Model tests of T2-SE-A1 on midship bending moments in regular waves

uN r 3:GU

').

:oh:t?OJrr

Experi;nerJal Towing Tank

at

Department of' Naval -rchitcture,

Faculty of Er'inecrng, Kyuhu Univerit.y

F1kuoka, Japan

ARCHIEF

lab.

v.

SckeepsbouwkunJ

Tech&sche Hogeschool

Deift

/

MODEL TSSTS-ON T2-SE-AI

ON MIDSHIP BENDING M0MENT3 IN REGULAR VAVES

by J. FUKUDA

Asst. Prof. of Naval Architecture

1. Summary

Model tests of T2-SE-AI on midship bending moments were carried out in September

_1960,

at the Experimental Tank of Kyushu University, under the sponsorship of the Wave Load Committee of the Society of Naval Architects of Western Japan. Jointed model, cut in two blocks at midship, was tested in regular head seas having varions wave

lengths. To investigate the dynamical effect cf weight distributions on midship bending moments, model was tested in two different

conditions. For the one of these conditions., ballasts on model were

distributed so as to be similar to actual ship in full load. For the

other condition, centres of gravity of fore body and aft body were shifted about 2% ship length towards ship ends, and radius of

gyration of model was slightly lengthend. Then, motions of tnod.el in

two cases were somewhat different, under the sarre condition of wave

and speed. Therefore, values of midship bending moments in two cases, influenced by ship motions and more over by weight

distribu-tin

were considerably different from erch other.

(Note: Undr the same sponsorship, the other tests of T2-SE-AI model satisfying the three cnditions that having different weight distributionSand keeping

constant radius of gyration, were carried. out at the

Mitsubishi Experimental Tank at Nagasaki, in December

1960. In these cases, the motions of model are identify one another under the same condition of wave arid speed.

Therefore, bending moments are influenced only by weight

distributionS.)

2. 1ode1 description and testing equipment

The wooden model was cut in two blocks at mid ship, arid jointed

with pivots and connecting rod.

The midship beading moments were

measured by means of strain gauges on both sides of cantilever.

Ship motions were measured by means of potentiometers

attached to

guides at F.P. and A.P.

ivodel was towed in free to heave and pitch,

with constant speed restrained to surge.

FIG.l shows model setup

for tests.

Main dimmensions of T2-SE-AI model are shown in Table I.

Todel was. tested under the two conditions, (A) and (3).

In (A)

condition which satisfies, approximately, the weight distribution

of

actual ship in full load, rriodel is slightly sagged in still water.

In (B) condition, model is condiderably hogged in still water.

Details of (A) and (B) conditions are shown in Table

A

and

For motions of model (heave and pitch), virtual weight equivalent

to inertia effect of guide is represented as

at F.P.

at

A.P.

(see FIG. 1)

In Table, andJ

weight particulars are

expressed. in statical and dynamical condition.

The fallowing items are measured.

heave

pitching angle

midship bending moment

wave height

ship speed

Tab-le I M.in dimrnensions of T2-SE-AI model

Scale ratio

Length between parpendiculars (L)

Breadth (B)

Draft (ci)

Displacement in fresh water

Mock coefficient

Water plane area coefficients

Centre of Buoyancy from Centre of Floataticn from

L/

14,7

1.800 m 0.243 m 0.107 m 34.30 kg 0.73 0.83

0.004

L fore, 0.014 L aft 2.27

16.79

7.40

TahlellA Model particularsin (A) condition

Statical Dynamical

Weight

Fore body

17.3tkg (o.So

w) /8.12 kg

(o.o6 w)

Aft body

6.9.çkg ( o.'14'1- w) /7.72 kg ( o.'q' w)

Total 34(3Okg (

1.000 w) 3St4 kg

(1.000 w)

C.G from midship

Fore hod.y 0.3/S m ( o., L) 0.3*0 m

(o.j89

L) Aft body -o.322m (-o./79L)-0.3

m -o,2L)

Tatal o.007m ( O.004L) o.007 m ( 0.004 L)

Mt. of inertia about Go

Fore body kg - m 3.200 kg - m

Aft body .37/ kg - m2

3oO(

kg - m

Tatal kg - mz 6.ZOr kg - m

Rad. of gyration about Go

Fore body. ( o.Z/4L)

o.qzo

m ( o.213 L)

Aft body O.3?m ( o.2oL) o.ii2 m ( 0.229 L)

Total o.fl0m (o.Z/IL)

of/6

m ( o.23/L)

Natural oscilating period

Heaving

o.8Z

sec.

Pitching .0.77 sec.

Tableff9 Model partjcularsin (B) condition

Statical Dynamical

Weight

Fore body

/7.kg (

w) 18.IZkg (

o.O6

w)

Aft body

/6.?5kg (

o.'q' w) 17.72kg ( o.4V w)

Total _{34&3Okg (} 1.000 w)

_S4kg

₍

j.00 w)

C.G from midship

Fore: body 0.332 rn ( 0./96 L) oyi' m ( 0.208 L)

Aft body

-o.3?

m -o.i?f L)-O.Zm

-o.2/.Z

L)

Tatal

o.007rn (0004

L) o.007rn ( aeo4L L)

1t. of inertia about Go

Fore body 2.2J. kg - m2 3.41? kg

Aft body 2.8th kg - m

378

kg

-Tatal

£709.

kg -

rnZ

6.?S1

_{kg - m2}

Rad. of gyration about Go

Fore body 0.406 m ( c.zz L) o.i8 m ( o.z/3 L)

Aft 'cody 0.4/Om ( o.228L) ( o.z'7L) Total o.qoêm

( o.227L) o./m ( o.z3L)

Natural oscilating period

Heaving

0.2

sec.

