LR 257φ - User's Manual - calculation of ship responses in regular waves by strip theory

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TITLE:

LR 2570 - USERS' MANUAL

CALCULATION OF

SHIP RESPONSES

IN REGULAR

WAVES BY

STRIP THEORY

R.& T.A.

REPORT NO. 5116

AUTHOR:

A.

Blixeli, Civ. ing.,. C. Eng.

DEPART?'NT:

Structures Section, Research And Technical

Advisory

Services..

PRINCIPAL:

J. I.

Mathewson, C. Eng..

CONTENTS

PAGE NO.

INTRODUCTION

GENERAL DESCRIPTION OF THE PROGRAM

2

LLOYD'S REGISTER OF SHIPPING

71,

Fenchurch Street, London, E.C.3

April, 1972

LR 257

USERS' MANUAL

CALCULATION OF SHIP RESPONSES

IN REGULAR WAVES BY STRIP THEORY

1.

INTRODUCTION.

1.1

This report describes the Society's Strip theory

computer program

_{(LR 257) which calculates the}

moments, shear forces, motiOns and accelerations

for a ship in regular waves.

_{The proqram will}

evaluate responses for up to 21 cross sections

within the length of the vessel.

- 1.2

_{The practical use of the program as described}

herein is straightforward1 the input and output

instructions being presented sequentially.

For

the associated theory, reference should be made

to

LR 2570 - Theoretical Manual CI), where

a detailed

description of the theoretical approach is given.

1.3

_{For ilitistration the complete input and some}

output for a 290,000 ton tanker are given.

1.4

Although the program calculates transfer function

data only, it forms part

f a gnera1

_computer

based system for calculating ship motions and loads

in irregular waves, (2).

Is C rtilcatC is issued upon the terms of the Rules and Regulations of the Society, which providC

_that:

"The Committees of the Society use their best endeavoura to ensure that the functions of the Society are properly executed but it is to be

derstood that neither the Society nor any Member of any of its Committees nor any of its Officers, Servantsor Surveyors is under any circumstances

iatever to be held responsible or liable for any inaccuracy in any report or certificate issued by the_{Society or its Surveyors, or in any entiy in the} 'gister Book or other publication of the Society or for any act or omission, default or negbce of_{any of its Committees or any Member thereof}

2.

_{GENERAL DESCRIPTION OF THE PROGRAIVI}

2.1

Input

The unit system

in

the program j

governed by the input

values of the water density

_and

_{the acceleration due to gravity.}

Some typical units are shown below.

Water

density

sI

t

tons/ft

tonnes/m

Acceleration

of gravity

ft/sec2

ft/sec2

In/sec2

Resultant

Title card

Any alphanumeric title information, used to label jol

out-put.

The firSt 30 columns are used as a label for the stored

TDP (two dimensional properties) and response array files.

ThUS subsequent runs using the file must duplicate these first

30 columns which are then checked against. the file label before

using the storeddata.

This avoids inadvertent use of an

incorrect file.

Card 2

(*) Format 12

Option control card

Each option control tag is given a value, of 0, 1 or 2 where

the meaning of each is given below.

The eleventh entry of the

catd, the number .of ship segments, corresponds to the even niniber

of equal. length segments, or strips, into which the. ship hull is

divided lengthwise for calculation purposes.

Letter

Co luinn s

1-2

3-4

Tag description

Integration

Moment

3-The dimension N should then be in lbs., tons or tonnes and

L in metres or feet and T in secs.

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 option, are marked with an asterisk (*)

The first ten cards (0 to 9) are considered the basic data set,

while subsequent cards are the. conditional data set. Fig.

1..

Card .0

(*)

Blank

Card 1 () Format A80

Options avai:lable

Caic. moments only,

use summary mass

properties

1:'Calc. motions only,

use maSS distr.

2: Caic. moments, use

-mass diStr.

0: Simple summation

NS

L

M

1

Read TDP file

(file 10) print out

TDP data

2: Read TDP file

(file 10) no print

out

0: Suppress closure

calcs.

Calc. and print out

closure results

0: Dimensional

Non-dimensional

Torsion axis

0: Centre of gravity

()

Waterline

Number of ship segments

Point respbnse0: Suppress caics.

çalc. and print out

point reSp!A

.(rel. motions and

acce leratiOñs)

Print output

:

Suppress printing

Future use

Future use

Output

1

C

D

5-6

7-8

Mass dist.

ruture use

0: Input masses

1: Input weights

E

9-10

Degrees of

freedom

0: Vertical plane Only

Vertical and lateral

plane

2: Lateral plane only

11-12

Future use

G

13-14

TDP file

Generate TDP file

write on disk

(file 10)

H

J

15-16

17-18

19-20

21-Z2

23-24

25-26

27-28

29-30

Moment closure

Output form

Card 3 () Format 4'IS

Disk card

Columns

1-5

Starting address for writing results

on disk.

If = 0, no results will be

written on disk. (-)

6-10

V)

'

Number of speeds

(-)

11-15

Number Of headings

(-)

16-20

Number of X/L's

C-)

Card 4

(*) Format lOX, 4F10

Unit system card

Columns

11-20

Ships length (L)

21-30

Water density

(M/L3)

'-'

31-40

Acceleration of gravity (L/T2)

41-50

. .

Ship displacement (M)

Card 5

(*) Format 4FlO

Hull form cards

Columns

1-10

Section waterline breadth

(L)-11-20 -

.

Section area. coefficient

()

21-30 -

.

.

Section draUght

(L)

31-40.

Section centroid

CL)

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: of segments, NS, is 20, and the integration option tag, A,

is 0, then 20 hull form cards are. required which corresponds to

the hull at statiOnS

½ ,

1½,

2½.

19½

if the

integration tag, A, is 1 then 21 hull form cards are required at

stations 0, 1,

2

-- - - 20.

The entries for sectional waterline breadth, area coefficient

(sectional area/(local breadth x local draught)

)

and draught

arestraightforard.

.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 motion

calculations, then approximate centroids are calculated based

on

the area coeffiient and draught (using a two-dimensional versIon.

of the Moorish Approximation).

Card .6

(E>O) Format 2F10

Lateral plane

Co luinns

1-10

11-20

Sect i ona 1

Columns

1-10

11-20

21-30

card

Ship vertical centre of gravity (L)

Radius of gyration in, r011 CL)

mass properties cards

Segment weight or mass CM or

Segment vertical CG. (L)

Segment radius of gyration of roll CL)

-6-These cards are used only if the moment option tag, B, is 1

or 2 in lieu of the summary mass properties card above.

One

card is used for each section to be specified, in the

same way

as Card 5

This card is used only if the degrees of freedom option tag,

E, is 1 or 2

The ship vertical CG is measured from the

water-line, positive upwards.

Card 7

(B

0) Format 2F.10

Summary mass properties card

COlumns

1-10.

Radius of gyration, longitudinal (L)-H

11-20

Longitudinal centre of gravity (L).

This card is used only if the moment Option tag, B, is 0.

The longitudinal centre of gravity is measured from amidships,

positive, forwards.

CäuinnS

1-10

11-20

21-30

31-40

o

Run control tag and wave amplitude CL)

Initial wave length (L)

.

Final wave length (L)

Increment in wave length (L)

The, first entry on each card is the segment weight,

or mass,

depending on whether the mass distribution option tag, C, is 1 or

0.

The second entry

the segment vertical centre of gravity,

which is needed Only for lateral bending moment calculations,

is measured, positive downwards, with respect to the ship's overall

vertical centre, as, specified on the lateral plane card above,

card 6., ,Since it is required that the vertical

mass moment

integral, Eq.

(56.) ref (1), should satisfy the specified overall VCG,

the input segment VCG's are shifted by an equal amount, up

or

down as necessary to balance exactly the vertical

moment for the hull..

This minimises the effort required to obtain precise balance 'in

input data preparation.

The final entry, the segment radius of

gyration of roll, is needed only. for torsional moment calculations.

If no entries are given, the overall ship value.is used at each

segment.

Card 9 () Format 3110

Moment station card

Co lwnns

1-10

1O

_{_- First station for moment calculations}

11-20

_- Last station for moment calculations

21-30

- Increment between stations

'The parameters on this card determine the ppsion along the

ship hull at which the moment calculations are to be performed.

Station numbers are defined as' 0 at the forward end of the first

segment, increasing to NS

,

the. number of segments, at the after

end of the last segment.

_{If the calcu1atons are required.only}

at one station, then the first two entrieS on the card should be

equal t'o that station number.

' .

Card 10 (*) Format 7F10

Run control card

0

41-50

Initial ship speed (/)

5 1-60

_/

Final shp speed (L/T)

6 1-70

_/,

Increment in ship

speed

(L/T)

The first entry, the run control tag, determines the. program

continuity.

