AD-752 468

PROGRAM SCORES - SHIP STRUCTURAL RESPONSEIN WAVES

Alfred 1. Raff

Oceanics, Incorporated

51

Prepared for:

Ship Structure CommitteeNaval Ship Engineering Ceftter

July 1972

DISTRIBUTED BY:

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

lill III --

PROGRAM SCORES-SIHIP STRUCTURAL

forpv. mis m -iot h s cbi , thse

NATIONAL Tt:C:-NICAL ToC14 P19,IU~ORtAT!O-N SERVICE J

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'A7 I15

SHIP STRUCTURI COMMITTKEA4 INTERAGENCY ADVISORY

COMMIYTEE DEDICATED TO 44PROVINGTHE STRUCTURE OF SHIPS

MAEABER AGENCIES: ADDRESS CORRESPONDENCE TO:LINI TED STATES COAST GUAMI SECXTARYNAVAl S)HP SYSTEMS COLWUA SHMP STFRUCTLU COMMITTEEMILITARY SEALWIT CONSAI4O U.S. COAST GUARD HEADOUARIERSMARITIME ADMINISTRATION WASHINGTON. D.C. 20591AMERICAN WU-MAU OF SHIPM? N

SR-1741972

A major portion of t-z effort of the Ship Structure Committeeprogrm has been devotoa to improving capability of predictingthe loads which a ship's hull experiences.

This report contains itails of a computer program, SCORES,Which predicts these loads. Details of the development andverification of the program are contained in SSC-229, Evaluationand Verification of Computer Calculations of Wave-Induced ShipStzuctural Loads . Additional information on this program maybe ofaid in SSC-231, Further Studies of Computer Simulation ofSlamming and Other Wave-Induced Vibratory Structural Loadings.

Coments on this report would be welcomed.

Sincerely,

Rear Admiral, U. S. Coast Guard- ."- d Chairman, Ship Structure Committeei ii i i i ii............... .... ...

".

II

UNCLASSIFIED 41S rt Clai fi4t.if o~n

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DOCUMENT CONTROL DATA. R&D~ ~~~bI i~.fg~~'.qFil. NJ 1 .1b 7.t -i 4 'jlg .i Imun T nn I-., W. -leJ hn Iit. ,ee report a~I. 1-ulhd)

IO'. .A -- , *C't W-.p..ralea oth.I r. rrl. btVO ''1!l CLA,$I 'C 0IC,SUnclassified ?Oceanics, Inc.Plainview, New York

Program SCORES -- Ship Structural Response in Waves

4 0rCSCRIPII v E NOTE, (Type olf rport aid enclr,,Ste dat-l I

A* -. 4OQ ,IS (Flt.. n ft, ud. V!X ~ s. I ) '0WtlI. I

A. I. Raff

6 REPOfl' DATE T*OTAL -40 01 PAGES 17b No or REFSf July 1972 5368CONTRACT OP GnAl.! NO IdOQIGNA!OAR% REPORT ! DAS

P.O#E1

NOE 1__0

N00024-7-957 0EP REPOR .,OIS) (Any other n~mbetA rhoe nr"y be asignedthis *epo.l)

SSC-230t I S CI' PUTION STAEMENT!

Unlimited

R T Naval Ship Systems CommandInformation necessary for the use of the SCORES digital compu-

ter program is given. This program calculates both the vertical andlateral plane motions and applied loads of a ship in waves. Striptheory is used and each ship hull cross-section is assumed to be ofLewis form for the purpose of calculating hydrodynamic forces. Theregular and irregular wave results can be obtained, including short

crested seas (directional wave spectrum). All three primary shiphull loadings are computed, i.e. vertical bending, lateral bendingand torsional moments.

All the basic equations used in the analysis are given, aswell as a description of the overall program structure. The inputdata requirements and format are specified. Sample input and out-put are shown. The Appendices include a description of the FORTRANprogram organization, together with flowcha;-ts and a complete cross-referenced listing of the source language,

"DD ItR' (PAGE UNCLASSIFIEDS/N 0101.807.6801 Security C,,liificatio !

"" .I

ii- - ~ , - - ---------*---..-.-*-...--,

r-A

SSC-230

Final Report

Project SR-174, "Ship Computer Response"( to the

Ship Structure Committee

PROGRAM SCORES - SHIP STRUCTURALRESPONSE IN WAVES

byAlfred I. RaffOceanics, Inc.

under

Department of the NavyNaval Ship Engineering CenterContract No. N00024-70-C-5076

This document has been approved for public release and

L sale; its distribution is unlimited.

U. S. Coast Guard Headquartm'sWashington, D. C.1972

ABSTkACT

Information necessary for the use of the SCORES digital compu-ter program is given. This program calculates both the vertical andlateral plane motions and applied loads of a ship in waves. Striptheory is used and each ship hull cross-section is assumed to be ofLewis form for the purpose of calculating hydrodynamic forces. Theship can be at any heading, relative to the wave direction. Bothregular and irregular wave results can be obtained, including shortcrested seas (directional wave spectrum). All three primary shiphull loadings are ccmputed, i.e. vertical bending, lateral bendingand torsional moments.

All the basic equations used in the analysis are given, aswell as a description of the overall program structure. The inputdata requirements and format are specified. Sample input and out-put are shown. The Appendices include a description of the FORTRANprogram organization, together with flowcharts and a complete cross-referenced listing of the source language.

ii

pJ

- -. -..- ' -

7I

CONTENTSPage

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1

METHOD OF ANALYSIS ............ ...................... 1VERTICAL PLANE EQUATIONS ....... ................... 3LATERAL PLANE EQUATIONS ........ ................... 8WAVE SPECTRA EQUATIONS .......................... .. 16NON-DIMENSIONAL FORMS ...... ... .................... 19

PROGRAM ORGANIZATION ....... ...................... .. 20GENERAL ................ ...................... 20RESTRICTIONS . . . . . . . . . . . . . . . . . . . . . . ... 21RUNNING TIME ............ ......................... 22

DATA INPUT ........... ........................... .. 22UNITS ........... ............................ .. 22DATA CARD PREPARATION ......... .................... 23SAMPLE INPUT .......... ......................... 30

PROGRAM OUTPUT ............ ......................... 29DESCRIPTION ....................................... 29SAMPLE OUTPUT ............ ........................ 32

ERROR MESSAGES .............. ........................ 37

ACKNOWLEDGEMENTS ..................................... 37

APPENDIX A - PROGRAM DESCRIPTION ...... ............... 38

APPENDIX B - FLOWCHARTS ...... ................... ... 40

APPENDIX C - LISTING ........ ................... .. 52

ii1

I4

-V . - -- - - - - -- -

r SHIP STRUCTURE COMMITTEEThe SHIP STRUCTURE COMMITTEE is constituted to prosecute a research

program to improve the hull structures of ships by an extension of knowledgepertaining to design, materials and methods of fabrication.

l ! RADM W. F. Rea, III, USCG, ChairmanChief, Office of Merchant Marine Safety

U. S. Coast Guard Headquarters

Capt. J. E. Rasmussen, USN Mr. E. S. DillonHead, Ship Systems Engineering Chief

and Design Department Office of Ship ConstructionNaval Ship Engineering Center Maritime AdministrationNaval Ship Systems Command

Capt. L. L. Jackson, USNMr. K. Morland, Vice President Maintenance and Repair OfficerAmerican Bureau of Shipping Military Sealift Command

=It

SHIP STRUCTURE SUBCOMMITTEE

The SHIIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committeeon technical matters by providing technical coordination for the determination ofgoals and objectives of the program, and by evaluating and interpreting the re-sults in terms of ship structural design, construction and operation.

