, .,.

‘,‘+.,

I .;,

$7*” ““:’” ‘“””

SUMMARY OF INVESTIGATION OF MIDSHIP

P ““””s., ‘-,

BENDING MOMENTS EXPERIENCED BY

1: MODELS IN EXTREME REGULAR WAVES

5X-1 57

Final Reportof

Project SR-157“Model in Extreme Waves”

to the

Ship Structure Committee

SUMMARY OF INVESTIGATION OF MIDSHIP BENDING MOMENTS

lXPEIUENCED BY MODELS IN EXTREME REGULAR WAVES

by

John F. DalzellStevens Institute of Technology

under

Department of the NavyBureau of Ships Contract NObs-88509

Washington, D. C.U. S. Department of G ommerce, Office of Technical Services

December 18, 1963

,,

----- . .. ...—,.... . . . .

SSC-157

.....L

Y. *— . .. ... >q.p -, - “-= ,’ -—, —+=-, --- ~~.--’.---’---7 ---’= -. :’- ,-- .-, --””-=- ‘3. .. .. ... .. .. . . . . . ...

..-.;.

,..,.—. -,,A–,.., A—. ,.~,! .>. ,- .,. . .,. —. —.-

ABSTRACT

This report summarizes experimental research to investigate

the possibility of a physical upper limit on midship bending moments

being reached in regular waves of height significantly less than the

theoretical upper limit of stability forprogressiv~ wave$ (~~ = 1/7)”

The experiments included variation of ship type, of distribu-

tion of loading and of freeboard as model parameters. The ship types

investigated were a modern cargo vessel, a large tanker, and a mod-

ern destroyer. Each model was tested at various speeds in regular

head and following waves of several different lengths and of a wide

range of heights.

No significant upper limit of bending moment was found.

However, the study establishes more firmly the grossly linear de-

pendence of midship bending moment on wave height, even for ex-

treme wave heights which may be encountered in service. These

findings strengthened the case for determining design wave bend-

ing moments on the basis of statistical analyses of ocean waves

and/or resulting bending moments.

,,

CONTENTS

●

●

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Models and Technique s....... . . . . . . . . . . . . . . . . . . . . . . .

Test Program .

Data Reduction .

Different es

● ✎☛✎✎✎☛✎ ✎ ✎✎✎☛✎☛✝ ✎☛ ☛☛✎☛✎☛ ● ☛✎✎✎✎✎✎ ✎ ✎ ✎

. . . . . . . . . ..*.... . . . . . . . . . . . . . . . . . . .

between Models . . . . . . . . . . . . . . . . . . . . . . . .

Trends of Bending Moments with Wave Steepness . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1

2

4

5

7

10

11

11

12

—

INTRODUCTION

khowledge for design purposes of extremewave bending moments on ship hulls in irregu–Iar storm seas is restricted to a relatively lim-ited number of full scale ship observations,Efforts are currently being made toward deter-mining design wave bending moments on thebasis of statistical analyses of full scale andmods 1 data, an approach which requ~res consid-erable expenditure of t~me and funds.

A possible alternate approach was detailedin Ref. 1. This approach involves the use ofmodels in vary steep tank waves to determineif a physical upper hmlt on wave Ixndlng mo-ments exists. An abbreviated p]lot study em-ploying this approach was conducted, and theresults (reported in Ref. 1) indicated that llm-iting kend~ng moments might h reached in reg-ular waves of a height sigruflcant ly less thanthe theoretical upper limlt of stability for pro-gressive waves.

The present investigation was lnit]ated tosee if the indications cited In the pilot studywould apply more genera lly. The program in-cluded a broad variation of wave lengths,wave heights, and ship types, and Included in-vestigations of the effects of radical altera-tions of ireebaard and we~ght distr~butlons inone ship type. A moderate variation of mode 1speed In head and following waves was alsoincluded in the program.

The methods used agd the results obtainedin this study are contained in Refs. 2 and 3,This report constitutes a summary of the mate-rial in those references.

MODELS AND TECHNIQUES

A relatively full account of test techniqueis contained In Refs. 2 and 3. The generalmethods followed those developed at the David-SOn Laboratory and elsewhere over the last tenyears. All test work was conducted in DLTank No. 3 (300’ x 12’ x 6’) in which only thehead and following wave cases are possible.The significant difference between the presentand the past experimental work was in thesteepne:-s of the waves employed.

Figure 1 illustrates the severity of the testconditions. The pictures are selected framesfrom two motion picture sequences. Each col-umn of pictures is from the same sequence and

..;F

bm!.y ~

. 1[ ,,.:.,,q ‘“ “’-,,,.y :;-.’: - ,-..::.

~ti . .— P-- .. . -

‘$; , ,.,,,..>, ,.

