Experimental determination of bending moments for three models of different fullness in regular waves

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Lab.

_{v. Scheepsouwkunde}

Technische Hogeschool

Deli

010 LABORATORY FOR SHIP STRUCTURE RESEARCH

UNIVERSITY OF TECHNOLOGY

- DELFT

EXPERIMENTAL. DElE RMINATIOÑ OF BENDING MOMENTS FOR

THREE MODELS OF DIFFERENT FULLNESS IN REGULAR WAVES

IR J. CH. DE DOES

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. Report No. 65

Janùary .1960.

EXPERIMENTAL DETERMINATION OF BENDING MOMENTS

FOR THREE. MODELS OF DIFFERENT FULLNESS IN REGULAR

WAVES.

by

Ir. J.Ch. de DOES

Preliminary draft

that Z'.esu.ts

1

24

Chapter 6 discussion or results

and conclusions 29

Chapter 7 comparison of observed

aM calculated midship

bending momenta 35

Chapter 8. final remarks 58

Acknowledgement 40

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r

III

TABL AND FIGURJ

pag.

Table I Previous tests

₇

II Main dimensions of ship models. 16

III Test programme 21

t,

IV. Proude numbers at which water.shippage started 25

Fig. I Wave bending moment amplitudes as measured

by different authors.

t1 _{2 a-b-c body plans of the CB}

0,60; CB 0.70

and CB = 0.80 models. 't

3 the models

t, ₄ _{weight and sectional area curves}

't

5 block diagram

6 sample oscillograph record of bending moment

't

7

dynamic calibration device

8 test arrangement

9

forebody of CB 0.60 and 0.70 models

t

₁₀ _{motion amplitudes and phases}

U t, t' 13 14 15

't ₁₁ _{wetness of forecastle deck}

't _{12 a-b-c-d-e} _{test results for measuring sections}

t,

12 f relation between conventionally calculated and.

measured bending momenta.

maximum longitudinal bending moment distribution

for O.0 model

dO. .70 model

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1V

Chance in longitudinal bending moment over one periód for .70 model.

do. .80 model.

comparison of conventionally calculated bending moments with experimental values

comarisoxi of calculated and measured bending momentat service speed.

Fig. 1.6. 't 17

t

₁₈ 't 19

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.-1

SUMMARY

Three modela of the Sixty serles Parent Forni were tested in the Deift Towing Tank in order to determine bending moments in waves. The models were made of fibre glass polyester laminates and strains were measured by

means of resistance strain gauges

in 5

_{sections Of each}

model. The blockcoefflcionts of the models were CB 0.60,

0.70 and 0.60 resp. Runs were made In regular bead _seas

with wave height varying from 2r/L 1/l.8 to _1/.30

and in waves having a length of

A

/L 0.75, 1.00 and

1.25 resp. .

After a short description of previous work In this field the test set up is discussed and test data of all three models are given.

A discussion of the results is followed by a

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-2-I1TIUCTIQN

It is common practice in shipbuilding to base astrength

calculatión on several simplifying assumptions.

The ship being considered as a beam is assumed to be in a state of statiè equilibrium in a troohoidal wave of

ship length and of

a height of 1/20th of the wave length

By the well-b'own method of integrating

the load curve

twice a hogging moment is obtained

when à

_{wave crest is}

amidshipS and a

sagging moment when a trough is amidshipE

Byconibining these momente, with the bending moment in

smooth water that

can

be easily calculated the maximum

positive and negative.bending moments of the vessel under consideration can be determined.

As the hull is assumed to behave as a simpe beam, the

stress

distribution can be computed. .Exprienoe provides

the Bllipbuild.er with an "allowable stress" in judging

the strength of his newly designed vesael.

It is

clear that the stress derived in this-way fr a new design can be of valuo only 1f it is used for the

purpose of

comparison

with the values

of stresses

cal-culated according to the same standard

_method

for

axis..-ting ship8 that were found to be strong enough in

ser-vice. However, itis equally clear that it has nothing to do with actual stresses as met underservice condi-tions.

Since shipbuilding develo»es and ship dimensions increase rapidly.the need for a more rational approach to the

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problems connected with a more scientific treatment are many. They may be divided into two main groups.

what is the behaviour of material, ship's .strùctures and the ship as a whole under actual service condi-tions.

what is the magnitude of the various lOada imposed on a ship during Its life time.

With régard to A it will be olear that an allowable stress, derived from a laboratory tensile test on a test bar, combinedwith a safety factor.can no longer be con-sidered to be adequate for use in actual strength calcu-lations. Low frequency testing and programmeT6ding is necessary in order to obtain more information about the behaviour of material and of structures in particular. Theoretical as well as experimental treatment otthese problems will require much attention in order to come

as close as possible

to

the possibility of designing

"fail safe" or "safe life" ship's structures.

This goal

can only

be reached ii' the load spectrum

to which the ship

and

its structures are submitted, is

exactly known (as mentioned under B). In the first place knowledge of the sea and weather conditions that will be met during the expected lifetime of the ship is necèssa-ry. This problem has to be solved by oceanographers and

shipbuilders together and

is given much

attention

nowadays all over the world. The response of the ship,

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in the hull of a sailing vessel will be composed of the following items (local influences omitted).

B I a bending moment caused during the construction

B 2 a bending moment in smooth water, caused by the

difference in weight and buoyancy curves..

B 3

thermál influences, caused by the difference in

temperature of air and water.

B £4. a bending moment in waves.

B5

vibratory infittences.

B 6 slamming influences.

It will be clear from the above, that nothing will

be gained by trying to improve the convential static

calculation as discussed abov, for instance by

substitu-.ting the

standard wave height by a more realistic wave-height as met at sea,or by introducing dynamic effects.

However, this comparison method, that has proved its

value in the pasti has-to-be--replaced by a method in

which all the items, mentioned under B are incorporated and that will provide the actual loads dependent on type

of ship and sailing route. The next step is to design atructúres, that are stroxg enough to withstand these loads. The better our knowledge is of the actual loads and the more we know about the safe life of a. structure under these loads, the smaller the safetyfactor.canbe. In this report teste to determine the wave bending

moments (itemB4) are described. Thoteata were carried

out in regular head. seas with-three-dT-i-f-ferent-mode.lS

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Wave length, wave height and model speed were varied. Of course this is only a small feature of the solutIon of. the problem. In actual service the ship will meet

irregular wave

petterns from différent directions, which will cause horizontal, vertical as well as torsional moments. However, as a first approach the testing. in

regular head seas is considered usefull. asa means to gather the necessary information which is needed to

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2.

_Bi!liogray.

The f iret Successful modél tests to determine, ship

x'esis-tance were carried out by William Fraude _already

acentu-ry ago.. Therefore it is aomewhat'astónishing

_{that the}

experimental determination of. bending _{moments and shear}

forces in model tanks has been a véry recent development.

Oly in 1936

_{'thè first model experiments. on the}

lóngitudi-nal strength of ships _{were carried, out in Japan by 8ato}

(1)' and thesey.tegs _{were continued unti]. the end of}

world war II. The breaking.of

two destroyers of the

Japanese fouxth fleet in ₁₉₃₅ _{in a violent typhoon} _gave

the impulse t.o carry out _{these experiments. The model} _was

constructed of brass plate, its _{longitudinal members}

being to scale in

more or lesa

simplified form. Much care

was bestowed on' the instrumentation and _{to a large extent}

electronic measuring instruments

were used tó measúre heave, pitch, wave height and stresses. Electro-magnetic

strain pic-k ups. were installed _{át several pointson4eck_}

and bottoni for the _{determination of stresses. The major}

pàrt of the test data was lost,

due to war

_{'damage. In}

table I

the principal data of the

_{tests are summarized}

and in fig. I the test results in reguÏar head _{seas of.}

ahp length are given.

Prôgresaive'wo _{on the technique of model bending}

moment

tests was carried out by Lewis _{(2'). His first model of}

a T2-8E-A1 tanker was cut in.

two halves.

