Program SCORES - Ship structural response in waves

I ENCE TO A E RS SSC-230 Final Report on

Project SR-174, Ship Computer Response' to the

Ship Structure Conïnittee

PROGRAM SCORES - SHIP STRUCTURAL RESPONSE IN WAVES

by

Alfred I. Raff Oceanics, Inc.

under

Department of the Navy Naval Ship Engineering Center Contract No. N00024-70-C-5076

This docwent ae been approved for public release and

sale; its distribution ja unlimited.

U. S. Coast Guard Headquarters Washington, D. C.

ABSTRACT

Information necessary for the use of the SCORES digital compu-ter program is given. _{This program calculates both the}

vertical and lateral plane _{motions and applied loads of a ship in waves.}

Strip theory is used and each ship hull _{cross-section is assumed to be of} Lewis form for _{the purpose of calculating hydrodynamic forces.}

The

ship can be at any heading, relative _{to the wave direction. Both} regular and irregular wave _{results can be obtained, including short} crested _{seas (directional wave spectrum). All three}

primary ship hull loadings are _{computed, i.e. vertical bending,}

lateral bending and torsional moments.

All the _{basic equations used in the analysis are given,}

as

well as a _{description of the overall program structure.}

The input data requirements _{and format are specified.}

Sample input and out-put are shown. _{The Appendices include a description}

of the FORTRAN program organization, together with flowcharts and _{a complete} cross-referenced listing of the source language.

11 METH V L w N PROC G P P DAT L E C PROC C E RRC AC K

CONTENTS

Page

INTRODUCTION i

METHOD OF ANALYSIS I

VERTICAL PLANE EQUATIONS 3

LATERAL PLANE EQUATIONS 8

WAVE SPECTRA EQUATIONS 16

NON-DIMENSIONAL FORMS 19 PROGRAM ORGANIZATION 20 GENERAL 20 RESTRICTIONS 21 RUNNING TIME 22 DATA INPUT 22 UNITS 22

DATA CARD PREPARATION 23

SAMPLE INPUT 30 PROGRAM OUTPUT 29 DESCRIPTION 29 SAMPLE OUTPUT 32 ERROR MESSAGES 37 ACKNOWLEDGEMENTS 37

APPENDIX A - PROGRAM DESCRIPTION 38

APPENDIX B - FLOWCHARTS 40

(

t

Capt. J. E. Rasmussen, USN

Head, Ship Systems Engineering and Design Department

Naval Ship Engineering Center

Naval Ship Systems Corranand

Mr. K. Morland, Vice President

American Bureau of Shipping

The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research

program to improve the hull structures of ships by an extension of knowledge

pertaining to design, materia)s and methods of fabrication. RADM W. F. Rea, III, USCG, Chairman Chief, Office of Merchant Marine Safety

U. S. Coast Guard Headquarters

Mr. P. M. Palermo - Chairman

Mr. J. B. O'Brien - Contract Administrator Mr. G. Sorkin - Member

Mr. H. S. Sayre - Alternate Mr. I. Fioriti - Alternate

U. S. COAST GUARD

LCDR C. S. Loosrnore, USCG - Secretary

CAPT C. R. Thompson, USCG - Member

CDR J. W. Kirne, USCG - Alternate

COR J. L. Coburn, USCG - Alternate MARITIME ADMINISTRATION

Mr. F. Dashnaw - Member Mr. A. Maillar - Member

Mr. R. Falls - Alternate

Mr. R. F. Coombs - Alternate MILITARY SEALIFT COMMAND Mr. R. R. Askren - Member

LTJG E. T. Power, USNR - Member

AMERICAN BUREAU OF SHIPPING

Mr. S. G. Stiansen - Member

Mr. F. J. Crum - Member

iv

SHIP STRUCTURE SUBCOMMITTEE

The SNIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Comittee

on technical matters by providing technical. coordination for the determination of

goals 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 RESEARCH

Mr. E. S. Dillon Chief

Office of Ship Construction Maritime Administration Capt. L. L. Jackson, USN

Maintenance and Repair Officer Military Sealift Comand

Mr. J. M. Crowley - Member Dr. W. G. Rauch - Alternate

NAVAL SHIP RESEARCH & DEVELOPMENT CENTER

Mr. A. B. Stavovy - Alternate NATIONAL ACADEMY OF SCIENCES

-Ship Research Comittee Mr. R. W. Rumke, Liaison

Prof. R. A. Yagle, Liaison

SOCIETY OF NAVAL ARCHITECTS & MARINE

ENGINEERS

Mr. T. M. Buerinann, Liaison

BRITISH NAVY STAFF Dr. V. Flint, Liaison

COR P. H. H. Ablett, RCNC, Liaison

WELDING RESEARCH COUNCIL Mr. K. H. Koopman, Liaison Mr. C. Larson, Liaison lE

t'

p. B

i

C s C

i

t

t

C

E NT

AR IN E

son

I. INTRODUCTIOI' ch

ge This manual describes

in detail the use of SCORES,

i-jch is a digital computer program for the calculation of the

wave-induced motions and loads of a ship. Both the vertical and

lateral plane motions are treated, so that results for vertical

bending, lateral bending and torsional hull

moments can be

ob-tained. The principal assumptions of the method are

that the

motions are linear, can be solved by "strip theory" and that

the ship sections can be approximated

by."Lewis forms" for the

purpose of calculating the hydrodynarnic forces, that is, the

required two-dimensional added mass and wave damping properties

Both regular or irregular waves can be

specified, and for the

latter multi-directional (short crested) seas are allowed.

SCORES was written in the FORTRAN IV language and

checked out and run on the Control Data 6600 Computer using the

SCOPE operating system (version 3.1.6). The program is

un-classified.

The method of analysis used in SCORES is outlined below

in Section II. All the equations of motion and loadings are

given. In Section III, the organization of the SCORES program

is 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. ErrorTnessages which can appear

during program execution are described in Section VI.

The Appendices include a description of the FORTRM

program organization, flowcharts for each subprogram and a

com-plete cross-referenced (to the flowcharts)

listing of the source language.

II. METHOD OF ANALYSIS

The analysis used in SCORES was developed and investigated

to some extent in work supported by the Ship Structure Committee.*

The exposition to be given here will serve as a convenient listing

of the equations, but for the full derivation and explanation

of

the analysis method, the references listed should be consulted.

*Kaplan, Paul, "Development of Mathematical Models for Describing

Ship Structural Response in Waves," Ship Structure

Committee Report SSC-193, January 1969 (AD 682591)

Kaplan, P., Sargent, T.P. and Raff,A.I., "An Investigation of the

Utility of Computer Simulation to Predict Ship

Structural Response in Waves," Ship Structure

Committee Report SSC-l97, Jurie 1969 (AD 690229)

Kaplan, P., and Raff, A.I., "Evaluation and Verification of Computer

Calculations of Wave-Induced Ship Structural Response."

Ship Structure Conriittee Report SSC-229, July 1972.

(

ttee

n of

re-gation, at speed c, is considered fixed in space. The ship then

travels, at speed V, at some angle, with respect to the wave

direction. The wave velocity potential, for simple deep-water

waves, is then defined by:

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

(1)

where a = wave amplitude

c = wave speed

2rr

k = wave number =

A

X = wave length

z' = vertical coordinate, from undisturbed water surface

positive downwards x' = axis fixed in space

t = time

The x-y axes, with origin tG the center of gravity of the ship,

translate with the '}iip. The x' coordinate of a point in the x-y

plane can be defined by:

x' = -(x+Vt) cos +y sin 8 (2)

Then, the surface wave elevation n (positive upwards) can be

ex-pressed as follows:

In x-y coordinates we have:

(3) since where n c2 g i = i = w u = k (x + Ct) = acceleration a sin t Z '=0 of gravity

n = a sin k

E-x cos

B + y sin B+(c-V cos 8)t] (4)

n =

Dn

-V ----) n (x,t)

and e

dirot1o7 f h.p trsv.1

it ip.., V

A. Vertical Plane Equations

The coupled equations of motion for heave, z (positive

downwards), and pitch, e (positive bow-up), are given as:

Tt1z =

3

Fig. 1.

Wave and Ship Axes Convention

and.. D

n =

= -akg sin k

I-x cos

S+y sin ß-f(c-V cos s)t)

The results of the equations of motion, etc., will be referenced to the wave elevation n at the origin of the x-y axes,

that is: n = a sin k(c-Vcos ß) t or n = a sin t e where 2t = _{(c-V cos S)}

is known as the circular frequency of encounter.