NAVAL SHIP ENGINEERING CENTER OFFICE OF NAVAL RESEARCHMr. P. M. Pal-ermo - Chairman Mr. J. M. Crowley - MemberMr. J. B. O'Brien - Contract Administrator Dr. W. G. Rauch - AlternateMr. G. Sorkin - MemberMr. H. S. Sayre - Alternate NAVAL SHIP RESEARCH & DEVELOPMENTMr. I. Fioriti - Alternate CENTER

U. S. COAST GUARD Mr. A. B. Stavovy - Alternate

LCDR C. S. Loosmore, USCG - Secretary NATIONAL ACADEMY OF SCIENCES -CAPT C. R. Thompson, USCG - Member Ship Research CommitteeCDR J. W. Kime, USCG - AlternateCDR J. L. Coburn, USCG - Alternate Mr. R. W. Rumke, Liaison

Prof. R. A. Yagle, LiaisonMARITIME ADMINISTRATION

SOCIETY OF NAVAL ARCHITECTS & MARINEMr. F. Dashnaw - Member ENGINEERSMr. A. Maillar - MemberMr. R. Falls - Alternate Mr. T. M. Buermann, LiaisonMr. R. F. Coombs - Alternate

BRITISH NAVY STAFFMILITARY SEALIFT COMMAND

Dr. V. Flint, LiaisonMr. R. R. Askren - Member CDR P. H. H. Ablett, RCNC, LiaisonLTJG E. T. Powers, USNR - Member

AMERICAN BUREAU OF SHIPPING WELDING RESEARCH COUNCIL

Mr. S. G. Stiansen - Member Mr. K. H. Koopman, LiaisonMr. F. J. Crum - Member iv Mr. C. Larson, Liaison

- I

I. INTRODUCTION

This manual describes in detail the use of SCORES,which is a digital computer program for the calculation of thewave-induced motions and loads of a ship. Both the vertical andlateral plane motions are treated, so that results for verticalbending, lateral bending and torsional hull moments can be ob-tained. The principal assumptions of the method are that themotions are linear, can be solved by "strip theory" and thatthe ship sections can be approximated by-'Lewis forms" for thepuz-pose of calculating the hydrodynamic foxces, that is, therequired two-dimeitsional added mess and wave damping propertiesBoth regular or irregular waves can be specified, and for thelatter multi-directional (short crested) seas are allowed.

aCORES was written in th: FORTRAN IV language andchecked out and run on the Control Data 6600 Computer using theSCf!PE operating system (version 3.1.6). The pzogram is un-classified.

The method of analysis used in SCORES is outlined belowin Section II. All the equations of motion and loadings aregiven. In Section III, the organization of the SCORES programis discussed briefly. An explanation of input data card prepara-tion is given in Section IV, and of program output in Section V.An example problem is shown. Error messages which can appearduring program ex.ecution are described in Section VI.

The Appendices include a description of the FORTRANprogram organization, flowcharts for each subprogram and a com-plete cross-referenced (to the flowcharts) listing of the sourcelanguage.

II. METHOD OF ANALYSIS

The analysis used in SCORES was developed and investigatedto some extent in work supported by the Ship Structure Committee.*The exposition to be given here will serve as a convenient listingof the equations, but for the full derivation and explanation ofthe analysis method, the references listed should be consulted.

*Kaplan, Paul, "Development of Mathematical Models for DescribingShip Structural Response in Waves," Ship StructureCommittee Report SSC-193, January 1969 (AD 682591)

Kaplan, P., Sargent, T.P. and Raff,A.I., "An Investigation of theUtility of Computer Simulation to Predict ShipStructural Response in Waves," Ship StructureCommittee Report SSC-197, June 1969 (AD 690229)

Kaplan, P., and Raff, A.I., "Evaluation and Verification of ComputerCalculations of Wave-Induced Ship Structural Response."Ship Structure Committee Report SSC-229, July 1972.

i /

2The relationship between the water wave system and theship coordinate axes system is shown in Figure 1. The wave propa-gation, at speed c, is considered fixed in space. The sh'.ip thentravels, at speed V, at some angle, 8 with respect to the wavedirection. The wave velocity potential, for simple deep-waterwaves, is then defined by:

w= -ace cos k (x' + ct)w(i

where a = wave amplitude

c = wave speed

k = wave number =

S= wave length

z' = vertical coordinate, from undisturbed water surfacepositive downwards

x' = axis fixed in spacet = time

The x-y axes, with origin at G, the center of gravity of the ship,translate with the ship. The x' coordinate of a point in the x-yplane can be defined by:

x' = -(x+Vt) cos 8 +y sin 8 (2)Then, the surface wave elevation n (positive upwards) can be ex-pressed as follows:__

g1 1 :w =a sin k (x' + ct) (3)

since c2 =

where g = acceleration of gravity

In x-y coordinates we have:

a sin k [-v cos 8 + y sin 8+(c-V cos 8)t] (4)

2n5 =( -V --L-) T1 (x, t)t at axI= akc cos k [-x cos 8+y sin 8 + (c-V cos 8)tJ t5)

~~ -

3direction of ship travel

at speed, V

I I=

I 'k4B II

wave direction of axis fixed inpropagation at speed, c space

Fig. 1. Wave and Ship Axes Cohivention

and..D= D;NU =-akg sin k [-x cos S+y sin 8+(o-V cos O)t] (6)

The results of the equations of motion, etc., will bereferenced to the wave elevation n at the origin of the x-y axes,that is:

n = a sin k'(c-Vcos 8) t (7)or n = a sin wet

e

where

an e (c-V cos 8) (8)eand we is known as the circ.ular frequency of encounter.

A. Vertical Plane Equations

The coupled equations of motion for heave, z (positivedownwards), and pitch, 0 (positive bow-up), are given as:

mz= i dx + Z (9)xs

X b

- dZ x dx + (w (10)y xS~s

wherem = mass of shipI = mass moment of inertia of ship about y axisy

dZ- local sectional vertical hydromechanic force onship

Xs, Xb= coordinates of stern and bow ends of ship,respectivelyZ w, Mw = wave excitation force and moment on ship

The general hydromechanic force is taken to be:

dZ Dt [A33 (z-x6+V) (11)

' where

Sp =density of water

local sectional vertical added mass

Nz' =local sectional vertical da ning forcecoefficient

B* local waterline beamand

14' =pg 2R~~ (12)

withratio of generated wave to neave amplitude for Ivertical motion-induced wave

Expanding the derivative, we obtain:

5dZ (zxo2V) ..S- A ~(-1 - z 1I- (;-x6VO)

- ogB* (z-xO) (13)The equations of motion, (9) and (10) are then transformed intothe familiar form as follows:

a'z + bi + c'z -d8 - e6 - g'e = z (2 )

Ae + B8 + cO - Dz - E - G'z = Mw (15)

The coefficients on the left hand sides are defined by:

a' =m+ fA dx

b= N' dx -V d (AVf fI c= Jg B*dx

d=D= A' xdxIe = N'xdx -2V AIdx-V xd (A3),z i3'3

g'= pg B*xdx -Vb

i 33 (16)A =Iy+ A x 2 dx

;3All

6 '

Nzx 2 dx -2V Af xdx -V x2d (A33 )

C Pg B*x2dx-VE

E fNzxdx-V [xd (A3)G'= pg B*xdx

where all the indicated integrations are over the length of theship.