The next three entries determine the wave lengths to be used.

in the calculations.

The increment should always be positive,

so that wave length increases from initial to. final value.

The last three entries are similar parameters for. ship speed

and should always, independent of the value of the run control

tag, be punched.

Card 11 (E>0). Format. FlO

Roll damping card.

Columns

1-10

. .

Fraction of critical roll damping

(empirical data)

(-)

Run Control

Tag

.

Action

Greater than 0.0

.

Continue

calculation, using

this as wave amplitude- Usually

1.0, then wave amplitude becomes

unity.

0.0 (or blank)

.

Stop calculations, .read new

basic data set

-9-This card is used only if the degrees of freedom option tag,

E, is 1 or 2.

The calculated wave damping in r011,at the natural

roll frequency

,

is increased so that the total damping is

the specified fraction of critical dampinci.

The addttiona.l

roll damping thus determined initially is then used for all

subsequent calculations specified by the conditional data set.

Card 12

(*) Format 3F10

Wave angle card

Columns

1-10

0.

initial wave angle (Degrees)

11-20

.

Final wave angle (Degrees)

21-30

Increment in wave angle (Degrees)

These entries specify the wave direction angles to be used

in the calculations, where 1800 is head sea and O° is following

sea.

Stri ti on

S

The. main restrictions in the program concern the following

items:

Maximum number of ships cross-sections

-(stations 0 to 20)

21

Maximum number of wave angles (headings)

inonerun

.. . .

=

13

Maximum number of wave lehgths in one rim

=

51

2.2

Ca1cuiation of the TDP array

Before solving the

equations

of motion, the program

cal-culates and checks the two Lewis form parameters for each section.

and after that calculates and Stores the TDP (two-dimensional

properties) array, i.e. A,

A2,

M5, Nsf M, N5,

_{'r' NrI Frsf}

and Nrsifor25 diffent frequencies.

At the particular frequencies

which arise at the required ship speeds and wave angles (headings),

the program interpolates on these 25 fixed values of the

appropriate TDP property.

FOr the vertical oscillations, Grim's method (3) is used

to obtain the values of A3 and

A.

For the calculation of the two-dimensional properties in

lateral and roll oscillations, M5, N5, M, N, 'r'

_NrP

_Frs

and

the method of Tasai (4) has been programmed.

In general1

these methods can be carried out to increasing degree of

numerical accuracy.

However, to reduce. running times to practical

values 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 had not yet been explored

in detail, results in the order of 1% accuracy or better are.

obtained for average sections over a wide frequency range.

2.3

Output

The output frbm. LR 2570 can be in three forms- printed

paper, disk files and plotted graphs.

The printed output depends of course on the option control

tags set as input.

However, each output Section ths described

below, though in any given run not all sections will .be printed..

Each section starts a new page and is labelled with the

title information and date.

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

as processed.

Then the conditional data are printed out, fig. 2.

If any of the Lewis form parameters has been changed and

if the TDP array is calculated, diagnostic messages concerning

these may then appear.

The next output is the listing of the

TDP array for each station

aYd each frequency,fig. 3.

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 is then printed.

The next output item is

the calculated moments and shears at each ship station, as,

pecified

on input data card 9, grouped for each wave lenath, or fEecTuency,

for a given Ship speed and. wave angle,

f:ig. 4.

If the moments and

shearsare calculated at only one station (usually midships),

then the output is omitted and the results are listed with the,

motion responses.

Then the vertical plane responses are printed

out, viz, heave, pitch and a summary table of the vertical

bending moment at midshipsf 1g. 5.

Next, the lateral plane responses, viz, sway, yaw, roll

and Summary tables of the lateral bending moment and torsional

moment at midships are given, fig

6..

This is followed by a sumnxP.ary table for the vertical

and lateral shear at midships,,.fig. 7.

Finally, the point responses are printed, viz. absoiute

vertical accelerations at FP, CG, AP and at CG max port!

starboard side, relative motions at F? and AP,f 1g. 8.

As each run with, eg. 4 speeds, 13 headingS, 51 X/L's and

19 stations will produce more than 560,000 numerical values an

automatic disc writing procedure has been developed in order

to store all results on a direct access file..

Other programs

then read the appropriate results for plotting and further

calculations, i.e. long-term predictions of response, hull pressure

distributions etc., Some plotted transfer functions are shown

in Figs. 9 - 12.

2.4

Error messages

Various error messages may appear in the output and cuase

program termination.

Each will be labelled with the subroutine

which found the error and possible a brief note to determine

the type of error..

Some messages give error riumnbersas explained

below:

Subroutine

Error No.

Explanation

PRELIB/C

Too many sections, wave lengths,

wave angles etc.

PRELIB

1

Sum of wéihtdistribution

distlacement

DISPL(WTS.)

_{.- DISPL.>OO2}

DISPL

PPELIB

2

Hull volume inconsitent with

displacement

DISPL.(VOL). - DISPL

_>002

DISPL

- 12

P RELIB

3

Longitudinal centre of

buoyancy

longi. centre of

gravity

cois. 1 - 30 only

Errors in the calculation of the two-dimensional properties

wilibe self-explanatory.

if an error is found in the energy

balance check on the results of th

two-dimensional lateral

motion calculation, however

then a rnesssage is printed, but

calculations proceed!

It has usually been found that such

errors in the energy balance check have little influence on

the calculated two-dimensiona

properties.

A. Blixell,

Surveyor to Lioyds Register

of Shipping

9,.

Mathewson,

incipal Surveyor to Lloyd's

Register of Shipping

LC3 - LCG

> 0.005

LBP

P RELI C 4

Error in range or increment of

variable conditions

PRELIC

5

TDP calculation incomplete

.13

-3.

REFERENCES

1.

BLILL, A.:

LR 237

- Theoretical Manual.

Calculations of Sh±p P:sponseg In Regular Waves by

Strip Theory,

.

& T.\.S. Report No. 5103, Lloyd's

Register of Shiping,

1972.

(In preparation).

2..

Simulation by Computer of Motions and Sea lOads

for the Design of Ships and Offshore Structures.

Environmental Loads and MotiOns Group, R. & T.A.S

Report No. 5105, Licjfs Register of shipping, 1972.

GRIM, 0:

Die Schwingungen von Schwiinmenden

'Zweidmensiona1en Korern, H.S.VA. Report No.1117, 1959.

TASAI, F.

:

Hydrodynamic Force and Moment Produced

by Swaying an

Roiling Oscillations of c1Inders

on the Free

Surface..

Rsorts of

Research, Institute

of Applied Mechanics.. I<yushu University, Japan,

D Dota NO

0

3 4 5

Lft.

t-S ol Application

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PUNCHING INSTRUCTIONS

Application

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TANICER FULLY LOADED LR2570

RUN ON

9itO?1

OPTION CONTROL TAGS .- A B C 0 E F G H I J K L N N

1 2 1 0 1 0 0 0 1 0 1 0 0 0 NO. OF STATIONS - 20

FIRST RECORD NO. 1 NO.. OF SPEEDS 4 HEADINGS 13 LAMDA/L 51 STATIONS ON DISK 19

BASIC INPUT DATA

a.

or, -7.095 GYRADIUS,ROLL 17.499

DERIVED RESULTS

OISPL.IWTS.) ' 291183.69

LONG. C.B. 7.943 (FWD. OF MIDSHIPS)

0ISPL.(VOL.)_291176.5O

LONG. C.C. 8.230 (FWD. OF MIDSHIPS) LONG. GYRADIUS a 79.195 GM - 8.616

TANI(ER FULLY LOADED LR2570 CONDITIONAL INPUT DATA CARD PRINT OUT

1.0000 33.0710 1686.6208 33.0710 0.0 7.7280 2.5760 0. 1000 0.0. 180.0000 15.0000

FIG. 2

LENGTH - 330.71 DENSITY 1.025000 DISPL. = 21184.19 GRAVITY 9.80664Q

STATION BEAM AREA COEF. DRAFT i-BAR WEIGHT ZETA GYR.ROLL

-0.0

59450

0.7000 19.9750 9.4880 321.6909 0.0 8.1120 1.00 33.4670 0.8000 19.9750 9.5240 6792 2891 0.0 11.4720 2.00 48.4310 0.9000 19.9750 9.5590 16389.8203 0.0 16.2k90 3.00 51.6940 0.9760 19.9750 9.8050 18634.0273 0.0 18.0040 4.00 51.8160 0.9950 19.9750 9.9150 21864.2500 0.0 18.1940 5.00 51.8160 0.9950 19.9750 9.9150 15410.4297 0.0 18.1940 6.00 51.8160 0.9950 19.9750 9.9150 9157.8984 0.0 16.1940 7.00 1.8160 0.9950 19.9750 9.9150 12009.1094 0.0 18.1940 8.00 51.8160 0.9950 19.9750 9.9150 19206.1836 0.0 18.1940 9.00 I.8160 O.9°5O 10.9750 9.9150 19212.9844 0 0 18.1940 10.00 51.8160 0.0950 19 9750 9.9150 19186.6953 0.0 18.1940 11.D 51.9160 0.9950 19.9750 9.9150 20342.6641 0.0 18.1940 12.00 51.8160 0.9940 19.9750 9.0080 20837.0391 0.0 18.1790 13.00 51.8160 0.9910 19.9750 9.8970 19013.5469 0.0 18.1500 51.8160 0.9770 19.9750 9.8000 18480.7539 0.0

