Midship wave bending moments in a model of the cargo ship California State running at oblique headings in regular waves

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MIDSHIP WAVE BENDING MOMENTS IN A

MODEL OF THE MARINER-CLASS CARGO

SHIP "CALIFORNIA BEAR" RUNNING AT

OBLIQUE HEADINGS IN REGULAR WAVES

SSC-2 02

This document has been approved

for public release and sale; its

distribution

is unlimited.

SHIP STRUCTURE COMMITTEE

NOVEMBER 1969

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SHIP STRUCTURE COMMITTEE

MEMBER AGENCIES: ADDRESS CORRESPONDENCE TO:

November 1969

Dear Sir:

The Ship Structure Committee has sponsored a series of studies relating bending moments and strains

on towing-tank models to those on actual ships. The

enclosed report presents towing-tank data on the

Cali-fornia Bear

for which full-scale data has been

previ-ously obtained.

This report is being distributed to persons

interested in the Ship Structure Committee1s work.

Your comments would be appreciated. Sincerely,

C. P. Murphy j

Rear Admiral, U.S. Coast Guard Chairman, Ship Structure Committee

UNITED STATES COAST GUARD SECRETARY

NA VAL SHIP SYSTEMS COMMAND SHIPSTRUCTURE COMMITTEE

MILITARY SEA TRANSPORTATION SERVICE U.S. COAST GUARD HEADQUARTERS

MARITIME ADMINISTRATION WASHINGTON, D.C. 2059t

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SSC -202

Technical Report

on

Project SR-165

"Bending Moment Determination"

to the

Ship Structure Committee

MIDSHIP WAVE BENDING MOMENTS _{IN A MODEL OF THE MARINER-CLASS} CARGO SHIP CALIFORNIA BEAR RUNNING AT OBLIQUE

HEADINGS IN REGULAR WAVES

by

E. Numata and W. F. Yonkers Stevens Institute of Technology

Hoboken, New Jersey

under

Department of the Navy NAVSEC Contract N00024-67-C-5218

This docwnent has been approved

_{for public release and}

sale; its distribution is unlimited.

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

November 1969

2c2

iuiv6i'

SCHE EPSCONSTRUCTIES

TECHMSCfE !ICGESCHCOL DELFT MEKELWEG 2

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ABSTRACT

Vertical and lateral wave bending moments were measured at the midship section of a 1/96-scale model of the C4-S-1A

MARINER-class cargo ship CALIFORNIA BEAR. The model was self propelled

through a ship speed-range of 10 to 22 knots at seven headings to regular waves of lengths between 0.2 and 2.0 times the length be-tween perpendiculars; moderate wave heights not exceeding 1/50 of

the model length were used. Results are presented in charts of

bending-moment-amplitude/wave-amplitude versus ship speed, with

wave length as the parameter. Two ship loading conditions,

rep-resentative of actual westbound and eastbound trans-Pacific voy-ages are covered.

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CONTENTS

PAG E

INTRODUCTION

i

DESCRIPTION OF THE EXPERIMENT

2 DISCUSSION 6 CONCLUDING REMARKS 7 ACKNOWLEDGEMENTS 7 REFERENCES 15 APPENDIX 16

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The SHIP STRUCTURE COMMITTEE is constituted to prosecute a research to

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

design, materials and methods of fabrication.

RADM C. P. Murphy, USCG - Chairman Chief, Office of Merchant Marine Safety

U. S. Coast Guard Headquarters

Captain W. R. Riblett, USN Head, Ship Engineering Division Naval Ship Engineering Center

Captain T. J. Banvard, USN Maintenance and Repair Officer Military Sea Transportation Service

Mr. J. J. Nachtsheim - Chairman

Mr. J. B. O'Brien - Contract Administrator Mr. G. Sorkin - Member Mr. H. S. Sayre - Alternate Mr. I. Fioriti - Alternate MARITIME ADMINISTRATION Mr. F. Dashnaw - Member Mr. A. Maillar - Member Mr. R. Falls - Alternate Mr. W. G. Frederick - Alternate

AMERICAN BUREAU OF SHIPPING

Mr. G. F. Casey - Member Mr. F. J. Crum - Member

OFFICE OF NAVAL RESEARCH

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

MILITARY SEA TRANSPORTATION SERVICE

Mr. R. R. Askren - Member

Lt. J. G. T. E. Koster, USN - Member

SHIP STRUCTURE COMMITTEE

SHIP STRUCTURE SUBCOMMITTEE

The SHIP STRUCTURE SUBCOMMITTEE acts for the Ship Structure Committee

on technical matters by providing technical coordination for the determination

of goals and objectives of the program, and by evaluating and interpreting the

results in terms of ship structural design, construction and operation.

NAVAL SHIP ENGINEERING CENTER U. S. COAST GUARD

iv

Mr. E. S. Dillon

Chief, Division of Ship Design Office of Ship Construction Maritime Administration

Mr. D. B. Bannerman, Jr. Vice President - Technical American Bureau of Shipping

CDR C. R. Thompson, USCG - Member LCDR C. S. Loosemore, USCG - Member LCDR L. C. Melberg, USCG - Alternate CDR L. A. Colucciello, USCG - Alternate

NAVAL SHIP RESEARCH & DEVELOPMENT CENTER

Mr. A. B. Stavovy - Alternate

NATIONAL ACADEMY OF SCIENCES

Mr. A. R. Lytle, Liaison Mr. R. W. Rumke, Liaison Mr. M. L. Sellers, Liaison

AMERICAN IRON AND STEEL INSTITUTE Mr. J. R. LeCron, Liaison

BRITISH NAVY STAFF

Mr. H. E. Hogben, Liaison CDR D. Faulkner, RCNC, Liaison

WELDING RESEARCH COUNCIL

Mr. K. H. Koopman, Liaison Mr. C. Larson, Liaison

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LIST OF FIGURES

TEXT FIGURES

PAG E

Body Plan of CALIFORNIA BEAR ₃

Vertical and Lateral Bending Moment Balance ₃

Profile of CALIFORNIA BEAR (Photograph), and Bending Moment Balance in Position Across Model _Cut