_{The bending}

moment was determined by _{measuring the, relative}

deflect-i

9fl QfZoreánd--aterbÓdyafto.r_a_c_{a-ii-bra-t ionwjth_the}

*

Numbers in parenthesis -refe.r to the _{lis.t of referenoes}

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32851

TÂLE I

PREVIOUS TESTS

-AUTI4OqS - 17PE OF SHIP E0UtT 1: WS1tILAL 1IN MOrSEL bIHENSOI4S bl.00Ic t&FÇ1CIDIT C&FACIEJII NUMBER OF CUT$,c&STRAIN - Ril1J4AR HARAS ME.ASUPEMENTS RMAR4S >1 - -Lx B x if în C5 C

SATO DESTROYER 45 BRASS 7,40 x 069 x 024 054 0,76 667,5 0,95-4,45 0,52

e

LEWIS T2-SE.A1 405 WOOD 4,46 x 0,498x 0,086 0,74 0,83 48,6 MIDSHIP SECTION 1,00 , 0,37 Ø

o

e

AIITA AND

EXP SkIP - BRASS 600 x 080 x 0200 083 067 797 MIDSHIP SECTION sos is os // //

TEST AT REDUCED

WACIINII AND

PASS UR 400 447 0240 008? 066 -080 478 0,50i50 -040

LUTZ AND %c L FORE

IW4BALL TANISER 426 WOOD 4,52 r 0,245x0,098 0776 -084 20,7 MIDSHIP SECTION

1Áo L AFT 20

0,5044,50 -0,40

DALZELL STRER 67 WOOD 474 r 0485 r 0064 054 075 III MIDSHIP SECTION 050-200 -- 060

AO.

CHRISTENSEN T2 SE M

TANKtR 50 WOOD 3066 x 0h45 x 0183 074 083 472 5 MIDSHIP SECTION_{L AFT} -"i 0Th-225 OSO '/ O

/

OCHI V-FORM

---

22 BRASS 6,00 x 0,826 r 0,555 0,744 0,836 4334

SEPR0PED

-.

-t» FORM 22 BRASS 6,00 r 0,826 r 0,355 0744 0,829 4334

DALZELL 57 SERIES 405 WOOD 4,463 r 0,497 r 0,087 0,68 078 47,4

T

405 WOOD 4,463 r 0,49? x 0,087 0,74 0,83 48,6 MIDSHIP SECTION - 4,00 ' 0,25

0 0

- 60 SERIES 405 WOOD 4,463 r 0,49? r 0.087 0,80 0,67 20.4

UNIVthSITY 60 SERIES 50 PLASTIC 2,438 r 0,325 r 0,430 0,60 0,706 64,9

- - 47,5% FORE

- 5 %FORE

60 SERIES 50 PLASTIC 2,436x0,348x4459 0,70 0,785 82,9 MIDSHIP &CTION 75I,25 0,50 >

5 %AFT

-47,5% AFT

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aid Of known mo!nenta..In

addition

_{to bending moment}

motions and wave height were aleo measured. _{Runs were}

made at varg speeds in. regu:Lar head and followinß

seac of ship length and a wave height of

21'/A

1/20.

Sorno results are given in fig. 1.

Moreover a number of teste was carried out in irregular

waves. Although some of his results had

_tO

_{be withdrawn,}

due to unreliability caused by inertjaeffects of the cantilever beani of the dynamometer, Lewis' paper gives

aneicellent review of testing technque,. _{our present}

status of knOwledge and valuable rfcommendation _for

further research.

Tests on a simplified ship model were carried out by AiUta and Ochi (3). They again made use of a model constructed of brasaplate. Stresses were measured using wire resistance strain gauges.It may be noticed that

test results are given for a reduced draught of abòut

60% of full draught and that only stresses _{are given.}

Therefore the bending nioment has been deduced _{from their}

report by calculating a moment of inertia _{from the}

des-cription of the model as given by the authors. As neither

the midship section nor the relation between _bending

moment and stress was given,tho reliability _{of the}

results as presented in fig. I is unknown.

Similar rests as described by Lewis were carried

out at M.I.T. by Wachnik and Robinson (Li.). _Theirmodel

was that of a Holland America Line cargo and passenger

vessel of 17.900 töne displacement, cut _{at the midship.}

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section and

at the forward quarter point. The three parts

were ooinected by an aluminium bar, on which strain

gauges

were motthted. The test procedure vas somewhat different from previous tests. The towing force was chosen ,n such a way that the model obtained service speed in smooth water; lxi fact the smooth water speed varied from

Fr-. 0.07. to 0.20. Due to the loss of speed in waves of

ship length and a height 2r,, 1/20 the speed range

decreased to ?rs 0.07 to 0.10. Probablywail. influences of the tank affected the results at these low speeds.

The same test procedure was followed by Lutzi and Kimball (5). Their model of a tanker was cut at three points, viz, the midship section and at 10% of thé length

fore and aft of the midship section. Here too the speed loss in wavès of ship length and a height of 1./20 of the length was considerable and consequently bending momenta wore measured only at relatively low speeds. Although

their teat results show a better agreement with the results of other investigations as shown in fig. I it may be dc,ubted. if the given vaÏúes for the bending moment

are free of the influence of wall.effect.

Tests on a destroyer model both in regular and. irre-gular waves were published byLewis and Daizell (6). The model was made. of wood and cut transversely at the midshi

section. The author applied the same technique as in the

earlier tests at the

Davidson

.thodel tank, viz, the

measurement of the relative displacement of the two

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-10-agreement with ßato's tests turned out to be quite

eatis-factory. The model

was tested in regular head and follo..

wing seas atvarioue speeds. Wave length was varied from

"VL.=o.5o

to 2.00 and the wave height was chosen as

i ¡zi.s ana. 2r 1/20.

The clasif1cation society Noreke Ventas sponsored

a test programme

that was carried óut in

the Trondheim

towing tnk by Christensen, Ltveit andMirer (7). Their

modeiwas again that of a P2-SE-Al tanker haying a length.

of 10' againet.4,79' of

the model tested by Lewis.

Bending moment and shear force dynamometers were desigried

on the same pninoiplea as described in (6). Tran8verse

cuts were made at

the midship section and at fore and

after quarterpoint. A relatively high bulwark was fitted

in order to prevent the shipping

of water over the bow.

The tests carried out at Trondheim makèit possible to

compare results of tests

carried out

in various tanks on

analogous models. As appears from fig.

I the

scatter in

teat results as obtained by various authors cannot be regarded as negligible. Therefore it seems to be worth-111e to continue similar tests in order to discover the

causes of the above-mentioned differences. As already

many teste have been carried out on models of the

T2..BE-A1 tanker lt may bé of advantage to use this 6hip

for fttrther research in this

field.

The influence of ship form upon strength and slamming

was jnveetiated by Och (8). Po brass model6 having

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V and the other U sections forward. The construction of the models was similar to that of an actual ehip.

The paper deals mainly with slamming phenomena, but deck

and, bottom stresses in regular waves of different lengths and heights are also given. The main conclusions as Zar as bending moment is concerned are as follows: the ben-ding moment is rou.ghly proportional to wave height, it

is smaller

than compúted,

even if the Smith correction

is included, the effeot of speed. isnegligible at speeds below pitching synchronism and bending momenta gradually

increase at higher speeds.

A very interesting series of. tet5 was publishedby

Daizell (9). Three

tanker models having the same

princi-pal dimensions but different fuilnessee

were run in regu

lar head.and following seas and

in irregular head seas

for the measurement of bending moment at thé midship

section. The fine model was chosen from the Series Sixty,

the model of mediumfullness

was agai-n the-112 SE-A-1

tanker, and the full model

was taken from the

Todd-Forest

Series 57.

Testing technique was "ETT standard".

A model teat with a. free model running in waves can give only information on the total wave bending moment. However, this bending moment consists of a number of

components. Therefore,

the.

judging of test results cannot

be complete without an analytical treatment. The various oQUlpOflente of the wave bending moment are:

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-12-These changes are caused by the waves and the pit-ching and heaving motions.

.2. loads dué to the reduced water

pressure in the wave

caused by the orbital movement of the water particles (Smith effect)

3.