The wave excitation, the right hand sides of Eqs. (14)and (15), is given by:

xb dZZf= JZx dx (17)

xs

Ix 1J 4b dZzw dx (18)

The local sectional vertical wave force acting on theship section is represented as:

dX 3 3 pgB*n + N; ;+-kA (19)

E I-ix

7where h = mean section draft. Substituting the expressions for n,Sand j from Eq. (4), (5) and (6), with y=O and applying theapproximate factor for short wave lengths we obtain:

dZw -kh a kg)sin(-kx cos 8) +xe-(--=B-*ae

kc (NzT-V cos(-kx cos h Cos a ot + (agBe-Ad kg)e3 33

cos(-kx cos B)-kc Nz'-V - A-x- sin(-kx cos 6 sin wet .

sin si sin 8+

~=~o e(22)

B_* sin B si

The value of is approximated by:

S=HCs (21)

where H local section draftCs= local section area coefficient

The steady state solutiow of the equations of motion areITobtained by conventional methods for second order ordinarydifferential equations, using complex notation. The solutions areexpressed as:..

z =zo sin (w et+5) (22) ,[

e = 0o sin (w et+C)

where the zero subscripted quantities are the amplitudes and 6c are the phase angle differences, i.e. leads with respect to thewave elevation in Eq. (7).

The local vertical loading is given by:

df z dZ dZw-- -dm (z-xe) + - (23)(

8where 6m = local mass, per unit length.

Eq. (23) is simply the summation of inertial, hydrodynamic, hydro-static and wave excitation forces. The latter terms are given inEas. (13)and (20). The vertical bending moment at location x isthen given by: 0

S~dfz

x x

and is expressed in a form similar to the motions, i.e.

BMz = BMzo sin (Wet+G) (25)

B. Lateral Plane Equa,.ons

The coupled equations of motion for sway, y (positive tostarboard), yaw, k (positive bow-starboard), and roll, (positivestarboard-down), are given as:

[x= dYx [ dx+Yw (26)

I S

I -I x dx+N (27)

x

sSI x #= - d x -m g G - + K w ( 2 8 )~Xs

where I = mass moment of inertia of ship about z axis iI - mass moment of inertia of ship about x axis

Ix mass product of inirtia of ship in x-z planeSxz

-'g -L4W wan~

9 1dY dY local sectional lateral hydrodynamic force on ship

dKdK local sectional hydrodynamic rolling moment on ship

Y' Nw, Kw = wave excitation fcrce and moments on ship

T = initial metacentric height of ship (hydrostatic).The hydrodynamic force and moment are taken to be:

=dY DD 4 (+x.V)_Fri -N. (y+x-V,)+ N

(29)+ 6G' (Ms$) M + N

d= -0 FrI-M.s (y+x,-Vi) -Nr$+ Nso (y+xi-Vp)

(30)-- DOG- (M,$) - O N$ - - dY

where O = distance of ship C.G. from waterline, positive up

M = sectional lateral a( -d massNs sectional lateral damping force coefficient

NO sectional added mass moment of inertia due to lateralMs motion

Ns = sectional damping moment coefficient due to lateralmotion

r= sectional added mass moment of inertia INr = sectional damping moment coefficient

Frs = sectional lateral added mass due to roll motion

Nrs = sectional lateral damping force coefficient due toroll motion

and the sectional added mass moments and damping moment coefficientsare taken with respect to an axis at the waterline.

a0

The additional roll damping moment to account for viscousand bilge keel effects is taken as a particular fraction of thecritical roll damping, as follows:

Nr* = r Cc/L-N (W ) (31)where Nr* = sectional damping moment coef,.icient due to viscous

and bilge keel effects[ = fraction of critical roll damping (empirical data)Cc = critical roll damping

L = ship length (L=Xb-Xs)

WO = natural roll (resonant) frequencyNr(,) = value of Nr at frequency w.

The critical roll damping is expressed in terms of the naturalroll frequency by:

Cc =2 mg G-Mw-w

2" (32)with mg= mgGM

x(I + fIr (,)dx)

where the integral is over the ship length. The calculation ofthe natural roll frequency, w , as indicated above is carriedout by means of successive approximation.

Expanding the derivatives, we obtain

-Md(y+xi-2V) + d N +xP-VP

(33) . ~dFrs

(F+0- M + Nrs+W NsV (-x + -G )S (M Fs+M)]; [VIr (X+ )dK +OGMs*+ F V G"+['X + 5- rrs+6GM) + 3YTX

(34)-N -N* +( _GM +Y'-2V,)r r

+ U s d%

O[ +5G NS-V so +5GP

IThe equations of motion, (26)0, (27) and (28) are then transformedinto this familiar form:

a21y 22i+'24 a 25 + 26 ~ 27*+a28$ = (35

a 3 y+a 32 y+a 34i+a 35*+a 36 *+a 3701a 18 +a 39 = "

The coefficients on the left-hand sides are defined byr:

aJ Msdx a 2 [N~dx-V fd(M11 12 + ='

a14 =fM sxdx a,,a5 fNsxdx -2V fMsdx .-V fxd(M9 )

Da 16 =-Va 12 ,a 1 P ~rdx - Ufm dx ,(36)

a 18 f Nzsdx + U6_V ld(Ms)-cWGJNsdx + V d(F s

a2 M J~xdx ,a 2 N JNxdx -V Jxd(M)

24 +JSXd a - Nsx dx-2VM d- d(24 z ~ d 25 f~d- (-. if

37)a 26 =-Va 2 2 , a27 -I~ z JF rs xdx -OG fM sxdx

aJNrsxdx+rGV Jxd(MS) N xdx+V Jxd(Fa 2 8 s f - rs~

I12

a 1 msdx -U- fM dx ,

a 1 -fsd W X+ d(M fV5_d(M)

a3 1 =-Isx -f'Msoxdx - ,G J Mxdxa35 = -JNsxdx - Jsxdx +V xd(M s )+V 5-G xd(Ms )-2Va

a 'a

a 3 6 =-Va32 ' (38)

a 3 7 r.+ firdx +OG sodX +U fFrsdX +6 2 fMsdxa3 8 = J(Nr+N)dx+

- sdX IrX+2 sxa 9 = N mg + TG_ JN5 dx +OG- JNdx +0G-2 N sdx

- d (I r+5-G d(Ms)+5 Jd(F +O-G2 d(M)

a 39 =mg Um

where all the indicated integrations are over the ship length.

The wave excitation, the right-hand sides of Eqs. (35) isgiven by:

JI SdYY w = x d- w dx (39)Yw dx

xs

Nw dx x dx (40)

XbdxKdx - dx (41)

X%s/

t 13

The local sectional lateral force and rotational momentdue to the waves acting on the ship are represented as:

rY Dvw dM Dvw dMdxY (PS+Ms) Dt VVw S +NsVw+k (MsD-- +V = ]

sin sin 8____ ____

____(42)

sin ,

dK~_ _D(M v)+ B*3 Dv~sin sin a)

a- -Dt sTw- Dt so- 7TB* sine

__dYw- MG d--x

-O (43)

where vw = lateral orbital wave velocity

S = local section area

- = local sectional center of buoyancy, fromwaterline

The lateral wave orbital velocity is obtained as follows:

w

vw = - akc e sin 8 sink x cos, + y sin 8+ (c-V cos 8) (44)

and then we have:

DV = akg e-kh sin 0cosk L-x c. 8+ y sinB+ (c-V cos,) (45)cstt(

14

After substituting these expressions and expa'-ling terms, we obtain

dY wdYW T cos wet + T2 sin wet (46)

with TI = T:3 4 co s T6 + c T5 sin T 6]

T2 T T3 -gT4 sin T6 + c T5 cos Tsin /7r* sin

T= -ake-kh sin8 rB__* sin a

T = pS+M -kMs

T5 = Ns-V a + k V

T6 = -kx cos B

dKwand a-= T7 cos wet + T8 sin wet (47)

wi T 7 = T 3 T9 cos T6 + c T 0 sin T6]

T T3 g T9 sin T6 + c T 0 cos T

T 9 P! _so-5OG T4

dMT N +V - O-G T10 so dx 5

The steady-state solution of the equations of motion are expressedas:

a YO sin (wet + K) (48)

sin (wet+ ) (49)

0 e

15= sin (wt + V) (50)

where the zero-subscripted quantities are the amplitudes and K, aand v are phase angle leads with respect to the wave elevation.