Pitching

o.0

sec.

Go: centre of gravity of model

3-3. Test program

Various tests

were carried, out in waves and in still water.

Tests in regular head seas

having various wave

lengths were made

for

(A) and (B) condition. Tests in still water, to determine

_the

bend-ing moment d.ue to waves produced

by towed model, were made for only

(A) condition.

Table . Test program

In waves Instill water Model condition (A) anti (B)

0.7, 1.00 Wave length

L

/.0 / Wave

height

= 43_

()

only

Speed range

Fr.

0 to

0.35

Fr. = 0 to

0.55

L

= ship length = wave length

!Lu. = wave neignt

Fr.

= roude ' s number

4. Test

results Ship mations

Ship nations are shown in FIG. 2--9, i.e., heaving amplitude and phase lag to wave, in FIG. 2-'5, pitching amplitude and plase lag to wave, in FIG. 5-8, where:

= heaving amplitude = pitching arnl:litude = wave height = = wave amplitude

A

wave length =

= max. wave slope

I

tuning factor for heaving = tuning factor for pitching

A

or

was derived from natural period of heaving or pitching in still water. Phase lg was decided from following

definitions:

heaving motion p: plus, down: minus

pitching motion bow up: plus, bow down: minus zero piase lag of mOtiOfl corresponds to max. heave or

pitch with wave crest at midship. Midship bending moments

Iax. Midship bending moments and whose phase relations to waves are shown in FIG. lO 13, where:

M

= max. hogging mt. (+) or max sagging mt. (-)

p = specific density of water

= accerelation of gravity

M

-

pLzB.H

Midship bending moment at runs in still water(M)is shown'by

the expression of

I-, Ms.vr.

Mean amplitude of midship hendng moments, i.e., mean of max. hogging moment and max.

shgging

moment is shown

in FIG. 14 - 17, by

the expression of

MHIV1S

C

_-

_flLR5LP

Mw

= max. hogging

moment (+) = max.

sagging

moment (-)

Test results in low speed range, i.e., Fr. = 0 0.15, may

a

/

ps*

r,.r,

f.re

cft

,de

,t. of

nert.a. of Q

nt.

of

nert

of 4a

r,..r,.r4----ptentO$WteT

of (f

pottIt#..OPtVter of

4&

dispV. of FJ

dssplt.

of

64.P

-f(4_--p4tC(.$/ t2ft1i

KP4I4

FIG.I

(D5r

of wiodd setup for measurement)

(B.nd"1 ,2t.)

0

I.4,

12

HEAVE

0(A) CONDITION

(B)

0.75

Mw

=

L0

Q2O'

0

-

-

.,. 0 1

0 .

-PHASE

/

LA

180

90'

74,t eJgQ2

0

0.I0

0.20

0.30

1.2 _CONDITiON

B)

HEAVE

!HASE. LAG

=1.00

HwE

oJO

020

F'. 3

0-12

_{0(A) CONDITION}

1.0

0.6

04

0.2

HEAVE

.PHASE LAQ

/

/

/

/

= 125

0

IV

020

0

F''. 41

-12-0

0

-'3-Il

I'

HE

AVE

4(D\

4

HwI

I

-/

,

,

A

0.8

0.4

0.2

90

0

PHASE LA

p

-0)0

p

o.0

0. 0

90'

-9O'

PIPIIILT.._

PHASE LAG

PITCH

1.2

_{0 (A)CONDITION}

1.0

0.6

04

2

oj0

=O.'T5

0.20

O30

6

0

'.4

12

PITCH

(A)CQND)1toN

'1

L

L

-

____4-_

I

'0

&

-. .-.

-

pIpp.,--L

o

*

0.4

02

H

0=-'

-o.0

Q20

F14.

0.6,

0.4

O.2

,9o..

PITCH

PHASE LAG

0.10

1.50

0.20

Hv_

o.30

0

0

-/7-FL-. to.

0

0

1

BENDINQ MOMET

M=C?9L2B

(A)COWDITIOH

STILL WMTR

L

=

H0G 0.02

-002

SAQ.

pp.-o

9 Os

-L

0.10

II1OIP

FiG. 1/

)

BENDJN

-M-C?LB-

2

MOMENT

= OO

_{O(A)CONDITION}

x STILL WATER

H_j

L

45

.

:

-002

SA(.

o.:iIUIPPU

_____

90

PHASE LAQ

1

0.10

F'-

0.20

0. 0

BENDING MOMENT

L

F'-. /3

BENDING

M=C?L2B*

MOMEPT

STILL WATER

HO

-001

ii1I

1

I!!'

!!E:

0.10

F'

0.

FIG. f4L

FIG-. IS

A

22

BENDING MT

I

=075

o (A'COND

(B)

H

yL28H.

_{L = 45}

C

0 10

Fr.

0.20

0.30

BENDVIN

'.--

_HMS

MT.

V

0

V /

(A)COND.

(8)

LOO

H

-VL -

V

C

0.O2

\\

V

ocn

1:1

- -

V V o V

o

V V

-0

_.A--V VV

°

0

-0

010

Fr

020

&30