Iloads due to inertia forces. These forces are

determ-ined by the mass of the ship,thé mnss of entradeterm-ined water and the dstribution of these masses over the

length of the vessel.

14, loads due to damping forces. The damping forces are

composed of two components., viz. wave d.ainpïng and viscous damping.

The first complete analytical treatment of the behaviour of a ship in waves and of the induced bending moment was

given byKriloff (io)

in 1896.

Although much work :18

been carried out since that time a complete and reliable method. of calculating the bending moment is still unknown Mention should be made of a very interesting paper by

Jacbos (11) in which a diit comparison

wasma&e-be#ween-the calculated bending moment and wasma&e-be#ween-the bending moment as determined from tests on the model of a T2-SE.A1 tànker in the Davidaon towing tank. Usè was made of the strip theory and a reasonable agreement bètween calculation and test was found. However, there is still a lack of

information o the influénce of three dimensional effects

and of free surface ffeots on

virtual

mass

and

damping.

It may. be expected that more information will become

available in the

near future,

as, especially

In

the

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experitlwor.konthis 13 experitlwor.konthis

-matter is in progre8..

The above waa the reason that no analytical calculations

weze made for theinodele tested in the

De].ft towing tank.

Comparison of the test results with static calculations

in which the Smith effect was included was thought to be

sufficient for the time being.

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_1L_

3. Desort.tiou of models inodelmatertal and testin

oui.-ment.

The usual method. of measurIng the bending moments Induced

tua model when sailing in.waveois the use of a modi

divided at one or more sections. The different parts are connected by astructura]- member which has the

relative comparable strength of the. ship. The bending

moments can be measured for instance by means of strain

.gages on thé cónnecting bar, which has to be calibrated

in terms of bending moment. Sometimes, a pivot io used to connect the different parts and the relative deflect-ion of the two parts is restrained by a stiff

electro-nical dynarnoineter.

LÌ

As described in chapter 2 a second method makes úse of brass models, which are provided with strain gages.

In thiscase rather large models are necessary in order

to obtain a measurable stress

inbe model.

For the tests discussed in this report three modelo were

made of fibreglase polyester laminates. Vàluable ad'iioe

and practical assistance by the Plastics Research

Insti-tute T.N.O. at Del±' t resulted in proouringa material.

which behaves aoàording to Hooke's law and of which the

value of Young's mothlus Is small. Thus a measurable

stress is ensured when testing even a rathèr small model in waves. The first model to be tested was constructed

by the Plastics Research Institute, the second and third

model were made by thé technicians of the Deift towing tank.

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Series Sixty Parent Forms as published in (12). The

length of the ehipmodels under consideration was the same

for al]. three models, however, breadth and draught showed

some variation as indicated in table II. Each model was supplied with a forecastle, a poop and a midship deck-bouse. This deckhouse was also used to pass the electri-cl connections of the different.. pick-ups to the towing

carriage. The block coefficients were. 0B 0.60; 0.70

and 0.80 resp. figs.

2 a, b and c show the bodyplans,

f ig 3 shows the three modela.. Table II gives the

princi-pal data and fig.. 14 sbow theweight distribution of each

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16 -PABLE II

Main dimensions of ship models

Service speed 0,268 O 208 0.149

Symbol '4.210 W 4214 W '4.214W-Bk

Lenth

on waterline

_.I1wl 247.9 cm. 247.9 cm. .247.9 cm Lngth between perpendicu-lax's Lbp 243.8 cm. 243.8 cm. 243.8 cm Breadth B. 32.5 cm. 34.8 cm. 37.5 cm Draught d 13.0 cm. 13.9 cm. 15.0 cm Depth at D _{17.4 cm.} _{17.5 cm.}

191 cm

Displacement 62.9 kg. 82.9 kg. 109.9 kg

Bi ockc oe ff ici ent C3 0.600 0.700 0.800

Waterplane area coefficient OW 0.706 0.785 0.871

Midship section area coefficient 0.977 0.986 0.994 Prismatic ooefficieñt Op 0.61'4 0.710 0.805 L/B 7.50 7.00. 6.50 B/d 2.50 2.50 2.50 L/d 18.75 17.54 16.?5 Scale ratio 50 50 50

Radius f gyration 0.25L O.25L 0.25L

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17

-The models were manufactured in the' following manner. First a paraffin-wax model was made in the .tra4itional manner. A female mould, was constructed on this model, the material for this mould was also-glass-reinforced plastic The ship model itself was built up in this female mould and contained three layers of Libre-glass. Thé thickness of the shell was about 2 mm. Young's modulus of the

material in longitudinal direction,, determined

experimen-tally on a test bar, was

_7,35

x 1O

kg.cm2.

A somewhat

more 'extensive description, of. the manufacturing of the models-is given in (1.2). Electrical resistance stràin.

gauges were, built in into the sides of' the model at five cross sections, vIz, the midship section, two sections.

in the fore .body and two sections n'the after body,thus

providing the strain along the length of the vessel. This

method has the advantage that the befld±ng moment curve

over the length is easily obtained. On the other haùd

it was .not possible to get, information on the shearing

forces. For each cross section eight strain gauges wére

used from which four were used as active and four as

dummy gauges (f ig.5). By'using four active gauges each

measuring station was compensated against the influence

of local bending öL the ships sides. An example _{of the}

registration obtained from the penrecorder is-given in

fig. 6. 'As this record was made at high speed añd high wave height, the curves show some noise. Nòrmally smooth curves were obtained but this sample has been chosen to show the.. effect of a slamming impact on the recording.

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18

-required in order to translate measured strains in ben-ding moments caused some difficulties. Under static

loading the model material produces some creep, involving a greater strain than will be obtaiñed under dynamic

low-frequency loads of the same magnitude as met under

towing cònditons. Therefore a ynamic calibration device

was

built of which fig. 7 shows the arrangement. This

apparatus loada the vessel by means of four

springs in

such a way that the

measuring

sections of the ship are

subjected to a pure bending moment. Dynamic loading is

obtained by moving the upper plate

in

forward and. aft

direction by which the adjustable exoentrios caused the springs to apply asine load to the model. Both frequency

and load were varied during the calibration. It appeared

from thia calibration that the model material followed

Hooke's.

law

exactly in the frequency range, to which the

model wa6 submitted in the test conditions, viz, from

0.7 cps at zero speed to 1.8 eps at Fr 0.30. This

cari-bration was repeated several times during the test pro-gramme but no measurable deviation was found. The weight distribtition was chosen in such a way as to give a

longi-tudinal gyradius equal to 0.25 L. This gyradius was

ad-justed with the help of a pendulum table. The natural freqùency reduced to scale oS the two node vertical hull vibration was about what might be expected for the actual

ships. These frequencies were determined in two manners, viz, by excitIng the model with a small vibration exciter and by giving the model an impact at the bow. The resulte of the vibration tests will be treated elsewhere.

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19

-The testing procedure was as follows. -The model was

towed with a constant towing force by _{means ofa gravity}

type dynainometer and alight _{.suboarriage. This}

dynamo-meter reduced the towing force to one-fifth of the towing weight and as a result the acceleration forces due to surging on the towing weight were also reduced to

one-fifth. This sub-carriage was guided

by.a

horizontal rod

and ball bearings. The towing force was applied to the model at the centre of gravity. The speed was varied from

zero to Fr _{0.30 at various wave heights and} _{wave lengthE}

The model itself was guided

_{by two}

_{vertical rollers}

sli-ding between two pairs of horizontal _{tubular roller guideE}

connected. to the towing carriage. In this _{way the model}

was free to

heave, pitch and surge, but rolling _and

yawing were prevented. The speed of the mädel was obtain-ed byineasuring the speobtain-ed of the towing carriage, which

speed was automatically corrected _{for the relative}

dis-placement of the model with regard to thé carriage. The foltowing ttenïs-were measured:

heave

pitch êngle

e) wave height _{recorder I}

d) _{emersion of f orebody at}

section 18

wetness of forecastle deck at

section 18 bending moment in .5 sections

J recorder II

Heave and pitch angle _{were mèasured by means of low}

friction -proc isionpotenti ometers. _{-For--the--recording_of}

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20 -the wave height a wire resistance wave height

pick up

was attached to the towing

carriage in a fixed

position

at about 1,5

meters in

front of the model. The wetness

of the fore castle deck and the

emersion of the foro.'.

body were meásured. by means of two pairs of

electrodes

between which an electrical circuit was

opened,

respeoti-vòly closed by the water. In fig.

