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rRCHIEF

INTERNATIONAL SYMPOSIUM

ON

"SHIP HYDRODYNAMICS

AND

ENERGY SAVING"

(MADRID, SEPTEMBER 1983)

Lab. v. Scheepsbouwkund

Technsche Hogeschool

Dell!

SPEED LOSS OF A CONTAINER SHIP ON THE DIFFERENT

ROUTES IN THE NORTH PACIFIC OCEAN

IN WINTER

BY

J, FUKUDA AND A, SHINKAI

(2)

SPEED LOSS OF A CONTAINER SHIP ON THE DIFFERENT

ROUTES IN THE NORTH PACIFIC OCEAN IN WINTER

BY

J. FUKUDA AND A. SHINKAI

ABSTRACT

Speed loss of a container ship i-n

rough seas is estimated theoretically based upon the statistical method by taking into consideration the criteria of heavy ship responses such as deck

wetness, slairuning, rolling, vertical and

transverse accelerations.

The results of these analysises are utilized into the statistical prediction of cruising hours of the ship on the

C.i±ferent routes between Tokyo and San Francisco, includinq the northern cireat

circle route and the southern route

al.ong the same latitude line., n tffë

North Pacific Ocean in winter.

According to the prediction results in winter, the west bound voyage from San Francisco to Tokyo should be made on

the southern route and the east bound voyage from Tokyo to Sari Francisco would be admitted sometimes on the northern

great circle route but should be mostly made on the southern route.

1. INTRODUCTION

When a ship navigates in a moderate

seaway, the speed will be- more or less

decreased by the added resistance due to waves and winds. In a rough seaway, the speed will be, more decreased and further-more the ship will be suffered from the heavy responses such as deck wetness, slamming, rolling, vertical and trans-vers accelerations. Therefore the ship has to 'sometimes slow down the speed in order to keep away from the critical situation due to such heavy responses. And, in a extremely heavy seaway, the ship would be obliged to slow down much more or to change the heading angle against the waves.

It is well known that the heavy re-sponses such as bow deck wetness', bow bottom slamming and vertical bow

acceler-ation are found in head seas and in bow

seas,

and

the severe rolling and trans-verse bow acceleration are found in

fol-

-1-lowing seas, quartering seas and in beam seas, and that those heavy responses are usually controlled by slowing down the ship speed and occasionally by changing the heading angle against the waves.

Ac-cordingly, speed loss of the ship in rough seas would be much more dependent on the severity of such-responses than on the added resistance due to waves and

winds.

-From such a vIewpoint, in this

pa-per, speed loss of a fast container ship an the different routes between Tokyo and San Francisco in winter is

investi-gated theoretically. byutilizinq the,,.

wave statistics in the North Pacific Ocean. Expected speed and cruising hours

Thbh of the east bound voyage and the

west bound voyage are estimated statis-tically on the northern great circle route and on the southern route. Obtain-ed results are comparObtain-ed and discussObtain-ed.

2. SHIP SPEED IN SHORT-TERM SEAWAYS In order to estimate the critical speed for keeping away from the danger-ous situation due to the heavy responses such as-deck wetness, slamming, rolling, vertical and transverse accelerations, the short-term prediction works have been made for a fast container ship in

irregular sea waves from different di-rections. Method and procedure for the prediction works are outlined below.

Fig. 1 shows the relationship be-tween the ship course and the wave di-rection. Table 1 shows the main particu-lars of the container ship.

-The solutions of -ship motions- of. surge., heave, pitch, sway, yaw and roll

in regular waves from different direc-tions can be obtained by the aid of the advanced strip method (Ref. 1, 2). An

by using tnesoiutons of motions, the

response functions of

Z : relative vertical displacement

r

(3)

vr: relative vertical velocity b tween bow and wave surface

e : roiling angle

vertical bow acceleration transverse bow acceleration can be calculated.

A short-term seaway can be formu-lated by using ISSC wave spectrum (Rf.

3), as follows. [f(w)]2 (2/w)[f(w)]2cos2 : -ir/2 <X < ir/2

(1)

= 0 : elsewhere where [f(w)]2 = exp[-O.44(w/w)4] (2)

w : circular frequency of a compo-nent wave

= 21r/T, T : average wave period

H : &ierage wave height

x: angle between a component wave direction and the average wave direction

Then, the variance of a certain re-sponse s can be obtained by the aid of the linear superposition technique (Ref. 4), as follows.

HEADING ANGLE:

ö=1-tp-ir)

S

rig. 1

Ship course, wave direötion

and heading angle

2 2 R (s) = (2/ir)f f -1r/2 0 - 2 2 [f(u)] cos x dwdX () where

R2 (s) : variance of a certain

re-sponse s

response amplitude of s as a function of fre-quency and heading angle for a component wave

heading angle between the ship course and the average wave direction

According tO Eq. (3), the standard. deviations of various responses are ob-tamed and defined as follows.

R(Zr) : standard

R(v)

: standard

R(0) : tandard

:. standard R(ay) :. standard

The probability that a certain os-cillatory response s exceeds a constant

level s can be given as follows (Ref.

5). q(s>s1) = exp(-s, 2(e)] (4) deviation deviation deviation deviation deviation of Zr of v r of e of Of

Table 1

Maui partictllaE Of a container ship

Length between perpendiciflars (L)

175.000 H

Breadth. moulded (B) 25.400 M

Depth moulded (D) 15. 400 M

Draught mOulded (a0) 9.500 N

Displacement (W) 24,742 T

Block coefficient (Cb)

0 572

Midship coefficient (C5)

0.970

Water plane coefficient (C)

0.711

Centre of gravity abaft midship (G)

0.0142 L

Centre of gravity above water line (OG)

0.0021 d0

Metacentri height (GM)

0.1053 d0

Longitudinal gyradius (icL)

0.2400 L

Transverse gyradifs (KT)

0.3300 B

Heaving period (TH) 7.50 SED

Pitching period (Ta)

7.15 SEC

(4)

R(Zr) 10.8 0.6 0.4 0 2

10

-2

-4

-6

(Z)

N4SEc

= 135° -0.1

.0.2

03

-Fig. 2

Standard deviations of relative

verti.cal displacement between

bow and wave

(in bow seas)

qcsL)x102

(SL) = 2(H/L)21r1[q(SL))

0.1

0.2

03

-

Fr

4

Probthilities of occurrence of

bow bottom slananing (in bow seas)

I--- I

0.1 0.2

0.3

-

Fr

Fig. 6'

Standard deviations of vertical

bow acceleration

(in bow seas)

Fr

Fig. 3 Standard deviations of relative

vertical velocity between bow

and wave

(in bow seas)

R(e)

(8) = R(8)/(H/B)

10.4

0.3

0.2

0.1

Fig. 5 Standard deviations of rolling

angle

(in quartering seas)

4

3

00

= R(Vr)/H/7

0.1 0.1 0.2

03

-I I ---I- - -0.1 0.2

= R(a)/g(H/L)

03

Fr '4 6

a45°

I. 0.2

03

Fr

Fig. 7 Standard deviations of

trans-verse bow accelerations

(in quartering seas)

(5)

where

probability that a

oScil-latory response s exceeds a constant level

In, a seaway of larger wave height,

the standard deviation R(s) will be

q(s>s1)

6 = 135°

P. (Z.) =

or r = 3.639/H

": possible to navigate without speed loss x: impossible to navigate

Table 4 Critical ship speedfor rolling

(in quartering seas) 6 = 45°

R(0) =R (0)/(R/B) 2.982/H

': possible to navigate without speed loss x: impossible to navigate

larger and the peak value of s would occasionally exceeds a critical level.