<“: . .,.,; - i?-..,.1- ;.>

--,

a a

b

r <

i

SPKED: ZERO

FIG. 1. MARINER

d

SPEED: ~ Iixo’:s

(MODEL .2251 A-VI)WAVE LENGTH: 1 .z5L -- WAVE HEIGHT/LENGTH: 1/9 HEAD SEAS

shows the model at intervals of abcut one-fifththe wave encounter cycle in waves of heightabut equal to one-ninth the wave length. Fig-ure Z indicates schematically the tank test set–up and the method of towing and restraining themode 1 to motion in a single plane . Figure 3 i 1-lustrates the method of connecting the twohalves of the mode 1 with a moment balance.

The se Iection of particular ships to mode 1was based on the philosophy that they must re-present good current practice in design and beof a type hkely to appear in quantity in thefuture. Three investigations involving changesin mode 1 parameters were carried out:

1. Variation of weight distribution intype

2. Variation of freelmard in the same

one ship

ship type

-2-

@ HEAVE “AS, (.0”S7,S,”,0

?0 MOVE vERTICALLY OY

ROLLERS IM SULICARRIAGE]

@ SUBCARRIAGC,FREE IR SURGE,(OOUOLERAILS REsTRAINROLLING MOTIOk, ABSORB YAwMOMEMTMD SWAY FMCE.)

@ ‘Nu? CRACKER” (YAW RESTRAININGARMS TO HOLO MEAvE MAST,)

@ TwO AUXILIARY RAILS (PROVIOESWAT , YAW AND ROLLREsTRAINT TH ROUGH

SUDCARRIAGE. )

@ SALL CHAIN LOOP (ACTIVATESTnA?E.OUCER WWICH MEASURESDISPLACEMENT OF SUDCARRIAGlfRELATIvE TO MAIN CARRIAGE. )

●ITCH P!vOT

,.*: ..A, :..,. ,.. ?

FIG. 2. SCHEMATIC OF TOWTNG APPAR4TUS .

.

3. Two additional differentparison with the first

I;

INSTRUMENTATION

ship types for com-

The frost ship type chosen as part of all threeinvestigations was the Mariner, Fig. 4, whichwell represents current high-speed, dry-cargoship design. The second ship type was that ofa giant tanker, Fig, 5, representative of cur-rent trends in bulk carrier design. The thirdship type chosen was a destroyer, Fig. 6.Two extreme variations of weight distributionwere carried out on the Mariner model, and onevariation of freehard was also carried out onthis design, Fig. 7. Table I summarizes thecharacteristics of all models tested, and fig-

IWAVE●ROBE

._.>.,\,,.. . . .. . . ,:. , .-.

17---77

FIG . 4. MODEL DRAWING, BASIC MAFUNERHULL - MODELS 2251A-~, 2251 A-V2, 2251 A-V3.

ures 8a and b show wsight distributions employ-ed in the models.

TEST PROGW

A pre Iiminary test indicated that fine cover-age of all speeds in head and following waveswas unnecess~y. In addition, the magnitudesof the tow forces invo Ived when the first mode 1was towed at high speed in extreme head wavesindicated that the highest practical Fro ude

-3-

.

●

—.STWUT WI

_.d-l.l.L.A.l.l/L. A.L.L.;.+.++.+. $.+.+ .*.*.+.–>0 8? In ,, ‘L 83 ,. ‘~ ‘z “

FIG. 5. MODEL DMW’ING, MODEI, 2251D -GIANT TANKER.

FIG. 6. MODEL DRAWING , MODEL 2130-IXSTROYER.

\

!0

LwJ

FIG. 7. MODEL DRAWING, MODEL Z251B -INCREASED FREEBOARD .

a--L$111111111

J

‘*’”I I I I Ill

,, FP

(b)

FIG. 8a and b. WEIGHT DISTRIBUTIONS.

. ------ —

..-... . ., .... ....... .... .. .. ..,, ,.... *&...,..& . . .

-—- -- A---- - :? - ----- .- -* A-SY-..*-L.-.L——--— —---- —-—-- —---- .&2

fi>minalModel Scale

Length oh 20 Stations.inches

bar. inchesDraft Inches

D:splarcment , Pounds. F.W.~,/q

Cb

c~

L/: L/i~)*. Esisr

Lc3, 7 Station Lemgth E“sm X

Oyradlus, $ Station Length

Natural ?1 tehing Period, ScC.

Natural Heaving Period, Se=.

Natural Prequeney or Vibration, CPS

R“eeboards: Aft, InchesFwd, lrrhes

V. C.G. , inches

Hfi= H2D5, F@ SE?’ION

Weight, lbs.

LCG Fwd X , lrrhen

VCG, lnchea

K_ . $ Station knKth/2

WelEht. lbs.

LffiAft M , inches

VG, inches

K~, $ Siation Lengthft2

-4-

TABLE 1. MODEL CH.ARACTEHSTICS .