The local lateral and rotational loadings are given by:

dfdY dYd = - Sm (y+x-rf) + a- + (51)

xdmx XB*UK)

S- - 6m. y2' + 6m4(-+xi) + pg - - s OG) -g 5m4dK dK+ a -+ - (52)

where local center of gr-avity (relative to ship C.G.)positive downlocal mass gyradius in roll

and the hydrodynamic and wave excitation terms are given in Eqs.(33), (34), (46), and (47).

The lateral bending and torsional moments at locationx are then:

01

roxbI dfBMy(xO) or (x-xo) dxY dx (53)xs J

y 0 ob dx

TMx) jj or : -: dx (54)and again they are expressed in this form:

BMy = BMy 0 sin W et + T)I (55)

TM = TMxo sin (e t + v)

16

The requirement on the local vertical mass center is:

6m.Cdx =0 (56)Ixs

Similarly, the requirement on the local roll gyradius is:

J 6my 2 dx = Ix (57)x

The product of ine:'*:a in the x-z plane is defined by:XbI xz 6mx~dx (58)

C. Wave Spectra EquationsThe wave spectrum for calculations in irregular seas is

considered to be a separable function of wave frequency anddirection as follows:

S ( S,.) = SI(w) W for O

17

2

where a2 = mean squared wave amplitude.

r Since we impose:

SS2(p) dui = 1.0 (61)

we then have:

al= J S(1 )dw (62)Additional statistical properties are formulated from the meansquared amplitude:

jt a2a (63)a avg = 1.25 arms64)

al/ 3 2.0 arms (65)

al/ 1 0 = 2.55 a rms(66)

where arms = root-mean-squared wave amplitude

aavg = average (statistical)wave amplitude

I- -

18

a =s ignificant (average of 1/3 highest)1/3 wave amplitude

a1/ic= average of 1/10 highest wave amplitude.

Neumann Spectrum (1953)This frequency spectrum (as used) is given by:

SI( = 0.000827 g2 3 -6e2g2-2U-2 (67)

where U = wind speed

The constant is one half that originally specified byNeumann so that this spectrum satisfies Eq. (62). Thus, originallythe Neumann spectrum required only a factor of 1 in Eq. (65),instead of 2.0.

Pierson-Moskowitz (1964)This is given by:

S 1 M = 0.0081 g2-e-74ge--.-7 4g (

and was derived on the basis of fully arisen seas.

Two Parameter (1967)

M A-B& 5e- (69)

where A = 0.25 H1/3

B = (0.817 2i -T

H1 / 3 = significant wave height (=2.0a1 / 3)

T= mean wave period

This spectrum is usually used in conjunction with "onserved"wave height and period, which are then taken to be the significantheight and mean period. This spectrum is similar to that adoptedby the I.S.S.C. (1967) as "nominal", except that it is expressedin circular wave frequency instead of frequency in cycles persecond.

S1I

77-

19Uni-Directional Spreading (Long Crested Seas)This is obviously:

S2 (u) = S(M) (delta function) (70)

Cosine-Squared Spreading

= 2 cos2ji (71)2 1T

Responses

All of the motions and moments calculated are consideredto be linear and the principle of wave superposition is assumed.Thus for each response a spectrum is calculated by:

S = IT(w, 1u)] S (wi) (72)

where Ti (w,) = response amplitude operator (amplitude of responseper unit wave amplitude)

We then have, similar to the wave amplitude:

1 = Si(l dw dp0

22

61() IT S ddu (73)ITI where a.2 = mean squared response amplitude.SEqs. (63) - (66) then apply to each response.

D. Non-dimensional Forms2

Frequency parameter: e Hj tw

20

motion amplitudeNon-dimensional linear motion (heave, sway):a

Sa

ENon-dimensional angular motion motion amplitude(pitch, yaw, roll): 2 a

Non-dimensional moment: BM z(orBM or TM )og B,*L~a

Shear ForceNon-dimensional shear: Se Forceog B*La

III. PROGRAM ORGANIZATION

A. General

In general, the SCORES computer program has been arrangedand organized to both keep a) the coding simple and fle:cible (forS~possible future modification) and b) the running times low (forobvious reasons). Thus, precision of computation has not been ofmajor priority in program development. This approach is consideredreasonable at the present time because precise correlation (toless than about 5%) with independent data (model or full-scale ex-periments) is not envisioned, and the theoretical analysis itselfis an approximation.

Aside from the actual coding and data structure in theprogram, which will not be discussed here (see Appendices A, Band C of this report), this approach manifests itself primarilyin two aspects. The fir't is the precision with which the local, ortwo-dimensional, sectional ae-ed mass and damping characteristicsor properties, are calculL.=d. For vertical oscillation, the methodof Grim* is used. For the two-dimensional proparties in lateraland roll oscillations, the method of Tasai** has been programmed.In general, these methods can be carried out to increasing degreesof numerical accuracy. For practical purposes of keeping runningtime reasonable: these calculations have been limited. For examplein the lateral and roll computations, the infinite series of termsrepresenting the velocity potential is truncated to nine termsand only 15 points along the Lewis form contour are used for leastsquare approximation purposes. While the full range of sectionproperties and frequencies has not been explored in detail, resultson the order of 1% accuracy or better are obtained for averagesections over a wide frequency range.

Grim, 0., "Die Schwingungen von schwimmeden, zweidimensionalenKorpern," IISA Repcrt No. 1171, September 1959.

Grim, 0., and Kirsch, M., private communication, September 1967.**Tasai, F., "Hydrodynamic Force and Moment Produced by Swaying and

Rolling Oscillation of Cylinders on the Free Surface,"Reports of Research Institute for Applied Mechanics,Kyushu University Japan, Vol. IX, No. 35, 1961

21A

The second aspect of program organization is related to theabove. While the computations of the two-dimensional propertiesare limited as described, they still are relatively lengthy. Thatis at a particular condition of ship speed, wave angle and wavelength, the bulk of the computation time would be 'devoted to thesecalculations rather than the formation of the coefficients,wave excitation, solution of ship motions and the resultingcalculation of applied moients. Therefore, it was decided thatrather than calculate for each frequency at each cross-sectionthe above mentioned two-dimensional properties, instead thc two-dimensional properties are calculated first at 25 values offrequency over a wide range and then interpolated (or extra-polated) for each subsequent frequency. The results of the initialcalculation over the frequency range are saved in the computermemory for the calculations at hand, and can also be saved on apermanent disc file (or magnetic tape storage), for later usage.In chis way, a large range of ship speeds and headings can be run,each over the appropriate frequency range, without excessively,high running times. The interpolation procedure used is asix-point continued fraction method: which gives results that aregenerally well within 1%.

In other respects, the SCORES program is organized in afairly straightforward manner. The input consists of:a) basic data which specify the hull form and weight

distribution and

b) conditional data which specify the speeds and waveparameters.

Repeated sets of conditional data can be run with the same basicdata, that is, for the same defined ship. A fair amount 'of inputdata verification is incorporated into the program.

B. Restrictions

The main restrictions in the program concern the followingitems:

SMaximum no. of ship cross-sections .......... 21(stations 0 to 20)

Maximum no. of wave angles (in one run) ...... 25Maximum no. of wave lengths (in one run)....51Maximum no. of sea states (in one run) ...... 10The core storage requirement is about 25,000 cells as

compiled on the CDC 6600. This includes the program instructions,data storage and system routines to handle input-output systemcontrol and provide mathematical functions. It would be possibleto decrease this core requirement via program overlay andlinkage techniques, should the need arise. However, it probablywould be relatively difficult to fit the program within a 12Kcore restraint.

I -~ A

22The word length on the CDC 6600 is 60 bits. No loss in

overall computational accuracy would be expected if this werereduced, as in other digital computers, to 36 bits.