However, in a seaway of lower wave height, the standard deviation R(s) will be rather small and the peak value of s would rarely exceeds a Oritical level.

By utilizing Eq. (4), the criteria

of various ship responses, such as deck

6 = 135°

cr1

= 2(H/L)2ln(q (Srn] = -3.007104H2

": possible to navigate without Speed loss

x:. impossible to navigate

Table 5 Critical ship speed for vertical

bow acceleration (in bow seas)

6 1350

= P.r

aH'W

= 37.67/H

°:

possible to navigate without speed loss

x: impossible to navigate H -P. (Z) cr r 4 6 , 8 10 - , 12 (SEC) 14 - -(M) - - (KT) 0.375 24.2 24.2 24.2 24.2 24.2 24.2 1.25 " " II 2.25 ft ° " " '. " 3.25 '. ft ft '. " " 4.25 " " " " " 5.25 l " " ' 6.25 0.582 ' ft ft " ' 7.25 0.502 " 5.4 11.3 8.25 0.441 " ' 0.4 5.0 14.1 " 9.25 0.393 ° x 1.4 8.5 21.8 10.25 0.355 " x x 4.2 13.7 11.25 0.324 " ' x x 1.6 8.4 12.25 0.297 ' x x x 5.2 13.25 0.275 x x x 2.6 14.25 0.255 " x x x 0.6 15.25 0.239 " x x x x x I I I I I H q (SL) cr -T: 4 - , 6 , 8 10 , 12 , (SEC) 14 (H) _ (K') 0.375 24.2 24.2 24.2 24.2 24.2 24.2 1. 25 " " II 2.25 ft ' 3.25 4.25 n II " ft ft " ft " ,, II 5. 25 ft ft " " 6.25

-0.0117

ft " 7.25 -0.0158 " 10.4 14.3 " " 8.25 -0.0205 3.3 7.8 16.1 ' 9.25 -0.0257 " x .3.0 10.4 20.6 10.25 -0.0316 " x x 6.0 14.2 11.25 -0.0381 " x x x 2.5 9.7 12.25 -0.0451 x x x x 6.0 13.25 -0.0528 x x x x 2.9 14.25 -0.0611 x x x x 0.5 15.25 -0.0699 x x x x x H R (8) or - 4 , 6 8 - , 10 12 . (SEC) 14 (H) (KT) 0.375 24.2 24.2 24.2 24.2 24.2 24.2 1.25 U ft II ft fl II 225 ft " U U 3.25 " II ft II U II 4.25 ' " ft O ft 5.25 ° " " " 6.25 ' ft ' " 7.25 " " ' 8.25 ft " -

'

" 9.25 1 II U ft 10.25 0.291 ft ft " " 11.25 0.265 ' ° ' 10.5 6.3 12.25 0.24-3 " 13.8 8.8 3.6 1.3 13.25 0.225 " " 12.6 7.1 1.4 x 14.25 0.209 " " 11.7 5.8 x x 15.25 0.196 ' " 10.7 4..6 x x -- I - I I I I H

R(a)

T: 4 6 8 I 10 I 12 --(SEC) 14 - (H) - - (KT) 0.375 24.2 24.2 24.2 24..2 24.2 24.2 1.25 " ' ' ft I ft 2.25 " 1 II II ft ft 3.25 " " " ft 4.25 " " " ' 5.25 7.18 " " ° ft II 6.25 6.03 15.0 16.3 .23..3 " 7.25 5.20 " " 9.8 11.1 16.7 " 8.25 4.57 ' " 6.8 8.1 12.9 19.3 9.25 4.07 " " 4.4 5.8 10.1 15.4 10.25 3.68 I 3.0 4.2 8.1 12.5 11.25 3.35 " ° 1.8 2.8 6.4 10.5 12.25 3.08 °

3.7

0.8 2.0 5.0 8.7 13.25 2.84 I 1.9 x 1.0 3.8 7.1 14.25 2.64 1.4 x 0.4 3.0 6.0 15.25 2.47 x x x 2.0 4.6 Table 2 Critical ship speed for bow Table 3 Critical ship speed for bow

(6)

'V

wetness, slamming, rolling, vertical and transverse accelerations, will be

deter-in.thed as follows (Ref. 6, 7). (a) Deck Wetness

Probability of occurrence of bow deck wetness is given by

q(DW) =

= exp[-f/2R2(Z)J

where

q(DW) :. probability of occurrence of

bow deck wetness effective bow freeboard

criterion of bow deck wetness is determined for safety side as follows.

R(Z) = R(Z)/H < R(Z)

(6)

crr

= R(Z)/H

= CL/H)

iA2in[q0(DW)] (7)

where

q0(DW) : critical probability level fOr occurrence of bow deck wetness

By assuming

1/50 (Ref. 8)

Table 6 CritiCal ship speed for transverse

bow acceleration (in quartering seas) 6 = 450

Rcr(Uy) = R.(u)/g(H/L) = 28.25/H

"! possible to navigate without speed loss g impossible to navigate

and substituting

= 0.0582

e lO.18M) into Eq. (7), it results in

3.639/H (b) Slamming

Probability of occurrence of bow bottom slamming is given by

q(SL) 5 jointed probability of

q(Z>df) and q(v>v0)

e*p[_d/2R2(Zr) 2 2 Vcr/2R

Cv)]

whéré q(SL) : probability of occurrence of bow bottom slamming

df. boW draught

v r: threshold relative velocity be-C

tween bow bottOm and wave sur-face

Criterion of bOw bottoñ slamming is detetmined for safety side as follows.