2251 A-’V’-1

?&rl ner

rlsslm>2C. O

1:1OL

60, c0

8.76

3.20

38.1

2.72

0.61

0.98

1110 .,

1.h2 Art

24.3

0.70

0.75

16.5

2.30JI.05

3,3b

17.9

12.10

3.32

26, g

20.2

12.32

3.37

25.5

Mar5ner

Cargo h570.0

1:104

60.01

fi.763.20

38.1

2.72

0.61

O.*

14C1.45 N’t

15,9

0.60

0.75

17.2

2.3o0.05

3.14

17.96.o43.U6211,8

20,2

6,93

2.85

21.8

Mariner

car&o-mks5?0.0

1:104

60.00

8.76

3.20

38.1

2.72

0.61

140

1.*S Art

30+3

O.sc

O,m

14.1

2.3o4.05

3,36

17.9

15.88

3.43

28.2

20.2

15.72

3.30

32.0

17.912.10

3.3426.8

20.2

12.33

3.44

25.5

~Gla./tTa>Kcr

WS1$RE95. o

1:179

60.00

8.85

3.26

52.0

2.70

C.BO

0.99

172

0.32 FwC

22.7

0.70

0.80

13.7

1.%2.52

2.62

26.6

1~.46

2.6o

23.2

25, k11.592.6525.2

:] 7(,

De=Trcye:

Dezi&r.

3E?, c

~:L7,~>

65. j7.302,32 ?wL?2.6& Aft

25.1

.?.92

0.55

62

3.:3 Art

23.4

0.60

0.65

10.7

1.373.4k

1.23

11.2

12.08

1.o6

23.9

13.9

14.56

1.37

25.6

numkr would not be in excess of O. 13. The of moment, motion and wave amplitudes . Thepre Lminary test also indicated that the situa-tion where the model was drifting helplesslyastern under the influence of extreme waveswas a practical case worth investigating . Thereresulted a standard test program for all sixmodels. This program is summarized in TablesH and 111. It may he noted from the tables thateach model was tested in five speed-headingcombinations in waves of five or six differentlengths. As full as possible a coverage ofwave heights was attempted. In all, approxi-mately 1100 test runs were made, and out ofthese about 600 runs were selected for analysis.

DATA REDUCTION

Each run resulted in an oscillograph recordof midship bending moment, pitch, heave andwave elevation. Because of the steepness ofthe waves, only a nominal regularity was ex-hibited in the tiaces and it was necessary toaverage the maximum and minimum excursionsof a numker of cycles to arrive at an estimate

averaged measurements were suitably non-dimensional zed and grouped according tomodel, heading, speed and wave length (shut120 groups in all). A mean curve was fitted toeach set of test pints representing the varia-tion of moment or motion with wave steepness.Figure 9 and Table IV are sample pages for onetest- qroup from Ref. Z . All fitted curves wereterminated before representing an unreasonableextrapolation of data.

It was found in the initial stages of theanalysis that the moments measured at zerospeed in head and following seas were nearlyenough the same that analysis of the zero-speed following-sea case could be deferred.An analysis of the transient kehavior of themoment measuring system was performed andit was oancluded that the amplitudes of momentindicated on the remrds would include little,if any, of the effect of sudden impact.

In order to compress the data, summary

.-

—.

-5-

TABLE 11. TEST PROGRAM MARINER MODEL AND vARIATIONS .

●

Model 2z51A.v2 Hull as DesignedI,cargo,’ Mavcd Amidships

I SpeedWave Length /klodel kngtb “

Fleadmg c~ags~. .50 .i5 1.00 1.25 i.50 1. ;3

1800 Zero 5* 5* ( 5* 5* 4*,, Forward 4 5

*5 4

,, Driftinz 6 b * ,5 4~o

Zero 5 5 5!,

Forward 5 5 5 6 4Hull as Designed

Model 225 lA-V1 Model 225iB Radical Increase m FreeboardDesign Weight Distribution Design Weight Distribution

Wave Length/ Model LengthSpeed Wave Length/Model Length

SpeedHedchng Classif. .50 .75 1.00 1.25 1.50 1.75 Headng Claus if. .50 . 75 1.00 1.25 1.50 1.7lbl)o Zero 4 6* 7* 8* 8V 3* 1800 Zero ● 5* 5* 5* 4*

,, Forward 4 b 5* 5 b ,, Forward 4 5 5* 5 4,, J3rlftinK 415 5*5 _4 ‘1 riftinp

b-~

4 5 5* b 40

7*?O 4

‘h

—&_l-_ —. .–Q,?_ kero 5 5 5,! Forward 4 I–7 5[5 4 ,, urwarti 3 5 5

I Hull as Des, gneciModel .Z251A-V3

“Car Ko ‘z Moved to Ends IWave Length/ Model Length

SpeedHeading Classif. .50 .75 l.oq 1.25 1.50 1.75

180: Zero A*.; -::...~,* 5* ~:

,, _4_!.L -...5* 5 4,1 Driftin E 4 5 ~+ 5 4

A_. —._ ._Zero 5 5. .—!, Jorward 5 5

TABLE III. TEST PROGRAM GIANT TANKER ANDDESTROYER MODELS .

