Bending and torsional moments and motions of a T2-SE-A1 tanker model in oblique regular waves

(1)

SHIP RESEARCH INSTITUTE

MINISTRY 0f TRANSPORTATION

700, SHINKAWA, MITAKA

TOKYO, JAPAN.

&NDING .tND CR.$IGI4?L CTENTS A.ND NCTICNS (F A

T2-&-Pa TANKER

(DEL IN C;BLIQUE IGULAR WAVES

FthNTED

TO

(2)

BENDING AND TORSIONAL MOMENTS AND MOTIONS OF A

T2-SE-Al TANKER MODEL IN OBLIQUE RECJLAR RÏAVES

(aauftiiii Yarirxouchi Kunjo Gda

Akihiio Ogawa

Abstract

The torsional moments, vertical and horizontal bending moments as well as the ship motions were measured on a T2-SE-A1 tarer iìde1 in

oblique regular waves. The hull of the model was made of wood and cut into two parts at the midshipsection. The moments were measured by a

dynamieter that connected two blocks. The wave height was kept constant, Hw/ L 1/1.5. The wave lengths were k/L 0.35, 0.50, 0.75, 1.00, 1.25

and 1.40, where the model was running with the angle of encounter of 135° to the waves (bow sea). Also the standilig tests with the angles of

encounter from 90°(beani sea) to 180°(bead sea) were carried out at A./ L 0.50 and 1.00 for the supplementation.

Introduction

In order to get the quantitative as well as the qualitative

informa-tion ori the moinforma-tions and moments, especially on the torsional moments

experienced in oblique waves, a series of tests was carried out.

This was performed as the successive work of the previous one (1), which one of the authors particioated in, concerning the motions and vertical

bending moments on the model of the same lines advancing in head seas.

As the first report of this experiments, one case of encounter angle 135° and the supplementary case of the model standing in waves

encounter-ing by various angles from c.o 180° are presented here. Though main

part of this paper concerns only to one angle of encounter, the authors dare present this, considering the fact that very few have been reported

on the torsional moments.

rodel Guide

The tests were

carried out at the Mitaka Ship Experiment Basin i

(3)

-2

( 80 in

x

80 in

x

4,5 in

_).

To facilitate the tests, the Basin was

furnished with a

new model guide as is shown in Fig. 1.

The

guide

was ccviposed of a wire rope and light-channels, and looked like a slender

suspension bridge. The suspended

channels

were used as the guide-rails,

fer a

nall cage which was towed through towing wire

driven by an electric motor. The model ship and the control pannel on

the shore

were

connected

by electric wires

supported and carried by

the cage which foflowed the

running model

As the guide

system was fixed

at the

position, the course of the model was limitted

to two

directions, 450 and 135° to the wave for the time bejn.

The model ship, of course,

could run

freely

without any

restraint except

the flexible

e)ctric wires frcrt the cage.

3. Model Ship

The model of T2-SE-Al tanker was made of wood. The principal

particu-lars

of the model

a re shown in

Table 2 The hull va s cut a t midship

-section into two

parts. Both parts

were

connected by a dynamoineter at

the section.

The dynamometer was a steel pipe with the diameter of LOrnin,

the thickness of Saimi

and the length of 220mm.

_The vertical and horizontal

bending

moments and also the torsional manents at midship were obtained measuring the stresses on the

dynamane

ter by means

of

resistance

wire

strain gages.

The natural

frequencies of two-noded hull vibration of this model

determined by this dynamoineter was rather low canpared with the frequency

corresponding to that

of the actual ship,

_{for the necessity to get the} rather nall section modulus of the steel pipe

to obtain a measurable

stress on the pipe. This did not however harm

the

_{measurement at all,}

(4)

ç

at the same time, the longitudinal weight distribution was arranged to

be possibly app roxLma te to that in former experiment ( i ), a s are shown

in Fig. 3.

4. Description of Experiment

The tests were carried out by the self-propulsion method. The test

program is given in Table 3.

The followings were measured in the tests.

