Midship bending moment of a destroyer in irregular seas

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THE. FACULTY OF ENGINEERING, KYUSHU UNIVERSITY HAKOZAK1, FUKUOKA, JAPAN

MIDSHIP BENDING MOMENT OF A DESTROYER IN IRREGULAR SEAS ( ABSTRACT ) BY JUN-ICHI FUKUDA JITSU SHIBATA HISAO TOYOTA PRESENTED TO

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MIDSHIP BENDING MOMENT OF A DESTROYER

IN IRREGULAR SEAS (ABSTRACT).*

JUN-ICHI FUKUDA**

JITSU SHIBATA*** HISAO TOYOPA***

1. Summary

In this paper, the authors _{tried the theoretical evaluation}

of

heave, pitch and midship bending moment of a destroyer in oblique _head

0

waves by means o _{strip theory, and estimated} _{the statistical values}

of them in irregular head seas by the method of St. Denis and Pierson'.

The derived statistical values _{were compared with those calculated}

ap-proximately in long-crested _{irregular head waves.}

The calculations were carried out on a destroyer whose _main

par-ticulars are presented in Table 1.

2. Heave, Pitch and Midship _{Bending Momen,t}

in Oblique waves

Consider the case when a ship goes forwards with a constant _speed

V among regular oblique waves with heaving and pitching _{motions as}

shown in Fig. 1. Assume that

the breadth of ship is small as compared

with the ship length and wave length, and ignore the drift, _{yaw, sway,}

surge and roL. of ship. _{Then, the surface elevation of wave encountered}

* The detail O.f the paper is reported in _{the Jourual of the Society} of

Naval Architects of Japan, _{Vol. 114}

₍₁₉₆₃₎

_{p. 78}

₈₇

** Kyushu University, Fukuoka

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with the ship can be expressed as

where,

27r/A'

Z7(/(A/cos)

=

_iecosL

w,=

w+le*V

w

(:acceleration of gravity )

A:

wave length

angle between ship course and wave direction

t : time

x : co-ordinate fixed tO midship

hoP: amplitude of 8urface wave

With the aid of stripwise theory., the equations of heaving and

pitching motions are expressed as followings, approximately,

= F

,

tb+ E

+

=

M

By solving the equations (2), the heaving motion () and the

pitëhing motion ( ) are obtained in the form of

=?cow2t

Sfl

Wet

0cos(cit*X5)

A=ocos(,*z+cvt)

₍₁₎

c

_cosw.t

_-

_{sct wet}

COS (Wet +

The thidship bending moment

(7)

is obtained by the calculation using the solutions (), in the form of

=

cc0SWetZs nwt

Z0cos(wt+J')

The calculated results of

; ç and ?IZO in the cases of

300 _and 600 _{are presented in Fig. 2,}

3 and 4 in the non-demensional

ex-pressions as followings

(4)

where,

p

density of sea water

L : ship length

B*: ship breadth

In the figures, the mark of ( / ) indicates the synchronism Of

3.

Heave, Pitch and Midship Bending Moment

in. Irregular Seas

The statistical values of heave, pitch and midship bending moment

in the irregular head seas represented with Neumann's wave spectrum can be estimated by means of St. Denis and Pierson's method1.

The formula of Neumann's wave spectrum is

-2I

2 Z

[r(w,Z)]

=

E:

-21

fVW

cos2Z

=0

₂ Where,

Coa

3.05n12/secS,

V: wind velocity (m/sec)

: angle between wind direction and component wave

direction (Fig. 1)

Then, the energy spectrum of heave, pitch or midship bending moment is obtained generally in the form of

- Z - 2

[ S(w,Z)J = {rcw)J

IR(w,Y')Jcos

2'

(7)

=co/

0

0/f&0, /ii =

(_)

heaving

(A

1)

or that of pitching

(A

I

(5)

where,

=

9

: angle between wind direction and ship course

is the response amplitude operator of heave, pitch Or

midship bending moment, and can be deduced from

(5)

respectively as

followings,

=

I

[R,(w,k)]

I)

The cumulative, energy density of heave, pitch _{or midship bending}

moment is obtained generally as following,

Jf'7r(w)JZfw,yr)J2cos2zvx

.