18.16O

15.00 51.7550 0 9390 19.9750 9.5630 1a7o4 9531 0.0 17.6070 16.00 50.6090 O.068C 19.0750 9.1?OO 18743.7109 0.0 16.4080 17.00 47.1400 0.7660 19.9750 8.6470 8627.3964 0.0 14.1800 18.00 40.7520 0.6230 19.9750 7.8270 3934.9290 0.0 11.1800 19.00 30.7850 0.4050 19.9750 6.0140 2783.1169 0.0 8.2100 20.00 16.3070 0.5820 19.9750 1.8180 630.6709 0.0 10.1700

TANKER FULLY (.0*080 (.02570

TVO-OTMENSIONAL SECTION PROPERTIES P009.

P4M.

4-PRIMEI33) AI8AR)S0 N-SUB(S) STA -0.0 0.0 INPINITY 0.0 6.3768 01 0.0100 5.371E 00 8.6608-06 6.3738 01 0.8309 3.9808 00 7.4908-05 6.4095 01 0.0600 3.0958 00 2.8455-04 6.7041 01 0.1000 2.438E 00 7. 399E-04 7.0048 01 0.1000 1.9288 00 1 5408-03 7.4081 01 0.2100 1.5308 00 2. 76)!- 03 7.°IZF 01 0.2800 1.2178 00 6. 446-O3 8.4681 01 N-SUB(S) M(S.PHI) 0.0 5.2706 02 8.8016-04 5.265E 02 1.3961-02 5.339E 02 8.1348-02 5.464E 02 3.0498-01 5.6468 02 B.922E-01 5.891E 02 2.2281 00 6..1OCE 02 4.9628 30 6.5026 02 N(S.PHI) 0.0 7.1768-03 1.131E-01 6.5338-01 2.6208 00 6.9788 00 1.7120 01 3.7368 01 1-51)8(0) 4.9328 4.923E 4.9748 5.0608 5.1868 5.356E 5. 5601' 5.7638 03 03 03 03 03 03 03 03 N-SUB(R) 0.0 5.8928-02 9.2946-01 5.3716 00 1.9916 01 5.7476 01 1.4116 02 3.0826 02 F-SUO(R.S) *.SU8(R.S( 5.2706 02 0.0 5.264! 02 7. t75E-0. 5.3581 02 1. 1356-01 5.513! 02 6.5B5E-0. 5.7318 02 2.4556 DL 6.O3RE 02 7.1336 OO 6.4088 02 1.766! 0J. 6.9078 02 3.8946 0 0.1400 0.7531-Cl 6. 584 F-03 8.9375 01 1.000! 01 6.7188 02 7.3628 Ô1 5.8818 03 6.0721 02 7.1226 02 7.760E 01

0.4500 7.922E-Ot 0. 1201-03 9.032E 01 1.0098 01 6.6366 02 1.298E 02 5.7505 03 1.070E 03 7.1348 02 1. 3851 0

0.5500 0.6700 6.5576-01 5.6076-01 .1.19'E-02 1.5228-02 8.4015 6.8231 01 01 2.86!! 01 6.0338 3.9396 01 4.791E 02 02 1.9978 02 2.6621 02 5.2376 4.2428 03 03 1.6448 03 2.1068 03 6.5876 5.3386 02 02 2.1598 C 2.9190 02

0.8200 4.18E01 1.1E-C2 4.6346 01 4.596E 01 3.2028 02 2.9858 02 3.0198 03 2.430E 03 3.678602 3.3306 0

1.0100 4.7428-01 2. 2778-02 2.6996 01 4.5971 01 1.8796 02 2.8428 02 2.032E 03 2.304E 03 2.2721 02 3.2356 C. 1.25'O 1.3500 4.9171-01 5.46C8-01 2. 628e_0Z 2.8748-02 1.5086 9.5716 01 00 6.1048 01 1.1178 3.570E 01 7.8106 02 01 2.4208 02 1.9360 02 1.4791 1.2516 03 03 1.934! 03 1.5146 03 1.4646 1.1491' 02 02 2.0166 02 2.3078 0 1.0300 2.4500 6.3286-01 7.3336-01 2.9525-02 2.812E-02 7.8408 8.316E 00 00 2.956.E 01 6.8606 2.4008 01 7.0766 0.1 01 1.4656 02 1.0718 02 1.1698 1.198E 03 03 1.1048 03 7.6378 02 1.1238 1.2546 02 02 1.7918 0 1.3406. 0 3.8500 8.2945-01 2.4081-02 9.8281' 00 1.9226 01 7.6675 01 7.6371' 01 1.2228 03 5.045E 02 1.4466 02 9.734! o, 3.8000 4.7000 0.1576-01 0.8531-01 2.0 748-02 1.642E-02 1.1968 1.3996 01 01 1.5018 01 8.209! 1.1556 01 8.7806 01 01 5.2368 01 3.5158 01 1.2376 1.2340 03 03 3.1088 02 1.8196 02 1.6608 1.8608 02 02 6.7408 0. 4.513E 01., 5.8000 7.1000 1.0438 OC 1.0818 00 1. 2401-02 0.2965-03 1.6068 1.7878 01 01 8.7578 00 9.0096 6.6378 00 9.2076 01 Cl 2.3138 01 1.52Q0 01 1.2148 1.1835 03 03 1.009! 02 5.414! 01 2.0366 2.1158 02 02 2.OIBE 01,. 1.8866 0 8.7000 1.1131' 00 6.7365-03 1.945E 01 5.0095 00 9.1888 01 1.008E 01 1.1468 03 2.8768 01 2. 2966 02 1.1698 01.

10.7000 1.133E 00 4. lOSE- 03 2.081E 01 . 3.771! 00 9.070801 6.6318.00 1.1058 03 2.4478 01 2.3858 02 7.160E

17* 1.0 0.0 .0.0100 0.0300 INFINITY 1.5341' 02 1.1041' 02 0.0 2. 6428-04 2. 1856-03 6.6658 6.752E 6.942E 01 01 01 0.0 1.8078 2.5296-03 1.8295 3. 970 8-02 1.8788 02 02 02 0.0 6.8716-03 1.0766-0) 3.2516 5.3078 5.4325 02 02 02 0.0 I 8668-02 2.9145-01 1.8078 1.8298 1.8780 02 02 02 0.0 6.870E-0 IoOTS1-0& 0.0600 8.44'8 01 7. 9031-03 7.253E 01 2.2758-01 1.9578 02 6.1308-01 5.6348 02 1.6568 00 1.9578 02 6.1396-01

0. 1000 6.6788 01 1.0641-02 7.6828 01 0.299 8-Cl 2.C65E 02 2.227E CO 5.9098 02 5.977! 00 2.066E 02 2.2278 0

5.4226 01 3. qznE-02 8.1861 01 2.3206 00 2.1918 02 6.182E 00 6.2218 02 1.640E 01 2.1928 02 6.1838 CL