Xb dx + Z dx w /:TV. (6) (9)

where

= density of water

A3 local sectional vertical added mass

N' = local sectional vertical damping force

Z

coefficient

= local waterline beam

and ix s where m = I,= mass dz dx x , S

The general hydromechanic

dZ

-DtI

ship mass of ship moment of local sectional coordinates respectively = wave excitation force A'

(-x+V6)

33

inertia of ship about y axis vertical hydromechanic force on

of stern and bow ends of ship, force and moment on ship

is taken to be:

I-N'

(_x+V8)_gB*(z_x9)

z (li)

N'

og2w31

₍₁₂₎

With

= ratio of generated wave to heave amplitude for vertical motion-induced wave

I

{ N' J

(-x+Ve)

dZ__

_{- A3 (zxe+2V6)} -dx - pgs*(z_.xE) (13)

The equations of motion, (9) and (10) are then transformed into

the familiar form as follows:

a'z + b + c'z - de - e - g'e = Z (14)

Ae +B +Ce - Dz - E

-G'z

The coefficients on the left hand sides are defined

by:

a'

= m+

JA3dx

b=

c'= pg

d=D=

e=

g'= pg

A= I +

y N' dx -v d (A3)A

(v'

V pp._J L4J(

r\L\

TM

(-cL

&11_ B*dx

Nxdx -2v

B*xdx -Vb 1

A3

X2dX 5 A 3dx-V =

xd (A3

(15)

C =

where all the indicated _{integrations are over the length}

of the ship.

Nxdx-V

G'= g B*xdx B*x2dx_VE -s

The local sectional vertical _{wave force acting on the}

ship section is represented _as:

w-dZ + (N'_V dA3 -z _dx xd (A3) The wave and (15), is given z w M w

'dZ

excitation, by: dx

the right hand sides of Eqs.

dx (14) (17) (18) s rX dz ix e ₍₁₉₎

where Fi = mean section draft. Substituting the expressions for

r,

and r f ror

Ec.

(4),

(5) and (6), with y=O and applying the

approximate factor for short wave lengths we obtain:

dz w -kh - = - ae ((N'-V 3\ z dx ) cos(-kx cos B)lcos Let + d.A33 cos(-kx cos B)kc z dx sin sin B

- sin

c

The value of Fi is approximated by:

Fi = HC6

where }-: = local section draft

C5= local section area coefficient

The steady state solution of the equations of motion are

obtained by conventional methods for second order ordinary

differential eauations, using complex notation. The solutions are

expressed as:

z = z sin (w

t+)

o e

7

r(pgB*_A3 kg)sin(-kx cos B) +

L = e sin (w t-4-c)

o e

where the zero subscripted quantities are the amplitudes and

c are the phase angle differences, i.e. leads with respect to the

Wave elevation in Eq. (7).

The local vertical loading is given by:

df z dz dZw - óxn (z-xe) dx 2 (23) sin(-kx cos B) (gB*_A;3kg) sin t e (20) (21) (22)

t.

where 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 in

Las. (l3)and (20). The vertical bending moment at location X0 is

then given by:

X s

where I = mass moment of inertia of ship about z axis

= mass moment of inertia of ship about x axis

= mass product of inertia of ship in x-z plane

o s or Xb X o df z (x-x0) - dx (24)

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

BM = BM sin (

t+)

z zo e

B. Lateral Plane Equations

The coupled equations of motion for sway, y (positive to

starboard), yaw, p (positive bow-starboard), and roll, (positive

(25)

starboard-down), are given as:

r Xb my = xs dx+Y dx w (26) Xb

i;

= s x dx+N, (27) I - I = dx-rng (28) X XZ

5)

5)

3)

dY

= local sectional lateral hydrodynaraic force on ship

local sectional hydrodynaxnic rolling moment on ship

= wave excitation force and moments on ship

= initial metacentric height of ship (hydrostatic).

The hydrodYflafliC force and moment are taken to be:

=

-E

[ M

(+X_V)_F

-N

(+x-V) +

dl< dx

=

-E [Ir_Msq ('+x-Vi) ] N3+ N5

('+x-V)

where 0G = distance of ship C.G. from waterline, positive up

= sectional lateral added mass

N5 = sectional lateral damping force coefficIent

M sectional added mass moment of inertia due to lateral

motion

N = sectional damping moment coefficient due to lateral

motion

'r = sectional added mass moment of inertia

Nr = sectional damping moment coefficient

F = sectional lateral added mass due to roll motion

Nrs = sectional lateral damping force coefficient due to

roll motion

(29)

(30)

and the sectional added mass moments and damping moment coefficients

where _{Nr* = sectional damping moment}

coefficient due to viscous

and bilge keel effects

= fraction of critical roll damping (empirical _data)

C _{= critical roll damping}

L _{= ship length (LXb_Xs)}

= natural roll (resonant) frequency

Nr(() = value of Nr at frequency w4.

The critical roll damping is _{expressed in terms of the}

natural roll frequency by:

C = 2 mg with w

=[

mgGM

4 dK dx + fI(wq»dX)

The additional roll damping _{moment to account for viscous}

and bilge keel effects is taken _{as a particular fraction of the}

critical roll damping, as follows:

N * = ç_r C /L-N (

c r (31)

where the integral is _{over the ship length.}

The calculation of

the natural roll frequency, _{w , as indicated above is carried}

out by means of successive _{aproximation.}

Expanding the derivatives, _{we obtain}

dY + v-.--.. N

= -M5(y+x-2V)

dx

(+x-V)

(33) dF dM +

(F+

_M)

₊

[N+

N - V ( dx + _! j; dI dM 5 s4ì

I +5M

+F +5M)1+ Lv(

r S4 rs s (32) 2

t N

_{+ N}

_{+ N}

_{+ 5}

_{y ¡_rs} rs s cx - N _N*

1

+ (M

+ 5

M5')

(+xV-2V)

r r S + 11 (&M84 &M \ -N + Ö-G N -v s dx

+0G

S dx

The equations of motion, (26), (27) and (28) are then transformed

into this familiar form:

=

=

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

+ 1M dx , a12 = JN5dX-V Jd(M5)

a11=m

_js

a14 = JM xdx , a15 - JN5xdx -2v JM5dx

-v

ixMs)

s a16 = -Va12 , a17 = - dx -

5

JM5dx J

rs

a

= -

IN dx + V Ja(M5)_ fN5dx + V jd(F )

rs

18 j rs a = IM xdx , a22 JN5xdx -v Jxd(M ) s 21 j s a = I + JM x2dx ,

a5 =

JN5x2dX_2V JM5xdx-V Ix2d(Ms) 24 z s a26 = -Va22 , a2 xz -

f

xdx

-5

JM8xdx - -I 1N

xdx+5V

Jxd(M ) - 1N xdx+V

JXd(Frs)

s

Js

a28 =

- J

rs

(34) (36) 37)

= N

(35) w

The local sectional lateral force and rotational moment

due to the waves acting on the ship are represented as:

= (pS+M5)

Vv a- +N

V

+k -M -

+V S

r

Dv dM ( Dv s w

sDt

dx w1 sin

T

Dt

T

SmB

ay

-5--

_dx

where y_w lateral orbital wave velocity

S = local section area

= local sectional center of buoyancy, from

waterline

The lateral wave orbital velocity is obtained as follows:

V =

w

v = - akc

e' smB sink

cosß + y sinß+ (c-V cosB)t]

h1)

and then we have:

Dv

-w -kh

- akg e sin B cos k [_ cos + y sin B +

(c-V cos B)tl (45)

l---(M v)+p

Sz N V dK I (B*3 -) fE::! Dt s w Dt s w sin -r-

Sifl

ß (42) (43) A sin

a =1 +

II

dx

+5

1M dx + dx

+52 IMdx

37 x _J r _j s j rs a38 -LIixJ+ td(M

)+5

Id(F )±2 j'd(M)]

j sq J rs a39 = mg GM

where all the indicated integrations are over the ship length.

The wave excitation, the right-hand sides of Eqs. (35) is

+ 5

dx

+5 1N

dx

+52

j

_(rj

dx

j J rs s 12

J

dx

I

given by: x1-dY Y w = dx dx (39) X s dY N w K w = s xl-' ' x dx dx (40) (41) dK w

-dx a31 a 32 a 34 a 35 a36 = _-1N = -I = _rN J =

_jMsx

-

-Va32 - fMSdx dx - 1N dx +V s

Js

J _JM5q,xdx - JM xz s xdx - 1N xdx +v s _J

s

xdx .1 1d(M ) +V

5

Jd(M sq s fxd(M )+V

5

1xd(M )-2Va31 s4 J S > (38)

After substituting these expressions and expanding terms,

we obtain

dY_w

--T1co$wt+T sinwt

_e

_{2 e}

with

T1 = T3

[gT4

cos T6 + C T5 sin T61

T2 = T3

[_gT4

sin T6 + C T5 cos

-Slfl

Sifl

T3 = - ake

si.n

T4 = pS+M5-kM5 dN s T5 N8-V

+ k V

_dx

T6 = -kx cos B

dK

and

--T7coswt+T8sinwt

e e

with T7 = T3 [g T9 cos T6 + C T1

_{sin T611}

T8=T3

_{[_gT9sinT6+c}

B*3

-T9 = p

_---

-Sz

-M5

-0G T4

dM +V

T10 =

The steady-state solution of the

_{equations of motion are expressed}

as:

y = y

_o

sin (w t + K)

_e = i

Sin (w t + a)

o

e

iB*

-r-

smB

T10 cos TIJ

(46)

(47)

V

15

sin

(w t + y)

(50)

o e

where the zero-subscripted

quantities are the amplitudes and K

and y are phase angle leads

with respect to the wave elevation.

