Predicting long-term trends of deck wetness for ships in ocean waves

AICHLEF

tab

v. Scheepsbouwkunde

TecFrnsche Hogeschool

De!ft

With the Compliments of the Author

Prepicting Long-Term Trends of Deck Wetness for

Ships in Ocean Waves

By

Jun-ichi FUKUDA

Reprinted from the Memoirs of the Faculty of Engineering, Kyushu University, Vol. XXVIII, No. 2,

FUKUOKA JAPAN

1968

Prelicting Long-Term Trends of Deck Wetness for

Ships in Ocean Waves*

By Jun-ichi FuKuDA Professor of Naval Architecture'

Summary

A method of predicting the short-term probability of deck wetness and the long-term probability of "Wet-Deck Navigation" is proposed, along with results of its application to cargo ships operating in the North Atlantië.

Vertical bow motions relative to the waves have been evaluated theoretically for geometrically similar ships of various sizes at different headings to regular waves and at different speeds, based upon the linear strip theory and the linear superpositiOn technique., According to those results, relationship between the short-term probability of deck wetness related, to bow freeboard and the

significant wave height of irregular sea has been determined in correlation to the average wave period, heading angle and ship speed. Then, the long;term proba-bilitiesof "Wet-Deck Navigation" where the short-term probability of deck wetness will be larger than 1/10 have been predicted for different seasons and for various wind forces by the aid of the long-term wave statistics in the North Atlantic.

The following trends of deck wetness related to the bow freeboard àrë con-cluded .from the predicted results.

The probability of deck wetness is large in head and bow seas, and small in following, quartering and beam seas.

The probability of deck wetness decreases with decrease of ship speed, but the influence of speed is rather small in the speed range beyond 10 knots.

The large sized ship has less probability of deck wetness than that of the small sized ship.

The full ship form has less probability of deck wetness than that of 'the fine ship form.

In the North Atlantic, the probability of deck wetness is large in winter and small in summer.

In the North Atlantic, the probability of deck wetness increases with increase of wind force, but this trend is moderate in extremely heavy weathers.

1. Introduction

The phenomena of green water getting on the deck of a ship operating in rough seas, that 'is, "Shipping of Green Water"

is considered to be caused mostly by the

relative vertical motions between the ship

* This paper will be published in Japanese at the end of 1968 in Journal of the Society of Naval Architects of Japan, VoL 124

and waves due to oscillations of the ship

in waves. While the occurrence and,

severi-ty of shipping of green water are dependent on the height of freeboard and the arrange-ment of superstructure, green water will more frequently get on deck at the bow in

head seas, at the stern

in following seas and at the midship in beam seas.

It is supposed that the shipping of green

water at the bow in head seas can be caused,

motion relative to the wave surface due to pitch and heave exceeds the bow freeboard, but it occures at the stern in -following seas when the vertical stern motion relative to the wave surface due to pitch and heave

exceeds the stern freeboard. And in beam

seas, it is considered to be caused at the midship when the relative vertical motion

between the deck edge and wave surface duc to roll, heave and pitch exceeds the freeboard at the midship. Thus considering

the fact that the largest cause for shipping of green water lies in the relative vertical motions between the ship and waves, we can evaluate the short-term - probability of deck wetness due to shipping of green water

by analysing the relative vertical motions

of the ship in- irregular seas.

On the other hand, there have been col-lected and analysed the detailed data on the long-term frequency of ocean waves in the world sea areas and- routes. Accordingly, if we can-evaluate the short-term probability

of deck wetness for a ship in irregular seas, it will be made possible to predict

statisti-cally the long-term probability of "Wet-Deck Navigation", where the short-term probability of deck wetness exceeds -a certain value, for

the ship operating in a sea area or a route by utilizing the long-term wave statistics in the sea area or the route.

-Here the author will consider only the problem of deck wetness at the bow caused by the vertical bow motion relative to the wave surface.

As to

researches of this kind, number of publications have been reported by Lewis1> and other authors29.

Most of them have, attempted the short-term

predictions of deck wetness in waves, exept few works by Newtons) and Nordenstrom9 which contain the results of long-term pre-dictions on deck wetness for ships in the

North Atlantic. In, this paper, -the author

have proposed a method of the short and

long-term predictions on deck wetness for- a ship in ocean waves, and tried the- long-term predictions of "Wet-Deck Navigation" for

cargo ships- operating in the North Atlantic. Influences of heading, speed, size and fineness

of ship on deck wetness are discussed, and the long-term trends of deck wetness are

investigated for different seasons and for various wind forces in the North Atlantic.

2. Short-Term Prediction of Deck Wetness in Irregular Seas

The variance or standard deviation of

vertical bow motion relative to the wave surface in the short-term irregular sea can-be evaluated, if given the wave spectrum representing the sea state and the response operators of relative bow motion in regular waves, by the following equation based on

the linear superposition method10.

It f2 COO -R2 = - [A(o, 0 -- zY12[f(o,, Z)]2dwdX (1)

J.)JO

-2 where - -

-R standard deviation of relative bow

motion

R2: variance of relative bow motion

[A(w, 0 - X)]: response amplitude of

rela-tive bow motion in regular waves at a heading (0 x)

[f(w, Z)]2: directional spectral density of sea waves coming from a direction x

w,: circular frequency of component wave .0 : angle between the ship course and

the average wave direction

X : angle between a component wave

direction and the average wave direc-tion

Here let us adopt the modified

Pierson-Moskowitz wa-ye spectrum (ISSC spectrum)'1

as a spectn.im representing the irregular sea where the significant wave height is equal to H and the average wave period

T, as

follows:

-[f()]2 = O.11H2w1(w/a>15

exp{ - O.44(co/w1Y4} (2)

where

-Owoo, w1=2r/T

[f(co)]2: spectral density of sea waves H : average wave height according to the

visual estimation (asumed to be equal

to the significant wave height) T : average wave period according to the

visual estimation

If assumed the (cosine)2 ditribution for

the directional spreading funètion of the

spec-tral density of sea waves in the range from - 2r/2 to r/2 with respect to the average

wave direction, the following equation is obtained.

7r/2_<co_<'r/2 [[(co, X)] (2/r)[f(co)]2 cos2 X:

} (3)

= 0: elsewhere

On the other hand, the response operator of vertical bow motion relative to the wave

surface fOr a ship navigating in regular

waves with a constant speed and a constant heading can be calculated

by using the

solutions of heave and pitch based on the

modified strip theory'2"8>.

Accordingly, if we carry out the

calcula-tion of (1) by using, the wave spectrum

expressed by (2) and (3) and the response

amplitudes calulated by the theoretical

method, we can evaluate the variance R2 or the standard deviation R of the relative bow motion for the ship navigating in the short-term irregular sea, where the signifi-cant wave height is H and the average wave period T, with a constant speed and a con-stant heading to the average wave direction. Assuming that green water gets on deck at the bow when the magnitude of vertical

bow motion relative to the undisturbed wave

surface exceeds the bow freeboard, we can evaluate the expected probability of deck wetness (the ratio of the frequency of deck wetness to the frequency of relative bow motion) in the short-term irregular sea ac-cording to Rice's theory'4, as follows':

-

f

f (f/L)2

- exp1

2R2 J exp1 2(R/H)2(H/L)2 where

q: expected probability of deck vetness

in the short-term iftegular sea

bow freeboard

L: ship length

And we obtain the following equation from (4).

(f/L)2 L2 loge (1/q)

2(E/H)2 H2

From the equation (5), we

/2 log(1/q) (R/H) where

Hs>q>: the significant wave height of the

short-term irregular sea where the expected probability of deck wetness will be q

Since R/H can be evaluated as the func-tion of average wave period, heading angle and ship speed, the critical significant wave height H>> will be obtained as the function of average wave period for the ship nàvi-gating in the short-term irregular sea with a constant heading and a constant speed.