(10). (SL) = 2(H/L)2ln[q(SL)] = _(df/L)/[R(Zr)/H1 cr''

2/[R(V)/Hv'7]2

(11) cr(S = 2(H/L)2ln[q(SL)] (12) where

g r(SL) critiOai probability level

c

for occurrence of bow bot-tom slamming By assuming Vcr/i = 0.09 = 1/100 and substituting df/L 0.0543 into Eq. (12), it

-3.007x.1O4xH2

(13) Cc) Rolling

Probability that rolling angle

ex-Oeeds a. certain level e is given y

q(8) exp[-02/2R2(e)] (14) H

R()

-6 8 10 12 (SEC) 14 (H) . . 0.375 24.2 24.2 24.2 24.2 24.2: 24.2 125 II ft U u ft ft 225 " 1 3.25 425 " ft .. ft ft ft ft ft 5.25 " 1 625 ' " ft ft " 7.25 " ft I. U 8.25 ft " ft " ft 9.25 ft " ' " ' 10.25 ft " " " U ft 11 25 2.511 ' ft. I, ft 12 25 2 306 ' 11 5 13 25 2.132 " 13 9 7 6 42 " 14 25 1982 " " 11.5 5.0 x ' 15-25- -.--- 1.852 " ' 8.7 3 2 x x ..- I - I I --I-- I (Ref. 9) (Ref. 8) (df = 9.5M) results in

(7)

where

q(0)

:

probability that rolling angle

exceeds a certain levelO

Criterion of rolling is determined

for safety side as follows.

(0) = R(8)/(H/B) <

cr

(0)

R(8)/(H/B)

Table 7

Critical Ship speed for all

responses

(in head seas)

6 = 1800

(15)

": possible to navigate without speed loss

x

impossible to navigate

Table 9

Critical ship speed for all

responses

(iS beam seas)

90'

": possible to navigate withOut speed loss

x: impossible to navigate

where

critical level of rolling angle

q

cr

(8)

: critical probability of ex

ceeding for the rolling

angle

By assuming

= (B/H)

Ocr

v 2 115 (0)1

Table 8

critical ship speed for all

responses

(in bow seas)

6 = 1350

": possible to navigate without Speed loss

x: impossible tO navigate

Table 10

Critical Ship speed fo

all

responses (in quartering seas)

": possible to navigate withOut speed loss

x: impossible to navigate

(16)

H 4 6 8 10 12 14 (N) (KT) 0.375 24.2

24.2

24.2

2.2 24.2

24.2 1.25 2. 25 ' " " ° ° ft I, II 3.25 ° " " " 4.25 " " 0 j 0 5.25 " " 23.5 6.25 " 14.2

10.7

21.1

7.25

?.4

4.4

11.3

23.7

8.25 " x

0.7

6.0 155

9.25 ° x x

28 10.2

10.25 x

x

x

6.0

11.25 " " x x x 3.0 12.25 x x x x

0.6

13.25 " x x x x x 14.25 ° x x x x x 15.25 " x x x x x I I -I--

--I

--H 4 6 8 10 12 (SEC) 14 (M) - (KT) 0.375 24.2 24.2 24.2 24.2 24.2 24.2 1.25 " " Is U II UI

225

U U fl 3. 25 ft -0 fl 4.25 II ft S . 25 " " II

6 25

' "

20 5

21.5 " 7.25 " "

5.4

11.3 21.9 " 8.25 "

0.4

5.0

14.1 "

9.25

x

3.0

8.5

19.7

10.25 " ' x x

4.2

13.7 11.25 " x x x

1.6

8.4

12.25 " x x x x 5.2 13.25 x x x x

2.6

14.25 X x x x

0.5

15.25 " x x x x x H 4 -6 8 -10 --12 (SEC) 14 CM)

-

-- (KT) 0.375 24.2 24.2

24.2

24.2 24.2 24.2

125

" " " "

2.25

II il II II II 3.25 ft II II U ft

4.25

'

" " "

5.25

" " " U 6.25 "

'

" ft ' '

7 25

" " " " " 8.25 fl I.

925

" "

100

II 10.25 " " x 15.3 ° 11.25 " x x

5.4

20.].

6.0

12.25

'

x x x x x 13.25 ' x x x x x 14.25 " x x x x x 15.25 ' x x x x x -- I t I.- - .5 -H T 4 6 8 10 12 (EEC) 14 (M) (KT) 0.375 24.2 24.2

24.2

24.2

24.2

24.2

1.25 ' ' ' " ' 2.25 UI 0 3.25 "

'

II II UI 4.25 "

'

' " 0 5 25 " - " II 6.25 " " " " " U 7.25 U 8.25 ° " ' " U 9.25 ' ft I U 10.25 11.25 " 10.5

6.3

' 12.25 " x

8.8

3.6

1.3

13.25 x x x 1.4 x 14.25 " x x x x x 15.25 x x x x x

(8)

= 0.436 (25°)

Eq. (16) results in

Probability that vertical bow aç-celeration exceeds a certain level a is

given by Z

=

exp(-a/2R2(a)]

(18)

where

probability that vertical ac-celeration exceeds a certain

level a1

Criter-ion of vertical bow

accelera-tion is determined for. Safety side as

follows.

= R(a)/g(H/L)

crz

(19)

crz

= R(a)/g(H/L)

= CL/H) ...(a/g)

cr0

= 1/1,000

critical level of. vertical bow

acceleration

q(a) : critical probability of

ex-ceeding for the vertical bow acceleration

By assuming

Table 11 Critical ship speed for all

responses (in following seas) a - 0°

°: possible to navigate without speed loss xz impossible tO navigate

-7-Ce) Transverse Acceleration

Probability that transverse bow ac-celeration exceeds a certain level a is

given by

q Cay) = exP(-a/2R2(a)] (22)

where

g(ay) probability that transverse bow acceleration exceeds a certain level

Criterion of transverse bow

accele-ration is detcrrnined fOr safety side as follows.

= R(y)/g(H/L) < Rcry)

(23)

Rcr(cLy) = R(ay)/(H/L)

where

a critical level of transverse ycr

bow acceleration

critical probability of

ex-'

ceeding for the transverse bow acàOleration a cr By assuming aycr = 0.6g,

a) =1/1,000

(Ref. 7) Eq. (24) results in

cry

28.25/H (25)

Systematic calculations of th.e ship

short-term seaways have een .carried out tor ranges o Froude iiber Fr, heading angie 6 an average

wa!eriodT..

Typical examples of the calculated

results are shown in Figs. 27.

Figs. 2, .3, 5, 6 and 7 show the

di-menSionléss standard deviations R(Zr)/Hs

R(Vr)/H/7t R(9)/(H/B), R(a)/g(H/L)

and R(a)/g(H/L) as functions of Froude number, and Fig. 4 shows the dimension-less probabilities of occurrehce of bow

bottom slamming as functions of Frouc3e ntnber.