The local lateral and rotational loadings

are given by:

df dY dY w dx -óin

(y+x1.-) +

+

aT

drr B*

-- .f óm (y+x)+ g - Sz -SOG dK dK w + .- + cix x

where local center of gravity

(relative to ship C.G.)

positive down

'y = local mass

gyradius in roll

and the hydrodynamic and wave

excitation terms are given in Eqs.

(33), (34), (46), and (47).

The lateral bending arid torsional moments

at location are then: BM (x

yo

) = TMx (X0)

I

s 'X_o or X o a-Xb s

arid again they are expressed in this form:

BM = BM sin

(w t

+ T)

y yo e dn

- dx

dx TM = TM sin (w t + y) x xo e (54) (55) .xo df or (x-x) dx (53)

I

=

xz

xs

C. Wave Spectra Equations

The wave spectrum for calculations in irregular _{seas is}

considered to be a separable function of wave frequency and

direction as follows:

S

(o,')

_{= S1() S2()}

_for

_O<w<

(59)

and - <

where S _{= directional spectrum of the seaway (short}

crested sea spectrurn) circular wave frequency

= wave direction relative to predominent direction

S1()

_{= frequency spectrum (long crested sea spectrum)}

S2(u)

= spreading function

The SCORES program includes various spectra that _{can be}

chosen as desired. _{However, in all cases, the following}

relationship between the spectrum, or spectral _{density, and the}

wave elevations, or amplitudes, is used:

The requirement on the local vertical mass center is:

f X

j

_xs

5m. dx = O

(56)

Similarly, the requirement on the local roll gyradius is:

Xb

6my2dx

_{= I}

₍₅₇₎

1x

_s

The product of inertia in the x-z plane is defined by:

Xb

r

2

where a2 = mean Squared wave

amplitude.

Since we

impose:

r 2

1.0

r 2

we then

have: 2 0

Additional statistical properties are formulated

from

the mean

sQuared amplitude: a

1.25

a avg rms a

=2.Oa

1/3 rins a

a1/10 =

2.55

_rms

aavg average(statistical)wave

amplitude

(60) (61) a

S1 ()d

(62) Where arms =

root-mean-squared wave amplitude

I

rins

a1

3 = significant (average of 1/3 highest)

/

wave amplitude

a1/10_ average of 1/10 highest wave amplitude.

Neumann Spectrum (1953)

This frequency spectrum (as used) is given by:

(w) = 0.000827

g23_6_22w 2

2

(67)

where U = wind speed

The constant is one half that originally specified by

Neumann so that this spectrum satisfies Eq. (62). Thus, originally

the Neumann spectrum required only a factor of

'T

in Eq. (65),

instead of 2.0.

Pierson-Moskowitz (1964) This is given by:

S1(w) = 0.0081

g2_5

74gUk

/ ₍₆₈₎

and was derived on the basis of fully arisen seas.

Two Parameter (1967) = A Bw_5e.th (69) where = 0.25 H1/32 = (0.817 T

= significant wave height (=2.0a1/3)

T = mean wave period

This spectrum is usually used in conjunction with "observed"

wave height and period, which are then taken to be the significant

height and mean period. _{This spectrum is similar to that adopted}

by the I.S.S.C. _{(1967) as "nominal", except that it is expressed}

in circular wave frequency instead of frequency _{in cycles per}

Responses

All of the motions and moments calculated are considered

to be linear and the principle of wave superposition is assumed.

Thus for each response a spectrum is calculated by:

(

S1(,i) =

r

_{[T. (wti)J}

_S (72)

where T1(,) = response amplitude operator (amplitude of response

per unit wave amplitude)

We then have, similar to the wave amplitude:

T

t.

a.L =

i

o 1g 2 S.(,p) d dì

S1() d

where a.2 = mean squared response amplitude.

Eqs. (63) - (66) then apply to each response.

D. Non-dimensional Forms

L

Frequency parameter:

=

i- H

du (73) t!

Urii-Directional Spreading (Long Crested Seas)

This is obviously: = ó() (delta function) (70) cosine-Squared Spreadin S2(u) = 2- cos2 . (71) ri i

Non-dimensional moment:

Non-dimensional shear:

III. PROGRAM ORGANIZATION

A. General

Non-dimensional linear motion (heave, sway):

BM (orBM or TM ) z y X

g BLa

Shear Force

øg BLa

motion amplitude a

In general, the SCORES computer program has been arranged

and organized to both keep a) the coding simple and _{flexible (for}

possible future modification) and b) the running times low (for

obvious reasons). _{Thus, precision of computation has not been of}

major priority in program development. _{This approach is considered}

reasonable at the present time because precise correlation _(to

less than about 5%) with independent data (model or full-scale

ex-periments) is not envisioned, and the theoretical _{analysis itself}

is an approximation.

Aside from the actual coding and data structure in the

program, which will not be discussed here (see Appendices A, B

and c of this report), this approach manifests itself _primarily

in two aspects. _{The first is the precision with which the}

local, or

two-dimensional, sectional added mass and damping characteristics

or properties, are calculated. _{For vertical oscillation, the method}

of Grim* is used. _{For the two-dimensional properties in lateral}

and roll oscillations, the method of Tasai** _{has been programmed.}

In general, these methods can be carried out to increasing degrees

of numerical accuracy. _{For practical purposes of keeping running}

time reasonable, these calculations have _{been limited. For example}

in the lateral and roll computations, _{the infinite series of terms}

representing the velocity potential is _{truncated to nine terms}

and only 15 points along the Lewis form contour are used for least

square approximation purposes. _{While the full range of section}

properties and frequencies has not been explored in detail, results on the order of 1% accuracy or better are obtained for average

sections over a wide frequency range.

* Grim, O., _{Die Schwingungen von schwimmeden,}

zweidimensionalen

Korpern," HSVA Report No. 1171, _{September 1959.}

Grim, O., and Kirsch, M., private communication, September 1967.

**rjj, F.,

_{"Hydrodynamic Force and Moment}

Produced by Swaying and

flollinç Oscillation of Cylindcrs _{on the Free Surface,"}

fleports of flesearch Institute for Applied Mechanics,

Kyushu University Japan, Völ. _{IX, No. 35, 1961}

Non-dimensional angular motion motion amplitude

(pitch, yaw, roll):

21

The second aspect of program organization is related to the

abcve. While the computations of the two-dimensional properties

are limitea as described, they still are relatively lengthy. That

is at a particular condition of ship speed, wave angle and wave

length1

the bulk of the computation time would be devoted to these

calculations rather than the formation of the coefficients,

wave excitation, solution of ship motions and the resulting

calculation of applied moments. Therefore, it was decided that

rather than calculate for each frequency at each cross-section

the above mentioned dimensional properties, instead the

two-dimensional properties are calculated first at 25 values of

frequency over a wide range and then interpolated (or

extra-polated) for each subsequent frequency. The results of the initial

calculation over the frequency range are saved in the computer

merory for the calculations at hand, and can also be saved or. a

periranent disc file (or magnetic tape storage) , for later usage.

Ir this way, a large range of ship speeds and headings car. be run,

each over the appropriate frequency range, without excessively

high running times. The. interpolation procedure used is a

six-point continued fraction method which gives results that are

generally well within 1%.

In other respects, the SCORES program is organized in a

fairly straightforward manner. The input consists of:

basic data which specify the hull form and weight distribution and

çonditional data which specify the speeds and wave

parameters.

Repeated sets of conditional data can be run with the same basic

data, that is, for the same defined ship. A fair amount of input

data verification is incorporated into the program.

B. Restrictions

The main restrictions in the program concern the following items:

Maximum no. of ship cross-sections 21

(stations 0 to 20)

Maximum no. of wave angles (in one run) 25

Maximum no. of wave lengths (in one run) .. . 51

Maximum no. of sea states (in one run) 10

The 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 system

control and provide mathematical functions. It would be possible

to decrease this core requirement via program overlay and

linkage techniques, should the need arise. However, it probably

would be relatively difficult to fit the program within a 12K

L

1f

The word length on the CDC 6600 is 60 bits. _{No loss in}

overall computational _{accuracy would be expected if this}

were

reduced, as in other _{digital computers, to 36 bits.}

A special system subroutine called DATE is _{used which}

provides the current _{date. This is used only in the}

heading on the output.

C. Running Time

The following approximate _{times are for running}

under the

SCOPE operating _{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 300 increments

from head to following _{seas), 21 wave frequencies}

(to adequately cover the spectral

energy bands) and 5 sea states, the incremental

time once the

program was compiled, loaded and the TDP Array was

calculated, 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 data card input to the SCORES program.

A. Units

For calculations in regular _{waves, there are no inherent}

units assigned to _{any of the variables in the}

program. _{Thus, the}

user is free to choose

any desired set as long _{as they are}

consistent for all input parameters. _{The units are established}

by the input values

of water density and gravity acceleration.