3. Long-Term Prediction of "Wet-Deck Navigation"

Available long-term frequencies of ocean

waves are given for the world sea areas

and routes as functions of significant wave height and average wave period which are

classified into

a number of

divisions of small intervals respectively. It is, therefore;

possible to predict the long-term probability

of occurrence of the "Wet-Deck Navigation ",

where the short-term probability of deck wetness exceeds a certain value q, in a sea area or a route. For example, we can pre-dict the cumulative number of days during

which the expected frequency of deck

wetness will exceed once per ten times of

wave encounter for every 50 days voyage in

winter, or the cumulatjve number of days

of such "Wet-DecL{.Navigation" during every 200 days voyage per year. It is also possible

to predict the long-term probability of oc-currence of such "Wet-Deck Navigation" in

the storm seas of Beaufort No. 8 for instance.

Let p(H, T) denote the long-term proba-bility' density function

for the

sea state

where the significant wave height is H and the average wave period T. Assuming 'that

a ship operates always *ith a cOnstant speed

and a cOnstant heading 0 to waves, the

(6)

the critical significant 'wave height of the short-term irregula sea beyond which the expected probabity of deck wetness will be larger than q, as follows:

(f/L)L

(5) can determine

dimensionless standard deviation of relative

bow motion R/H can be obtained as the

function of average wave period T by the

theoretical method described in the preceding section. Therefore the critical significant

wave height H,(g) (which gives the limit of significant wave height that the short-term

probability of deck wetness exceeds a certain value q) can be also obtained as the functiOn

of average wave period T according to the

equation (6). Accordingly, the long-term probability of "Wet-Deck Navigation" where

the short-term probability of deck wetness will be larger than q can be given by the

following equation. roo roo

-3T=O JH=ES(q)

Qq(0) _\ p(H, T)dH dT (7)

where

Qq(0): long-term probability of "Wet-Deck

Navigation" for the heading angle 0, where the short-term probability of deck wetness will be larger than q p(H, T): longterm probability density

function for the sea state where the significant wave height is equal to H and the average wave period T Q(0) is obtained from (7) as the function of heading angle 0 when the ship operates

always with a constant speed. Accordingly, if the long-term probability density function

of heading angle could be known, the long-term probability of "Wet-Deck Navigation" for the case when all headings are taken into account can be obtained by the

follow-ing equation.

C2'r

Qq= Q(0) p*() dO (8)

0

where

Qg: long-term probability of "Wet-Deck Navigation" fot all headings, where

the short-term probability of deck

wetness will be larger than q

p*(0): long-term probability density func-tion for the heading angle to waves We can hardly determine accurately the function p*(8) because it is actually subject

to the sea state, ship speed and other factors,

but if we could approximate

it as being

uniformly distributed over the whole range

from 0 to

2zr,

the equation (8) may be

simplified as f011ows.

1

= _{Q(0) dO (9)}

2ir jo

As mentioned above, the long-term proba-bility of "Wet-Deck Navigation"

for a

constant heading is obtained by (7) as the

functiOn of ship speed and that for all

head-ings by (8) or (9) also as the function of

ship speed.

p(H, T) in the right side of (7) is given actually in the form of the long-term wave frequency as the function of significant wave height and average wave period which are classified into divisions of small intervals respectively. Hence the integral operation of (7) will be practically performed by the

numerical method. And the integral opera-tion with respect to the heading angle 0 in (8) and (9) will be made also by the

numeri-cal method where being the range of

0

from 0 to

27r devided into a number of small and equal intervals.

4. Predicted Results and Discussions

The prediction method on deck wetness was applied to the two kinds of cargo ship

forms, i.e., Model 4210 W (Gb =0.60) and

Model 4212 W (Ch=0.70), which were selected

out of Series 60153.

For the purpose of

investigating the influence of ship size on

deck wetness, predictions were made for number of ships which were similar in hull

forms below water line but different in sizes.

The full load condition was considered for

all ships and the longitudinal radius of

gyration was assumed to be equal to 25 % of the length between perpendiculars. For

the bow freeboard, the minimum value was adopted in accordance with the rule of the

Conference on Load Lines in 1966, as follows: 1.36 (in meter) (10) f=0.056L (i

-500)C+0.68 where L<250 m C=C,,

: C,,068

C=0.68 : C,,<0.68 112 Jün.ichi FUKUDA

f : bow freeboard at the fore perpendicular

L : ship length

Gb: block coefficient

Other principal particulars of ship forms are shown in Table 1.

At first, there were calculated the standard

deviation R of the relative bow motion in the short-term irregular seas and the critical

significant wave height H(1J10) beyond which

the short-term probability of deck wetness will exceed 1/10 for all ships. Then, the

long'term probabilities of "Wet-Deck Naviga-tion for q>1/10 ", where the short-term

prob-ability of deck wetness will be larger than 1/10, were evaluated for different seasons,

during all seasons and for various wind forces by using Walden's data16

on the

long-term wave frequency in the North Atlantic.

While the procedure aud results for the short-term prediction of deck wetness are given in Figs. 1-40, those for the long-term prediction of "Wet-Deck Navigation" are shown in Figs. 11-16.

Deck Wetness in the Short-Term Irregular

Seas

The modified Pierson-Moskowitz wave

spectra (ISSC spectra) are showü in Fig. 1, where the following exptession is used for each case of T=4, 6, 8, , 18 sec.

[f(w)j2/H2 = 0.11oE(a/o1)'5

x exp { - 0.44(a,/w1Y4} (11) In Figs. 2 and 3,

there are given the

examples of the calculated response ampli-tudes of relative bow motion (at the fore

perpendicular). The following, notations are

used in the figures.

Z0: amplitude of relative bow motion in

regular waves h0 : wave amplitude

A wave length

heading aflgle to regular waves

(çl' = 00 _{head waves)}

Fr.: Froude number

Such, response operators as shown in Figs. 2 and 3 were calculated based on the modified strip theory12> for a range of Froude number

and for a range of heading angle.

Standard deviations of rëlàtive bow motion

were evaluated by (1) for ships Of various

sizes in irregular seas, where being used the wave', spectra shown in Fig. 1 and such

response operators of relative bow motion as

shown in Figs. 2 and 3. Calculated results are illustrated in Figs.

4-7, where the

dimensionless values of R/H are shown as

functions of heading angle 0, Froude number

Fr. or v"L/A.

In Fig 4, R/H 'is given as the function of heading angle 0 to the average wave

direction (0 =00: head waves). In Fig. 5,

R/H is represented as the function of Froude number Fr. Those figures show the examples

for ships of 150 meters length.

In Figs. 6 and 7, R/H is represented as the functiOn of \/L/Ae, where

A0=gT2/27r (12)

g: acceleration of gravity

corresponds to the length of the regular wave which has the period being equal to the average wave period of the irregular

sea.

Figs. 6 and' 7

in which R/H (the dimensionless standard deviation of relative bow motion in irregular sea) is shown as the function of \/L/Ae correspond to Figs. 2 and 3 in which Z0/h0 (the dimensionless amplitude of relative bow motion in regular

waves) is represented as the function of \/L/A. It can be made possible to represent

R/H as the function of \/L/Ag in the

dimen-sionless expression, because of the calculation

method for R/H according to the equation

(1) where being assumed the wave spectrum

in the form of (2) and (3).

The bow freeboards are shown in Fig. 8,

which are determined according to the Con ferenec on Load Lines in 1966. The bow

freeboards given in the figure correspond to the minimum heights regulated by the rule and the larger freeboards will be adopted for actual ships. But the following

calcula-tions on the short and 'long-term deck wetness related to the bow freeboard were carried out by using the bow freeboards given in Fig. 8.

Calculations of H3(1/10), which corresponds to the critical significant wave height beyond

114 S Jun-ichiFUXUDA

which the short-term prbbábility of deck

wethess will be largel- than 1/10, were carried

out for air ships and the results for ships of 150 meters length are shown in Figs. 9 and 10. In the figures, H8(1J10) is represented

as the function of average wave period. For the case of "q = q1" insted of "q = 1/10," the critical significant wave height will be easily obtained by the following equation.

