Comparison of bending moment model tests in regular waves with full scale measurements at sea

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ORE CARRIER MODEL TESTS

Comparison of Bending Moment Model Tests in Regular

Waves with Full Scale Measurements at Sea

(Project S-15): by Allan IvarsóÌi 1963 Report No. 35

STIFTELSEN FOR

SKEPPSBYGGNADSTEKN1SK FORSKNING

THE SWEDISH SHIPBUILDING RESEARCH FOUNDATION

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FOREWORD

Since ₁₉₅₆ the Swedish Shipbuilding Research Foundation

has carried öut stress measurements on ships at sea.

The results of the measurements have been published in

three reports, of which the last one was issued in 1962. It

wasfound desirable to extend the measurements by performing

both model and full scale tests on a ship of a length of

about lO m and a block coefficient of about O,O. This

was decided in order to get a comparison between er1ier full scale and model tests Of a fast dry cargo ship and the

present tests.

The earlier model tests had been carried out by the Division of Ship Design at the Chalmers Universitr of Technology in 1960. The present tests have alsO been per-formed by the Division under the supervision of professor

Amiders Svennerud.

The work haè been possible through grants from:

The Swedish Technical Research Council

and

Axel and Margaret Ax:son Jòhnson's Foundation.

The measurements on board the ship have been carried

out through the courtesy of the Grängesberg Co.

Gothenburg in September 1963 Gusta! Backr

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S tM4ARY

Model tests of wave bending moments have been performed

ori a 11+000 tons dw bulk carrier and the results are compared

with full scale measurements on the same ship. A comparison

is possible thanks to a new methbd based on theoretical wave spectra and oceanographic measurements in order to predict long term distributions of stresses from mòde. data.

Predic-tions from the full scale measurements are made according to a method proposed in ref. /3/. The different predictions are then compared. For the sulk carrier the agreement is

excellent.

A comparison is also made in the same way för a fast

dry cargo liner In this case the bending moment predicted from model tests is 30% greater than that, based on full

scale measurements

The model- tests, the predictions and a number of

pos-sible influences are discussed. Compàrisons of modelteet

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TABLE OF CONTENTS

Sid.

SHIP DATA, THOD AND EXTENT O' IVAStJREMENT 1

1.1. The Ship and the Model 1

1.2. Presentation

of

Resülts and Accuracy 2

DISCUSSION OF RESULTS 5

CONCLUSION 10

L1.. REFERENCES 11

5. APPENDIX Ï 11+

5.1. Estimat±onof

the

long

term distribution 16

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1. SHIP DATA, METHOD AND EXTENT OF MEASURENT

1.1. The Ship and the Model

The ¿hp is a 14.000 tons buJk carrier built in

1959 having all accommodation aft.

toad distributions f.ro a nt3jnber of fill or

almost full loaded voyage conditions have been

exa-- mIned i order to get a sufficiently accurate value

of the radius of gyration.

Data Ship Model

m m Length b.p. 140.36 3.905 Beam

19.51

_O,5L.2 Draft

8.86 _0.246

Center of bouyancy 0.6% fwd of L/2 Block coefficient

Water plane coeff. 0.86

Moment of inertia _14.9.42

n4

214.6 am

Section modi.ius 6.36 I 41. cm3

Radius of gyratIon 0.25 Lpp

025 Lpp

The wooden model was divided arñidships and at

the quarter points. The parts were connected by

aiu-mJ.num bars according tò fig. 1. The ga.ps between the joints were sealed with thîn. rubber tape. By

arrang-ing the bars in the described way the section odu.1us

will be smaller than if the same moment of inertia

had. been obtained u.sing a single bar. There was no trouble observed by vibration of the model.

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2-The bending momeht and shear forces were measured

at each section. Strain gages in full bridge circuits

were used. To meaure the shear force the difference signal betwe two bridges at a distance of 10 cm was taken. Because öf low âignal output from these bridges a too high amplification was needed and therefore the

accuracy was i.ot sufficient. What concerns the bending

moment gages, there was no trouble and the acduracy obtained by static calibration was about 2% (standard

deviation).