(Photograph) ₄

Weight Distribution Diagram (Displacement 16,840 _Tons;

Drafts 23.70' Fwd, 25.55 Aft) ₄

Weight Distribution Diagram (Displacement 13,900 Tons;

Drafts 19.25' Fwd, 22.55' Aft) ₄

Vertical Wave Bending Moments (Drafts: 19.25' Fwd, 22.55' Aft; 20 Knots)

8

Vertical Wave Bending Moments (Drafts: 19.25' Fwd, _22.55' Aft; 20 Knots)

8

Lateral Wave Bending Moments (Drafts: 19.25' Fwd, _22.55' Aft; 20 Knots)

9

Lateral Wave Bending Moments (Drafts: 19.25' Fwd, 22.55' Aft; 20 Knots)

9

Vertical Wave Bending Moments (Drafts: 23.70' Fwd, _25.55'

Aft; 20 Knots) ₁₀

Vertical Wave Bending Moments (Drafts: 23.70' Fwd, _25.55' Aft; 20 Knots)

10

11

Vertical Wave Bending Moments (Drafts: 19.25' Fwd, 22.55' Aft; 20 Knots)

12

Lateral Wave Bending Moments (Drafts: 19.25' _{Fwd, 22.55'} Aft; 20 Knots)

12

Vertical and Lateral Wave Bending Moments (Drafts: _23.70' Fwd, 25.55' Aft; 20 Knots)

13

Vertical and Lateral Wave Bending Moments (Drafts: _23.70' Fwd, 25.55' Aft; 20 Knots)

13

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PAG E

Wave Bending Moments (Drafts: 19.25' Fwd, 22.5Y

Aft; 20 Knots) 14

Wave Bending Moments (Drafts: 23.70' Fwd, 25.55'

Aft; 20 Knots) 14

APPENDIX FIGURES

Vertical Wave Bending Moments (Drafts: 19.25 Fwd, 22.55'

Aft; 1800 Heading) 17

Vertical Wave Bending Moments (Drafts: 19.25' Fwd, 22.55'

Aft; 180° Heading) 17

Aft; 900 Heading) 18

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vii

A-15. Lateral Wave Bending Moments (Drafts: 19.25' Fwd, 22.55'

PAG E

Aft; 1800 Heading) ₂₀

Aft; 120° Heading) ₂₁

Aft; 60° Heading) ₂₂

A-23. _{Lateral Wave Bending Moments (Drafts: 19.25' Fwd, 22.55'}

Aft; 30° Heading) ₂₂

A-25. _{Lateral Wave Bending Moments (Drafts: 19.25' Fwd, 22.55'}

Aft; 0° Heading) ₂₃

A-25.

Vertical Wave Bending Moments (Drafts:

_23.70'

Fwd,

25.55'

Aft; 1800 Heading) ₂₃

A-27. _{Vertical Wave Bending Moments (Drafts: 23.70' Fwd, 25.55'}

Aft; 180° Heading) ₂₃

Aft; 1500 Heading)

23

A-2g. _{Vertical Wave Bending Moments (Drafts: 23.70' Fwd, 25.55'}

Aft; 1500 Heading) ₂₄

Aft; 120° Heading) ₂₄

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viii

A-32. Vertical Wave Bending Moments (Drafts: 23.70' Fwd. 25.55'

PAG E

A-33. Vertical Wave Bending Moments (Drafts: 23.70' Fwd, 25.55'

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INTRODUCTION

In 1960 the Ship Structure Committee authorized Davidson _{Laboratory to initiate}

a research program entitled ''Bending Moment Determination,'' using ship-model _tests

to investigate hull bending moments in regular and irregular waves.

The initial phase of this program, Project SR-l57, covered investigations of

trends of midship bending moment as a function of wave steepness in models of

a MARINER-class cargo ship with variations in freeboard and weight distribution,

a destroyer, and (3) a tanker. _{Dalzell''2 concluded that, within practical}

operational and design limits, no dramatic upper limit of wave bending moments at

amidships is to be expected as the ratio of wave height _{to wave length increases to}

a value of about 1:9.

Since this conclusion was limited to midship bending _{moments, and} _{it was known}

that maximum moments under certain circumstances could occur elsewhere, the next

phase of the study, Project SR-l65, examined the longitudinal _{distribution of}

bend-ing moments in a MARINER-class cargo-ship model _{in regular waves of extreme steepness.}

Maniara4

concluded that, within practical operational limits of _{speed for the MARINER,}

maximum wave bending moments would occur in the region from amidships to 0.]25L aft

of amidships. _{Thus the practice of concentrating on midship bending moments both in}

design studies and _{in full-scale measurements appears to be justified.}

Another part of the investigation involved the testing of the MARINER model in

high irregular waves to obtain time history records of _{wave bending moment and wave}

elevation. _{Wave and bending moment energy-spectra were computed and used to derive}

equivalent regular-wave bending-moment ''response operators'' which were shown to be in reasonable agreement with response results obtained from model tests in regular waves.

Such favorable agreement inspires confidence ¡n the alternate procedure of

using a ''response operator'' from tests in regular waves to predict the energy spectrum

of bending-moment response of either a ship model _{in a known wave-spectrum or a ship}

in a real seaway the energy spectrum of which can be determined. _{Before taking this}

latter step, however, it is necessary to demonstrate satisfactory correlation

be-tween model and ship bending-moment responses.

Over a period of years, full-scale statistical data _{on midship bending-moment}

responses have been collected by the Teledyne Materials Research Company (under

Project SR-l53), on several vessels including (i) the MARINER-class _{cargo ship}

CALIFORNIA BEAR operated by the Pacific Far East Line in _{trans-Pacific service}

between San Francisco and Yokohama and (2) the cargo ship WOLVERINE STATE operating

on the United States-Northern Europe route in the North Atlantic Ocean. _Davidson

Laboratory proposed the conduct of scale-model tests of these vessels at various

speeds and headings in regular waves, to obtain bending-moment _{response operators.}

Webb Institute of Naval Architecture, _{in a parallel effort, proposed an analysis}

of statistical data for the ships and the prediction of ship bending-moment

statistics from Davidson Laboratory's model-test results. _{The tests of the}

WOLVERINE STATE model have been reported ¡n Reference _5.