= H3(1J10)/ \/1og10(1/q1) (13) where

HS(Q): the significant wave height of the

short-term irregular sea where the ex-pected probability of deck wetness will be equal to q1

When the bow freeboard takes the

dif-ferént height "f1" insted of "f," the critical significant wave height is given as follows.

.hTs(q1)(11) = ₍₁₄₎

where

H3()(f): the significant wave height of the short-term irregular seas where the expected probability of deck wet

ness will be equal to q1, when the bow freeboard takes the height f1 Now, from the

results obtained ade,

we can find out the general trends of

rela-tive bow motion in the short-term irregular

eas and of deck wetness related to the

bow freeboard, as follows:

The dimensionless standard deviation

of relative bow motion R/H takes the largest

value in head seas and decreases a little in bow seas, and it decreases almost by half in following, quartering and beam seas as compared with that in head seas (Fig. 4)

The dimensionless value R/H increases

considerabily' with increase of ship speed in head seas except the case in sea waves of the short average period, but in following seas it decreases slightly with increase of

ship speed (Fig. 5).

'In regular waves, the dimensionless

amplitude of relative bow motion Z0/h0 takes the largest value in head waves of

/i7=0.9.1.0 (Figs.. 2 and 3), but in:

irre-gular seas, the dimensionless standard

devia-tion of relative bow modevia-tion R/H takes the

largest value in head seas of _/L/A = v"27rL/g IT = 1.1 L2 (Figs. 6 and 7). Accordingly, the critical significant wave height Hg(q) beyond which the short-term

probability of deck wetness will be larger

than a certain value q,

for instance 1/10,

takes the smallest value in head seas of

= 1.1-1.2, i.e., in the case when the average wave period T is nearly equal to

v'L/2 (Figs. 9 and 10).

The relative bow motion of a fine

ship form is larger than that of a full ship

form.

The standard deviations of relative bow

motion in the short-term irregular seas which

are obtained above have been evaluated by

using the modified Pierson-MoskOwitz wave

spectra (ISSC spectra) and the calculated response operators of relative bow motion

according to the modified strip theory. There

is a question whether the short-term sea

state - can be identically represented with

such a wave spectrum as given by (2) and (3) only according to the two parameters of

H and T, and also a question how is the

relationship between the visually estimated

values and the instrumentally measured ones

for the significant wave height H and the average wave period I. And there is

an-other question how is the reliability of the

calculated response operators of relative bow motion.

_{As to the former question, we}

have not sufficient 'knowledges except a few

informations by oceangraphers and we hope that the available data will be presented as soon as possible. On the latter problem, available reports have been published

re-cently. According to the report of

Norden-strom,'7 it is pointed out that the response

amplitude of relative bow motion calculated

by using the strip theory is generally lower than the experimental value. The similar tendency has been found in the latest model

tests made by Tasai at the Kyushu

Uni-versity. (to be published). Dutch authors'8

have made the comparison, between

applicability of the strip theory seems to be larger than the limitation of the theory and the satisfactory agreement between calcula-tion and experiment is found except some

cases. The author believe that the calculated

response operator of relative bow motion based on the modified strip theory will be sufficiently valid, at least for the practical

purpose. But if the calculated respOnse

amplitude of relative bow motion i lOwer

than the correct value, it is feared that the dimensionless standard deviatiOn of rlative bow motion R/H evaluated by using the

calculated response amplitude will be

under-estimated and therefore such critical

signi-ficant wave height H2(1/10) as given in Figs. 9

and 10 will be overestimated in dangerous side. Considering such cases, we. should

remember that the results of the long-term prediction on "Wet-Deck Navigation" de-scribed below might be also in dangerous

side. In the near future when we find the improved method of representing the short-term irregular sea with a wave spectrum

and that of calculating .the response operator

of relative bow motion, we shall be able to make the short and long-term predictions on deck wetness more accurately by means

of theoretical method.

Long- Term Predictions of " Wet-Deck Navigation"

There are given the long-term wave fre-quencies in the North Atlantic in Tables 2 and 3, where Walden's data'6 from the nine weather ship stations are summarized for

the different four seasons and for the various Beaufort numbers. By utilizing those wave

frequency tables, the long-term probabilities

of "Wet-Deck Navigation (q>1/10)," where the short-term probability of deck wetness related to the bow freeboard will be larger than 1/10, were evaluated for all ships of

different sizes,operating in the North Atlantic.

The results are shown in Figs. 11.-16. Fig. 11 shows the long-term probability

Q1110 of the "Wet-Deck Navigation (q< 1/10)"

evaluated for ships of 150 meters length operating in the North Atlantic in winter.

Q1110 for a constant heading is obtained from

the equation (7), and Q1110 for the case

when all headings are thken into considera-tion from the equaconsidera-tion (9). In the figure,

Q1110 is represented as the füiiction of ship speed.

The similar results as shown in Fig. 11 are obtained for all ships, which are geo

metrically similar in hull forms belOw water

line but different in sizes, and for the four

seasons By summarizing those results Fig. 12 is obtained, where the long-term probability Q1110 of the. "Wet-Deck

Naviga-tion (q>1/10)" is given as the function of ship length fOr different seasons with pa-. rameters of heading and ship speed.

Further Fig. 13 is obtained, which shows

the long-term probability Q1110 of the "Wet-Deck Navigation (1/10)" throughout the year,

by taking the average of

Q1110 for each

season

In the next place, Fig. 14 shows the

long-term probability Q1110 of the "Wet-Deck Navigation (q>1/10)" evaluated for ships of 150 meters length operating in the storm

seas of Beaufbrt No. 8 in the North Atlantic.

The similar results as shown in Fig. 14 are obtained for all ships and .for various

Beaufort numbers. By summarizing those results Fig. 15 is obtained, where the long-term probability Q1110 of the "Wet-Deck Navigation (q>1/1O)" is given as the

func-tion of ship length for different Beaufort numbers with parameters of heading and

ship speed.

On the other hand, Fig. 16 shows the

long-term probability Qj1 of the "Wet-Deck

Navigation (q>1/10)" for ships of 100, 150

and 200 meters lengths as the function of

wind force by using

the parameters. of heading and ship speed.

From those results of the long-term predic-tion on "Wet-Deck Navigapredic-tion" in the North Atlantic, we can conclude the following

trends of deck wetness related to the bow

freeboard.

a) The long-term probability of

"Wet-Deck Navigation" is largest in head seas and decreases a little in bow seas, and it is extremely small in following, quatering and beam seas as compared with the case in head seas.. (Figs.. 11 and 14)

116 Jun-ichi 'FUtUDA

b) The long-term prObability of "Wet-Deck Navigation" increases generally with increase of ship speed. Hence the speed

decreasing is effective for decreasing the

probability of deck wetness, but this effect can not be so much expected in the higher

speed range beyond 10 knots. (Figs. ii-16) The longterm probability of "Wet-Deck Navigation" decreases with increase

of ship size. (Figs 12; 13, 15 and 16)

The longterm probability of "Wet-Deck Navigation" for a full ship form is smaller than that

of a

fine ship form. (Figs. 11-46)

As far as

it is concerned with the

long-term probability of "Wet-Deck

Naviga-tion" related to the bow freeboard, the

height of bow freeboard regulated by the rule of the Conference on Load Lines in 1966 is too small fOr a small ship and a fine ship or too large for a large ship and a full ship.

In the North Atlantic, the long-term

probability of "Wet-Deck Navigation" is

largest in winter and smallest in summer.