5 the

bottom contact

is ind.iòated as "slamming contact" although

emersion of

the forebod.y does not necessarily involve a slamming

impact. The position of the different pick-ups le shown

in fig. 8. In fig. 9

the

forebod.yof the CB 0.60 and

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-21-¿4 _{Test proranune.}

havIng a wave length of

Land 1.25 L. The test

The tests were made in waves

respectively

A

0.75 L1 1.00

programme is given in table III.

TABLE II]: ),

IL

Test Programme

2rj

MOdel 0B = 0.60 CB 0.70

060

Speed range

Fr=O.00upto

0.30 Speed range

Fr0.0OuptoFr'0.00up

0.30 Speed range to 0.30 o

®

0.75.

1/8

1/4.0 1/30

.

1/4.8 1/4.0 1/30 I 00

®

1.251/4.0

1/11.8 .1/30

®

.

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22

-For the' two £ner models it appeared to be impossible to

make'measurements at a wave height of 2r/À 1/30 due

to severe ship motions, which'caused.bwnping of

the

model

on the carriage. A

change in the test set-up mde it pos-sible to carry out these tests with the 0.80 model.

All three models were tested in thé epeed.range from' Fr = 0.00 up to Fr e 0.30. Especially for the fuller

models the higher speeds are far in exoèse of the service

speeds according to (11) and

as given in

_{table II.}

However, the investigation of these high spéeds provided interesting information with regard té the bendimórnen.t.:

Although

measurements

were also taken in the lowèr speed

rango these

results are not very reliable dueto wall

effect' as indicated by

Ge'rritsmain (14).

'Therefore

the

results in

the

'range between Fr 0.00 añd Fr 0.12 are

indicated in the various figures by thinner lines

or

dotted lines.

After each series of ' .nwa_number o reruis was carried

out so 'as to have á

check on the'obtained values. More-over the bending moments produced by the modelß own waves in still water were measured. The values obtained in calm water may be influenced to a small extént by the towing

f.orcó, as this force and the ship 's resistance will

induce a strain in the ship's

hull. Therefore all hogging and sagging moments are corrected'for this calm water moment. This appears reasonable as this moment'js purely

'static. The bending moment range

in waves, viz, the sum

(28)

-23-ship' s owii wave train,

_{as. these waves will cause only. a}

(29)

Test results.

a. Ship motions.

The motions of the ship, viz, pitch angle, heave and pháae angle are givén in fig. 10. The test results are présented in the form of non-dimensiOnal motion

amplitu-des and

5<

and the phase angle

ii

between heaving and pitching, where

= pitch amplitude

Z0 heave amplitude

z1r2

maximum wave s lope

Infact the testresults as published by Gorritenia in (14) are shown in fig. IO. The results obtainèd in the tests discussed in this report were checked against Gerritama's results and the agreement turned out to be excellent. In the above-mentioned report attention is drawn to the fact that the motion amplitudes and in particular of the pit-ching motion9 are smallest for the fuller models.

Seôond-

-2k-ly, it is shown tìit for wave heights less tharr 1740 L linearity of motions with wave height is within the. experimental error and even for a.wave height of 1/30 t this approximation proves to be valid in many oases.

Speeds

which produce synchronous pitching and heaving

motina are indicated in figs. 12a, b, c, d and e.. where

.JÌ

is: the resonance factor for heave and.

fl,

the

resonance factor for pitch.

Natural circular frequencies for heave and pitch were

(30)

-25--b. Slamming and wetness.

Unfortunately the "slamming contacts" were fitted to far aft, viz, at frame 18. The motions of the ship were, not severe enough to cause excessive emersion of the fore body and not once during the tests,, described in this

report, 'the electrical circuit was opened. . .

The resulte of the dok contacts are given in fig.11 The following table shows the. speeds at whiçh the

shippa-ge of water started.' .

TABLE 1V

Speed at whIch water slippage started

CB . 0.60 0.70 0.8Ö .1/11.8 1/11.0 . 1/11.8 . 1/11.0 1/11.8 1/11.0 _1/30

2r/L

. ' . Fi' Fr ,.. Fr Fr Fr Fr . Fr ' 0.180 '0.200

0117O.110'

1.25 - 0.220 ., -.

À'

IL

1.00 - ' - - -. - - 0.122 0.₇₅ . -

-,

-

.

-

.

-

-.

-L

The critical range in which not every encouñtered _wave

was shipped was, rather narrow _{A very small increase}

in speed was sufficient tç change thed.rycóndition into the condition where every encountered wave was shipped. It is self-evident that this applies only to a 'condition in which regular waves are encountéred. It appears from

(31)

26

-serious fr the longest wave tested and that the greater the block coefficient the lower the speed at whiôh the shippage.of water starts.As too many independent varia-bles, as for instänce flare, freeboard fOre, and

synchro-nism of motions play a part no general conclusions can -be drawn from these results.

c. sending moments.

To start with, some runs were made to investigate the tnfluence of the wave height on the bending moment amplitude. For this purpose only the CB = 0.70 model was tested in regular waves, varying in height from A/48 L to 1/20 L. In general a good linearity was found

and for wave heights leaB than 1/30 L the differences were within the- experimental errors. In 1/20 L waves

large amounts of water were shipped and in this case some scatter of the test results was found. It was remarkable however that in moat oases the influence

of the shippage of water on the b.nding moment amplitude

was rather small. -

-After these preliminary runs, in which also the- electro-nic instruments were tested the test prôgramrne'as

indi-cated in table IIÍ wascarried out. All data from the regular wave tests are plotted in figs. 12a, 12b, 12c, 12d and 12e. In each of these figures the results for one of the measuring sections of each of the three models are summarised. These results are shown with respect to speed and wave length. Thebexdthg moments

(32)

27

-are given in the fórm of a dimensionless parameter C,

where:

o M IA = bending moment

2 tZ

density of the water

7=

acceleration of

gravity wave amplitude In all figures 12a up to 12e the total range of bending moments is given rather than a hogging moment in one and

a sagging moment in the other direction. This is done

because the experimental determination of an amplitude is much more accurate than the division into two cornpo-nente, the latter being dependent on the exactness with which the zero line can be determined.

As explained in chapter ₃ hogging and sagging moments

are corrected for "calm water moments" due to the ship's

own wave train. However the bending moment amplitude is

independent from this "calm water moment".

The curves as shown in fig. 12 were corrected by drawing

cross curves, which represent the maximum bending moment

distribution along the ship's length for a certain speed and wave length.

Therefore curves in fig. 12 do not represent the mean values of the data assocthated with a particular cross section.

At. section of the 0B= 0.70 model the resistance

(33)

28

-during the test, resulting in unreliable test data. Theréfore, they have been omitted from fIg. 12d. The cause of this was a breakdown of the waterproofing.

The CB 0.80 model was. towed far beyond the sérvice

speed. At these speeds the: model shipped considerable' amounts of water and the obtaining of reliable test data

offered more difficulties than with the finer models.

In 'consequence a certain scatter of test data could not be avoided.

(34)

.9

-6. Discussion of results and conclusions.

In the following a discussion of the test results is given. However, in comparing the results obtained with the three models, it must be kept in mind that not only the fullness of the models was varied, but that there were also differences in breadth and draught.. The ratio B/d was kept constant for the models and equal to 2.50, but the ratio L/B was 7.50 for the CB = 0.60 model,' 7.00 for the CB' = 0.70 model and 6.50 for, the CB = 0.80 model.

Trend.of bending moment with speed.

As can be seen from fig. 12c there is a gradual, but ïn most cases rather small increase of midship ben-ding moment range with increasing speed f or all the models.' However, the

B = 0.80 model that was towed far

in excess of service speed showed at these very high speeds a rapid decrease in bending moment. The same

phenomenon was also noticed with the CB _{0.70 model,}

but only in long waves C 1.25).