This report describes the tests of the CALIFORNIA BEAR model _{at Davidson}

Lab-oratory, under Project SR-l65, and presents the wave-bending-moment results which

have been used by Webb Institute in their model-ship correlation _{program under}

Project SR-177.

Two ship loading conditions were used in this experiment. _{Both were taken}

from the reported cargo and tankage distributions for actual _{trans-Pacific voyages}

of the CALIFORNIA BEAR, on which the Teledyne Research Corporation _{had installed}

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-2-DESCRIPTION OF THE EXPERIMENT

Model

The tests were conducted on a 65-inch (1/96-scale) fiberglass model of a

stand-ard MARINER-class cargo vessel. This model was originally built for the tests

reported in Reference 3. Figure 1 shows the body plan. The model was cut at a

point corresponding to 260 feet aft of the ship's fore perpendicular. The two halves

of the model were connected by the standard Davidson Laboratory two-component

bend-ing-moment balance, illustrated in Fig. 2. This balance consists of two pedestals

with an integral flexure beam of cruciform cross-section milled from a single block

of aluminum alloy. The componental deflections of the beam in its vertical and

lateral planes of symmetry are mechanically amplified by linkages and sensed by

linear variable differential transformers. Figure 3 is a photograph of the model

in profile and a photograph of the setup of the bending-moment balance across the model cut. The midships cut was sealed with a thin sheet of rubber fixed to the hull with vinyl-plastic electrical tape.

An electric propulsion motor was installed to turn a stock four-bladed

pro-peller of approximately the desired scale diameter. The rudder was built to scale

and was operated by a servomotor which formed part of an automatically controlled steering system.

Loadinq Conditions

Pacific Far East Line made available complete records of cargo and tankage distributions for nine voyages covering two years of instrumented operation between January 1966 and December 1967.

Two representative loading conditions were used for ballasting the model.

For the first condition, representing a full load of cargo typical of a westbound

voyage (San Francisco to Yokohama) of the CALIFORNIA BEAR, the loading condition

chosen was that of westbound voyage number 33 of October 1967. The mean draft

on this voyage was nearly identical to the average of the mean drafts of nine

westbound voyages, numbers 25 through 33. Figure 4 is a weight distribution diagram

for westbound voyage 33, and shows a displacement of 16,840 tons at a mean draft, at mid-voyage, of 24.6 feet with a trim of 1.8 feet by the stern.

The second condition was meant to represent a low-density, dry-cargo loading

typical of an eastbound voyage from Yokohama to San Francisco. The average of the

displacements of the nine sample eastbound voyages was 12,000 tons. This value

was too low to be simulated on the model. To facilitate proper ballasting of

the model, the cargo-loading of eastbound voyage 25 of March 1966 was chosen. Figure 5 is the weight distribution diagram for this voyage and shows a displace-ment of 13,900 tons at a mean draft, at mid-voyage, of 20.9 feet with a trim of 3.29 feet by the stern.

Reported cargo and tankage distributions were used to simulate each loading

condition on model scale. Each half of the model was ballasted to the desired

scaled values of weight, LCG, and pitch gyradius. Gyradius was checked by

sus-pending each model-half from a knife edge, oscillating it as a compound pendulum,

and measuring its natural period. The gyradius was calculated from this period

and the distance from the knife-edge to the CG. Tare weights were substituted for

the bending-moment balance to permit separate ballasting of the model-halves. The vertical center of gravity of each half was adjusted to a common value based

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i

-3-13

Fig. 1. Body Plan of CALIFORNIA BEAR

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Fig. 3. Profile of CALIFORNIA BEAR

Fig. 5. Weight Distribution Diagram Displacement: 13,900 Tons Drafts: 19.25' Fwd, 22.55' Aft

-4-Fig. 3. Bending Moment Balance in Position Across Model Cut

Fig. 4. Weight Distribution

Diagram Displacement: 16,840 Tons Drafts: 23.70' Fwd, 25.55' Aft net 50 20 500 300 200 00 A. P. 500 ¡.00 00 200 loo

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-5-on the reported loading. Ballast was adjusted laterally to obtain the scaled

value of the natural rolling period of the complete model. The ship characteristics

for the two loading conditions are tabulated below.

TABLE OF SHIP CHARACTERISTICS

Length Between Perpendiculars, ft . . . 528.0

Beam, ft 76.0

Displacement, long tons

Draft

Fore perpendicular, ft Aft perpendicular, ft Mean, ft

LCG aft of amidships, ft

Pitch radius of gyration, ft

Natural rolling period, sec

Fo re body

Displacement, long tons LCG forward of amidships, ft Pitch gyradius, ft

VCG above baseline, ft

Af te r body

Displacement, long tons LCG aft of amidships, ft Pitch gyradius, ft VCG above baseline, ft

Apparatus

The experiment was conducted in Davidson Laboratory's Tank 2 (75' x 75' x 4.5'). This facility includes a wavemaker along one 75-foot side of the tank, a wave

ab-sorber along the opposite side, and _{a movable bridge spanning the tank.}

The bridge

supports a monorail carriage driven by a servo-controlled _motor.