(Fig. 12)

In the North Atlantic, the long-term probability of "Wet-Deck Navigation"

in-creases with increase of wind force. But in heavy weathers, its increasing trend becomes

moderate. (Fig. 16)

Those trends described above have been

concluded from the predicted results

accord-ing to the method proposed in this paper. Because of the weak points in calculations

of R/H or H8(1/10) which are pointed out in

the preceding discussion, the reliability of the predicted results may be not perfect. However the trends of deck wetness related to the bow freeboard concluded here will be valid for the practical purpose. It is possible to predict the long-term probability of' "Wet-Deck Navigation" where the short-term probability of deck wetness exceeds a different value q1 instead of 1/10, to make predictions for a ship which has a different freeboard, and also to do in the other sea areas than the North Atlantic..

5. Conclusions

The author has proposed a method of

the short and longterm predictions on deck wetness, and shown the examples of 'its application to the two kinds of cargo ship

forms. The long-term predictions of "Wet-Deck Navigation," where the short-term

prob-ability of deck wetness related to the bow freeboard exceeds the level of 1/10, have

been made for ships which are similar in hull forms below water line but different

in sizes by utilizing the long-term wave

frequencies in the North Atlantic. From

the predicted results, the following conclu

sions are found as the general trends of

deck wetness related to the bow freeboard.

The probability

of deck wetness is

large in head and bow seas and small in

following, quartering and beam seas.

The probability of deck wetness can be decreased by decreasing ship speed, but this effect is little in the speed range beyond

10 knots.

The large sized ship has less proba bility of deck wetness than that of the small

sized ship.

The full ship form has less plobability of deck wetness than that of the fine ship

form.

'In 'the North Atlantic, the probability of deck wetness is large in winter and small

in summer.

In the North Atlantic, the probability of deck wetness increses with increase of wind force, but this trend is moderate in

extremely heavy weathers.

The reliability

of the

predicted results

may be not perfect because of some weak

points in the calculations. However the trends of deck wetness related to the bow freeboard concluded here will be valid for the practical purpose. The more accurate

predictions will be made possible if' improver

ments are brought on the short and long-term wave statistics and on the theoretical

method of calculating the response operators of ship motions.

Acknowledgements

The author wishes to express his deep

thanks to Mr. Ichiro HATA and Mr. Shigemi TSUTSUMI, who are the staff of the Depart-ment of Naval Architecure, Kyushu

Univer-sity, for their cooperation in this work.

References

E. V. Lewis: Ship Speeds in Irregular Seas" TSNAME, Vol. 63 (1955)

J. L. Tick: "Certain Probabilities Associated with Bow Submergence and Ship Slamming

in Irregular Seas" JSR, Vol. 2, No. 1 (1958) R. Tasaki: "On the Shipping Water in Head

Waves" Journal of the Society of Naval Architects of Japan, Vol. 107 (1960)

0. Krappinger: "Freibordvorschrift" JSTG (1964)

M. K. Ochi: "Extreme Behavior of a Ship in Rough Seas" TSNAME, Vol. 72 (1964) G. J. Goodrich: "The Influence of Freeboard on Wetness" NFL Ship Rep. 60 (1964) J. Fukuda and J. Shibata: "The Effects of Ship Length, Speed and Course on Midship Bending Moment, Slamming and Bow Sub-mergence in Rough Seas" Memoirs of the Faculty of Engineering, Kyushu University, Vol. 25, No 2 (1966)

R. N. Newton: "Wetness Related, to Free-board and Flare" TRINA, Vol. 102 (1960) N. Nordenstrom: "Calculations of Wave-In-duced Motions and Loads. Progress Report No. 5. Ship; Motions Relative to the Waves" DNV Report No. 66-5-S (1966)

M. St. Deñis and W. J. Pierson, Jr.: "On the Motions of Ships in Confused Seas" TSNAME, Vol. 61(1953)

"Report of the Committee 1 on Environmental Conditions" Proceedings of 2nd ISSC, Deift (1964)

J. Fukuda: "Computer Program Results for Response Operators of Wave Bending Moment in Regular Oblique Waves" Memoirs of the Faculty of Engineering, Kyushu University, Vol. 26, No. 2 (1966)

3. Fukuda: "A Practical Method of Calculat-ing Vertical Ship Motions and Wave Loads in Regular Oblique Waves" Note Presented to the Rome Meeting of the Committee 2 on "Wave Loads, Hydrodynamics" ISSC, August

(1968)

5. 0. Rice: "Mathematical Analysis of Random Noise" The Bell System Technical Journal, Vol. 24 (1945)

F. H. Todd: "Some Further Experiments on Single Screw Merchant Ship Forms-Series 60" TSNAME, Vol. 61 (1953)

H. Walden: "Die Eigenschaften der Meer-swellen im Nordatlantischen Ozean" Deutscher Wetterdienst, Seewetteramt, Einzelveroffentli-chungen Nr. 41, Hamburg (1964)

'N. Nordenstrôm and B. Pedersen: "Calcula-tions of Wave-Induced ,Mo"Calcula-tions and Loads. Progress Report No. 6., Comparisons with

Results from Model Experiments and Full Scale Measurements" DNV Report No. 68-12-S (1968)

W. P. A. Joosen, R. Wahab and 3. J. Woortman: "Vertical Motions and Bending Moments in Regular Waves. A Comparison between Calcu-lation and Experiment" ISP, Vol. 15, No. 161 (1968)

118 Jun-ichi FFJKUDA C.) w 0.3 3 I-0.2 0.1

Table 1 Particulars of Ship Forms

[f (w)]2/H2= 0.11 w'(w/wJexp[-0.44 Cw/w)4]

w =2t/T

Fig 1 Modified Piersori-Moskowitz Wave Spectra (ISSC Spectra)

Model Number 42l.Z 42l2I

-Length-Breadth Ratio (L'B) 7.500 7.000

Length-Draught Ratio (Lid) 18.750 17.500

Breadth-Draught Rato (Bid) 2.500 2.500

Block Coefficient 0.600 0.700

Water Plane Coefficient 0.706 0.785

Midship Coefficient 0.971 0.986

Centre of Buoyancy from Midship 0.01St. (A) 0.005L (F)

Longitudinal Gyradius 0.250L 0.250L.

I

ISSC(1964) WAVE SPECTRA

0.5 1.0 1.5

2 0 2 Cb0.60 Fr=0 e=o°

---:

=0.05

-

---:

: =0.10 =b.15 ii1 S : =0.20

!: ,'\'

. =0.25

-

/

Cb0.70 e=o° -:Fr.=Q

----:

=0.05

---: =O.IO

=0.15

----:

=0.20

-

_:'/,.'

1,1.

\

/1/i.

/"i

il/I

-05

I0

15

20

-o

Fig. 2 Response Amplitudes of Relative Bow Motion in Regular Head Waves

05

I0

'5

a.0 IE7K 6 0 N

H

3 6 0 N

H

3

4 3 0 6 0 N 4

F'ig. 3a Response Amplitudes of Relative Bow Motion in Regular

Waves from Different Directions _(Cb=0.60)

05

10

1.5

20

Cb=O.60

Fr.0.l0

1?= 00 = 30

- -: =

60

=90

: =120 - : =150 =180

k

T'"

--Cb=0.60

Fr.0.20

'=

00 = 30

= 60

:

- -:

:

=90

=120

A

=150 =180 120 Jün-ichi FITKIJDA

05

I0

15

20

2 0 3 2 Cb=070

Fr.0.l0

: 00 = 30

= 60

- -: .

_: .

=90

=120

- -:.

_{: =150} =180

:

- -/

-Cb=0.70

Fr.0.20

f= 00

____:

= . .

- -:

=90

-: =120 : =150 =180 -

_A-i-"

05

(0

'5

2.0 iE7 Fig. 3b Response Amplitudes of Relative BOw Motion in Regular

Waves from Different Directions (C,00.70)

05

I0

15 2.0 L7 0 N. 4 6 0 N

0.8 .0.6 0.4 0.2 0.8 0.6 0.4 0.2, 0 0 30 60

9.