In those Figs., noticeable trends are found between the ship speed and the ship responses. Namely, except some

azcr .= 0.8g,

0(a

= 1/1,000 (Ref. -4 6 8 10 12 (SEC) 14 0.375 24.2 24.2 24.2 24.2 24.2 24.2 1.25 - 0 0 0 N -2.25 ° N N N UI .25 UI _ UI II 4.25 " UI 5.25 N N N II 6.25 " 0 N Ut 7.25 " UI UI UI 8.25 0 UI N It 9.25 II N 0 0 UI II 10.25 II It N UI N 11.25 UI x s a. a 12.25 x x N 13.25 II It x x 1 N 14.25 x x x II 15.25 x x x X ° d . -cr(8) = 2.982/H (17) Eq. (20) results in (d) Vertical Acceleration

crz

= 37.67/H (21) V-2 (a CL/H) -. (24) where

/-2 ln((ay)]

(9)

'V

cases in seaways of the short wave

peri-ods, those ship responses can be reduced

by slowing down the speed.

other cases of different headings. those

ponses can nó' always be reduced by

ecriie speec. According to the

e1culated

tsinbluding the whole

cases of different headings, bow deck

wetness,

bow

bottom slamming and

verti-cal

bow

acceleration can be reduced by

slowing down the speed in head seas and

in bow seas, and rolling and transverse

bow acceleration can be also reduced by

slowing down the speed in following seas

and in quartering seas. In other cases,

those ship responses can not be

effec-tively reduced by slowing down the speed.

From the curves shown in Fics.

2. 4,

5,

6and

7,

critical Froude numbers can

be otiiiia

E[c

Uwave héig1t

Ii an

wave period T, by using critical

values of

crr' cr''

r(0)t

crz

and

cry

which are calculated

by Eqs. (8),

(13), (17),

(21)

and

(25)

as functions of wave height H and wave

period T. Those results for each

re-sponses are summarized in Tables

2". 6,

in

which critical Froude numbers are

con-verted into speeds in knots, and the

niaxixnum speed without speed loss is

as-sumed to be

24.2

knots (Froude number:

0.3).

Such results as shown in Table

2 '. 6

are obtained fOr a range of heading from

0° to 180° at intervals of

22.5°.

Those

results give the critical speeds for

each response, that is, bow deck wetness,

bow bottom slamming, rolling, vertical

bow acceleration and transverse bow

ac-celeration. In some cases in seawavs of

larqer wave heiqhts. critical speed for

a'certain response can not be obtatned

Intnose cases, the severe resnonse

oc-more frequently beyond the

criti-]J probabiflty of occurence even ifThne

Speéa would be

decrea'eqi fn h rn

By summarizing the whole results

for each response, the critical speeds

8

for all responses are obtained as shown

in Table

7'll.

3. LONG-TERM SHIP SPEED IN SEA ROUTES

In order to estimate the expected

speeds

T1

cruising hours of the

con-'tamer shp on the different routes Ee

Eeen Tokyo aidSan Franci

in winter,

when_the most heay,yeatrier is probable,

Ttediction workshave been

carried out b

utilizing the waVe

sta-istics in t e Nor

'aci ic cean

- f.

10) and the short-term prediction

re-sults described above.

Fig. 8 shows the great circle route

and the southern route between Tokyo and

San Francisco.

Examples of the wave statistics in

the North Pacific Ocean are shown in

Tables

12

and 13. Table

12

shows wave

frequency in sea area "MO5W" on the

northern great circle route in winter,

and Table 13 shows wave frequency in sea

area "Wl4" on the southern route in

winter. Such wave statistics are

avail-able for each sea area on both routes in

winter.

Tables 14 and

15

show the average

heights of 1/N highest waves in each sea

area on both routes in winter. As shown

in those Tables, wave heights in the

northern great circle route in winter

are rather larger than those in the

southern route in winter.

Tables 16 and

17

show the

proba-bility distributions of wave direction

in each sea area on both routes in

winter. As shown in those Tables, the

most probable wave directions a-re found

in a range of

270°'337.5°.

In seaways of larger wave heights,

as found in Tables

7". 11,

the ship can

not navigate unless the limits of

criti-cal probabilities of occurrence for the

severe responses are taken away. Such a

extremely stormy voyage occures in cases

of the symbol "c" in those Tables. By

utilizing the results in those Tables

50°

40°

30°

TK:

TOKYO GREAT CIRCLE

-ROUTE SF: SAN FRANCISCO -MO 5W WO 5

NMO

I2SF

TK EIOt'EIIN MI2N MI3N SOUTHERN ROUTE/

W15

- - - MI4W W14

1500E 70 E 170°W 150° W I-30°W

-Fig. 8 The great circle route and the southern route between Tokyo and San Francisco

(10)

and the w7vè frequency in on both routes in winter, probability of occurrence

trernely stormy voyage can as follows.

each sea area the expected of the ex-be calculated

Table 13 Wave frequency in sea areaW14 On the southern route in Winter AREA W14

(MEAN HEIG}IT 2.77M)

9

where

[Q1]6: long-term probability of.

oc-currence of the extremely stormy voyage for a constant heading angle in a sea area

Si

Table 12 WãVè frequency in sea area MO5W on the great circle route in WInter AREA MOSW

(MEAN HEIGHT: 3.18M)

WAVE PERIOD T

-05 05-07 07-09 09-11 11-13 13_SEC CALM TOTAL

H:00

075M 138 9 2 15 4 168

0.75- 1.75

1642 471 227 29 27 6 2402

1.75- 2.75

1549 1200 1160 322 159 56 4446

2.75- 3.75

788 1255 1311 311 289 86 4036

3.75- 4.75

227 576 910 246 160 137 2256

4.75- 5.75

37 .140 .367 86 97 30 757

5.75- 6.75

12 50 147 58 75 35 377

6.75- 7.75

17 152 111 48 64 33 425

7.75- 8.75

14 30 44 23 52 22 185

8.75- 9.75

5 14 29 12 58 16 .. 134

9.75-10.75

1 5 29 6 19 11 71

10.75-11.75

2 2 6 1 11

11.75-12.75

5 8 8 2 4 27

12.75-13.75

1 3 1 1 1 5

13.75-14.75

3. 2 1 1 5

14.75-

1 1 1 4 4 11 CALM 5 5 TOTAL 4431 3911 4351 1168 1010 443 9 3.5323 MAX HEIGHT 15 00 14 00 16 00 15 00 15 00 16 50 16 5DM WAVE PERIOD T -05 05-07 0 7-09 09-11 -