Suspended from the carriage is a six-degree-of-freedom motions apparatus which

is servo-driven to follow a self-propelled, automatically _{steered model} _{in waves.}

A vertical heave rod rides _{in bearings on the apparatus and} _{is attached to the}

model through a three-degree-of-freedom gimbal. _{Power and control wires for the}

rudder and propulsion motors, as well as signal cables from the bending-moment

balance, are led upward to the carriage and thence to _{a recording and control station}

at tankside. _{The moment-balance output signals were fed through} _{a Snborn 350-1100}

Series carrier amplifier system, and then through Krohn-Hite Model 335 low-pass active

filters to minimize high-frequency ncise in the records. _{The signals were then}

dis-played by a visicorder Model 1108 as time histories _{on oscillograph chart paper.}

ne heights of all regular waves were calibrated before model _{tests, by}

traversing the "reading" section of carriage travel with a resistance-type wave

probe at the model location. _{The resulting records of wave-elevation}

time history Eastbound 13,900 19.25 22.55 20.90 9.9 123.0 14.4 6,129 105.0 68.9 24.0 7,771 100.5 70.3 2L.0 Westbound 16,840 23.70 25.55 24.62 8.8 123.6 16.7 8,073 98.2 66.5

270

8,767 107.2 71.4 27.0

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-6-were reduced to obtain the average wave height for each wave length at each bridge

heading. During each test of the model, the wavemaker speed-control was adjusted

to maintain the wave period used during the wave calibrations. This procedure was

preferred to the measuring of the wave elevation during each model run, because it

is known that model-generated waves can influence wave-probe readings.

Test Procedure

The bridge was positioned for model headings of 180 degrees (head seas),

150 degrees, 120 degrees, 60 degrees, 30 degrees, and zero degrees. At each

head-¡ng angle, at least eight wave lengths were tested and a minimum of three speeds

in the range of 10-22 knots, full scale. A nominal wave height of 1/50 of the

model length was used for all waves except the relatively short ones, for which a

reduced height was substituted. The mean speed of the model was averaged over a

distance of about four model lengths (20 feet).

The bending moment balance was calibrated periodically by applying known moments to the model while it was afloat.

Data Reduction and Presentation

Time histories of vertical and lateral bending moments were reduced to obtain

the average range of moment during the 20-foot interval of model travel. The

phase between the two moments was also determined.

The moment data are presented in dimensional form (bending-moment-amplitude! wave-amplitude in ft-tons/ft) as trends versus ship speed for all wave-length!

ship-length ratios at a given heading angle; separate charts are presented for

vertical and lateral moments. Figures A-1 through A-25 of the Appendix contain

the results for the 20.9-ft mean draft condition; Figures A-26 through A-45 present

the results at 24.6-ft mean draft. The reported bending moments are due solely to

wave-induced loads and are measured with respect to a still-water datum.

Still-water hogging moments were 86,000 ft-tons at 20.9-ft mean draft and 70,000 ft-tons at 24.6-ft mean draft; these are calculated values.

Phase is presented as the lag of lateral moment behind vertical moment for a

given wave-length/ship-length ratio. The phase results are consistent with a

heading-angle convention of representing head seas by 180 degrees and following seas

by zero degrees. At intermediate heading angles, the waves approach the port bow

(150 degrees, 120 degrees), the port beam (90 degrees), or the port quarter (60 degrees, 30 degrees). Each phase angle is the lag of starboard lateral moment behind hogging vertical moment, with a starboard lateral moment corresponding to

a hull-deflection curve which is concave to starboard. The phase results are

presented in tabular form in Tables A-1 and A-Z of the Appendix; a single phase value is given for each combination of heading angle and wave-length/ship-length

rat io.

DISCUSS ION

The object of this investigation was to obtain wave-bending-moment response

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-7.-prediction-and-correlation project. The moment curves and phase results in the

Appendix are convenient and practicable for the purpose. Sample response-curves

for the average Pacific crossing-speed of 20 knots have been constructed from the charts in the Appendix and are shown in Figs. 6-13.

The double peaks in some of the vertical-moment curves, Figs. 6, 7, 10, and

Il, have been documented by investigators at the St. Albans Tank in England (most

recently by Murdey6), but only for head seas. Murdey, with the help of

analy-tical predictions of the inertial and hydrodynamic components of veranaly-tical moment,

explains why the peaks occur. He shows that each component contributes one peak

to the total vertical moment. Fukuda,' using an analytical prediction technique,

has found double peaks in vertical-moment response curves for other heading

angles.

A typical set of vertical-moment response curves, Figs. 6 and 7 for example,

shows a consistent tendency for the moment peaks to shift to shorter wave lengths

as the heading angle changes from O or 180 degrees to 90 degrees. In 180-deg

head seas the peak moment occurs in a wave length about equal to the ship length.

Thus it may be visualized that maximum sagging moment occurs when the trough of

such a wave is at amidships with wave crests near each perpendicular. To obtain

a similar wave-ship geometry, at a 120-deg heading, the wave length should be

about equal to the effective ship length (i.e. , L cos ) where L is ship length

and L is heading angle.

Figures 1/4-17 show trends of wave bending moments versus wave length/L cos

for the various heading angles at a ship speed of 20 knots. This method of w

plotting shows that the moment peaks generally occur at a constant value of

wave length / L cos of about 0.9.

Figures 18 and 19 show cross-plots of moments versus heading angle at a

value of wave length / L cos of 0.9; with certain exceptions, noted by

asterisks, these are curves of peak values. Data were taken at too few headings

to permit definition of the angles at which maximum moments occur. However, the

general headings at which highest values occur are head _{seas for vertical moment}

and bow seas (about 130 degrees) for lateral moment. Both moments exhibit

secondary peaks in quartering seas (about 50 degrees). These trends are in

general agreement with analytical predictions for a ship of similar fineness,

7

by Fukuda.

CONCLUDING REMARKS

The primary objective of this experimental model _{investigation was to obtain}

wave-bending-moment data and to reduce them to a form usable by Webb Institute

for correlation with full-scale measurements. _{This has been accomplished and the}

general trends of the results appear reasonable when _{compared with published data.}

Analysis of the results shows that peak moments tend to

occur--At a constant value of wave length/effective ship _{length, and}

In head seas for vertical moment and in bow seas for lateral moment.

In view of the self-sufficient nature of these _results, _¡t _{is recommended}

that no further model testing be conducted in connection with the CALIFORNIA BEAR project.