Thé methods of iiig pitch ánd waves and the

töwing ari'angement are described in ref. /2/.

The extent of bhe measurements is given in Table I.

The tests were run at the Swedish State

Shipbu.ild-ing Eqerimentai Tank, Gothenburg,

1.2. Prêsentation of Results and Accuracy

The results are presented in the fig. 2- a.s

non-dmensional coefficients and as response amplitude

operators e They are plotted against the frequency of encounter as this parameter is weil suited to take

care of the variations in speed and waïe length and furthermöre is suitable when computing response

spec-tra.

The units of the different test data are given in

Table II.

It is also necessary to get an estimation of the

accuracy of the results. This was investigated by a pooled variance of 6 measurements. The accuracy is

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X X

2.60

X

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Test Data Pitch Heave Acceleration Bending moment e = Pitching angle y Heaving motion x = Acceleration M = Aòtual moment h = Wàve height

À

Wave length

Ail va1ues are peal to peak values0 - Lf- -Table 110 Unit amp/max wave yAi cm/cm xìh òrn/sek2/cni kgcm/cm

Tablè lila Accuracy of results,

slope (rad/rad)

Test Data _{Standard Deviation}

Pitch Heave

Acceleration force P.P.

aft. .P.

Bendiig MQment fore l/L. Point

aft _1/4 V? amidships Speed Wave Length Frequency of Encounter o.oii rad/rad, 0.03 cm/cm cm/sek2/cm L#..5 cm/sek2/cm 6.6 kgcm/cm 6.9 gcrn/cm 11.0

kcm/cm

O.03 knop O m 0.06 iad/sek

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2.

DISCUSSION OF RESULTS

One purpose òf these tests was to get a cornpàrison

between model and full scale measurements of the midship

bending rnoment ö

the bulk carrier and on a previoisly

tested dry cargo liner, M/S Canada', /7/.

The comparison of the model results is shown in

fig. 9 wheÌe results from Dutch investigations /13/ have

alsO been plotted. The momënt

are here put into a

dimen-sionless form defined in the figure..

The buU.c. carrier- must

be said to have a shape similar to what Swaan has named

1311V. Considering the high blockcoefficient of O.7

the

results seem to be low. The

Can.ada

however,

th a hull

form between IJVIT and UtJV and a blockcoefficient of

0.65 seems to have high values. To what extent this conclusion

is right or not is hard to determine. There seems always

to be a wide scatter in

todei results obtained by diff

e-rent iiivest.igators, even if the saze ship is tested,

which will be seen in fig. 10, taken from

/5/s It is

interesting to note that ev'en for a destroyer, having a

block cÒefficiënt of

the mothent coefficient is as

high as fr the T1Canada.

The most probable rêason for the scatter seems to be

different loading conditions o

Norwegian investigations

have shown that there are great variations even if the

radius of gyration is kept constant /10/.

One of the most important problems, when measuring

bending moments on a model, is the load distribution

especially as the radius of gyration seems to be an.

iñ-sufiOiexit parameter to describe the condit.on.

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it may also be of interes to compare the model results with the ordinary static calculation. In a. static

L/20 standard sine wave without the Smith còrrection the

amplitude operator for the midship bending momen is

lO kgcm/cm or, expressed in. terms of the coefficient in fig. 9.,

380 x lO.

The beïiding momeht in a 1OOwav at Ô speed is

roughly half the static valué, which has .1so been found

b most of the inestigators.

During the preparation of the teSts a method was de-'rêloped in order to get from model to reality. The basic idea was the spectrum method, first proposed by St. ]Jenis

and Pierson in 1952 /6/, combined with the long term

stress distributions obtained by 'Bennet /3/. The most

difficult thing was to get expressions of real wave spectra. Recently a set of several hundred spectra have

been published by Pïerson

45/,

computed at the New York

University from wave records taken on the British Weather-ships0 An investigation of these spectra, performed by Goodrich at Webb Institute of Naval Architecture under a contract with the American Bureau of Shipping /16/, has

shown that the Darbyshire formulation /i/ gives the best average agreement as to shape and peak frequency.