-1113

CALM TOTAL

H:0005M

327 18 9 8 401

0.75- 1,75

1639 120-3 563 243 153 39 86 3926

1.75- 2.75

835 1639 1610 749 390 174 125 5522

2.75- 3.75

294 863 1188 692 392 184 63 3676 3.75

4.75

96 339 606 421 222 122 - 36 1842

4.75- 5.75

30 102 218 167 104 39 10 670

.5.75- 6.75

33 97 119 87 56 392

6.75- 7.75

21 60 61 52 39 1 234

7.75- 8.75

3 14 28 28 29 102

8.75= 9.75

1 13 23 15 16 6 74

9.75-10.75

1 4 17 5 17 -. 44

10.75-11.75

. 1 1 3 5

11.75-12.75

2 3- 5 8 18

1275-13.75

- 1 3 4

13.75-14.75

1 1 1 3

14.75-

2 2 2 3 9 CALM 54 4 28 86 TOTAL - 3275 4248 4398 2539 1455 730 363 17008 MAX HEIGHT - 5.50 10.00 15.00

15.00 -- 15.00 -

16.00 - 9.50 16.00 .1 1 P(H.T)dHdT. (26)

(11)

p. (H,T) : long-term probability

den-sity of occurrence of a seaway of average wave height H and average wave period T in a sea area Si H5: critical average wave height for

the extremely Etoriny voyage as a

function of average wave period T

and heading angle *5

211

d*5 (27)

where

i]all: long-term probability of oc-currence of the extremely stormy voyage for all head-ings in a sea area

long-term probability density of occurrence of heading angle *5

can be determined as a function of wave period T and heading angle *5 by taking the lowest wave height whiOh

cor-respond to the symbol 'tx -in Tables 7 " 11.

P(H,T) is given for each sea area on both routes in such a form as shOwn

in Tables 12 and 13, and can be o tamed by using the long-term probabili-ty distributions of wave direction in

10

-each sea area on both routes, which are shown in Tables 16 and 17, and the ship course directions in those sea areas.

When considering the whole distance of the route, it follows that

[QT)*5* [Qj]*5*(lj/lT) (28)

tTali =

i]allUi"lT) (29)

where

EQTI*5*: long-term-probability of

oc-currence of the extremely stormy voyage for the whole distance ofthe route when

the most probable heading *5*

is considered in each sea

are a

EQTlall: long-term probability of oc currence of the extremely stormy voyage for the whole distance of the ráute when

all head-ings are considered

ii: course length in a sea area S lT: the whole distance of the route

Long-term predict-ions on the

ex-pected probability of occurrence of the extremely stormy voyage have been made

for the container ship on the. different

routes between Tokyo and San Francisco

in winter., including the east bound voya.ges and the west bound voyages, by

Table 14

Average heights of 1/N highest waves in each

sea area on the great circle route in Winter

Table 15

Average heights of 1/N highest waves in each

sea area on the southern route in Winter

SEA AREA EO5S EO6N MO6S MO6N MO7N M04 MO5W W05 W06 W09 W1O W13 TOTAL

1/10 HIGHEST 4.95 6.51

6.80

6.51

7.01 7.30 7.30

6.56

6.38 6.33

5.26 4.49 646M - 1/30 HIGHEST

6.57

8.55

8.59

8.22

8.50

8.91

9.23

8.31

794

7.85

6.74

5.61

814M 1/100 HIGHEST

8.20 10.47 10.49

9.88 10.04 10.56 11.16

9.85

9.65

9.46

8.52

6.99

983M 11AXI14UM

14.00 15.00 20.00 12.00 13.00 16.00 16.50 13.50 15.00 13.50 12.50 10.00

20M

PERcENTAGE OF

6 49

6 29

7 52

3 47 5 45

4 63 18 41 18 24

7 25 13 40

2 84 601100 00%

SEA AREA E1ON E11N M12N N13N M14W W14 W15 Wl2 W13 TOTAL

1/10 HIGHEST

6.08

6.58

6.69

6.44

6.22

6.36

4.95 5.40 4.49 599M 1/30 HIGHEST 8.04 8.21

8.38 8.41

8.14 8.21

6.27

6.93

5.61 770M

9.78

9.65 10.05 10.27 10.19 10.32

7.39

8.44 6..99 945M MAXIMUM -

14.00 13.00 1500 17.50 18.00 16.00 12.50 12.50 10.00

1800M PERCETAGEOF 5 14

5 13 10 26 10 26 20 53 20 5310 26 10 44

7 45 100 00%

(12)

means of Eqs. (26), (27), (28) and (29).

In order to make obvious the trends of difficult voyages on both routes, pre-dicting calculations have been carried out in 1/10 highest waves and in 1/30 highest waves in each sea area on both

routes.

Prediction results are summarized

in Table 18.

According to those prediction re-sults in winter, it is found that the

extremely stormy voyage, occures more

frequently on the northern great circle route than on the southern route, and the west bound voyages are always much more difficult than the east bound

voyages on both routes.

Then, the method of predicting the

Table 16 Probability distribution of wave direction in each sea area on the great circle route in Winter (H> 2.75M)

*: most probable direction, 0°: from north to south, 90°: from east to west

180° from south to north, 270° from west to east

Table 17 ProbabIlity distribution of wave direction in each sea

area on the southern route in Winter (H> 2. 75M)

*: most probable direction, 0°: from north to south, 90°: from east to west

180°: from south to north, 270°: from west to-east

EO5S EOGN MO6S MO6N MO7N M04 MO5W W06 W06 W09 W10 W13

0.0° 9.5 5.1 5.0 4.1 3.4 2.8 2.0 4.6 4.3 4.5 3.5 7.6 22.5° 8.3 4.2 4.1 3.7 2.8 3.7 2.7 3.8 2.4 2.8 1.0 3.3 45.0° 6.6 2.9 3.1 3.4 2.6 3.6 3.8 4.2 1.7 2.5 0.4 1.7 67.5° 5.1 1.9 2.5 3.1 2.6 3.3 4.9 4.8 1.5 2.6 0.3 0.9 90.0° 4..7 2.2 3.1 2.7 2.3 3.9 5.2 5.3. 1.5 0.3 0.4 - 112.5° 2.9 1.7 2.0 2.4 2.5 3.1 4.5 5.0 2.3 1.8 0.5 0.3 135.0° 2.6 1.6 1.8 2.5 2.7 3.1 4.4 4.8 3.3 2.7 1.6 1.6 157.50 -2.6 1.7 1.9 2.6 3.0 3.2 4.4 4.5 4.4 3.9 3.,9 3.0 180.0° 2.6 2.2 2.6 2.2 3.9 2.7 4.2 4.0 5.3 4.9 10.0 4.2 202.5° 3.2 2.3 2.7 2.7 4.0 4.2 5.5 4.4 6.1 6.3 9.1 4.5 225.0° 3.8 2.5 3.4 4.4 5.2 7.1 8.1 - 6.8 8.6 7.3 9.4 4.5 247.5° 4,5 3.9

