Further model tests to determine wave loads on a T-2 tanker

DET NORSKE VERITAS

P. O. BOX 82, OSLO

FURTHER MODEL TESTS TO DETERMINE WAVE

LOADS ON A T-2 TANKER

The Influence of Variation in Weight Distribution

and Draught on Shearing Forces and Bending

Moments in Regular Waves

BY

CHR. MORER AND M. LOTVEIT

REPRINTED FROM

SHIP STRENGTH

FURTHER MODEL TESTS TO DETERMINE WAVE LOADS ON

A T-2 TANKER

The influence of variation in weight distribution and draught on shearing forces and bending

mo-ments in regular waves.

By

C h r. Miirer* and M. Letveit*

INTRODUCTION

The present report forms a continuation of ref.

[1] and gives further results from the T-2 tanker

model tests series at the ,Norwegian Ship Model Experiment Tank in Trondheim, sponsored by Det norske Veritas. These tests were undertaken with the main purpose of investigating the influence of

the longitudinal weight distribution on the wave

bending moments and !shearing 'forces along the hull girder.

The first series of model tests in regular waves,

the results Of which were published in ref. [1],

covered three different weight distributions (de-fined as Condition I, II and III) having different

still water bending moments amidships while

keeping the mass moment of

inertia constant.

Condition I, being the basic load distribution of the model, was approximately that of a loaded

tanker.

The nekt series of model tests covers a variation in the mass moment of inertia while keeping the

still water bending moment amidships constant.

This involved the running of two more load con-ditions (IV and V) with the same still water bend-ing moment as the basic Condition I.

In order to olbtain further information as to the influence of extreme values of the two parameters

in question (the mass moment of inertia and the

still water bending moment amidships) two more weight distributions have been tested, Condition VI giving a very large moment of inertia combined with a large hogging moment, and Condition VII giving a very small moment of inertia combined with a large sagging moment.

Finally,

in order to investigate the size and

distribution of wave loads in a ballasted draught condition, a series of tests with the light model with an additional weight forward (Condition

*) Det norske Veritas, Research Department, Oslo.

3

VIII) resp. aft (Condition IX) have been run. The influence of trim was thus also recorded.

The present report contains a detailed descrip-tion of these Condidescrip-tions (IV, to IX), the test pro-gramme involved and the results of the tests. PARTICULARS OF MODEL AND LOAD CONDITIONS

The model is a wooden model of a T-2-SE-A1

tanker in scale 1 : 50. The model has been cut into four parts and joined together by means of

specially designed flexure beams which also serve as parts of the bending moment and shearing force

dynamometers. The joints are situated at

amid-ships and at the quarterlengths. In these three

sections the bending moments and shearing forces

are measured by means

of inductive pick-ups

recording the deflections of the flexure beams. A detailed !descriptionnf the instrumentation and the calibration involved is given in Appendix B and

C of ref. [1].

The towing arrangement of the model was

designed to allow full freedom in pitch, heave and

surge and continuous records of these motions

were obtained simultaneously with the forces and

moments. The regular waves were generated by a special type generator, and wave height and profile were recorded during all the test runs.

The main particulars of the model are as given

in Table I. For the 'body plan and further parti-culars, see Appendix A in ref. [1]. Machined,

circular iron weights

fixed in position by two

rows of screws (20 in each row) were used to give the model the desired weight and weight 'distribu-tion in each load condi'distribu-tion. The model was loaded

down to load waterline and floating on an even keel in all of the loading conditions referred to,

except Conditions VIII and IX.

The weight distributions of the four new fully

35 3 0 2 5

° 20

a

_J

u15

5

0

1- 10 LiJ Ui

0 5

_J U) 0 LIGHT MODEL CONDITION 1. --- CONDITION IV. CONDITION 7. P Fig. 1.

in Figs. 1 and 2 together with the basic load

Con-dition I and the light model weight distribution. Some characteristic data for the four conditions in question are given in Table II. The data have

been made dimensionless by dividing all weights by the displacement of the model and all lengths

by the length of the model. The four parts of the

model have been numbered from aft.

The weight distribution of the two ballast con-litions is given in Fig. S.

TEST PROGRAMME

The tests for the new loading conditions were made in regular waves having wave lengths of

A= 0.75 L, 1.00 L, 1.25 L and 1.75 L, where L

is the length between perpendiculars of the model. The former loading conditions (I, II and III) were

also tested in waves of A = 0.60 L and 2.25 L.

These extreme wave lengths were omitted in the

new tests as the wave length range from 0.75 L to 1.75 L has been found to cover the most im-portant wave lengths as fax as wave loads are

concerned. Condition IX was tested only in wave lengths 1.0 L and 1.25 L.

4

-Main particulars of model

TABLE I.

Length between perpendiculars Length of waterline

Breadth moulded

Depth

Draught loaded

Displacement in fresh water Wetted surface

Block coefficient

Centre of buoyancy forward of L/2

TABLE II.

ER

3.066 m L lwl 3.128 m 0.415 m 0.239 m 0.183 m 172.5 kg 1.900m2 CB 0.741 0.3% of L Loading Condition IV V VI VII

Radius of gyration of the

model in percent of Lpp 22.1 25.8 28.9 19.4

Weight in per cent

Afterbody 48.8 48.8 48.8 41.4 Forebody 51.2 51.2 51.2 58.6 Part (1) Aft. 10.9 16.4 23.9 10.9 Part (2) 37.9 32.4 24.9 30.5 Part (3) 40.9 33.1 25.4 48.3 Part (4) Forward 10.3 18.1 25.8 10.3

j

- A.. L B -D d ,S .

