On the bending moments of a destroyer in regular waves

On the Bendir

1ments of a Destroyer

in Regular Javes

by

Nasaiiaru Noz ski

CCYNTENTS Su.iiary i Introduction i Tank xperimerit i 2.1 Nodel Ship i Test Method. 2 2 .3 :esured Items 2

24 static Load ?es 3

. Test Result

1.

Ship ctionz 3

3 2 Bending nonent in Stili Water 3

3 Tffect of i'he Ship speed upon The 3ending Moment 4

4 ffect of The Wave Height upon The Bending Moment 5

35

3,6 Longitudinal Jist.ribution of The I3ending Moment. 5

3.7 Oscillation Moment Based upon Slaing .... 6

4. Conclusion - 6

i

-3urrnry

Ta: exnrirnents for a destroyer node], have been carried out at Neguro

I'odel Basin to investigate the longitudinal bending riomerxts in regi1ar

waves. This paper describes the test procedure, test results, and soue

coriblusions.

Thé hull of the model, 8 ri long, was made of wood and separated in eight

blòFks at seven sections. Each bloclt of the hull, i n long, was jointed by

a steel girder whosç litudinal bending rigidity was sinilar with the act-a

ual ship.

Beding moments at seven sections were obtained by measuring the bending

strains on the steel girder by means of résistance strain gages Test were

made in regular waves having heights of h/L1/5O, 1/30 and 1/20, and lengths

of./L

Introduction

A large numhr of ests have recently been reported upon the 1itud.inal

i

n

bending moments of the merchant vessels in reg'inr waves, while a smriall

nriber of tests upon such high speed vssc s :s :estroyers have been nade

pu11ic. In view of their particularity, however, the retention of high speed

is 'required for the naval vessels Ln m eases, ever, in storr' weather.

I order to give a reasonable desin, it is especia1l.r necessary to

under-stand correctly the £orcem

iLIposed

A. the first step of this irwestign.tio:, -:e have recently carried out tank

experitents of the destroyer model at Meguro Xodel Pasiri.

This reort covers the above test.

Tank a-eriment 21 ::odel Ship

sepa-2

rated into O blocks, i in long each. locks are connected with each other by

means of steel girder. Principal dimensions of the model are outlined in

Table 1. Steel cirder rerresenting the lonritudinal strength of the model

is the vertically symmetrical Htype continuous girder , whose hendin

rigidity distribution for the lentb direction is similar to that of the

actual shir. ( refer to Fig. 2 ) Therefore, the vertical oscillatien moment

at the sling may be similar to that of the actual ship.

have paid close attention so that the equinrient extending over a few

bIcks,i.e. the motar coupling shaft, the water prevention device, bilge

kel, etc. may not affect he hull rigidity.

Th weight distribution of the model is as shou in Fig. , and almost

sim!-lar to that of the full condition of the actual ship. The loaded heavy

arti-cies ( motors, ballast weights, etc. ) have been set to the steel girder so

direct as possible.

22 Test Method

When the model self-rrorcfled, the rolling, yawing and drifting were

rest-rited by the guides, while the pitching, heaving and surging were kert free.

When the towing carriage agreed with the model in velocity, the measurement

has been made. The test conditions are shown in Fig.4. and the experiment

phto in Fig.5. In the experiment, 9 sorts of the wave length, 4.8 rri-'24 m

were used. As for the wave height, 16 cm (1/50) was chosen within the limit,

whre the response seemed to be linear. In order to observe the non-

lineari-ty, we have additionally made an experiment for the wave height, 27 cri (L/30)

and 40 cm (1/20).

2.3 Measured Item

T1e item measured are as follows:

(a, Bending moment, 7 sections (connectIon of strain gages shall be refered

to Fig. 2)

(c) Heaving ( measured at the point 27 cri before the centre of gravity of

the model )

(d)Vertical acceleration at the bow and midship

(e) Wave height

(î) 16 min cine

One example of the record is shown in ?i.g.6

Static Load Test

Betdg moments have been evaluated in comparison with the result of the

static load 'cest ( in a hogging and sagging conditions ) previous]r given

on he ground. The static load test was made in a status of the stèel

gir.-der alone, aid in a test condition ( equipped with the wooden portion of the

huì, water-tight rubber, etc. ). Almost the saie result was obtained, and

welD. agreed with the calculation. It has, therefore, been found that

arr

othr rart than the steel girder had no effect upon the hull rigidity.

3. rest Result

Soirie exa1es of the test result of the bending moments and the ship motions

will be shown hereunder. The standard of the bending moment is a status, in

whih

poirt. At the low speed, the tant: wall interference effects on the measured

vaiies for the bending moment and the ship motion. The tcchnical terms and

mar'-s used are a shown in Table 2.

mark in the graphs shows the ouantity in the still water. fhen the

quanti-ty neared in still water was shown in terms of non-dimensional value, the

wa height was estimated at 16 cri (L/50) for cowenience sake.

