On the longitudinal strength of a supertanker in regular head waves

:THE FACULTY OF ENGINEERING, KYUSHU UNIVERSITY KAKOZAKI, FUKUOKA, JAPAN

ON THE LONGITUDINAL STRENGTH OF A SUPERTANKER IN REGULAR READ WAVES

BY JUN-ICHI FUXUDA JITSU SHIB4TA HISAO TOYOTA PRESENTED TO

ON THE LONGITUDINAL STRENGTH OF A SUPERTANKER IN REGULAR HEAD WAVkS (ABSTRACT)'

JUN-ICHI YtYKUDA" JITSU SHIBATA**' HISAO TOYOTA"!

1. Summary

The authors present the results of _{theoretical evaluations of the} heaving and pitching motions, shearing forces and bending mominte acting on ship hull of a supertanker in regular head _waves.

The numerical calculations _{were performed on the both of full, load} and ballast condition. _{The derived results of ship motions,}

midship

bending moments, longitudinal distribution of shearing forces and bending moments, etc. and the differences of them in the both conditions were investigated. _{Further, the midship bending moments among irregular head}

seas were treated by the simple statistical method.

2. Method of Theoretical Calculations

When the ship goes forward with the constand speed among regular head waves whose surface, elevation _{is expressed by}

(I)

the equations of heaving and pitching motions are given with the aid of

* The detail of the _{paper is reported in the Journal of the Society} of Naval Architects of West Japan, Vol.

_{26 (1963)}

** Kyushu University, Fukuoka ***Mjt8ubjshj Shipyard, Nagasaki

stripwise method as followings,

cd'

=

F

A4

c'1, + +

E

_+Q.

= fyi

where, P and M are given in the form of

F

₌

F;. cosw,t F,sc.* co,t

_F

CQS (Wti- D(,)

M=McCOSWQttV1sSiiflWetMoCOS(Wet+M)

The solutions of the equations of motions (2) are obtained in the form of

= cC0Wt S1WQt

0cós(wet+O()

₎

(açL)

4) 4coswt

4)sc,zw.t

_0cos(w2tfl.)

_J

Then, the shearing force and the bending moment at the position of Z, are obtained by the calculations using the solutions (4)of the equations of motions (2), in the form of

(S)

= ?12cc0Sw.t - WZsS&fl

Wet

m0coS(w1t

s').

The detail of the calculating method is mentioned in _{the papers by} the one of authors1'2 .

The nomenclatures and the co-ordinates are indicated in Table 1 and Fig. 1,

The numerical calculations were applied to the supertanker whose main particulars were shown in Table 2 and _3.

3. Ship Motions

3. 1 Coefficients of miscellaneous terms of equations of' _motions

The coefficients of miscellaneous terms of equations _{of motions (2)}

are calculated by the stripwise method and shown in Fig. 2 -

_5.

In Fig. 6 and 7, the miscellaneous integrated values of

ps (additional.

mass for section) and W (damping coefficient for section) of the fore and aft

body are shown. V

3.

2 Eiting forces and moments

The heaving forces and the pitching moments (3) are calculated by the stripwise method and shown in Fig. 8 and

_9.

In the figures, double prime () or triple prime (I") indicates the Froude-Kriloff's eiting forces and moments

with

Smith's effects or Without. (Fig. 10 is omitt-ed)

3. 3 Heaving and pitching motions

By solving the equations of motions (2), the heave and pitch are obtained in the fo;m of (4). The obtained results are presented in Fig. 11 and 12. . In the figures, the synchronism of the heave or pitch

is indicated by

(fl

_{= / )} or

(A = I)

(Fig. 13 and 14 are omitted) 4. Shearing Forces and Bending Moments

The shearing forces and the bending moments at the positions di-viding the ship length into eight equal Intervals are obtained in the form of

(5) by

the calculation using the solutions (4).

4. 1

Shearing

forces and bending moments at mid8hip

The calculated results of the shearing forces and the bending

moments at the midship are, presented in Pig. 15 - _{17. In the figures,}

the synchronism of pitch or heave is indicated by (/j _{= / )} or

(A1

I)

. In Fig. 16, the statically calculated midship bending moments based on Froude-Kriloff's hypothe8is are also shown, there

double prime (1) denotes the case with Smith's effects and tripple prime

(") without. .