60

7.8 8.5 11.7 11.6 9.7 11.4 8.9 10.5 5.5 270.0° 5.1 10.7 15.9 17.3 18.7 21.1* 176* 13.2* 14.4* 12.9 j4].* 11.5 292.5° 10.0 25.8* 20.5* 19.7* 18.9* 14.6 11.2 10.5 13.1 14.3* 13.6 14.6 315.0° 13.5 20.4 15.9 14.1 12.8 8.4 6.7 8.3 11.1 12.6 12.2 17.9 33750

150* 109

95

73

61

3532

63

86

96

96

183* TOTAL 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% E1ON E11N M12N M13N 1114W W14 W15 W12 W13 0.0° 7.4 6.2 4.6 3.6 4.3 4.6 5.8 5.4 7.6 22.5° 5.6 4.0 2.8 2.2 2.8 4.6 3.3 3.5 3.3 45.0° 4.1 2.9 1.9 1.7 2.7 4.8 2.8 2.9 1.7 67.5° 2.7 2.1 1.3 1.3 2.8 4.8 2.7 2.7 0.9 90.0° 1.5 1.1 0.8 0.8 2.6 4.1 2.2 2.1 0.4 112.5° 1.4 0.9 0.7 1.2 2.1 3.4 2.2 2.1 0.3 135.0° 1.5 1.1 1.3 1.5 1.9 3.1 2.5 2.9 1.6 157.50 1.5 1.7 2.2 2.2 1.7 2.7

29

3.9 3.0 180.0° 1.5 2.6 3.6 4.3 1.9 .4 3.6 4.5 4.2 202.5° 2.7 3.2 4.6 5.6 3.4 2.6 4.1 5.1 4.5 225.0° 4.6 4.8 6.0 6.4 4.8 3.9 5.3 6.3 4.5 247.5° 8.9 7.6 8.3 7.9 6.9 6.4 7.1 7.7 5.7 270.OD 21.1* 14.3 13.4 12.7 12.6 12.7 10.6 9.7 11.5 292.5° 15.0 17.0* 18.6* 20.2* 18.8* 15.9* 14.9 13.8 14.6 315.0° 11.5 16.5 17.1 17.2 17.5 13.9 15.8* 14.5* 17.9 337.50 9.0 14.0 12.8 11.2 13.2 10.1 14.2 12.9 18.3* TOTAL 100 0% 100 0% 100 0% 100 0% 100 0% 100 0 100 0% 100 0% 100 0% - - -- -- --- I I I I

(13)

expected speed and cruisIng hours on the sea route are described below.

By utilizing the short-term

predic-tion results of critical speeds for each response and for all responses, and the wave statistics in each sea area on both

routes, which are shown in Tables 12 and 13, the expected speed can be obtained

as follows.

= I

1 V5p1(H,T).dHdT (30)

= I .[E(V5)]6p(6) d5

(31)

where

[E(V5)]6: expection of sustained sea

speed for a constant

head-ing angle 6 in a sea area

Si

EEi(Vsflaii: expection of sustained sea speed for all

head-ings in a sea. area S1

V5: sustained sea speed as a function of wave height H, wave period T

and heading angle 6

The sustained sea speed V is

de-termined according to the short-term prediction results, which are shown in Tables 2'6 and in Tables 7't'll, as the critical speed for each response or that

for all headings. However, from the practical viewpoint, it is assumed that the ship would maintain the lowest speed even in rough seas, fOr instance, 8.1 knots for this case of the container ship, even if the critical speed given in those Tables would be lower than this

speed and the syinbpl "x" would denote

"impossible to navigate".

When 1/N highest waves are

consid-ered in a sea area S, in order to indi-cate obviously the speed loss of the ship in rough seas, the following Eqs4 should be employed instead of Eqs. (30) and (31). [B fT

i's'

(l/N) =

p()dH dT

(32) 12 -(33 )

in which H* should be determined so as to be satisfied with the following Eq.

I

I P(HT)dHdT = 1/N

(34)

0 H*

Then, the expected cruising hours in a sea area can be easily obtained as

follows.

(35)

[t.]11

1i/i(Tsfla1l

(36)

where

[t1]6: expected cruising hours for a constant heading angle 6 in a sea area S

[tilall: expected cruising hours for all headings in a sea area

Si

When considering the whole distance of the route, it follows that

[tT]6* = Z[t]6* (37)

[tT]ll = Z[t]11

(38)

where

V

[tT]6*: expected cruising hours for the whole distance of the route when the most probable heading angle 6* is consider-ed in each sea area

[tT]all: expected cruising hours for

the whole distance. of the

route when all headings are considered in each sea area Then, the average speed for the whole distance of the route can be ob-tained as follows.

- IN 1/10 HIGHEST WAVES IN 1/30 HIGHEST WAVES

HEADING AGAINST WAVES MOST JOBABLE ALL HEADINGS MOST PR0B1BLE ALL HEADING

or ROUTE HECTION . EAST -BOUND WEST BOUND EAST BOUND BOUND EAST -. BOUND WEST BOUND EAST BOUND WEST BOUND ON GREAT CIRCLE ROUTE

ON SOUTHERN ROUTE 0.0088 0.0072 0.0602 0.0487 0.0207 0.0126 0.0395 0.0322 0.0264 0.0215 0.1807 0.1462 0.0620 0.0379 0.1185 0.0967

VsT(6) =

(39) VST(all) = lT'[tT]all (40)

Table 18 Expected probabilities of the extremely stormy voyage on the greãr circle route and the southern route in Winter

(14)

Table 19 Expected cruising hours on the great circle route in Winter (for all respses)

GREAT CIRCLE ROUTE (IN 1/10 HIGHEST WAVES)

CASE (A): FOR MOST PROBABLE WAVE DIRECTION CASE (B): FOR ALL HEADINGS

CASE (C): WITHOUT SPEED LOSS (SPEED: 24.16ICT)

-

13

-SEA AREA EO5S EO6N MO6S MO6N MO7N M04 MO5W

URSH

AND ITS PERCENTAGE

290 62 6 49% 281 66 6 29% 336 66 7 52% 155 16 3 47% 243 72 5 45% 207 06 4 63% 824 34 18 41%

COURSE EAST BOUND 56.04° 58.98° 62.87° 66.12° 69.07° 72.60° 81.63°

DIRECTION WEST BOUND 236.04° 238.98° 242.87° 246.12° 249.07° 252.60° 261.63°

WAVE DIRECTION 337 50° 292 50° 292 50° 292 50° 292 50° 270 00° 270 00° MOST PROBABLE LEAST BOUND 258.54° 306.48° 310.37° 313.63° 316.57° 342.60° 351.63°