0.7108 4.916E 01 6.7661-02 8.6468 01 5.362E 00 2.3015 02 1.4176 01 6.482E 02 3.7405 01 2. 3028 02 1.4180 01

0.2800 3.0601' 01 1.0518-01 8.8408 01 1.0546 01 2.3371 02 2.760E 01 6.541E 02 7.2308 01 2.3301 02 2.760E 01

0.3600 0.4500 0. '500 3.3930 01 3.074! 01 2.8728 01 1. SC 66-01 2.0231-01 2.5758-01 8.5178 7.5938 8.2788 01 01 01 1.7736 01 2.2368 2. 5458 01 1.9825 3.1876 01 1.6336 02 02 02 4.04E 01 6.5146 01 8.0498 01 6.2378 5.5428 4.6228 02 02 02 1.188E 02 1.66'! 02 2.0328 02 2.239! 1.085! 1.637E 02 02 02 4. 5856 0, 6.5148 01 R.04q8 o.. 0.6700 0. '200 1. 0 100 1.2500 1.330' 1.0500 2. 4500 3.0500 3. 8000 4. 7000 2.7561' CI 2.726f 01 2.7838 01 2.9228 Cl 3.124E 01 3.3736 01 3.6246 01 3.8438 01 4.030E 01 4.175E 01 3.1 786-01 3.8146-01 4.421E-01 4.8928-Cl 5.1258-01 5.030801 4.62?101 4.0021-01 3. 2631-01 2. 5688-01 4.8111 3.4548 2.3968 1.6915 1291E 1.1105 1.0995 1.1906 1.340! 1.5108 01 01 01 01 01 01 01 01 01 01 3.6088 01 1.2558 3.7606 01 9.1308 3.671E 01 6. 5831' 3.4136 01 4.9835 3.0616 01 4.1858 2.6418 01 3.9566 2.2145 01 .4.1341 1.8188 01 4.5188 1.4526 01 4.9006 1.1428 01 5.4728 02 01 01 01 01 01 01 01 01 01 8.9668 01 9.1618 01 8.1228 01 7.0586 01 6.778E 01 5.5338 01 4.364E 0! 3.3168 01 2.4061 01 1.6016 01 3.648! 2.7971 2. 1861 1.831E 1.6856 1.6856 1.7788 1.9105 2.0538 2. 1826 02 02 02 02 02 02 02 02 02 02 2227E 02 2.2296 02 2.0678 02 1.8028 02 1.4926 02 1.1588 02 8.5236 01 6.0118 01 3.9091 01 2.5526 0! 1.259! 9.1930 6.6550 5.0805 4.3168 4.1355 4.369E 4.8171 5.3681 5.9168 02 01 01 01 01 01 01 01 01 01 8.9635 0, 9.1555 01 8.7111 0). 7.841! 0, 6.7371 01 5.5286 0 4.3418 0& 3.3018 01 2.404! DI 1.7008 0.' 5. 0003 4.2081 01 1.0645-0i 1.6825 01 8.8448 00 5.9038 01 1.1408 01 2.291E 02 1.5551 01 6.420! CI 1. 1641 01 7. 1000 6.3735 01 1.'

0-

01 1.8398 01 6.830E 00 6.2646 01 7.6056 00 2.3778 02 9.269E 00 6.8445 Dl 7.8628 O) 8. 70C3 4.4398 01 1.1 34-01 1.070! 01 5.230! 00 6.5635 91 5.0018 00 2.4456 02 5.3218 00 7.201E 01 5.1690 CL 10.7000 4.4918 0.1 8.6791-02 2.1028 01 4.OI1E 00 6.8218 01 3.2268 00 2.4996 02 2.9666 00 1.4941 01 3.3486 00 STA 2.0 - 0.0 0.0 7.8955 01 0.0 -3.5785 01 0.0 l.86 03 0.0 -3. 'C 01 0.0 '68-04 8.0191' 01 6278 01 -5.1318-03 5.425E-03 - -5.134E-O3 -03 8.3181 0) 1' _{01 -7.7008-02 '.7326-0 706E-Oa.} e.orllr -4.1090

--

I '. .iTA 70.0 0.0 yprMITY ,.?776 01 0.0

.0

3.281! 03 i..

4.0.

.a2. ,.895! .123E 02 02 0,0 - 6. Y)0C-G 0,0100 0.0300 0.0630 0.1000 0.1C0 O.21') 0.2009 0.3600 0.4500 0.S00 0.6700 0.8200 1.0100 1.2530 1.5000 1.9500 2.4500 3.0580 3.9268 01 2.9006 01 2.24E. 01 1.1938 91 1.4''.E 01 3.170! 01 0.7011 CO 0.074w CD 6.909! 00 5.8368. 00 3.0516 00 4.4418 00 4.0320 00 3.8488 00 3,9055 00 4.170! 00 4.6141' 00 5.1356 00 6.. .-Q5 5.4086-06 Z.CL.7!-03 5.3I61'O3 1.1038-02 1.9001-02 3.2071-02 4.9068-02 6.7778-02 q.T'E-O2 1.1015-01 1.5405-01 I.459'-Ot 2.42'E-Ol. 2.°C0E-01 3.3705-01 3.700601 3.8708-01 5.8271 5.0358 6.1116 6.3625 6.69'E 7.0525 7.3071 7.3006 7.4598 6.3QE 5.2738 4.560! 3.3251 2.46IE 1.930! 1.5605 1.'47E 1.4741 01 01 01 01 DL 01 01 01 01 01 01 01 01 01 01 01 01 01 1.0156-03 3.'.. - 1.5058-02 3.9171' 02 9.1641-02 4.0695 62 -3.63E-01 4.200802 9.5451-31 4.36SF 02 2.2826 00 4.5466 02 4.7836 00 4.702! 02 8.9091 00 4.7561 02 1.471! 01 4.6168 02 2.1391 CL 4.2320 02 2.798! 01. 3.6056 02 3.246! 01 2.OcOE 02 3.3941 01 2.1668 02 3.2671 01 1.6886 02 7.979! 01 1.4216 02 2.5996 01 1.301E 02 2.2031 01 1.2031 02 1.8336 01 1.31'! 02 6.3956-03 1.0018-01 5.7106-01 2.0171 00 5.8268 CO 1.3741 01 2.83ff 01 3.1875 01 8.3961 01 1.1948 02 1.5111' 02 1.7108 02 1.7181' 02 1.5740 02 1.3518 02 1.0911 02 8.4406 01 6.3316 01 3.294! 03 3.3255 03 3.3748 33 3.444003 3.5318 03 3.6231' 03 3.6746 03 3.693E 03 3.596E 0 33345 03 2.94F 03 2.5051 03 2.1206 33 1.0626 03 1.120E 03 1.6161 03 1.6728 03 1.6881 03 6.299E-Ol 3.011 0)) 1.206! 01 3.6135 01 0.4556 Cl 1.729! ('2 3.1201 02 5.0035 02 7.0171 02 8.1618 02 9.6636 02 9.436! 02 8.3311' 02 6.8228 02 5.1646 02 3.6798 02 2.502! 02 3.9361 4.229! 4.408! 4.6C'E 4T858 451,75 4.7438 4.3141 3.7555 3.0016 2.3196 1.0476 1.5076 1.071 1.5305 1.6006 02 02 02 02 07 02 02 02 02 02 02 02 02 02 02 02 02 t.0OZF-C! 5.7201-0.;

Z.'8

0'

5.41'!

0 1.5376 0. 2.9f',E CI 5.2005 01 o,: 1.2258 0. 1.5.3E 07 1.7711 C'.. 1.7036 02 1.6508 67 1.426E C, 1.158! 02 9.0028 01 6.7706 Di 4.8466 01 3.8003 4.7000 5.6831 00 6.1806 00 3.8478-01 3.6608-01 1.570! 1.6995 01 01 1.4871 01 1.3675 1.1865 01 1.4206 02 02 4.5518 01 3.177E 0! 1.706! 1.7195 03 03 1.5931 02 9.723E 01 1.7151 1.820! 02 02 3.3921 01 C. 5.8300 6.6348 00 3.3408-01 1.8381 01 9.293E 00 1.4658 02 2.139E 01 1.7228 03 5.6456 01 1.023! 02 2.2866 0). 1.5168 7.1000 8.7000 10.7000 6.0096 00 7.3008 00 7.5468 00 2.013101 2.5706-01 2.1871-01 1.9718 2.0946 2.2061 01 01 01 7.233E 00 1.498! 5.5381 00 1.5206 4.2195 00 1.5326 02 02 02 1.4055 Cl 8.7925 00 S.176E 00 1.1198 1.7106 1.6988 03 03 03 3.2035 01 1.7515 01 9.0048 00 2.0076 2.077! 2.136E 02 02 02 9.605! CO 6.091E CL

NATURAL #OLL FREQUENCY S 0.47905

CALCULATED WAVE DAMPING IN ROLl. 7.26305 04

A!:OITION4L VISCOUS DAMPING IN ROLL 9.74726 05

IMIKER FULLY L'JADED 182570

FIG. 4

SPEEO WAVE FRE0 777R0 WAVE ANfLE . fM0Ø

WAVE5H!P STA- VFRTTCAL RFNfl.41.

