Systematic Calculation of Freeboard

(1)

JIn,uaníschcr horb

Bundesministerium für Verkehr

- Progress Report No. 4

-Systematic Calculation of

Freeboard

FE Nr. 40306/94

Deift UrlvorsIty of Techncloy

S

_{Hyromecìanlcs}

_Laboraorj

Library

Mekeweg 2 - 2628 CD Deift

The Netherlands

(2)

-1-nnantcbcr 1tcqb

Progress Report Number 4

Systematic Calculation of Freeboard

by

Dr. -Ing. Hans Meier (expert in charge)

Dr.-Ing. C. Östergaard (project manager)

Abstract

This progress report is the continuation of the following interim reports: ,,Progress Report" [1],

,,Progress Report Number 2" [2] and ,,Progress Report Number 3" [3]. These previous reports described basic methods and the investigations of first principle calculation and related design

(regression) formulae of freeboard, applied to three master models, identified as F6, F7 and F8, under systematic variation of their principal dimensions [length, beam, draft] and their block coef-ficients CB. The 288 ships selected for freeboard calculations in [3] were geometrical variations of the FLOKSTRA - ship [2,3]. Decisive input parameters for freeboard calculations were the short

term exceedence probabilities of deck floodings, with the ships operating in those waves that

yielded the modal value of the long term probability density of relative motions. The applied long term wave statistics reflect North Atlantic mean weather conditions [4]. Hydrodynamic calcula-tians of relative motions, as shown in [2], were based on the PANEL method [1]. This report num-ber 4 deals with ship performances under extreme weather conditions.

1.

Ship Data

From the master ships F6, F7 and F8 [3], variation number 444, further on identified as ,,ship

444", with principal dimensions of [L B d ] = [282.31 m 32.6 m 10.87 m] was chosen for

the present investigations. Ship 444 has dimensions similar to the original FLOKSTRA ship,

namely

[L B d]

_{= [}270m 32.2m l0.85m]. Corresponding block coefficients were

C5 _{= {}0.6 0.7 0.8] for the three ships F6, F7 and F8 respectively.

The figure in Appendix C gives an impression of the lines of ship F6 with a freeboard of 2.854 m, a standard sheer and forecastle, as described in Table 5 of [3]. The figure shows 25 non-equidistant

stations, as the were used for nonlinear calculations with the computer program DYNBEL, see

Section 2. Lines of the two other ships F7 and F8 are transformations of the F6 lines, see Section 2 of [3]. The freeboard values of the F7 and F8 ships are 3.432 m and 3.21 m, respectively. Deck floodings of the three ships were calculated using these data. Table i in Appendix A gives a list of

(3)

-2-so defmed principal dimensions, freeboard values and, in addition, the wave parameters upon

which the freeboards calculations were based.

2. Nonlinear Analysis

AU calculations of relative motions previously reported in [1,2,3] were based on linear theories. On

using linear theory, the response operators (transfer functions) of relative motions provided the

necessary information for statistical evaluation. The transfer functions for ship motions and rela-tive motions at selected stations were calculated modeling the ship hull only up to the designed load waterline (DWL).

Normally, linear calculations of the ship response to waves are confined to light and moderate sea states, since nonlinear effects generally dominate the response in severe wave conditions. For rela-tive motions, in particular incident waves, the effect of the hull above DWL was thought to be sig-nifïcant. In particular, the effect of non-vertical sides between DWL and deck contour of the ship and time varying hydrodynamic coefficients were considered a major effect on the ship response in severe wave conditions.

For nonlinear calculations, a simulation program DYNBEL, originally developed by a Hamburg based consulting firm [5} for the calculation of wave loads, was used to estimate relative motions with respect to the undisturbed wave contours. Thus, the comparison with results from linear the-ory is limited to incident waves.

The program does not consider gravitational and dynamic loads of water on deck. Wave contours exceeding the deckline (deck floodings) are treated as if the ship side above the deck contour ex-tends indefinitely in vertical direction, thus preventing water from overflowing the deck, which would increase gravitational deck loads. Observing these conditions, DYNBEL could be used to validate or correct results of linear calculation by PANEL.