ACKNOWLEDGEMENTS

The authors wish to thank two persons who made significant contributions

to this investigation: _{Mr. V. J. Bahorich, Superintending Engineer, Pacific}

Far East Line, for furnishing an extensive amount of information _{on the loading}

statistics of the CALIFORNIA BEAR; and Mr. M. J. Chiocco, for conducting the model investigation of the westbound loading condition.

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Vertical Monnt Amplitude i",ve Amplitude IO 000 5, 00O 10,000 5,000 Ft-Tons Ft 60° Heading -8-o 30 Head,ng o O Heedina 2.0 o 0.5 1.0 1.5 2.0 Wave Length Ship Length

Fig. 7. Vertical Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft Speed:

20 Knots

0 LO I '5

Wave Length

Ship Length

Fig. 6. Vertical Wave Bending Moments Drafts: 19.25' Fwd 22.55' Aft Speed: 20 Knots

Vertical rjce,ent Arnplitode

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Lateral Morneet An,plitude Wave Arl jtud

IO 000 5,000 10,000 5,000 -9-. o 0.5 1.0 2.0 Wave Length Ship Length

Fig. 8. Lateral Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft Speed: 20 Knots

Lateral Moment Amplitude

Wave Amplitude

O _0.5 _1.0

1.5 2.0

Wave Length

Ship Length

Fig. 9. Lateral Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft Speed: 20 Knots

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Vertical Mompnt Amplitude Wave Amplitude 10,000 S 000 Ft-Tons Ft Ft-Toe,s Ft _{120° K1adlng} p

-10-180° Heading 1SO° He.4lisg

o 0.5 1.0 1.5 2.0

Wave Lenqth

Ship Length

20 Knots

Vertical Wø,nent Amplitude Wave Anlitude

0 0.5 1.0 1.5 2.0

Wave teeqth Ship Length

20 Knots

10,000

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Lateral Moment Amplitude Wave Amplitude 0, 000 5 000 IO, 000 ,000 Ft-Tons Ft Ft -Tons Ft -11-0 0.5 1.0 1.5 2,0 Wave Lenqth Ship Length

Fig. 12. Lateral Wave Bending Moments

20 Knots

Lateral Mo,nent Amplitude

Wave Amplitude

0 0.5 1.0 1.5 2.0

Wave Length Ship Length

Drafts: 23.70 Fwd, 25.55' Aft Speed:

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20 Knots

-12-Uteral

MOn,ent Aeplitvde Wave kept i fl,de

8.00 6,000 'v.000 2 000 .000. 2.000 Ft -Tvn Ft

Wave Lenqtfl

Ship Length cot vv,

HEAD ING O 0° D 30° ¿5 60° HEAD I HG O 80° D 150° , 20°

k A p p

e e 0.5 0 1.5 2.0 2.5 3.0 O" O O n 0.5 .0 .5 2,0 2.5 3.0 0.5 .5 2.0 2.5 3

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Vertical Monent Anpiitcde Wave Aeplitude 6,000 4,000 2,000 Ft-Tong Wave Length

Ship Length cot V.a VENTI CAL

Fig. 17. Vertical and Lateral Wave

Bending Moments Drafts: 23.70' Fwd,

25.55' Aft Speed: 20 Knots

-13-Fig. 16. Vertical and Lateral Wave

Bending Moments Drafts: 23.70' Fwd,

25.55' Aft Speed: 20 Knots

Vertical Moment Amplitude

Wave Amplitude

Late al Moment A.npiitude Wave Anpiitude

6,000 Ft-Tong Ft

0.5

Wece Lenqth

Ship Length cog

1.0 2.0

HEAD I NG

Lateral nennt Anni itude LA T E RA L ₀ 0 Wave Aepi iOud

D 30° HEADING 0 80° LATERAL _o _50° A loon 10,000 8,000 6,000 1. .000 2,000 HEAD i NG o o D 300 A 60° 0.5 1.0 2.0 2 .5 3 .0 1.0 2.0 3 .2 4,000 2,000

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Moment AvpIi1de Wvn vplitode

Wave Length Ship Length tot

-Keding Angit dep

Fig. 19. Wave Bendinq Moments

Drafts: 23.701 Fwd, 25.55' Aft Speed:

20 Knots

-14-Mov,evt Avplitvde Wave Anpiltode

Fig. 18. Wave Bending Moments Drafts:

19.25' Fwd, 22.55' Aft Speed: 20 Knots

Wv Ltngth

Ship Length von

Heading AngIe A, deg

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-15-REFERENCES

DALZELL, J. F., An Investiqation of Midship Bendinq Moments Experienced in

Extreme Reqular Waves by Models of the MARINER Type Ship and Three Variants. Ship Structure Committee, Serial SSC-155, January l964.

DALZELL, J. F., An Invest iqat ion of Midship Bendinq Moments Experienced in

Extreme Requ lar Waves by Models of a Tanker and a Destroyer. Ship Structure

Committee, Serial SSC-l56, February l964.

MJkNIAR, N. M., Invest iqation of Bendinq Moments Within the Midship Half Lenqth

of a MARINER Model in Extreme Waves. Ship Structure Committee, Serial SSC-l63,

June l96L+.

t4ANIAR, N. M. and NUMATA, E., ''Bending Moment Distribution in a Mariner Cargo

Ship Model ¡n Regular and Irregular Waves of Extreme Steepness,'' Davidson

Laboratory Report 1091+, Stevens Institute of Technology, March 1968.

CHIOCCO, M. J. and NUMATA, E., "Midship Wave Bending Moments in a Model of the Cargo Ship WOLVERINE STATE Running at Oblique Headings in Regular Waves,'' Davidson Laboratory Report 1299, Stevens Institute of Technology, October 1968.

MURDEY, D. C., ''On the Double Peaks in Wave Bending Moment Response Curves,''

Trans., Royal Institution of Naval Architects, 1968.