( a ) Vertical and horizontal bending mceients and torsional moments at midship

( b ) Ship motions; pitching, rolling and yawing (azimuth)

( c ) Vertical accelerations at bow ( SS 9

1/4 )

and stern ( SS

3/4 )

( d ) Rudder angle

( e ) Model speed and locus ( f ) Wave height and length

The model was controlled remotely from the shore through electric

wires. Signals of C a ) to ( d ) were

recorded in the " visigraph

'

recorder on the model,

arid

( e _{) and (} f ) were

measured

ari recorded on

the shore. The signal of ( d ) was sent back to the indicator on the

control pannel on the shore simultaneously for the convenience of

cont-rolling.

5. Test Results

The test results are presented in Figs. 4 to 14. The bending moments

are expressed in the form of dimensionless parameter, C = _/ gL2BE.

As the model was free-running completely, the adeciate method to measure the encountering wave at the model

position could

_{not be found.}

Accordingly the phase angles of motions and moments with respect to the wave motion could not be obtained. Here the phase angles referred to the

(5)

4

vertical bendtng moment were shown in the figures.

It is regarded to be

soriewtiat usefull to show them, because it ïs shown by Fukuda

(

2 ) that

in regular heading waves the mximum amplitude of the hogging ( or sagirig )

moment occurs when the crest (

or trough )

of the wave passes by the midship.

Then the moments and the motions will be giben by

a

i(ct + Lay),

Ets representing the pha

4es

in

these figures.

The positive signs

for the a.tplithde are chosen as follows:

( i

)

Hogging moment for

the vertical bending

(

ii )

Bow and stern bending to port for the

horizontal bending

iii ) Anti-clockwise twist looking from

fore and aft for the torsion

iv ) Bow ascending for pitch

(

y )

tarboard dipping for roll

(

vi )

Bow drifting to starboard for yaw, and

( vii )

Downward direction for

acceleration

The positive signs of the motions were chosen to

correspond to the

right-handed coordinate system, in which the z-axis pointed downwards,

and

that of the vertical bending moment was

_{conformed to custom.}

The base line of the vertical

bending moment was referred to the

reading at the standstill

state in

still water.

It was difficult to decide

the zero-line in horizontal

bending

and torsional

moments. This was mainly

because, it was very

dIfficult to keep the course of the model just under the

guide rail as the Basin was outdoor one and it was necessary'

to steer very

often in some cases

for instance in

_{breathing of the wind, and the rudder}

forces caused

comparatively

large amount

of horizontal bending and torsional

moments.

In the same

reason, the drift angle and the rudder anglt could

not be determined absolutely.

Above all, various external conditions

restricted the speed of the

model in

the

range of 0.3 to l.Im/s ( F

0.04 to 0.20 ).

(6)

5

6. Discussions and Concl'sions

From Figs. 4 to 14 the following could be mentioned:

( a ) The amplithdes of vertical bending moments at

the 135 °angle of

encounter are usually less than those in

corresponding heading waves with effectively the same length.. ( Fig. 4 )

(b )

In most

cases there is no big difference

between the amounts of

hogging and

the sagging moments.

( Figs. 4, 8 and 11.

)

( c ) In low speed

range the vertical bending moments show

similar

tendency to the pitching angles with the variation of the speed.

This is clearly sho'wn

in Fig. 15, where the vertical bending

moments

and the pitching angles are plotted taking

the cr.ilar frequency

of encounter as abscissa.

( d ) In the tested

range of speed, the maxiiiia of the

horizontal bending

and the

torsional moments occur in the vicinity of

X/

L 0.60

('"-e/L

0.85 ) and >/L

0.50 (>efL

0.71 ) respectively. The curves of the vertical bending moment vs ¡\/L however are not

sc simple ( Figs. hand 12 )

i. e ) The amount of the

torsional moment is small in all cases as supposed

beforehand . Figs.

5, 8 and II ),and this result coincides on the

whole with one of the test

results of same kind (

3 ).

( f ) The relations between the phase angles of moments change very little

with speed ( Fig. 5 ).