-_ J

10

The wave height was kept approximately

con-stant at abt. 75 mm, i. e. the wave height model

length ratio hill, 1/40.

The speed range covered for all wave lengths

was:

--

CONDITION =I

--- CONDITION IX.

AP

LIGHT MODEL

(FOR TESTS IN BALLAST CONDITIONS ONLY.)

Fig. 3.

5

Fig. 2.

Modd speed: 0 1.65 m/sec.

Corresponding ship speed: 0 22.5 knots

Froude number: 0 0.30.

Several reruns were carried out in each series of runs in order to have a check on the recorded

values. (.0 Ui CC 0 L,_ Li (f) 5 0 1:111AN !

-I i Alf?

FP

35 30 LIGHT MODEL --- CONDITION 7E. CONDITION ILL. 25 o 20 L _ !

P1

EP

F-1

--TEST RESULT PRESENTATION

As it the former report all test results are

presented in a dimensionless form. The .bending moments have been given by the bending moment coefficient:

Cm

y L2 Bh

and the shearing forces by the coefficient

C Q

Q

7LBh

Where;

M = wave bending moment,

Q = wave shearing force,

L length between perpendiculars,

Fig. 4. Pitch variation with speed.

B = breadth moulded.

= wave height (from crest to trough),c specific gravity of water.

If the variation of bending moments and shearing forces with wave heights is assumed to be linear,

these coefficients are independent of scale and

wave height.

The instrumentation had practically' nol-

zero-drift and, therefore, it was possible to s-plit the

bending moments and shearing forces into sagging

and hogging moments and positive and negative

forces.,

The sign convention applied Is as follows; - Sagging bending moment -= positive

PITCH DOUBLE AMPLITUDE

-- -CONDITION -VI. CONDITION V. CONDITION Sr. CONDITION 'El I[ RADIUS OF GYRATION 0,289-L9p- 1 RADIUS OF GYRATION 0,258- L"

RADIUS OF GYRATION O221-L,

RADIUS OF GYRATION '0,194 1,,,

,---,-

,.. -6 '/L=1175 '14111111111111 I

IIMINIII

I 3 2 1

III

2

---

7. ---

' L-- - - - -1 1 ,--:-. , 005 010 2, 4 6 8 -NS 1320 FR.

10 12 16 16 18 ifi SHP SPEED KNOTS

PITCH DOUBLE AMPLITUDE

6 1 14. =0-75 .. ii _{-- --..} -1 I 'I L-. -- ... --,., -400 I , i I

Milla.

<

-

hilL

'1-

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MI

5 s

AMIIIIIIEE

1 , _,. . 005 0,10 , t 0 /5 0,20 FR.-°:30

181

20 .126

8 SHIP, SPEED KNOTS

h

=

2 6 025 215 025

Shearing .force positive when the sum of 'upward

'directed forces is in excess of the .downward

directed forces for the part of the hull, situated aft of the section in question.,

The zero position refers to the condition when the

model is floating at rest in calm water. The test

results are not corrected for the bending moments and shearing forces introduced by the wave system

of the model at constant forward speed in calm

water.

As was also the case with ref. [1] this report

is concentrated on giving the results of the bend-ing moment and shearbend-ing force measurements. In

order to give an impression of the motions

re-corded, Fig.

4, which gives the results of the

recorded pitching of the four loaded conditions,

has been included. The pitch angles are presented in dimensional form as 2 ,p L/h, where qi = pitch

double amplitude in radians. Fig. 4 shows the

variation with speed at the various wave lengths..

For conditions IV and VI the results were also obtained for A/L = 2.25. In Fig. 5 cross curves.

are given by plotting pitch amplitude over radius,

of gyration. This figure clearly demonstrates the

increasing influence of radius of gyration on pitch-ing at increaspitch-ing speed.,

7

Fig. 5. Pitch variation w th radius gyration,

RESULTS OF' FULLY LOADED CONDITIONS

Wave Bending Moment and Shearing Force a:si

Function of Speed

The observed test results are given as the mean

amplitude value from the oscillograph record of each single run. Figs. 6 and 7 show the bending

moment coefficient and Figs. 8 and 9 the shearing

force _{coefficients plotted to a base of Froude}

number and ship speed. The 'observations are

indicated as marks and the curves are faired and

drawn as mean curves. Each diagram represents

one wave length and contains the values from the

three model sections (midships, forward

quarter-length, aft quarterlength). During the runs for

Condition VI there was a failure of the instrumen-tation for recording shearing force amidships, and no recordings of shearing forces amidships were taken for this Condition.

In Figs. 6 and 7 the maximum bending moments

occurring

at any section have been indicated

wherever they exceed the measured values amid-ships. These maximum moments have been read off the curves shown in Figs. 12 to 15.

