A19 W- x CL 0 to0C - 0 -4 )- - o m m

0 1 0C I- - J( N I n~il 3.Un9 -_jM Xh & e nIOL 6 1 9 UIIU I. 05- 1 0A - -aaI~. a -a. 0..s0- -- p-IU- 0. 00 I. I nz ( nU1- -LA-n0aflLAanf ZW

-i a CL 4 444444444u~ " Z. n.J Wi W w ~ w .w ~ w it

0~~~~ Va a ar ar aZ arMo C: r-00

U U UouuOvUwuUOUvuuuuwuu(.,00000000000000000000

LU

Z

I-

- in a in 0 In 0 In 0 in 0 In- o Nc' In

178

ul

92

0 M -4J)k(tCM -N V ~ M -N qM t M

0 i

D D -

Ln - cnu

co - . -- 1 -411.. 0

c 0in 11*11.t.o w - u- J N 2;l 7 *0Z.- -

C4 z - .- U.n - C ft- -

I.-.Oft- 0 I IO C;.0

lz . a X N.J u. L WW m U.6.01 1060-u * i .D 0*WI La

0Z LZI:, - .4 - L1 u LLct~~ 0~t O .1 .1- w V ,. -"

u 0 z . - W 14 o~..N.

N- Cl Zu 01 .Z a A.u- - -;x ZZZ LAWMt1 - 1 O

N..0. 1w -0 (A 11. 4I W-1. W -ul Z L* * I- OM- 0000-nO u m u0- ina 1.

* 1- * a.~- *w W U *I - 9 -JUJI-Wo mIIU1 M- I- 0 Z ~ wWO.OUU)-ID4 - 4a1 Z 3W

000(900 0.4 'j co .C o2 x4 I-ft *0 ::) - (zu

II -I -o-I In U.Z-6J uwun-. wt

I-.~ 9- 0 0 Z- 4ZE -,( *4 .0t *4 f 41ZU

wm0 00 en an,.cn 0~U 0 o. .z3139-A-3 B Z u u cc LL . L&L , U , U. wJ'-Jf U.I-wZw 1(

O~nOO~fl-(4 t-4 00 *.( ZZ ~~t

0C~ Mf ID I fIn I - -- 'S00 0 11 01.0N. to') U - (Nco-41.1I Jl I t - I

q O III WIJ ft 4 O C--ft 0-f - ~* t Il1799

N M f M :

0

UA

z c

0 0.to x -0.q IA 1.

-. LAu. . .x -. V in

00 to

U. x a C;4u O- 03 E

U, (I.- * n n

to, 00 0 2

00 - . Li 1- in I(A 00 11 A 3 3 IM, 0 0 0* 0- 0 0 -.1 4 0 -

0. 1 LL I - L34 30 (A ; 0. :I

uJ '- -J 2 173 0 N 0 14Ao u 0- Li 4 14 w. I.- *. cm 0 I.9 -. in 0 (r - 0.I0 411 Qcc x - . e 0 1. -CO * LA inK

I - InI CA -C Li I 4 In w -J -J12 C1 00 CL L GD in 0 -.0 -. 13 0 U) ME 2 Inu nxIA 1-- 4o -C . L 44 &. z -j 111, x

*I- at . + 0 Li . w* 1100 - 4C x (A InII L0 I.- T * n Z Lnt- Inrt- -I > I-- x x0 I in a W 0 (V - llO ) CID.--J 0n In. 42 . (A Iu In z t* x In -0W-( 00 K - E K .

x C0 -: S 0- . Ci* Inz to 4 -C K IUo Z In- N InwC-N 0C'*n N i 0 DJ w x -

c. U) MO- I:U 0; . -C m m-.~)- (A . ~ . 4(A In C In K*J-4 In~ I.A. I Li 0 ca- o - X..0-1 I' 1IL 0 U- 4 1,- 0 In

o I- -1. 3~ 0.I In 1r-01- 00 0.-J s tA In XKn 0I I I n10 K- > In 0 2 7 .- -(D c -XKKx > 1-I 4I nO-I01 t" - rO

1- I. I/ I- x1- 0. M 0 Ol- O1- ;-J *- 4 *- I- - 39 vd N4 .0. - -J .3 T In In 0 In 1XIn0.-KOx O--K* toT 3 . I t 1: 0 39 304 -04 -f 1 30x.40 1-0 Li z c.-0-- nc-c. - to4 -* 4 D T4 T1 -C 14 In . .

4 I - U _j 4 In W t InIn In Vn InnK *-.- LI 3j 04 M04 In0. Cr- c0.- :3 .- ~ - C40 --1 ( 4-1 Z InA I- IM I L to x :3- 7 .0 In -A n n M Cflor CL W j > - #-- la 1., 1, n 0 1- K. x I- In0.In InA .LAI or II *n C4 I inO

Z 30 3IL Ij 2- - 02020 40 .LO0 * . I Int to0-- 0 o 4 (At- La -.. 1 0. 43 In D > >L0 3. ix Li I-. 0 . In E - ti0 4. .9 :

LI) L I 0 -I -0 0Cd 0- d4n 410 4 C 43 43V - -InA 39 -. 0 of1 Lti 3r it (A.l I 0 1,- * -II 43, 431 of l u.1 .. U a IiII

P.. I.- - IN wl IL I 11 u - - C& 0 u It it to 1.m - 2. 2 z in 3 n In 0 m In t *2 IL a, a 1 11 I . Cli .10 0 10 00 0 2 :) 0 OIIi 1 0 a ll ;,n 0a CO it it (A I' I'd 11 1'

In 1 0 u : 3 z-j -1J- m* I~ 0 - - - - 010 -; !In- 'n0 "Inw ~~0 In 0 m 0 C) LLin 0In 3 InAI 000 to I Inn(n A L INI'4A 01110 t L, -UiNn

00V 1 3 m -i 4Z .J0-j3IMw nL4 44 < 3IC- m&3 a 3-3 am *- %- 3-3 .-

In ~ ~ t 0n 0 0, 0 0 I U- > 0 4 4 0 0 0 0 U0. a0. In 0.

08

Ic

o7 D

*0 000000000000000000000000000000000000000000000000000000000

0

I0

z

IIn

IA -AW

-.1 -j -4

w- W W 0 0 l'- 3 rLL 00 Ln (al 0.

W w +4 + x I In00 4AO tov 3in .-1 3; 13

L)0 U. U. LA 0 > . 03It000 U.

W-U , -. In t* .0 49 *~ IF 0 0 co -j

-C a I-I.- * . U. 0- 0 - 0 u 0iI- LSUW- C'0 C3 0 A W * I.

C' IA .-j 3 3 x~f OW IA 0o I- 0 C' M0-C .- I, y* 0 0 -10 uz - *0: C 0..

:3 co A Z 0AIn x~ 40s-.. - fC C3c0 In Ill 0 M.0. W E Of I- 1- d-M -;-I -0.014

1r3 a- W3 LL 0D :--C >00 V) , rI

U-IA ILI I.4m 0 a. -.. .4 MA M~ X.- . u 0W

0 ~ ~ A V) +3iI .

LL 0r 34 0. IAnIAU0 4 u 0.00M. M tf

0 0 3 R0 In *L wI 00 I .. +W -C -i --- Z -- - - ------ 0.

+ Il 01 3 OA. 1. -A I ~ UW U W 0.-0.-W W U WW W 0 II-I'd +1 0 X.11 > >I X00 0 . 0 I 0 Ck- - - .- - - 1 l CL- - - - - - 1 1 l 1 1 .

000. 00. I- 0.; 000 3c01 d33 33 W ol .3x <2 033333on. ItI- . j 2 j XXc Lc >CJI O t nM- TL nt Di

30+3 - rC r W ' ' L + +V

00 0 00,1 0 00 t 1w 0 w 0 W' oo4 000W W X a:W W W WW W W

0 I

0 In 0 In 0 In 0 In 0 in 0in to C- r- co co0 0 0

181

oD o

r;-w O-9(or Co

o ~ ~ o 00 0 0 0 0 0 0 0 0 00 000 00 00 0 0 0 0 0 0 0 0N. -kkk T x M m C.) m~~~kkk~~~~kkkk~~~kkkk~~~kkkk~~~kkkk~~~

0 00 00 0 0C.

-w xU. on 1 .9 'I - I-. 9to4 .A C'W)J ~ W 1 4 i .LJ LJ *

Cck)I ID Q-. Z- -0 1 I M C

.. -. I .- * >9-l Ut . . .Ci 1, ; CIl9 (4Zr-lU 4 11 01102 of0?u0 itQ 0 4CooW LA* CY) -LLLL M. 11 - .- .-

ak f-.1 - *U-rlOOfl, U- UIt l9 U-0 tc In tWU- I

9-* 119 U UllZt-U-fl -. 0 C) I -1 -i -.1 .-uIN-4 -N LJ U- .-. .4 4 ca V) C- c1k-4 1..1U - *O M J >- .i Z4 0 Z . a4 t 11 1 if." -

-1 -or .4 .-. t-0 u 11 Dwo 15 0 0 -ak 4 Q01 ciz (A 1: 141 of 2 Ag Um XU X 0. 0 05 m'0 ak 1') 11**- 0~1 Q, ~- - z coi im a 0 C:,( U) -

LqL *.J 0 C. - 1k ,) *U& -INC I * .- k3 .U1k' CN ,i. *uk U1k M-. Z -O U-I -- 171 1D15 *w.') W.Zu - ci :-J*~ 0 W9.-9q r- D..- m0 a: 91141 N4l5 > M1> - 0L *. M t

b. C)0LUZ 4 - 009-f 4 >. ~- IxZ->.- *0 Z I 1A00 00 -0 . - - 1 1- -I- wl~k I C14 x >-1-U> l'Z4) ll)1k1>J1k9-~ U. W -.0 _ :r -x z - -J.4 a: o9-I - C) .4 1: M . L tl -C t* am C7 . , 11 09 - >.0 l. = - --

(1) 2O M 9- 9- 1 k0 I U) L If) u) N C .0 tu..>o o or~)C :3 *1 9 -I'~l 44

0 " 0o ; I') 11 >k~lJJ wkk--1 'r * :3 3- 1-- (1) wU)144 - -- 44 W. It

0 D0 . w zU .1k- L 1 -- U 4r -1 A 1. 1. C,4 0. .. 1--I QC 1. ciU.QU-99I...

9 IX -0 9- U If) U. M0 *ci T' --- -I' 1- 0- 1- IN Nuo- uIDL9.-3:- -3: 0: -.. 0 MZI3: ODN:N-393~-:-:-393'U 0:Ik c0N

x- M 9-VC or 1iI U)9D 1-9 T - 9.-~m ~ (N 1- 9.1- or m o- m.. . . . . . .

or I0 00- on 0 ;- 0 0 D 0 U) 00 . 0 Z X.0- N~- N .- 1,- C0 c -, 0 -; (N CN 133' IN U. LL')U 1N WJ W o- ft

0 ) 0 4 0 Im) ;: 0x 0U)) 0L 0' 0' *In 0 U! 0" z U)

-9 .4 cit .1 ci c 4 4 4 4 4 4 4 4 x x ;4 1'K-222r 22 2ccz.4 t c r o r r r c r z c C w M M I W

9- 0 0 a 0 0 0 0 C D0r

0 n o w o i)on 0 0L 0 0 on 0 on 0 in 0 U)C -C4 V. ci on u4 4n .0 N) M IqDn i -

182

C,

OW

o 0cl: z

1o to 0.I .

