On the bow emergence of a bulk carrier in irregular head waves

THE FACULTY OF ENGINERING, KYUSHU UNIVERSITY HAKOZAKI, FUKUOKA, JAPAN

ON THE BOW EMERGENCE OF A BULK-CARRIER IN IRREGULAR HEAD SEAS

BY

JUN-ICHI FUKUDA YUJI ONO

PRESENTED TO

ON THE BOW EMERGENCE OF A BULK-CARRIER IN IRREGULAR HEAD SEAS

JTJN-ICHI FUKUDA* YUJI ONO'

1. INTRODUCTION

The problem of slamming or whipping of ships which have full type of hull, form as oil-tankers, ore-carriers or bulk-carriers is ch more

noticeable in recent years as the results of steady increase of ship speed and fullness of hull form. The oil-tankers can be loaded with suitable ballast waters on their empty voyages in rough seas, but the ore-carriers and bulk-carriers in ballast conditions can not be freely ballasted and

suffered frequently from slamming or whipping in storm seas unless they decrease 'the ship speed. The phenomenon of slamming or whipping is much related to the relative bow motions with respect to the sea surface.

The large amplitude of vertical displacement between the bow and sea surface in rough seas causes the bow emergence and consequently the slamming. In the last ten years, the only study on the possibility of .tatistical predicting the occurence of slamming was performed by Tick

except the few study denoted by Shade recently in the report of "Committee on Slamming" I.S.S.C., 1964, Delft.

The authors present the results of study on the statistical pre-dicting the bow emergence of a bulk-carrier in rough seas. They tried first the theoretical evaluation of relative motions between the bow and water 8urface in regular head waves on a ship in three different ballast conditions. Then, the statistical prediction o: relative bow motions

with respect to the wave surface in storm seas was performed on each

ballast condition. Finally, the critical fore draft for the bow emergence was estimated by using the derived results in storm seas.

2. Bow motions in regular head waves

Consider the case when a ship goes forward with constant speed V among regular head waves whose surface elevation can be expressed as

(1)

The equations of heaving and pitching motions of a ship are given with the aid of atripwise theory, as the followings:

lIZ)

ABCtDt't=fr1

By solving the equations of motions (2), the heave and pitch are obtained in the form of

/' o5Wet

-

64.4 Wt

'c4 (ct

(3)

=

=

Cfr Wet 9544fl

cZ

coii (W.et _1')

Then, the vertical motion of the bow which is distant longi-tudinally from the midship is obtained as

z= zfR, =

Zccc" Wet

Z'4eaLajet

Zco4(Wet

).

(41)

where

+

-

) cA*,

Z'

=

-

) 4s

because upward heave and bow-up pitch are positive.

The relative motion between the bow and wave surface is also obtained

12

as where where

Zr/oZ,cetZrsiWrtWet

Zr(Wet1Ezr)

(S)

ZrZc'CdfQX ZrZ44'flX

The vertical velocity of the bow and the relative vertical velocity between the bow and. wave surface are obtained as the followings:

(6)

Ur 7Jr/I?o 1r

c*dWt

1J

nwt

J'coi (wet

(7)

-

-t , _-:

U '

IT t' - W _C'frd

X

And, the vertical acceleration of the bow is expressed as

=

=

cCO

Wet

- Xs'J'fl We

t

Xco-cJ

(wet

8of')

()

2

*

I

0(c - We Ze ,

-

We2

Z

In the waves of large amplitude, the relative displacement between the bow and wave surface may exceeds the draft of bow in still water. Then, the bottom of bow should emerge out of the wave surface for a time in a period of encounter and plunge into the water after that.

Put

the draft in still water at X, as , the formula of

40(z)

=

d (Xi)/Zr (r,)

gives the critical wave amplitude for the emergence of bottom at X, in regular waves.

The numerical calculations of the formulas of (5), (4) and. (5) were performed on a bulk-carrier in three different b8llast conditions whose

particulars were shown in Table 1.

The calculated results are shown in Fig. 2 5. The amplitudes of

motions are shown in the figures, but the phases of motions are omitted. In Fig. 2, the amplitudes of heave and pitch are indicated with non-dimmensional expressions as the followings:

/

=

4) r

/

(/0)

The amplitudes of vertical displacement and the amplitudes of rela-tive vertical displacement between the ship

and

wave surface at xO.5L (F.P.), O.4L and O.5L are shown in Fig. 3 5 with non-dimensional ex-pressions as the followings:

z:=

:= ZrO/o

(9k)

(/1) As shown in Fig. 2, the tuning effects on heave and pitch are rather remarkable in the deep draft conditions (Cond. liT in Pig. 2 c), and the speed's effeäts on ship motions are so too. The bow motions which are

where

associated themselves with the heaving and pitching motions are rather severe in the deep draft condition. The same tendencies are noticed on the relative motions between the ship and wave surface (Fig. 3-5). These characters of ship motions may be rather harmful to the

improva-ble advantage of ship in deep draft condition related to the bow e-mergence.

3. Bow motions in irregular head seas

In section 2, we have obtained the response operaters of relative bow motions with respect to the wavesurface. Now, we can estimate

statistically the relative displacement between the bow and wave surface in rough seas whose

energy

spectra are given.