A general increase of bending moments and

shearing forces with increasing speed can be

oh-PITCH DOUBLE AMPLITUDE

s A krIVS - s '1 I I 0 KNOTS I 6 i 10 ,

4

71 101-0T5 , ..m.--;--2.."---genwm

41

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will..

pi

e Cli.10WFC2IP

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Ilreilio-II 10

-

14 11 1O 4 25 30'

RADIUS OF GYRATION' PI PERCENT OF L,p

PITCH DOUBLE AMPLITUDE

I

6,

I Akm1/,25

urgrAvp--

A.. __ma

A

Pik

..i.w.

riWti. .40.14_11

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rev ail, al

or

KNOTS I

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20 25 30

RADIUS ' OF ,OIRAT1 0NI IN 'PERCENT OF Lop

I

served from these figures, although with some exceptions, especially for Condition V. As in the earlier tests (ref. [11) the most marked variation with speed is found for the sagging moment at the forward quarter length, especially in Conditions IV, V and VI.

The contrast between the small bending mo-ment valves of Condition VI and the very high

Fig. 6. Bending moment test results. Conditions IV and V.

moments of Contiditon VII is striking and interes-ting.

Bending moment and shearing force as function of

wave length

The variation of the midship bending moment

with wave length is given in Fig.

10, with one

diagram for each loading condition and with

KOS., MAX MOMENT

IN Ma

LOADING CONDITION Di' . ::: AFT SECTION

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Fig. 7. Bending moment test results.

Conditions VI and VII,

LOADiNG ,CONOIT1ON VIII

,MIDSMIP -IN MAX MOMENT Am, SECTION 015 012 008 I) TA.r 025' ,

wit

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MAX.MO NT ANY SECTION on ',.1, ' 008 u 1 004 ?'/L. -QM wow-- -.reload S

-...," § .012 012 .?, ?`/L -100 -I III I ... a-^ -e---,___ _ --e 00 .012 .012 It, 1 /L 1,25 I. 0 ...._...2 .. -- .6.--- .- 4 ..-004 ooa 6 2 012

---° .012 /L -1,75 ,008 .0 --, X

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SHIP SPEED KTS.I I

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Fig. 8. Shearing force test results.

curves of constant speed plotted to a base of LA.

For LA -= 0 we have infinitely long waves, which means the calm water condition.

In general the maximum bending moment is found between A/L ---- 0.75 and 1.5. The two

Conditions IV and VII show a rather similar trend in the variation with A/L, the maximum moment

occurring for A = 0.9 L at zero speed and for

higher values of A./L at higher speeds up to

Conditions IV and V.

=- 1.3 L at 18 knots. We recall that these two conditions represent the low moment of inertia

side of the test series.

Also the other two conditions V and VI show

a similar trend in the moment variation.

The

values are quite constant between A./L 0.75 and

1.25, although with a tendency to form two

dif-ferent maxima, this trend being more pronounced

in Condition V. These two conditions represent LOADING

-

CONDITION V. 006 ir. . - MIDSHIP 0 ---FORWARD AFT Ak r °75

inamin

---...,...-sia

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...somm

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Fig. 9. Shearing force test results.

the high moment of inertia side of the test series.

The variation of the shearing force at the for-ward quarterlength with wave length is given in Fig. 11, plotted in the same way as the bending

moments in Fig. 10.

A general trend in this case is an increased

va-riation of shearing force with wave length

at increasing speed, especially in Condition IV where also the largest shearing forces are found.

--- 11

Condition VI and VII.

Quite in accordance with the bending moment

curves, the two Conditions IV and VII give one maximum shearing force for each speed in the wave length range between 0.75 L and 1.25 L, while the two Conditions V and VI give rather

constant values in the same range, although with a tendency to show two different maxima, the one

at A/L =- 1.25 and the other at a

A/L = value

below 0.75. LOADING CONDITION W. . MIDSH1P 006 o --- FORWARD -or611111111141.

--- '4.--MR

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10 12 14 16 SHIP, SPErD, ICTS,

LOADING CONDITION VI . . UP Ci08 ° FORWARD 7 At. 0,75

.

I.

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2 468

12 14 16 C'25 FR C)3° SHIP SPEED KTS. . 2

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--AFT

-Fig. 10. Variation of midship bending moment with wave length.

Distribution of maximum bending moments over the model length

The distribution of maximum bending moments for the four loaded conditions is given in Figs. 12 to 15, one diagram for each wave length and with curves for constant speeds. As the maximum values of the bending Moments do not occur

simultane-ously at all sections, the curves shown are not .instantaneous bending moment distributions for

the model, but the envelope of such curves for one

period of encounter. The run 'of the curves is

determined by the end conditions, the recorded bending moments at the three sections and the

,slope of the curves at those sections 'obtained from the shearing force values recorded at the instants of maximum moments.

When comparing the curves shown in Figs,. 12' to 15 and recalling the general variation in radius

of 'gyration (from 0.289. L for Condition VI_ to

I

0.194 L for Condition VII) the conclusion that the radius of gyration is no explicit parameter for the bending moment variation and distribution appears

quite obvious. All the same, there seems to be a

general tendency for increasing maximum bending

moments with a reduction in radius of gyration. Also the influence of speed appears to be more

pronounced for the small radius of gyration con-ditions.

In a more detailed analysis of the bending

mo-ment curves of the different loading conditions

comparison should the made with the weight

curves of Figs. 1 and 2, and also with the previ-ously tested conditions (I, II and III) of ref. [U.