The speed at which he bending moment range of the CB = 0.80 model attained a maximum was lowest in the

longer waves, whereas, on the other hand the speeds that cause synchronism are highest for the long waves.

Similar bending moment Curves, showing a gradual' increase followed by a maximum and next a decrease,

(35)

-30-Christensen). Theoretical bending moments calculated by Jacobs and Maday(15). also showed this trend.

The maximum in these calculations occurs at a somewhat lower speed than found in theteets discussed here. In the first place the differences in thé ship's lines will bè responsible for this (the calculations were

carried out for a LIB ratio of 7.11.1 and a B/d. ratio of 2.6). Secondly the bending moment is very sensitive to alterations in the weight distributiOn because of the.acceleration effects. In (15) the gyradius of the

three models varied from 21

.9 to

23.9% L, whereas

the plastic models had a gyradius of 25,0% L.

Any conclusions whether the bending moment range for

the CB 0.60 and CB 0,70 mòdel also show a maximum

cannot be drawn from the testS as described in this repOrt as no runs were carried out at speeds above

Pr 0.30.

In general analogous curves, as found in the midship section were measured in the four other cross sections. Only in the aft section the variation with speed is

substandtially lower and up to service speed the bending

möment is ròughly constant. .

b. influence of wave length on bendin oment.

There is no clear indication as to the wave length at which maximum bending moments occur. This does not. hold ibr zero speed where the bending moment shoWs a

(36)

-31-maximum, at a wavelength that is about equal to ship

length. To be e*act the wavebending moment

range is,

largest for the C 0.60 model when

A/L

0.95,

for the CB 0.70 model when

AIL

1.00 and for the

0.80 model when

A/L

1.10. In all other cases

t'e

A/L

ratio at which the midship bending mòment.

reaches a maximum is dependent on speed. The above was algo found in the tests described in (7).

o.

Trend

of bending moment with ii2creasing block

. coefficient.

In short waves, viz.

A/L

0.75

the bending moment

coefficient

C. for the

_CB 0.70 model is somewhat smaller

than for the C.. = 0.60 and CB 0.8.0 models at the same

Froude number. In longer

waves, viz. -AIL 1.00 and

AlL

1.25 this, coefficient increases with increasing

fullness. In the àpeed

range Fr

0.10 up to Fr

.0.25

and in waves of' /L 1 .00 the trend established by

conventional

static calculatinna. w.th 3mith effect

in-cluded:is clearly followed. This phenomenon is clearly

illustrated in fig. 12f,

where C as

derived from the

test results is plotted gainat C ás obtained from

conventional calculations. .. .

In this'fgure.test resu1ts from öther iñvestigators are also shown. In those cases, where no results of conven-tional calcùlatlons were knöwn, an approximative method

(37)

-

32-The effect of. wave heIght on the bending moment coefficient.

An almost linear relation between bending moment and wave height was found. This conclusion holds both for the hogging and sagging moments and for the bending moment range. In general the deviations from linearity were within the test accuracy.

However an exception was found in waves of'

= 1.25 where the sagging moment increases with wave height at. the cost of the hogging. moment in the higher speed range.

The influence, of the shippge of water.

The influence on the midship bending moment of the shippage of water over the bow is surprisingly small. An analysis of the teat results shows an increase of

the bending moment of about 4 to 6 percent.. This increase is of.the same magnitude as the experimental errors.

Distribution of maximum bending moments over the ship's length.

The maximum bending moments in hogging and sagging condition for. the three models are plotted in figs.13, 1k, and 15 over the.length of the ship..00nsequently these curves represent the envelopes of the bending moment curves occurring over one period.'

(38)

33

They are obtained by deriving croas curves from fig.12a up to e. From figs.' 13, 1k and 15 the following

conclu-sione can be drawn.

the section in which the hogging moment reaches its maximum value does not coincide with the section in which the sagging moment attains its maxImum..

the location of the section in which the hogging or sagging moment reaches a maximum, i.e dependent on speed and on wave length ratio.

òonsequently the ratio between hogging and sagging moment is dependent on speed and wave lengt1\ ratio.

k) the maximum bending moment range (hogging + sagging)

does not occur in the midship section, which shows that. the requirement of the classification societies, to main-tain midship scantlings of structural parts over one half of the length is a sound one.

5)

at high speeds the curves differ more and more from.

those baBed on conventional calculations. Especially

the CB 0.80 model shows a remarkable deviation. In

this model the xaeximum sagging moment occurs in a cross

section at a considerable distance forward of the

midship

section. This

phenomenon was also

observed in unpublished

tests by Det Norake Ventas with á T2-SE-A1 tanker.

g.' Variation of bending moment with time.

Fig. 16 and 17 show, the change in longitudinal bending

(39)

CB 0.80 model. These figures are deduced from one single run, for which was chosen.the one nearest to service speed. Hence, there may be some deviation from

the results as presented in figs. ILl.. _{and 15, which'}

represent the mean value obtained from _{all the tests.}

Figs. 16 and 17 show how a sagging, morneñt is transformed into a hogging moment over half a period. The heavy

loading of the fore body Of the _CB _{0.80 model as}

mentioned.under (e) is also clearly apparent in fig.17. Unfortunately, the phase angle between wave and the

bending moment could not be determined _{very reliably.}

as the model was free to atirge and the _wave

height-meter was attached _{to the carriage in a fixed}

posl-tion. Therefore, the phase angles _{re omitted from these}

figures. Roughly estimated the phase _{lag between lave}

and midship bending moment is rather small and

acàording-ly a maximum hogging moment _{occurs when a wave' crest is}

about midships and a maximum sagging _moment, _{hen a wave}

(40)

35 -7.

Com.arison of observed and calculated midahi. bendin

moments.

a) Conventional calculations.

For the three models, conventional calculations were made, both with and without Smith correction. The experimental values of the bending moment ap-peared to be much smaller than the calculated

values when no Smith correction was included. Even if the Smith correction is taken into account, the experimental values are still smaller. In fig. 18 the results of tests and calculations are shown. The sagging moments are rather close to the calculated values, at least if the Smith

correctiôn is included, whereas the hogging momenta are substantially smaller. This last statement does not hold in all cases as the ratio between bogging and sagging moment depends on speed. In fig. 18 the test results axe_gieñ_for_only on speed which is the same for all three models,

(Fr 0.15). This speed correspoñds to service

speed of the C3 = 0.80 model, but is rather low for theother two models.

In fig. 12f a comparison is given for four diffe-rent speeds. In this figure, computed bending

moment coefficients are plotted against experimen-tal values. All calculated values are given with Smith effect included. The influence òf block

(41)

36

-this figure. The increase in bending moment with increa-sing blockcoefficient plainly follows the trend obtained from conventional calculations. For completeness, the results of other investigations are plotted also in this figure. In those cases where conventionally calculated bending moments were not knwon, approximate values were derived by means of Swaan's method as described in (16). In nearly all cases the experimental values are well below the computed ones. As ship's form, gyradius and weight distribution were different for the various models a close agreement between the various test results cannot be expected. However, an exception must be made for the

tests with the T2-SE-A1 tanker. In this case the weight distribution and ship form were analogous for the four models tested. Experimental errors, tank dimensions,

(k

model scale and test arrangement may have, affected the results and may be responsible for the differences. Obviously this problem needs furthèr research.

b) Calculations according to the strip theory.

Jacobs and Maday (15) computed the bending moments for the three E.T.T. models tested by Daizell. An excellent agreement was found in áll three cases. The experimental values, obtained in regular 1/51 waves for hogging and sagging condition, coincIded largely with the analytical values. In fIg. 19, the bending moments at service speed

(42)

bending moments at service speed as measured on the three models discussed in this report, are also shown in f ig.19.

Taking into account that the E.T.T. models had à somewhat different weight distribution, the agreement is surpriing-ly good. However, it must be remarked that at other speeds somewhat larger deviations are found. The fact that with the E.T.T. models the maximum in the bending moment curve occurs at a somewhat lower speed than with the Deif t mo-deis is reponsible for these differences.