Model 2251D GIANT TAN3UCR

I II

Wave Length/Model LengthI Speed , , , , , I

Headm - Clas sif. .50 .75 1, 00 1.25 1.50 1.75

80 0 Zero 4 5* 6* b* 6* 4*

Forward 4 4 5* 5 4

,, 5*~riftin~ 4 5 5 4

0° Zero 5 5 5,, Forward 5 5 5

Model 2130 DESTROYERI

I Wave Lcn Eth/Model Length ISpeed

l-]He tins cla~sifc .50 .75 ,1.00 1.25 1.50 1-751800 %rg –.—_ 1. 4*,JL I 5*15*14*

,! JFgrw_azd _.4_ 5 5* 5 4,, Driftin~ .+_. ._5 J*_ .2 4c)-–” “- z;;-- ‘- 5 5 5—— —- — .—. ----

,, Forward 5 5 5

a. Numberfi m the blocks indicate the number of goodrune c.btalned in order to cover the range of waveheight. Blank* ind, cate no run& attempted.

b. *indicates a motion picture record of the modelin the highest wave.

a.

b.

Numbers in the blocks indicate the number of,goori runs obtained in order to cover the range

of wave heights. Blanks indicate no runsattempted

*Indicatefi a motmn picture record of the modelin the highest wave

plots of the famed hnes for moments and mo-tions for each model, heading and speed wereprepared. Figure 10 is a typical bending mo-ment vs. wave steepness PIot, one of 24 suchplots appearing ~n Refs. 2 and 3. All kendingamplitudes are referred to the midship momentexlstlng In the model afloat in calm water; thatis, wave bending moments only’. The scale onthe right of Flg . 10 lS compensated for the stlll-water moment for 1llustratlve purposes.

A. Differences Between Models

While not a primary object]ve, a measure ofthe var~ation In bending moments from model tomodel was obtained and exhlblted ]n the formof cross plots, examples of which are shown inFigs. 11 and 12. (Moments for SPeClfl C SteeP-nesses plotted on a base of wave length. ) Onefinding In the analysis of differences betweenmode 1s was that a particularly important mode 1variable is the average moment of model weightabcut amidships. This influences wave kend -ing moments because It appears to be the majormodel var]able In the component of moment pro-duced by pitch and heave accelerations. The

-.-. ,.“ —m,--. —,.. .-...= - .— .. . . . . ... . .. ——..- . . . . . . . . .

. . .

-!,.>

. ,,. . . . . —.....-~:-—-.,.,, . .!.=. ——-. !... J

-6-

MODEL Z2<IA-UI TEST GROUP 1.1122125

WAVE LENGTH : ~ L M3DEL HEADING’ l&2°

APPROX MODEL SPEED’ v/m= 0.12 t. 0.14

Sc

T* 32- -

m -muwE 2!4--

:n

20- -m-ml

a ls- -

Fw tz--A507 *.

4- -

— o- —

.Ott

* .M-

m-

< .0, - -

R’a +0 - -

2u ,12- -Jaum ,44-

,16-

,1a-

FIG. 9. SAMPLE TEST RESULTS.

net bending moment is considered to be thealgebraic sum of the integrated hydrod~amlcpressures on the hull (here termed “hydrodyna-mic moments”) and the internal reactions resul-ting from the acceleration of the model. Thesigns of these components are opposite andthus if the hydrodynamic moment remains con-stant, a greater mass acceleration moment mayresult in a smaller net bending moment. Thetest results supported the hypothesis thathydrodynamic moments were roughly cnnstantsince wave bending moments decreased asweight was concentrated more towards the enckof the model. (Unfortunately, such action ad-versely affected the seakindliness of the mo-del. ) Conversely, when weight was moved to-ward amidships, moments increased (and sea-kindLiness was improved). Figure 12 showsthe net bending moments and the derived“hydrodynamic” moments for the four Mariner-

MODEL 2251 A- Vl, hIARINFR, PARENT

MODEL HEADING: l&c~, HEAD SEAS

APPROX. MOOEL SPEEO : vl~- 0,0

L/7+

.Dol, _L/lo

+- ,001

.001, - *

:.0012 -

I 50

,0010 ,’

*- .OoOn- L/20

$TA1 IL I —- ,.00

,000s -

—0,000, –

,Wz -

0

,oOOr -

.W04 -2

.Oooa – I.001

Boo, -

<

,0010

,Oolt

,0014

.001,

+HOG—

- .002

1 1 I 1 I 1 1

+

FIG. i O. SAMPLE FAIRED LTNE SUMMARY.

type variations. It demonstrates by virtue ofthe “collapse” of the hydrodynamic momentsthat the primary source of the differences lE -tween net moments measured in the weight dis-tribution investigation was the mass accelera-tion moment.