Some typical units _{are shown}

cater Density Gravity Accel. Resultant Unit s tern 23 ft. -lbs . -sec.

iave direction angles are always specified in degrees,

rather than radians.

iowever, for spectral calculations in irregular waves, using

either the Neumann or Pierson-Moskowitz spectra, the SCORES

pro-grarr. assures ft.-sec. units, full scale. The input wind speeds

used to specify spectral intensities, or sea states, are then

assumed to be in knots.

The following input data description indicates typical

consistent u:iits for all parameters. Other systems of units

could be used, as noted above.

B. Data Card Preparation

Every data card defines several parameters which are

required by the prograr; each of. these parameters must be input

according to a specific format. "I" format (integer) means that

the value is to be input without a decimal point and packed to

the right of the specified field. "F' format (floating point)

requires that the data be input with a decimal point; the number

can appear anywhere in the field indicated. "A" format

(alphanumeric) indicates that certain alphabetic characters or

title 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, parameters

not required by the program for a particular problem need not be

specified.

The card order of the data deck must follow the order in

which they are described below. Cards which must be present in

every run, regardless of options, are marked with ari 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

ft. -tons-sec.

l-80 A Any alphanumeric title

information, used to label job output metric ton/cu. meter 1Í,

t

meter/sec. meter-metric ton-sec. lbs./cu. ft. tons/cu. ft. ft./sec. ft./sec.

The first 30 columns _{are used as a label for the TDP}

array file.

Thus, subsequent _{runs using the file must duplicate these}

first

30 columns which _{are then checked against the file label}

before

using the data. _{This avoids inadvertent use of an incorrect}

TDP file.

2) _{Option Control Card (*)}

Columns Format

A

B

C

D

l-2 I _{Integration option control}

tag

3-4 _¿ I _{Moment option control tag}

5-6 I _{Mass dist. option control tag}

7-8 cl I _{Wave spectra option control}

tag

9-10 1 I _{Degrees of freedom option control tag}

li-12 / I _{Directionality option control}

tag

13-14 I _{TDP file option control tag}

15-16 ₄ I _{Moment closure option control}

tag

17-18 _f I _{Output form option control tag}

19-20 ¿- I _{Torsion axis option control}

tag

21-22 I _{Number of ship seg-rnents}

Each option control tag is given _{a value of 0, 1, 2 or 3}

where the meaning of each is given in the table _{below. The last}

entry of the card, the number of _{ship segments, corresponds}

to the

even number of equal length _{segments, or strips, into which}

the

ship hull is divided _{lengthwise for purposes of}

calculation.

OPTION CONTROL TAG INTERPRETATION

Letter Code Tag Descriptor Integration Moment Mass dist. Entry Options Available 0: Simple summation 1: Trapezoidal rule

(0:'1Calc. motions only, use

' _{summary mass properties}

i: Calc. motions only, _use

mass dist. Calc. moments,

dist. 0: Input masses l: Input weights'

Wave spectra _{0: Regular waves}

Neumann spectra

Pierson-Moskowitz spectra Two parameter spectra

(continued on next page)

2: _{use mass}

25

OPTION CONTROL TAG INTERPRETATION, Continued

Options Available

0: Vertical plane only

Vertical and lateral plane Lateral plane only

O: Uni-directional waves 1: Cos-sq. wave spreading

O: Generate TDP file write

on file (Tape l)

Read TDP file, (Tape lu), print out TDP data

Read TDP file,(Tape 10), no print-out

O: Suppress closure calcs.

1: Calc. and print out

t

closure results (6'; Dimensional

T:

Non-dimensional 0: Center of gravity 1: Waterline -- ¡ 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 determine the units to be used for all other parameters, except as noted

earlier.

Hull Form Cards (*)

Columns Format Entry

1-lo F 'Section waterline breadth (ft.)

11-20 F - Section area coefficient (-)

21-30 F Section draft (ft.) 31-40 F Section centroid (ft.) H Moment closure I Output form J Torsion axis Letter Code Tag Des criptor E Degrees of freedom F Direction-ality G TDP file

One card is used for each section to be specified, _{in order}

along the ship length starting at the bow. _{For example, if the}

number cf segments is 10, _{and the integration option}

tag is 0,

then 10 hull forni cards _{are required which correspond}

to the hull

at stations 1/2, 1 1/2, _{2 1/2, ..., 8 1/2, 9 1/2.}

II the integration tag is 1, then 11 hull form cards are required at

stations 0, 1, 2, 3 _{9, 10.}

The entries for sectional waterline breadth, area

coef-ficient and draft are straightforward. _{The fourth entry,}

the

section centroid, is _{measured downwards from}

the waterline . If

no entries are given and _{the centroids are needed}

for lateral plane motions calculations,

approximate controids are then

calculated based on the _{area coefficient and draft}

(using a two-dimensional version of the Moorish Approximation).

Lateral Plane Card

Columns 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 option (1E

tag is 1 or 2, indicating

lateral plane calculations. _{The ship}

vertical c.g. is measured from the waterline,

positive upwards. Summary Mass Properties Card

Columns Format Entry

l-10 F _{Radius of gyration,}

longitudinal

'I..

(ft.)

Y.' ,»

11-20 F

Longitudinal àenter of gravity

This card is used only _{if the moment option}

tag is 0.

The longitudinal center of gravity is _{measured from amidships,}

positive forwards.

Sectional Nass Properties _Cards

Column Format _Entry

1-10 F _{Segment weight,}

or mass (tons, or tons-sec2/ft.)

11-20 F _{Segment vert.}

e.g. (ft.)

21-30 F _{Segment roll gyradius}

(ft.)

These cards are used only if the _{moment option tag is}

i or 2, in lieu _{of the suztnary}

mass properties card _{above. One}

card is used for each section to be _{specified, in a similar}

mariner as the hull form cards described _earlier.

The first entry on each card is the _{segment weight,}

or

mass, depending on whether the mass dist. _{option tag is 1,}

or 0, (ft.)

Cc J. umn

27

respectively. _{The second entry, the segment vertical}

center of

gravity, necessary only for lateral _{bending moment calculations,}

is measured, positive _{downward, wi}

res ect to the ship's over-tcal center, _{as specified on the}

ateral plane data cà'!

above.

Since ís required

that the vertical mass moment

integral satisfy the specified overall _{v.c.g., the input segment}

v.c.c.'s are shifted _{by ari equal}

amount, up or down as necessary to exactly balance the

vertical moment for the hull. _This

minimizes the effort

required to obtain precise balance in input data preparation.

The third card entry, the segment roll _gyradius,

is needed only for torsional moment _{calculations. If no entries}

are given the overall ship

value is used at each segment.

8) _{Moment Station Card (*)}

Format _Entry

1-lo '- I

First station for moment calculations

11-20 I

Last station for moment calculations

21-30 I _{Increment between stations}

The parameters

on this card determine where along the ship

hull the moment _{calculations are to be}

performed. _{Station numbers}

are defined as zero at

the forward end of the first segment.

increasing to N, the number of segments, _{at the after end of the}

last segment. _{If the calculations}

are required only at one station,

then the first two _{entries on the card should}

be equal to that station number.

The moment results _{at only one station are stored for}

subsequent irregular _{seas spectral calculations.}

In the calculations over a range of stations

at which moments are calculated (and

printed), then only _{the results at midships}

are stored for the subsequent spectral calculations.

The first entry, _{the run control tag,}

determines program continuity:

9) _{Run Control Card (*)}

Columns _{Format Entry}

l-10 N_F

Run control tag arid wave

- _{amplitude (ft.)}

11-20 -F _{Initial wave length,}

or

frequency (ft. or rad./sec.)

21-30 F _{Final wave length,}

or frequency

(f t. or rad./sec.)

31-40 F _{Increment in wave length,}

or frequency (ft. or rad./sec.)

4]-50 _F

. Initial ship speed

(ft./sec.)

51-60 F _{Final ship speed}

(ft./sec.)

61-70 F

Thus, if the run control tag is not greater than 0.0, then

the remaining parameters on the card are irrelevant. A blank

card, for example, is used to stop calculations and proceed to read a complete new set of data starting with the title card

1) above. This parameter is also used as the wave amplitude, and

is usually set to 1.0.

The next three entries determine the wave lengths to be

used in the calculations. If the wave spectra option control tag

is 0,

indicating

regular waves, then these entries are the initial,

final and increment in wave length. If the wave spectra option

control tag is greater than O, indicating irregular wave calculations, then these entries are the initiál, final and increment in wave

frequency. The increments should always be positive, so that wave

length, 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 initial

and final values should both be set equal to it.

10) Roll Damping Card

Column Format Entry

l-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 calculations

are included. The calculated wave damping in roll, at the natural

roll frequency, is increased so that the total damping is the

specified fraction of critical damping. The additional roll

damping thus determined initially is then used for all subsequent

calculations.

li) Wave Angle Card (*)

Co lurrtn Format Entry

l-10 F ¡- Initial wave angle, degrees

11-20 F Final wave angle, degrees

21-30 F Increment in wave angle, degrees These entries specify the wave direction angles to be used

in the calculations and are always given in degrees. For

calculations with uni-directional waves, the meaning of the

parameters is as indicated. If the directionality option control

.