4. 2 Longitudinal distributions of shearing forces and bending moments

[3

The longitudinal distributions. of the Shearing forces and. the bending moments derived from the calculated results at the positions dividing the. ship length into eight equal intervals are prestented in Fig. 18 and 19.

4. 3

Midship bending moments in irregular head seas

The statistical midship bending moments in irregular head waves (long-crested waves) are obtained by means of St. Denis and Pierson's inethod3 utilizing the pesponse amplitude operator of midship bending moment

_('/fl0/,(0)

and Neumann's wave spectruin".

The statistical estimations were tried in the fully develope4 seas corresponding to 10, 15 and 20 rn/sec. winds andthe not-fully developed seas corresponding to 25 rn/sec. Winds with 40 hours duration.

In Fig. 20, the. wave spectrum

[r(w)JZ

in the formula of (Energy Spectrum of Waves)

ZL.

C0

Zj/iw

_w

2

where, C

_3.05

(m2/sec')

: acceleration (in/secZ)

-j: wind velocity (rn/eec)

are shown.

In Fig. 21,

several examples of the energy spectrum of midship

be4ing moment

[r(w)]2[20/4,]

are illustrated.

The cumulative energy denSity of midship 'bending moment is obtained by

z

(6)

Then, the averageof highest 10 percent values of midship bending moment is obtained from the following formula by Longuet-Higgins',

1lZoc///o)

=

K(,/,0)

Y

(

=

1.

O ).

The calculated values of are presented in Fig. 22, and compared with the conventionally calculated midship bending moment with or without Smith effects.

5.

Diacuasion and Conclusion

The differences of weight distribution and underwater hull-form between the full load and the ballast condition are consid.erablly re-markable, and much differences on the ship motions, shearing force and bending momenta acting on ship hull yield in regular head waves;

The heaving and pitching motions are severer in the full load conditions than in the ballast conditions. _{The differeuces of heaving} motions in the both conditions are remarkable, especially at high _speed, but those of pitching motiona are not so much.

The midship bending moments in the ballast condition are somewhat larger than those in the full load condition.

-The maximum bending moments occur at the positions near the midship. _{These positions shift forwards in higher speed, and this}

tendency is remarkable in the case of full load condition, and not so in that of ballast.

The maximum shearing forces occurs at the positions nearly (L/4) distant from the midship. _{These positions shift forwards in}

higher speed. This tendency

i8

_{remarkable in the case of full load} con-dition and not so in that of ballast. -

-According to the estimation in irregular seas;

The averages of highest 10 percent values of the midship bending moments estimated in long-crested irregular head waves are somewhat larger in the case of ballast condition than _{in that of full} load.

calcu-lation with Smith'seffects is nearly equal to the average of highest 10 percent values estimated in the not-fully developed seas corresponding

25

in/sec. winds with 40 hours duration, in the both conditions of full load and ballast.

References

J.Fukuka : _{"On the Longitudinal Bending Moments of a Ship in Regular} Waves" JSNA of Japan No. 110

₍₁₉₆₁₎

JFukuka z "On the Longitudinal Bending Moments of a Ship in Regular

Waves (Continued)" JSNA of Japan No. 111

₍₁₉₆₂₎

M.St.Denis and W.J.Pierson Jr. : "On the Motions of Ships in

Con-fused Seas" TSNANE Vol.

_{61 (1953)}

G.Neumann : "On Ocean Wave Sp.ectra and a New Method of Forecasting

Wind-generated Sea" Technical Memorandum No. _{43 Beach Erosion Board} ) M.S.Longuet-Higgjns * "On the Statistical Distribution of the Height

of Sea Waves" Journal of Marine Reserch Vo. 11 No.

_{3 (1952)}

Coefficient of Miscellaneous Terms of Differential Equations of Motion

Ap

Amplitude and Phase Angle of Heaving Force Pitching Moment Heaving Motion Pitching Motion Shearing Force Bending Moment Ship Speed Wave Length

Circular Frequency of Encounter

*( IDI)'

+Z.V

PIg.I

Table I Nomenclature Symbol a, b, C d,

e, g

A, H, C D, E, G

2343671

LH

'p

p density of water, j : acc. of gravity, k =2r/)b, .4.,: amplitude of wave elevation Non- Dimmensjonal

af--, b/L, C/pELB

d/-, ciLt, g/pjL2B

A/-, B/4, C/pjL3B*

D/, E/!f4. G/pjL2B*

7

F,, 1,4, a $M Fo.=Fo/pjLB*ho, a Mo.A4/-}pIL2B*ko, j, C,, ac C,/k,, ac 0,.

s.