U. C Z X 0 wn x - -j U-- : a. I to

I C14 l- WO CL 0

40 .M x - D zO 0In -A- 1& -J 014JZ

o 3 0 u 4 o> C2 In Y! MJ 40 c- r

LL fil ccC' el Qd) 0rX1F0 O r .3Z 3A -1 In U-j 48 4> 1.

>. N. 00 A2 a0 0W > Nr

-4 Z1C- M m oU- 4 In -I 2 w(

4; 02 < -1 )(I (U '1- 420 0:3.- C) - ** 00n I- 0 L

C'C0 M c;(L0 In 2Er0U- n a 0; )0 < z I.- U- -0 l0-0

0>o -M - 0 0 0 0 0 0 Z-1 '-r 0u Z. CL 0 4- Z04 10 0- 04 -o c _ aC - 0w NJ1-

20.0 -C20 02 or 4 4 NWflO .c! c4 <- 2 INAx* wU-O MC) 00. . 0U 2 4I

II r . m m -*- In) Xf IN0 -J WZ Z- -j4INc-.- z ~ f -4a 0 -'4 00C C 0 cox I-W 'A-

IF(0.4 0O AI- r 0. 4 !2 U- i x -0A!,o .m 02 34 2. 0:,I*I -.

03 uu 39ZC 0 (A x' 4 0 ~ -1 0 LL uAWNO4 >-0 (AC' n -U z w -0 <n 0: 2r N. I,- w INI:. Z)-'A > ED X .- a U) 0-0 N- 0JI-2U0 MCz C') 4ii - I.- j M Nn CLn m--0.xJ 4

4aM:)0 2- xI In : 1- 0 0.4 CO 00 w3 zu.i

II C 0 4 ICU .) Z. 40. c 0. 4n 0 - C13 4 4 40l 0n enA 3 n *in OW :3 IC U-0- A U x' I N C', 0

to 0 I- I,- (A l0 In 0 39 -3 1- '-' <N - U' In-cr -i 1.- 03 -J LL 0 0 4n 4 01- U' 0-0 0- N 0

CL *i coI M M l' C3 2> 0 0 V) 0. 4W4 -W C) (o "uu NU ooz in. 2 mn -1a w (A 4L 2i <0 . I- 1- 7 m' N4L C 3

0 11 0>0 1.-C' In -Ja u~ I-In 1-)-i T- 1 -w 'I2(1C n I N 'A-Zi39 0 J U 3 - z. 4 1- In a-0 0 : 7 z1 0.Z-- . N 1-a- Z Z WI It-)0 W n a - N. z U'- 0 U-IL- 40 IA fNI0 0

3 a z LL In * 1-n x0 In 0 0 I A-isI. l'Z- 0.I--"-.4Uo. -2- -m 5 ". Ic 0.4 <i- 2- ZIC I.- I- 'A0 lE 0---N0 . 01

4 0 C; 4-. 0 20 CL -4 IA 2 z ~ 0n~~ N-21- 22 1 0 1-4 4.m" U' 9.In 4-2 0; -0 4.,1 0. -2 -C U' I- 44- A : U.4' - 4 IC 1.

N. 2 z . W;; z' z~ - 0.3 1l' 1- 0- *S -4 0f It 0*l-44 - 0 0.M N. fn 0. to 0A 0 IN 1- 2 0i N 0.N N cc- < 1-J N - n4

c2 cm aMI 2. 2 I- 2 2- w x N II 1 L) 1- I- A-1 NU IA ' - -C A

to IA In 2 2 j 2 w 2 E a .4 -1 0. -1 a. ZuIn DA0 0 0 u 0 A 0 0 0 2 0 -x U -9z I0

4J C

0

I-

C1 C4C mvqnnt

183

uj

- - - - - - - - -

Uoh L i Uwu i L JL uu j jW WU UU L jU I JU L UW W JFJU JWU jW W WU jL jU jU>

+ ~ - q ( ~ - A ~ ~ -~~. e q

LL

(3 I

41 0 W uuuuJuJ4 ~ W uuUU W J~uu LJ W u W W W W W W~ ULA JuWLLJU W W J W0 LNp A-

Nu 44 4 4 4u4 4 44i4 4 4 ~ 4 4 04 4 44 44 44V4 44 .01- CC, II -CIC

(Ax4 LIna

Q *1-0-0 (

It -L - +C ax I.

*i o 0 0-

OD 4 0.90<-0 ,in a 0 c0L 01 *

C- N 4 -Zm J JL0 -j u

+- A C .w U (A -J 0 4X0 0 4j -1 -00 N- n - IP

0 * -JCL In('0 0. CL 0 0 4 .

C, "u Lu O(A r)(AVL rU w L L -q j Lucc cc 4* V,0 qv 1 . ,0 L 0 04 w 10. C4ciaw i - .N .

(A I-9 0 00 0.4~L In a A.-L

Lu Z- -1 -0 IA 40 Z .z

LA) -J L) 40 0 (LW 0g-

4~~~1 4 L..JnI

I -1 .A ~ CJ- ~(1 0. in 0. 0*0 0. (A0 n

r (A la Z- m 00 0 ' N

Z AA W 0-O- -M I-4(

AD-AIVV 533 DAVID W TAYLOR NAVAL SHIP RESEARCH AND OEVELOP NT CE- TC F/ 20/A

DOCUMENTATION FOR SWATH SHIP RESISTANCE AND PROPULSION PREOICTI--ETC(U)

UNCLASSIFIED DTNSRC/SPD-0927-02 L3.ffflIlllffff

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEIr3

1.0o

S i .1 ll1j,.8

11111_L.25 1i'~ l.4M1I II II K L~' A

C4 - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

at

LL.

IFn

o. I-.

> > -9

cc + zz 4A(rauI-- 1. I-nzz t

LL LL 44 <h -LL. Cl- +0 .

*0 40 4c U10- A n14 1.- -3 -3 - c -C -

J (2 i- (A

* X Y> n A N z n.xo0. -c 4nI x+3 -1 3: - t 0 w u

u 2- 2 V4zzzin151 - :

UA n Vn MZ 4 0 is It 0n-C . t zIo 0N 40 4 .1- o ' w 0A-n- .a. Z 2244a.rX - I.-t C4 Z t33 - + (0 NL Z

0 .0(f~ 0'-J W - - ** U) _UIL L - 221i-4 -4 In -Z .9 1.4 9Z t t t1 d " . U_ - X

.4 CrI itC T = 1 - 0' t' 4 a31 it13t.1 Y * M 0 .1.+ - - . SZ U A-- 0 iI z-. z -

0- 02 is UU3X Y ~ .- 3. <II (I-..- Ix -C If 0.N -20 41 O A 4 *> 0 ofJ )( -- 3 0 a - -i In0- nL i I

-In- U) 9---4 10 o- 14l~3 0- wt 0< 4~uo ) 2 -- w-- - U0 C l S I n f( 2 - VW-- #W c 30--1- 1- alCV D 2 v 4_ 1

04U. C Int )z +3-t.t- 31 3- 0L- U- -j C 4 - 2 7 o- a: z.0 J 20 -V4 - ZZZACA InzILZ L lic 140 - 1 .a- 0 0- In Ot .I'- 0C---4-JO. O + s.- N-- 0 UI I- M-J n 1E3 00. z*4- 4 1l13+ Al Cl&-4 Z- - 4-. 0 i I- w

oo U~i9 0 e401I'I~ -1 4 LL 40 *4W a 4 0- 2 .9 )- 4

3- -- 'n 11 rf40 44 - M.. - W -n-. u1or r( I u1-40I~~~-V- -0 f- -- t~ a- 17 asw - I-

.---. l C4~nn IJ&.-~In.0 n 4 n to0 -

11C41I>UWU0 4-~0--4~~J-I~J U '('0 ~ -18- 5

aa-

0

o (3- -. . I.- - qq qq 4 UJIlfl f

i coV -I

+ 0 -a uI-U4 0. ci j w ; U;w0L

T-0 x w

z I-O 30. 03 U] OjUL

LL- 0. ':1--. 1

-j 4J 331-

3 -l CI ( -0>00.-j - '- CR z rIL& .

+. 0J ..0 *Zd 10 0IIUD CL CRC- u 1.- .4 0.4

to 4M- . .4A1 Co Cc W ILCX ;0 4 2(1 CRU u 31

ZO 3 2. *. 00 Wc -% n

I.1 U _ Z In 1-- .9 1-o.CR 0 C2- ( .0 a: ). >( .

z 0 -, -31 - 01 -0

Ix * 0 - 0 44 0- I ;a 0 3.Cw 0 a R1 U 0)1-- -

W 0- U. 04 0 IL4LL I- WCL3 0mR 3 (0 0 u I..- A 0. . 44-

* U. -. f *l .44 w cc1 N 0:4 z C4 zU lco to(9 00 N 0 *- 4 W'us

3 U. * 0 %L CR I0 2 C.. 0 (CIC 0 Z 00 1- 4

- 4 l -,4 2 0.t;I- 4. It (A IL 3-31 00 0 4 30; 0. -C X *- >I td JIwI )

I. U .4 W-9 M L lo- 04 lo- *4 N 4 CR %L I.- t 1- -. 0 . .9 u 2. -I 0 CR -LA U. CR l'-

o 0 z id,9 .0C CR 0. 2. 0 4 L I. z44_ _-9 z. 4 .49( 9 4. CR1 U. .9 W cc CR ILW C -x0

w 4A- L :3( 0-. 09 ('4 Z .4 It *> + CC01>01** j It (9(0. CR1- 0 u ,6 L O 40 c- IL 0. 4 9 0J 4m 0 W I ,1

4 =1 0 -0 CR 4-. - 0 I- ;4 4 : :> - InI IL zR C 0 W- 40. IF *R C4 - - 1- (Ai I.- 40.ol- -9 a 30

m 0 "- -C 0W &- 0 .4 0 *OC i 3 I 0 CRA

a z 0 ; - z z - z c0,C, - 0 0) M w I t -0 -.- -W c I.-0 IL 0- -Z a9 - CR- 2 2 IL .L -'. I 4 ILt

0. IA c- inC' -- 0.IL -C u In 000 47 0-o2t0 O 0 " a4 44 0- -. wR IL0 - &Z CR 1 - CR .I Z -Z It 44 -C s t

W V 3 0 u 49 a1 wC -- 3 0 LL 0 0 0.. 4 do 4 wWCC 02

V.. 31- u 0. U.- u U 20. u IiLI ( U] 00 4 4uu 4W u99QC Q

4-~ ~~ ~ In 0 in1 0 In.0 010 CR *-L 4 4 *uC2- wl .*~-.. - --* l U 2 4 J C4 *. m' 4 0-- 112C I- 40 01 1 44

4 1 0 -. (99 . -.CR~ 3 04 ~ 00 0 ~ 0C.W~ CCR~ .-. 4.186 C

0

toq

0 0

0'.U.