1.20 150 180 e (DEG) 0.8 0.6 0.4 0.2 0:8 0.6 0.4, 0.2 0

Fig. 4 Standard Deviations of Relative Row Motion in Short-Crested irregular

Waves as Function of I-leading Angle (L lSOm)

0 (DEG) Cb=0J0, L= 15GM -. ..=0J.,0... GSEC

Fr.0.20

IOSEC . 6SEC

4.

I I i ) 30 60 90 120 150 1:8 CbO.6O., L= 150M Fr.= 0I .0 .. SEC -1 I

Fr.0.20

0.8 0.6 0.4 0.8 0.6 0.4 0.2-0=0° (HEAD SEAS) i6 0= 160° (FOLLOWING SEAS) 6 SEC to 18 4

/

4 SEC 0.05 0.10 0.15 0.20 0.25 Fr

Fig. 5 Standard Deviations of Relative Bow Motion in Short-Crested

Irregular Waves as Functions of Ship Speed (Ll5Om)

to =8 SEC 0. 8 0 rig 0 = 0° (H:EAD SEAS) -0.6 - t-4 0 '-3 (0 1

_"-'-3 0.2

- 4,!

-t lb 0. (p 0 0 0 = 180° (FOLLOWING SEAS) 0.8-0.6- 6 SEC

124 Jun-ichi FUKUDA

1.0

0.5

15 ao

VLJXe(Xe=ZT2)

Fig. 6 Standard Deviations of RelativeBow Notion in Short-Crested Irregular Head Waves as Functions of VL/Ae

C0.6O

----:

- . Fr.=0 =0.05 =010 -

0.l5

----j:

=0.20

----:. =0.25

Cb 0.70 0 =0.05 =0.10 0.I5 =0.20 . Fr.

-

_-:

-:

.9 5

I0

is

'L/A (Ae= 0

05

$ 0.

20

t2) 1.0 0.5 0

1.0 0 5 1.0 0.5 0.5 10 1.5 2.0

-

Xe(AeT2)

05

10 15

20

- I L /Ae (Ae T2)

Standard Deviations Of Relative Bow otion in Short-Crested Irregular Waves from--Different Directions as Functions of

tZ

_(Cb=O.6O) Cb=O.60 -. .Fr. 0:10 -e 00

----: =

_---U. 30

= 60

-

---:

--:

=90

=120 = 150 =180

/__.___

çbo.60

-

____.: e.:

00 Fr.=020

---:

- 60 -

=90

=120

----: =150

- _{- :} =180

ed

-

--,

--

-126 Jun-ichi FKUDA

10 15 2.0

iE7X( )e T2)

Fig. 7b Standard Deviations of Relative Bow Motion in Short-Crested Irregular Waves from Different Dirèctións as Functions OfrE7 _(CbO.7O)

Cb=0.70 Fr.'O.lO

:=

60 ---: = = 90 =120

---:

₌₁₅₀ =180 O0 -Cb0.70 -Fr=O.20 = :

--

=90

=120

- -:

----: =150

=180 O.Oo

/ E.

/ -

-/

7_

-.---2

0.5

[0

20

IL/Ae(Ae=rT2)

0

05

I .0 0.5 0 l.0 0.5 0

0.08

Fig. .8 Bow Freéboards According to the Con.fexence on Load Lines 1966 0.60 I - 0.02 0 I Cb= Cb= 0.70 I I OO 25 150 175 -200

LM

o

4

I I I

6 8 I 0 12 14 16 18

T (SEC)

Fig. 9 Significant Wave Heights of Short-Crested Irregular Head Waves,

Where the Expected Probability of Deck Wetness !!q! Will Be 1/10,

as Functions of Average Wave Period (L 150 rn)

Cb=0.T01 L=150M,0=0° IS Cb=O.60, L= I 50M, 000 I8 I I

0

--:

r.= 0,

'C- := 0. F 5

=0.05,

n----:

0.2O

= O.4O, v-- :

0.25

6 = 0° 180° =30,150 =60,120 =90 1 2 14 1,6 I8 T(SEC) 8 ₁₆ 0 14 I 12 I0 8 6 4 2 0 4 Cb= 0.60, L= l50M, Fr.0.20

0= OI80°

=30,150 =60,120 =90, 6 8

i0

12 14

Fig. ba Significant Wave Heights of Short-Crested Irregular Waves from

Differ-ent Directions, Where the Expected Probability of Deck Wetness "q" Will Be 1/O,as Functions of. Average Wave Period (Cb =0.60,, L = 150 m)

Cb=O.TO, L=150M, Fr.''0.I0 T(SEC) Cb=0.70, L= 150M, Fr.'0.20

".---

_;---0 0

9/

1 / /'s. / / .', / /

:0= O,8O0

30, 150 =60,120 =.90, I I / 6 8 10 12 1:4 16 lB T(SEC)

Fig. lOb Significant Wave Heights of Short-Crested Irregular Waves from Differ-ent Directions, Where the Expected Probability of Deck Wetness "q" Wi]

Be 1/10, as Functions of Average Wave Period (CbO.70, L 150m)

Q 4 04 = 0,l800 = 30,150 =60.120 =90, I I 6 8 I'O 12 14 16 8 18 16 0 '4

I

12 10 8 18 16 0 14 I 12 I0 8 6 2 04

- Wave Period (8cc) -Sue overAll Periods 5 7, .11 13 15 17 0.75 16.80 1 10.16 4.03 2.95 0.44 0.4934.87. 175 63.881125.831 61.64 1 21.28 1 2.29j O.4Oj 0.17 0.87 276.36 2.73 2165,128.61128.63 35.13 3.84 0.26 0.09 0.49 318.70 3.071 51.791 93.031 37.421 6.721 0.761 0.161 0.19 0.52 : 18.81 : 45.23 : 19.96 353 1.03 0.09 : 0.32 89.49 575 014k 489L'6871.1177L 238L 054: 009L 005 0.05 2.74 8.83. 8.13 2.62 0.49 0.10 0.03 22.99 6.75- - - .. 0.071 1.851 4.161 4.07 1.901 0.231 0.03 0.14. 12.45 8.75 0.02 0.91 1.68 2.99 2.17 0.14 0.09, 0.07 8.07 - - I 0.35. 1.01 1 1.36j_ 1.451 0.35 1 0.02 0.02 4.56 0.02 0.07 0.03 0.02 0.14 11.75 - 1 1 0.02 1 009 1 003 1 1 0.02 0.16 12.75 0.02 0.09 002.. 0.13 13.75 - 1 -1 1

j

0.03 1 0.05.1 O.O2J 0.02 0.12 14.75 - I I 0.09 0.09 15.75: 1. L Sum over All 106.20 345.96 367.13 145.24 27.52 4.38 0.88 269 1000.00 HcightS

Wave Period (sec)

-Sum overAll Periods -5 7 9 11 13 15 17 0.75 47.96 24.70 8.92 3.55 1.09. 0.11 0.04 146. 87.56 -1.75 139.66 1201921 90.08 1 20.64 1.2.30 1 0.44 1 0.11 1 1.40 .456.55 2.75 28.71 141.621109.33 19.46 .230 0.35 0.07 0.68 302.52 - 1 1 51.701 13.891 1.53 1 0.17 1 1 0.23 106.40 0.23 6.53 15.05 7.15 1.07 0.05: 0.23 30.31 O.04 _1.351 3.831 284 1 0.301 0.091 1 8.45 6.75- 0.05 , 0.72 : 1.77 1.23 0.47 : .0.11 , , 0.05 ,- - .- ,- - 4.40 775 017 °58L 067 005k 002L 002 002 153 875 11.75 10.75 0.02 , 0.09 : 0.58 0.60: 0.12 0.02 005: 007, 0l2 I . 0.04 , 0.02 0.05 0.02 _{1 1 1} 0.05 1 1 1 0.02 1.43 024 0.06 0.14 1275 : : 0.05: : : : : 0.05 1375 005 14.75- 1 1 1 -1. 1 1 1 15.75 -F 0.02k F I 1 1 0.02 -Sum

-over All 220.18 4i2.6 281.93 70.15 9.42 1.34 - 0.24 4.13 1000.00

Heights

-Table 2b Wave Frequency in the North Atlantic (According to Walden's Data)

Sumrer (for All Nine Weather Ships) (56,931 Obs.)