Ship Notiori

show the pithing and heaving motions. They represent that the

peac is riere evident in the double amplitudes of heaving than in those of

P.hing.

4

A

shown in ?Ig.U, the sagging moment ( - ) is arisen at each section

dueto the wave caused by the hull itself, when the shin gradually increases

its speed in still water. When the speed

s more increased, the sagging

moment reaches

he min. value in order from the section close to the bow,

andj

decreases 'when the speed becomes higher than that. The min. value in

the;midship is found. in the neighbourhood of Froude number 0.41. It seems

to be natural, because the profile of wave is close to the sagging condition

at

bis speed of the ship.

3,3 Effect of The Ship Speed upon The Bending Moment

Whén the change in the bending moment caused by the speed of ship is

evalu-ateI in non-di.inensional terms at each section, Fig.12 and 13 are obtained.

The bending moment in the wave at each section fluctuates around

bend-ing moment in still water. I it is assumed that max. value ( hoggbend-ing moment)

of the bending moment at a certain speed is

min. value ( sagging mient)

and the moment in still water Me,, the following general trend is observed

thoughout al]. the wave lengths nd the ship speeds:

(a), At the section in rear of the midship (34), M _Ìlw= Ncw-MB. In other

words, the bendin moment fluctuates almost around the Maw.

(b) At the section in front of 33, (.IiSW-) is a little larger than (

If the ship speed becomes higher, therefore, the bending moment at each

section leans toward the sagging greatly, and the absolute value of

sagging moment becomes larger than the static standard calculation value

(refer to Fig.15).

In Fig.12 and 13, the scillation moments measured in the cases of the

waves as high as L/30 and L/ZO are illustrated. When 4 points of the same

mark are

plotted in relation to a definite ship speed, 2 points of the

outside show the max. alitude including the oscillation, while the

other 2 points of the inside show that excluding the oscillation

s

3.4 Effect of The Wave Height upon The Bending !loment

Th bending moment coefficient for the wave height, L/30 is compared with

that for the wave height, L/5C ( refer to Fig.12 and 13), and the followings

arejound: At the wave length, O.GL O.BL, the ship motion is small, and

little effect of the wave height is observed. When the motion is serious,

a cnsiderable decrease is found in the neighbourhood of the midship.

Fröm this fact, it is evident that the bending moment becomes non-linear,

wheñ the mot ion becomes larger. When the wave height becomes L/"O, the

bend-ingìznent coefficient greatly decreases.

3.5 'fect of The Wave Length upon The Bending Ioment of The Midship

Fi .12 shows that the bending moment of the midship fluctuates around the

saging moment in the still water at a wwe length.

Inrefcrenc to the double a1itudes (refer to Fi;.l4), the foflowings areL ohscr.red:

(a) Within the limit of ÀO9 1.2L, the peak is in t'e neighbourhood of

Froude number C.4. When A'O.GL, or more than 2.OL,no peak is found,

and the bending moment is snail,

(b When the wave length is l.1L, the peak is largest. Next to that, it is

large in case of the wave length l.2L. In case of the wave lengths, 1.OL

and OSOL, it is almost the sane. As a whole, no large difference is

observed.

36 Longitudinal Distribution of TheBending ;:oment

WIen A =1. OL, Fig. 15 shows a longitudinal distribution of the bending moment

coEfficient at the model speed of 0, 1.8, 3.5 r/sec. At any section, the

hoing moment somewhat decreases, and the sagging moment remarkably

increa-ses, when the speed becomes higher. In the above figure, the curves of the

bending moment coefficient evaluated from the static standard calculation

arò plotted. They are evaluated, er th. full condition is statically

bal-a'cd in relation to the weve of À=L and h=L/20. :o 3mith correction is

6

of .5 n/sec., nd the moment coefficient evaluated fron the static

calcula-tion in relacalcula-tion to the midship reveals that the total amplitude is aJrtost

the saiie, and that the absolute value of the calculated moment for the

sag-girg r.ornt is less than the measured value.

Oscillation I:oment L7ased upon Slamming

Wen the wave height is LISO, little oscillation moment is generated. For

th yayo height L/O, the measured max. oscillation moment was caused in

the nidshin, when A=i.1L and V =3.0 rn/sec. it has been revealed that

.-o. 0096. where:

min. bending moment including oscillation

s

moment

14 : min. bending moment excluding oscillation

moment

4.1 Conclusion

The tank experiments for a destroyer model were made to investigate the

lthigitudinal bending moment of the hull, and we have gained several

conclu-sIons, wbch will he roughly enumerated as follows:

(a) In high speed, considerable sagging moments are corne out at each ship

section even if in still water. Longitudinal bending moment in regular

waves at the section in rear of midship fluctuate, the centre of f

luctu-ation being nearly the sagging mOEnent in still water independently of wa

lengths. Therefore, estimating 5he stress caused at the midship

of

the actual ship, thc absolute values of the stresses can be obtained

rrodmateJy, by correcting the zero point of statisticalvalues,

cal-culated from the stress seectrum, as much as the sagging moment in still

water et the ship speed concerned.