(9).

w0 -lr/z

where, ct)0 is determined by the fetch and the duration'.

Under the a8sumption that the short-term distributions of the heave,

pitch or midship bending moment may be represented by the _Rayleigh

dis-tribution, the statistical values of those can be obtained according to

the following formula by LonguetHiggin),

= K(,/) V E

(k'(,, = /.4L2

, .

i. 8o )

(10)

where, A(,/) represents the average of heighest (100/n) _{percent values of} amplitude.

The averages of heighest 10 per cent values of heave, pitch _and

midship bending moment in the irregular head seas (the _{case of} ₉

00)

were calculated. The ca8ea in the fully developed _{seas corresponding to}

10, '15

_{and 20 rn/ste. wind and that in the not-fully developed seas}

(6)

were considered. The spectrum of waves for those seas are shown in

Fig. 5.

Several examples of the calculated results of

[r(W)j

{R(w,/'-)J

_in

are presented in Flg. 6 --- 8.

The averages of highest 10 percent values of heave, pitch and

midship bending moment are shown in Fig ₉ and 10.

The midship bending moment calculated by the conventional method

without Smith'seffects and that calculated with _{Smith's effects are shown} in Fig. 10. _{The each of them is nearly equal to the average of higheèt}

10 percent values in the not-fully developed seas corresponding to

25 rn/sec. wind with 40 hours duration or that in the fully developed seas corresponding to 20 rn/sec. winds.

Now, the cumulative energy density of heave, pitch or midship

bending moment in the long-crested irregular head waves whose energy

7t 2

spectrum is given by

_-b-

[.rii;J

_{is obtained by the following,}

(9)

Then,

is calculated and shOwn in Fig. 11.

In the case of heave,

K'> /

_{and in the. case of pitch or midship}

bending moment,

K, < /

_{(except the range of lol wlhd velocity)} _or

< I

. Therefore, the statistical values calculated in the

long-crested irregular waves are lower-estimated in the _{case of heave, and}

over-estimated in the case of pitch or midship bending _{moment, as}

corn-pared with those caluculated in the short-crested _{irregular waves.} _But,

(7)

References

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

Con-fused Seas" TSNAME o1. 61 (1963)

G.Neurnann : "On Ocean Wave Spectra and a New Method _{of Forecasting}

Wind-Generated Sea" Technical Memorandum NO.

_43,

Beach rosion Board

W.J.Pierson, Jr., G.Neumann and R.W.Jamee : "Practical Methods for

Observing and Forecasting Ocean Waves by Means of Wave Spectra and

Statistics" U.S.Navy Hydrographj. Office

_('955)

4) M.S.Longuet-Hjggjns : "On the Statistical Distribution ofthe _Height

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Fig. 1 Co-ordinate I.0 '-5 0.5 is L ..s_ -I 4 Z 1.5 ,.Z5

Fig. .2 (a) Heave in Regular Oblique Waves (i1=O°)

1.0

I-05 '.0 Os .1 1.0 4 2 -,ji.zS * -60)

/,/7.\

,-->--' ,'..'

-'-.

0.4

7

P. 0.2 0.3

---:

0.4 0.3

1/ Áç!)

'.3 -i.e L/.' 0S 06 0.5 A7L C - 30)

-.

0.4 0.5 (1 tA..!)

FIg. 2 ('b) Heave in Regular Oblique Waves (0=-3C)

05

(I :4_l)

1.3 us -, 075 aa o.j )7i.

Fig. 2 (c) _{Heave in Regular Oblique Waves (çb=6')} Table 1. Main !articulars of Ship

Length bet. pp. (L) 115.Om

Breadth (B) 12.Om Draft (d0) - 4.Om DiBplt. (W) 2,890 Block coefft. (C6) - 0.511 L/B 9.58 L/d0 28. 8 B'/d0 3.0

R&d. of gyration in air 0.242 L

Na2ural l'leaving Period 4.62,ec.