HEADING ANGLE WEST BOUND 78 54° 126 48° 130 37° 133 63° 136 57° 162 60° 171 63°

EECTED SPEED IN E.BOUND 24.01 23.80 23.87 24.05 23.92 23.92 - 23.82

1CTOTS FOR CASE (A) W.BOUND 24.01 20.75 20.30 20.46 20.24 16.99 16.45

EXPECTED CRUISING E.SOUND 12.10 11.84 14.11 6.45 10.19 8.66 34.61

HOURS FOR CASE (A) W.B0UND 12.10 13.57 16.58 7.58 12.05 12.19 50.11

EXPECTED SPEED IN E BOUND 23 50 2316 23 06 23 26 23 20 22 60 22 12 IO'OTS FOR CASE (B) W.BOTJND 23.74 21.83 21.45 21.57 21.01 19.79 19.93

EXPECTED CRUISING E.BOUND 12.37 12.16 14.60 6.67 10.51 9.16 37.27

HOURS FOR CASE (B) W.BOUND 12.24 12.90 15.70 7.19 11.60 10.46 41.36

EXPECTED CRUISING

12 03 11 66 13 93 6 42 10 09 8 57 34 12

HOURS FOR CASE (C) -.- -

-SEA AREA W05 WO6 W09 W1O W13

.--TOTAL COURSE LENGTH 816.66 324.42 600.06 127.32269.16 - 4476.84 IN SEA-MILES 18.24% 7.25% 13.40% 2.84% 6.01% 100.00%

AND ITS PERCENTAGE

COURSE -EAST BOUND 96.37° 106.42° 113.38° 118.47° 120.82°

DIRECTION WEST BOUND 276.37° 286.42° 293.38° 298.47° 300.82°

WAVE DIRECTION 270.00° 270.00° 292.50° 270.00° 337.50°

-MOST PROBABLE LEAST BOUND 6.36° 16.42° 0.88° 28.47° 323.32°

HEADING ANGLE WEST BOUND 186.37° 196.42° 180.88° 208.47° 143.32°

EXPECTED SPEED IN E.BOUND 24.13 24.02 24.06 24.16 24.14 23.98

IU'OTS FOR CASE (A) W.BOUND 17.90 18.85 18.96 22.13 23.60 18.99

EXPECTED CRUISING (E BOUND 33 85 13 50 24 94 5 27 11 15 186 67

HOURS FOR CASE (A) W.BOUND 45.62 17.21 31.64 5.75 11.40 235.80

EXPECTED SPEED IN E.BOtJND 22,76 23.38 23.43 23.94 24.09 23.01

ENOTS FOR CASE (B) W.B0UND 21.41 21.17 21.46 22.93 23.61 21.34

EXPECTED CRUISING E.BOUND 35.88 13.88 25.61 5.32 11.17 194.60

HOURS FOR CASE (B) W.BOUND 38.14 15.32 27.96 5.55 11.40 209.82

(15)

Tahle 20 Expected cruicing hours on the southern route in Winter (for all responses)

SOUTHERN ROUTE (IN 1/10 HIGHEST WAVES)

CASE (A): FOR MOST PROBABLE WAVE DIRECTION CASE (B): FOR ALL HEADINGS

CASE (C): WITHOUT SPEED LOSS (SPEED: 24.161(T)

-

14

-SEA AREA E1ON E11N M12N MI3N M14W W14 W15

246 34 246 34 492 69 492 69 985 38 985 38 492 69

AND ITS PERCENTAGE 5.13% 5.13% 10.26% 10.26% 20.53% 20.53% 10.26%

COURSE EAST BOUND 90.000 90.000 90.00° 90.000 90.000 90 00° 90 00°

DIRECTION WEST BOUND 270,00° 270.00° 270.000 270 00° 270.00° 270.00° 270.00°

WAVE DIRECTION 270 00° 292 50° 292 50° 292 500 292 500 292 500 315 00° MOST PROBABLE LEAST BOUND 0.00° 337.50° 337.50° 337.500 337.50° 337.500 315.00°

HEADING ANGLE WEST BOUND 180 000 157 500 157 50° 157 50° 157 50° 157 50° 135 00°

EECTED SPEED IN E.BOUND 24.01 24.05 24.08 - 24.01 23.98 23.98 24.13

ENOTS FOR CASE (A) W.BOUND 20.29 19.27 18.55 19.52 20.05 19.10 23.46

EXPECTED CRUISING E BOUND 10 26 10 24 20 46 20 52 41 10 41 09 20 42 HOURS FOR CASE (A) W.BOUND 12.14 12.79 26.56 25.25 49.15 51.59 21.00

EXPECTED SPEED IN (E BOUND 23 55 23 61 23 61 23 62 23 43 22 94 23 99 ENOTS FOR CASE (B) W.BOUND 21.86 21.16 20.49 21.06 21.62 .21.44 23.45

EXPECTED CRUISING E.BOUND 10.46 10.43 20.87 20.86 42.06 42.95 20.54 HOURS FOR CASE (B) W.BOUND 11.27 11.64 24.05 23.39 45.58 45.96 21.01

EECTEDcROISING 10.20 10.20 20.39 20.39 40.79 40.79 20.39 SEA AREA W12 W13 . . TOTAL -- 500.94 357.42 4799.88

AND ITS PERCENTAGE 10.44% 7.45% 100.00%

COURSE EAST BOUND 76.41° 81. 34° DIRECTION WEST.BOUND 256.41° 261.34°

MOST PROBABLE

315 00° 3-37 5Q0 WAVE DIRECTION

MOST PROBABLE EAST BOUND 301.41° 283.84°

HEADING ANGLE WEST BOUND 121.41° 103.84°

EXPECTED SPEED IN E.BOUND 24.10 24.14 24.04

ENOTS FOR CASE (A) w.B0UND 23.67 24.00 20.47

EXPECTED CRUISING E.BOUND 20.79 14.80 199.68

SOURS FOR CASE (A) W.B0UND 21.16 14.90 234.54

EXPECTED SPEED IN E.BOUND 23.76 24.09 23.52

ENOTS FOR CASE (B) W.BOUND 22.45 23.63 - 21.78

EXPECTED CRUISING E.BOUND 21.08 14.84

-- 204.09

HOURS FOR CASE (B) W.BOUND 22.31 15.13 . 220.34

EXPECTED CRUISING

(16)

Table 21 Expected cruising hours on the great circle route and the southeru route in Winter (for each response and for all responses)

MOST PROBABLE HEADING

ALL HEADINGS

-

15

-IN 1/10 HIGHEST WAVES IN 1/30 HIGHEST WAVES

GREAT CIRCLE ROUTE EAST BOUND WEST BOUND EAST BOUND WEST BOUND

DECK WETNESS 7D_183H 9D_10 0H 7D_202H 13D10 9H SLAMIIING 7 -17.7 9 - 5.3 7 -18.6 12 -20.4 POLLING 7 -17.9 7 -17..3 7 -19.2 7 -17.3 VEICAL ACCELERATION 7 -17.4 9 -11.7 7 -]7.4 12 -10.9 TRANSVERSE ACLERATION 7 -17.6 7 -17.3 7 -18.2 7 -17.4 ALL RESPONSES 7 -18.7 9 -19.8 - 7 -21.4 13 -16.6