LENGTH TION £MPLITU)E PHASE

RUN DPI _9110171

0E.. WMFNT AND SHEAR D!STRIRUTTOI'I RESULTS (NON-OINF'ISTONAL)

(4TFRAL RENO.MT. TORSIONAL MONENT VERTICAL SHEAR LATEDt. SHEAR

AMPLITIJOE. PHASE AMPLITUOE PHASE AMPLITIInE PHASE _{AMPLITuDE P4AçF}

1.3650 01000

r

2.8101-05 113.0 1.1971-04 36.1 7.1311-05

-24.3

.4.1571-04 112.2 2.093E-03 39.1 1.3650 0.1000 2 4.157EG5 112.2 2.C°3E-04 39.1 5.485E-05

-17.6

6.4451-04 135.0

2.06F-03

1.3630 0.1000 3 7.130r-05 126.5 3.237E-04 0.L 3.5371-05

-18.4

4.5931-04 147.5 2.2101-03 74.5 1.3650 0.1000 4 8.3391-05 130.8 4.1001-04 57.3 3.3741-05

-46.0

4.5331-04 89.3 1.6411-03

7,j

1.3650 0.1000 5 1.1091-04 112.2 4.8041-04 57.2 4.3051-05

-42.7

1.1l0E03

88.2 1.7611-03 48.7

1.3650 0.1000 6 1.814E-04 106.3 .5.8471-04 54.7 3.54E-05 -29.1 1.3111-03 111.1 2.2601-03 1.3650 0.1000 7 2.4101-04 111.6 7.tSaE.04 55.9 2.1S7E-05 -42.1 9.4121-04 128.0 2.047E-03 68.4 1.3450 0. 1000 8 2.711F-04 113.1 7.89n1-04 59.2

2.7091-05 -737

6.6021-04 100.2 1.255E-03 68.9

1.3650 0.1000 9 3.OSSE-04 109.2 8.287E-04 57.8 3.2631-05

-67.9

1.0201-03 90.0 1.0041-03 3Q 7

1.365') 0.1000 10 3.6671-04 107.3 8.8091-04 56.0 2.0231-05

-70.7

1.01'iF-03 112.7 1.243E-03 47,1

1.3450 0.1000 11 4.0731-04 110.1 9.5131-04 56.5 2.2361-05 -128.9 4,3491-04 145.5 7.259E-06 89.q

1.3650 0.ICOO 12 4.0181-04 111.1 9.5171-04 58.4 4.001E-05 -130.8 2.702E-04

-27.9

5.9781-04 -150.4

1.3650 0.1000 13 3.8701-04 101.3 8.084104 5R.2 4.0001-05 -129.3 4.7051-04

-4.6

1.0691-03 -109.4

1.3650 0.1000 14 3.8375-04 104.8 'h474E-04 56.8 3.767E-05 -148.1 3.8211-04

-64.0

1.136E-03 -123.')

1.3630 0.1000 15 3.4921-04 106.4 7.8481-04 58.4

6.554-05 -163.2

1.2461-03 -78.8 2.3071-03 -142.9 1.3650 0.1000 16 2.5951-04 106.5 6.350E-04 63.9 9.1671-05 -148.4 1.9691-03

-65.6

3.627E-03 12q4 1.3650 0.1000 17 1.566E-04 96.3 3.9951-04 66.2 7.6891-05 -135.7 1.8911-03 -61.8 4.1721-03 -115.5 1.3650 0,1000 18 8.3721-05 79.2 2.1791-04 62.6 5.7271-05 -149.5 1.4601-03

-79.7

_{3,6471-03 '119.1} 1,3650 0.1000 19 1.7011-05 47.3 4.330E-05 104.8 3.9211-05 164.6 8.372E-04 -100.8 _{2.1791-03 -117.4} 0.9652 0.2000 1 8.9281-OS -165.3 2.4981-04 139.5 5.7761-05 90.5 4,5611-03 -133.8 7.3001-03 -174.8 0.9452 0.2000 2 4.5611-04 -133.8 7.3C01-04 -174.6 3.1101-05 -120.8 8.0151-03 -109.0

1.201F02 -137.0

0.9652 C.2000 3 8.5311-04 -113.1

1.3'31-03 -147.7

1.9001-04 -80.1 8.467F-03

-78.6

1.5801-02 -107.2 0.0652 0.2"30 4 1.160503

-47.3

1.9771-03 -127.1 2.5051-04

-55.2

7.3611-03

-49.9

_{1.730102 -81.2}

0.9632 0.2000 5 1.3561-03

-84.1

2.579E-03. -109.5 2.6671-04

-29.0

5.8441-03

-25.3

1.7581-02

-57.2

0.9652 0.2000 6 1.6591-03

-74.9

3.0631-03 -94.5 2.7001-04

-1.9

3.7461-03

-15.4

1.5851-02

-35.1

0.9652 0.2000 7 1.532E-03 70.9 3.3701-03

-82.6

2.4511-04 24.3

2.1291-03 -39.2

1.2191-02

-14.6

0.0652 0.7000 0 1.6371-03

-70.6

1.4881-03 -74.4 1.9141-04 54.0 2.8951-03

-69.8

7.1641-03 4.0 0.9652 0.2000 9 1.8221-03

-70.7

3.4881-03

-70.7

1.3151-04 87.6

4.4021-03 -63.2

1.9801-03 3.4 0.9652 0.2000 10 2.0741-03

-60.0

3.534F-03

-71.3

6.6641-05 110.7 5.4731-03 -44.1 3.1471-03 -100.0 0.9682 0.2000 11 2.3241-03

-64.7

3,7631-03

-73.2

1.309E-05

-3.5

5.7781-03

-18,4

6.1791-03 -82.9

0.0652 0.2000 12 2.482E-03

-58.6

4.1411-03

-73.0

1.1211-04 6.9 5.507E-03 15.4 7.622E-03

-50.4

0.045? 0.2000 11 2.47E-03

-52.0

4.476E-03

-69.4

2.344E-04 30,0 5.554E-03 57.2 8.8821-03

-6.3

0.9652 0.2000 16 2.2951-03

-46.0

4.5661-03

-62.7

3.7041-06 51.2 6.6311-03 94.3 1.2171-02 39.2 0.9652 0.2000 15 1.9611-03

-41.2

4.269E-03

-53.6

5.076E-04 72.2 8.1821-03 119.9 1.7481-02 73.2 0.9V.52 0.2030 16

1,9161-03 -38.5

3.529E-03 -42.5

_{6.1391-04 94,2 9.751F-03 136,1 2.3071-02 101.2} 0.9652 0.2000 17 9.8931-04

-38.6

2,3931-03 20.4 6.1161-04 111.5 1.0411-02 142.4 2.5791-02 126.8 0.9652 0.2000 18 4.7411-04

'40.3

1.1611-03

-13.3

4.313E-04 143,5 8,9271-03 143.4 2.2051-02 146.7 0.Q652 0.2000 19 1.0041-04

-56,4

2.4531-04 8.6 1.4041-04 171.4 4.7411-03 130.5 1.1611-02 166.7 0.7881 0'3000 L

4.10Eb5 -27.6

3.3775-04

-78.5

1.4431-04 -111.2 _{3.4851-03 19.1 1.1771-02 -4Q.6} 0.7081 0.3000 2 3.485E-04 19.1 1.1771-03

-49.6

2.1531-04

-39.8

8.0601-03 41.9 2.052E-02

-25.'

0.7881 0.3000 3 8.2171-04 39.1

2.2711-03 -32.2

3.952F-04 6.6 1.0541-02 65.7 2.4711-02

-2.1

0.781

0.3000 4 1.3181-03 54.6 3.30t)1-03

-17.0

5.7001-04 28.4 1.0811-02 90.5 2.6811-02 24.2 0.7561 0.3300 5 1.7191-03 68.6 4.3686-03

-1.4

6,7701-04 47.0 1.1741-02 115.8 3.0021-02 53.5 0.1881 0.3000 6. 2.1461-03 83.2 5.2175-03 15.8 7.1781-04 71.1 1,4241-02 131.6 3.54q1_02 81.0 0.7881. 0.3000 7 2.6831-03 96.8 5,082F-03

34.6.

7.4271-04 96.6 1.588E-02 144.8 4.1341-02 105.2 0,7081 0,3000 8 3.2211-03 108.9 6.6931-03 54.0 7.1271-04 120.2 1.5981-02 162.0 4,598E-02 127.6 0.7881 0.3000 .9 3.6541-03 1.20.2 7.3531-03 73.2 6.2721-04 147.2 1.5351-02 -178.1 4.6131-02 148.9 0.7881 0. 3000 10 3..954E-03 130.1 7.Q34E-03 91.7 5.6791-04 -171.4 1.424E-02 -151.5 4.9141-02 170.0 0.7081 0.3000 11 4.0961-03 140.4 8.391E-03 109.0 6.0691-04 -137,6 1.2771-02 -134.9 4.1211-02 -168.1

0.7881 0.3000 12 6,0411-03 149.0 . 9,4841-03 124,9 7.6001-04 - 8 1.135E-02 -108.9

4.371102 -164.0

O.7891---0.3000--13-

-03

156.4---6.215-03 -139.6 -9.64

1.067E-02

-80.5

4.0311-02 -I'

0,78*1 0.3000 162.5 7.482E-03 153.3 _{'13E-02 -.54.2} 3.857E-"

0.7891 0-

'41.5

6.2821-03 16.' .