.113 11in4 A o

zz uuU4<<<A 0 an;;;; W UU UWW u u U

U.* 4 4004< 94 < 4 O W

40 40 -j -_,-)- 3- 1-3 u 0 In u n 9A 4

ZZ 22 4 44 4 -3- 0 0 00 ju>.~ dI UI > 0 UL U )0Q ui AQ A

44 44 0M' . oJ oCLC a MJ W 1 WnO.GM4~t -- 44M4W444 Ou0 00usWOW n n tn t

-,- co 2 -C * o n * -00 IDaU O In

Iao 00404 0 toa on ?-- 3 1.-mu 34 4I 4 4 4 :0to 0 0*M* *.~+ z+ z + z :

-j -A I-3 W 4

o ~ ~ L I/ in..* ~ 1 3- . -%n -- -C1-Cd (3I-fIn0 ;o ; I; ; 0000++2 23ifWUZ Z + +3n C3k\ZEC 0 z 0.-2' 0.

0x UJCI 0uJ WWIJWZU. oOaO z U*h U O ~ l t

* 0* 41- ---- I1I2 f0/A 0 1.- 0 3IJI ;tI .0 of 3rto 1 3t

I Z2 Z 0 - 3c C1- 3 11~S (3 it ofI- In x to-1t.lI-l--- :a if 0I I -3r.111 .1111

0 2 ZZ3x3 V 11 If of-I u -W - - Z*z*~u x( -3 . Ia I2--Z*---3 z * Z- -.-

- 4 + *CCC * 1 -C 11: -0 .cc- .ccZ

-K go .01Ci W9 .4 C o Il0 o MCI M M-to1M3WM W- 0 t3 .- 3 1 A 4 4 44 0 0 0 -00.-1-3AI-A3 - 1. 393 1,- - 39-- - 1.- X - 1-3 1-

4 co II S

40 Z22z£00

o Q oW

M 0 U .

118

I-U-

13

to V)+--

oc

N 'A

z AZ

0 .2 .V7 2 Z- z z -=:- --

Z .in N 3 z

Wim IAz1.39 A 1 3

inI~ u Uc

I--9

in in to4~ M* -

o - - 9 0180

Iuw0t 0 N N M M M M v v v v v o m o o

x fC, f c99vg c fgI cxgN c f fxvxv cxx

to rnC. W t0 I-. I W C~I W ~ - A t0 C M U l

th x

Cc

44

Z 3 ; Ca.- co)C

IL1 - -

am 4A aIn X. -C' 2

0i w - -- Cl z >c a >c

u-a. a za aza= L 33&lAB W cca z 2Z ccZ. *a0 0a

or ar_.: a O :3 3 -,v) C. aL cr. Ix > 0- u.zm z a

a.. - 't~ >z 0 > 0 2* .*.4 C')')O a 39 m > 0 to . . . . . . 22 . a4r)_N z

.3 ---- - -- --- -- -- -- -- - CCCa .4 Lflz zz zm mm(Azm Nn N > 0 m 0 02Z l>0 wZZ Z Z O O ZOZCDOi

OfI R 3.;3 - ;L 1; *. "-.. . . 'A S l 'A.. ,-C

S9m -.---------- ----------- ---- 0 A.- .5-i-M l-0-AA A f N0 0N.ito a - - C') wZOZZZ ZZZwwml. .2Z_ 3 co (A u3 0 "

Ca w . Cn -to) ". . . . *9.xit i .- .-.- - - - - -- -31UtI faw _j C4 0 * -2 2 2 2 w n # o z .0 o i 1 f 1 - -- --- - 3 Z a.- 3

o . 2U - I.- VAU 2 $. --------It--uaZ-h'3.-iN-znzz -3 -1 3 .7n ga a2l - 0 - W a m -- Cit N - - - - - - - 3 infl w2; a .3 . . .. . . .

it- I. - on I.- )C 0 - W,,33 0 3 2 II 2 -Ut2 . -2 -) II z 2 a. z a II II z - - L-

IL~ - -.I -t a- -s- --Z-Z-----WZ2Z2Z Z2 -2 - 4 4 . wW 4- Ut IL 2 - "---------- . - 2 J...........N--- a--

4w W M .-- *4 m :03 .0.......ow.MO.........ow-0. o2Z--- -- -- -- -- CIOA I *CCCCIo w

~ IL ZC)Cl 0 ZZa a ~inn ai W~0u at us

. (i u U uau

w2

I-d

0 In 0 b, 0 b, 0 In 0 In 0 I- .C4 C4 m' v'a i n

189

040CWa 3

+

U'0 eln'~ot

eAq

0 0

u UUCuU OC.u 0I~ ,-.

.- -.x.

t.. -W

U) Ua 0 2 V

C0 44 4

* ~1 tJ

2 z CA i20 0

£ %4 -4

Z - 9- ..

in 0 9

II

4C

(0

t 4 4 4 4 4 4 4 4 4o. UA~. > > ,. > > > >

lz +w~wuw ww wuw w4A

am 2

z -

I--

uJ -9i

U UA

I.- 14

O x - (A gI. of 4 +

u >1 2- -4 :>3

c z 0 i! :4 * 93

r- 4L Z2 >X 0 21. a O0 U I. z0.

O1(.- 4 n 0 2 . c1 0 1 61- 4A -'( -a

&* 0 Q- -. 4 2l. >O-.+-A n. ,(UaIZ-

0-4

In to19

I

4

0 W

CIO Z

0 zUUUIU

a..CU.

u 0 L"

4 0 u <

+ +

4w 4 4 u z U

sa- > 2

0 WO Cl;-at 1 02(AA x C1 0t-i

co LJUJ 0 I

00 02z= cca 0 0 1.- ; u (

(A '. 0 16W.

33 3 03 > Cl 4 0

W ow 4 0M a !-0 0 +-jIz -

- 10 0 it 0 .Z Z -. Z Or0 O (l I2 L

1- /1 -l of -1 4)_ t1 o Z; o9

1 1. In 02 Z. ofc2 u 1- 44 a+ 0m Lo

InZ -n

m~~U 0 0- *

-~~ 20 4en1 .

4- 0 -. U) N = t O192

.usILI

KM Mo-MMC4 C4 mII 4C

IIIoin W- t0 m O0-d qn

0 1.- CIC4C4Vca

(D :3 0 LI.LI;

+. 1-33 3 33 3 33 33 33on > I t

z iU>

ac u

3(8 -J.

nD 0 a -

v) to 7

1L IS- 0

(Al I. 01

4)- 0z OZDZ -l 0.40 x .- W C- a Or

Ix w 2 in

O -

1.. -4A 4 xI. 4(0.- 0) C) 4. 4

D I D it n I- (At 0n I* ~ in -. D+ -

co 2- zI IT 0 0 #W0- U CL 4 (+W

Z. ZW 0-0- 'I- 2 Li

o x o) -. 40 Tc 0ti ii to-c toIr I Z4 u a 0- x .- 0 - 3

. 2I -W Z. of0 IA W 0. z 4Io 0. -Z COX - 0 ocWi

#A 44) u u a '-t in .ill. 00 I. -) - -

3 ~ u 0. 41J- (0q z o z q 0 sU

0- W ~ ~ ~ C .'.0- I W 4 0 - 154-

C. 193i hdl)

"m ow!!0 ~

-zzzz~zzzkz: kzz2zzzzzzzz

It

I.-.

ae 93

de -C

no.--aa Z f-Z

9z V) L)0

06 C0

CL In MOr. ul a at - Z-

ww - nI-C xI Ni AI .

a-

ww

to=1%a ()I

Zi 194JW* o.4

U U) -ogo

lw

C,

In o

In .- .; o

LI)n:3- 3 3333 3 3 33 3 3 33 3 3 33 33to3 3 33 3 3

o n -f 22--'-'. U )UU)'

In';V

cr t,

to (A - ;Z 0.0.t0 C4 tU) 33 I I--

:D 1, 0 .. iC+ In <a. 0 COm -3 ~ll o m mmD MA 3 to'Aw-C4m m- w('U

r I-LI) 4 m-* < m4w c ci- 4 z a 0 D =0 *: 33

CL 3 -WU 3: 30I nVz" ini .... 3 3

U- (A I. n+ +C) -T in w3hU. 0o LI)C it) 11 11 I t t o 1 I 1 C4- 1

- 0 -' 'L -CaOW4

C- 4i --- =1 4 t,. zXM., oD A Aso411 0: LI)0. ; ;C r;r :a C

1- CO -- tC m' it m t i it In 4n cn )t n A AI CO 3 o0 -3 0 0 coU

co In (A

D: 0- 0 0-D O -.In Qh' u)II C') 0 000 33AV)t

3I aIn( 0V)V 0

I.- -C - . 3 3 Z3 3 ZZ 0A '

In IC 3~ 3 3 3 3oI in 4In W ) 2C C

*0:~ ~~ ~ 3U) m' mC) . C4O4OC4O

'A Z 3 + ++++ 4+++4 C')195i

'Si

N4 TL Df DM00 NM -WM0 N()q0L -0.4 N"mN"NNc n(1 9mmM )m r I T4

0

w M'n V)13 z0 c

N.I U-L U-----UUUU U-U-UU-U--U-U-UIn

(D 1-4 1 It 10 fl AIQ0 a Ix .4 0 LL) 0+ W ULJ Z 00 CL z 0 0

03 'r Lw 00 - 3- 'A w A -J

a D Z. * 4 ' I* 0. -I *

cD 0 va U -C Z U-5- *<za- L U L u4i

U. Z w1 (-nI) 0 4 - .3

- Z,- - 0 0o

<Z ' .40)Z 0 'Dz A n) If; ::5 z I.-..2 Z z 0-ZZ

Z 'f) U)22 DU. (A 4 .. ks 04- -1U.4 0 03 in o 0 !!j .

L . 'I zO> f2 - - U .