Condition IV. With increasing wave lengths and speed the moment curves form one peak value on each side of amidships, especially in sagging. The peak moment values in sagging and with AA --=7 1.25 moves:near,ly as far as to the quarterlen

LOADING CONDITION VI . 1.01 1111:008 I ! )004 004 ' -77-. V , -' --- V=10 -- V=14 ' V=18 0 KNOTS KNOTS KNOTS KNOTS ._..._.. ,

--- ,

I

11 . ---:'x,. -.012 ... ----...-1.14:6111P [ I 025 050 1.7,5 075 125 100 125 150 lao -, 0.75 LOADING CONDITION 131 -.012 d 004 lo I 008 ,., .012, .y ' 0 --- V=10 V=.14 -- V=18 KNOTS -KNOTS ! . KNOTS -..-- .____. KNOTS I ,,,... ! I !

-MIDSHIP -.,,.."'" 1 ! , 1 I ! 025 050 -1 175 075 125 ., 100 125 150 190 075 LOADING CONDITION V

.

!012, n 004 V- 0 ---V r 14 --- V .18 ,KNOTS KNOTS KNOTS 1 KNOTS All 00 ...

,

---. 00 012 I ! -, Aitilli -MIDSHIP ...,._ 025 050 )1% 175 125 4.00 125 IA 075 1

LOADING CONDITION VII _

..c.' .012 008 1 .004 L

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El

mi l,

1//7

MP '.

BIM=

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1 , 00 Dog 012i k.-i -.- V = 14 _KNOTS V=18 KNOTS ' _III

IIIIII

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, ' MIDSHIP MIEREPANIMMEZ 025 050

-

100 125 150 IA 4_ 175 125 100_{) _} 0.75_,

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-Fig. 11. Variation of shearing force at forward quarterlength with wave length.

The magnitude and position of the peak moments

in the forebody for A/L = 1.0 and 1.25 at high

speeds are worth while noting. The same trend of moment distribution, even more pronounced, was

apparent in Condition II. A comparison of the

weight curves of these two conditions reveals that

they are very similar, with large weight

concen-trations in the vicinity of the quarterlengths. Condition V is characterized by a rather small variation of bending moment with speed, except at the small wave lengths. The maximum moments

at all wave lengths and speeds are found in the vicinity of the midship section. At wave lengths above 1.0 and forward speed the curves show a

peculiar trend of forming secondary maxima out-side the quarterlengths, especially in the forebody. The weight curve of this condition is characterized

by weight concentrations amidships and at the very ends of the model.

13

Condition VI gives moment curves which in

many respects are similar to those of Condition V.

The peak values amidships, however, are less

pronounced, and a variation (increase) with speed is apparent up to A/L -= 1.25. This condition too,

gives the additional peak values outside the for-ward quarterlength for larger wave lengths, at A/L = 1.25 and high speed this value even exceeds the midship value. The weight curve in this case shows a rather small weight concentration amid-ships and two concentrations outside each guar-terlength. The moment curves of Conditions V and VI suggest that inertia effects of weight

concen-trations outside the quarterlengths may give rise to quite large wave bending moments very far

towards the ends, especially sagging moments at high speeds and in waves longer than the vessel. Condition VII gives moment distribution curves

characterized by very large peak values near

LOADING CONDITION IS/

...--008 II -0 0 i

INEWS1

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61.

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_FORWARD s 008 025 __ Ak 050 075 100 175 1 1co 125 75 150 LOADING CONDITION 71 "8- 006- 004-0 004-0? SI V= i-.) --- V . 10 -.- V=14 -- - V=18 KNOTS KNOTS KNOTS. KNOTS ..._..._... .._ _.---.. .."

--

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LOADING CONDITION 1:0I

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--

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--050 175 1 075 135 Too too 125 150 1_4 075 -___..

Fig. 12. Longitudinal distribution of maximum bending moment. Condition IV.

amidships both in sagging and hogging and a very pronounced increase with speed, especially in the longer waves_ Very much the same trend was

ap-parent in Condition III of the former test series, and the moment curves of these two conditions,

.are very similar. Even the remarkable falling off and shifting forward of the 18-knots curve at A/L,

Fig. 13. Longitudinal distribution of maximum bendingi moment, Condition V.

1

LO has been repeated from Condition III to

Condition VII. A difference between the twO

conditions seems to be that whilst Condition III

had its maximum moment values very near OT very

little aft of amidships, Condition VII has the peak

values a little forward of amidships. Comparing

the weight curves of these two conditions, we WADING CONDITION V. is°7 1 008 .II = V. 0,KNOTS "r-- V.10 MOTS - -V.14 KNOTS - --V. le mars ,--- .-'-.N ..,... 1/4...

..,....,.-3

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7

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--- FP !

/r

' A4_ .1,25 .or22- 008-<-7 I ...0,... ...-- ...----III .... ....,,,,,,,,... '',. - ,.. ....--- .----1,75 _ FP

LOADING CONDITION IV.

° ' . 0 KNOTS --- V=.10. KNOTS -,- 14- 'KNOTS --, V. 18 KNOTS ,,,:,.. . ..-.." ,...9 -. -....k.... . ,...,':...."..'' .4..., ...%.! ,..:..--,...- I : ... ,. .."- FE' 11

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IS . II',.. / k' IP° 0 _{----:f.%://_} ,-"---N \ `:;, 008

/

...-..-:---....