Ship parameters and wave spectra define the input data to DYNBEL. In the present investigation, statistics were based on 10 sample records of 20 min operation time, where each sample was ini-tialized at a random point in time. The simulated time records of relative motions were statistically evaluated using an event counting method, where the number of transitions from wet to dry were

recorded at virtual draft marks at the individual stations. Histograms of submergence of draft

marks were approximated by Weibull functions. The Weibull parameters provided by DYNBEL, separately for submergence and emergence (equivalent to positive and negative relative motions) served as input data for subsequent graphical presentation.

In the beginning, comparative runs of programs DYNBEL and PANEL for ship 444 at low speed

(F = 0.087) were confined to moderate wave conditions for the three block coefficients of

CB = [0.6 0.7 0.8]. Due to the particular limitations of DYNBEL, these calculations were con-fined to undeformed (incident) waves. As could be expected, they were found in good agreement, see Figure 1.

It was surprising to find that a second comparison for severe wave conditions yielded a similarly favorable agreement between DYNBEL and PANEL results. This made it necessary to verify the

nonlinearity in a specific test: For three wave to ship length ratios of X/Lbp_{= [ 0.8} 1.0

15] a

statistical evaluation of the absolute heave and pitch motions of the ship was carried out. The

(4)

-3-and 3.

The effect shows the

strongest influence of nonlinearity for

the wave length

X = 0.8 ship length, where the greatest wave steepness is associated with the greatest wave height of 16 meters. This result compares favorably with experiments of Yamamoto [6].

The good agreement between DYNBEL and PANEL results can possibly be explained as follows: Nonlinear effects on relative motions in a natural seaway, which is made up of many waves of dif-ferent wave frequencies (wave lengths), are small, because only a relatively small range of the

con-tinuous wave spectrum falls within the range of X 0.8 ship length to X = ship length, where

nonlinear effects are significant.

Nevertheless, even if the influence of nonlinearities is small with respect to motion amplitudes, it may be significant for the amplitudes of local and global loads, because load amplitudes are

pri-marily functions of acceleration and pressure amplitudes, which may be high if caused by non

harmonic motions due to the influence of bow and stem flare in high seas, compare the lines plan in Appendix C.

3. Variation of wave parameters

The results presented in Figures 5 to 16 were based on fixed parameter values of DF = [0, 2m]

p = [0.05, 0.1 ,

0.15] and F = [0.0, 0.087, 0.17,

0.25]. The diagrams of Figures 5 to 16

show plots of significant wave heights Ks against zero uperossing periods Tz for all possible pa-rameter combinations indicated in the systematic on top of page 4.

Each Tz, H5 parameter combination identifies a Pearson-Moskowitz wave spectrum. In Figures 5 to 16 the range of Tz, H5 combinations is limited by the survival envelopes [7]. Wave parameters outside the envelopes are extremely unlikely to be encountered. The dashed lines in Figures 5 to 16 identify operational envelopes [7]. Ships investigated in this project are expected to endure storms

associated with wave parameters below the operational envelopes intact and maneuverable and

without severe mechanical damages.

The range of wave parameters Tz 8.2 s 4 9.5 s, H5 = 5.2 m -> 6.1 in, defming the freeboards in this investigation, see [3], is given by the asterisk lines in Figures 5 to 16. This range was based on detRiled investigations described in [2, 3] of this project. In relation to all possible sea states it ap-pears to be so small that the use of, for instance T 9 5, H = 5.5 m can be considered applica-ble for any direct calculation of freeboard for ships similar to this category.

(5)

4. Results

Figure 4 is presented to explain the background for the understanding of Figures 5 to 16, which represent the results of the present investigations. Based on input data [CB, IJ, T J = [0.6, 10.3 m, 10.1 sI, Figure 4 shows the effect of deck floodings for exceedence

probabilities p = 2.5 % to 25 % in steps of 2.5 %. It can be seen that high deck floodings DF,

which occur with small probabilities p, are confmed to lengths position x near amidships and the forward perpendicular. Only these values are of further interest.