A special system subroutine called DATE is used whichprovides the current Aate. This is used only in the heading onthe output.

C. Running Time

The following approximate times are for running under theSCOPE operatin" system on the CDC 6600 computer.

Program compilation (RUN compiler) .......... 10.0 secs.Program loading into core ................... 1.0 secs.

Calculation of TDP* Array (21 sections,both vertical and lateral modes) .......... 25 secs.

Calculate motions, moments at one condition,(21 sections, both vertical and lateral

modes) .................................... 0.14 secs.Calculate spectral response, for each

spectrum, for each condition ............. 0.006 secs.Thus, for a run with two ship speeds, 7 headings (at 301 incrementsfrom head to following seas), 21 wave frequencies (to adequatelycover the spectral energy bands) and 5 sea states, the incrementaltime once the program was compiled, loaded and the TDP Array wascalculated, would be estimated as follows:

(2) (7) (21) [0.14+(5) (0.006)] = 50 secs.IV. DATA INPUT

This section of the manual describes the details of datacard input to the SCORES program.

A. Units

For calculations in regular waves, there are no inherentunits assigned to any of the variables in the program. Thus, theuser is free to choose any desired set as long as they areconsistent for all input parameters. The units are establishedby the input values of water density and gravity acceleration.Some typical units are shown below.

*Two-dimensional properties

23

Water Density lbs./cu. ft. tons/cu. ft. metric ton/cu.meter

Gravity Accel. ft./sec. 2 ft./sec. 2 meter/sec. 2

Resultant Unit ft.-ibs.-sec. ft.-tons-sec. meter-metricSystem I ton-sec.

Wave direction angles are always specified in degrees,rather than radians.

However, for spectral calculations in irregular waves, usingeither the Neumann or Pierson-Moskowitz spectra, the SCORES pro-gram assumes ft.-sec. units, full scale. The input wind speedsused to specify spectral intensities, or sea states, are thenassumed to be in knots.

The following input data description indicates typicalconsistent units for all parameters. Other systems of unitscould be used, as noted above.

B. Data Card Pre.aration

Every data card defines several parameters which arerequired by the program; each of. these parameters must be inputaccording to a specific format. "I" format (integer) means thatthe value is to be input without a decimal point and packed tothe right of the specified field. "F" format (floating point)requires that the data be input with a decimal point; the numbercan appear anywhere in the field indicated. "A" format(alphanumeric) indicates that certain alphabetic characters ortitle information must be entered in the appropriate card columns.

If the field is left blank for either "I" or "F" format,a value of zero (0) is assigned to the parameter. Thus, parametersnot required by the program for a particular problem need not bespecified.

The card order of the data deck must follow the order inwhich they are described below. Cards which must be present inevery run, regardless of options, are marked with an asterisk (*).The first eight types of cards are considered the basic data set,while subsequent cards are the conditional data set(s).

1) Title Card (*)Columns Format Entry

1-80 A Any alphanumeric titleinformation, used to labeljob output

- ' - N X A RN x

24

The first 30 columns are used a3 a label for the TDP array file.Thus, subsequent runs using the file must duplicate these first30 columns which are then checked against the file label beforeusing the data. This avoids inadvertent use of an incorrectTDP file.

2) Option Control Card (*)Columns Format Entry

1-2 I Integration option control tag3-4 I Moment option control tag5-6 I Mass dist. option control tag7-8 I Wave spectra option control tag9-10 I Degrees of freedom option control tag

11-12 I Directionality option control tag13-14 I TDP file option control tag15-16 I Moment closure option control tag17-18 I Output form option control tag19-20 I Torsion axis option control tag21-22 I Number of ship segments

Each option control tag is given a value of 0, 1, 2 or 3where the meaning of each is given in the t3ble below. The lastentry of the card, the number of ship segments, corresponds to theeven number of equal length segments, or strips, into which theship hull is divided lengthwise for purposes of calculation.

OPTION CONTROL TAG INTERPRETATION

Letter Tag SCode Descriptor options Available

A Integration 0: Simple summation1: Trapezoidal rule

B I Moment 0: Calc. motions only, usesummary mass properties

1: Calc. motions only, usemass dist.

2: Calc. moments, use massdist.

C Mass dist. 0: Input masses1: Input weights

D Wave spectra 0: Regular waves1: Neumann spectra2: Pierson-Moskowitz spectra3: Two parameter spectra

(continued on next page)

25

OPTION CONTROL TAG INTERPRETATION, Continued

Letter TagCode Descriptor options Available

E Degrees of 0: Vertical plane onlyfreedom 1: Vertical and lateral plane

2: Lateral plane only

F Direction- 0: Uni-directional wavesality 1: Cos-sq. wave spreading

G TDP file 0: Generate TDP file, writeon file (Tape 10)

1: Read TDP file,(Tape 10), printout TDP data

2: Read TDP file,(Tape 10), noprint-out

H Moment 0: Suppress closure calcs.closure 1: Calc. and print out

closure results

I Output form 0: Dimensional1: Non-dimensional

J Torsion axis 0: Center of gravity1: Waterline

3) Length Card (*)Columns Format Entry

11-20 F Ship length (ft.)21-30 F Water density (tons/cu.ft.)31-40 F Acceleration of gravity (ft./sec. 2 )41-50 F Ship displacement (tons)

The entries on this card are self descriptive and determinethe units to be used for all other parameters, except as notedearlier.

4) Hull Form Cards (*)Columns Format Entry

1-10 F Section waterline breadth (ft.)11-20 F Section area coefficient (-)21-30 F Section draft (ft.)31-40 F Section centroid (ft.)

1A

-I

26One card is used ior each section to be specified, in order

along the ship length starting at the bow. For example, if thenumber of segments is 10, and the integration option tag is 0,then 10 hull form cards are required which correspond to the hullat stations 1/2, 1 1/2, 2 1/2, ... , 8 1/2, 9 1/2. If theintegration tag is 1, then 11 hull form cards are required atstations 0, 1, 2, 3 ..... 9, 10.

The entries for sectional waterline breadth, area coef-ficient and draft are straightforward. The fourth entry, thesection centroid, is measured downwards from the waterline . Ifno entries are given and the centroids are needed for lateralplane motions calculations, arnroxirzte controids are thencalculated based on the area coefficient and draft (using a two-dimensional version of the Moorish Approximation).

5) Lateral Plane CardColumas Format Entry

1-10 F Ship vertical center of gravity (ft.)11-20 F Radius of gyration in roll (ft.)

This card is used only if the degrees of freedom op+.iontag is 1 or 2, indicating lateral plane calculations. The shipvertical c.g. is measured from the waterline, positive upwards.

6) Summary Mass Properties CardColumns Format Entry

1-10 F Radius of gyration, longitudinal(ft.)

11-2U F Longitudinal center of gravity(ft.)

This card is used only if the moment option tag is 0.The longitudinal center of gravity is measured from amidships,positive forwards.

7) Sectional Mass Properties CardsColumn Format Entry

1-10 F Segment weight, or mass (tons,or tons-sec 2/ft.)

11-20 F Segment vert. c.g. (ft.)21-30 F Segment roll gyradius (ft.)

These cards are used only if the moment option tag is1 or 2, in lieu of the summary mass properties card above. Onecard is used for each section to be specified, in a similarmanner as the hull form cards described earlier.

The first entry on each card is the segment weight, ormass, depending on whether the mass dist. option tag is 1, or 0,

27

respectively. The second entry, the segment vertical center ofgravity, necessary only for lateral bending moment calculations,is measured, positive downwards, with respect to the ship's over-all vertical center, as specified on the lateral plane data cardabove. Since it is required that the vertical mass momentintegral satisfy the specified overall v.c.g., the input segmentv.c.g.'s are shifted by an equal amount, up or down as necessaryto exactly balance the vertical moment for the hull. Thisminimizes the effort required to obtain precise balance in inputdata preparation. The third card entry, the segment roll gyradius,is needed only for torsional moment calculations. If no entriesS~are given the overall ship value is used at each segment.