' \ \

...s., \ \ / /,.,'

\ \ '

/1//

\

.004 _'...,;'./. /*/

\\\

\ \

004 AP, .f. ;)4.-.'... FP l ---'..." 114... 1,25 II 012 3

....-S....

r..i.r

...-2-_

-... ... -:-... ... ,... ..., .:... --- --- FP 004 ss -,... ,,..."... ....57<,/ -... I : Ak . 1;75 1.012 0,75 012 008-004 004-012

/

012

-Fig. 14. Longitudinal distribution of maximum bending moment. Condition VI.

find that both have large weight concentrations

amidships, i. e. they both have large sagging still

water bending moments. In Condition III the

weight concentration is symmetric about the

midship section, in Condition VII the concentrated weight, representing the whole deadweight capa-city of the vessel, has its centre of gravity a little forward of amidships.

15

Fig. 15. Longitudinal distribution of maximum bending moment. Condition VII.

LOADING CONDITION VI .015 .012-0 KNOTS -- V .10 KNOTS -- V =14 KNOTS --- v=18 KNOTS ,..1---.

.---... .. 008- 7" I AP FP 004,-

,

\ \

./.1 008-\., ,./../7 ,, .012- \''

.

-.17-, /.." 4 015- .015-.012-

,

./

\\

\ N .008- v." .../.

\\\

./

----i

004-

\\.,

xl._ .---AP "."--.--

.

-- -. ---,-

/

FP 004- _N.

. \

/

\.

_/

.008-

\

012- ..././ .

//

i_rwe ..., 015-.012-

./

---:,

\

\\,,.. \ \\ 008-

,,,','

A\

004-

Zr

\,.., ..".

/

P . \... \ N

/if

\.

\

0

a

012-

\ \

*

//

2 .--___.... = 1,25 015- \...._, 015-R .012, 008- _/..

\

\\\

.004-... .. ..7>7

\\\

_\

xl_ . __"--- ,z... ...--> FR AP 004

\

.008 '

.

\N.

_{-1 /}

-, 012

\

71/ =175 4

015-LOADING CONDITION VI.

02-008--

R-V= 0 KNOTS ---- V=10 KNOTS - V= 14 KNOTS - - v= le KNOTS __... ..--- . _,_....--- --:::--.---..'... --,.. --- 004-.. . - - ,..::- ,,-- . ... -..,, ,;>--. '''' ''. ' .. '''' ' '... ''N ' , . . . *... .. . xt_ I AP ...,..,..., FP 004- roe/ ..---'4 ... : 0,75 012-R ..-__..,..

-004- ---'''' ...;.,... ----....-- .", AP _{--,._}

-

...:%:.?" -*---7, FP-... _.-.. _{.__} 008-4 A/L =1,00 012- .012-....-- --008- ...-- ,....-D04- ,--,/...:,-- '....-... -- ---. 004-AP -... --....-..-.;-:- FP ---- ../ .,' .008-'4 A/L =1,25 012- 18-... 004- --_ -- _-ml_ AP --- -._ --..,..--- ---E P 004- --__ 008-k = 1,75 012

-/

°75 1008 a _',...

--Fig. 16. Longitudinal distribution of maximum sheering force. Condition IV.

Distribution of maximum shearing forces over the model length

Curves giving the maximum shearing force at each section along the length of the model for the three loaded Conditions IV, V and VII are given in Figs. 16 to 18. These curves are determined by

the end conditions and the recorded shearing

forces at the three sections.

Fig. 17. Longitudinal distribution of maximum shearing

force. Condition V.

The general impression of the curves is that the largest shearing forces occur in the vicinity of the quarterlengths and that the forward quarterlength

values in most cases are larger than those at the

aft quarterlength, especially at the higher speeds. Both the midship and forebody shearing forces are in general increasing with speed while the after-body values in many cases are decreasing.

LOADING CONDITION V MR -V' 0 KNOTS ---- V . 10 KNOTS 0 06, -- V ,. 14 KNOTS 004- - - V . 18 KNOTS ..--,,...--...-'=---...--, 0.02 .../i- - ---,.. .,... Ot (J. I 0.02-AP ,... T"---,..._. -...."--, 004 0.06 7Yir . 0,75 008 006 004 0.02

'...11AggialliftlIfiilligillill

01 (....,..i, A.P -..-.-. 5.-: 7 .. ,.., .. 0.02- -: .:;_ -7 , .-:. .- ; - . . --,----... 004 0.06 008-0.C6. 0.04' .... ... ..!;;' ...% 0.02. --- -2- .. .,..../... AP 0.02-

/

'Z.-, . 004-

,-..'.''

0,0& k ._1,25 0.08- 0.C6- 0.04-0.02. ....- ,_,..-AP FP 0.02- 0.04-aos- _lit.1,75 LOADING CONDITION N 008 - V . 0 KNOTS ow, __- v r 10_-.- KNOTS V . 14 KNOTS 004 -- - V . 18 KNOTS --- ./... 002 ,...-.:-.----....,...i..,,--- -.7---=-", U --,---... 0.02 --4.----..-.. -FP 0.04-006- _{A/L r °,75} aoe-

006-/

7...//'. /... r. /

,,. 7 7

\

--.L-, \ . 004- Ir.',.'' \ ,\: 0 (...) -- AP FP 002-7,

/

:,...7 - - ---.:1...,, ."----. -...Z--, ... 006- ---....L...-:,'" ?A. r 1,00 aoe-, V ...,. 006-.../ ..." ....* 004-el.