FUKUDA, JUN-ICHI, "Computer Program Results for Response Operators of Wave

Bending Moment ¡n Regular Oblique Waves.'' Reprint from Memoirs of the Faculty

of Enqineerinq, Kyushu University, Vol. XXVI, No. 2 (contribution to 3d

(26)

-16-APPENDIX

TABLE A-1. MOMENT PHASE ANGLES

19.25' 22.55' Aft

Drafts: Fwd,

Lateral moment after vertical moment.

Phases constant with speed from 10 to 20 knots. Headings Wave Lenqth Ship Length

30°

600 90° 1200 1500 0.20 - 200 -1-f0 175

-0.30

-

175

- 80

160

-o.Lo

165 150

- 55

170 135

0.50 -

1140

-

170 160

0.60

170 135 80 155 155

0.70

180 90 - 150 155

0.80

175 95 165 1145 155

0.90

190

-

1145 150 1.00 200 140 200 1145 1145 1.10 200 - - - -1.25

-

1145 1.50 205

-65

190 120 150 1.75

-2.00

220 - 11-fO

(27)

-17-TABLE A-2. MOMENT PHASE ANGLES

Lateral moment after vertical moment.

Phases constant with speed from 10 to 20 knots. Wave Lenqth Drafts: 23.70' Fwd, 25.55' Aft Headings 300 600 _90° _120° 150° Ship Length 0.20 - 85 - 140 0.30 - 165 - 150 0.40 190 160 - 160 130 0.50 180 155 - 150 145 0.60 - - - 145 -0.70 195 145 55 145 150 0.80 180 - - 140 140 0.90 - - - 135 1.00 180 90 130 140 135 1.10 - - - 140 1.25 ₁₈₅ - 185 135 145 1.50 185 75 175 145 1.75 200 155 - 135 2.00 - - -

(28)

-Vert cal Pte.ent AmpI ¡t,de

WVoe Aeplitade

10.000

Vertical Mocont Amplitud.

W.ae Amplitude

- 5,000

'5 Speed. (flots

20

Fig. A-1. Vertical Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft 180° Headi ng dace Length Ship Length 0.70 0.80 0.60 0.50 2 00 0.1.0 Atme Length Ship Length

Fig. A-3. Vertical Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft 150° Heading

-18-Vertical Mc,,,ent Aeg,ltuae

Waoe Ar,plitad

- 15,000

0,000

V.rti.l tto,nert An,plitude

Asce Amplitude ts,000 Ft;Toe, G c.V 5.000 Speed, (cot, o

Fig. A-2. Vertical Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft 180° Headi ng dace Length Ship Length 0.90 t .00 .25 t'so '.75 Wace Length Shjp Length

Fig. A-4. Vertical Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft 150° Headi ng 10,000 10.000 tu ______ .00 0.000 tu V __._._..__. ç' 0.60 I .25 0.40 'A 0.90 - 5,000 lu p, 0.50 .50 , IO IS 20 5 20

Speed, Knott Speed, (cut,

(29)

5.000

Vertical Mon.ent A,nplitude lieve Anplltude

Fig. A-5. Vertical Wave Bending Moments Fig. A-6. Vertical Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft 120° Drafts: 19.25' Fwd, 22.55' Aft 120°

Heading Heading 20 0 50 0.1.0 0.70 0.30 0 .50 Wage Length t1.ip Length 0.30 02 0.80 i: 0.60 O - D .00

Fig. A-7. Vertical Wave Bending Moments Drafts: 19.25' Fwd, 22.55'Aft 900

Headi ng

-19-5,000

Vertical Mottttnt Anrplilvde

Wave Anpiltude

V

Speed, Knots

Fig. A-8. Vertical Wave Bending Moments Drafts: 19.25' Fwd, 22.55'Aft 90° Headi ng 20 R 000 2.00 W... Langth Ship Length 0.1.0 0.10 0.60 o ₀₀ 0.80 A A & A A 0.90 0 .00 0.20 IO IV 20 Speed, Knott

ArVicel ton.ent Aetti itode Wane Length

Wave Anpiitde Ship Length

Vertical Matent Atpl Rude Wave Length

Wave Anplitde Ship Length

- 15.000 _f0215 0,000 0 o o o FI R 02 r' n '.50 IS 20 o A lO, 000 5,000

(30)

Vtrticál Pnent Anplitude Wave Amplitude 15,000 f100' 10.000 Ft 10

Vertical Itment Amplitude

Wave Amplitude 0,000 5,000 lo '5 lO 15 20 15 Speed, Knott 20 20 Wave Length Ship Length 0.1.0 0.30 0.80 0.20 Wage Length Ship Length

-20-Adrtical non,ent Aeplitude

Waue Amplitude

5,000 f11200

10,000

5,000

Wert cal tnpnpn A,,pl ittde

Wave Amplitude l5,O00 Ft-Tong 10,000 5,000 Lo Lo Speed, Knott

Fig. A-11. Vertical Wave Dending Moments Fig. A-12. Vertical Wave Bending Moments

Heading Heading 20 o Wave Length Ship Length 0.50 0.60 0.70 00 Lo 1.50

Fig. A-g. Vertical Wave Bending Moments Fig. A-lO. Vertical Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft 600 Drafts: 19.25' Fwd, 22.55' Aft 600

Heading Heading WOW. Length Ship Length 0.80 0,80 1.50 2.00 Pttu,, 0.1.0 IO 20 10,000 Q t 0.70 1,00 E o 5,000

(31)

Vertical Montent Amplitude

ldaoe Amplitude

5,000

-3,000

.3,000

Drafts: 19.25' Fwd, 22.55' Aft 0° Drafts: 19.25' Fwd, 22.55' Aft QO

Heading Heading

LaterOl Moment Amplitude Wave Ampi Ilude

3,000

Speed, Knott

Speed. Knott

Wave Length Vertical Moment Amplitude

Ship Length Wave Vntplltude

0.90 1.00 1.10 0.50 l.50 Wave Length Ship Length

Fig. A-15. Lateral Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft 150° Headi ng