Natural Pitching Period 4.42aec.

(9)

0 0

00 4 2 Li #23 I 0. 4 0) X7&

Fig., 3 (a) Pitch in Regular Obliqu Waves (=O0)

a

00

j.lh3

J _a4,

I,

to

Fig. 3(b) Pitch in Regular Oblique Waves (.3)

.40

0

Fig. 4 (a) Midshi B. M. in Regular Oblique Waves (0=00)

0 .0. 0.01 00 ₂ _1.5,25 _I 20 /A 2 I.3 l.3 I 0.75 0 as AL.

Pig. 4 (b) _{. Midship B.,M. in Regular Oblique Waves (0=30°)}

/

_\

8

Z 0

20 h./A

Fig. 3 (c) Itcb in Regular Oblique Waves (0W) _{'ig. 4 (c)} _{Midship B. M. in Regular Oblique Waves}

(0=60°)

(0)

-0.3

---:

0.4 3

(I: n

0.3 / ,

-.

-F,.oZ

- -

. 0

(3e°

--03 0.4 0.3

(1:

-,)

---.:

- S.. -':0 i: 0 -C!' -301 05 ,' 0.4 Fr.-0Z

/

-

-S..."

---.

I

_\

-,

(f'.VJ

--43 os

- : F,-oZ

0.3 0.4 0.5 "73 0 AT. 00 4 2 ,.3 .1.25 073 -1. 1.0 43 0.0 0.0 00 0 0. 0 . 02 . 0$

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0I Fig. 6 (a) 0.02-1. 0.0 -30 60 -

/ AF

F.- -e5 c3264e) (0.3) F.. 0.3 ,q 64C) 0.6 -. l..C, 1.0

Spectrum of Heave (v=2Om/sec)

\;.-I.'-'

\

S

r

.

04 0.6

0.8 - c

/ 2

Fig. 7 (a) Spectrum of Pitch (v=2O m/Iec)

G 0.2 0.4 06 08 (.0

i(/1.6

30.0 700 100

30

-Fig. 5 Numann's Spectrum of Waves

Fig. 6 (b) Spectrum of Heave (v=25mfsec)

(V.. - 75

-:f-o

30

I :A-?

'03): F.. 0.5 (32.640) (a,): F-aJ st4t '(0-:.!_j., '-.' a4 06 w(S) 10 30 / : (0.5) F.-. -0.5 1,32.6401 (0.i; F.- -0.3 l,,.640( 0 ₀₄ _. ₀

Fig. 7 (b) Spectrum of Pitch(v=25m/sec)

0.03,- (tfr_.- Z0,...) 3o 60 / A6- I (oil : F,. -0.5 132.64t) (03? F--aS ci.66t) (17 -75 f5)

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04 - wc.)

'.0

Fig 8 (a) Spectrum o Midship B M (v=2Om/sec) Fig 8 (b) Spectrum of Midship B M

(v=25m/sec) 04 - 0.6 0.6 WCC) 5 /0 15 Fig. 11 K', K', and K' 20 25 30 "V (..M6') (Va. -204) 3 0 6 0 / A,- / (0.3) P,.0.3 (32.643) (03) Fr. 0.3 iif.642) 3 I. 100 50 If' ..' I ioo Lv' -25 * - 0' 30' 6 0 / (o5).C,.- O.5(32.64tJ (03) 10 IS

--- 14

Fig. 10 Midship BM in Irregular Seas =O

S S

i0

(90(

P,.-0.2 C1JI.) 0.3 (./q.6 ) 04(26.'') 0.5 (32.6

---:

'7

(,0')

_(I3./)

0.3 ((Q6 3 0.4 (26.1 0.3 (32.6 - : F,.-0.2

:7/tI

.5 IC I. 20 2$

- 1,_

Fig. 9 Heave and Pitch in Irregular Seas(O=0°)

'S 1 10 1 .5 V. /5 4 K IC