4 3 0 * >. LU D UI I0. U- (, -O .A Z- w 0L (n 0 0

t> w0- . 3.) 0. *. * 3 UCI- LL 0 0 * in z- ' 0 0 0o uL

(f 'A 1Z.3" Z < m. 0 4 a x u /I:.5~~~~~ ~ 0 *---0.a 0 zL r33 0U

0 u aU* 9 A. U 0 4 0 0

Z O.A .- .3. 'In .. 0 5.. 0 0 Q ax 432 ~ ~ ~ I 5 Ua Ac').- > * + cr

0 'A tU, -- 2L.js LUJE 0A 'A Z -r a 0.4 LI, ofEr 0 uLj z 0 X Z ZO 0 U- U0I 3L 4 Z -

z *ZL US- --1i- >) >) U- -.- Z Z Z I

:3 co2-Uq U -5 00 > LnI ca z . U

0. 0r 'f U N 0 v' 0-- n L; 00 U U-0 0 (5- &a a r 00L3A <- U. . LL 0 U) 0 0' CL 00U

Z . i 4w *1 (n. CN 0 U)LA - .- Z 'As 0 ar -- 0W W 0 .0 ZUUZ U 0- I U. m L 0 xC LIu + 'LnI-U- LU 40* U0-UZ 0 W'AU) 'A w -V)- 'A I- C

5-c W 10 00 0 -*-.. .4 -z1 'A 4 'A 0 C z 2N- U) - x00 U U 0 *' z A a- (4 4: z A 0 > WiU U- 3

a- a- *L F4 0* 4 I f z w 12 1 - A a o 0. 4 + 0.4OZ 0W -9lA 1. 0 0 ::l ::- (A X0 'A U4 U) -0 +- Mo-C

(n u *Is . AIZ * LI (I I-- U- .4 * -j .4 I 0 I

go U- I.-U-L0MI.- 4 U U ---- OZ of .> 11 1-02m *D -j 000 A-1 0 4C 'A wU U) Wiz

0 (AU (A * U U----~ . u IC 00. 0 0.LUa + +

0

#--

(AL A 0 in 0n aA 0 A

-C4S ev m C.)4

196

us

U.

03

ca Lo~l)UUUU. li 4JJ.w~j 4 J J

o 4 000 0 0 0 0 00 0 0 0 0 00.- zU U.--wUU

00

Iii

d:( 00 z L I. )

2U) U u .) 0I-A In t) ..u

.1 u cr 0 , %Lcc aI 0 u

u- I. cs w

U) 0 3 Q~ 0 0,

4 n 0 0 z AU (n I.- u

o z (n -f -.. -iz

I- ul > C) D -iS w o) JJ 0 010

U n a: 0 0 )

!S 0 1 4 0 u 0 1F-. I- C- x ) L l

0 (n 0 - ui t2 0 0) 0 V)w U . U) -

LL U 2 U U S 0A0 (LL, Ix 4 Ux cc0 0 .

O ti U. 0 a) I - I U

lz *U - u nS I:o U (A to In ( a t (A (A X Z

a. 01x w 0 0 4t ccr C L o . 4 cx 1- us I.- 2 t

o o WJU 0 (A U) 0 ) .5- ):- LL U- U- M n 0 (Dw

0 . - ) 4 0U. 0S . 4 4 ~ 4 . N a U

uq .-. a vCl U) U)Q U) -

Inn -J In 0S U) U ) nn..

- C-190

Mi

0~

to >. 0C M mc rw ~ .

0

0z c

:3

) -d

0 0

+cr.

.7 - w 4

z- w . zU - i .q a.-C i 11 Lou e U -r- 4 I - li e )3 4

00

0i-

19

4

0

Mi

4A -* -- z .

W 0 3 -9

4T 7 cc 0 0 ('ua-~~ a -

z 1100.4 7 * 0 c A cc

CO t h- -j *n -x CL 'w 0 o a ; ZI OO c') 0 0

+, 11 -4 0* -' 4 Ix 0IDr 'A).0 -a In. 0

co 0. *t L..C) 00 Z Is -.5(j -. 0 3.- CL f zz - a- w I A

I- *W0.* 'A 'A 3 z 0 .

IA. IA 0 UhI -j) Wj -j wXa ix u.i -IX 0 j -I 29 0. 034w z0 2 a 'A4 'Ah 0 rC

0 z W0I 0 0- Oh- 15. 0. 'i*j-. *.J WI M 4 -.1--0 0 0r

I C sJZ 0.1' U. 22 c0W0 0x- L )LW 4 MI -1I . 0 - 002 0.

* Cc0 0U a4 A2 >4.. (:) -)(00 o ouj uj Ic U 4 0 M w W15 -1 cr a(2 - x /

0 a0..Uw - *u ~ aI-um! ciciID uZ * 0. h-h 0..0 4rz aa1

13. 4 0 WN 0. 0. 0 >-(1)0 t0a0 A (nz. -j a .l IA. 0 > o0.0. 'Af' -. 0

4C 0, -Z. *j u. 1-0 -l00.' 0. a a0- A co CL' 3A5h 00 ~ 4 50 5

'A 0. 0" - 004 .- ''A- 0 0 0) I LC

M 0 w <-.4 X w' -01' LL0.~0 W 1D4LW L a 0 0.00 xaI 0. ar WD Z 0)0 w -r 0. 0- 00. (Z0 -00.h'

0 3u* 0w 0 0 40 0..201.. W4-J lAr '.A.z

0 'A 0 -M - W* 4 l *0... 0 01 * X4 0 0.0 0. x. a U.aCL0 :, AC W 4.W 1 -hC' WI.1.40s W00..0 2u 4 LI0 - a1 -a x C C) u - (,3 WIL2a .OO -orZ r a 01-C..0 W 3C I 0 .4-GC0 C> *3L a ('1r -h- - W z aaM W X- 04 tL-00 IM 2 0 W- ir 44 -- 0. 4- tAh- --. Z0 IX.. UJ --C n i 0 C

0 n 0 I4&W- x 0.')' W) CI W 00.500. 0 LU 0) 0 0:C j -Cc a.5C a 0. --- 00& 1-00IL X ~ 5- . vh- 154 05 - A

z * C)L4 U 'A. a- Z 0f0ah-5a0 T0A0 (n-C P4 .1 z0 0 -0 0 0'A a0 0 U; 0.O - hhhI III0 e ll 0 0 1-* cc Wr 4;C

D *00.0 'A 000 It *Izl ~ l h ~ I z C4 D 0F 3ju L3 c x wcN. X u 20 (A 0 0I. A ' . N e 4 0 - a1'- 1-* .- 0 1- N. N. a=-o o MMW0Aibh 0. x w. *i wA0 ct I-

0~~~~. a9 aw~ a 0 > z 4.4.052 40 U.- I.---..-.so UJ X 0.AZ -;CLa 0 0 u xc-.

a. 'A a C4 . 0 -a.LN..hu

(JuIJCuuuQ U u 0000000000000000000 u u v 00Q wUt

119

La

o ~ O- Sn W C WwO-SnC D O-o0.-N DC-C

- .C M a a a a a0 ma aa aa a a a a aa ma Q aaC uDOa a a a a

SDOD

00

to C0c

cc I) -A .3 U A

0. 0.J :3M pV 0 0 I.

4. <r u Li - 0- cr 1

CL U.

au > Cc c :C- o) -4 viU : D I

z 0 -.. - I, !

0 - L) -. 7. ni 'R a o7 u cC . 0 w - 0 -J to0.5')L u 3

.a: .15 -l. SL) 0 L-f0 0

00 15 4 .5

C% .3 x -. > ) -- L L- n x a. LL M-

a a 4 cn w A * a. Li of z - 4o - il a. of U L C 4 - 0 0 -9 U5It-- xC

11 r n 0 d . 1- . 1- UJ 0. 0 ',I~Cri 4 0 r- -Cr Ir-( W a. C3 - 'o -1- (ox m

Oi sb 1- 4 r4 v 0 ;- m. U. 4 U(AD w ) -1 .11 0 01C >) - Ls. :. 2f X.w 0 Ot- -1 E0 C- I _j 2. 1.- 0c0.1 uD TC Cr F-- cLx 0 ) Lm 0I 0

a rf) (I L u U. A 4t U 39 0 D -il c

* -. U. - d'- : r~. ss . 0

'A C4 0-U 4 £5 f ~ a D L . .

-~ ~ ~ r 4 0- in50 0 0 -. - a 1C

0.- 0. n 0 * I01S 0 A D a%- m r 4

-~ i. n r-A - a. U200I

a ,

W a01 ell in- O 1. 4 .CCqfI

- 0U01f uW W W W W UW W W W W W W W ULJ W W Wu~uw w w w-'. 00 0 00 0 00 0 0 00 0 00 0 00 0 0 0 CL00 0 0

z 0U. oo- C

0 , U4 -C w- 0la. (3 W-3(A 0

wh D 0)u 0 nI -3 0I .0 n - M . .0 44

o 1 -2 -o to>- 1A on 0- -CA1 00 (1 2a. a. t

+ z aw .0) 4. n a.WD 0 w W . 0- wu

-0 V 0 cr 004a 0) 00. I. Wo

or a- 00 C .> mIAC 00 20 W) -- - O

0 00p C -. 0- .1 Cc.01- 0i 04M- Ma -0 0 W - 0 W

it.- CL Zi 00W A 0 W4 .03 C2 0l- .- m 4

zuW 111 0 3C~ 0 l0D0ixu m cc Z - a. --0n a. -2 0L dc- 1 A-

!Z! cue A 0 00( LI- CT w - .-. (3.(A -0

I. III - -0 -.1 0 .

a W - 00 WUL X. a. 00 1- w4 0 Z 2- W. X-u IXMM C.

a. Z.C oz0 a. Wn 0I CL 09cc -4 00 ! -- '0 m Co

CL (A. 4 39 U x 0 0. >. 0- 0-a aL U -CL U -A 0 0044 . -0 a W=W R

0cr 4s cc 0 4- 1- UJ .2 U) $o )-.(A ~ of 00 WL I P4 0A a. 0 - 0- z -

oa. 30 a 2 -o0UU - x a . W a. ag- - 0Je,0aI - 1 I 0T 40 m -0a- 4 4 0 - a.3 ( lz I4-. - 0 z .- - a. -0- a.

U) (a. 01 -w 3 - 0 100 ! 0 W; -11 W W4

IX 0z W 1-4 0 or. 0 to1 1 1.- 04 W:)4AU W 2 IE- o w1 001 wo 0. M- LJ 0j (0 ccO -W 20 0 a -J W II 0.)0 m. 4 ; 0. -C z

o4 ZA 40 Ix a. .-- Un Q. Cc 0 W U. 0 LU '.0. 0 4 -CL C7 0.W 0 - 0 - 0 01

0 4L 0 - - 0 0 w. g - a w m 0 > 4lz M- - l - . * * a =n . a. . w - o0

CL 'na. UU u- Q U U U ;wu a.U-U- -U.-J z .0 wn-0 0 ,0 -'a-- 0 L0.