(43)

- 38 -.

8. Final remarks.

The use of plastics, as a material for the construction of models, offers' the possibility of determining bending

moments in various cross sections ver the models' length

without the necessity of cutting the model in several

parts or of using extraordinary large models. When testing a mode,l made of fibre-glass polyester laminates in waves, the strain produced in the matêrial is of a magnitude that

can be measured quite accurately by means of wire

resis-tance strain gauges.. Moreover, there is no limitation as to the number of measuring sections or as to their loca-tion.

Local deflections of the shell, due to water pressure, can be kèpt small as Young's modulus of the material in

transverse direction is about three times as large as in the longitudinal direction, provided a suitable unidirec-tional fibre-glass cloth is used.

Moreover, byapplying strain gauges. bothorl the outaifie

and on the inside of the shell, the longitudinal straIn is not affected by local bending of the ships sides. The absence of cuts and flexure beams is attractive, especial-ly when self-propelled models are to be tested.

However, certain precautions are required. Decks and midship deckhòuses should be constrticted in such a way that ño interaction between hull and those Items is pos-sible. Dynamic calibration of' the modêl is necessary and cannot be replaced by a static bending test. This involves

(44)

39

-the necessity of building .a calïbration apparatus capable of producing a sinusoidal bending moment of which both amplitude and. frequency can be varied within the desired ranges.

Provided the tests are carried out with muchcare and reliable electronic apparatus is used for the measurement of rather small strains model experiments of the kind descriled in this report seeinto offer possibilities for analysing wave bending moments in ship models. An atten-dant advantage o1 models made of plastic is their cuita-bility for use in model vibration tests.

(45)

Acknowledgments.

The Author wishes to acknowledge the assistance of Mr. iI.J. de Ruiter and Mr. H.J. Westers in carrying out tests and calculations and the contribution of various members of the staff who assisted in the realisation of this projeçt.

(46)

-41-REFENC

(1] Sato-M. Model Experiments on.the Longitudinal Strength

of Ships. running among Waves.. E.T.T. réport nr. 614;.

Deôember 1956.

(2] LEWIS, E.V. Ship Model Tests to Detrmine Bending Momen

In Waves. Trans. S.N.'A.M.E.

_1954,

(3] AKITA, Y. and OCHI, K. Model Experiment on the Strength

of Ships, moving in Waves. Trans. S.N.A.M.E.

1955, p.p.

203-236.

(4) WACHNIK, Z.G. and ROBINSON, P.R. A Study of Bending

Moments in a Ship Model moving In Waves. Thesis M.I.T., May 1956.

LUTZI, P.C. and KIMBELL, E.D. Ship Model Bending Moments

in Waves, Thesis M.I.T May

_1957.

LEWIS, E.V. and DALZELL, J.F. Motion, Bending Moment and

Shear Measurements on a Destroyer Model in Waves. E.T.T. report nr. 656, April 1958.

(7]

CHRISTENSEN, H., LØTVEIT, M. and MtJREC.

Modellforsøk for a bestenime Skjaerkrefter og BØyemomenter i et Skip i regelmessige BØlger (in Norwegian). Report nr. 207, Research Dept. Det Norske Ventas. September1958

C ] OCHI, K. Model Experiments on Ship Strength and Slamming

in Waves. Trans. S.N.A.M.E.

1958, p.p. 345-383.

9]

DALZELL, J.F. Effect of' Speed and Fiülness on Hull

Bending Moments in Waves. E.T.T. report nr.

_707.

February

_1959.

[io]

KRILOFF, A. A General Theory of' the Pitching Motions

f ShIps_on_Wves and the Stresses Produced by this

(47)

42

-i1] JACOBS, WIR. The Analytical Calculation of'. Ship

Bending Moments in Regular Waves.

Journal of Ship Research, June 1958, p.p. 20-29.

12] TODD, F.il. Some further Experiments on Single Scréw

Merchant. Ship Forms-Sèries 60.

Trans. S.N.A.ME.

_1953,

_{PSP. 516-589.}

ALGRA, E. Reinforced Fibreglass as a Material for

Ship Models (in Dutch) Plastica vol. 12, no. 4 aprii

1959, p.p. 264-267.

GERRITSMA, J. Shipmotlons in Longitudinal Waves.

Internationál Shipbuilding Progress no. 66, Volume

_7,

Febr. 1960.

15] JACOBS, W. and MADAY, A. Comparison of Experimentally

Measured and Theoretically Estimated Bending Moments of' three Tanker Models in regular head Seas.. E.T.T. report

no.774,

July 1959.

(16] SWAAN, LA.., Amidship Bending Moments for Ships in

Waves. International Shipbuilding Progress. Vol.6 nr.6r

(48)

HG. I WAVE BENDING MOMENT AMPLITUDES (I4OG

GING + SAGGING) IN REGULAR M.. 4 WAVES

A$ MEASURED BY DIFFERE.NT AU1I4OR

C

0ß4

LWIS SATO

AND DALZ&L1. DESTROYER cc559

DESTROYER Ceii 0.539 V

-M Fr

-00 0.4 02 c 004-m5YE& CO,662 6O3EP1ES _CbO,68 60 SERIES C O68 2 2 4/54 4o

f---

-

DALZELLWAM1I --- DALZELL

-.-.

_//

N

004 00 04 0 C

fALZELL

bALZELL 12 TANtEP CBIO.F4

-u

-LEWIS

CHRISTENSEN

OCHI HERCHANT SHIP ,

-

---

--'

..I--.

V FORM

....TT

U FORM o O ftI 0.2 c EXPERIMENTAL MODEL 57 SERIES TAIIKEP CO,8S Cr0,80 CBO,??6

f---

- AKITADALZELL

DALZaL

LUTZI 0.04 0.4 0.2

.fr5

(49)

Li T

2

'V'ti

6 7

8

40 ₁₀ bUt ULWÄR% tECl

(50)

BULW4R.

(51)

BULWARK

- -

-I---::

o

20

FIG. 2c

MODEL 4214 W- b4 C6O,8O

(52)

.84)

;

\.

,1.

FIG. 3 THE MODELS

(53)

(54)

i K.C. 5 V. O5CILLATOR CON PA R ISON RIbG ACTIVE OUTSIDE Sb. ACTIVE INSIDE Sb.

FIG.5

BLOCK DIAGRAM

D.C. AMPLI FIER WETNESS CONTACTS

»

31..AMMIMG CONTACTS FIVE CHANNEL. PE.NRECORER

(55)

o

Lu

r

Ä:7

_{¡[7 ¡Ti.v 711}

L r Äiuiiiu

AIllIIWI

k

eli,

II$WWA

_ww*wwwi

._wI w

N,

_{wai àwi' a}

I1NZNWIMXPà 'WIINM IRU

_{aaviaawa aap}

pr

iLl&l

7a.aaaI

or

iiin:iiIlii

iiiun:.

A

Ii

Ihhthtth!NMIIIIJII1

I

r

(3

..

4

*

IUUU

a.

AUUI! UUIU

k ',

,-

LlP'ill'!i

\ \ \

TWO WOOLS VITlCAI. V%ATW

Nl-I

11011

-,

_riii

.*MMINS øI.C7

1

I

II..

MMIII

MM

[f

.7

/ IMIMMIMIMMI

L II. IlION III

I i

f llRI1l

L Il* I

-4gu.*

RIO

wowosli

w

FIG. 6

SAMPLE OSCILLOGRAPL.1 RECORD OF BENDING MOMENT

NOTL: AMPU PI CATION tPPER8 FOR EACH CR055 5CTION

I-f- I J

r'

o II. OH

z

(56)

nC 7 O'V!W CAL1ATD4 DVU. .4, .4, .4.

-î

-i.

-t

PLATE

j

flì

::: :'

I ECCENTRIC J Z. A. .USTMt ..