= 0,/hA,, $ F,, m,.

i

8 F, _{F,/pILB'ho, I} , = m,/pjL2B'h,,, .8 V

_Fr.=V/V1E

x/L w,Lf2j

Table 2 Máin Particulan

(Full Load) _(Ballast)

Length bet. p.p. (L) _{213. 00j} 213.00m Breadth (B) _{30. SOsu} 30. 50 Draft (d0) _{ii. 13} 5.70 L/B* 6.98 _6.98 L/d0 _19.14 37.18 B/d0 _2.73 5.35 Dsiplt. (W) _{58,882 S} , 1M( Block coefft. _0.796 0.742 W.P.A coef ft. _0.858 0.817 C. B. from _{3. 72a(fore)} -S. O3,.(aft) C. F. from _{-0. 49ai(aft)} 2. 59m(fore)

Rad. of gyration in air _{0. 240L}

0. 269L

Natural heaving period _{(Ti) 8. 78w.}

7. fls..

Natural pictching period (Te) _{8. 06.}

_{7. 18.}

Trim by stern _{0 m}

4. 46

Table 3 Main P8rticulars of Fore and Aft Body

(Full Load)

(Total) (Fore) (Aft)

Weight _{W 0.516W} 0.48.4W C.G. from Il _{0.017L 0.210L -0.195L} Buoyancy _{0. 525} 0. 475A C.B. from _{O.017L 0.214L} -0.199L

Water plane area

Centre of w. p. a. from gi _{-0. 002L}

O.499A 0. 217L

O.5o1A,

-0. 221L

Midship B. M. in still water _{-i, 600-m (sag. )}

(Ballast) Weight _{W 0.448W} 0.552W C. G. from _{-0. 024L 0. 3L} -0. 207L Buoyancy _£ 0. 452& 0. 548A C. B. from g _{-0. o24L 0. 194L} -0. 203L Water plane area

41., 0. 516A,,, 0. 484A,,

Centre of w. p. a. from fl _{-0. 012L 0. 215L}

-0. 204L

0. 1 4.-(aI4OLJ'L FiJL Leo.. -8.P.&IZC..14

I

(Fuji t4)

3.0 2.0 I.e .04 as

lb

-0.3 -0.s0

(Fuji L.)

200

-- Fr.

Pig. 4. 8Jt C1,11.) Pig. 4b I 00 ,JL 0.60 _0.75 .VL. - _{. o,} 0.20 2.041.5o 75 1.25 1.00 460 0.05 0.10 415 020

- Fr.

.056 .053 .054 -1.25 0 .5 _{w.'L/Z, /0}

P1,2

'S a zo 0.03 0.10 _ais

PIg. 5.

(8a.fti.a. C.S.) G/,fL8f (.7b)/FL'B 0.60 7$ 0.75 1.00 125 -.--

__=LcLLi

"(00 LZS .02 S 1.0 0.5 .03 I I .0 0 0.0.5 0.10 0,15 0.20

- Fr.

Fig. 5b

F4xj/w,_

\

\\

-jSXdXJ/W,L S

- wILft

Fig. 6s S .047 .046 0? (5

4

.0.1 2.o 00 5

-

f0 Pig. Ta Q2 w 0 0 5

./0

/50 - wi1L/2 Fig. Th

l0

£ ANGLE

:Fr-O

----:Fr.fo

0.10

/

,-.-0.15

,/ ,/

0.3 0.2 0.1 ° PHA iao a, -?0 -ieo_as -F.O

1.5 VL zb

Fig. 8$ HEAVING FORCE(&u

---:Fr.-0.io

0.15 0.20 #MA5E ANGL

/

.4)

-,

-, ---,

, /

-,,

-#--90 PITCHING MOMENT (8dt)

---:Fr-o.io

Ods 0.3 0.2 0.1 0 360 PHASE_ANGLE. 0.3 0.2 0.1 0 PHASE ANGLE fla. !805 A:

:Fr.-o ---:r,.010

I0 Fig. 9a 0.70 0.15 0.20 1.5 k/L 2.0

FIggb

F; 0.3 ,,(

/,

_/

:

I,

HEAWYNG FORCE (FuJI L..tS) _{PITCHING MOMENT r..0 L.u.)}

OS ₁₀

15 Al zo

o-PHASE ANGLE 18 HEAVING MOTION (FkLLL...