Plotting the maximum deck floodings DF of the top diagram in the Figure 4 for these two length positions of x = 120 m and x = 282.3 ,n (F P), against exceedence probabilities p, yields the bottom diagram of Figure 4. It reveals the highest deck floodings at the FP for probabilities smaller than 15 % and the highest deck floodings near amidships for probabilities greater than 15 %. It is obvi-ous that only the respective highest DF values are of interest for further evaluations.

4

Systematic of Parameter Variations for incident Waves

Systematic of Parameter Variations for Deformed Waves

A shift of the maximum DF position from one location to the other is the reason for the occurrence of directional discontinuities (knuckles) in the lines of constant Froude numbers F in Figures 5 to

C5= 0.6 0.7 0.8

r

_0.05

[Tz, Hs I DF = O

p= 0.1

Fig. 5 Fig. 6 Fig. 7

0.15

CB= 0.6 0.7 0.8

0.05

[Ti, H5] DF = O

p= 0.1

Fig. 11 Fig. 12 Fig. 13

0.15

_I

/

0.05

[Tz, Hs I DF=2m

p= 0.1

Fig. 8 Fig. 9 Fig. 10

0.15 _I

/

_0.05

[Tz, H5] DF=2m

p= 0.1

Fig. 14 Fig. 15 Fig. 16

(6)

5

16. Knuckle points are characterized by identical maximum deck floodings DF at the two length

positions. Maximum DF values at the FP are found right of the knuckle (high Tz values, long

waves), and maximum DF values near amidships are found left of the knuckle (low Tz values,

steep waves).

Both, ma_iimum deck flooding DF (wherever it may occur along the ship's length position x) and short term probability p of exceeding DF can be considered measures of the severity of the ship operation in waves. In Figures 5 to 16 each diagram describes a constant deck flooding severity defined by the two parameters DF and p.

All diagrams in Figures 5 to 16 are based on PANEL calculations, considering both, incident and deformed waves. DYNBEL results, in Figure 17, are given for comparative reasons only. Figure

17 shows a situation for deformed waves in three diagrams of C8 = { 0.6

0.7 0.8 _, and

F,, = 0.087, DF = 2 m, p = 15 % . PANEL not only needs less computation time but provides re-suits for both, incident wave and deformed wave responses. Applying PANEL results exclusively

was justified by the favorable comparison of DYNBEL results (nonlinear incident waves) with

PANEL (linear incident waves) results, not only for light and moderate waves, but also for severe wave conditions, see Figure 17.

Important results of this investigation are given by the four lines of constant Froude numbers F,, in Figures 5 to 16. This may best be explained with an example:

Consider ship 444 sailing with a speed corresponding to a Froude number of F,, = 0.25 in head seas, defined by spectral parameters [Tx, H5J ={7.4s, 8.5m}. This would mean a deck

flooding DF = 2 m, with an exceedence probability of p = 0.15 (point i in Figure 14). This

probability can be reduced by speed reduction. A probability of 10 % is, for instance,

reached for a speed corresponding to F, = 0.07 (point 2), and a further reduction to

F,, = 0.03 reduces the probability to 5 % (point 3). The deck flooding DF = 2 m takes place (in this case) somewhere near amidships.

Encountering longer waves (greater T values at approximately constant H5) at F,, = 0.25, shifts the maximum deck flooding to the FP position at Tz = 9 s (point 4), and, with further increasing wave lengths (greater Tz value), the same DF and p values are reached again at T = 13 s (point 5). If now the significant wave height H5 increases continuously at a con-stant T = 13 s, the speed needs to be reduced to keep the deck flooding at a concon-stant severity level until, finally, holding position at zero forward speed is reached (point 6).

It is understood that increasing wave heights lead to higher maximum deck floodings at given

probabilities p, or, which is equivalent, to higher probabilities at given maximum deck floodings of DF. With exceptions, the ship speed also needs to be reduced for increasing wave steepness. Thus,

diagrams 5 to 16 can also be interpreted as 'slow down' recommendations to the ship

nan-agement, conditioned on deck flooding.