Table 2a Wave Frequency in the North Atlantic (According to Walden's Data)

132 Jun.ichi FOKUDA

Table 2c Wave Frequency in the North Atlantic

(According to Walden's Data)

Autu, (for All Nine Weather Ships) (57,34O Obs.)

-

-Wave Period (sec)

- _{over All}Sum

Periods -5 7 9 11 13 15 17 075 13 38 881 345 162 0 19 0 30 2775 1.75 57.721118.461 60.02 1 14.951 2.67 1 0.35 1 0.05 1 0.58 254.80 2 75 17 70 125 84 126 92 30 19 3 68 0 51 0 21 0 47 305 52 3.211 52.301107.961 36.201 6.14 1 1.011 0.14.1 0.26, 0.61 14.58 50.82 25.55 5.37 1.59 0.16 0.24 207.22 98.92 0.09 20.911 14.581 3.521 0.49L 0.171 0.09 -44.84 - 0.05 2.62 12.94 9.24 : 3:02 : 0.45 0.14 0.07 28.51 .2' - 6.75 - - - -0.03 1 0.941 6.05 1 5.22 2.01 1 0.42.1 0.03 1 0.03 14.73 8.75 0.52-: 3.40 4.1-3 1.57 0.54- 007 0.03 10.26 0.021 0.10: 1.811 2-.42 _{0.941 0.611 6.14:} 6.o2.- 6.06 10.75 - H 0.18 0.03: 0.05 0.02 - 0.28 11.75 - I I 0.05 1 0.14 1 0.21 1 0.05 L 1 0.45 1275 : 0.03 0.03: 0.191 0.19: 1 0.44 13:75 - L 1 0.03 1 0.07 1 0.02 [ 0.12 - : : 002 : 0.03 : 0.05 : 0.10 14.75- '- '- -- -15.75 - -

:--: : - : -Sum over All 92.81 328.77 394.56 144.52 30.08 6.06 1.11 2.09 1000.00 Heights -

-Wave Period (Cec)- _{over All}Sum Periods 5 7 9 11 13 15 17 075 600 403 210 099 021 014 018 1365 1.75 2950 1 41.40 1 13.06 L 2.63 1 0.18-1 0.09 1 0.21 166.84 2.75 16.84 108.86108.02 37.87: 5.36 0.77 0.05 0.52 278.29 3.30 577 1114.74 1 45.03 7.50 1 0.91 1 0.13 1 0.34 229.72 0.79 24.20 64.76 36.45 9.26 1.93 0.18: 0.23 137.80 0.21 632 1 26.31 1 22.45 1 6.05 1 1.07 1 0.18 1 0.04 62.64 0.11: 5.34: 15.53: 15.80-: 6.23.: 1.29: 0.05 0.07 45.42 6.75- ,- - - - .- -

-.

- -0.07 1 2.47 . 6.86 1 10.94 3.80 1 0.84 1 0.09 : 0.04 25.11 8 75 0.02 : 2.67 : 7.86 : 4.12 : 1.33 0.02 - 0.04 [ 20.41 9:75 1.61 [ -2.44 5.34 3.78 1.79 [ 0.61 0.14 15.7i 10.75 0.20 0.23 0.36 0.16 0.09: 1.04 11.75 - 1 0.021 0.131 0.071 0.431 0-18 1

--

- 1 .0.83 12 75 - 0.11 : 0.39 : 0.57 0.29

..

1.36 13:75 - L 0.07 1 1 0.23 [ 0.18 1 004 1 0.04 0.04 .0.60. 1475 : 0.07: : 0.05: 0.16: oil:- 0.04: 0.05 0.48-15:75 - -L . 0.05 0.10 Sum . -over All 56.84 293.31 386.84 197.82 50.64 11.03 1.57 1.95 1000.00 Heights .

-Table 2d Wave Frequency in the Nô±th Atlantic

(According to Walden's Data)

Table 3a Wave Frequency in the North Atlantic (According to Walden's Data)

3 8eaufort (fer.All.Nine.Waethel Ships) (26,285 Obs.)

- Wave Period (5cc) Sum

over All Periods 5 7 9 11 13 15 17 - 0.75 58.69 30.82 9.78 5.5S 1.41 0.11 0.04 1.03 107.43 175 147.53 1235.21.Ll18.54 35.91 L- L 0.91 0.11 L 133 545.47 275 15 26 0636 101 99 37 54 476 076 027 049 257 43 0.88 13.92 33.14 18.15 L 2.78 _{0.42 L 0.04L 0.23} 0 08 1 52 5 74 5 40 1 60 0 34 0 04 0 08 14 80 5.75 - - : 0.19 0.95 1.07 1 0.49 1 0.11 0.04 1 2.85 0.04 , 0_OS , 0.30, 0.84, 0.30 0.19 , 1.75 2' -6.75 - ,- ,. ,- -1 0.19 0.08 1 0.04 -- -0.04. 0.35 8.75 - '- 0.08 0.04 0.08 0.04 0.24 2 - - -: 0.04 1 0.04 1 0.08 10.75- . - -11.75 - -1 L I I I L 1 0.04 0.04 12.75 --- . - - - - -13.75- - - -14.75- - - - 15.75-Sum over All 222.48 378.10 270.56 104.73 17.43 2.88 ' 0.54 3.28 1000.00 Heights

Wave Period (sec)

-- - - _{over All}Sum

Periods 5 7 9 11 13 15 17 0.75 - 25.49 :.- 16.09 4.85 2.01 0.33 0.37 49.1.4 1.75 127.08 1225.85 1103.10 1 25.341 :293 1 0.26 I 0.09 1 1.31 485.96 2.75 20.94 137.83 129.68: 34.48 4.07 0.54 0.05 0.59 328.18 - 1.83 1 24.45 1 48.65 1 22.67 1 4.31 1 .0.56 1 0.05 0.23 102.75 0 23 3 54 11 15 7 21 2 15 0 35 0 09 24 72 5. 0.021 0.371 1.87 1 2.151 1.08 L 0.191 1 5.68 0.02 , 0.14 0.73 : 0.84 , 0.21 , 0.07 , 0.02 2.03 .c .2 6.75 -..

..-

- - ,- - --- 1 0.05 : 0.19 : 0.37 0.12 1 0.12 1 : 0.85 8.75 0.09 0.07 0.12 0.14 0.05 0.47 2 - 1 1 0.051 0021 1 0.16 10.75 - 0.02 0.02 0.04 11.75- 0021 1 1 . L L 1 002 12.75-- - - -13.75- -14.75- - ,- - - -15.75- - _-: -sum- -over All 175.63 40843 300.38 95.19 15.39 2.16 0.21 2.61 1000.00 Iteights

Table 3b Wave Frequency in the North Atlantic (According to Walden's Data)

134 _{6un-ichi FIJKtTDA}

Table 3d Wave Frequency in the North Atlantic

(According to Walden's Data)

6 BeauIor,t (for All Nine Weather Ships) (41,349 Cbs.)

- - Wave Period (Ccc) - - Sue

overAll Periods 5 7 9 11 13 15 --17 075 645 377 158 059 007 004 013 1263 1.73 73.271146.221 63.561 13.751 1.82 0.26 1 11_L 0.89 299.88 275 33.23.185.02164.26 37.32 3.99 0.43 0.13 0.67 425.05 3.27 50.79 1 94.321 32.901 1 0.65 1 0.151 C.20 187.63