/'

...,_ ... NA 002- \ A. FP 0.02- "... .'2 004-._ -- --"--1.-.`- _/.%7 006- 008-0.0& 004--.= ... _' 0.02- -- ...,../.... - AP N FP 002- .--...- --....'"-,.... , ,.... ,V 0.04-0.06 _{ks 1,75} FP -1,00 A.P I N - -AP

7

Fig. 16. Longitudinal distribution of maximum shearing force. Condition VII.

Comparing the shearing force curves with the

respective weight curves it is worth while noting

that the two Conditions IV and VII with the

lowest moments of inertia and the smallest weights outside the quarterlengths show the largest shear-ing force values. One will also find that of these

two conditions with exactly

the same model

weights outside the quarterlengths, Condition IV has a good deal higher shearing force values in the

17

forebody at wave lengths 1.0 L and 1.25 L in the 10 to 18 knots speed range. The pitch amplitude

curves in Fig. 4 show that at these wave lengths

and speeds the model is pitching definitely less in Condition VII than in Condition IV. This would seem to be a clear indication of the great influence of inertia forces on the wave loads.

The very high shearing force values in the forebody in Condition IV are remarkable, and also

very interesting is the great similarity in the run

of the bending moment and shearing force curves of this condition at wave lengths 1.0 L and 1.25 L

and forward speed. This shows that maximum

wave bending moments and shearing forces may well occur at the same section. It should be pointed out, however, that these maxima do not necessarily

occur simultaneously, as a phase difference

be-tween them is quite possible.

RESULTS OF BALLASTED CONDITIONS The recorded values of the two ballasted Con-ditions VIII and IX are given in Figs. 19 and 20. Bending moment and shearing force coefficients

are plotted over Fronde number and ship speed

in the same way as for the other conditions. The variation with speed is very .sirnilar to the loaded conditions, although in the longest waves

in Condition VIII both bending moments and

shearing forces are quite independent of speed.

In Fig. 21 the midship bending moments and

the forward shearing forces for Condition VIII are plotted as functions of L/X. As will be observed the maximum bending moments seem to occur at shorter waves than was generally the case for the

loaded conditions. The forward shearing force

curves show maxima between X/L = 0.75 and

1.0, and quite remarkable is the great variation in speed of the positive maximum force.

The distribution of maximum bending moments

over the model length for the two conditions is

shown in Figs. 22 and 23. The form of the curves

is very similar to those of Condition I in ref. [1]

with the normal tanker weight distribution.

Gene-rally the maximum point is

not very far from

amidships, with a small shift forward with increas-ing speed. The influence of speed is quite

mode-rate, except for the hogging moment at the

smal-ler wave lengths.

At X/L = 1.75

the bending

moment is quite independent of speeds below 18 knots. In general the hogging moments are larger than the sagging ones.

The shifting of a weight from the forward to the after end giving Condition IX a trim by the

stern does not seem to 'have any marked influence

LOADING CONDITION VIII

V . 0 KNOTS 0.06- ---- V .

--

10 KNOTS 14 KNOTS ----7, 004. - .- V . 18 KNOTS ---1--- _NI\ 002 ... **,..`

\\

AP .---L. /2/ ED 0.02 _.0'./ ,..,.._-,. _...,.---., .." .." 0.04 --i--- ...---.

,'

0.06 _{'V, = 075} 008 006 0.04 ,.,...:-;,=--\. = ..4-- ...--"....-002 ,...-

\

F 0.02

'

0.06 . ---0.04 0.080.06 0.04 -....--. ....-.../".5....----",:.,... ..,.,, --,

4

FP AD 0.02 ...'" 0.06 _{N_ .125} 0.08 0.06. 0.04 0.02 - IIIIIIIIIIIIIIIIIIIIIIIIII--C3 c., MgllIllIll AP FP 0.02 ."'-- ----_-.---,-,--,_,-..-77:---:-. ... .--..-_-,Z,

i

0,04-006 Ai_ '1.75 AP,.. 0.04

on the bending moment 'distribution, however, a

small general increase of the bending moments,

especially in the forebody, has taken place. The 'distribution of the maximum shearing forces over the model length is shown in Fig. 24 and 25.

The form of these curves is also very similar to those of Condition I and to some degree also to Condition IV. The largest shearing forces are

Fig. 19. Bending moment test results. Conditions VIII

and IX.

found at the quarterlengths, with the forward

values in most oases higher, at high speeds in the shorter wave lengths even much higher, than the aft ones. In general the forces in the forebody are

increasing with speed, in the afterbody they are

decreasing, and the variation is much more

pron-ounced for the positive forces than for the

nega-tive.

A small reduction in the positive and a small increase of the negative shearing forces

in the

forebody seem to be the effect of shifting the

weight from forward to aft. CONCLUSIONS

This experimental study represents a continua-tion of the model tests in regular waves given in ref. [1], and all the test series referred to in these two reports together should cover the most extreme

longitudinal distributions

of weights and their

influence on the magnitude and longitudinal distri-bution of waveinduced shearing forces and bend-ing moments.

A number of general conclusions to be drawn

from these experiments will

be given below.

Strictly they should be valid only for the hull form

--MIDSHIP --MAX MOMENT

LOADING CONDITION SCOI 0 ---- FORWARD IN ANY

--

AFT SECTION .12 o 008 004 X c..., 008 8 . 012 - '/L-0,75 _...4.