Run Control Tag Action

Greater than 0.0 Continue calculations, using this as

wave amplitude

0.0 (or blank) Stop calculations; read new basic

data set

29

tag is greater than 0, indicating calculations for a directional

wave spectrum, then only two choices exist. If the initial wave

angle is 180.0 the calculations proceed for head seas only,

including the wave directionality. If the initial wave angle is

nct 180.0 the calculations proceed for all angles from following

seas to head seas, in steps according to the wave angle

increment

ipécified.

In both cases the integrations with respect to wave angle

use the saiie increment, as specified.

12) Wave Spectra Card(s)

Columns Format Entry

1-lo I No. of sea states (wave spectra)

..L ?

li-15 F First spectra parameter

16-20 F Second spectra parameter

21-25 F Third spectra parameter

(5 col. fields)

56-60 F Tenth spectra parameter

This card is used only for calculatiorEin irregular seas

(wave spectra option control tag is greater than O). The first

entry 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 parameters

to be specified are the wind speed, in knots, for each sea state. For the two parameter spectrum (option tag equals 3),

the parameters on this card are the significant wave heights

for each sea state. A second card is then used which

contains

the mean periods for each corresponding sea state, as the spectral parameter entries specified above.

C. Sample Input Deck

A sam1e input card deck listing is given on the next

page. The units are meters, metric tons and seconds.

V. PROGRkM OUTPTYT

A. Description

The printed output from the SCORES program depends on the

option control tags set as input. Each output section will be

described, though in any given run not all sections will be

printed. Each section starts a new page and is labeled with the

title information and date.

The first part of the output is a listing of the basic

input data as processed. This defines the hull form and weight

distribution. 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 TDP

array is calculated diagnostic messages concerning these calculations may then appear.

The next output will be the listing of the two-dimensional

proüerties (TDP array) for each station and each frequency. If

the data is being read from file, this output can be suppressed.

For lateral plane calculations, the natural roll frequency and

roll damping information will then be printed.

Then, the vertical and/or lateral plane responses will be printed out with all frequencies, or wave lengths, for a given

ship speed and wave angle, on the same page. For irregular seas

calculations, this will be followed by a print-out of the

response spectra and statistics (long crested seas). These pages

will be repeated for each wave angle at the initial ship speed.

Then directional seas calculations results will be output, if

secified. The output is, of course, then repeated for

additionally specified ship speeds.

B. Sample Output

A sample output listing, in abbreviated form, is given

following the sample input listing.

Sample Input Card Deck Listing

iULL 1flQJ O.4' DLUC' (T'(> PÎ. ..r 0fl OCAN1CS pRr j(1 O. O93

1 2 1 ' _i n I 1 1 »i

9.Mflbo5

ou.nn .n

'ri

'o.o'\

14.39 _.12

i.i

2.94 i.n 85R

Q

27.Se .9 fl 1.

2i.7 -

-- .9.1 L03 -27.7 .Qee 2T.S7 .Q. 21.7 .9,4 1.1 2P.7 .9M 1.03 71.S? 9e4 1.03 - - - --- -27..7 9e 1.03 2?.7

9.

1.03 V.57 9t 1.03 27.24 .91 1.03 594

I

1.03 23..6 .7a - 1.0 - -19.03

4?

¡.03 13.87 .419 , 4.41 .53 -l.94 l.9k0?t en ,. '81.3 1203.2 2'0 3db T '331.4 e33 1.4 3344 9 1 bd. e 48e.4 14.3 4 -3433.4 3'b'. I 314". 1 -r2 9 48_I. T _\ 120.3-t _{1 1n} 1.0 0.J15 1.3079 one1 b.bPST e.,27 1.Q 0.10 -10.0 ?o.tl 1 4.4 -10.0

O6 ì1

GQT.RLT.

960

CALCULATE MOMFOIS 47 STATIOPu 10 ()u!VLt PESLJLTS S00.41.

e.or

'_.___ -

sToo0o

-- SPtCTS* Pub. wgvt.

3it

3'

Sample Input Listing

SE.i!0Sf' WJLL 5.. 5LUC (TdO 481. '.0. 100 Sl

007708 COø1.Q. TIC.- - I C I) F F G I .)

- I I 3 1 -0

i 1T

j*TC ?.PL'! lThl'r.

- ¡91T

r'E.0TrY 1.025000 OIS9L. 4I?b.é' 0P4u110

RISPL.(WT5,1

OCOa#ICS Ppl'JEC! 80. 1093

S'

e. 1970

0. Or 5T*TTNS . pt

-y

li 514710,. 84.. 400* C0L. (70*01 -8aP 016uT ZETa IVE. ROLL

-- _{- 0.00 0.0000 0.0000 (1.0000 1l.000. 260.6000 0.0000 8.9s02} 1.00 14.3900 .6720 11.0300 5.fl44 451.3000 O 0000 8.9002 -2.00 3.00 ?2.'n71'21.580e .5291 11.030C'11.0300 5.i?S,5.75'. 2.04.3000103.2CC1 0. 00000. 0000 8.9402 --.or 7T00 1 1.0T00 3650T0Ijo (1.00011 -1.96Cr 5.00 77.50(10 .9910 11.0300 S.51 'OSC.7000 0. 0000 8. 9402 -0.OL 27.5100 9940 11.0300 5.e92. 6331.4000 0000 6.9602 7.00 27.5700 .99.0 11.030' 5.eQ?... 4331.4000 0. 0000 8.9602 -- b.00 27.5700 (1 11.0300 5.92 3366.6000 0.0000 8. 9602 9.00 27.5700

ÇL

11.0300 16'..4000 0.0000 0.9502

27.SOÖo

s;o

n .obC.S.2-

160' O 00 0'VD 000

11 0G 27.5700 .090 11.0300 5.492' 1"3.5000 0.0000 8.9602 - 12.Ò0 27.Ç700 .Q3L 11.03O 5.89i 2195.0000 0.D000 1.9602 13. 0G 27.5700 99C 11.0300 5.*7. 3291.7000 0.0000 8.960? - - 11.0300 3633.6000 -- 0.9502 15.00 2?.2.Dr

0(

11.0300 5.22'. 3465.1000 0.0000 0. 9602

TÏ o

17.00

23.'

2.QDT.52C

.7550 ïi;oloo11.0300 4.9é7,4.e.?5, 3146.30001955.1000 0.Oøoø0,0000 8.9602

- 1..30l' f.2?0 11.0300 i.3á3 721.9000 0.0000 0.9802

13.P7'O .'190 11.0300 3.378o 401.3000 0.0000 0.9602

zc.00 .e10o .300 1.1000 .377, 120.3000 0.0000 8.9602

tU1C. .o'r I

8 .-vrwTSMTDS7 . o ovoi. .r. 9PDrr.53

-t0'41. C.. 46?5 1Fw. O! #IVSWIPS, L'WG. 80ø*IUS E 435l 6 1.7e

SE1(S 0f' WLJLJ

'.

0.8' PuLUC (TOO Pu#T. 80. 100 51 000A81CS PRflJECT 80. 1093 SEP 24' 1970

ThOTTOAL-ThPP'rm3Ta co'r PD0J7 OUT

1.0000 .3157 1.3079 .0451 6.c?57 0.5257 1.0000

.1000

10.0000 170.00(10 20.000v

I s.a -0.' -7.0 -0. u -0.0 -0.0 -0.11 .0.0 -0.0 -0.0

-

Tu.o .01.8 -0.01 7.tj -0.0 -0.0 -0.01 .0.0 -0.0 -0.0

SE'.O(S fl MULL FOP. 0.$0 (ILOC. (TOO SPI. wO. 100 S) OCEI810S ,OJECT

wIv SPECTOAL 0(05100. TUO P4RAWE'OFP. ISSC 1947 5,0070*

00. 1093 $! p. 1970 .361 .408 --.451 .498 -3.32E - I610 -. 12.254 ¡2.954 - -11.7'3 .431 1.456 .578 - - 8.208 .72? 4.546 1.173 .533₄₄₃ 747 .512 3.19?2 961 1.263 -. .371 .313 2.331 .90? I .&'7 _{w,.. A ('If'} 2.073

-.9',

.99? .1.18. -1.037 .961 AsO. 2.539 1.042 Sir,. '.140_5.217

Sample Output Listing, Continued

StWI,S r." «uil ,nR. n.r.0 I.iuCr

Itrio wet. NO.

t.fl-flrNFISlOPiiL SICTION PWflP1WtIIs

100 SI

OcrANICS Pr,OJICY NO. ¡093

SP 4 1910

r NI. O. P*H*F. A-0w 'tI0I

*(tl*WISO. M-SUN(ÇI ri-SUI(S) MIS.PHII riIS.Pp4II p-SijqlPp r4-SUIIPI P-SUIU.5) wSjl8.%t Sta 00 0. 0.00110 tNFlNlT 0. 0, 0. 0. 0 0, 0. 0. .0100 u. 0. 0. 0. 0. n. 0. 0. 0. 0 .0100 i. n. 0. 0. 0. n. 0, 0. 0. 0. u, Or00 0. 0. 0. 0. 0.