-

0.33 9.12 25.02 14.92 3.14 0.56 0.04 0.17 53.30 1 1.171 4.681 5.411 1.471 0.111 0.021 12.86 .r 6.7$- 0.04 : 0.52:- 1.69:'.- 2.06 0.89 0.30 0.06: 5.56 - 1 0.091 0.561 0.56 0.41 1 0.071 1.69 8 75 0.09 0.22 0.32: 0.28 : 0.06 0.97 975 L L °°4L 007 °15L °11L 037 10.7$- -- - - .4-11.75- °°2L L L L L 0.02 12.7$- - - -13.75 - L I 1 0.02 _I - I 0.02 14.75.. . . . ',. - -15.75. - _{- -} -Sue over All 116.61 396.79 355.93 107.92' 17.59 2.59 0.51 2.06 1000.00 Heights

- Wave Pcriod (see)

-Sue ever All Periods 5 -7 9 11 13 15 17 0.75 0.85 L 0.94 0.63 0.24 0.07 .0.07 2.80 1.75 23.27 1 53.36 1 22.98 1 4.52 1 0.31 1 1 0.02 1 0.22 104.68 2 75 27 06 162 91 145 64 30 52 3 53 0 36 0 05 0 41 370 48 5.34 86.88 1165.84 1 51.07 1 6.67 0.87 0.17 1 0.31 317.15

-

0.73 24.18 66.55 31.91 5.97 1.38 0.10 0.41 131.23 0.101 4.961 17.22 1 15.86 1 3.60 1 0.48 1 0.10 1 0.02 42.34 .e 8.75 - 0.02 1.86- 6.41 7.38. 3.31.- 0.51 0.07, 0.65, 0.051 0.361 1.69 1 2.81 _{1.40 1 0.31 1} 0.05 0.02 19.61 6.69 8.75 0.02 0.46 0.89 .1.14 0.89 0.31 0.05: 0.02 -3.78 - 1 0.051 0.17 1 0.411 0.22 1 0.22 1 J 0.ó2 1.09 10.75 0.05 0.02 0.07 11.75 0.02 1 1 1 0.02 1 1 1 0.04 12.75: 13.75 -0.02 -, - - - - 0.02j 0.02 0.02 14.7$- '- - - --15.75- - - -Sue over All $7.46 335.96 428.07 145.86 26.01 4.46 0.62 1.55 1000.00 Heights

Table 3c Wave Frequency in the North Atlantic (According to Walden's Data)

Wave Period (sec-) Sum overAll Periods -5 7 - 9 11 13 15 17 0.75 0.24 0.44 0.67 0.16 1.51 175 2.75 68B 1415,

669, 146, 028

004, _012 15.81 82.59 78.32 17.95 2.49 0.24 0.08 0.51 2962 197.99 6.13 95.05 L164.26 53.24 _{9.02 L} 1.31 . 0.47. 329.48

-

1.42 43.31 120.76 5.4.03 9.68 2.61 0.24 ,O.36 232.41 0.24 _{12.89 L 49.16 L-3587 L} 7.08 _{1.03 L-°16 L} 0.12 106.55 0.08 7.40 22.26 21.55 6.73 1.15 0.04 0.08 59.29 . 6.75- - .- '-- 2.77 : 10.17 3.68 0.75 0.04 0.12 23.50 8.75 0.04 1.42 3.28 5.30 2.85 0.55 0.04 -1-3.48 - L 0.55 1.23 1.38 _ 1.70 0.55 0.16 5.57 10.75 0.12 0.12 0.24 11.75 - L -- L L 0.08 0.08 0.04 -- _ 0.20 12 75 - - 0.04 0.04 0.08 13.75 - . L 0.04 0.04-14.75- - -

.,-

- 0.04 - 0.04. 15.75-Sum -over All 30.84 260.57 452.72 201.27 43.75 8;31 0.60 1.94 1000.00 Heights

Wave Period (sec)

--

Sum

over All Periods 5 7 9 11 13 15 17 0.75 0.07: 0.63 0.42 0.28 1.40 1.75 1.26 4.21 2.25 0.98 L 0.14 L- 0,07 L 0.07 8.98 2.75 4.49 25.75 26.60 6.46 1.68 0.07 0.14: 0.49 65.68 4.63 L 57.40 94.87 36.14 L 6.95 L 1.26 _{0.35 L} 0.42 202.02 1.61 47.22 124.07 57.60 13.1.9 3.09 0.35 0.84 247.97 0.70 18.10 82.18 L 48.42 11.22 2.74 0.84 0.35 164.55 0 35 16 00 57 48 45 33 12 35 2 18 0 28 0 07 134 04 .c

6.75.

- ,. . - - - -0.42 1 .8.98 29.54 L 30.95 9.96 L 0.77 L 0.14 : 0.42 81.19 8.75 0.07 6.81 14.55 25.19 10.31 2.04 0.21 0.14 59.22 - .

L 39

6.18 L 9.62 : 6.74 L 2.53 0.63 : 0.07 29.56 10.75 0.14 0.35 0.42 0.35 0.28 1.54 11.75 - L 0.07 L 0.28 L .0.35 L- °77L 0.14 L : -- 1.61 12.75 0.21 0.35 0.63 1.19 13.75 - I I 1 0.28 1 0.28 1 0.07 1 0.63 14 75 : 0.07 0.14 : 0.07 0.07 0.35 15:75 I O07 -over All 13.60 189.32 438.67 262.44 74.71 15.31 3.01 2.94 1000.00 Heights

Table 3f Wave Frequency in the North Atlantic (According to Walden's Data)

8 Beaufo.r.t (for All Nine Weather Ships) (14,245 Cbs.)

Table 3e Wave Frequency in the North Atlantic (According to Walden's Data)

136 -Jun-ichi FUKUDA

Table 3g Wave Frequency in the North Atlantic (According to Walden's Data)

9 Beaufort (for All Nine Weather Ships) (4,014 Obs.)

Wave Period (sec) .Sua

over AU Periods 5 7 9 11 13 15 17 0.75 - . 0.25 0.25 0.25 0.25. 1.00. 1.75 0.75 L 1 1.74 0.251 1 - 1 1 4.23 2 75 - -1.74: 10.21 8.97 3.49 1.25 : 25.66 1.741 23.431 116.94 5.48 _0.501 1 87.71 0.75 29.91 : 75.25 41.37 : 15.20 8.22 : 0.75 : 0.25 171.70 1.00 17.95' 72.26 44.11 13.70 [ 4.24 0.25' 153.51. 19 69 74 75 59 05 23 93 3 49 0 75 0 50 182 16 .c -675 ,- - - - -' 12.21 48.34 49.84: 15.94 4.48 0.75; 0.50 132.06 8 75 0.25 11.71 33.64 49.09 : 24.92 : 10.71 0.50 0.25 131.07 7.72 : 18.19 1- 32.65 19.19 1 8.221 3.24 : 0.50 89.71 10.75 1.25: 2.74 0.50 0.25 5.24 11,75 - L L 0.50 1.741 1.74 1 0.751 1 4.73. 1275 075 025 199 274 075 648 0.75 P0.50 1.491 1 _{0.25 2.99} 13.75 - L L L L - L L _J_ 0.50 0.25 : 0.25 1.00 14.75- .- ,-15.75 - 0.75 _0.75 Sun

over All 6.23 136.57 374.26 303.02 128.82 41.86 6.74 25O 1000.00 Heights

- Wave Period (seb) - Sun

ovéi All Pefiods 5 7 9 11 13 15 17 0.75 --- . - -1.75 - 1 4.44 2.221 -1 - I - - I . 1 1.11 7.77 2;75 0.56 6.66 6.66 0.56 14.44 3.75 --- -1 43.87 e .-,s 0.56 18.88 38.31: 25.54, 9.99: I l2.77 50.521 31.091 13.331 11L 0.51 98.84 112.71 0.56: 17.77: 63.84: 48.8: 23.32: 6.66: 1.67: 0.56 163.23 .c 6.75- - ---.,- - -- 1 15.55: 56.07 1 50.52: 22.21 0.56: 0.56 151.03 875 : 12.77: 39.97: 59.96: 32.20: 4.44: 1.11 151.56 6 66 31 65 L 47 74 18 32 44 0 56 189 87 10 75 8.88 4.44 1. Ii 1.67 1.11 17.21 11:75 - I I 2.221 1.111 6.661 1671 : 11.66 12 75 : 0.56: 0.56: 8.33: 10.55: 0.56: : 20.56 13 75 L 0 56 78 2 78 0 56 0.56: 4.44: 1.67: 0.56 7 79 7.23 14.75- .- r - - -0.56' 1.11 0.56 2.23 Sum 6ve1 All 4.46 108.28' 316.4S318.l2 179.89 51.10 16.12 5.58 1000.00 Heights

Table 3h Wave Frequency in the North Atlantic (According to Walden's Data)

0 S

030

20

/

/

₀

//

__Q______ 110 ALL HEDINOS -,-9Q0 0 0 WINTER

:0-

0°

=30

-

=60

- 90

: =120 =150 =180 0 10 15 20 SHIP SPEED (KT) WINTER

:0=

0°

----: =60

=90

:=

---:

=150 --=180 000 0. - C - 0 1

--

----

Pc.