- :Pr-O

Fi-. -0.10 0.15 0.20 '.5 1.0 0.5 OS 1.0 Fig. 11* '.5 1.0 0.5 0 PHASE ANGLE

0

90 1805 1.5 2.0 F. -0.!3 azo

.L.-.__----

a-/0 /5 zo Fig. lib PITCHING MOTION (F1J1 L.4) -- OS PHASE ANGLE /0 _{/5 --VL 2.0} Fig. 12&

Ifi

l.0 as 0

4 -,

PHASE ANGLE Fig. 12b :F-.O.,O 0.13 0.20 .AIL 2.0

/2

IUr.L

:iaiu -.

-.. :Fr. -0 0 Fe.. -0.10 0.15 0.20

.06 O 4 O 2 0 -180 PHASES ANGLE

t.

06 .04 .02 0 a-o : 0° -0.5 - Fr.=O --- : Fr.- 0.10 0-li 0.20

4L

1.0 Fig. 15b 1.5 AlL 2.0 SHEARING FORCE c$ BENDING MOMENT AT X 100 fFwJiL :8da.o 06 .04 .02 0 / ao Li . --18(1 FM; .03 .0 2 .01 0 0 : At-I PHASE ANGLE. 0.1 02 Fr 03 Fig. 11 F,-. -0

----:F,..=O.tO

-.--:

0.15 0.20

BENDING MOMENT AT . (Ba.Lta4t)

.03 .02 0 I 0 o5 PHASE ANGLE Fig. 161' 1.5 A/L 10 ----.: Fr. = 0.10 )'/L 2.0

/3

-_i

/ - 1 'N 'I

,,'-: ':7

A_

\,

SHEARING FORCE AT . (FuJIL..4) BENDING MOMENT AT . (F1Ji L.o4).

05 1.0 15 -A/L 20

Fig.15a

SHEARING FORCE AT M (BaZet)

F 80 PHASE ANGLE,

o;A#J

:.Cr. 0.10 0,15 0.20

----:

0.f5 0.20

o :A-!

270°-I 80° 90--?0 _-0.08 AP r 0.02 150' 90°

\.

0.07 90° o 0' -90°- - 90'-Fig. 18a 270° I 80 90°

r

0 iiSTRiBuT/ON OF S.F. 4 aM. A/L-O.75 (FJt L'u.4)

_-_

₁₀₀ (Fr: 0 1 /25 DISTRIBUTION OF S.F. B.M. AlL = 075 90' (FaL Lo4 I (Fr. 0.10) Fig. 1 0.08 270' 0.04 -0.0S 1.00 1.25 1 0.08 270°-DISTRIBUTION OF S.F. B.M. :A/L - a 75 ,: 1.00 -90 AP I 90 (FizL2 L..S) (Fr. = 0.15) Fig. 18c DISTRIBUTION OF S.F. B.M.

---:

/00

----:

1.25 o.o8 (FdL L-4) (Fr.=0.20) Fig. 18d 1.25 0.08 0.04 -0.04 0.04 - oo4 -0.08 0.02 AP F?

DISTRIBUTION OFS.F. B.M. AJL-075 (BaiL...

---:

jo (F,-. = 0.15 ) 1.25 DISTRIBUTION OF S.F. 4' B.M. (8.1t C#n4 .AJL = 0:75 Fig.19a Fig. 19b 0/STRIBUT/oN OF S.F. 4' B.M.

--tA/L=O.75

----:

1.00 (BdU.4t C.4t,) (Fr.= 0.20) Fig.19e

/5

(Fr.= 0.10) 1.00 1.25

100

Fig. 20

Fig. 21*

400

MIDSHIP B.M. IN IRREGULAR SEA (FU L.4) F-.-oI0 C 0.13 (:3.3 300- ---': .0.20 (I1. C,--*A..-Ld -'-'-. S. E / I

-

I v.-zs..,

/

' 3 _I I 0 .

AI

0.2 04 Fig. 21b

a'

Fig. .5 /0 /5

- v._

MIDSHIP 8.M. IN IRREGULAR SEA

/6

$ g.

SPECTRUM OF Fr. 0 I 5 _{SPECTRUM OF}

_/

_Fr.0.2O

MIDSHIP if M. (13,3 4. _{MIDSHIP B.U.}

I' (17.045) zoo . .5M, 6S -/0 '5 20 23

V,. (')

Fig. fla 20 25