(57)

TOWING CARRIAGE DOUBLE GUIDES OW BALL BEARINGS di. PITCH 5TRA%N GAUGE GUIDE POl METER

HEAVE POT METER

SUB CARRIAGE WETNESS CONTACTS GRAVITY DYNAMOMETER

¶

L

HI

i

SLAMMING CONTACT5/T4o,o %L 47.5%L

47%L

,J

(58)

STRAIN

GAGEt/

CONTACTS

J;=070

I

FIG. 9 FOREBdY OF THE CB= 0.60 AND

CB= 0.70 MODELS

CONTACTS

C.W.L.

(59)

FIG.iO NOTIONAMPLITUDES AND PHASES IN REGULAR WAVES 1.5-PITCH C0O.8O 10 _{_0_O} A/t2S . o * /LO2L5 t5-HEAVE i425 --1Lth A/75

AT

135 _{PHASE LAG} _{HEAVE AFTER PITCH}

«e-0 ₁ O 0.1 Fr. - 0.2 0.3 1.0 PITCH c9eo.70 -- -- --- - -

-o .. Aj=t25 Q J À11e 0.75

:

HEAVE/\

o A ?/etO0 /L° 135

PHASE LAG HEAVE AFTER PITCH

o O.lfr..-.0.2 0.3

r

a PITCH C0=60 ".-....

s--,,'

_L°° HEAVE - -

4-r

0.5

//

1,0 .1+

-''

N

135-PHASE LAG HEAVE AFTER PITCH

i

(60)

CmaOÓO

C50170

FIG. H

TIME IPI % THE tECK WAS SUbMERGED

- NUMBER OF ENCOUNTERED WAVE5

IN % THAT CAUSED

WETNESS

WETNE5

OF FORECA5TL

1ECK

mn

%

C5 = 0,80 >'L=4,O0 L -¡

/

I, 50

0I

Fr.

02

03

$00

50-2.¼o

F C1O170 _/Çs=0,6O 0,4 Fr. 0,2

03 400-%

-

-,

I ' _{_} I /

r\

7 CO38O

/425

_,41iY

i'-.

i '2I 4

»

/

'AO

50 V//f

u

Oil

02

03

Fr. C

080

o 0

o

I0

(61)

PL.)

FIG. 2 TEST RESULTS FOR FORWARb SECTION 1

I%L M0b.L 4214 W-M C0.8O X=O.75 0.0 27.../ 2J7LY&O

j

27

j/

H.Cpg2rL2b

-T1

0.02

C--

H0G 0.04 SAG. 0.04 0.03 ci HO -SAG t

Fue

0.20 o_03 0.02 cl 0.04 M0I(.L 4210 W C 0.60

t075

27 27L=YAO M.Cpg2rL2b H000040 e ---_J____ ---. MOGUlS

.o--

_.

0J33 002 cl 0.03 HOG. -C,,25 0.03 0.02 0.40

FR--

0.20 0.30 0.03 MODEL 4212 W CB0,70

Oj'/4o

ax- yao M.Crg2rL2B 0.04 HOGGING 020 0.02 ci

_:

Q

--T

0105 0.02 0.03

-ci_____:-

°

::-5A6.

-t1

-I0.30

(62)

Fp---5%L MOIE.L 4244 W-4 CQ80

k

=0,75 o G M=Cr92rL2B 0lil

----i:

I!

SAGGING -403

----0.02

--c--.-_-

₁

-401 ----004 40

-

---E---jí

0.0

FR-

0.20 430 M0IEL 4242W C5=0,70 k=0.75 405-rc y40 M0,Crq2rL2 0.02 .-0-

'.

0.01 SAGGING

ki,00

405 402

co

4011 e.- --o - - -SAG. 1

--0.03 402 401° o SAG. ..1

I

4.. I °

Fit

020 0.50 MODEL 4210 W CO360 k=0,75 o M.Cpg2rL2B 40I HOGGING O 0

t4,00

0.05 4021 2 404 SAG.

----e-i 0.03 -41Ò 02ó 430 Fn

(63)

FIG i2C TEST RESULTS FOR MIbSI-IIP SECTION M0IL 424 W-M CO380 "L 0,75 0.03 0.02 Cl ¿ 0.O4f 2,VL=Z6 M=Cpg2rL2b HOGGING SAGGING - t,,I,00 0.03 002 :L;L 04,;

'tc RUN FROH WHICH FÏG. Il IS OE.OUCED 0.03 0.02: cl 0.04

tI25

-:_---

'----SAG. .I

i

4;. I

-FR-

020 050 0.03 MObEL 4210W - C 0,60 'tQ75 o 27 27=zO = _MCgg2rL2B HOGGING 0.04 ---SAGGING 000 0,02 . t 1.. )(1,25 0.03 0.02

cl-.-&..<___.

004e -SAG. --010

FR

020 - O,aO MODEL 4212 W - CO370 tQ75 o27=y

-=

y40 t4.Crg2rL2b 0.03

cl-HOGGIÑG

-. 0.04 SAGGING 0.00 04 0.03

C,

0.04

-.

J, 4I. r--.ç-cf RUN 140G -

-

.

-SA FR044 WHICH FI 46 li-

_I

IS OFJSUCEO - t,l,25 000 HOG

--SAG.

-_I <i 1 I

-0.10 0,20 050 FR

(64)

F I G.12d TEST RESULTS FOP AFT SECTION 4 5V.L MOL 4214 W- b4 CO38O { b.75 0,03

OO2'

o2'j

2Xo

MCpg2rL2

:oÇ

SAGGiNG -

{i.00

405 -0.02 cl o.o -HL HOG.

T'

__

SAG. 0.05 0,02 cf I 401

'Li.25

-

--T.--HOG. ---SAG.

FR-

° 405 0,02 cl 401 M0DEL 4212 W C= 070 cl 0,75 o 2X = McCr,2rL2b HOGGING --SAGGING 0.05 0.02 404

c---HOG. - ..__-SAG ¿p-0,03 0.01

--SAG. -«I 1 <I 0,0

_Fp--

0,20 MObEL 4210 W CBO,òO (=Q75 403

o2j.j

2XcYiio M..Cp2rL2b ---HOGGiNG 404 N lf.cl 1.00 1

--404 ___. ---MG.

4

403- -QO.

Ti

:O4Lf:J:

., t M 420 F

(65)

FIG TEST RESULTS FOR

FT SECTION 5

%Z5XLJ

0.05

0.02

001

MODEL 4214 'il-bA CB0.8O X=075

2X Y G 27L=Y3O MCg2rL2 hOGGING SAGGING - ---S 005 02 cl -=lIoo L

0,0S.

0.05 0.02 C -S--SA& .. <I 1I.

Fi

o2o MODEL 4212 W COI70 o 2X=Y4o MCpg2rL2B 00I SAGGING

cl.

QO SAG. 0,02 cl Q04 SAG. -,1 4

...

0.0 VO

MODEL 4210W C..Q6O tO.75

Q0-

-.----o 27..

27

M,C1'g2rL2 cf

L-0,04 -_.. t__S __ ---HOGGING SAGGING =iI00 0,05 - --cl -

-)(i25

0,Q5 - -0.02 cl 0.01

-..

HOG. SAG. -- . - ___________ ----S-.-0,40

FR-

0.20 -0.30

(66)

32852 FIG. 2r COMPARISON OF CQNVNTIONAL CALCULATION ANb TtST PESULTS O,I'J SAIO AJ%ITA 4 LEWIS O CMRISIEHSU4 + LEWiS S DALZEU. A DALZELL 2/ Yoo CB 066 074 0,60 A- A ---A £ DALZELL 2r1 0 DELFT UNIVERSITY C6 0,60₀ 0,70₀ 0,60₀ 0,05 611 o,

/

0,04

F

O +6

/

0,04 0.02 0,03 CCOMPUTED M Fp=0115 0,04 CCOMPUT,.D 0,02 0,03 Fp=O,20 FR=O,25 M 005 M

r2rL b

r92rL 0,05

////////

004 0,04 _t 0,02 0,05 0,04 0,02 0,05 0,04 C COMPUTED C COMPUTED

(67)

5 o 10 In

o

40Fp= 0,00

40-5 O 5-40

lo

Q

z

w

o

- FR= 0,15 FR = 0,20 - - ---FR

O25

FR= 0,30

-

---....---Cb= 0.60

-'t1,25 .t.=l,00 i.=oI75

F I G.13 MAXIMUM LONGITUIP1AL bENINGMOMENrbI5Tp%5uiI_ON

IN REGULAR WEAb 5EAS

FOR MODEL 4240 W

40 r---. N 15 - A.RP. t4I13WIP CT%0N F.P.P.