In order to use these spectra for a long term

pre-diction, it is necessary to combine them with statistics on wave observations. Such data are given by Roll /12/e

By a method discribed in Appendix I, the Darbyshire

spectra were modified to agree with the observed wave

heights and lengths. Thus each spectrum used in the

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-7-and an area -7-and frequency range according to actual obser-vations

The modified wave spectra were mü.ltiplied by the

response amplitude operator function and response spectra

Were obta±ned0

As described in Appendix I it was now possible to

compute a long term distribution based o1 model results0

On board the bulk carrier full scale rneasuz'ements have been performed0 A long terra distribution has also been cömputed based upon these.

To get a comparison öf the results from the full

scale measurements the stresses have been expressed as a

moment factor m. nl s. . z 'f L B C S = Stress Z = Section modulus L = Ship Length Beam C = Waterplane coefficient

The bending moment is also expressed _{as an effective}

wave height defined as the height of a sine wave, which by a conventional static calöulation without correction

for the Smith effect gives the same bending. moment _{as the} measured one.

The two distributions are shown in fig. 11. The

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For the 'Canad& long term distributions have also been computed in the same way. The result is shown in

fig.l2. In this case,however, the model prediction is

30% greater than the full scale prediction.

There are of course some different reasons for this

discrepancy.

As mentioned above the model test data of the Canada

seem to be rather high, probably depending on the load

distribution. During her lifetiine.a cargo liner sails

under the most varying load conditions. To obtain suitable mean of the load distributions in a single test is

diffi-cult. It will be necessary to exaiine several load

distri-butions and weight their influences on the total stress

distribution in a sound way.

The model prediction is rather simplified. Only head sea data are used and no account is taken of the influence of wave direction and short-crestedness. The influence of speed is considered in the calculation only by using zero

speed in high waves and 0.75 service speed in lower waves.

A paper by E.V. Lewis /17/ deals with the influence

of wave direction on the response amplitude operators.

Present analysis of full scale measurements made by the Swedish Shipbuilding Research Foundation is also

deal-ing with the same problem.

The intention is that these investigations will make it possible to refine the calculationin the near future.

The problem also has a statistical point of view. The given curves must be fitted with confidence limits.

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-9-As the number of full scale measurements of the Canada»

are rather few., the confidence limits may be wide. There may also have been faults thanks tó the weighting

proce-dure as the ship has only been sailing in the southern part of the North Atlantic, during the tests, and the

used wave statistics derives from all the weather ships0

Regarding the bulk carrier there are in most cases only two load conditions, fully loaded and ballasted, both

being rather tuiiforrnly distributed0 It may be easier to

get a significant load distribution of this kind of ship in model testing0 The statistical point of view must of course also be considered for this ship0 The number of full scale measurements is rather large, and the confi-dence limits are thus more narrow. During a great deal of the measuring time this ship has sailed all over the

North Atlantic, Even if the very clOse agreement of the full scale and the model predictions must be regarded

somewhat fortuitous the methodic must bè regarded

promis-ing0

When. refinements are made considering the factors

discussed above, and reliable model test data are obtained,

it should be possible to predict the stress distribution

of a sflip with a sufficient accuracy. When the analytical

methods of computing a ships response in waves ae

tested and found reliable, it will also be possible to make the prediction in an entirely analytical way.

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lo

-3. CONCLUSIONS

The main objective of a model test is to get infor-mation which can be applied to the real ship.

Regarding the beharior of the ship at sea it is ob-vious that the spectrum methodic is a praóticabie way,

when converting model results to ship responses, nOt Only for the short term but also för the long term

distribu-tion, The methodic is useful for all kinds of responses, as speed, motions, accelerations and forces.

Up to noi, one of the most important problem hã.s

been the lack of infOrmation of real wave spectra.