Some difference in moments was observedwhen freetiard was increased. Sagging mo-ments were observed to increase with an m-increase in freeknard.

It was observed that bending moments forthe three basic ship types increased ahcut inorder of fullness. Very large wave hoggingmoments were experienced by the Tanker mo -del.

-“i-

TABLE IV. SAMPLE TEST RESULT TABULATION.

B. Trends of Bendinq Moments With WaveSteepness.

Since it was very difflcuh to generalize

1

criterion was calculated for all test conditionsabaut trends of moment with wave steepness on and the results were grouped as follows:the basis of the 24 plots similar to Fig. 10, a

i

Class (++) 7> +.15numerical criterion defining the shape of thefitted lines was derived. A graphical illustra- Class (+) +.15 >y> +.05

tion of this criterion is show in Fig . 13. Thefamilies of curves plotted illustrate the shape

Class (0) +.05 >y>-. o5

of the curves for various values of the criterion Class ( - ) -.05 >y>-.l5

Y. Because the criterion was dependent on the Class ( -- ) -.15>yform of the equation fitted to the te~t Wints,families of curves are shown for the two most

wide ly different equations used. The y

;,.,,..

,. ... .+,..--—- -— A.~-=- .=.” ‘. -.-’ .“==+’ ““’-–._. .. . ,-.— -- - .,’..=---

-8-

p V3ML R!tJEP l,6a DEL :LEEL L(MF CO NV.

[1

/PAR EMT VI —

/ hi), : .1ocARGo4Ml DsHl P v> —-—

30 //-:1CARGG AT ENDS v 3

——.

INCREASED FBD 0 .. —----

:~} ~,~,

/’ ./’-”4 “HYDRO MOMENTS”

/

/,.’ .002 .002

/:MOMENTS

;.+ ~;},,,= .!0

,’, hlk=,o+

7

hfh~ .10 ,-,,+

/v3,/:::2

i -00 ;<<””’:_ ;~ 0“’

{/

7 —=.,..:, .001, ., . ...-.”

k

MOMENTS ,,.<&./v2 .,

/ ,,.” /

.-

hl~: .04 a <

/

h/i =04

/.’/+ a“ =--.::.:;:;:0 VI

V3—————,’ ‘

V3

PITCH o 0 0

100 1.25 1.50 1.75 I,@ 1.25 1.50 1.75 1.00 125 1.50 1.75

r

A/L_A ———;;, —V3

1=

k/L— . .

‘---- --- h/i ~ .04

——— V2 -... B1,00 1.251.50

VI V21.75 *= —--. _v~ ~. . . . . . . . . --. V 1.=

i/L.

a a

“’...

HEAVE -..-.4 Vz,Oo1 .001

‘~’ .&h,,, ,,0.001

f&B1h’A;’O

VI “~

,,,“,.. h/~: .04 ;002

v3, v2,v I,B

/ --’

/

/ ..~-

0l,w 1.2’3 1.50 1.75

h/L

FIG. 11. CROSS PLOT OF FPJRED MOMENTS AND MOTIONSHEAD SEAS FROUDE NO. 0.0.

.003r

1HYDRO MOMENTS

.002

k

f rK$

1

/“” ‘AR h~’c-’”

/:~”- ‘u

.001 ‘

}

,/---–:K ~,,;

. .a —–— —-DD

.04

.

MoDEL LABEL LINE co NV.

}

/’:,, h,, ,.,0 ;;:;; :,,,. :::”. ~30 - /

OESTROYER OD ——— —,, TKR.

/.002 MOMENTS

mw

/’

k

h(hx 10

g 20.g

/TKR_

hlh , .04 MOMENTS;m

/

y;: .Oo1m

. %“

;

~;h!?i2F:{F’” ~o 1.00 1.25 1.S0 1.75

A{L

FIG. 12. CROSS PLOT OF FAIllED MOMENTS

.003 1

AND MOTIONS FEAD SEAS FROUDE NO. 0.0.

-9-

.

I— 7: +0.30

FAMLY FOR LOWEST ,— +02 o

ORDER E0iJ4Tl ON

M

— +0.10— + 0.05

z=:..

R

FIG. 13.TION OF

L---- —-010

---- — -005

mMILY FOR WHEST\\\

\ — + 0.05

ofmR ECIUATION —+0.10\\ —+020

------- +O,qo

EXAMPLES: NUMERICAL CL&SSIFICA-FITTED CURVES .

These groups can he interpreted as follows:

1. Class (++) and (+): No limiting kndingmoment indicated by data.

i?. Class (0): Data Indicates onIy smallde patiLure from straight line.