This conclusion may be even better illustrated by Figure 18, where for ship 444, with a block

co-efficient of CB = 0.6 and constant parameters DF = 2 m and p = 0.15, the relative ship speed is plotted as a function of the wave height. The two diagrams are based on data from Figure 14

(deformed waves) and cause, due to the given range of zero uperossing periods from 10 s to 15 s, the maximum deck flooding DF = 2 m at the forward perpendicular FP.

(7)

-6-However, speed reduction cannot influence the deck flooding severity, given by DF and p values,

for certain extreme T, H5 conditions. For instance, in Figure 14, there is a subset of Tz, 11s

-values between the survival envelope and the curve signified by F = O (above point 6), where ei-ther DF increases for given p, or p increases for given DF with more severe Tz, H5 - value. This means that deck flooding severity increases with no possibility of nautical control in some identi-fied severe wave conditions (see Figure 5 to 16).

Hence, such conditions defme a set of Tz, H5 parameters where additional investigations into im-pact loads by water on deck deserve special consideration for unlimited safe ship operations.

Summary

Progress Report No. 4 was devoted to the investigation of suspected nonlinear effects on relative motions in severe weather conditions. However, the investigation with the DYNBEL program re-vealed only minor influences of the considered nonlinear effects, as was the case with the SOST program, applied in [1].

Both programs thus confirmed the applicability of a linear motion analysis method also for survival

conditions. For this, the Germanischer Uoyd PANEL method was used because of its ability to

defme relative motion with respect to deformed waves contours, which were found to be most Sig-nificant at the extreme bow region.

B ased on evaluations of ship in severe and extreme wave conditions, the influence of ship speed on deck flooding at given exceedence probability or, visa versa, on exceedence probability at given deck flooding, was investigated. Indications of nautical measures to keep the deck flooding

constant if wave conditions become more unfavorable were derived. The results also revealed

limitations of such nautical measures. It remains to draw attention to the fact that maximum deck floodings at the forward perpendicular indicate a greater danger for ships than similar deck flood-ings near amidships.

Discussion

Calculation of relative motions with the nonlinear program DYNBEL were confmed to incident waves. The results compared favorably with results of linear PANEL calculations, even for high and steep waves, see Figure 17. Thus, they permit reliable applications of PANEL investigations also for severe wave conditions. However, the substitution of a nonlinear approach by the linear one is justified for ships motions without considering water on deck influences. Therefor, some uncertainties still remain with respect to extreme wave conditions, where the consideration on im-pact loads by dynamic effects of green water on deck should be considered relevant also for fmal decisions on freeboard. In addition, there are still other factors that influence freeboard. They are

systematically treated in [81, and reference to this publication may finally lead to conclusions

(8)

7. References

[1] Germanischer Lloyd, Bundesministerium für Verkehr: Systematic calculations of

Freeboard, Progress Report, FE Nr. 40306/94, 17.MAR.95, 16 pages and Annexes.

[21 Germanischer Lloyd, Bundesministerium für Verkehr: Systematic calculations of

Freeboard, Progress Report Number 2, FE Nr. 40306/94, 1 8.JTJL.95, 14 pages and

Annexes.

Germanischer Lloyd, Bundesministerium für Verkehr: Systematic calculations of

Freeboard, Progress Report Number 3, FE Nr. 40306/94, 29.SEP.95, 10 pages and

Annexes.

N. Hogben, N.M.C. Dacunha G.F. Oliver: Global Wave Statistics, British

Mari-time Technology, Feitham, Middlesex, England, 1985, 661 pages

MTG Marinetechnik GmbH: DYNRES, Computer Code for the Calculation of

Nonlinear Ship Motions and Hull Girder Loads in Irregular Seas, Status June 1994, 73 pages, unpublished.

Yamamoto, Y. et aL: Nonlinear Effects for Ship Motion in Heavy Seas,

Interna-tional Shipbuilding Progress, Vol. 29, 1982.

William H. Buckley: Design Wave Climates for the World Wide Operation of

Ships, Part II: Naval Architecture Application, unpublished report, Oktober 1993.