-21-15,000 f

'

0,000 5,000

Lateral montent Amplitude Wave Amplitude 3.000 Tont 15 20 Speed, Knots Speed, Knott .75 2.00 Loa 15 20 Wave Length Ship Length Wave Langth Ship Laegth

Fig. A-16. Lateral Wave Bending Moments Drafts: 19.25' Fwd, 22.55' Aft 150° Headi ng 0.70 0.50 '.25 .50 9 9 p .7\ u'

0 0

0.90 050 0 p, .A..Ñ. 'to 0.110 lo 3,000 5 o 20 0.80 0.110 0.50 .75 2.00 0.60 .25 IO IS 0.60 0.90 1.00 3,000 0.70 O , OtO p 1.50 20 IO IO IO IO '5 lo 30

(32)

5,000

lo oc o

Speed. Keats

Fig. A-17. Lateral Wave Bending Moments Fig. A-18. Lateral Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft 1200 Drafts: 19.25' Fwd, 22.55' Aft 1200

Heading Heading -22-.5,000 5,000 g C) ,, 0 0 0.50 0.20 5 20 lO 15 20 lO 15 20

Heading Heading

Lateral nopent Ampi itude Wape Lemçnh

Waue Amplitude Ship length

5,000

o -O

&

0.70

o

0 so

20

I 40p.nt Amplitude Wave Lemgth

W.v. Amplitude Ship Length

5.000 O 0.90 tuAA A A .50 5.000 V u, '0' 0.00 0 0 0 C e0 0.00

ter.l ttnant AmpI itude Wave Leegah Panent Anm,litude

Wate Amplitude Ship Length Wan. Anelitude Ship Length

lo 15 20

(33)

Jeter. Homer. ApIItde Wave Amplitude 5,000 0.00 0.00 Wave Length Sisip Length 0.80 t .10

-23-3..t.r.t Mo..nt Amplitude Wave Length Lateral t'cnwnt Ampi itude Wave Length Wave 0a,pitvde Ship Length Wave Anpiltude Ship Length

5,000

io

II4o,eeet A_el lead. Wave Amplitude

5.000 Lvrt

5,000

u u

lis

Heading Heading 20 20 20 0.1.0 0.60 t_.50 WOre length Ship Length

Speed, Knott Speed, KAnt,

Drafts: 19.25' Fwd, 22.55t Aft 30° Drafts: 19.25' Fwd, 22.55' Aft 30°

Heading Heading Io is o 0.60 0.00 Is 20 .5,000 0.30 0.20 )0 is 20 I5 00

(34)

Pntnr Aepi tode W.oe Aeplitode ¡0,000 5 000 ¡5,000 ¡0 5.000 0.50 0.70 0.80 C

'°

--Speed, KtrotS

Fig. A-25. Lateral Wave Bending Moments

Drafts: 19.25' Fwd, 22.55' Aft 00

Headi ng

Wan. Length Ship Length

10 20

Fig. A-27. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 180° Heading C 0.80 ¡.25 0.50 0.50 Aeon Length Ship Length

-24-VertIpel qt.eent Wnpiitude Wane Pjnplltude

¡s.000

¡0.000

5.000

Sp.e. Knots

Fig. A-26. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 180° Heading Wave Length Ship Length Octe Length hlp Ltgth ¡0 ¡5 20 Speed, Knots

Fig. A-28. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 1500 Heading ¡.00 0.95 I .25 t 50 5.000 _Ft 'IO .25 .50 .75 2.00 ¡5.000 Ft-Tons 1.00 o 0.60 ¡0,000 .50 ¡.75 5.000 20

erticel MotrOnt doiplitude Vertital Moniert O.tplitude

(35)

Vert,col Moment Poitode

Wane nplit.da

cal tossent WoplItod. Wane onpIlt.de

Speed, Knots

Speed. Knots

Fig. A-29. Vertical Wave Bending Fig. A-30. Vertical Wave Bending

Moments Drafts: 23.70' Fwd, 25.55' Moments Drafts: 23.70' Fwd, 25.55'

Aft 1500 Heading Aft 120° Heading

15 20

lo 20

-25-Vertical Moment VInpllnude WOVe 00piitude

VeptiSol Moment Ñnplitude Wane Mnplituàa 2,000 .000 .000 000 2.00 Q

p.

t.00 1.25 Ship Length 0.70 .5° 10.000 A A

'

1.10 0.80 0.70 0 50 0,000 0.50 5,000 VI o )6 0.60 0.80 6,000 Q V 5 175 0.1.0 Speed. niions lo 15 20 Speed. Knots

Fig. A-31. Vertical Wave Bending Fig. A-32. Vertical Wave Bending

Moments Drafts: 23.70' Fwd, 25.55' Moments Drafts: 23.70' Fwd, 25.55'

Aft 120° Heading Aft 90° Heading

Wane Length Ship Length 5,000 WOve Length SO,0 Length 5,000 Ship 10,000 0.70 5,000 0.20 X lo 20 A A .25 'V I75

(36)

15.000 LLIcnt

0,000

5.000

Ver ti cal Mutent Pupt i tude WaVe P.nplitude 5,000 FI-bec 10.000 5.000 .00 .020 4 Speed. tette

Fig. A-33. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 60° Heading

15 20

Speed. Knots

Fig. A-35. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 30° Heading -0.50 0.70 20 W.V. Length Ship Length W.V. Le.gth Ship Length 0.70 ¡.00 0.50

-26-Vertical OWnent lWnplltud. Vertical Canent Pcçlitude

W.V. npiitWe dace PupItudt

5.000 Ft-Tons o 10,000 0 o 5.000 o 030 4

Vert V.1 no.0,5 - II tOde

WaVe eecl,tude

15,000

5,000

Speed. tflcts

Fig. A-34. Vertical Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 60° Heading 08V 4 20 Wact Length Ship Length

Fig. A-36. Vertic) Wave Bending

MomerTtsThrafts: 23.70' Fwd, 25.55' Aft 30° Heading Cae. 1.0geV Ship Le.,gth 0.1.0 ¡.25 __4r__V_____ 1.25 .50 1.70 o .o V 0,000 7V 10 Speed. ente.