3. Class ( - ): Data indicates limiting mo-ment above a steepness of 1/9.

4. Class ( -- ): Data indicates Limitingmoment below wave steepne 55 of 1/9.

Tabulated results of the classification of trendsare shown in Tables V, VI, and VII. The pri-mary conclusions of the study were drawn fromthese tables.

It was noted that the magnitudes of momentswere abaut the same for all the speed condi-tions except head-sea forward-speed, and thatthe highest moments occurred in the longestwaves. Thus for speed corlciitlo~s other thanhead-se= forward-speed, it was necessarY tohave Class (--) in almost all of the blocks per-taining to the longer waves for a model In orderto conclude that a hmiting moment was to beexpected In wave steepnesses less than 1/9.This was true in only one case, that of the de-stroyer hogging moments. In all other casessuch Limits es exist are indicated for w-evesteepnesses of ]/9 and much higher.

It was felt that the head-sea forward-speedcase could be ehminated for practical reasonsso that the trends in this case were not consid-ered in the formulation of conch slons. EIow-ever, if the trends for this speed case had beenconsidered where moment magnitudes exceededthose obtained in the other speed cases, noessent~al differences in the conclusions wouldhave resulted except that the lower limlt fordestroyer hogging moments might not have beencited.

The practical basis of these conclusionshinges on the trend of the moments measured inthe most severe wave lengths. Lmiting trendsdisplayed in other wave lengths may have littlepractical significance. In order to he 1P confirmthe conclusions obtained, a fresh start on theanalysis was mad? without bsneflt of fittedhnes or numerical manipulation. Every testp~int obtained in any wave condition and atall of the four speeds was pIotted on a singlechart for each model. (Figs. 14 to 19). Theonly differentiation htween points which wasmade was ~tween those for the impracticalhead-sea forward-speed case (sohd circles)and those for all other speeds (open cmcles).

Envelopes to the scatter of Wlnts weredrawn UP to a wave steepness of 0.10, exclud-ing the paints for the head-sea forward-speedcase. The e nve lopes were terminated at h/1 =0.10 &cause the long wave lengths which con-tribute many of the highest moments are notwell represented beyond this point. These en-velopes were superimposed in Flg. 20. It canbe seen that with the exception of the destroy-er hogging moments, the @nveloPes of all mo–ments measured at practical sPee~s In all mo-dels imply no limit at a wave steepness lessthan 1/9 and most imply no Iimlt k low the

-1o-

TABLE V. CLASSIFICATION OF TRENDS WITH WAVE STEEPNESS OFWEIGHT DISTRIBUTION INVESTIGATION.

I

0. 12 to k=1.00 -0. 14, !?5 -

1800 t-%t%

MOMENT AND MOTIONS.

N-OTATION

4 ● T.=..

0.0,

00

iHi!?&$~’O’-’’-’’’”’”’-’o. 1:1:--1 +*

. I o ,0 ;0 I

1,25 + . . . . “ “1”

180” 1, 50 0 0 . 0 1) (J o Lo

1“75 -_ Q o + + o 01+

L)olo to 1. Oc o 0 J.- L Q-1. !J 0 LJlolO 26 I,zd ~ o lx

1 . ...4 , 1

by ImpactND-No Data

+. 4

+, 3

-. 3

-4

++

I-+-i?

OE

+&

L

v--

theoret~cal limlt of stability (1/7).

It is interesting to compare these resultswith those of Ref. 4.. The experime nta 1 workof Ref. 4 was quite different from that reportedherein in that it dealt with irregular mode 1 seas.It was similar in two impartant respetis:

1. The mode 1 utilized was the same destroyermodel used herein.

z. The severity of the irregular waves of Ref.4 was comparable to the severity of the

re9ular waves of this study.

As in the present results, those of Ref. 4 implythat midskup bending moment ranges are rough-ly proportional to wave steepness over a verylarge range of steepness. (No distinctioncould be made in Ref. 4 between hogging andsagging moment trends). It is therefore con-sidered likely that the trends of bending mo-ment with wave steepness shown herein appro-ximate those expected for significant kendingmoment amplitudes in random seas of increas-

ing severity.

CONCLUSIONS

1. It appears on the basis of these studiesthat design wave bending moments are es sen-tially propoflional to wave heights which actu-ally may b encountered.

2. The present study, by establishing morefirmly the grossly linear dependence of momentson wave heights over a considerable range ofwave severity, has strengthened the case fordetermining design moments on the basis of sta-tistical analyses of sea waves and/or the re-sulting moments.

3. Within practical operational and designlimits for ships at either end of the cargo carry-ing spectrum, no significant limit on midshipwave bending moments in head or followingwaves is to b expected as wave steepness isincreased up to a value of almut 1/9. The sameresult is obtained for the sagging moments ex-

.

.