0

0. 0. 0, .1000 0. II. 0. 0. 0. o.

I.

0. 0. 0, .1500 0. 0. 0, 0. 0. Q. o, s. s. o, .l00 u, 0, 0, 0. 0. 0. 0. 0. 0. 0, 28(jn II. 0. 0. 0. 0. e. 0. 0. 0, 0. .3.00 u. 0. 0. 0. 0. 0. 0, 0. 0. lu .4,l)0 u. 0. 0. 0. 0. 0. 5. 0. 0. 0, .bÇ00 II. 0. 0. 0. 0. n. 0. 0. 0.

I.

U. 4100 0, 0. 0. 0, S, 0, 0, 0. .8?00 0. 0. 0. 0. 0. 0. 5, 0. 0. 5. 1.0100 0. n. 0. 0. 0. 0. 0, 0. 0. 5. 1.2800 U. Ii. 0. 0. 0. 0. S. 0. 5, 1.S500 u, 0. 0. 0. 0. 0, 0. 0. 5. l,uSOO u. 0. 0, 0. 0. 0. 0, 0. 0, S. 2.3U0 u. 0. 0. 0. 0. 0. 0. 0. 0. 0. 3,0500 I. 3.8000 u. 4.1000 u, 0. _0, 0, 0, 0. 0. 0. 0. 0, 0. 8. 0. 0. 8. 0. 0, 0. s. 0. 0. 0. 0.

I.

S. 0. s. s. S.8o00 u. 0. 0, 0. -0. -e. 0. -- - S.

-

--I.. 7.1000 Ii, 0. 0. o. 0. o.

I.

5. 0. S. 4,7000 u. o. o. 0. 0. 0. S. 0. 0. 0, 10.7000 U. 0. 0. 0. o. o.

I.

0. 0. 0. Sta 1.0 0.0000 lINtTy .0100 ¿.s?çr.OI .0300 2.I*#41.nl .0400 l.68411"I n. 1.61341-M 1.34231-03 4.07381.03 2.I98e.0I 2.2210.1.81 2.29141.01 2.39621.01 0. .00soi-oo 1.56491-02 9.06281-02 4.04051.01 4.9361.0l 7.12201.01 7.43171.01 0. 3.11301-03 4.90800-02 2.83241-01 2.25631.02 2,?0171.02 2,33,61.02 2,42951.02 0. 8.04050.01 0. 1.14750.53 I93490è01 3.11340-0T I.53"0-SI 7.12590.01 4.90900-U 5,04350-01 7.43920.01 2,13420-01 .1000 I.)130.0.nI .1500 ì.nA1.ol .2100 8.93747.00 2800 7.61921.00 .3600 a.8I040.00 4500 o.?sn1r.00 .8500 S,9411,l)0 .4700 5.nIl0F,flO

l.2I1'1-02 2.41180-fl? 4.13311-02 8.30061-02 0.96271-02 I.IR011-0l 1.405(-0I 1.Tsoor-oI

2.b4S1.0I Z.72e2Eu01 2.91311.01 3.02SI(,01 2.9'ISl.Ol 2.62J'E.QI 2.IOlfl.0l 1.SlOOt.0I .a.u6011-oi 9.62261-01 2.302I1.00 4.72101.00 e.3I07t.00 1.24241.01 1,50451.01 1.19031.01 1.06741.01 4.4007(.0l 4.92541.01 9.20821.01 4.91831.01 1.06381.01 6.26761.01 9.40901.01 I.04SL'00 2.97731.00 1.0T7100 1.44151*01 2.51411.0I 3.71441'ol 4.68691*01 S.22471'Ol

2.85441*02 2,11461.02 2,06391.02 7,93401.02 2.02ÌéL.02 249?31.02 1,99991.02 1,44300.02 3,25950.00 1.81080.0l I .04651.00 92300(.0O 0.4217!ÔOI Z,10740'Ol 5.95540.01 7.500 01.00 4.'I500'OI 9.21791401 1,14990401 -7.43791'Ol 4.94400.01 2.52000 .01 I.l1e30'02 1.91910.01 3,71130.01 ¡.39491.02 6,32110.01 4.10110.01 1.53390*02 4.95440.01 9,14000.Sl .0200 s.H7.Ìr.00 1.0100 6.12771.00 1.2800 8.53667.00 l.500 1.04011*00 1.50o l'99i1.n0 2.4500 e.I0791.00 2.01l11-0I 9.91891.00 2.19831-016.09431,0ß 2.25061-01 3.18601.00 2,13011-IiI 2.65391.00 1.H2TdF.0I 2.30211.00 1.41421-01 2.49371.00 I.83i?1.Ol

- 1.74301.01 l.57161.0I I,37'71.0I l.16191'ol 9.52251.00

2.92071.01 1.02091,01 1.l9S,.0l 9.12541,00 4.6071F.00 9.57501.00 5.2406001 4.0918040I 4.3Il01.OI 3,44391.01 2,92941.01 2.26311.01 ¡.00301.02 $,0884(.0I ,Ieml.o1 ',35090.0l 4.59481.01 5,03l6f.Ol

1.511U.oZ 3,00410.0I 1.35011.02 I.11S31.02 9,56150.01 1.27961.01 5.24100.01 S.27Th1'Ol ,I050.0I 4.losI0.Or-30130.01 4.1l050.5l .05700.01 3 .0 3 200 *11 .04001.01 2.90651.01 11590'0l 2.23140.01 3.0500 ri,51831.00 l.00ldF.01 2,91461,00 7.65141,00 I.12231.0I 1.69I01.01 8,ôsnO(.0I 3.60000.01 41411.01 ¡.45740.01 3.IoOö 8.8041uflO 4.7000 oO7??1.0Q 5.8000 9.2*901.00 7.1000 0,37651.00 6.65uF-0? 3.N93.1-"2 2.24811-02 l.JI0b1-02 3.81301.00 4 7181.00 4. 1491.00 9.41161.00 S.92(.00 4.42161.00 3.52621.00 2.49391*00 1.31311.01 ¡.49271.01 1,64051,Ol _1.17131.0I 1.20441*01 4.28281.00 5.39191'00 3.41161.00 4.27441.01 6.01.51.01 1.25.71.01 1.SloZ(.01 2.3l39(0I 1.41921.01 0,25391.00 4443M1.0O .64740.01 1.17130*01 9069f.O1 5.051)1.00 2,12170.01 9.34 ¡50.00 2,29700.01 3.49431.00 A7o09 '1,.76oF.00 10.1000 o.58497.rlo 7.93421-03 5.23121-03 5.95771.00 4.31161.00 2.05661.00 1.87791*00 1.06001,Ol 1.04671.01 2,10031.00 1.29101.00 7.43481.01 0,02661.01 2.96141.00 2.44200.01 2, 21170. 00 ¡.36980.00 2.55940.01 1.40991'00 STA 2.0 0.0000 INFINIlY .0100 1,08A01.0I .0)00 9.08611.01 .0600 3.4600E.7l .1000 3.01671.01 0. 4,00301-04 3.26121-03 1.lA021-0? 2,03141-02 -2.34161.01 2.34501.01 2.46111.01 7.0.0231.01 2.TOSSF.'l 0. 1.44771-03 2.59291-02 l.'9101-o1 5.48371-aI -2.38831.01 2.39441.01 2.40011.01 2.61111.01 2.81081.01 0. 1.31021-03 2.20011-02 1.29241-01 4.0549101 0,8q411.0l 0,93140.01 9.01791.01 9.15461.01 9,3.111.01 0, 2.35030.01 0, 1.15140-03 2.395,0.01 1.31700.01 l.0667('02 2.41960.01 2.20000-02 1.11990-01 2.61700401 1.79221-01 4.32140-01 ?.61l20.01 4,59410-01

e..r'.oI I.'.,.tUI 1)1 I.II-Uj 00IT070Ul J.EV?ET-Ui .1000 3.01871.01 2.83147-'2.?0b601.ni 5.43311-ni 2.01001-01 4.MS9E-ol .3o .01 0.32101.01 2.01120.01 4.0'77.01 cowrii,u!D ropo 81.1. CTT(108....