(b The double anplitude of the bending moment coefficient, which had been

experimentally measured, is aliost the same a that evaluated from the

static standard calculation ( /=L, h=L/20, no Smith correction). In

high speed, the single amplitude greatly leans toward the sagging moment

7

item (a). Therefore, the absolute values for the sagging moment

coeffici-ent become remarkably l2rg'r than the values get frcan the static standard

i

calculation.

(e) The model, having siri.lar bending rigidity with the actual ship, was used,

and the oscillation moenent of the slarnning could be approximately found.

In case of the wave length, l.].L and the wave height, L/O, the measured

for the oscillation reached the max, C.0096. It has been troved to

be so large as not to be neglected.

(d) As shown in ?ig.6, the quantities showing the hull motion suth as the

heaving, pitching, etc. are recorded as comparatively fine sine waves

over the range from the low to the high seed. On the other hand, the

bending mients of the hull are recorded as almost sine waves 2t the

lower speed than oude nimiber 0.25. Jhen the speed is higher than that,

the moments show an aspect considab]y different from the sine waves.

From this fact, it is conceivable that the responce function of the

bending moment is not simple, and that the estimate of the actual ship

stress at high speed based upon the power spectrum is more complicated

than that of the ship motion.

A&mowledgment

These experiments were carried out at 1eguro Model Basin of J, D, A,,

In, planning and carrying out this research work, we have received proper

adVice from Messrs. Mitsuo kanno and Eiichi .rJatanabe. In putting the

ex-periments into practice, meanwhile, we have obtained kind cooperation from

the staff of the Tank and Construction Laboratories We conclude this article,

Tabic? i

rincira1

articu1rs of liodel

Length betveen I'crpendicuiars, L

::nath oulded,

Deth i:oulded,

0.555 m

Draft

(i'u11 Condition),

d

C'.'7

Displacement,

)70 zg

B1òc: Coefficient,

0.519

Radius of Cbrration in Air,

C.247L

3c41e :tio,

r

1/16

Table 2

Nomenclature

L Length between Perpendiculars

B K Radin! of Cration V Model Speed X Wave length h Wave Height M Bending Moment

NJ. Bending Moment in Still Water

C Bending Moment Coefficient

fr Density of Water

Acceleration of Gravity

Z Double Amrlitudee of Heaving

Dieplacenent of Heaving

Double Amplitudes of Pitching ( in Radian )

Pitching Angle ( In Radian )

FIG.

i

STEEL GIRDER

+

+

'vOODEN HULL

Ii

---i.5---+

+

1-OUTPUT

OSCILLATOR

o

FIG, 2

SHIP SECTION AND ARRANGEMENT OF STRAIN GAGES

J

1JL

L

BLOCK 8 BLOCK 7 BLOCK 6 BLOCK S BLOCK 4 BLOCK 3: BLOCK 2 BLOCK I

7I.I

I2I.6

I46.I'<

I5'?.I

156.8K9;

I62.?

?6.Ì'<

555K5

S7

S6

S5

S4

S3

52

SI

HG, 3.

WEIGHT CURVE

o

4

3

_FOLLOWING

SEA

t

3.0

2.0

I.0

08.

0.6

FIG.4 TEST

CONDITIONS

i

11

i

uuii

.iIi u i

,usissu:

iilUIR;

o

.S-YMBOL WAVE--Hf GH1F

I6cm(l_/SO)

z'

27

(L/30)

N

cm (L/20)

HEAD SEA,.

zsec

(A) h=I6cm

(B) h=27m

(C.) h4Oc

FIG5 MODEL RUNNING N REGULAR WAVES

À h=I6.-' SPEED C) y

FI.6

OSCILLOGRAPH

RECORDS

()8.Om ,ft=I6crn)

'.j

(A) SPEED=O

(B) SPEED=I.8/

(C)SPEED

= 3.5rnisec

m

I

m

z

o

H

o

z

DOUBLE

AMPLITUDES

OF

HEAVING,Z/h

io

_-0-5

o

50

X

h3L

À

QL

05

FiG, 8

HEAVING MOTIONS

I

o

a

D

-j

Q-LiJQ

O'

MODEL SPEED,V//L.g

02

Q3

04

Z 20

I

o

H

o

D

HO

j

U-30

-o-

o---

o

X

+

o'

O6L

O-8

09 lO

2

5

k

''

-- -

W

-J

D

o

«

Ef-2-On

_-_-__j_____

Q----30 '

Ql

02

03

04

05

MODEL SPEED V/IL.g

FIG,

PITCHING MOTIONS

«L

20

ria

z

H

o

o

D

H

-J

û--Lo

IO L

o

o.'