0n a. in. 0I*~04 0 Cu-.

a. In201

CL

01LI

t- 000000O0000O00O00O0O00000000000O00O0(200O00O0O00O

* 0

z 0

00

a 0- MC-, iIn U- -U' in

z w C 0 L

4 4 00. )- i

z In 0.- *

I- () Op

0. or It ~ I..I.L IL-Cl 0 cxIL 03 a 4

0 4 . .4tW Li' 0M > I

- 0.-. I, 4U3 w. U * woo

-3 -3 Z - 0 ) -, -

iw fl- :F -4

4 to- 4.0 1-0(' IL -0- 40. M U' M. >( in N) j qwUU w Ir -UU

M- x. - I- I- +4 + a 0 U.' In ++-* .> ZL ---- u M- 0

N. I L..,~- in U' ('CC w0 1'* 0 mA' C' - C) 0 - > -in C3,r- 0 z v, X)

It P Wi u- 0F U M- 0. I-i 0 (0 0 '4 -'0---0 l'-> :11 :3 L, 0. j; ; -.- n U~

L < In :3 L 4 U -'-() n o 002 z;Dl 0 z. La 0-0 +- +L a) F+01- W t- ++ ,0 > W0 4 U0- at 1- U' ;; ;--;I 0 0:!N--0. UD If 0 a ' J(N.0 X0 t(vioo

in 411 -l3- 0 *U -to - -i .0 (4 IL 0.-

ii -U~ 0.~ * -O Lii U 3 U. U~ - . ~ O2-. .. U~1- w c 0 0 z -* -. co 0 0 -- ' 'r-U- --

0 a, i 0.0 x 0C~' I WC. w m-I aN Q - l0IU 0--N-0 UJ0 M .W -. z 4 -j - U' IL . 1- 0 ---- 0 W U.. ---- al

a. 00M U a.W .0 -. UIn 4 u 'l - l- -0 '+) a4 D. I U-0 F-cir 00 in .U)n w & .- 19 M. -J I OUu. * xD U., U ow," O.-bUL) It 0-

r- UJI M li. w U' . . 0 0 - .0 0 Z 0-f It O 99-.- 3 -- M. -1 19- In -0 NIt 0- O1... .. 0 L 01U 0 0 Z 1- N 00 -C 0.0 - 1 I.- I- 00wo 4 > 11 20.cr % tIL4 ' U UW.- 11 IN O9 00. CL > x. II.- w gU' L-0m U IILt. 0.- x (0.a0

61I '0 *- . .- *L U. II C; CW w 0t 0. in I- U- I . . ILI 0.-I U J .

o -4 0 z a -2 29 :l flO w~ W0 .- 0- 4yw.0 4 itw U 3cr r 2 2 9 w U-' U' -0.L Uf 9-3 U X % 1.- 'M > U u x Uj& M -in ::)t cr c I.I -fi 00 0 O 0 ' -'i. 2 0 02 z

M. (A 0.L U U 00. 0 OW U111 [a 0a. =)U'O in MIt 0 0CL In t

UUUU U U U U U u 000 000 i'4 000 at 4%U'2

I.-00

Inin a U, 0 in toi 0 In 0n

-~- - '4(4 I in i

202

Ixc c ZC

ID

W UJWW

0 a

0 v

o oIZ Im

ISIh

IA

*0

020

C M MItIo~ !

0.v

7D

I-. 000O00000OO0000000O0O00)00OOO00COOOOO

to

0-

0 -..- 0.-j t

0: i/b w -1 0 1~0. 0o 0.-.- I-

0 0 0- - .NI-. 0. a: -.

03n T 4

cU ton P4-a su 0 -: u t0-X

o <. 9- 4z C

Q -9 U) It 'Nr"'A IL 0. 40.U-W 0 4r 4 r4 LL U.(

o l -- > u- 0(I ua. b-m -'L -t 0.a0 0.1tN.O

0 mJ 3 4r0 01/ 0 z

of I- 4A 0-n In/b ~ ~oCILo .0-- Wa- It :I- 1 1-

0. P.- > I* ( In - I a0: Ccin

-L 0 L W3 0 C, 4 Ol "D

II 1 zA 0.0 fcnfl0 I/b .01 *Z I.0.0,-N- -I ir a:WC in -JW0 ad I - t- W w 4b>>U

0. M0L. 41 t--- I x-- cr ).xUN I- a- Co 0. 1-1( 0 m-.I0..-' 0M50L1-

o, I.- )o. - -J a> M. CC..U 10100 .. 1- '-af0 0- do- 0 -0. 4 -Z I ~-C. xco u 2 1WO .- 04 -- 4/ . .1.- in(C-OI I rUux aT' 0. 1.0 cc 00r4 W '-. .)Wu 00 A 40W. 2 0. W.. 39 N U! --.. 0 0.0 I( .' w0-

CL C4 NW. N 0 *'0 t- 0. -1iN~t- 0 . N C.. * ((4b- Z 0.. -- (30.

0 . 2 ab W ~ -' 0 - . Za-4 L > 0oe t-02 0 WO- 0 U .4 "..LOb

0o - in W 0.0. 0.WOin . in

020

0 o

to CLoc4~ m( ,0 o-

00

-z OOOoO02000000I-J t

IL WuJ WW W UW D WW W

z zU

ID 0. U1r l

I j 0

4 - IxX 0 ar- -

V) C'd IJ W 3=) 0 In I.-

U0. .9fD olLa

U. 33 -. - An

C-4 ~ ~ -(In W r I0 0 00 0 C o-441

th 0CCL or a.2 M . 0wfaonfJo

I- 0 0000w00

fo9 . w in w

I-

o T M44<00 CE 444<

Cf. 000000W0

on 0 -3)--.'0. ~ ~ ~ e 20500.. )*CC)

0. 0 3333srmuam61

lb

IL

-~00000000000000000000000 00000000Looofl0000CJ000000000.)Q00009- 000000000000000000C)OOOC000000000000000000000000000OOO(OOOO

0. -C~ 0 -OF 40 u IA u

> -.1.3 lb0--0 ~ -3 1.- 2jweL * L- W -AA

o1 3; b- W. I. I. w III

+ Wi Zn W cc j U-ID Z3 U-- 0L L)l~

w U- w 0 A -- - -- - N n O inT~ U& 0W C. 0 3w4 - x-I

U! ZI x ZA z - liW----0 cr I-

Or 0 0 Z .-j w~ :4**.I&- . - - 0 7 A'

0- CI CX z 0- U- 3.fl >- x w- 4c Cb 4 C'- 44 COC) d(04C4 -A Ib-I

lx WZ wU-nAe In In - -,-0 _.j Ir 00 T

401 ww atC L)~b CL~o > w,- 1 mo W .c -jo 0

3 I-- >- < mb X-. 0 0 4 "0Li 0(. Oz . -Z -J>4IZ~w of 0-. 0 -

L ab 0 A Z Z -'L~ (~ b O 02w O 'j In Cr ) 0 C - C) '~- In z-J z z

4r N In -- I D L0Z W a - 10 1Z~- 1 - 00 x

1-- 03 1-- X - 1C 0 ~ XC- -- bbb c y x -0C* 0a C W !--a tJZ , zbZ Z 0 (0 -- W

S Zi .. *'r b- -- Wi ZZ W . Z.. bb- - it bI 3clt 0OW 2 0- 0I--b i-L A Q L.S!0(J . 10-C ( Cs23 w. W0I O l Z 0UI(A WAJW ----- 0 ;-. ~3U ; 0- I, rin

I - In I l -- 1 73 20 b-0~U ---. UZZU-- an M- CL

CL z D. toZ COCL Wix0. 4 L4.U--U- 4ZZ00)- .w z0 1 z W in > U)1.L Lx J -ru. ' W ,.UW Wr-b I- -I- - L UO 4WWJ j> W f--00O U-U- W0Intno: AMO(A:n* Ln - -U

-Ci4Mc c0 0 -i CL 0 4 W Illm -- :WWWWwo CO -. teD - aLo ~ C z 4:-C c2mw 00 -W-0Ub- 0 .- NN N C (N(WW

0 i OW 4> ) L L 04 <WW 4U0L)- Cb-. Z.~ - 0 ;; 0 - 0MI- b S-- 04n - In 1.4- -4 4WZ A0.Z .~2 2O - b b- !NO

CL In LW Z2 IW0- -W -j -j a b- 3 u ~ - - z .JIn0on o I2 . > In4 0O W W Wn 7<)~ L---b0 w u Tw0:3 z<r xin 0) M~-- z

C -4 0-WZU> WCYOO O O4WO O.--. 0 - p-" mo uvm mlx - Ix-Ow 0 Z! 1 4 Ya u> 0-f(~3 C 0 -1 b 0 Clo InO U-0.- WO I (-AOUS-- , 40 a a-'.) w-j x 0a OZI 1Z 6 1 4 c U- IN t- A;WW 0-1

4 - Z 0 0 It l- CL L CLZ 0-bbC -1 6 1 1 ; ub C I 06' 0 G- WO-J ibr-. W0- dr 00-a 116611116111 1I(I-N#f6~t* ** 110 (A1

a N3 R 1--( 00-~~ CII 0lV - 00 0 1. 0 b-sOC.- b.. - -

LaW 0-j ub 3 - l'- 0 z C Z 0- W I 0 _C- CO- -C 0-4 04 - .0-0U I.- CL x U. Z a -4Q----- 111b00 In0 z WZ'- 1 b- -1 ---- 1

Ln-O w - a 9 : Z 1

o- W - Wj -I-W

- n 0in 0 in 0 In 0 In 0 in(m (N M) M) V I In

206

-~-~ - - -~ - - - - - -- -

0

z 3d

or -3 P) I.- Oz 1 0 uW 0 O -W4O . - e

0 Z1)C;0to W+ C: -j ,

qt -,,. - W Wc LU

C6 *i -.4 ;: -8w z c In

o~ X L&.. -W W -

1- U. w 0.. A- 1

0 U. I- U-U. +4 L 0 w cW.

.1 *n---0 0i '- w0 Lniia i I. ui0 1 n - 4-w - x ex

C-i-- * U) 0 CL -Cu

Z - 0 0.0 0 * I - tI U. U. WctCS U -0 in 0 g 10- 0 UJ U. LaJ 0

w I' 04-c.J 0a 0 z WAV

t, L. U. tij-. Ut :: L.3 wA 4 x z.01ft IA L LL UZ00 WW'U- tu &L I-I Z ui1-0 ujU .uLAU s4 00 L,, U z i-1- 4 0- ft to

U; Mf3. UUI 40 0 zO 4a to

0 t0 UZ* 00tt4 f N U U

0 C3 aw (0 ; *4 t a z -if N z-000 10 ZfOf ('Cdl 1 .Qw 3L Z40 'I0 0

.0 wI 0-- tfliJj if .0 . 00 -. 0 - 0M > qo . u af - -0. 0 CdC 0x -If z 0Zf 01-1 T +00T 2 : 0 0- -i UJ MI 0.4 ('- .