(68)

X o S 40 -lo 5 X 4o-Fu=0120 5 o 5 40 45 -40 o lo 45 (940 z

¿o

(D R = 025 RO13O A. PP.

S.-C =0,70

lo

R 000

i25

t= l00

= 075

--r

-MIDSHIP &.CT%OW -.- -S..-- .. '.z:::5. S-.-F.P.P.

-

-...-FIG. 4

MAXIMUM LONGITUDINAL bENbING MOMENT DISTRIbUTION

(69)

45 IO 5 M)

00

X I

riio

t.. 25 20 45 40 5 o 5 IO 45 25 20

5

I0 5 o I0 40

FR 025

A. P. P.

-MIbSHIP SECTION

CBOSÔO

-- t=0,75 -. ... F. P.P. FIG. i5 MAXIMUMLONGITUßINALENDiNGMOMENTbI5TRIBU-TION

N REGULAR HAb SEA3

FOR MODEL 4214 W-B4

5

40

20

'5

(70)

0,005-0,0(0 0,005 0 0.o05-0.005 0,005 o 0,005 0,010 0,005 O 0,005 0,040-0: 0,005 0,040

APP. MIISNIP &.CrnION FP.P.

HOGGING

SAGGG

FR=O,200 /L=l,OO CB=O,7O

FIG. 16 CHANGE IN LONGITUbINÄLBENbINGMOMENT OVEP

ONE PERIOb FOR MObEL 4212 W AT 5ERVICE SPEEb

H H - v1 o 0,005 0,04O o 0,005 0,005 o 0,005 0,010 0,005 o o 0'005

(71)

X e-0 0,005 0,040 0,015 O 0,005 - 0,040-0,005 - _HOGGING 0,005 - SAGGING 0,0l0-0,005: o 0,005 O,010 T 0,005 0 0,0O5-0,005 o 0,005 0,005 o: 0,005 0,010 -o 0,005 0,040 0,045 o 0,005 O,OIO-0,045 A. P.P. FR =0,462

{=4,00

CB=Q,8O MIFSI1IP 5CTION FP.P.

FIG. 47 CHANGE IN LONGITUbINAL BENbING MOMENT OVEP ONE PEPIO FOP HObEL 24 W- bh AT SERVICE SP[.Eb

(72)

323e

0,020

0,04 5

0,010

0 STATIC CALCULATION

STATIC CALCULATION, SMITH EFFECT INCLUDED

® EXPERIMENT.

FRaO,45

01005 k W

T.z

X 0,8 0,9

o

0,005

0,040 0,045

0,020

o

II

u

+

FIG-48

COMPARISOWOFCALCULATEß bENDING

MOt4ENT5

WITH EXPERIt4EKTAL VALUES

o

ta

o

u

II

u

(73)

FIG. 19

COMPARISON OF CALCULATEb ANb MEASUPE.b

NING MOMENTS AT 5ERVICE SPEED

CALCULATION (JAcoBs)

ExP. SERIE5 SIXTY

---EXP. DALZELL

0,02

-)IOGGINO

---u

- --

-0,04 SAGGING

I

0,70 0,75 0,80 0,85

(74)

ARCHI EF

Issued by the Council

REPORT Nô. 3S.

2-r

vT

April 1960

L4CLltE

H

STUDIECENTRUM i.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE

AFDELING SCHEEPSBOUJV. - PROP? MEKELWEG - DELFT

(NETHERLANDS' RESEARCH CENTRE T.N. FOR SHIPBUILDING AND NAVIGATION)

('SHIPBUILDING DEPARTMBNT - PROF. MBIthL WEG - DBLPT)

o

ÉXPERIM]NTAL DEI ERMINATION OF

RENDENG

MOMENTS FOR T

E MODELS OF DIFFERENT

FULLNESS IN REGULAR

WAVES

by.

(75)

REPORTS AND PUBLICATIONS OF THE NETHERLANDS RESEARCH CENTRE T.N.O FOR SHIPBUILDING AND NAVIG4TION

Reports

No. i S The determination of the natural frequenciee of hip vibrations (Dutch).

By prof. ir H. E Jaeger. May 1 S O.

No. 2 Confidential report, not published. July 1950.

No. 3 S Practical possibilities of constructional applications of aluminium alloys toship construction. By prof. ir H.: B. jaeger. March 19 5 1. '

No. 4 S Corrugation of bottom shell plating in ships with all-welded or partially welded bottcms (Dutch).

. By prof. ir H. E. Jaeger and ir H. A Verbeek. November 195 1.

No. S S Standard-recommendations for measured mile and endurance trials of sea-going ships (Dutch). By prof. ir J. IV. Bonebak.kér, dr ir W. J. Muller and ir E. J. Dieb1February 19 2.

No. 6 S Some tts on stayéd and uthtayed mastsand a comparison of experimental results and calculated stresses

(Dútâh) . .

By ir A; Verduin and ir B. Butgbgraef. June 1952. .

No. 7 M Cylinder wear in mathie diesel engines (Dutch).

By ir H. Visse, December 19 52. .

No. 8 M Analysis and testing of lubricating oils (Dutch). .

By it L N. M. Malotaux and ir J. G. Smit. July 1953. . .

No. 9 S1 Stability expeçiments on models of Dutch and French standardized lifeboats.

By prof. it H. E. Jàeger, prof. Ir J. W. Bonebakker and J. Perebooin, in collaboration svitb 4. AudIgé. October 1952.

No. 10 S On collecting ship service performance data and their analysis. By prof. ir J. IV. Bonebakkr. January 1953.

No. 11 M The use of three-phase current for auxiliary' purposes (Dutch). .

Byir J. C. G. van Wijk.. May 19,53.

No. 12 M Noise and noise abatement in marine engine rooms (Dutch),. By Technisch-Pbysiscbe Dienst T.N.O. - T.Ñ." April 1953.

No. 13 M Investigation of cylinder wear in diesel engines by means of laboratory machines (Dutch). By ir H. Visser. December. 1954. '

No. 14 M The purification of heavy fuel oil for diesel engines (Dutch). By A. Bremer. August 1953.

No. 15 S Investigation of the stress distribution in corrugated bulkheads with vertical troughs. By prof. ir H. E. Jaeger, ir B. Burgbgraef and' I. van der Ham. September 1954.

No. 16 M Analysis and testing of lubricating oils II (Dutch).

By ir R. N. M. A'. Malolaux and drs J. B. Zabel. March 1956.

No. 17 M The application of ew physical methods in the .examintion of lubricatingoils.

By ir R. N. M. A. Malotaux and dt F. van Zeggeren. March 1957.

No. 18 M Considerations' on the application of three' phase current on board' ships for auxiliary 'purposes especially with regard to fault protection, with a.survey of winch drives recently appliedon board of these ships and their influence on thé generating capacity (Dutch).

By it J. C G.. van Wijk. February f1957. r

No. 19 M Crankcase ex,losions (Dutch).

By ir J. H. Minkhorst. April 1957.

No '20 S An analysis of the application of aluminium alloys in' ships' structures.

Suggestions about the riveting between steel and aluminium alloy ships' structures.

By prof. ir H. E. Jaeger. January 1955

No. 21 S On stress calculations in helicoidal shells and propeller blades. '

By dr ir J. IV. Cohen. July 1955.. . .

No. 22 S Sorne ñotes on the calculation of pitching and heaving in longitudinal waves. By ir J. 'Gerritsma. December 1955.

No. 23 5' Second eries of stability experiments onmodels of'lifeboats. .

By ir B. Burgbgraef. September 1956.

No. 24 M Outside corrosion of and slagformation on tubes in oil-fired boilers (Dutchjo