MODEL SPEED V/ILg

+

Jh

02

03

04

05

-4-FIG, O

HTCHtNG MOTIONS

0.0025

_Jcü

o

- 0.0025

0.005

00075

01

MODEL SPEED, V .'Lg

FIG,

i

BENDING MOMENT IN STILL WATER

L)

-r----

_--__fl-I

MODEL SPÈÊD,V/YLg

--001

_-0-02

Msw

₅₀

30

₂₀

03

j

FIG,12- I

BENDING MOMENT AT

SECTION

-'-

t')

o

XI-0L

0.Ot

0.Ot

r

)

IO L

o---- - - -- - -

01

MODEL SPEED.

02

03

04

05

-00I

Msw

_p.L2B

o

h--002

FtG,12-2BENDING MOMENT AT SECTION

-001

-002

f

_SL2Bj

O

h'

-_50

X

- 30

--20

03

FIG,12-3 BENDING MOMENT AT

SECTION

3

04

05

001

LOL0

0

-

4:0

0l

MODEL SFEED,V/v"Lg

'I

001

__xÏ_

-_00t0---.--.

-002

LOL

0I

MODEL SFEED,V/JLg

_{pqL2 B°}

i-L

-i--) Il5

-'-h--'--20

-X

02

-X

03

0,1

05

F1G,I2-4BENDIN

MOMENT AT

SECflON

4

0o

XLOL®

e-.----0.O

-002

k

-30

+- h

_____x-

FIG,12-5 BENDING MOMENT

AT SECTION 5

04

05

03

01

'J

'-MODEL SPEEDVYL-g

00I

-00l

-002

>HQ L

01

MODEL

pg

o

h--X

h=-+

h-- ___

o

FtG,12-6BENDtNG MOMENT AT SECTION 6

I X -X +

03

04

05

A-00I

_00I

_{- 002}

LO L

--

---O

MODEL SPEED,V//

Msw

pqL2.0

o

h-)(

h-+

FLG,J2-7BENDNG MOMENT AT

SECTION 7

04

05

03

02

001

(J

-001

002

->06L

MODEL SPEED, V//L g

Msw+

ßgL2B

- 50

30

0,I

FIG,13-I BENDING

MOMENT AT

SECTION

05

0'OI

-00i

-002

X

08 L

MODEL SPEED, V/IL g

Msw

pgL2B.

- 50

30

₂₀

Ql

02

FIG,I3-2BENDIN

MOMENT

T

SECTION

4

u

03

04

05

Q

OOi

_-00l

002

O9L

01

MODEL SPFFD, V//L q

Msw

---50

kL

30

0'3

04

05

FIG,I3-3BENDNG

MOMENT

AT SECTON

001

001

-002

01

MODEL SPEED,

V/IL

Msw

03

F1G113-4BENDING

VOVENT AT SECTION

4

4

05

COI

_o

COI

_-002

\

12 L

₃₀

20

0)

MODEL SPEED. V//Li

o

Msw

pg. (?B

h-50

02

F'G,13-5BENDING

MOMENT AT

SEC1ION

4

4

o

_o

COI

\z I5L

0I

MODEL SPEED,V/'LLg

03

FIG,13-GBENDING

'v1OMENT

A

SECOTION

4

04

001

i:

u

-001

-002

20 L

pgLB

O h-

t'

30

+

0I

MODEL SPEED,

V/Lg

03

FIG,I3-7BENIING

VOMENT

AT SECTION 4

04

-I-05

001

-001

_-002

-01

MODEL SPEED, V/IL g

Msw

O

02

FIG,13-8 BENDING

MOMENT A

03

SECTION

4

04

C5°

\

3OL

u

H-

z

o

z

o

z

w

m

o o

003

0---001

002

---n---.

06L

08

o-9

_-2

20 30

-h-_L_

- 50

o-0

0!

02

03

MODEL SPEED, V/JL g

FGI 4

BENDING MOMENT AT SECTION

4

04

05

IO L

k-L_

''-50

o

Om/sec

o---

_-o---

X

18 m,ec

_{35 Yec}

STATIC CALCULATION

00

AP

001

S7

I N5JLL._WIER

_.;______%_----

.---),---.--S6

S5

S4

S3

S2

F.P

FIG, 15

LONGITUDINAL DISTRIBUTION

OF MAXIMUM BENDING MOMENT