4--004 o ----0 o - --- -0 o 3 .008 004 --- -1-.---F.2_ ...-''' , a 012 ... "-0 -_

I

.012 008 .004 008 012 Y,,4 1111111 _,._---,...-

--004.EMMISELIM

---- ----_,

MIME

hMEMB

11

012 008

.004 11/11/1111

En

.004 008 012 0.05 010 05 0-20 &25 FR-030 2 4 6 8 10 12 14 16 SHIP SPEED KTS LOADING CONDITION DI

-mJUSH, --MAX. MCMLXXI

0 ---- FORWARD IN ANY AFT SECTION .., .008 ...___...--j- ..., _,. - ..., X (./ 00 ________.._ 1 1.. -06..._ .008 .-...., C 012 L o n I 008 ...--...sr 004 -.-=---.0.-=.7.6- .._,__-.----.5-004 008 9 :5 0.10 0.15 0.20 0.25_FR--°. 2 4 6 8 10 12 14 16 SHIP SPEED KTS 012 1.75 012 .012 1.25

and the block coefficient (0.74) in question. We are inclined to think, however, that with some

reservation, especially as to the influence of speed, most of them can be applied also to vessels with

both lower and higher block coefficients, thus

perhaps covering the majority of merchant ships

from the general cargo liner to the mammoth

tanker. In this connection reference should be

made to the experiments carried out by de Does

19

Fig. 20. Shearing force test results. Conditions VIII and

IX.

[2] on three models with different bloCk

coeffi-cients (0.60, 0.70 and 0.80) and the experiments by Wachnik and Schwartz [3] with the model of a Mariner class vessel (CB = 0.624). The weight

distribution

of the former series

can best be

compared to our Conditions I, V and VI, and of

the latter to Condition I.

1. The magnitude of the wave bending moments

and shearing forces is dependent on the three

parameters speed, wave length and weight

distribution.

A general increase with speed has been

found for wave lengths between 0.75 L and

1.75 L, with the largest variation for the forward sagging moment and the forward

positive shearing force. For wave lengths

equal to 0.6 L and 2.25 L the forces and

moments are nearly independent of speed.

The influence of speed on the wave loads is not the same for the different weight

distributions. The speed influence seems to 'be greatest when the radius of gyration

is small.

In most loading conditions and speeds the maximum shearing forces and bending mo-ments occur in wave lengths between 1.0 L

LOADING CONDITION us 008 0.06 MIDSHIP o--- FORWARD A -- AFT I ' VL.1.00 __ t 1 004-: ---,-Le, o .0.02 -0.04 006 ,... --,...Ne Q08 0.06 Q04 0.02 CJ 002 Q04 -Q06 008 - l> I , ,, ... 1 005 010 2 4 6 8 05 10 12 W0.20 14 16 025 0 FP -SHIP SPEED 0 KTS LOADING CONDITION MU 008 006 004 002 0 U Q0 MIDSHIP o-- FORWARD -- AFTo /11- 0.75 ---.-_.---± -Q04 008 0.06 Q02 0 002. 004 006 '/I.400 ,....6 NIMINIMMI .

Mil

-- -- --- --O ----. , 008 0.06 0.04 0.02 c_., 006 421.25 .0 -, ....o. -tr .--a... --- "Tr 008 006 004 "A*175 002.

_.-4r--.

---*--c-, I 004 006 -008 -7== ° --°- ° ...v...-.Je.---.... --o .. ----A Os olo 6 8 05 10 12 ato 14 16 025 _{FR -}0.30 SHIP SPEED (TS -002

.

125 . -o 04 I

---. 4

Fig. 21. Variation of midship bending moment and shearing force of forward quarterlength with wave length. Condition VIII..

Fig. 23. Longitudinal distribution of maximum bending moment. Condition IX.

Fig. 25. Longitudinal distribution of maximum ,sheating

' .foree. Condition IX.

;I

LOADING CONDITION la1:1

me-(19C1 004 .0.02 v - 0 KNOTS -- V10 KNOTS .7.-- V 14 KNOTS V 18 KNOTS ' --,, ";-'---..->'- ---../...---I II I .-_____ I I' 1 k FOR WARID . 025 >41. 050. 175 075 1;25 1.00 1.25 1.50, LA__ 1401 075

LOADING CONDITION YEI

10121 6 DOB-i)01; .004 .008 g ,012 V . '0 KNOTS ' ---- V10 KNOTS -- V14 KNOTS i - V18 KNOTS I .... "--..5-7::;--_______ , . ...---7:-.--. . 11 I ..' 1 I ,

---__ NnosHIP I 'I 025 0-50 075 1-00 1;25 MO .--1Ail_ 175 15 tpol 075 LOADING CONDITION IX V= .0 KNOTS ----,- V=11,0 KNOTS , 1 006 .--- V. 14 KNOTS -004 '---... V. 18 KNOTS

/ .

.>"/ On

-A.P EP -002 77-- - - _. . . -00 _//12'1.0.0 _ r--006 0.04

Z

.N.

'.r'

0.0 1 al ,..., r ,,,....;....---__----, ..---../. [ 1 fi ;0.0 ! 0.0 ,o.o. li p

..._..----.

....,0, 1 _..., ---:-: --___ Fe, A/L:1.25 LOADING CONDITION IX .012 v-OKNOT5 ----V10KNOTS

'

--_---.... V 141KNOTS ... .CO8 .004 ---,-V":118KMOTS .,../' ..."' ' .... .."- .,-,-i N. .\\ .ss. , \*.. IL, AP --- FP I O044 "...