TABLE VI. GLWSIFICATION OF TRENDS WITH WAVE STEEPNESS OF MOMENT AND MOTIONS.FREEBOARD INVESTIGATION .

Hydro. }iydro.

P]tch Heave sd~ HO g

I I I I \

1--(UI

,++1,-. . 4 4 t--–t-jo- 1 !+ + I1+:+.

““‘-I. 0.—-—

-:-; 0,

,0.0

p=rienced by the nava 1 type but not for the hog-ging moments; in which case an uPPer wavehogging moment limit is suggested at a wavesteepness of almut 1/9.

RECOMMENDATIONS

The present study involved itself only withmidslmp knding moments for reasons of eco-nomy, even though it was known that under cer-tain conditions higher wave bending moments

● may develop elsewhere along the ship length.It is considered of importance to ascertain ifthe conclusions of this study pertaining to com-

& mercial ship types also hold for moments allalong the length of the ship. If similar conclu-sions can b drawn for moments elsewherealong the length of the ship, no fu!ther develop-ment of this type of experiment would be recom-mended.

NL)I” AT1~N

●’I”racr

L)ibtnrted

by ImpactND-No Data

REFERENCES

1. Lewis, E. V. and Gerard, G. : “A Long-Range Research Program in Ship StructuralDesign, “ Ship Structure Committee, SerialSSC-124, November 1959.

2. Dalzell, J. F.: “An Investigation of Mid-ship Bending Moments Experienced in Ex-treme Regular Waves by Models of the ~Mariner Type Shi P and Three Variants, “To be published by Office of TechnicalServices as PB-181 508.

3. Dalzell, J. F.: “An Investigation of Mid-ship knding Moments Experienced in Ex-treme Regular Waves by Models of a Tank-er and a Dsstroyer, “ TO be pubtished byOTS as FB-181509.

-12-

TABLE VII . CLASSIFICATION OF TRENDS WITH WAVE STEEPNESS OF MOMENT AND MOTIONS.SHIP TYPE INVESTIGATION .

O.lzto I-

o. 14, 1. 25 -* IJ* 10* .0 -w - -lJ. 00 + O*] O*, O*1“ 50 ~ 4

180° 1.75 ::’ :3,;’ =+= ‘=’ :- ;+:-” :“ “:- -:: ‘-I* ‘::!:*---- -.

0.0, 0.7< 0 0 _:- -o_ .+ ___ L

7

+,+ :- --

1.00 - - - 0 - -- 0-._:;.; ;. .6. . * “r --01~“.

—.— . —, I1.25 . 0 0 -: - +: ~. ‘_ lo , Q _o_ -t -

L ‘:

‘O]i7.—180° 1.50 . 0 .Z - L ..:1 . .— ..L~!- .f ?. ._?o (-J 10,0

1.75 0 ; - 0 - -: 0 -1+ o 0 0 6 010

-o. o& to 9.75 0 fi. ,,~. o .0 . .Q- ,?1.00 0 ~ o 0 0 . 0

.: ~;.: ;. .;- -.;. ; .;$

-0. 15 4-7.25 0 Q o 0 . “OJ_o o +!0 ‘+ - ,0!0

180° 1.50 :. 0 ~._ - .0 -- U t ,0 .0 !-0 1 0 .-dli=1.75 . 0 0 0 + -- 0 +10 --101+ --1010

0 16to 1. OQ o 0 0 0 0 - 0 00 .0 _o_ .+ o .l.~g.O 26 1.25 -. (1 o 0 + = ~ ,. 0. o_. + 0, + .- 13jo

00 1. 5C . + o 0 + - 0 010 +- + 0 - NJJI o

NOTATION

*Trace

Distorted

by Impact

ND-No Data

4-.

-4

4. Dalzell, J. F.: “Some Further Experi -ments on the Application of Linear Super-Wsition Techniques to the Reswnses ofa Destroyer Model in Extreme IrregularLong-Crested Head Seas, “ DL RePort 918,Septemkr 1962.

NOMENCLATURE

B Maximum mode 1 beam

9 Acceleration due to gravity

H Draft

h Wave height

A Wave length

h/A Wave steepness

L Model length on 20 stations

LBP Length between perpendiculars

LCG Longitudinal center of gravity

EFA Average midship kending momentdue to acceleration of model mass

IIM Part of IiFA in phase with measured

knding moments

0.00

Ps

I(

I6

0.0 (

/0.0

/’ o0

0 h/Ao 0

01/720o l/mlml/su7

I fJ4

WVE STEEPNESS

L/20 STATIC

o

t

HOG—

L

FIG. 14. MEASURED BENDING MOMENT DATA---- ALL WAVE LENGTHS AND SPEEDS. MODEL2251A-vI; PARENT MNNER.