-02 -337

3.R#.

0,799' " 4.6R9E-' .

-17.6

-17 2.263E-.... _0 _{...'.13E'05 -146.4}

_..

_{. 'c03}

_119.2

..O.000 19 8.7381-05 -.... £u.1

7,576-06 -136.3

2.040E-0, 7.3361-04

132.'

5.0000 19 2.0929-05

-14.0 ... c-C6

-9.4

1.5785-04

-*9.0

8,776E-04 171.1 2.7181-04 159.8 0.1011 5.1000 1 1. 4061-05 46.2 4.6701-06 144.1 2,8641-06 -117.6 8.3001-04 20.5 1.8561-04 -14w. 5

0,1Qll

5, 1000 2

9.'131O5

2fl,5 1.8661-05 -146.5 1.3061-05 176.0 1. 6421-03 16.8 2.Z32E-04 -133.9

0.1°l1

5.1)00 3 1.7631-04 19.2

2.3'.IE-05 -1452

2.311-05

lie..?

1.9191-03 17.1 6.0211-05 30.9 0.1011 5.1000 4 2.7455-04 18.2 1.2546-05 -149,1 4.4231-05 -170.4

_1.ME-03

_{10.6 5.5235-04} 59,3 0.1011 _5.1000 5 3.412F-04 19.4 3.52*5-05 75.2 5.6141-05 -178.1 1.4341-03 15.4 7.5401-04 59.0

;c.ioii

5.1000 . 6 4.170104 18.3 6.4991-05 64.1 6.5321-05 -170.7 2.1221-03 _{5.5. 3,6931-04}

_-27.0

0,1011 5. 1000 1 5.4951-04 14.1 4.528F-05 22.6 1.2261-05 178.8 2.9341-03

-0.8

1.216E-03

-18.1

0.1011 5.1000 .8 7.OIBE-04 10.4 8.0806-05

-48.6

7.7101-05 170.9 2.7491-03

-3.6

1.4631-03

-80.3

0.1911 5.1000 9 6.1571-04 8.2 1.4321-04

-62.3

1.9861-05 -117.9 1.02*5-03

-7.6

1.2331-03 -17.6

0.1011 5.1000 10 8.8741-04 6.6 1.971E-04

-66.2

8.1-RE-OS -175,6 1.0101-03

-16.5

9.9741-04

-74.6

0.Ioli

5.1000 11 0.150104 5.3 2.4161-04

-67.3

7.9011-05 -113.0

3.6321-04. -77.4

6.6398-04 -68.7

0.1911 9.1000 12 8.910104

'.3

2.6421.04 -66.8

7.540105 -169.0

1.0701-03 -158.9

_{2.236-04 -35.1}

0.1011 5.1000 13 0.13%F-04 3.3 2.6071-04

-64.7

6.0511-05 -166.7 1.9241-03 -169.6 2.9761_04 71.1 0.1011 5.1000 14 7.0141-04 2.3 2.4201-04 -62.1. 8.066F-05 -163.5 2,4951-03 -172.4 5.3991-04 03.7 0.1911 5.1000 15 3.6601-04 1.4 2.1ISF-04 -50.3

4.840105 -159.5

2.9671-03 -174.9 8.6021-04 106.6 0.1011 5.1000 16 4.0531-04

0.3

1.5955-04 -56.0 3.4055-05 -153.6 3.4671-03 -176.1 1.3721-03 112.1 .0.1911 5.1000 17 2.102104

-2.7

7.7051-05

-45.1

1.0211-05 -146.3 _{3.2131-03 -177.4 1.385E-03. 117.7} 0.1911 5.1000 16 8.5151-05

-8.4

2.655E-05

-21.3

7.1731-06 -135.9 1.998E-03 178.5 7.2071-04 131.6 0.191.1. 5.1000 19 2.0771-05 -1.3.8 7.2501-06

-10.9

1.4971-06

-86,7

0.5031-04 .171.6 2.6551-04 158.1

FIG. 5

9/10/71

TANKER FULLY LOAf)Et)

_L2570

SDFEI 7. 7290 _{WAVE ANCi.} RUN ON

60.00 DEG. _{VFPT!CAL PLANE RESPONSES}

(NN-flfMENS,.11

i0ipqr _{W4VE WAVF/SHID}

H F A V E _{P T I C H}

VERTICAL F%EP4f).MT.

F P F C) I) E N C I F S LENGTH LENGTH AMPL. PHASE AHPL. PHASE _AMPItTUDE

PHASE 1, 14 0.G6910 I _799.17 0.A9'40 .AL044 0.ccl3c

.9l51

O.45400

0.4.34

r),41!qA 3,q40i. O.175c9 C. 6.9j

0.564

C.41?5

0.1?!73 31 15 C.3r5,? 0. 27 . 781 3

r

C,2?R',3 (',730 0.?176e, 0. 26260 '.257Q6 ('.75347 0.?407j 0.24516 C.2433 0.23763 0.23600

.2'7?

C.727c3 P. ".4i 3.22163 0,21587 .7t317 3,73r47 0.7OoIA 0,71049 .2r1'

0.j1io

0.10717 C,9so' c'.Iq3oL 0.19114

.o

0. cOp12 Ô.54336 0.4°896 0.46361 0.43400 0.41104

c;

0.3342

.3523

0.34492 C',3296 0.37211 0,31217 0.3C1',g

C.2935

0.2q77

0.29394 0.27451

0.2si

0.26203 0. 2765 0.2.5270

0,7433

.7g46

0.2359 0.23174 0.22916 0.22474 0.22148 ('.?1936 0,73537 0.21250 0.20975 0.20710

O,24c6

0.20211 ,1Oo7s 0.19747

O.1Q2

0,10314 fl.lQic.

0.19900

0.l°717 0,1q53o 0.1P343 .0.19172 0,13002 0.17935 0.17674 33.071 99.213 132.2 165.355 198.426 .231.47 2A4.5 237,639 330.710 3',3,781 396,8

420.93

462. 94

496.0s

529.136 562,207 629. 369 661,420

694.41

727.562 760,633 793.7os 826.776 859,947

80.Qj

59.C)6O 092.110 1025,201

10527

1091.34; 1176.414 1197.496

11°C.5.

1273.628 1256.690 1280,770 1322. 940 1355,912

138.°A3

142?.0 .1455,125

14R.1q6

1521.266 1554.339 1597,410 1620,479 3653o550 1686.621 0.1000 0,0059 0.p000 0.0139 0.3000 0.O615 0.4300 0.ISQi 0.5000 _9.323; 0.60Cc' _0,2446 0.7000 _O.383p

0.q000 O.4ci

0.°000

0.596

1.000

0,65s 1.1000 _0.7097 1.2000 0.7511

1.00a

0,795

1.05

0.8129 1.5C)C) 0.83 1.6000 0,8547 1.7000 0,8706 1.8000 _C.8841 1.9000 0,8056 2.0000 0,9055 2.1000 0.9140 2;20Dc _0.9215 2.3000 0.9230 7.4000 _0.933 2.5C0O 0.9389 2.60.30 _0.9434 2.7000 0.9474. 2.8100 2.°000 0.954; 3.0000 0.°572 3.1000 0.9509 3,2000 0,9623 3.3300 _0.9645

3.4000 0.65

3.5000

0.694

3,AQflo _0,9733 3,70o') _0,9717 3.9('OO

_0,73i

3.900.3 _0.9744 4.00.30 0,9757 4.1000

C.763

4,2000 0,9779 4.3000 0.9789 4.4000 0,9798 4.5fC0 0,9807 4.60Cc 0,9915 4.7000 0.q822

4.80000.9829.