(37)

Vertical Moeent PinpIltude Wt4't,ç.l Konent ß.epltud.

Wane delitut W.nt WnpI ilude

Latera Iflottent AtiçIttade

W.ce Aagtlltade 2,000 .000 .000 -27-5,000 on. 0,000 5,000

L.te.'al flottent Peel i lade W... taeptilud. Wane L.ngth Ship Leegth ¡.75 Weve Length rc_To, e C Vene L,gth Ship Length 0.68 4,000 Shtp Length 0,00 0.50 1.75 0.90 0.40 2, ttofl _o _O C I25 e 1,50 4.000 2,000 1.00 1.20 .50 4.000 0.70 Speed, Knott 20

-

Q 0.50 Otto

00

'.75

Speed. Knot. Speed, (not.

Drafts: 23.70' Fwd, 25.55 Aft 0° Drafts: 23.70' Fwd, 25.55' Aft 0°

Heading Heading

to 20

Speed, Knott

Fig. A-3g. Lateral Wave Bending Moments Fig. A-40. Lateral Wave Bending

Mo-Drafts: 23.70' Fwd, 25.55' Aft 180° ments Drafts: 23.70' Fwd, 25.55' Aft

Headi ng 150° Heading Wane Length Ship Length 0.80 10.000 .10 t .25 5,000 0.60 0.50 20 lo 20

(38)

Fig. A-41. Latera' Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 1200 Heading 5.000 5.000 * Speed, Smut.

Fig. A-43. Lateral Wave Bending Moments Drafts: 23.70' Fwd, 25.55' Aft 60° Heading

20

-28-Lateral flamee t W.epl t lude

Wave Amplitude

2,000

2.000

C

Fig. A-42. Lateral Wave Bending Mo-ments Drafts: 23.70' Fwd, 25.55' Aft 90° Heading 15 Speed. Knots 20 Wave Lnmgnh SStip Length l-75 4.- î 1,25

Fig. A-44. Lateral Wave Bending Mo-ments Drafts: 23.70' Fwd, 25.55' Aft 3Q0 Heading 0.50 0.1,0 1.50 Q Q 1.00 6,000 04.2 -ö 2,000 LA I 50 I. .000 060 o o o _0.70 2.000 2.00 2.1.2 00 0.70 082 2.000 1.00 D Q 0 ,'. 020 C t'; o

0-2 35 0.20 0 70 5.000 LS 0 z, 0.70 0.80 1.30 1.25 1.75 C

Lateral Moment 4,plitud. iMoneen Amplitude

Wate Amplitud. Wave Ampi itude

UCve LCmSth 5,000 FI-Tono Wave Length

nt SoIpL,mnh Ship Length

L. a1 MOee,,t leelitue A... OvepliOude Wave Lemqth ShIp Length C, _o 0.50 0.30 1.25 14.000 2,000 .4 A A 15 20 Speed, K,,.t, 15 20 Spend, Smelt 20 IO 20

(39)

Later. Hoe,ent Mpl i tud. 6e 2,000 f,ì0n2. 2,000 2,000 -W.oe Lenqth ti p Ltgth 0.70 0.90 .10 '.75 o

-0 0,50 X 0.60 L 0.80 lU 5 20 Speed, Knots

Fig. A-45. Lateral Wave Bending Mo-ments Drafts: 23.70' Fwd, 25.55' Aft

QO

Heading

o 1.00

7< 1.25

(40)

UNCLASSIFIED

Security Classification

DD FORM 4473

_1JAN54

I _UNCLASSIFIED

Security Classificaon

DOCUMENT CONTROL DATA - R&D

(Security classification of title, body of abstract and indexing annotation must be entered when the overall report s classified)

1- ORIGINATIN G ACTIVITY (Corporate author)

Davidson Laboratory

Stevens Institute of Technology

2e. REPORT SECURITY C LASSIFICATION

Unclassified

GROUP

3 REPORT TITLE

MIDSHIP WAVE BENDING MOMENTS IN A MODEL OF THE MARINER-CLASS CARGO _SHIP

"CALIFORNIA BEAR" RUNNING AT OBLIQUE HEADINGS IN REGULAR WAVES 4 DESCRIPTIVE NOTES (Type of report and inclusive dates)

Technical Report

5. AUTHOR(S) (Lest name, first name, initial)

Edward Numata

William F. Yonkers

6. REPORT DATE 7e TOTAL NO. OF PAGES 7b, NO. OF NEFS

Ncvember 1969 29 ₇

8e. CONTRACT OR GRANT NO.

N00024-67-C-5218 5e ORIGINATORS REPORT NUMBER(S)

b. PROJECT NO.

SFO13-O3-04, Task 2022 Report 1344

e. _{9 b. 0TH ER REPORT NG(S) (Any other numbers that may be assigned}

this report)

d. SS C-202

10. A VA IL ABILITY/LIMITATION NOTICES

Distribution of this document is unlimited.

1 . SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Naval Ship Systems Command

13 ABSTRACT

Vertical and lateral wave bending moments were measured at the

midship section of a 1/96-scale model of the C4-S-1A MARINER-class cargo ship

CALIFORNIA BEAR. _{The model was self-propelled through a ship speed-range}

of 10 to 22 knots at seven headings to regular waves of lengths between 0.2 and 2.0 times the length between perpendiculars; moderate wave heights

rot exceeding 1/50 of the model length were used. Results are presented in

charts of bending-moment-amplitude/wave-amplitude versus ship speed, with

wave length as the parameter. Two ship loading conditions, representative

(41)

IINCI

csrrvn

Security Classification 14 KEY WORDS Cargo Ship Ship Hulls

Ship Bending Moment Model Tests Water Waves LIN ROL E KA WI KB WI LIN ROLE Kc WT

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LIN ROLE