P.

Ahuan, W.A.

Cleary, Jr.,

M.G. Dyer,

J.R.

Paulling, N.

Salvesen:

The international Load Line Convention: Crossroad to the Future, Marine Technol-ogy, October 1992, pages 233-249.

9. Appendices

Appendix A,l: Table 1

Appendix B,1 - B,17:

Figures 1 - 18

Appendix C Lines Plan

7

(9)

Table 1, Data of analysed U444U ships

Appendix A, i

subdivisions for PANEL calculations: 42 stations non-equidist. subdivisions for DYNBEL calculations: 25 stations non-equidist.

"444' identifies

LBd =

100,000 m3 B =

3d

L

15,/Bd

ident. F6 F7 F8 Lmax 299.04 m 294.45 m 289.96 m Lbp 282.31 m B 32.6 m d 10.87 m D 13.724 m 14.302 m 14.08 m Cb 0.6 0.7 0.8 Dispi. 61500 Mg 71750 Mg 82000 Mg modal Hs 5.42 n 5.46 n 5.5 m modal Tz 8.61 s 8.67 s 8.74 s Fr.board 2.854 n 3.432 in 3.21 m Fr.b./D 0.208 0.24 0.228 Fr.b./d 0.263 0.316 0.295

(10)

16 14 12 10 Cb = 0.8 lis = )ni i modal conditions Tz=8.74s J

prob. = 0,1 incid. waves

DYNBEL

\

50 100 150 200 def. waves DYNBEL

/

PANEL 250 PANEL 300 50 100 150 200 250 300

Length coordinate x Lmi

. I 50 100 150 200 250 300 PANEL

Fibure i Comparison of DYNBEL and PANEL results,

applying moderate waves and different

block coefficients Cb

16

Ship '444" in head seas, Fn = 0.087

14 Cb = 0.7 Hs = 5.46 m Tz = 8.67 prob. 'n 0.1 s modal conditions "j 10 'n (j o 8 incid. waves df. waves (j (-j 6 DYNBEL '-j 16 Ship "444" in head seas, Fn = 0.087 14 12 Us = 5.42 Tz= 8.61 prob. = 0.15 Cb = 0.6 m s modal conditions 10 -incid. aves ef. waves

Length coordinate x [ni]

(11)

0 0.5 1 1.5 2 2.5 3 3.5 4 n

from wave height H = 2"n meter

0.4 0.3 0.2 0.1

O

-0.1 -0.2

heave statistic for wave length = ship length

Fn = 0.15 mean of minima mean value extreme maxima mean of maxima extreme minima -0.3 -0.4 0 0.5 1 1.5 2 2.5 3 3.5 4

n from wave height H = 2A0 meter

Fibure 2 Check of nonlinear effect on non-dimensional

heave statistics from DYNBEL results,

for wave heights from i m to 16 m.

for wave length = 0.8

O heave statistic * ship length 0.4 0.3 0.2 0.1 _-0.1 _-0.2 _-0.3 _-0.4 Fn =0 15 mean of mean of maxima minima mean extreme value minima extreme Thtd div. maxima o 0.5 1 1.5 heave statistic 2 2.5 3 3.5 4 * ship length O

for wave length = 1.5

0.4 Fu = 0.! 5 extreme maxima 0.3 0.2 0.1 _-0.1 _-0.2 _-0.3 _-0.4 mea mean of minima of maxima mCan extreme value minima __sld,, djv.