( g ) As the periods of

encounter

were

shorter

than the natural period

of roll of the model ( see Table 2 ) through the

tests, the maximum

of the rolling

angle did not appeared. ( Figs. 4, 9 and 13 )

( h ) The longitudinal bending moments show some

interesting

tendencia

under

certain circumstances. Figs. 16 and 17 represent the state of

the change of the vertical and

the horizontal bending moments over

(7)

the condition of

X/L - 05 at lj'

3.35° exceeds even the vertical

bending moment in

heading waves of

)\/L - 1.0

In these figures,

the rwbers of the

points indicate the time at 1/8 period

intervals,

O and 8 being the instant when the sagging

moment begins.

( i )

The resultant angular

oscillation composed of pitch and yaw,

as are shown

in the saine figures

( 16 and

17 ), show the tendencies

similar to that of the longitidinal bending moments.

Reference s

( i ) Y. Akita and K. Gda, Experiment2l

Determination of Bending

Moments for

T2SE-A]. Tanker Model in

Regular Wave

u

ISSC, Glasgow, 1961

( 2 ) J. Fukuda, " On the Bending

Moments of a

Ship in Regular Waves

Contim.ed ) ti

Journal of SNAJ, Vol. 111, 1962

( 3 )

E. }h.rnata,

Horizontal,

Vertical

arid Torsional Moments

Acting

on a Ship Model at

Oblique Headings to W'aves "

(8)

7 Table 1.

Nomenclat,ure

Hw

Wave height

X

Wave length

Xe

Effective wave length

/cos4x

V

Model speed

F

Froude rn.mber

V/f

4

M Moment

C

Moment coefficient -

M/pgL2BH

2 e

Double amplitude of pitch

2

Double iwplithde of roll

2X

Double amplitude of yaw

i

Angle of encounter of model's course to waves

F

Vertical acceleration at how

°'Á

Vertical acceleration at stern

Le

Circular frequency of encounter

Pae angle, ex.

: Phase angle of horizontal bending mnent

referred to vertical ber±ing mcient

Suffixes;

V

Vertical bending

H

Horizontal bending

T

- Torsional

(9)

Table 2.

Principal Particulars of Model

Length beten perpendiculars, L

/4.500

XT1

Breadth, B

0.608 in

Draft, designed full load, d

0.268 m

Di!plcement, V

0.530 Block coefficient, 0b

0.74 Lonithdinal center of cioyancy, LOB

-0.017 in

Scale ratio

1/34.0'?

Lone-ithdinl radius of gyrtiorx in air, K

0.25 L

Transverse metacentric height, GM

O.C35 in

Natural circular frequency of pitch, We

5.13 sc1

Natural circular frequency of roll, u24

2.78 sec

Natural frequency of vertical two-noded hull vibration

.50 cp

(10)

Tab].e

.

Test Prorrn

E

_{( Nornjz1 )}

_{10.0 ein}

* F - 0.04 to 0.20

-0

Renark ; The test results of motions and accelertons

_{ws converted into}

the nomin1 wave height in 1iner proportion.

Ncdn1

Acbial

Actual

90°

112.5°

155 157.5°

180

C

0.35

0.37

10.5

*

0.50

10.6

+ + ₊ ₊

0.75

10.0 *

1.00

0.99

10.0

+ + 4* + +

1.25

1.19

10.2

*

1.40

1.38

8.5

(11)

WIRE ROPE

Fig. 3.

DYWA MO METER AP /

4

5

Fig

2 FP 6

(12)

I1

flr

ii

___. j

J--.

WEIGHT CURVE

¿ri

(!)

n

j

WEIGHT CURVE

o f

J1

i

1-L4

r :

L.

L1p U

-I

ItL

F F I'

r1

L_ - -J-L, 'L r

j-L L L

u

r

i

-I

rT

ri

r-1 r-1

r'

-]

Ir

9 / 2 3

4

5 6 7

(13)

.0/O .Q15_

-lì

N

.2

N .37

-1J/=

/350

/ /

A O

Fi. ¿

¡Ca 1.4 b

/

b I. 5o

- - - -

- - -'z

.

7!