8) Moment Station Card egn

Column Format Entry

1-10 I First station for moment calculations11-20 I Last station for moment calculations21-30 1 Increment between stations

The parameters on this card determine where along the shiphull the moment calculations are to be performed. Station numbersare defined as zero at the forward end of the first segment,increasing to N, the number of segments, at the after end of thelast segment. If the calculations are required only at one station,then the first two entries on the card snould be equal to thatstation number.

The moment results at only one station are stored forsubsequent irregular seas spectral calculations. In the calculationsover a range of stations at which moments are calculated (andprinted), then only the results at midships are stored for thesubsequent spectral calculations.

9) Run Control Card (*)Columns Format Entry

1-10 F Run control tag and waveamplitude (ft.)

11-20 F Initial wave length, orfrequency (ft. or rad./sec.)

21-30 F Final wave length, or frequency(ft. or rad./sec.)

31-40 F Increment in wave length, orfrequency (ft. or rad./sec.)

43-50 F Initial ship speed (ft./sec.)51-60 F Final ship speed (ft./sec.)61-70 F Increment in ship speed (ft./sec.)

The first entry, the run control tag, determines programcontinuity:

28

Run Control Tag ActionGreater than 0.0 Continue calculations, using this as

wave amplitude0.0 (or blank) Stop calculations; read new basic

data setLess than 0.0 Stop program execution

Thus, if the run control tag is not greater than 0.0, thenthe remaining parameters on the card are irrelevant. A blankcard, for example, is used to stop calculations and proceed toread a complete new set of data starting with the title card ,P) above. This parameter is also used as the wave amplitude, andis usually set to 1.0.

The next three entries determine the wave lengths to beused in the calculations. If the wave spectra option control tagis 0, indicating regular waves, then these entries are the initial,final and increment in wave length. If the wave spectra optioncontrol tag is greater than 0, indicating irregular wave calculations,then these entries are the initial, final and increment in wavefrequency. The increments should always be positive, so that wavelength, or frequency, increases from initial to final value.

The last three entries are similar parameters for ship speed.If calculations are required at only one value, then the initialand final values should both be set equal to it.

"10) Roll Damping CardColumn Format Entry

1-10 F Fraction of critical roll damping(empirical data)This card is used only if the degrees of freedom option

control tag is 1 or 2 indicating lateral plane motions calculationsare included. The calculated wave damping in roll, at the naturalroll frequency, is increased so that the total damping is thespecified fraction of critical damping. The additional rolldamping thus determined initially is then used fon all subsequentcalculations.

11) Wave Angle Card (*)Column Format Enty

1-10 F Initial wave angle, degrees11-20 F Final wave angle, degrees21-30 F Increment in wave angle, degrees

These entries specify the wave direction angles to be usedin the calculations and are always given in degrees. Forcalculations with uni-directional waves, the meaning of theparameters is as indicated. If the directionality option control

29

tag is greater than 0, indicating calculations for a directionalwave spectrum, then only two choices exist. If the initial waveangle is 180.0 the calculations proceed for head seas only,including the wave directionality. If the initial wave angle isnot 180.0 the calculations proceed for all angles from followingseas to head seas, in sdteps according to the wave angle incrementspecified.

In both cases the integrations with respect to wave angleuse the same increment, as specified.

12) Wave Spectra Card(s)Columns Format Entry

1-10 I No. of sea states (wave spectra)11-15 F First spectra parameter16-20 F Second spectra parameter21-25 F Third spectra parameter

(5 col.fields) F56-60 F Tenth spectra parameter

This card is used only for calculations in irregular seas(wave spectra option control tag is greater than 0). The firstentry specifies the number of sea states (spectra) to be used(maximum 10). For both the Neumann and Pierson-Moskowitz spectra(wave spectra option control tag equals 1 or 2), the parametersto be specified are the wind speed, in knots, for each seastate. For the two parameter spectrum (option tag equals 3),tie parameters on this card are the significant wave heightsfor each sea state. A second card is then used which containsthe mean periods for each corresponding sea state, as thespectral parameter entries specified above.

C. Sample Input Deck

A sample input card deck listing is given on the nextpage. The units are meters, metric tons and seconds.

V. PROGRAM OUTPUT

A. Description

The printed output from the SCORES program depends on theoption control tags set as input. Each output section will bedescribed, though in any given run not all sections will beprinted. Each section starts a new page and is labeled with thetitle information and date.

The first part of the output is a listing of the basicinput data as processed. This defines the hull form and weightdistribution. Then the conditional data cards are printed out.For irregular seas cases, the wave spectra will then be printed,together with internally generated wave statistics. If the TDParray is calculated diagnostic messages concerping thesecalculations may then appear.

V3

f IIs4

30

The next output will be the listing of the two-dimensionalproperties (TDP array) for each station and each frequency. Ifthe data is being read from file, this output can be suppressed.For lateral plane calculations, the natural roll frequcncy androll damping information will then be printed.

Then, the vertical and/or lateral plane responses will beprinted out with all frequencies, or wave lengths, for a givenship speed and wave angle, on the same page. For irregular seascalculations, this will be followed by a print-out of theresponse spectra and statistics (long crested seas). These pageswill be repeated for each wave angle at the initial ship speed.Then directional seas calculations results will be output, ifspecified. The output is, of course, then repeated foradditionally specified ship speeds.

B. Sample Output

A sample output listing, in abbreviated form, is givenfollowing the sample input listing.

Sample Input Card Deck Listing

StRIFe 6', MULL FOQu; 0.4" tLUCK (TNO RPT. .0. inO b) OCEA41CS 'HRnIFCT %-U. 10d31 2 1 3 I 1 I I lI u

14J.0 1 9.0665 44176-4.00.04 .0 r0 414 ,JQ , il.OJ2 l.8,9 4A "0 4 31.4

27.54 O .9 11.01

21.b? QY1 41.4327:57

21.67 .9V4 11.03 1

21f.7 .9V4 11.(13Pt .57 QY4. 11;0127.67y .993 !1.0327.6? .9 :9 11.0321. 5.? . 4 1 1.0321.24 .9l 11.03P5 .94 .051 11 .03?3;46

.7b9 1 0S9 .6b3 hel 11."313 .8? .419 l.V

4.41 .53 I.24

-1.09A5 0.9V026

"481.3.2 .2406 6 340Y90*1

3 0.

4331.44331.4.168,.4

1684.43831443.8 ,219b .-3290: 73633.&346b,13166.3

1.0 0.3151 I.J3079 0.n41 6.5251 6.bo2b 1.0

10.0 17 .0 0.0,I- Ai 'o. -2 . - - -. .. _

10.0

, 7

31

Sample Input Listing

SEHIES 60 HULL FORM. .).HO bLCK gINO RPI. NO. 100 SI OCEANICS PROJECT NO. 1093 SEP P4e 1970OPTIONCONTHOL TAGS- A f- C I) F G H I J

F- P. I- 1 ?- 1 3 0--I 1 1 I1 NO. OF STATIONS * 20

BASIC INPUT DATA

LENGTH .193.00 OENSIfY * 1:025000015.... * ?6_46 _ GRAVITY a 9.80665A

STATION PLAN AREA COLF. DRAFT L-SAP ;EIGHT ZFTA GYRtROLL0.00 "100 0.0000 0.6000 fi00 40.600 0.000 a.960?