---- /

012 It 012 o . 008 .".:.:...7t --...,. ,004 -"...:::,... 1004 AR

,

... ....- PP 001 ,.1 -... o x 125 .012

-

-

-- ---.0.0G N -

----Fig. 21 Longitudinal distribution of maximum bending moment., Condition VIII.

.and 1.3 L, although in some cases,

espe-cially at ballast draught, in lower wave

lengths.

e) The two weight -distribution parameters introduced in these test series, viz, the still water bending moment and the longitudinal

ZL

Fig. 24. Longitudinal distribution of maximum shearing. fame. Condition VIII.

LOADING CONDITION Val

. . . 0 KNOTS ---V'10 KNOTS ob. _{--V.14 KNOTS .----...} , -- V=18 KNOTS' -. -002- - _---___

A

.... d . A.P \ . . FP

0

1 .

,

_:: 7L=0.7.5 .. ,

/

/

,7"-\\

, ,

./ ---7--\,:\\

-.,

Z

. s I a , A? FR -0.0 t , , . _. -77:.-,' 1 _4:100 -, ..- .

//

"... 1602-, '

'

''N\<\ ...----/ .a... I , AP F.P -.c06 .0.04 002 , _ m-,-7,-7=a- -05 i AR IF. P 102 I 1 0041 'OD& A/1-1.75 LOADING CONDITION TM . 012- °KNOTS o ---- V.1°KNOTS 130 8--- V.14 KNOTS , .--- V.3 8 KNOTS .0041-- ._.,. X ir 1 ---"= 1 A.P- FP 004 - . -57 008-IL .G75 .012 -. ; .012 - . AI .. -D°81 00411. --;----1

t:

N;.,.. AP I ",,...,.,, ....-- FP. `... .608-,- -.012 .../ -. 11L100. .0121 o -- ... , . 004 __-- --,-...-. ,-...-. ---. -'- - .. ., ,, .-...:- P .004, III .- __ ---Ali, 1 A/Lr1.25' .012 -012 . 0 . AO, .004 _...:---7. 1- ---, ' FP 00 I -....1. ---00 I IA L1:75 012, I -004--006- A 006 0.02-I I --004 -0.06- 1.2 5

/

008 -

.-moment of inertia,

are found to have no

explicit influence on the wave load

magni-tude. There is, however, a tendency for

increasing maximum bending moments and

shearing forces with a reduction in radius of gyration. In practice, this would mean that vessels with large sagging still water moments are exposed to higher wave loads

than the hogging loaded vessels.

2. The instantaneous longitudinal 'distribution of wave bending moments and shearing forces is

also to a great extent influenced by speed,

wave length and weight distribution.

The most marked trend in the speed

in-fluence is the shifting forward of the

maxi-mum bending moments and the general

increase of the iforebody shearing forces

(especially when the weight of the forward

part of the model is small, i. e. small

mo-ment of inertia) with increasing speed.

In accordance with the above-mentioned

fact that maximum forces and moments occur in wave lengths between 1.0 L and

1.3 L, the general effect of both speed and weight distribution on the load distribution

is most marked and pronounced in the

same wave length range.

Generally, the weight distribution may be said to have a very pronounced influence on the wave load distribution, and espe-cially the bending moment distribution is

found to be sensitive to any small changes

in the weight distribution. However, the results clearly indicate that neither the still water bending moment, nor the moment of inertia are suitable parameters for the

esti-mation of the correct wave load distribution along the hull girder.

The most general and marked connection 'between weight and wave load distribution seems to be that a weight concentration in a certain location along the hull always re-sults in a bending moment maximum in the

same location, and as mentioned above this trend is always most marked at higher speeds

and in wave lengths between 1.0 L and

1.3 L. Thus, a large weight concentration

amidships results in moment curves with

large peaks in the midship region (see

Con-ditions

III and VII), and concentrations

near the quarter lengths give moment cur-ves with two maxima, one at each quarter length (see Conditions II and IV).

The great influence of the weight distribution

upon the magnitude and distribution of wave

bending moments and shearing forces found in

these experiments is

due to variations both in

hydrodynamic forces and internal inertia forces. Static calculations of wave loads may therefore give quite misleading results, and it is

recom-mended that the determination of wave loads in

regular waves should be based on model tests of the type presented here or on calculation methods taking account of all dynamic effects.

ACKNOWLEDGEMENT

The authors wish to extend their thanks to

members of the Norwegian Ship Model Experiment Tank's staff for working out the test equipment and

performing the test runs, and to members of the

staff of Det norske Veritas' Research Department for valuable help in analysing all the oscillograph records and preparing all the diagrams.

REFERENCES

Lotveit, M., Miirer, Chr., Vedeler, B. and Chri-stensen, Hi.: ..Wave Loads on a T-2 Tanker Mo-del». European Shipbuilding 10 (1961): 1, pp. 2-32. Does, J. Ch. de: «Experimental Determination of Bending Moments for Three Models of Different Fullness in Regular Waves.. International Ship-building Progress, 7 (1960): 68.

Wachnik, Z. G. and Schwartz, F. M.: «Experimen-tal Determination of Bending Moments and Shear Forces in a Multi-Segmented Ship Model Moving in Waves.. David Taylor Model Basin Report No.

1743, July 1963. [21,