A T I = / Oo

--

Y

.7

_37

¡.32 1.3 L'

(ron-t (I))

MARI(5

À/L

---g---

/.3

--X----

1.19

0-

.99

.75

---+----

.50

----.---

.37

L) u- u--o _A o A

u-+x___x

',-

7, X

----z

---

V

o

D I .1

V--

V LI X V o _X

x

4 ---.025

Q2 O

t

o/O

N

(14)

TOR5/ONAL MOMENT COEFL,

C1-o

o

Ix

lo 14j n

lx

1< HORIZONTAL BEND!N MOMENT COEFFICIENT , o -o o

_PHAE,EHV

t'i o

o

O C) o PHASE, ETI,

(15)

YAWING ANGLE,2X t' (J o o 9D I i o S-ROLLING ANGLE ,

2

c 4

o

PHASE , Ev

il

X I L cto o

o

o PUASE ANGLE, I + ++ t K PITCHING ,4'VGLE ,

26 o

D

\

L

L '-o

o

o o 7' a

iì

PHASE ANGLE, Eov

o

i4

'I +

Ii)\C

\

o

i / _/ I

I

_/ I

/

i//o

¡I

cU o

(16)

j.

C

PHASE ANGLE, Eoçv

o

+

i'

H

PHASE ANGLE , EV

VERTIC4L ACCELERATION

AT STERN,

cXA

(g)

VERTICAL ACCELERATION AT BOW

(17)

TORSIONAL MT. COET. CT o

o

-O o

\

N

'y

t-N N N N -o

00

N.

+

/

t

/

_/

O

o

VERTICAL

BENDIN& MOMENT COEFFICIENT,

C

S-.

o

HORIZONTAL

BEWD7VG MOMENT COEFr,

'H

(18)

.5-0°

so

w Lb

2°

Lb o

4°

/800

t

-0° /350 ANGLE 0F ENCOUNTER

Fig. 9

--4---

-co 90° / 0

/:;5°

900 VI

(19)

o

(Q

VERTICAL ACCELLk14TION AT .STERN,O('A

(g)

VERTICAL ACCELERATION AT BOW

(20)

.02

.0/

0 .0/

o

t

C V,

.0/

-J

o

k

.5

.5-w =/

1.0 f-0

À/L

WAVE LEWGT/-! / MODEL LENcj-Th' ,

À/L

o 1.5

'4

0

I I I LO - I-5

2.0

EFFECTIVE WAVE LENGTH /MODEL LEWGTI! ,

Fig. U

(21)

.02

.0!

.003

- 002 .001

o

'

N

¡

N

--\

Àei= .7/

I'=

¡350 p 0

.5

1.0 ¡.5

À/L

Fig. 12

0

¡.0

WAVE LENGTH 7 MODEL

LENGTH ,

X/L.

j I j

I I

O - .5 1.0 1.5

2.0

EFFECT! VE VV'AVE

LENGTH / MODEL LENGTH

(22)

50

00 ><

WAVE LENGTH/MODEL

LENGTH ,

A/L

40

=

/35-- /35--_

/4

'o

o O .5-

1.0 ¡.5-Fig. 13

9 .5

/.0

,k/L

¡.5

o

.5

i.o

¡.5

20

EFFECT/VS WAVE LENGTI-1/MODEL LENGTH,

Ae/L

//

/

z

/

r

VV

- /0 - /4-Q .5-

¡.0

¡S

(23)

.3

.1

-o o o

.5

1/

N

Fig. 1h.

1.0 À/L

'.5

o

.5

¡.0

1.5

WAVE LENGTH/ MODEL LENGTH

,

À/L.

-3

g

.2

I_3 S°

E ETE CT! VE

WAVE LENGTH/MODEL LENGTH

,

(24)

o

In (M

o

(A) °

n

o

\

PITCHING ANGLE, 20

I J I I T ¡

/++

'

xxç

\

N

0\

VERTICAL MOMENT COEFFICIENT, Cv

o

-5AG

o

HOG-V o o

7

LP U o

00 o

r

Ir! () -ç o -n

-4-/

_/

0\H-/

_/

+1

(25)

4 À/L= I. O

Fig. 16

3,-o,

2

Q

MH (Bow fo 5LarboaY4) MH (Bow fo porf) X (Bow fo pori) X (8aw to 5tarL'ord)

I I I f

6 4 2

2

4

6 30 20 ,0

/

2'

30

2_

(k.-rt)

/

SCALES for SCALES for

(26)

w = / o