.9000

0,836

5.0000 0,9842 5,1000 O,9343 -12.9 0.0007 137.1 0.0oq -97.8 0.0336 -3.3 0.032o 81.0 0.1192 137.6 _0.1991 154.3 0.2605 161.9 0.3064 166.2 0.3410 168,q _0.3677 170.9 0.3834 17',3 0.4049 173.4 _0.4197 174.2 0.4290 174.9

_O.4c'

175.5 0.44c5 175.9 0.4518 176.3 _0,4571 176.7 0.4619 177.0 0,4659 177.2 _0.4693 177.4 0.4723 177.6 0.4750 177.8 _0.4774 177,9 _0.4795 178.1 0.4814 178.2 0.4832 178.3 0.4847 178.4 _0,4861 178.5 _0.4874 178.6 O.4R8 178,7 0,4396 178.7 0.4005 178,9 0.4914 179,9 _0.4023 179.9 0,4930 179,0 0,4937 179.0 0.4044 179,1 0,4950 179.1 0,4955 179.1 _0.4961 179,2 0.4066 179.2 0.4970 179,2 _0,4974 179,3 0.4978 179,3 0.4992 179.3 0,4986 179,3 0,4989 179.4 _0.4092 179.4 Ø,4qq 179.4 0.4993 -56.7 -160.3 63.7 -48,4 -80.1 -3;,g -85.2 -85,9 -96.3

-6.6

-86.9 -87.1 -97,3 -87.5

-7.6

-87.7 -87,8 -P7.e -88,0 -88.1 -88.2 -AB, 2 -83.3 -98.3 -88,4 -88.5 -98,5 -99,5

-R.6

-88,6 -99,7 -89,7

-R,7

-98.9 -88.8 -89,9 -99,9 -i3q,q -88. 99,O -99,0 -99,Q 89,0 . -99.0 -89,1 -89,1 -89.1

_9,j

-39.1 3.667E-04 2,074E-03 3.954E-O3 9.396E-03 1.325E-02 1.457E-02 1.419E-02 1.II1E-02 1.184F-02 1.061E-02 9.493F-33 8.4QIE-03

7.625-03

6.975E-03 6.224E-03 5.659F-03 5.166E-03 4.734E-03 4.355E-O3 4,OL9E-03 3.7?2F-03 3.458F-c'3 3.221E-03 3.00°F-03 2.819F-o3 2.646E-o3 2.499F-03 2.347E-03 2.217E-03 2.C93E-03 1.990E-03

1.99E-03

1.797E-O; l.712F-O3 . 1.633F-03 1.560E-c3 1.492E-03 1.429E-0; 1,369E-o3

, 334-3

1.263E-03 1,214E-o3 1.169E-03 1.126E-03 . 1,036F-03 L.049E-03 1.012E-O3 9.782E-04 0.463E-04 O.158...o4 8,874E-04 107.; -69.0 130.7 70.5 47.0 37,7 32.7 29.2 26,6 24.5 22.8 21.4 20.1 la,0

1,o

17,1 16,3 15.6 14,9 14,3 13.7 13.2 12.7 12.3 11.0 11,5 11,1. 10.8 10.5 10.2 9.9 9.6 9,4 9.1 9,9 9.7 8.5 8.3 9.2 9,0 7.8 7.7 7.5 7,4 7.3 7.1 7.0 6.9 6.3 6,7 6.6

TANkER FULLY LOAOEO 182570

RUN ON 9/1O71

FIG. 6

I 7.7280 WAVE ANGLE 60.00 DEG.

E ENCOUNTER WAVE WAVE/SHIP S N

3 I) E N C I E S LENGTH LENGTH AMPL.

LATERAL PLANE RESPONSES (NON-DIMENSIONAL)

A V Y A N

ROLL

LATERAL B.M.

PHASE AMPL. PHASE AMPI. PHASE AMPI. PHASE

TORSIONAL NC

AMPL. PI4

5') 0.6309 33.071 0.100 p.007 -86.6 0.000 73.6 0.001 -157.4 8. 8995-04 56.0 2.023E-05 70

52

O.581

66.142 0.030 138.4 0.005 -8.8 0.014 3. 534E-03 -71.3 .664E-0'5 110

.81 0.5434 99.213 0.300 0.030 -42.9 0.320 -158.4 0.102 -26.4 7.9345-03 91.7 5.6795-04 -3.77 25 0.4990 132.284 0.400 0.083 -67.8 0.032 16.0 0.185 -21.0 2.2055-02 77, .3 1.5555-03 -165 04 0.4636 15. 355 fl.500 0.044 -31.7 0.112 10.1 0.090 -100.3 2.323E-02 74.5 2.0185-03 -166 73 0.6349 198.426 0.600 0.107 66,5 0.186 6.9 0.362 -120.2 1. 948E-0 2 73.4 2.0675-03 -166 5 _{0.4113 231.497 0.700 3.219 81.9 0.246 5.0 0.546 -111.7} 1.5235-02 72.5 1.9ÔTE-03 -166 25 0.3008 264.568 0.800 0.317 86.7 0.293 3.7 0.651 -106.5 i. 3.665-02 71.6 1.6955-03 -167 5') 0.3734 2°7.639 0.900 0.396 88.8 0.329 2.8 0.717 -103.4 8.8855-03 70.7 1.4005-03 -167 IS 0.3592 310.710 1.000 0,461 89,7 0.357 2.0 0.761 -101.4 6. 8165-03 69a 7 1.3085-03 -168

16 0.3448 363.751 1.100 0.514 90,3 0.380 1.4 0.790 -100.0 5. 25°E-O3 68,6 1.151E-03 -isc

4') 0.3329

36.852

1.200 0,557 90.5 0.397 0.9 0.83.2 -99.0 4.0925-03 67.2 1.0iTE-03 -170 96 0.3221 429.923 1.300 O 594 90.7 0,4 12 0.5 0.827 -93.2 3. 2125-03 65.6 9.0295-04 -170 (.8 0.3124 462.096 1.400 0.624 90. 7 0.423 0e2 0.838 -97.6 2. 5455-03 63.7 R.055E-04 -171 '4 0.3035 40'5.065 1.500 0,650 90.8 0.433 -0.1 0.847 -97.2 2.031

_E-o

.3 61.6 7.2275-04 -172 12 0.2954 529.136 1.600 0.673 90.8 0.441 -0..3 0.854 -96.8 1. 63 2E-03 59.1 6,5155-04 -172 11 0.2875 562.207 1.700 0 6.2 90.7 0.448 -0.6 0.859 -96.5 t. 3215-03 56.3 5.8995-04 -172 1? 0.?PQO 595.278 1.800 0.709 90.7 0.454 -0.7 0.863 -96.2 1. 076E-03 53.0 5.3645-04 -173. 21 0.2745 628.349 .1.900 0.723 90.7 0.459 -0.9 0.867 -06.0 8 8325-04 40.3 4.8975-04 -173. 52

0.285

661.420 2.000 0.736 90.7 0.462 -1.0 0.869 -95.8 7. 3295-04 45 0 4.484E-04 -173. '0 0.2629

64.491

2.100 0.747 90.6 0.466 -1.2 0.871 -45.6 6. IO7E-04 40.1 4.1235-04 -173. 10 0.2576 727. 562 2.200 0. 757 90 6 0.669 -1.3 0.872 -95.4 5. 145E-04 34,6 3.8035-04 -174. 46 0.2527 760.633 2.300 0.767 90.6 0.472 -1.4 0.874 -95.3 4. 3905-04 28.5 3.5135-04 -174. 85 0.2480 703.705 2.400 0.775 90.6 0.6 74 -1.5 0.874 -95.1 3.80 45-04 21.8 3.23E-04 -174 0.2436 826. 776 2.500 0.782 90,5 0 476 -1.5 0.875 3. 3575-04 14.7 3.0355-04 -174. 7 0.2395 859.847 2.600 0.789 90.5 0.4 78 -1.6 0.876 -94.9 3.02 15-04 7.4 2.829E-')4 -174. 27 0.2355 8°2.918 2.700 0.795 90.5 0.480 -1.7 0.876 -94 8 2.7755-04 0.1 2.6445-04 -174, 80 0.2317 925.989. 2.80.0 0.800 90.5 0.431 -1.7 0.876 -94.7 2. 5975-04 -7.0 2.4765-04 -174. 0.2742 959.060 2.900 0.805 90. 5 0.492 -1.8 0.877 -94.6 2.472E-04 -13.7 2.3235-04 _3.74! )? 0.2247 9'12.130 3.000 0.810 90.4 0.48' -1.9 0,877 -94 5 2. 38 5E-04 -3.9.8 2.1835-04 -175. 0.2215 1025.201 3.100 0.814 90.4 0.484 -1.9 0.877 -94.4 2.3215-04 -25.1 2.0565-04 -175,. LI 0.7184 1058.272 3.200 0.818 90.4 0.485 -2.0 0.877 -94.4 2. 289E-04 -30.3 I.938E04 -175. 0.2154 1091.243 3.300 0. 8 21 90.4 0.486 -2.0 0.876 -94.3 2 260E-04 -34.7 1.8315-04 -175.

U

0.2.125 1124.416 3.40') 0.825 90.4 0.487 -2.1 0.876 -94.2 2. 240E-04 -38.5 1.7335-04 -175. FT 0.2097 1157,486 3.500 0.828 90.4

a.