0. CU. 0 0.- -U.. CL0 .-'d~ -1)D 0 (3r 0-0 1) 11-C 74 00-11 +7 * -UL' -LL WaO4 ----- j- -t~ In. -w U.-tCLat - z

CL 10 C-4 0 0 11 w c ftl-0 (3 aao 0.Uw % U. ..0 D - - =)~J I-- *'0 .. 2IX ft._j W -Z III it ftI11W z -j e 2 0.- zOa 1 LaU W* CO

4 UH-.-WO-. ('. .-- U-~ 3 a 40t-- W04-OW - OW3W-J0010WD W: CO. )+J O-. 4IflJ..jW -u-I- D..I- 4 ft:Z W D *01

N. 2 -U.I-'-u. -'-JJ 0. 2 (r7~f4 00.-.0II4UU.00440 U. 00 00- UO-0O .. 0

r- to L0.W0-ML.3W &&Qu0m0 u ' 00 OM W3z z-- z z~-- Z00 a0U 00 0U. 0W-0 0 Q0' 00u U.--a -00

0 C)

Q4 in 00 00 u 000 Qu 0100000 j 0 010000 - C14

0

20

C%

0000000mot,00000 WOOOOCmqOf tot UoO;NMOCI-~~m m mm m CO O O O CC O O C OO 00 qq qn.iOCOCCOXII110111

-----------------------------------------.. IZ .0. .0. .0. .0. .0.

0

(A0 n C A( n AI AI ni

IL

z Ci) GO

0 133-1>. 0. OrU

1.1. 3) <( in4

0 33 -0 a Q 0 IC4 3 S 0 It -

C>3 a >- C3C3 a I. C04

0 al :I7 0 I. c . C00 C-o N. - -00 0 .

0 0C '-0. 02 l'- 0.I. t C >- 0 0 CO :x0.CO Z. Or N>- . N 1- 1.- 1, 0 0Z 0C- 00 -00 CIL ; -C00 - 0. in Z 0.0

* ~ ~ . >.' 0.- > x 0 0 0 0-J-C3 ON 0- 31 1.- - 3 0

o 0 -3 a .z a 0 m F- 3 0 3 w0 1-Cx ;w 00. I COO 4 m - 3N 42> w 0. -3 )r- 0 :4r-* z -r. 00- 0 11 0 -3 ( 4 (N 0j 0.LU

0. 70.7z to 0. -. . ) - 0I Or C)Z n - 1 z rO '1; 4- a2 x a~ 1 > i a -., 0 Z W.- -:aw<20 It- WI of-- > I.-0C :r too 0 Nc0 UC X5.MX ax . 11 Of ~ 3 -JD z-- x0 1 1- z 0.'0 0 01 00Z -J >.0 w0Ji 1 -0 0 0.1 11_a*1 C

MO ( -.cX- C1- 0.-0 . 01-.-->0 f.00 05 U - 30 aO .73v

1- 3 l4- W 3 J039 310.0.3CD4 w.U1-1-

30>->ll~~~U (T)-- 3 Z111

Or0 0. 471 0 00

0

1- ('4( 0Ini 0 C in

20

to

o uj

1.0.

0L

ac '

0.-

-3 U CV(N-j

C4 0. 0>

I.- toI -w :

o -, 'no Z*

0 -1 Ix &

cc -. IL2>u1.go .4 1. 9is L 1-

o oz $. L

I.-.- 4 %(A

o in 0 209XL

.X -. .a ... ..

Iii

4L

D

w > 0 ; 0; 0; ( 0 (N

4 C;- ' 0 (4 C4

0l .- 0j 0 -D -(N -- -- - .- -

0 z L, I I ii I111.11114C

o U l *i Zr ) Ln CNUWU WJUUWUULU (~0 (D 0 0 .- y (0L 7+D -. Z (A 0 DL CO - L c -7 ~~N r- a) o

o LU .1 4 x co m Oz 0 l cc)(NwIa)DL3q m (N I) 1) 0 0;

ID~" 00l 4 01 ,, COO COCW C -( N;U(1 C

Z 44 r- ,Z 0L 4r < z 4 I I I I I I - 0 D (N N 0 0WOi > >- a 3C C C

-U- 0 I 012 3, ~ j -W IJIJ W (N t; 0 1; (N CN (N 0, m V a O V 0 04O z 0 LA IC ) CO O IOC I (I I I I I I I

-j LU.- >D - u 1J3JULL L L L lJ LfuCOjNOf( I'-j COO(N.C-tfl N (0 0 .- (N 4 0 0ca II .) 0 M0J)C = M i M Z N- 1N X M

( W s.- r- W T (-1dl 1 0OCO -j O 3) ( C;) 0; 0 1 - N 00hi. C4r- wu. -- tf~l~-( -'(DN (Ni -- m 0) 0! (N) a

-40 'D OTMr .0M0 -M Y o C ; 11N r 2 J- 4 1I 0 0- D 0 0 w 0 0n

010L C 44 W .......................... .............. . . . . 1 .C! . C. 0

cr - > 0 CL0 4 - n (- cN - N(-NC ) 00- TC 00- 00LU -04 x OZ ( I 11 I I1 1 1 . .. .

cr 0 Z u q t mU a) aA'~O) - z c40- o O a) )0 0 N 0COFI 000 -0- -0 0Z. Q 0 Lw - 0 -7 M .f N 0 iI~ O ' LO n .7 0 .n (3 CI .

*~~~ 00Z auIr . "NI~l0,.--( C..( 00m N--I 00. "-mx

1 CL0 (AZ cr< C N7c

S W L4 C4'-~ 1 1 1 1 0 1 1 1111 1 1 NC 30 C

S .(A x W.- < Z : , -C- - U WWLUW WOIW L.J mW U) 00 0 (N; r C0( 00-0 W = A 0: J3 n - in IO-C I . - c " .' c

0r ul w -(-LUlI u 1W 1-i -L O))NL)~O0NOCC~lPlW If)jO) U 00-0 -(,0 m 0 O 00N.1 w4 (Ar Zin >n (D 440- OC ID~- W UW4 14 WO m C) 0-ON T 0m 1 020Wn -CD LI)1 N N LT;'~ OIDOI C;C,0;CV Cu o ( 2C- I z (A 27 (N WWC - 0 -C,-i ') 7WO-DO C -

ZL 4 D-j LU -4 n n 0 N OD W 0 M 0 inN( -0- 0-; MOIN60- ) '

z L4I - Z W2 q> 0 1 1 1 1 010( 0-(((NN~ '-N 4 1 OI-0 00 a -- ONO

o u 1- U U 0 0 -- -1 1 (N.. . . . . . . . . .- . . N. . . . N. . . . . . . . . . .

t - I20 z > 0. " -- c4I "~O0W4OONN)' (w)(' c;N(( "oo >(I. 0 U4 ZZ - 1 LU (A aL 1 44 3 U .C 4 (N - r' O I I I I I-. . . . ..47 c!c

z N.0 W w w W 0- 0 0 2v W(.0 C; M M C4(t) i Mv- 0-- 000 (NOC 43. -IiL>i W- 4 r I- q (---~n--( o .~-4 a)((N I-OOI I-O( r)C -(NO 1 C ; ;

zi 4 - C'- Ur ~ ir 0i 040 z -M IJ IN I 0DC C )C W I N m i in ( 0oC 000 0(N-D 0. --- u - --14 ------- < ----T 0 - 0 0 n N t(O(N (D - N( W-NN)(NN .(

o -i i0 (At C 1-0C 0 0 000

4 r2 " c 7c

0 C

z

- in 0 n 0 in 0 tol 0 loin(N (4N m' m1 11 tn L0

210

Os0 C TI -O 10 NM1 nWIC h0I oowl

4 U Q U U U Q U UU U ~ u u u o u-1 -1 -1 -1 - j A0.1 -1 - . 1 -1 - . -1 - . . 1 - 1 -1 - . 1 -1 -1 - A -

4 C. K C- C. l C.14 4- 9-t1 C-u L )Uuu )UuuuUuuuUL

1. -30toD D D D D ~ ~ ~ r W w I ~ ~ D 0

00

Q I. U.

43

4 - +2

a *vz I

-04

IT 4 I UC

c;~~L 0L -: .

0 c; - 0.-- -

t- u3

a Cl -C. : -, ;11O u U. )-

t- 4-4 01UI n n N u .

Z- 0 0 11 - I

WI IL -X u uuc

-9 0 InA 0l a in 00 inl ) Ok i

44 U4 - C-4 )~ N

o~t in in--3 -00 -1 *3o- W.> ~

('4 IS Z *211

o n

t.- 0000000000000000000000000000000000000000000000000000000000 0(0000000000000000000000000000000000000000000000000000000

I. a -A

ID 2 WA UJL7 f3 or aQQ+ zW U J(D (I ~-3 -. L,

z 0. 00

u. u a!. uU

0 4- ID WL-j 0

x ujI 0 0 I- C-4

- U) 411 i) C4

OY --jZ z . *u wW wJ 2-It 44 .1J-00 0

- U. 4 N 4C*4- w Z- - -. (

WA 4> -t i 4 uU. -7U a -iT to - - .- I 141-4 - 3 2 -.1 IT 04 ui uJ 00r. a u0 44 -, 00(3 ( 0

N. U k - - Lt 00-

c 0 IT r Or O- 4+4*~~0 4-W 2L 0C +n Cy. 0 - '*I.Z Xk U, 1 0 * .4 %- < N -- 0 I

23 4 on14 CD 03 m N 1&. 1 C.C) tn 00 IM LU 0 in 0 C. n- 0 0+

o1+ . -44 +4 + Ir 0 111II Z Ih n *0- 1k 0-- 44 1-- 04-

I-- 0. -x.-- -j -C' 2! 2!4 9-'C a! 04

0 a-- O- - -C0 - -0 044 - -)J-j L0 2001 4x Aw 0- I U. U-- W -i -0 0 W O N. (N 0 1 11 N- L+ +W -..-1k o 1k(11JO w 0 :3. - W O -- 0 J44 4 C

V 01m k I- or or 09 1.-- 9L 0W '-s- 0- - -4 W UW 'l-WOW41- 4.1 =11 w w P- 0 ; 0.- 0 -1 UJ0( -. J 0 IM) .0 j - 0 .11 1112112

0 41.- I. (5 0 !I N 0 C 004 C; x. .Ni4 4 00).iW M W Z0 + - z -41 - lW C. I. N - j 0Cdw~ LUW 01LJ0 -. U - .4. - W-1 U14 W 1,--- L4.20 -WUJ0 - ( C 20-0-

0. - U) 2*1 Ir N. 1- 13 491 1 4 342 01 ci (NI 11 -j,2II0.4Dgou 14 cc (3 I42 4 4) .41 444 ., 2-.*- _ 44-2c w !1 2o u- z o0 aX- 0-.' MOZ Z4'44 C,-4 Z!(N44.- 1z Z

c a 0 L - o--2-- *4- o0~ 4 2 0 -00 0 N 0J 0 N 00 0ca a -9 1- 1.- z it(A1144-- z -,--- t 1- Z

20 UJ Z OZ 0 0.NI.4L. 00 0UUWU- 00 OU. 00In u ix 0 w u L1- 04- 2- uJ (0.a'0 00 0.-' 00u

00 IN M

0000000) U 0 U 411 C4 04 IN IM on 411 U)

lo-

0

Into 41 041 in 0 U) 0 on1 0 in1

-4 - (4 (1) () 1 14 U) 41

212

40

K. 0 0 0 0 0 0 0 0 0

0

0C

(0 CL -u0 "!CI.4n. L 0at

, 30LC

oi 3 . ,I-0 1C 2 cc

CL L I-. C-IL I 1 A0C

I- I j

ft 131- U n:

oC 0 0 - 0

o - -- Z 7(4

It 04 .0Iq(in 0I-tI in I l

f.-0-..

o on-t- 21

mo-wCNrm twlo Nn ((r

CD-1- j-1- j - j - j - j - j - j - 1-14j -1 - j -1-1-1- . . 1 -1-1- - 1 -1-1-1 - . . 1-1-

0 Ld

oU W

to 0 00

2W

I.-

06

0 00

M Lt LT-

* I-

0) In (a

a. 00

- iaini

_j U; U.