Although the simplified method used in this repört has shöwn proising results, refinements must be made.

Thanks to a recent work of Pierson /15/ it is now

possible to get expressions of real gave spectra. Inves-tigations on the influence of wave diection have been

and a±e made. Thank to these works, among others,

possi-bilities have at once turned up to refine the spectrum methodics in general, in order to predict ship behavior

with a sufficient accuracy, provided th:at reliable model results are Obtained.

To cònfrrn the theories, it is neöe5sary that model tests and full scale measurements are carried on hand in

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- 11

REF ERE NC ES

Bartsch, H.

Statistische Metoden zur Untersuchung der Bewegungen. eines Schiffes im Seegang.

Schiff stechnik

6(1959)30, s.

6(1959)31, So

5-92

Bengtsson, B.

Förskeppsformens inflytande p& fartygs egenskaper i vâgor.

VI Nordiske Skibstekniske Ârsrn'de, NSTM, Nyborg 1961,

32 s.

Bennet, R., Ivarson,A., Nordenströzn, N.

Results from ±ui1 scale measurements and predictions

of wave bending moments acting on

ships at

sea.

Swedish Shipbuilding Research Foundation

Report No

_32.

Gothenburg

1962, 52 s.

.L.. Darbyshire, J.

À Further Investigation of Wind Generated Waves. Deutsche Hydrographische Zeitsóhrift

12(1959)1, s. 1-15.

De Does, J.C.

Experimental Determination of Bending Moments for

Three Models of Different Fullness in Regular Waves. Netherlands Research Ceiitre T.N.0. for Shipbuilding and Navigation0

Report

36 S

Deift, April

1960, 22 s..

St Denis, M., Pierson, W.J.

On the Motions of Ships i.n Confused Seas. Trans.

Soc. Nay.

Arch. Mar. ng.

61(1953) s. 2O-357.

Ivarson, A.

Modellför,sök för bestäxnning av böjande moment i ett ordinärt lastfartyg.

Chalmers Tekniâka Högskola

Institutionen för Skeppsbyggnadsteknik

Göteborg, Juni

1960, 29 s.,

. Ltweit, M., MUrer, C., Vedeler, B,, Christensen, H.

Wave Loads on a T-2 Tanker MOdel

European Shipbuilding

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12 -9. Korwin-Kroukowsky, B.WG

Some Similarity Relationships for Towing Tank Models

Used in Combined Ship Structural and Hydrodyna.c

Experiments

David Taylor Model Basin

Structtial Laboratory

Note 631

Washington, August 1961, 17 s.

10e Korwin-Kroukowsky, B.W.

Theory of Seakeep:ng

Söc. Nay. Arch0 Mar. Enge

New York 1961, 360 so

li. Pierson, W.J., Neuman., G., James, R.

0bseririg and Forecasting Ocean Waves.

U.S. Navy Hyth'ographic Office

Publa No 603

NewYork, 1955, 2L1. s.

Roll, H.U.

Height, Lengtb and Steepness of Seawaves in the North

Atlantic.

Soc. Nay. Arch.Mar. Eng.

Technical and Research Bulletin No l-19

New York .195e, 9

s.

Swaan, W.A., Vôssers, G.

The Effect of Forebody Section Shape on Ship

BehaviOur in Waves.

mt. Shipb, Progr.

(l96l)3, (July), s. 279-301.

Wachriik, Z.G,, SOhartz, F.M.

Experimental Determination of Bending Moments and

Shear Forces in a. Multisegmented Ship Model Moving in

Waves.

mt. Shipb. Progr.

10(1963)101, (Jan.) s. 12-24.

Pierson, W.J., Meskowitz, L., Mehr, E.

Wave Spectra Estimated from Wave Records Obtained by

OWS Weather Reporter and Weathèr Explorer.

New York University

New York, 1962.

Goodrich, G.J.

The Prediction of the Long Term Distribut±on Of

Bending Moient Coefficients.

Webb Instittte of Naval Architecture.