(12)

o -0.1 -0.2 -0.3 -0.4 for length = 0.8 * length pitch statistic wave ship

n from wave height H = 2An meter

mean of minima mean value extreme minima 0 0.5 1.5 2 2.5 3 3.5 4 0.4 0.3 0.2 0.1 O _-0.1 _-0.2 -0.3 -0.4

pitch statistic for wave length = ship length

n from wave height H 2An meter

Fibure 3 Check of nonlinear effect on non-dimensional

pitch statistics from DYNI3EL results,

for wave heights from I m to 16 m.

s s

0.4 0.3 0.2 0.1 O _-0.1 -0.2 -0.3 _-0.4 Fn = 0.15 mean of _{mean of} maxima minima mean extreme extreme max value minima ima o 0.5 1.5 2 2.5 3 3.5 4

pitch statistic for wavelength = 1.5 * ship length

0.4 extreme maxima 0.3 0.2 0.1 Fn = O mean 15 f maxima std. d'v. extreme maxima mean of maxima std. div. Fn= O 15 mean value mean of minima extreme minima O 0.5 :' 1.5 2 2.5 3 3.5 4

(13)

18 16 14 12 10 Cb = 0.6

Ship "444" in head seas, Fn 0.087, deformed waves

prob. = 12.5 %

prob.=25 %

deck flooding at x = 120 m

delta(prob.) = 2.5 %

prob. = 2.5 %

"deck flooding at fwd. perpendicular

Appendix B, 4

0.05 0.1 0.15 0.2 0.25

prob. = short term probability of exceedence

Figure 4 Maximum deck flooding DF, wherever it may occur, as a function of short term probability of exceedence p. DF = DF(p I [Tz,H ,F,_II)

0 50 100 150 200 250 300 Length coordinate x [mJ m s Hs = 10.3 Tz = 10.1

(14)

18 16 14 12 10 8 6 4 2 Cb = 0.6 prob. 0.05 deckfl. O Cb = 0.6 prob. 0.15

Ship "444" in head seas, incident waves

Zero uperossing period Tz [s]

2 4 6 8 10 12

14 16 18 18 16 14 12 5 lo (1 8 e "3 o 6 g:0 4 2 o o

Ship '444" in head seas, incident waves

Fibure 5 Wave configurations, defined by [Tz, Hs], for 4

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb

0.6 18 16 14 2 4 6 8 10 12 16 18 10 12 14 6 4 2

(15)

18 16 14 12 lo 18 16 14 12 lo

Ship"444" in head seas, incident waves

Cb = 0.7 prob. 0.05 deckfl. O Cb = 0.7 prob. 0.15 deckfl. = O

lO

12

Zero uperossing period Tz [si

18

()

16-Ship '444' in head seas, incident waves

2 4 6 8 10 12

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb

0.7 E 14-Cb = 0.7 prob.O.1 _{deckfl. = O} 12 10 4) > '4 8 Q 6 14 16 18 2 10 12 14 16 18 4 6 18 16 14

(16)

18 16 14 12 10 8 6 4 2 0

o

18 16 14 12 10

Ship "444' in head seas, incident waves

Cb = 0.8

prob.

0.05

dcckfl.

o

10

12

18 16 14 12 10

Ship "444" in head seas, incident waves

Fibure 7 Wave configurations, defined by [Tz, Hs}, for 4

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb = 0.8

16 2 4 6 10 12 14 18 2 4 8 10 12 14 16 18 2 4 6 14 16 18

(17)

18 16 14 4 2 O O 2 4 6 8 10 12

Cb = 0.6 prob. 0.15 deckfl. 2 m 2 4 6 8 10 12

14 16 18 18 16 4 2 Cb = 0.6 14-prob.0.1 _deckfL2m O O 4 6 8 10 12

Fibure 8 Wave configurations, defined by [Tz, HsJ, for 4

Froude numbers Vn, at a given maximum deck flooding DF = 2m and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb

0.6 18 16 Cb = 0.6 14 prob. 0.05 deckf1.2m 12 bi) 10 18 14 16 16 18 14 Ship '444"

in head seas, incident w)ves

Ship "444" in

(18)

18 16 14 12 10 4 2 o o Cb = 0.7 -prob. 0.05 deckfl.=2m 17 0.25 2 4 6 8 10 12

14

16

18

18 16 14 12 10

Cb = 0.7

prob.irO.1 _deckfl.a2m Fibure 9 Wave configurations, defined by [Tz, Hs], for 4

Froude numbers Fn, at a given maximum deck flooding DF = 2m and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb

0.7 18 16 Cb = 0.7 14 prob. 0.15 E deckfl.=2m 12 2 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18

Ship "444" in hèad seas, incident waves

Ship '444

in head seas, incident waves

(19)

18 16 14 12 10 18 16 14 E 12 rfj 10 4 2 O O Cb = 0.8 prob. 0.05 deckfl. 2 m

Ship '444" in head s&, incident waves

2 4 6 8 10 12 Cb = 0.8 prob.=0.15 deckfl. 2 in

14 16 18 18 16 14 E 12 10 4 2 O O

Ship '444' in head seas, incident waves

Cb = 0.8

prob.