487 -2.1 0.876 -94 2. 2. 224E-04 -41.9 1.642E-04 -175. 5 (.207t 3.190.656 3,600 0.831 90.4 0,4 88 -2.1 0.876 -94.1 2.2125-04 -44.9 1.558E-04 -175. 4 C. 2046 1.3. 628 3.700 0.833 90.4 0.4 88 -2.2 0.876 -94.0 2. 2005-04 -47.6 1.481E-04 -175. 1' ').2C21 1256,699 3.800 0.836 90.3 0.488 -2.2 0.876 -94.0 2. 1895-04 -49.9 1.4085-04 -175. A 0.1007 1290.770 3.900 0.838

903 0.489

-2.2 0.876 -93.9. 2. 1775-04 -52.0 1.3415-04 -175. R 0.1975 1322.840 4,000 0,840 90.3 0.489 -2.3 0.875 -93i9 2. 164E-04 -53.9 1.2795-04 -175. 0,1983 3.355.912 4.100 0.842 90.3 0.489 -2.3 0.875 -93.8 2. 1515-04 -55.6 1.221E-04 -175. )6 0.1931 .. 1388.983 4.200 0.844 90, 3 0.490 -2.3 0.87S -93.8 2. 137E-04 1.1665-04 -175. 2 0.1911 1422.053 4.300 0.846 90.3 0.4 90 -2.4 0.975 -93 8 2. 1225-04 -58.5 1.115E04 -.175. 8 0.1091 1455.125 4.400 0.848 3 0.490. -2.4 0.875 -93.7 2. 1065-04 -59.8 1.068E-04 -175. S 0.1872 1498.196 4.500 0.849 90.3 0.490 -2.4 0.874 -93 2. 090E-')4 -60.. 1.0235-04 -175. 1 _{0.1853 1521.266 4.6C0 0.851 90.3 0.490 -2.4 0.874 -93.6 2.0725-04 -62,0 9.909E-05 -175.} 0,1835

15c4.31q

4.700 0.852 90. 3 0.490 -2.5 0.874 -93.6 2. 0555-04 -62.9 9.414E-05 -175. '0 0.3.817 1587.410 4.800 0.853 90.3 0.490 -2.5 0.874 2.0365-0.4

-63.8

9.0425-05 -175. O.18)0 162r.479 4,900 0.855 90.3 0.490 -2.5 0.873 -93.5 2.01.5-04 -64.7 9.6925-05 -3.75. 0.1784 t65'.'SO '.000 0.856 90. 3 0.490 -2.5 0.873 -93 5 1. 98 E-04 -65.4 3.3615-65 .175. I 1686.521 _{5.100 0.857 90.3 0.490 -2.5 0.873 -93.5 1. 979E-04 -66.2 8.06flE-05 -3.75.}

TANKER FULL'f LOADED LR2570

RUN ON 91OF71

FIG. 7

SEE0

7.7280 WAVE ENCOUNTER F R F 0 U E ti C I E S WAVE ANGLE WAVE LENGTH

60.00 DEG. SHEAR RESPONSE RESULTS (NON-DIMENSIONALI

WAVE/SHIP VERTICAL SHEAR LATERAL SHEAR

LENGTH AMPLITUDE PHASE AMPLITUDE PHASE

1.36498 Oo63086 33.071 0.1000 1.016E-0-3 112.7 1.243E-03 -47.9

0.°65l9 0.59812- 66.142 0.2000 5.473E-03 -44.1 3.147E-03 -100.9 0.78907 0.54336 99.213 0.3000 1.424E-fl2 -157.5 4.914E-02 170.0 0.652',9 0.49896 132.284 0.4000 1.586E-02 15-7.7 4.718E-02 166.2 C.-61044 0.46361 165.355 0.5000 I.306E-02 137.5 3.114E-02 169.2 0.5572S 0.43490 198.426 0.6000 9.629E-0-3 122.9 1.848E-02 176.3 0.51591 0.41104 231.497 0.7000 6.SBOE-03 109.2 _{1.066E-02 -172.7} 0.4B259 0.39083 264.568 _{0.8000 4.631E-03} 93.5- 6.371E-03 -157,0

C.494Q

0.37342 297.639 0.9000 3.451E-03 75.7

4.267E-3 -135.6

0.4314

0.35823 330.710 -1.0000 2.825E-fl3 57.2 3.418E-03 -113.1 0.41156 0.34482 363.781 1.1000 2.543E-03 40.5 -3.159E-03 -95.8 0. 39404 0.33286 396. 852 1.2000 2.432E-03 27.3 3.076E-03 -84.4 0,37558 0.3?211

429.23

1.3000. 2.3Q3F-03 17.3 3.021E-)3 -77.2 0.3641- . 0.31237 462.994 1.4000 2.374E-03 10.0 2.°52E-03 -72.6 0.35244 0.30349 496.065 1.5000 2.355E-03 4.6 2.871E-03 -69.7 0.34125 0.29536 529.136 1.6000 2.-330!-03 0.5

2o777EO3

-67.9 0. 331r6 0.2.9787 562.20-7 1.7000 2.298E-03 -2.6 2.678E-03 -66.7 0.32173 0.28094

55.278

1.8000 - 2.258E-C3 -5.1 2.576E-03 -66.0 0.31315 0.27451 628,349 1.9000 2.214E-O-3 -7.1 2.476E-03 -65.6 0.30522 0.26851 661.420 2.0000 ?.167E-03 -8.7 2.-379E-03 - -65.5 0.29196 0.26290 694.491 2.1000 2.119E-03

10.0

2.256E-03 -65.5

C.29I't 0.25765 727.562 2.2000 2.068E-03 -11.1 2.198E-03 -65.6

0.28462 0.25270 760.633 2.3000 2.017E-03 -12.0 2.-11SE-03 -65.8

0.27861 0.24804 793.705 2.4000 1.967E-03 -12.7 2.036E-03 -66,1

0.273'O 0.24363 826.776 2,5000 1.91SE-03 -13.3 1.962E-03 --66.4

0.26769 C. 7394s 859.847 2.6300 1.870E-03 -13.9 1.8°3E-03 -66.7

0.26269 0.23550 892.918 2.7000 1.823E-03 -14.3 1.829E-0-3 -67.1

.C.2576 0.23174 925.Cqq 2.8000 L.777E-03 -14.7 1.768E-03 -67.4

0.25347 0.22516- 959.060 2.9000 1.733-C3 -15.0 1.711E-03 -67.8

0.24Q21 0.22474

92.130

3.00OO L.AQIE-03 -15.3 1.657E-03 -68.2

0.24516 0.22148 1025,201, 3.1000 1.650E-03 -15.5 1.607E-03 68.6 0.24130 0.21536 1055.272 3.2000 1.611E-0-3 -15.7 1.559E-03 -69.0 0.23761 0.21537 1091.343 3.3000 1.573E-03 -15.9 1.514E-03 --69.3 0.23609 0.21250 1124,414 3.4000 1.536E-03 -16,0 1.471E-03 -69.7 0.233'2 0.20975 1157.486 3.5000 1.501E-03 -16.1 1.431E-03 -70.0 C.2215') _{0.20710 1.140.556 3.6000 l.468F-03} -16.3 1.393E-03 -70.4 0.22440 .0.20456 1273.628 3.7000 1.435F-03 -16,3 1..357F-03 -70.7 0.22143 - 0.20211 1256.699 3.9000 l.404E-03 -16.4 1.323F-03 -71.0 0.21867 -

O,1975

1299. 770 3.9000 1.374E-03 -16.5 1.29O-03 71.4 0. ?15 0.19747 1,322.840 4.0000 1.346E-03. -16.5 1.259E-03 -71.7

0.2131.7 0.19527

1355.I2

4.1000 - 1.318E-03 -16.5 1.230E-0-3 -72.0

0,21062 0.19314

1s.9s3

4.2000 - 1.2,91E-03 -16.6 1.202E-03 -72.3

C.2q16

0.1°105 1422,053 4.3000 1.266E-03 -16.6 1.175E-03 -72.6

!. 2r67R 0.1 808 I 656. 125 4.40-00 1. 241E-03 -16.6 1. 149E-03 -72.8

C.'2f349 0.18717

1490.16

4.5000

1.217E-03 -16.6 1.125E-03 -73.1

C. 7C1'-A 0.19610

1'?I.26

4.6000 1.1°4F-03 -16.6 1.101-01 - -73.4

C,LOQIO - 0.18345 1554.118 4.7000 1.172E-03 -16.5 i.079E-03 -73.6

r, 19702 0, !e172 1597. 410 4.8000 1.

I5CE-03

-16,5

1,57-O3

-73.9

0.i50

0.19002 1620.479 4.9000 1.130E-0-3 -16.5 1.016E-03 -74.1

C.1104

0.17t35

1653.660

6.0000

_1.110t-03

_-16.5

_1.017-03

-743