1.00 14.3900 .8720 11.-300 5.-4, 4uI.3O00 0.0000 8.96022.00 2,OA .A940 11.0300 S.ISi 1203.2000 0.0000 8.96023.00 ?6.5800 .9290 11.0300 5.754n 2406.3000 0.0000 8.9602

-4.00 27.S460 .9700 11.0300 -- 5.404i "3850;1000--- ... vo 'S.0"89602-5.00 27.S700 .9910 11.0330 S.481n 409047000 0.0000 6.96026.00 750n .9940 11.0300 5.492o 4331.4000 0.0000 890

27.57008.9602

7.00 27.S700 ,qV40 11.0300 5.49? 4331.4000 0.0000 8.96028.00 27.$760 .9940 11.0300 5.492a 3368.8000 0.0000 8.96029.00 27.5700 .9940 11.0300 5.492n 16#4.4000 0.0000 8.9602S.. 0-27.S?0 --. 4940 11.0300-- S.4926 1684.4000 0 -00000--- 3.9602 4-

11.00 27.5700 .4940 11.0300 5.et 1443.8000 0:0000 8.9602 f12.00 27.5700 .99-3o 11.0300 5.4&9'1 2195,8000 0.0000 8.960213.00 27.67an .9(490 11.0300 5.4744 329007000 0.0000 8.960214.00 27.5T0n .9680 11.0300 5.3971 3633.6000 0.0000 8.960215.00 277.200 .9210 11.0300 S.2249 3465,1000 00.0000 8.9602

*16.b0 2S.9600 Asio ll.o00 "-.967 3146.3000 "- 0o000 8.9602"17.00 23.460 ,7580 11.0300 4.625p 19!)5.1000 0.0000 8.96021A.00 19.#,30n .6270 11.0300 4.143* 721.9000 0.0000 8.960219.00 13,8?nn .4190 11.0300 3.376o 481.3000 0.0000 8.960220.00 4.4100 .5300 1.1000 .3777 120.3000 0.0000 80602

"OG a ;-1.04 9 6YRTUS, RQLL - 8.960...CALCULATE MOMENTS AT STATION 10

UtNTYLO RESULTS.ISPL.(WT5.J . 44126.50

LIa -. Ti-F~Trlrd r MOT tS1tPSr- NxSPtvo.tIO. 48077.S3

LON4. C.G. 4.82; IFwD. OF PICSHIPI LAInG. GYPADIUS x 46.159 aM 3 1i78

SERIES L FORM- O.HO HLUCK (TNO HPI. NO. 100 S) OCEANICS PROJECT NO. 10q3 SfP 2p4 1970

CONDITIC14AL INPIUT DATA CART PRINT OUT

1.0000 .3157 1.3c79 .0451 6.'257 b.5257 1.0600.1000

- 10.0000 170.0000 20.00001 . . . -40. -0.0 :OU -q.0 -0.0 -0.0 .0.0 -0.0 -0.0

. ."* -0.0 -0.0 -0,0 .A0.0 -0.0 -0.0

SERIES 60 HULL FORM, 0.80 HLOCK (TNO RP;. nO. 100 S) OCEANICS PROJECT NO. 1093 SEP Ptl 1920

WAVE SPECTRAL I)LNSIIY, TWO PARAMETER. ISSC 1967 SPECTRAS1G.T. ,4004I NP 14. ]~000SPECTRA NO. I

wAVk FOE,.

.361 1.32A

.406 P.610

.451 12.254%.496 12.954.541 11.743----------------

.631 7:886

.6f6 6,aOh 1.173 .533

.72? 4.846 1.21I ,43

.61 3 ?,037 1.263 ,3?1"A*sf- 2 .331 "-1.3011 .313

,:992 1,7 "b RPS. 2.073

03?? -11,1 AVG. 7.539

2.03? ,9611.08? *fH4 SIG. 4.146

'. ,- ? -" 6 -AVI/I- S-,27 - -'.'---

32

IV I. 6a6I np000000000000 0000000000i 0000.

0 ~ ~ 0 In a* a inv5-1 0 -

ag.; F.J* 0000 000 00 0 0 0 NlVu* WI a a I 0 J-5 A

0 00 000 0.000 00001 0000

on MCNwr EONV000 x-A0N@ W W n W

*CE0n 0 t-O* D1I0.*C0-N Go

.00 in a11...

000 00 00 00 00 00 00a0 _* t:..%Vina aIL1W54 Whih WWS.bJW Z tvWW. hJS.

~,S~mNsD.~~INN ~ 044 a: :z000 00 00 Ia. OM %vl

*t' N tN N Cy IV N t N PNNC.- -. ~~000 000707000000000000000* - wwwwWu*WwW~WW*W wU= hSWWhawW WWSWOW,

LOM* a* 40k4100 WCN C4415PNCO .*C-.w19 if C-04l W lP.11a,

V)~ 0000000000a40000000ac ;;%.*000 J O e NNNyypih4NPSNN- - - en*' nh 41 1.P.-W0 a06N009O

Mal Mf40000 0c;0-.; -a :a 0F) a 000000000000000 00 00o ~ S.JWWWWWW..sWWWWWdWWWWWW WWW9 WWWsJ

C~AN -M C. M0 a9s. D04.0041 0 CM*L)-540 0l9 .N P 0, 1 00(P95

C~~~' in1-- -- -- -- -- --- -- -- 00 - - - -

4J Z 0a000a00C OCOOPO O4! FCIDPCOFOO&OeOM C'000000 00000--- - 'yCU 2 WWUUIUWW W.hiWjgih5W41 WWUh~..,h, S5.WWI W

C)- CD zm r.. 4 0 mm!t kn#S l C43 N -C& 0 00in E mom" 4 CP a 5 0-

00500 ~ ~ 0--~0PC >(190

cc I -pu "-q~ 00.000000000000 00000 'a0 000

I ry M 1'. a. Op-*P! 0 03 7 m p a m A.S .1 .W N * 9 9 55 .(54 .(J~I1. . .... .... ... a *

- o~~~1 4.. . . . .. . p.l NO-5 1.4f:45 J;;0Z 4154 C

0000 cc~ 0 0 0 0 0 00 0 000 aCc ocOCwWLW.WWShS.hJ.WWW WWW WOIN %WMWWW5 2~~~~~ ~~ IN S 5..5 N03 0IU M1455 Z_ v fu m M

- 3 -- oe fl.39.00 O~iWI 59-~'.. 3-5fuU. ~~~!il .1% *0* N N .940It3, U 3 4000

Z3. 1 1. ;C;OZ440 SY - 3 4.5CI --0000.5 N0N.0 .60N0 051 553945.

o 1 0000000000000000000 NJNNIS39NJ-.CPNNME45O. SSJJNN4-MU.W

coo *0 0C 0Ceo.000000*cc C0. CC 0 'Do-l Ctc .5 55 3 . .5 11 . C51t3.5.5. It

o -~ ~ ~ em USt- 2, h4W W W W.5JW.IJ.IJW5.JI1. S.J54S.J

in~ ~~.