Fig. 11 Long-Term Probabilities of "Wet-Deck Navigation (q>l/lO)" on the

North Atlantic in Winter as Functions of Ship Speed (L= 150m)

to-. -U

--

-AjNGS

----

0 90 0 '0 I

-

In ) 5 10 15 20 SHIP SPEED (cT) 0 S. 0 30 20

V

40

CbO.6O, ALL HEADINGS

HEAD SEAS n. -I

-____+__._ SUMMER 100 150 200 L(M) I0

a

30 30 20 20 i0 Cb0.60, :ALL HEADINGS HEAD SEAS 301-4.'

_I'.

_SA' I .

20r

-k,5_"5 WINTER 'S 40 +5 _S..' .5 5'.'

.'.'

'S -S

-

-'S _{A 'S}

Fig. 12a Long-Term Probabilities of "Wet-Deck Navigation (q> 1/10)" on the North

Atlantic in Different Seasons as Functions of Ship Length (Cb0.60)

I-. (5)

00

SPRING 0: Owr AU TUMN 0: OKT

+: 5,

a: 10 40$'.'_{I' 'S} A: 10.

+: 5'

x :15 I 'S.'.' x :15 40 'S.' 3'' .'\S..' S..'_'.5 N 'S 20

_'N

200 L (N) 150 100

0 $

-

101 0 c 40 30 20

-

: HEAD SEAS SUMMER 20 I0

c_________

₀ 4OLc .. '----S -S -_'9'.__ HEAD SEAS WINTER

Fig. 12b Long-Term Probabilities of "Wet-Deck Navigation (q>l/lO)" on the North Atlantic in Different Seasons as Functions of Ship Length (Cb0.70)

40 30 SPRING ° 0i<T

+: 5

-

_,IO

x:15 -40 304\ AUTUMN o: OKT

+: 5

x :15 100 I50 200 L CM) 100 150 200 - L (N) 0

0 1 --4---

_---+

-k -q55

---I--- -100 150

Fig. 13 Long-Term Probabilities of "Wet-Deck Navigation (q> l/l0)1t on the

North Atlantic during All Seasons as Functions of Ship Length

200 L (N) 40 20-40 0 S.. 0 30 201-= 060, : ALL HEAD I NGS - ---HEAD SEAS Cb=0.70, :ALL HEADINGS HEAD SEAS ALL SEASONS OKT

+ ₅

L:I0 x:15

'k

ALL SEASONS 0: OKT

+: 5'

A_:10 x :15 'S \ io -S. 'f_._._ _{-_-x..} 0 l00 1150 200 L CM)

8 BEAUFORT :9= 00

--: =30

: =60

= 90

: =120

: =150 =180 00

_3__.

-.--=---1015 20 40 20 / 8 BEAUFORT :0= 00 = 30

-

=60

=90

- : =120

=150 =180 0=0°

---60° ALL HEADINGS 10 5 20

SHIP SPEED (1(T) - SHIP SPEED C,cT

Fig. 14 Long-Term Probabilities of 'TWet-Deck Navigation (q>l/lO)" on the North

Atlantic for Beaufort No 8 as Functions of Ship Speed (L=l5Om)

0 0 5 e0 0

a

40 20 / /

//

// / 80 0 S.. 0 60 LI HEADINGS 90°

-:ALL HEADINGS HEAD SEAS 100 8 BEAUFORT

80f.

60 b A +_

.?v .-.-

-.o-____ ----_ - _-r 20 ci 0 LQEAUF0RT

r.

0 --S ____

Fig. iSa Long-Term Probabilities of "Wet-Deck Navigation (ql/lO)" on the North Atlantic for Different Beaufort Numbers as Functions of Ship

Length (CbO.6O) OKI

+: 5

:IO :15 100 I 50 200 L (N) 100 150 200 L CM) Cb=0.60, :ALL HEADINGS :HEAD SEAS

80 60 6 BEAUFORT 40 0 - 80-0 10 BEAUEORT 80+----. -+ 40 I-20 HEAD SEAS 100 8 BEAUFORT ___-f___ 40L ----20,

Fig. 15b Long-Term Probabilities: of "Wet-Deck Navigation (q>l/l0)" on the

North Atlantic for Different Beaufort Numbers as Functions of Ship

Length (Cb=O.TO) HEAD SEAS too 4 BEAUFORT 0: OKT 80- +: 5 A tO 60 -40 100 200 L (N) 150 0 150 100 200 L (N)

too

7060 -50 40 30 20

-

tO-Cb=0.60, L=IOOM

0: OKI

-i-: 5

A:lO

x :15 U / 10 20 :ALL HEADINGS 161 30 40 50 60 70 WIND VEL (KT) 911101

I''

BFt

i90

080

70 -60 50 40 -30 20 10 II OKI

+: 5

A: 10 :15 10 20 30 40 50 60 70 - WIND VEL (KT) 161

Ill

181 191

Fig. lôa Long-Term Probabilities of '!Wet-Deck Navigation (q>l/l0)" on the

North Atlantic as Functions of Wind Force (L 100 m)

/ 1101

Ill'

BFT. 4 11 100 Cb 0.70, L lOOM 4 151

I 00 Q 70 60 50 40 30 20

I0

0 0 :ALL HEADINGS - _{HEAD SEAS} 0: OKT

+: 5

: 10

/

10 20 30 40 50 60 70 WIND VEL (KT) J8J 9 II I0I

Ill

BF 1. 100 90 0 80 70 60 50 40 30 20

-

10-0: _01cr

+: 5

x :15 0 0 10 20 30 40 50 60 70 - WIND VEL (KT) II 41151 ALL HEANINGS :HEAD SEAS

'TI

"/f

I,

II

I, , // _/f / _// II / II / II + d ,I I 1/ 1 / /

fi/

I // II _/ / II I II I II II _{/ /} II / / 1 / 181

Fig. 16b Long-Terni Probabilities of "Wet-Deck Navigation (q>l/1O)" on the

North Atlantic as Functions of Wind Force (L = 150 in)

1101

lilt

BFT 4

11 6

0

80 70 60 50 40 30 20

-

10-0: OK-I. + :. 5 A: 10 :15 ALL HEADINGS :HEAD SEAS 20 30 40 50 60 70 WIND VEL (KT) 6] 181_{I 9]}1101

III I

BFT.

0

8070 60 50 40 30 -20

I0-0: _OKT

+: 5.

A: 10 x :15 10 20 :ALL HEADINGS HEAD SEAS 18]I 9 1

Fig., 16c Long-Term Probabilities of "Wet-Deck Navigation (q>l/l0)" on. the

North Atla.ntjc as Functions of Wind Force (.L200m)

I

30 40 50 60 70 WIND VEL. (KT) 10]

liii

BF T. 100 Cb= 0.60, L=2OOM 100 Cb-0;70, L=200M 0 4 5] II

tI