Working Paper

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13

-17. Lewis, E.V.

Trends f Bending Moments in Irregt1ar Seas.

Webb Institute of Naval Architecture

Progres Report on Phase of Research Project for

American Bureau of Shipping New York, Sept.

J.962, 20 So

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2 i y2(f-f0)2 Hf /y H2 df = 23.9 y exp H = O.001 y w2 Tf = l/ = 1.9l y w

1.11+ T113

= Tf H1,3 = 1.61+ H

The assumption is made that the heights and periods given by Roll are H1,3 and T13.

H13 = 1.61+

O,OO1 y w2 = 0.0133 y w2

i i

T113 = 1.914. y w/l.11+ = 1.70

y w

APPENDIX I

MODIFIED WAVE SPECTRA AS A BASIS FOR PREDICTION

OF LONG TERI4 DISTRIBUTIONS OF STRESSES

In an attempt

to

get expressions for realistic wave spectra a method is used combining the theoretical spectra, found by Darbyshire /1+!, with the measurements of North Atlantic wave conditions made by Roll /12/.

The use of the Darbyshire spectrum is proposed as a result of work at the Webb Institute of Naval Architecture by Lewis, Goodrich and Bennet. Some of the reasons are ex-plained on page 6. The Darbyshire foulatiOn also has a

factor y which originally takes account of the influence.

of fetche This factor is used in the modifidation to make

the area of the spectrum to agree with the observed heights, thus taking account of a hypothetical fetch and duration.

Notations: See end of 4ppendix.

According to Da.rbyshire:

+

Ö.O1+2)f

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15 -y w =

O.01331

H y w

l.701

T113 (9) Eliminating w gives: y = (1.70

T,3 1V0.01331

H1,i3 1/3 from () f0 = 1/l.iL T113 from (5) H = H1/3406L4.

The values of H13' and T1,3 are taken from the

col-lection of data given by Roll for the weatherships A-M. See fig. 13.

H, y and f0 are inserted in (1). The spectrum is now

fitted with a set of coefficients giving the desired sig-nificant height and period.

Typical Darbyshire spectra for y = 1 are shown in

fig. li..

The response amplitude operators from the. model tests are transferred into, full scale values and multi-plied by the corresponding ordinates in bl-ie wave spectrum thus giving a response spectruma

As this calculation is enormos1y laborious the

computation is written in ALGOL for the Swedish

FACIT-elec'troniò computer

The observations of the weatherships are gròuped both in period and height intervals. For each is a figure

.giving the percentage of occurrence of the interval. A spectrum is obtained for each interval giving the proper

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P 16 P

-significant heigit and period defined by the class

aid-point.

Account of the influence of speed is taken by using

response operators beóngi:ng to zero speed and

75% of

service speed. The zero speed operators are used in

high significant waves.

is now gee1l accepted that the short term

distribution of wave stresses is the Rayleigh

distribu-tioi. Thè properties of this d

ibutior are determined

by one single parameter, the roöt mean square value. This

parameter will bedisignated by the letter r. To

charac-tense the above mentioned response spectra it is

suffi-cient to get an etimation of the r-value.

The results f the computation will thus be a

nusn-ber of r-values, one for each percentae figu.re.

5.1. Estimation of the long term ditnibution

If

Rayleigh distribution is asswed the

probabili-ty to exceed Xk: P(xk)

F(xk) = e

EP(xk) =

for one single r-alue.

The prObability that thiS single rvalue will occur:

(is the sainé as the peröentae figure)

=

The tötal probability

-C'

exceeding xk

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17

-5.2.

I'Totatîons

f = Wave frequency.

f0 = Frequency of class having highest energy when spec-trum is

split

up into equal frequency intervals. = Square root of the sum of the squares of all peaks

in the spectr.

= Square root of the sum of the squares of the peaks

of the unit frequency interval centred round t

-1 secs ..

y = Nondimensional function of fetch which originally

approaches 1, when the fetch approaches infinity. Used in the modification y

also

may get values

greater than 1.