33

"00000000000000 0000000000000000W0000 0000000001******44**& sg'sge*2..... 2.4wooiiihhhhhhiliiihhhhh 15hi H. iiihhh~iW h~iibit ihhhhh ih0009p *o o-44 ON-U 0' *0.UO l-04o 4a

i.ON~bft 1~Me 40 4 C 0 g0 M.0S0 00 4 000~J( * 0#10

0.0p. .6.00 Z.#U: On. .04,. ft 03 ... 0 4 M lo 0

000 00 000 40

4444 -p0 t0 04. "run W 40000dO 40 00 0*0009.-000~..00NNW Nj .0Mvnz00.40004ft

* ...... ,. 0 *,***.*ww

109 4000 1`= 04000 100e , 9 .44..400 00

0 0 0 0 ooooa I10 10o oa on oo0 0 0 0000%. 00 p000".OO

o '. 0 0 noG cIi) 40T no I-0 0 0 . . 4 . 40010

4 00 . 1 6-...aI I I -- - - - - -

0 ma a,. N0*B1eB*.B* **. 4m 4p V.I0 - PIhhh.iiiiiiii. ihhhhh &i hiiiIW.kh Wiiihh Miihh Mi W . h h hi 0hinPNO

1~~~h 1II 1 tgo.0 -0 -04 - - -

04040.J14g01 z v v 00009

**BB*B*B * 0.. ..*. , . . .. .. . .. .. iBBB**BI0iiiiiihhhhh .iiihhh hi .lhhhhhhhhhhiiiiilhhhhh .iih hi .. iit-i ihi

4J0...0000004 ....00..000 C0004 0 00 .0 a 0

00- - - - - -0000 M100000- 004110 00- - -

coccco oeecoMceocc woe ~ c o~o C C O O C a4 "00 0 000

...4. Cal 0~0c B Z - a0 00 .-. 90 0 1 . .4 0 0 0 p 0~i3I**.1i 060*00..0*14 0 00T*0. 0 0.0.0. 0. 0 ,10*..0.10. 400 -0000 -4 0.S WWWW~z..WzWW~wWWW *W* 4*w 00ww1W4 ?U

Vo gsw 4In a IMOM 400-.004 000 .. 1AN04440M.5flwe10 00400%s:-.1 xM0~~~~ ~ ~ M o, a ,aM.0amIq o a

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37

VI. ERROR MESSAGES

Various error messages may appear in the output and causeprogram termination. Each will be labeled with the subroutinewhich found the error, and possibly a brief note as to the typeof error. Some messages give error numbers as explained below:

Subroutine Error No. Explanation

PRELIMB/C 0 Too many sections, wavelengths, wave angles, etc.

PRELIMB 1 Sum of weight distribution#displacement

PRELIMB 2 Hull volume inconsistentwith displacement

PRELIMB 3 Longitudinal center ofbuoyancy # long. center ofgravity

PRELIMC 4 Error in range or incrementof variable conditions

PRELIMC 5 TDP calculation incompletePRELIMC 6 TDP file lable # title data,

col. 1-30

Errors in the calculation of the two-dimensional propertieswill be self explanatory. However, if an error is found in theenergy balance check on the results of the two-dimensional lateralmotion calculation the message is printed, but computations proceed.It has usually been found that such errors in the energy balancecheck have little influence on the calculated two-dimensionalproperties.

VII. ACKNOWLEDGEMENTS

The SCORES program derives from earlier basic ship motionprograms originally developed in the Department of Naval Arch-itecture at M.I.T. in 1963-64, and subsequently updated atNSRDC. Thus, while the program concept is not wholly original,the increased level of both complexity and flexibility inProgram SCORES results in a new generation program with littleresemblence to its predecessors. However, the earlier work isacknowledged as the root source for the present development.

The initial phase of programming for Subroutine TDIR, thecalculation of the lateral and rolling oscillation two-dimensionalhydrodynamic forces based on the method of Tasai. was carripdout by Dr. Y. K. Chung.

38

APPENDIX A "' PROGRAM DESCRIPTION

The SCORES program, written in FORTRAN IV (RUN FortranVersion 2 under SCOPE Version 3 for CDC 6600 computer), isstructured in a fairly conventional manner. The main programserves as a control for the job processing, calling varioussubroutines as required. The major program loops over ship speed,wave angle and wave frequency are established in the main program.Data are transferred among subroutines via labeled common blocks,each subroutine accessing those blocks specifically required. Aspecial common block labeled PROGRAM is used and shared by manysubroutines for storage of intermediate calculation data.

Subroutine PRELIMB reads, processes and stores the basicinput data. Preliminary calculations are performed and the dataare checked to some extent for self-consistency. Subroutine PRELIMCreads, stores and processes thL conditional input data. Preliminarycalculations are performed including spectral density calculationsand print out (via Subroutine PAR) if required. Then the two-dimensional properties are obtained, either read from file orcalculated via Subroutines CKLEW, ZIPSMO and TDLR.

Subroutine CKLEW simply calculates the two Lewis formparameters for each section and checks them against criteria toinsure positive contours. If necessary, the section area coef-ficient is increased to satisfy the criterion. Subroutine ZIPSMOcalculates the two-dimensional properties for vertical oscillation,while Subroutine TDLR does the same for the lateral and rollingmodes. The latter routine follows both the method and the notationof Tasai. Subroutine MATPAC is used by ZIPSMO for solution ofsimultaneous equations.

If lateral plane computations are required, Subroutine ROLDis used to calculate the natural roll frequency and the additionalroll damping, to approximately account for viscous effects.

The basic ship response calculations at a given conditionare performed by calling Subroutines ALINT, COEFF, EXCITE, "'OTIONand BENDSH, sequentially. Subroutine ALINT finds and stores thevalue of each required two-dimensional property by continuedfraction interpolation in frequency parameter (equal to circularfrequency of encounter squared times draft divided by accelerationof gravity). Subroutines COEFF and EXCITE calculate the coef-ficients and excitation, respectively, in the equations of motion:which are then solved in Subroutine MOTION. Subroutine BENDSHthen calculates the local loadings and integrated moments. Closureresults are calculated, if required. Throughout all the calcula-tions, subprogram function SINT is used as a simple integrator.

The ship responses "t each speed and wave angle are printedout by Subroutine TNIRPA, including closure results if required.If irregular seas are used, Subroutine STATI then cc'-ulates and

?I

39

print the response spectra and statistics for long crested, oruni-directional, seas at the particular ship speed and waveangle. Only the integrated spectral response at each wave angleis saved, so that the response spectra for short crested seasare not available. For short crested seas results, SubroutineSPREAD is used after the full range of wave angles has beendepleted. The integrated responses over wave angle are computedand printed.

After completion of the specified calculations, controlreverts to Subroutine PRELIMC for additional cases with thesame basic data, that is, the same ship. If no additionalcomputations are required, normal program termination occurs inSubroutine PRELIMC upon input of a run control tag less than 0.0.

Only one special system subroutine is included in the program.This is referenced in the main program by CALL DATE (DTA, DTB)which provides the current date in the argument variables asHollerith data (DTA = MMMbDD,bI9,DTB=YY).

Program SCORES - Input Data Card Summary

ConditionsCard (see legend FormatNumber below) Parameters Entered (4 Columnsl

1 , Title information A802 * Option control tags; number of

segments 11123 * Length; density; gravity; displace-

ment 1OX, 4FI0

Breadth; area coeff.; draft;centroid (each station) 47I0

S5 OT(E)>0 VCG; roll gyradius (ship) 2F10S6 OT(B)-O Long. gyradius; LCG 2F10m

7 OT(B),O Weight; VCG; roll gyradius (eachstation). 3F10

8 * First sta.; last sta.; incrementfor moment calcs. 3110

9 Run uontrol tag; initia2, final andincrerent in wavelength, or freq-quency; initial, final and incre-ment in speed 7F10

o 10 OT0)>0 Fraction of critical roll damping 7i0... 11Initial, final and increment in

wave angle 3FI00S12 OT(D)>0 No. of spectra; parameters .... I10, 10F5'0 o OT(D)-3 Additional corresponding parameters l0X, 10F5

Legend for conditions: * - always necessary in data deck.OT(-}>- necessary only if Option Tag indicated

meets condition shown.

S0

40

APPENDIX B - FLOWCHARTS

Flowcharts follow for the mainprogram and each subroutine. Thereferences given on the flowcharts,such -s C-01 etc. (above and on theright of the symbolic outlines)correspond to numbered comment cardsincluded with the FORTRAN source.program, and listed in the nextappendix.

I

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52

APPENDIX C - LISTING

The complete FORTRAN IV source decklisting for Program SCORES is given.The numbered conWpent cards, such asC-01 etc., are cross-referenced onthe flowcharts in the previous section.

3*09*41. SCOACS 121.00I.0U13127.101(1..21.T*Ut.IPEOUTPU?.TA*IOCI

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