It > r It2 Cl 0Cto 4 DW) Ut 0N 0. r I

Z n OA-U 0 0Ll CIN'n 0 x9(1

0 (IXfU ift) zt ~ > ' . (4 0 -C:3 0 Z IC4r4 o

9-00 -1 (1 00 L - 09wnoaDo no0 +k 2,* .*~ L n L-u Ll

9-c - i .9 ., 2 t d ~ ( LJ 3. U *-J 9f- ! U

:3 0. in x C;f19 4 - - -- - - 4 04L in

a. UJ u4 -ttt 0uO( J u~~J WuJ uw 1 -0 001C -4 nJiInuIn a. x it In) V *1 0) )9 99999949N 1 MM , - -M-4 1- - at: 9 (it Z)

I4I- Ac -o mt u)IIWa & 0n cio1N.. viJW W UJ W W .. 9 ,.J.4n - .99 MIn 0 -c rH if -In1- I Ui ~ . 9O NLa0941fl t-4W( M -(091- .- ara :3 o, 0: 03 CO Oh - .

it-co ZO I.-- t4 o. a1 4 - C (ML )~- U~ W N N-0- .4l9 M C', a.1 o a. a*far-0 x of 0 01 in C , i - 0) (.10 (0 47 fld'0(0 C L 1 9 l MW44 0- 4 mo0 01 4i 00 0

I.- I, t-u N. * It M N CID--40--G)o)0)n6t- 17 (3-.-itit 1:n z ZS u in 0u U.--9 ("D #0-w 9-f~~~~~- w" Zr 2 r ,In r1 -1 D 0 D 4 t I 0 . U N-- 0W C2 q m "0~~~ ~~ 1:1 0 ft ft(9..-m00-90 e00 (0Ian 4~~.0 4 u.0 4 a

A . -- - -a --I~0-n .91J0-a i - -- - -- t -t-O.s-Z, -n-ZO I.~

uI u u u. II n-0Ll - t- u49 9 + 9 0 (C u u

I.-

0a.to

- In 0 in 0 In 0 In 0 In 0 InI') I' MC) V Is In W)9

214

us

C;o n O tot40

In toMf

0cc

I.-

0 -4

a i0) 0

#A2 100

0ol" I

- - --- C 4 4C 4C

01

IL

I-

o LL

0

o co L.w0 4

(0 CL .0)

U0->-9

a. a

a. 00L LI- v w- Z-

fz 0In uI

I.-C11

in 0 InI)o~ 1

0 'wA'w w ww w w w w w www w www w w ww w w w w w w w

to

. 0

0

00

0

cc z U

. 0 0) z

o o v * s xx03 II- w01 VC

0 >' I 9 _ 1 A - l

or ~ ~ ~ 0 4 Xz 40_W J L) D - - - -Jx A01 u+ 1

too - 4 - -

-; -Mi 0L Z L . z_L) o l nit I x_ o n - -2c4 o- 0 *0 --

in In4 Z- 0 l I c 0 4 jC -1 0 ..i:7o

w m - 0 N0 O on - 4 + I14 *Z Iw ZI -I . C Cw - w W tA -L + - O - Z - a. + -i - .-

ot , C 0 4- 0 W t2 0 -i'j. Il I.- I. Z, is 4I 0L 14 ,.?6I -i -A j 1 a 4+

z a a tto- f- t4 * .9 9m 0 -2D 02 1 4aw .0 4A CL cr U I 4j 0- 11 U. Cs W -j I-N 3Z N 'I t i & 3

*I of 10 x ( 0.- C' -0, _ - Lf x U) 00 C- .9 ~ x :3 cc 23 -I 2+-ii f3 3M

-C - 3 $A C'.( 2U 0 I. _ j Z * it 44 zD -2 A *I . 1 j0- >i (40-C . _j ft- -A !D 0l- z '--4-*D JJ_ NIx -) W i *U . a A- W ('X I-- to * j of2 -3 -2 o -0 31 i .

So0 U) _jZ-~ *) 0-. 0. a00- - 0W 1 -i 23 020 J0(NE a aL A4AW 0 a-t( -VaO 0- U *-'O~- .4O u )(U)O - - Z (*1 ZU-.J 040

in 0R - - O. UI 2,L-4.J 0 0-* 1 2 * U ~ Z -w. Z 4 2' -0 0 - 8 4 0 0.~-- ~ 0U ~ - .-

4u Q u 0 (.0 3. .4 5 I O -..- 1 u *0. ' ' S 5 WuA

I.- - . ..- f.( W 0 0 * 0 I U 0 W -0 M A 2 U .U

0 U0W - -. l .2. - Z 2 -. i I .Z . ~ I 2 0 8 20M 4 4 11- W U-.s5 Z ~ S 5 24- --- '.-

t) 0 0Inn 0 in

-U mU In-00

21

4

amIn

o w oww momw Qlo tic qmo-

oUWWUJWWWWWWWWWL*WWWWW

'z

+(0

22I.-+

ww

Ir,

aL 0

f- C- 1 - 0.x1 1 .) - -

P..- M o-0

2 0. -- InO: 000wo o

-3zo TM .m 0

ca 2 w- 0O * 0 -~ ~n -M

* J .U*'

0 ~ In .- 0n

'7 - r-21

Is

Ixo o ~ ~ m o o In ~ -,In o- mmo~m ,-r

u I.: .-- i 3w' ~ qq n n

n :- )

L 0 0 0 c 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

-.- ( W UJU WU IS EEUJJUEEU uJEEEEUWUWUUEUEWUUJJUEEUWUUUUUUJJWE~- W-r#

o. ceUAM IUUUU U U U U(jU U U U U U U U U U U 0 U U U U U J J

7 0 0 4 u cU. -.1 (a . x - . w

IL to. 0 AE0U -J

Zl z* 80 0 4I.- U(A U0 U !L >0

U.1 -9 U) m z wLit

E .D: 0 u WE. 0. U 4 tI. 2 $- 0 4 z AI. ,

I U0 >0. U U-> - - 0 dlIlm "I I/. U. d& 4i z a) En s

.- 0 00 I n to *-

U. (A IIIA Q -E EU - U -.1 2 z:

0. 05 l- > 0I- > a to .- I UP

- 5- SW SW 4 U) x 0s 00 1. on- 20! Co u.- u.- -92 0C

>J w aU 00 3 W. I. U) +U + EU- -GoS. : S-- 5-.A. 2 a -EU 9:Ta14i0 CL 5

L)S I- U U 1'. u I.- 0 -j x E<< ;LL) IE >U IC >A 24

Z A (1 I1 0i 0 4 I000400 00U 0r on> 5- 0 Ix -L -i -C xUU

4~L .0 4 *I4 mZ 0 ---

2 0 1:13 4- a2 5- 2 -a 5C a4 A :3--

z. III - u3.- 1 2 ;; Z0 5- -: !2-0 tS U -> .> -to a mO U a I - U 0 -U- -9 w)-)-)- 4001 U

-. 0 >. XE ZE I-S to $A -** 2 415*5ES u s-u i- 5- 2: :I -: 0o > US UI -9E ~ O U - l--- 0 222 0.I

u U) 0 UJ EUU A2 2 a 5 1-4 z ZU-- *> -- 5 000 M >--- -j 0( 0CL 0 w E D 0..-. 0.9- It1. 0 U) IA 2- U) -. I 000 0 0 0.Z 1 1 3 C,0

to0L Ln -. 10 U0 U. (A. a -> itf WU - - - - "'12 -----)I. 4 WI WE0- PC C -E -6 a:) -.- z z- a.-- 0 2 3-

3 nU U z z- w.E z - o 0 -C ZW U) -J 4.- C l a a. Z 0

0o 9- 4 - C 2.q EU 00 z -- t 0- 4r 0- &&4 2. - L. U.ES I. D4 2 -~ ww 4r *--.I 0 1.i- >. u l'+ - U.1 X M -- )

0. a 0 & -/) a./ 4 00 a..E- - U . * -00I.- 00 - U

:) 4i U) 2 x) 5- 0J U -E 0- z SSA 0 - 5- 111 Mao* ~ ~ 06 UU 01* 05* D.sI WU) 0 0. Q/ . E 4 0 U A .- E)I

u. 0z 20 2 (0- - . 2 2 -- E 5f i- U 00~45CL 52 U 0 C 0 .- 4--2S0-E 2 C42 2

Q% 5- 0 0 0 22 vuuv ~uv-. u u-. UU 055.U>->- L- >->J-

0 In2 2 0 0- - 0 IW 02 In aiU)~ ~ CIA- 219S U U wJ 0 U 0U 0 >-

o -goal

EU 00 0

C4

w w

to 03zz 0-

+ 0 cc 0 LU

0 V) aaIT w CE V)(

ID 2j 490- c 0 4ha 4.2 -. u 3 iE

+ 9 >~ 0r oL0ulou 2 a-0 1-00ti1

:3 7 - 0 CLC -I z -Z iJ4 zu 4 aD I

or. 4 >a U2 Oa

L) a J 0 C . -9 0 V) jx A e -- 0i 0.U 1-

* 20 .1. z z LU4 az - --- LU w (n z

43 4(~ .4 *- L-* u mm AcIL L 4 (a In I flf .tn(n0 2 xLLU - 4 4C Cc.- U

t D 0 - a T- - 0'-. LI * 004 2 ("n4 i :0 0 - 4

> Z-2 0 -J z z zUZLLU In co a .n u. -4 4 A

(A *D 0- 0 ILILO -nEa CL :F' j z L,.O .0- .-.LU a - , -J zt X- - 2

N. m . 0 )- (nO 0 -4 > LUI3 21.- 2 ) . >-> I 4I.- X w w

0 4 04 V) 4 A -C >.* 2

Ix T WLOOU* 4 9-1- x Cr10 In4

z Z 0.- Mw 0 -- u- 0 LA0 x .4j - 0.- 0(4 0n - (D Nn1. LU 22 z U w ( x 1 o - Z- 20- x N