Tf = I/f0

H113 = Mean height of highest third of the waves observed on a wave record. Sometimes called the significant

wave height0

T113 = Mèan. period of the highest third of waves observed

on record, sometimes called the significant wave

period.

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Fi'g. 1. Body plan and measuring equipment

IL

J

7 'r

//

LI

'

't

/J

____/

IL&vo

.

Iì

/

L

M

I//I/U

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Fig. 2. Dimensionless Pitching Motion

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Fig. Li.. Acceleration Fore Perpendicular

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i.j

i

Fig. 6. Bending Moment. Fore Quarterpoint

Fig. 7. Bending Moment. Aft Qu.arterpOìflt

HiIflhIIIr:1tIIflUIIIIUII

flhuIIIIHIIIIIIII11IHhlII

LH

huH: f

:IIHH,flHuIHINIIH

_UNg11111R

1UUIHIIIIRHIIHIII:

R'.

pi

u.

jitÌWi1ïii#!

_lIA;

I

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1 Doubis ApIitde Height, ISO zio too 100 50 r

Fig. . Bending Moments Amidships

C io I r C WM&!.E 'i.---î - I

H

I

fi: SENßWG flavr.

f : ß(MJ/TY 0f WATÇ : GAY/TAT/ONAL ACC.. L P?OOEL LENGTH. 5: SEAOTH ANO (: WAVE HEIGHT. Speèd, )op 1

teo

i 6 t..._1 X :... Ht5 (t): i .

tih

i...

Fig. 9. Comparison of Results from ref. r13j and 1)+1with the Present Results.

*adféc C. P,

-

C4« 24.7 0.780 all CANADA 217 0.650 02! V .W4AN V 240 4100 0

o

O

5WAANLV .wAANWLV ..pwlU

+

--

WCRRl rAi 07W 021 WACHNI/ 24.0 a2 020 z.s LW/L (.'YQ LO LO 1.3

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C _pg_L1M 14 Pr bALflLL T2 TAfl CQJ4 LZILL

.

_.

LIWIS

--

CI3TtMII s ocw N

Voz'ç bending morne,,! an:pli/udrs (hogging + sagging) iii regular ¿IL ¡ Uds,; as measured h Ji/ferro! au/hors

Fig. 10. Scatter in Test Results shoin by De Does, ref. /5/.

c C VES&I C. 61 C5.O,68 603tP&5 c1.o,oe 0,662 23

24/

f---

btIMLZ(LL OLZL

.-..--09 94. .0,. Fre-U

MUSlI. M3TOYER CoO539

i SATO STOYSP Cb.O.539

C o.'

1 Fr°

AKITA D1NTh.LM99L C183 SaLs

ç..oeo % i

lI7dL i LUTh TÀNI(EQ _{Ce 0776} Oft o.2

Fr. U

(28)

--h -2 -f 2 -0 -ß -6 -h B 6 (ARJ 8ULK CAR,/tR

FIg. 11.

Loig Term Prediction from. Model and

Full

Scale Test Data. Actual Bulk Carrier

Fige 12.

Long Term Prediction from Model and. Full Scale

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Fig. 13. Frequency Distributions of Classes of Wave Heights and Periods from Roll ref. /12/.

WEATNERSHIP

f1

ros: o Totol No. of Observoons:.396 '__.ø.

-:

-N,j1

E

L

ri' -,

-Ii

i

1/

/ ¡1 / c . . /

i.

/ . .

1

-I I; r ¡ / i / J

/

'

Y

7

'r . y

V

I ¡ ri

'ti

i ¡ i

/

r

1. I

A

/

,/.

/

'I!

Jf

il

i

iI1di1

ìii!d

''

//44

¡

//

/

if r r

41

,1.10 ,

' x

r

pr

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d

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ill

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I!II

Wave height in

m

(30)

30 20 10 0 -0,04 0 0,04 y (f-f0) secs -' 0,08 o 20 t- I I I

I.

-0,04 0 0,04 0,08 0,12