Sample Output listing. Continued

1300 3.3*1 I1-? P 9M'#9 nl 1.37130.00 3.03907 * 0 I i. 19111 *00 9.61791*01 I .0JIL'00 3.00037*01 0.397 30 *05 .2100 ¿ I 4n67 n I 9.35141-02 3.14501.01 3.07121.00 3 23977 * 01 3.29021*00 9N3oE *01 3596.00 3.24101*01 3. 209 3E 00 .2000 I 0610.0 I 1.4I63F-I 3. 1376F 01 6.80811 .00 3. 70547.01 9979ç1 .01 6. 67 031. 00 3.29041.01 O .3 129F * 00 3300 I 71 10E *n I l.o;IiF-i p oit 11.0 I 031 37 01 3.09577.01 I .075Il-*Oi 04 7 11,0 I I IOU 2F 01 3. 09100.01 1.07390.01 .4300 .3300 .0.700 $70 O 1.0100 1.2600 1.5300 I 6 111F * i I 'E .n1 i 35 1*7 nl 1.30317.01 I .3,.707*OI 1.77100 *01 I. 39F .n I

2.ÇÇ9'f-°l 3.1 3501-li 3.30957-nl 0.13 11F-01 0.06767-nl O 3334E -01 4.1 1?J1-I

2 E 01 I .0l I .310.77.01 8. 18 19F .00 5. 64 201 00 I.60837 .00 2.71011.00 .41037.01 2. t345 Ir .0 I I. 50 15E .0 I .38131 * 01 2.0 730F * Q 1.82077*01 77987 01 I. 0807f * Dl 2.03451*01 .77881.01 9.60017.00 2.11500.01 .0.0601.0 1 5. 39166. 00 2. 0871E .0 i .3)507.01 2.37 137.00 1.97007.01 .35007*01 4. 30?17..0l I. 7905E '0 I 90 34 71*0 1 I .39700.01 2.00907.01 1. 50 797 *0 I 080ÇF .01 2.OIIOFOi 2. 08111.01 1.0.091.01 2.33267.01 1.09307*01 2.731*0.01 7.SioE.0l 2.32051.01 9,64837.00 2,11091.0 I 1.OI.SE.0l 2.59007.01 3. 00 7. 09 III 01 '.33,57.01 2.33061.01 2.42077.00 1.9 7$ il. 0 22e 11 .01 2.00217.01 0.9604E-0 I 1.10200.01 7. 4ÇOt, 3.0300 3800Q 4.1000 3. 0000 1 Inno TI100 10.7000 ol 01F nl ¿ I i i .01 ¿.liQItfll 2. 2017E '0 I 2 33° II .n I 2. 31377 .nl 2. 00 33E ,0 I 2.4 7601 *0 F ¿.00217.01

3.57017-01 I .390i7-0l 1.21 loF0i 7.iQ4(-02 3.9593E-02 2. 036 It-n? 1.0791W-0? 4603 07-03

2.0033E 00 2 .0. 057E .0 0 1. 000 17 00 3.17067.00 4.3909E .00 5.03337.00 S.Si4t .00 6.07830.00 4.49iO41 .00 1400E .01 6.4O99F01 I .3330E'0I 9.00.647.00 -9.19107-0 i 1.?980E*01 1.603E .00 .6.1 730E-01 1.03071.01 6.00037.00 5.06137-02 1.82631 .00 4.60027*00 $ .99837-01 S.67,3100 3. 30.9 37 00 1.77297*00 3.941 11.00 2. 70081* 00 2. 530 07 * 00 2.64140.00 -- 1.73371400 2.11291.00 3.70317.00 1.63831 .00 3.011 07.00 I. 0050E .00 2.13900.01 -3. 70c.01-0I I 066E0l 5l7nE .01 1.79751.0 I .0.26890.01 1.30050.01 S, 31 .01 I.'I3S10l -S. 03101-SI 1.0 3690 .01 S.9007.0l 1.0336(401 2.00201-01 7.14611.00 6 .00137 .01 7.08711.0l 1.07101.00 3.T)It.00 0.10.07.01 0 .54 667 00 1.91867.00 3.97601.00 6.20*01.01 2,79630.00 7.79076.00 2.11737 00 02fl9L.Dl 1.63000400 3.31101401 I. '00 é337O1.9l 9.20361.01 4.12001.01 1 1690F *00 S7s 30 0.0000 I$cIwItv n. 2.54,01.01 0. 1.03110.01 0. l.40o4(.02 8. .03170.01 0. .0100 0300 '.3335r.0I 6.88131*01 3.30117-04 0.37007-03 2.S84N7.0I 2.13941-03 1.04130.01 -I .Sl'3F-04 2.30441.01 3.39917-02 l.0000E.01 -1.31510.03 2000..AE*07 1.11097.05 240i0(.02 S.eiISl.03 .00571.01 l.93IS1-S0 .01101,01 .1.6053E-03 .00.06 S.löt0.7.ñl 1.32l4r-Ii2 ?.I461r.0I 3.9514E01 -1.13937,01 5.91331-04 709327.07 1.99331-05 .10917401 1.5737E-01 .1000 .1300 .2100 0.07070.01 3.37037.01 ¿.90101.01 3.6131W-0? 1.11llt-0, 1.18507-nI 3.06201.01 7.13)37-01 3. 70 94f 01 I.97'6(,00 3.41ó 17.01 0.42291.00 .2360700l 0.22627-02 .30137,01 2.50107-01 .53897.01 5.00317-01 7493(.52 2.31160.03 2.50191.0? 3.I7011-0? 2.31122.0? 1,1387E-01 .231007.01 4.231.1-0 2 .30207.01 2. 30307-0 I .36031.01 9.01110.01 7.3 (.3 .2000 3600 .4000 .3500 4?00 ¿.sOlq!.ni ¿.38501.01 ¿.70017.61 2.20617.01 2.26347*01 ¿.34200.01 1.77227-01 2.0700E-01 3.13057-nI 3.7233E-01 4.27$J7nI 0.61b10.0I

3.34407.01 A.ISoll.00 2.93017.01 1.24200.01 2.31377.01 1.60U7E.0F I. 11007 .01 1.01631.01 1.22007.01 1.89840.01 0. 0 00) 11. II 1.86760.01 .70917.01 .3493( *00 .1*237.01 4,7o4370I .61030.61 3611400 .36391.11 1.03320.01 .03036.01 i.21007*0l 6.73157.00 l.41?47.0l 25243E.52 0.79321-01 2.30241*02 1.1183(00 !,34107.02 3.39031400 25o3001.02 3.90600.00 2.33331.0? 1.44907.00 2.01110.02 .16021.01 .71167'OI 2.1330! ' .70500.11 4.71301.00 .61717401 7.50517 00 .36107.01 I .03310.01 .03901.01 I, 20131 ' 01 0.16417.01 1.4,610.01 1.0100 1.2300 2.o6407.n1 2.Ai°1*fll 4.83777-nl 6.6123E-01 0.00901.01 1.13337.01 3.16117.00 1.60171.01 3.20361.00 I.bMbME.0I .6.1030.7_0? i.63007001 200031.02 2'433(.02 .41291401 3.10131401 I,6n671'01 73711.oI .3,44317.0? 1.63961 .01 i .53fl0 I"00 24300

.10677.nI 2.95*7'flI 3.00037.FIi 4.00.ltIF-ñt 3.1032E-01 2.2109E-01

P.3iJ0(.o0 1.39290.01 -2.&6I4r.061.A20lt'01 2. 14107.00 1.17590.01 -4.63907.00 1.30477*01 2.04127.00 9.63811.00 -5.!068r.01 1.31110.01 2.04081.02 2.3*01.02 2.3370(002 91000.01 -?.63777'00 I .61710.01 .9*331*01 .0.66007.01 I .i 001 0l .10671'01 -3.82247400 1. 31697 '0 I 3.0500 .i.i9631'OI 1.30137-01 3.02391.00 1.13737.00 b.I$07E.0I 1.08000.01 2.32122.02 .532770l .6.20341.00 1. 00307 .01 .e000 e 1000 0.0000 1.1000 3.21317.01 3.333*7.01 3.31380.01 J.00007.nI 7.0400E-07 3.0300F02 j.2309(-02 2.0ooF-o3 3.14ii7.00 6.00910.00 3.9lAS7.00 0.3400(400 0.41037.00 4.61267.00 -5,44037.00 3.12397.00 0.15690.00 3.01301400 ;*.70037105 8.70897.00 ¿.13247,00 -4.06300.00 2.00231.00 2.3I9('0? 2.31917.02 -7.32370.02 2.33331.02 .17977.01 -6.0103E'01 1.330.0!. 00 0.33661.00 3.4190f.00 6. 1,947 *00 9.43161.00 40.7*577.0* 0330I7.09 3,36631*00 .4.00607*01 2.93231.00 I.100' 10.7000 7.43301.01 3.03370.01 7.6226E-OS 6.25017-04 6.26001.00 2.1307(400 3.0319r.00 1.07040.00 6.393I1.00 1.67040.00 -2.90787.00 1.11420.00 2 30377402 1.970*0.00 .3.13051401 1.901e! .00 ?.34q01.0? 1.11177*00 -2.90301.00 1.20377.00 * 00 0.0000 1001017V I. 2.111.0.11

I.