6- -j 4LU0. (nO0 cr c 0 -Z 3 LUOaL 49 xD LU x 4 -1 44c 2 at -0 -J m~O U i Lcr - 0 4 a XI x - 0.0 D co0

In 0 1.- r 2 ar 00 0 :3U 4A -C x2 0 C) - )c 0. 0. 4 LC 0 0 -j W .4 ('4

D - L-r .-- LU 0 *-0z - m'wLZ 2-ZH of 0 Z.- .>

N - -'4 -'' M' _~j MMf 0) 4-. V - OrP. 9 - Z)0-1 P- I-1 1- w . b- x 3

V C 0 040C.0.0 0 0a- 00 X IlD 0 -0 0 -U-j .4 oJ I M in -J -.3 .- - _j -CL.- _j-

Ca I (OLU z L C aL 0. aa a a aL 2 0-LU-02 x I.- LU -0 cr .42

-i -JO *-Z cc w -iJ -JO -i 2 *- .JZw -i I.9 .4n~ LU 0 0 .4 ' .9x 4C.4 cc. or .- L W 4 *- -a a4 4 wI00A u 3 4 42 I4 39 Ur 4CL F 4 LU O-

LU 0I 0

La

0or

o an o In o In 040 to r- wS000

cL

220

o

o ~ ~ ~ ~ !o oh-cNmmoe'q 04 C4 04cm

It, -00 0 0 0 00 0 0 0 0

to u

UJI

z U3

>4

'A.

; -C 4Z4Z 0

l- u I

Co. Z ZJ

*0 44 Op

4o; I a; (A E 21I- .- h4 2i, Z a

0 - L0 x wUIuI. o ITl- UJ -, - jj j I Iu 1

h 20 - 0 te I. -C 11 r u It o uuwIn I. , ) z -.1 In ui IM Z Z Z2 1.-

0.

11U U Uhau u

Il

I n I n 0 221

0 Lu2~

-~T;;M ao ooo oooOo OOooO WOoNaOOGmo-mooooNMO~toooM a ooorot-:o 4 4 .4 .i .J .J .J .i .iCIA.J.. .. .J. .. . 4 4 .4 . .. . 4 . . 4 4 .4 . . 4 4 .4 . . .. 4 4 .4 . . 4 4 .4 . . 4 4 .4 . . .J .4 .

IJ

a .i -WD 040 f+ 0.

ID74 0-T Lam (

I'In '- 0

ca I-

.4 ... 0

u 00aMi 2An 01 )--

:L Ix >-

7 00 0

1" -3 r

2 f2 - x in' 00 to I

0 Z. -J W I-- >O-j In I.-S40 0x 0 4 0

Z) Of .4 c.- j V 0 (0 (. 00 zft II 0-- x I-cc x 4WC *-- u a re 0 ft

0 z Z2 X )(L > wD I4II~ )- I . 4. (A u n 0 9 - 0

2--2 *I cc ..Jt. .4 _ > 0 -*- Xa Z' - 0 I-* 0- - x 0 . - it ca +D 4 it

0x 6- J u4 0> 0 L 2 0', - > of 0n ,-.-0 Ix .4 ud 01 W . uj : I 1>1 w+ z U.-q.

.4 2 > Z l'- l- 1- (3- It -I- *)0A)-to-aL I . 000 0q I- 4W 1---4279-U070 W m- J-I

v W . -A0 .4 . -i '.2 -. 0 I- >J - -J 02 .--- 4. W 2r- wi 1.4 0In u...- ( - wD 11 > ->.-'0S-- >> I- Il fl')O .- WI.

I. go1I~ >2 z aL 4mO~I 01 0 -D- l-J- ZZ7296-x x 2 00 -(( it1 It aW X.. - i -j I z 00 00--IIOO.Ja 0

r- I.- us 0- *-j 1- -...&. -1 0 M m it toZ> 4 <D goI .- 1i4-q 00u 0>I-l- I.-I 0 0D zU~ 0 JJ In Wd Z ZZ (i i i i to _j 91-j to C T XZOU0-'-It0-- 2Z Z0 ;Mi us 2 5 000 (A -- 3 If j X> 0~0 U U Z u.-4 U0 00a-ULIM .. i- .LLJA La :m22 Z2Zx-ZZI>II '4.- > >0 00U>-00 490 4-C -0 t 222 - I.6-., W4.- ft.-.J 000 .-. 011

0 4i. f - uuuxxC.4

00 0 v m 00

001In

mn fn

222

- Owwwww in-r-lr--trS-

t0000000000000000000000

o l

z. ~O.O

0

I&.U

z 0IV o

a ,00 - z-U;u

IA. uz

C4z C

9L

C-

0 22

CL

0.

U)

0.-

CL

o o

0

30

LO 00

S.D -A 0

*~ CD-J0 2 ; -t

>: 1. 4 - 6 > 'I':CI. 0

4 r 4 4 2 4 - Z~~4 - 0 -JC1 , cM I C w + ' 0, ----

0 3C 0 u

4 Ix X- - (X -2 )K

o o0 .-- flu - :)

0. 0. 00 0l. U -_j - 0 w- - - :L

v 00 S.. U 3 0 ~0: 4X - )- _ - O~ 4 orLLU

1 0 0. 00 z~3 z 0 C E r.

In 0 3_ I.-(

0~ ~~~ u CE 4L 4 - - *C-Qa

0 U0 0 -' - - a0-r -0 E 5 U J -+ 0 --.0CL - >.- ~J*i-

UCEj Ii 4i U- - - > *'3.-w E4I C-C -U U

I.- 5 U. 0 0 -. - 0- --- . . .D.J /J O

a- 4 .J' - - - - -Z- U0.C )5KU ~- 3 >> *-IUJj-co - 4 0 4 -- *-.LJ-J Z U

In0 Z- 55 0 .J -03 -. U Z0.~~ -JI .5- f- 0 0- - U--2- w

4 34 .. J3 .J.J (n-.-OW - O224

00 000000000000000000000000000OOOO 00000000000 4-00000000Q

0

+- 1- 0

aJ I- c c)

- U.1

z U., ~.-*

I U., W u 0, fr. ~x 1 I U . x> 0 Cy C.) C,*2I

I- it U# 0

00 >C~ >AU 0 (a O~~+ -IL

o 4 U 0 .1(0 OlU.l>OZC~U0WJ.0 U (- 02 2

w1 0~ 4

0U. U U U UPw r -

- in u co a .-IInaU)0I

-n 1.- ~)L 4 -1 <nI

225

In

t- 0000000000000000 0cJO(J 0OOO 0O 000

to

toC

0

u C;

4

zr

C3ci a-

I. -r 1- 0 j(u QA - LI-- x(

to .-j 2 -LZ .- I

I-- o f . + -

o. Q- - U 02q CI- InitZJ -

-.,14 - m a:,) x - xI 14 * 1 :D + > 03-.zX

I- a0z .L z Za -) I- .- ct- z - Q~J (N CL 2 u n-.Z14.

c, , 0x .- CL 0-. 2I- of. .- ( 0 J L) >a- 20 02f 2 0--'C4 - 'C xm m

a rn- 21L- 1-*-- (A>uL 0(0 0z

e) to 0 N.Z C1 -i0 Id -- l2 I2-J4 0C-- Z W f iI '2 U Z&l1

0 in M1-- Zr-IICta.l

to w - r--c

226

- .-u--.- l____________

CLI

II

0 N N N N r.N NN N~J'N N

000to0 00 0 00 0 0 00

z-~~J~~J

Ix4.n

ID

a C

In 0

1- N L 0 C

.. 00(4jMS x -i -

I- Ix - - 1 . 1 3 00 0 5utoc

or W- 0 *4 x:ca 10 a --r )3r 0p -

In Difl 0 0 o - t 0 t,0owN- 0 0_. -la 0oIc 0 QOM

0 * 0l 1

In~ 0 n0 ~ ~ ~ c 227 4 0ZZ -01.

ru

9w

Nmm4W O:

~~~~C o o o o o

z f ~ ~ C

IIM

z n

c2 0

Itf>

In In-w)

9- .. U-

0. I - isn

z 4 21- 1. n> - - <W 00 u

I5 0 00( owm

0 228

ta

0TID

ox-u

In

I-

0

x) IX C< cc

InI -

ZI 4 I0

_j Z Z -ro >- 0 2 &

- cI.- (A 0) - 0 z

o 2 -Z 0 - Z( 0: t0 s LCa. Z - Z 1,- 1. _ ,

z. N. -1 11 0l 0 - 0.Z--

I- v. J O2D 0 C4 n( 0-a. 1-n4z -

4 N 9C 4W *NOa

ILIn

22

DTNSRDC ISSUES THREE TYPES OF REPORTS

1. DTNSRDC REPORTS, A FORMAL SERIES, CONTAIN INFORMATION OF PERMANENT TECH-NICAL VALUE. THEY CARRY A CONSECUTIVE NUMERICAL IDENTIFICATION REGARDLESS OFTHEIR CLASSIFICATION OR THE ORIGINATING DEPARTMENT.

2. DEPARTMENTAL REPORTS, A SEMIFORMAL SERIES, CONTAIN INFORMATION OF A PRELIM,INARY, TEMPORARY, OR PROPRIETARY NATURE OR OF LIMITED INTEREST OR SIGNIFICANCE.THEY CARRY A DEPARTMENTAL ALPHANUMERICAL IDENTIFICATION.

3. TECHNICAL MEMORANDA, AN INFORMAL SERIES, CONTAIN TECHNICAL DOCUMENTATIONOF LIMITED USE AND INIEREST. THEY ARE PRIMARILY WORKING PAPERS INTENDED FOR IN-TERNAL USE. THEY CARRY AN IDENTIFYING NUMBER WHICH INDICATES THEIR TYPE AND THENUMERICAL CODE OF THE ORIGINATING DEPARTMENT. ANY DISTRIBUTION OUTSIDE DTNSRDCMUST BE APPROVED BY THE HEAD OF THE ORIGINATING DEPARTMENT ON A CASE-BY-CASEBASIS.

I

DOCUMENTATION PREOICTI--ETCIU) DTNSRDC/SPD-0927 ...DOCUMENTATION FOR SWATH SHIP RESISTANCE AND PROPULSION PREOICTI--ETCIU) UNCLASSIFIED DTNSRDC/SPD-0927-02 EEEEEEIIIIIEIU)lEllmllhmEEm

Documents