2Zo/L Non-dimensionalIitude

heave double amp-

Y Quantity derived in the numericalclassification of trends

200 Pitch double amplitude

J/L Wave length to mode 1 length ratio

PH

(hog9in9 ~Ome~t/pgjJ~efficien’

Wave hogging momen

P~ Wave sagging moment coefficient

(sagging moment\pgL3B)

1%

Io

IFu

SAG—

0.001 -

L/20 STATIC

I t

t H~G

1-L

FIG. 15. MEASURED BENDING MOMENT DATA---- ALL WAVE LENGTHS AND SPEEDS MODEL2251 A-V2; MARINER, CARGO AMIDSFZP.

Approximate hydrodynamic wave hog-ging moment (WH - ~m)

Approximate hydrodynamic wavetigging moment (ps .~

RE)

Total hogging moment, wave momentCOIE cted for still-water moment

Total sagging moment, wave momentcorrected for still-water moment

Mass density of water

LIL

SAG

L/~0 STATIC

●

●

~“- --k—--— .— .--...-----.---=- --=--==-J&..---...rx=. . . . ..

-14-

●

00

0

/h 1A

Ino l.holmlnlw1

I I I I I I I 1

<02 “ m ‘8 ‘0 ‘2 ‘4

L120 STATIC

●

● ‘m●

HOG—

●

●

FIG. 16. MEASURED BENDING MOMENT DATA---- ALL WAVE LENGTHS AND SPEEDS MODEL225 lA-V3; MARINER, CARGO AT ENDS.

0.001

k,

Io

IP“

0.001

SAG

L/ZO STATIC

o

/,

CP”

h/k

I /20 1/10 1/9 1/8 1/7

1 I I I (

\

.02 .04 .06 ,0$ .10 .12 .14. . WAVE STEEPNESS

% ● J.*

r.,% .8

O(y ~&oo@

L/20 STATIC ~cvoo

I.-

L

FIG. 17. MEASURED BENDING MOMENT DATA---- ALL WAVE LENGTHS ATSfDSPEEDS MODEL

2251 B; MARINER, INCREASED FREEBOARD.

.

0.001

.

Io

I1

0.001

-15-

SAG—

000

0.001

●

/m“ o h/k

o I● 1/20 g 1/10 1/9 1/8 1/7

I I II I I I I I [ a

.100

\. .04 .060 .OB o .10 .12 .14,-: WAVE STEEPNESS

\

O*m o

@lm‘ o

\

‘o&0, . @o‘0°8.;*%O 0.,

k~oo”

a& :

HOG

0

0go

L

FIG . 18. MEASURED BENDING MOMENT DATA---- ALL WAVE LENGTHS AND SPEEDS MODEL2251D; GIANT TANKER.

IPM

0.001

●

●●

●

●● m

o0

0

/h/A

1/20 1/10 1/9 1/6 1/7

1“’’”

I

.02 .04 .06 .0a .10 .12 .14

WAVE S,TEEPNE S S

o0

0

[-

HOG

FIG . 19. MEASURED BENDING MOMENT DATA--+- ALL WAVE LENGTHS AND SPEEDS MODEL21 30; DESTROYER.

&

—

—....,.. - .!.L~- : ------ -“- , —=. - .. -—. —---~ .- —.. ‘-—.—.. -— .-—.-”-.. .&

0.001

Pa

I

o

I

PH

0.001

L

-16-

SAG

/

~ MARINER, CARGO AM IDSHIP

, — MAR INERI INCREASED FREEBOARD

/

// _ GIANT TANKER

/~ PARENT MARINER

/t //

—MARINER, CARGO

/< — DESTROYER

AT ENDS

hll

WAVE STEEPNESS

HOO

\_

.1 4

DESTROYER

MA RI NE R, INCREASED FREEBOARD

MARINER, CARGO AT ENDS

PARENT MARINER

MARINER, CARGO AMIDSIIIP

GIANT TAfiKER

FIG. 20. ENVELOPES OF MEASURED BENDING MOMENT DATAFOR SIXMODEM AT ZERO AND NEGATIVE FORWARD SPEED IN HEAD WAVES ANDAT IDG H FORWARD SPEED IN FOLLOWING WAVES.

-o 867-09!

..-.:...

,. .-,.-

-“..

-. .’---,-. ..>.’ ~...

.. ...

,?,”,.,.., ,: ”’!..,.,’-... .. . .. .

‘-j..,. .”

-,,. .,.:. .,,. ”,-.... .

. .. ..-.

~.,~$,-..:.:....,,.....-’, ,:..-” :,,!, . . . . . .. . . . . ~:.. . .

.-,... . ----

/.:.--”:

‘,, ,- ., :

-.-T

~, ‘-.,, ..,,:..”.... . . ,

? ,-:. .!.,; :,......~-,:.,,, -.:.

.. . . .

,-.., ,”,,... . . . ... )..:!: -., -.

.,, ..., .,”,,,.,