2.9340.Sl S. 4S2o4(.0P S. 2.53497*01 .0100 S300 .0600 1000 loon .2100 .2000 .3000 0300 5300

1.?13.f.nI S.331I7.flI 4.03057.01 3. 10607 .0 i J.?i 307*01 2.19171.01 2. 71' 07 .01 2.63207.31 2 .87371 *0 I

4.60037-03 I.6000E02 3.8513E-02 7.300IE-fl2 i .2103E-01 I

19007 -01 2.0 101F-01 3.D1i7-fli 3.523 1F-01 2.03337.01 2 13 -7.975S745l - 0.3 2.94991.,I .04I31-02 3.06066.01 1.1142E-02 3.13401.51 2.3300101 3.2 1790.01 0.16107-02 3.30211.01 1.56117-01 3. 43 IF * SI 1.63130.01 3.7.0037.51 2.3031(400 3.76007.01 1.23201*00 7.80031.01 6.34217.00 4.07237.01 3.3l29E00 3.7.3001101 9.10331400 0.22777401 1.1321f00 3.15207.01 lOE 'Ql 4.00131.0l 1.20030.01 7.00220.01 1.03920.01 3.50737401 1.79100.01 1 .10001.01 2 .00027.0 i 2.901 71.01 2.2383(401 I .531?'*0 2.97337.01 .44E.02 3.40'I0-03 3,00317.01 I 17301-02 .I0397.0t 2.13910.0? 3.22007.01 S. 10,97 .02 407çoE.b2 1.3391W-01 3.00397*01 3,43307-0 I .90721*02 0.39430.01 3.16170.01 I .23077.05 49o70E.02 2.64401.00 0.08210.01 3.32081.00 49o7!,*2 9.27007.00 0.23377.0* 7.17321.00 4.490001.02 1.08610.01 4.00210*01 1.20051.01 0.97807*02 1.11110.01 3.30831.01 I .797'EOI 492y47.02 2.47691*01 2.91707.01 7.20107.0l -jiï-__1r_i__

t

Sample Output Listing,

Continued

SERIES

AO

HULL EORM. 0.130 (ILUCII

(1(30 SPEED ,3S7 WAVE 131301E WAVE ENCOUNTER W*VT F R t O u E r I f S 00NoV13 RPJ. NO. lOO S) OCE*ÑICS PROJECT 130. ¡093 StP . ¡910 ¡0.00 flEo.

VERTICAL PIAllE RESPONSES INOPI.OIMFNS,ON*Ll

WAVE/SHIP .. E A V E P t T C N VERTICal. 13fN0.MT. LENGIH .MPL. PHASE ANPL PHASE AMPLIIUOE PW*SE .3lS70 .75019 6113.21? 3.2033 ll6I1 179.3 .Hl2q -ç.A 4.075E-O) 11.2 473.334 2.4525 -716t. 1713.13 .13089 '14.2 6.543F-03 14.5 40500 .29793 313.992 l.91?8 6657 1713.0 7?62 -97.4 9.603E-03 17.9 .41oo .31771 302.934 1.5696 S3o9 116.7 .625? -80.1 1.300E-02 21.1 .49610 .134131 250.3513 1.297? 3797 114.0 .5fl91 -77.4 1.631E-02 25.7 .5412o .74*?S ?1ti.lYo 1.09 77ST11i7 3134j --ri.r I.B95EV2 .513610 36103 179.2SI .921313 0961 142.6 .2591 -70.2 2.026E-02 34.6 .631*o .37014 154.561! -.13uOl 0749 59S .1449 -641 1.968F_02 39.9 .67650 .376R9 ¡34.637 .6976 1?54 31.0 .0523 -51.4 1.696E-0? 45.13 .72160 .313011 119.333 .6111 1391 23.13 .015q 131.3 1.237E-02 53.S .76670 3RI413 104.1371 .b431 1077 20.0 .0450. 113.1 6.193103 66.4 .1311130 .3799) 93.4913 :0513 12.4 .04131 12*.9 2.1641-03 116.9 BS6QØ .17371 MJ.IS 43413 0140 -913.7 .0131 ¡35.3 3.321E-03 -ISO.? .90200 -.30,13132 75.133 .3924 -0445 -139,9 .0117 160.4 4.3A3E03 -I3l.4 947*0 33977 613.692 p3559 0437 -143.2 .0086 -76.13 3.0691-03 -170.7 9927n .14106 -0,2.S90 .3243 02*1 143.3 .°13i -44.S S.2b?tO4 -90.3 .O]4O .33711 !.7.?6S .2967 00134 31.1 .0086 -32.4 I .67flE03 60.2 02*fl .3140.3 1.2.593 .2725 0210 30.3 .0020, 57.7 1.9313E-03 73.5 .17750 .794*1 413.469 .2511 OI03 14.5 ,0059 119.? 7.4S9E04 132.6 .17266 77161 -44.1311 .2322 0124 -132.9 0(139 127.5 1.911E-03 -*44.6 .21770 .24509 41.555 .2153 02i'l -157.13 0019 -713.8 2.316E01 l43.6 .262130 .21171 38.019 .2002 0165 149.0 .0052 -49.4 1.0081.01 170.7 .30190 .1*,0I( 16.02* .1066 02OU 72.7 .0035 05.1 I.R2i_O) #0.7 51* 20.0 flU000 IlITv 'I, .SIe.AI-0i 0. -2.Mlqer-0i 0. 6.63313E0I 0. -2.97961-01 .0100 ¿371FV0 ¡.4*bUfl3 .5427E-ni

4.1053E-05 -2.9h2E-0I -9.013941:-OS

6.71471-01

2.0124E-04 -2.9169E-01 -9.0895E-03

.0300

i..1IQ,f'0

I.I',-')?

.56137E-ni

6,1901:-04 ?.39hM0-0I -i.37'-o3 6.9q15Eo1

3.05611-03 -2.9997E-01 -1.3760E-03 .lThfln .MIIf.n0 .U(i5I10? .621131-Ol 3.Ji7L-03 -3.II72E-01 i.*n49103 7.le,1?1-01 1.6530E-02 -3.l231F-0I -7.4n791-01 .10(0 ¡.01F.flh( .72l,I1-0? .h91i-0l 1.tJ4I0E-O2 -3.2494E-01 -7,441321-02 746100-0l S.49851-02 -3.2563E-01 -2,4493E-02 .l5oo .IPf0f-('I I.9F-0l .7159E-ni

2.6235E-U? -3.33Qt-0I -S.93I(-02

7.67113E-01

¡.3415E-01 -3.3510E-01 -5.9127E-02

IDn

1.,'fl.1-nI 3.30130E-ni .70620-01 4.9M13L02 -3.32013E-01 -1.1373E-01 7b5'1-01 2.5917E-01 -3.34011-01 2M00 b1(,4-tlI ,.(U(1..flI 634$0..0i

7.13405E-0? -3.i8710-0I -j.80132E-0I

7.3*noEOi

4.1519E-01 -3.1999E-01 -I.843E-ol

33.00 b.?IOOE-nI 7.,Q'?E-0i .S3Il1-0l .06300 -01 -?.9*90E-0I -2.48771-01 6.79141.01

5.7410E-01 -2.91.90E-01 -2.4705E-01

4500

b.132*0f..r'i

i.U".n.00

.40130E-nI

.29*2E-01 -?.blolr--0l -3.0601E-0l

6.1401E.O1 7.11911-01 -2.6752E-01 -).03201-0l

r00

,.S0q4-nI i.jd0*00 .2HbSI-0l .45.0.1-01 2.008f0I -3.bf(013E-0I 5.4qclE-01

9.I909E-0I -2.3ø7E-01 -3.4474E-01

037'.F-oI

l.133lbE.00

70O

I?SSE.oI

.5580E-01 -2.1492E-Ol .3.8145E-Ol

4.9773E-01 9.99211-01 2.1369E-01 -3.1413E-01 .13700 o.i1n0Fo1 ?.JH''F.flO 0173.E-0i .6104E-01 -I.9276E-0I -4.0735(01 4.3143E-01 9.5333E-01 1.900l1-OI -3.9196E-01 ),UU0 uH073.oI 3.111131.(I0 Jq7u5102

.6126E-01 -l.7'97r-0I -4.22Q4E-01

3.9396E-01

9.8324E-01 -1.6994E-01 -3.91324E-01

1.2500

b.ohPll-ni

4.n32f.fl0

9.36J5E-02

.57161-Ut -1.6252E-01 -4.31991-Ol

348)3L.0t

9.9938E-01 -1.5412E-01 -3.9439E-01

1.S0n ,.I0l.1E_nI S.I13E.ffl 13.9413E-02 .4977E-01 -I.SS77E-0I -4.30221-01 ).23oE-0l 9.7473E-01 -1.42550-01 -3.8217E-01

I ')0

o.I943 -(I h. 5hhI .00 $.h619(-02

.J94S1-0i -1.5450E-01 -4.35751:-Ol

3I5q1-0l .4023(-01 -1.3'30E-01 .3.6222E.0I 2.4500 b.IILOE-nI M.7lb13F,fl0 13.5327E-n? .27731-01 -I.582tE-OI -4.2764E-01 3.14#7E-Ol

13.9049E-01 -1.2943E-01 -3.3711E-01

3U,Ofl i9fl-"I .1310E,flI 13.4952E.02 .l513'.-01 -l.04620-0l -4.0865E-01 3.3147E-01

9.3156E-01 -1.2121E01 -3.10591-Ol

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