Assumed wave spectra corresponding to the average sea states in North Athantic are shown in Fig. 6, which are decided to be satisfied with the sea states i.e. the significant wave height and the average wave

z)

period, based upon the figures given by Roll Those wave spectra are obtained by the following formula which is deduced by a similar method to

4-) that of Swaan or Muntjewerf

[rcw,r)32= 1rw)]cdZ

-4

where

w :

circular frequency of component wave

X

: angle between the wind direction and the direction of wave

propagation

significant wave height

[ r(w)]

Z_ cL

.e_C2/w

- wo

C,

_. i

/ ¶

(m/

C2

6z/Tz

(sec2)

Qwcz3

sec

)

T :

average wave period

C and C are decided as the function of wind velocity based on the observed sea states by taking account of the following:

Since the width S of wave spectra of the formula (ii) is equal to

( Z/3 , the significant wave height is decided by the formula of

i/3 K,

(E=Iz/3 ) V

where

Erff[r(w)]cXdwdX= *f[r(w)]2dw

K113 (E=Vz/3 )

=

By utilizing the results obtained in section 2 and the wave spectra given by the formula (ii), the cumulative energy density of the relative displacement between the bow and wave surface in the long-crested irregu-lar seas is obtained by

Er

fCZ(w)]2[r(w)J2dw

(/2)

- The average of the one-tenth highest values of relative displacement

(amplitude) between the bow and wave surface is estimated approximately by the following formula

Zr(s/lo) = 1<1/to

(E.V/3

). VEX,.

K1110(E=z/3 )=/.6

(13)

by assuming the width of motion spectra will be about

Z/3

, because

the wave spectra has a width of .

The calculated results of (13) on the bulk-carrier in different three ballast conditions are shown in Pig.

7-9,

and compared with the estimated

results in Neumann's ideal fully developed storm seas.

When Zr(s/:o)-

the draft in still water at xO.5L (F.P.), O.4L

n

sea surface. Therefore, the critical fore drafts for bottom emergence at x=O.5L, 0.4L and 0.3L are decided relating to the wind velocity 7Jor the significant wave height

H

by the figures for three different ballast conditions (Fig. 7--9). Thus, the curves of critical fore draft for the bottom emergence at x=0.5L, 0.4L and 0.3L are derived as shown in Fig. 10.

The classification societies recommend the minimum fore draft as followings

df /L

0.026 (

Nippon Kaiji Kyokai in Japan )

d5 /L ,=

0.027 (

Lloyd's Register of Shipping )

According to Fig. lOa, the critical fore draft for the bow emergence among the storm seas of 20 rn/sec. winds ( significant wave height is about 5.2 m.) can be estimated as followings

Ship speed ---

_4.4

kt

8.9

kt 13.3 kt

17.8

kt

d /L' --

0.0257

_0.0275

_{0.0291 0.0305}

Above results might be the acceptable ones.

Ref ere.nee

L.J.Tick : " Certain Probabilities Associated with Bow Submergence and Ship Slamming in Irregular Seas " JSR Vol. 2

(1958)

H.U. Roll " Dimensions of Seawaves as ntitmq of Wind Force Based upon Wave Observations by North Atlantic Weather Ships " ( English

Translation ) SNAME

₍₁₉₅₈₎

W.A. Swaan and H.Rijkin : ' 5peed Loss at Sea as a Function of longi-. tudina]. Weight Distribution " NECI of Eng. & Shipbuiders Trans.

Vol.

79 (1963)

J.J.Muntjewerf : " The Influence of Sktipform and Length on the be-haviour of Destroyer- type Ships in Head and Beam Seas " ISP Vol. 10

(1963)

a,b,c, d,e,g A,B,C, D,E,Q

Nomenclature

coefficients of miscellaneous terms of defferential e-quati3na of motion

d fore draft

Er cumulative energy density of waves

Ezr = cumulative energy density of relative displacement between ship and waves

F - heaving force

Fr. -

v/L

aoceleration of gravity

h - surface elevation of wave

- significant wave height

k

27t/A

L - ship length M - pitching moment

t = time

C

_{average wave period}

vertical velocity of ship

- relative vertical velocity between ship and wave surface

iJ - wind velocity V - ship speed

longitudinal distance from midship

longitud.nal distance from mideship to C.G.

z

vertical displacement of ship

Zr

-

relative vertical displacement between ship and wave surface

)

Th

a vertical accer?rati0fl of snip

(X a phaae angle of heaving motion - phase angle of pitching motion

phase angle of vertical motion

- phase angle of relative vertical motion a phase angle of vertical velocity

rr

= phase angle of relative vertical velocity

SQr

-

phase angle of vertical acceleration

heaving displacement pitching angle

Table 1 Particulars of the Bulk Carrier

Length between parpendiculars ( L ) Breadth ( B )

Deapth ( D )

Block coefficient in full load ( Cb ) Droughts in ballast conditions :

213.0

m

30.5

m

17.0

m

0 81

Cond.

I

Cond. ii: Cond. _1ff

-!0-Fore drought ( d ₎

3.47

in

5.70

in

7.93

in

Aft drought ( d )

7.93

in

7.93

in

7.93

in

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