WITHOUT SPEED LOSS 7 -17.3 7-17:3 7 -17.3 7 -17.3

IN 1/10 HIGHEST WAVES IN 1/30 HIGHEST WAVES SOUThERN ROUTE EAST BOUND WEST BOUND EAST BOUND WEST BOUND

DECK WETNESS-

8D_ 9D124H

8D95H

12D215H SLAMMING 8 - 7.1 9 = 8.9 8 - 7.9 12 - 8.9 ROLLING

8-7.1

8-6.7

8-8.0

8-6.7

VERTICAL ACCELERATION 8 - 6.7 9 -13.4 8 - 6..7 12 - 5.4 TRANSVERSE ACCELERATION 8 - 6.8 8 - 6.7 8 - 6.9 8 -- 6.7 ALLRESPONSES -

8-77

9-185

8-97

13-33

WITHOUT SPEED LOSS - - - 8 -6.7 8 - 6.7 8 - 6.7 8 6.7

IN 1/10 HIGHEST WAVES IN 1/30 HIGHEST WAVES GREAT CIRCLE ROUTE EAST BOUND WEST BOUND EAST BOUND WEST BOUND

-DEKWETNES - 8p 0911

8D136H

8D_135H

10D32H

SLAMMING 8 - 0.3 8 -11..9 8 -11.4 10 - 0.0 POLLING 7 -18.0 7 -17.7 7 -19.3 7 -18.4 VERTICAL ACCELERATION 8 - 0.5 8 -14.0 8 -10.1 9 -20.6 TRANSVERSE ACCELERATION 7 -17.8 7 -17.6 7 =18.6 7 =18.4 ALL RESPONSES 8 - 2.6 8 -17.8 8 -13.3 10 - 9.2

WITHOUT SPEED LOSS 7 -17.3 7 -17.3 7 -17.3 7 -17.3

IN 1/10 HIGHEST WAVES IN .1/30 HIGHEST WAVES

SOUTHERN ROUTE

--EAST BOUND WEST BOUND EAST BOUND WEST BOUND

DECK WETNESS 8D_17 0H 9D o H 8D_19 2H 10D15 3H SLAMMING 8 -10.7 8 -22.5 8 -18.3 10 =11.4 ROLLING

8-7.4

8-7.0

8-8.8

8-7.6

VERTICAL ACCELERATION 8 -10 4 9 - 0 4 8 -16 7 10 - 9 8 TRANSVERSE ACCELERATION 8 - 7.1 8 - 6.9 8 - 7.8 8 - 7.4 ALL RESPONSES 8 -12.1 9- 4.3 8 -21.8 10-20.7

(17)

where

V5T(6) : average sea speed on the

whole distance of the route when the most probable heading angle 6* is consid-ered in each sea area

VST(all) : average sea speed on the whole distance of the route when all headings are considered in each sea area

Prediction works on the expected Speeds and cruising hours have been carried out for the container ship on the northern great circle route and on

the southern route along the same

lati-tude line between Tokyo and San Fran-cisco in winter. In order to indicate definitely the differences between the prediction results on both routes, pre-dicting calculations are made by consid-ering 1/10 highest waves and 1/30 high-est waves in each sea area on both routes, and the lowest speed is assumed to be 8.1 knots even in rough seas.

Prediction results are shown in Tables 19, 20 and 21. Tables 19 and 20 show respectively the whole aspect of the prediction results on the northern g±eat circle route and on the southern route, where 1/10 highest waves are con-sidered in each sea area on both routes. Table 21 shows the summarized prediction results on the whole distances of both routes, including the cruising hours ob-tained by considering every individual response of bow deOk wetness, slamming, rolling, vertical bow acceleration and transverse bow acceleration, and by con-sidering all responses together.

When considering all headings in each sea area on both routes, character-istics of speed loss would be indis-tinctly veiled. However, when consider-ing the most probable wave headconsider-ing in each sea area on both routes, as shown in Tables 19 and 20, the east bound

voyages would be probably made in follow-ing seas and in quarterfollow-ing seas, and the west bound voyages would be probably made in head seas and in bow seas. and,

as shown in Table 21, bow deck wetness, slamming and vertical bow acceleration would be the main factors of speed loss in the west bound voyages on both routes.

According to those prediction

re-sults, the following trends are found on the expected speed loss and cruising hours on both routes in winter.

In both of the east bound voyage and the west bound voyage, speed loss on the southern route would be always less than that on the northern great circle route, but the cruising hours on the southern route would be slightly longer than those on the northern great circle route, except the particular case of the west bound voyage.

On both of the southern route and the northern route, speed loss in the

- 16 =

west bound voyage would be larger than that in the east bound voyage.

Cc) When the most probable wave head-ing is considered in each sea area, con-siderable speed loss would be caused in the west bound voyage, especially on the northern route.

4.. CONCLUSIONS

Speed loss of a container ship on the different routes between Tokyo and

San Francisco. in winter has been

evalu-ated theoretically by using the wave statistics in the North Pacific Ocean.

According to the results of short-and long-term prediction, the following conclusions are obtained.

Bow deck wetness, bow bottom slamming and vertical bow acceleration in head seas and in bow seas would be the main factors of speed loss in rough

seas

Wave heights in sea areas on the northern great circle route in winter would be larger than those in sea areas on the southern route.

On both routes, the east bound voyages would be most probably made in following seas and in quartering seas, and the west bound voyages would be most probably made in head seas and in bow

seas.

Speed loss in voyages on the southern route would be less than that in voyages on the northern route.

Speed loss in the west bound voyages would be larger than that in the east bound voyages.

Extremely stormy voyages occure most frequently in the west bound on the northern route.

Under those circumstances in winter, the west bound voyage from San Francisco to Tokyo should be made on the

southern route, arid the east bound

voyage from Tokyo to San Francisco would be admitted sometimes on the northern great circle route but should be mostly on the southern route.

ACKNOWLEDGEMENTS

The authors wish to express their deep thanks to Messrs. S. Kawachi, L. X. Gao, H. Akashima, H. Hamamoto and H. Ueda for their active cooperations in the numerical calculations.

REFERENCES

Motora, S.: "On Measuring of Ship's Resistance in Waves by Gravity Dynainometer Method, and Surging of Ship

in Waves". Journal of the Society of Naval Architects of Japan, Vol. 94, 1954.

Fukuda, J. et al.: "Theoretical Calculations on the Motions, Hull Sur-face Pressures and Transverse strength

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