0.1

deckft=2m

2

Fibure 10 Wave configurations, defined by [Tz, Fis], for 4

Froude numbers Fn, at a given maximum deck flooding DF = 2m and 3 short term probabilities of exceedence p, using incident waves. Block coefficient Cb = 0.8

2 4 6 10 12 14 16 18 16 18 8 10 12 14

(20)

18 16 14 12 10 18 16 14 12 10 8 6 4 2 o o Cb = 0.6 prob. 0.05 dcckfl. = O

18 16- 12 10

Fibure 11 Wave configurations, defmed by [Tz, Hs], for 4

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using deformed waves, Block coefficient Cb = 0.6

Cb = 0.6 prob. 0.1 deckfl. O 14 14 16 18 6 8 10 12 2 4 6 8 10 12 16 18 14 Ship '444

in head seas, deformed waves

Ship '444" in head seas, deformed waves

14 2 8 10 12 16 4 18

(21)

18 16 14 12 lo 18 16 14 12 lo 8 6 4 2 o o Cb 0.7 prob. 0.05 deckfL=O

Ship "444" in head seas, deformed waves

Cb = 0.7

prob.0.l5 _deckll.

O

10

12

Cb = 0.7

prob.9.1 _deckfl.

O

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using deformed waves. Block coefficient Cb = 0.7

2 6 4 14 16 18 4 6 10 12 14 16 18

(22)

18 16 14 12 10 18 16 14 12 10 Cb = 0.8 prob. 0.05 deckfl. O Cb = 0.8 prob. 0.15 deckfl.0 2 4

Ship 444 in head seas, deformed waves

6

8

10

Zero uperossing period Ti [si

12 14 16 18 18 16-Cb = 0.8 14-prob 0.1 deckfl.=0 12- 10 Ship "444

in head seas, deformed waves

Zero uperossing period Ti [s]

Fibure 13 Wave configurations, defined by [Tz, Hs}, for 4

Froude numbers Fn, at a given maximum deck flooding DF = O and 3 short term probabilities of exceedence p, using deformed waves. Block coefficient Cb = 0.8

18 14 16 2 4 6 8 10 12 2 4 6 10 12 14 16 18

(23)

18 16 14 12 10 Cb = 0.6 prob. 0.15 deckfl. 2 m

2 4 6 8 10 12

Fibure 14 Wave configurations, defined by [Tz, Ils], for 4

Froude numbers Fn, at a given maximum deck flooding DF 2m and 3 short term probabilities of exceedence p, using deformed waves. Block coefficient Cb = 0.6 For points (1) to (6) see Section 4.

18 16 Cb = 0.6 14 prob. 0.1 E deckfl. 2 in 12 10 18 16 Cb 0.6 14 prob. 0.05 E deckil. Ir2m 12 10 2 4 6 8 10 12 14 16 18

Zero upCrossing period Tz [s]

18 14 16 14 16 18 2 4 6 8 10 12

(24)

18 16 12 10 8 6 4 2

Zero uperossing period Tz [s] Zero uperossing period Tz s]

18 16 14 12 10

Cb = 0.7

prob.=0.1

deckfl. = 2 m

Fibure 15 Wave configurations, defined by [Tz, HsJ, for 4

Froude numbers Fn, at a given maximum deck flooding DF 2m and 3 short term probabilities of exceedence p, using deformed waves. Block coefficient Cb = 0.7

Cb = 0.7 prob. 0.05 deckfl.2rn 14 0 O 2 4 6 10 12 14 16 18 18 16 10 12 14 6 4 2

(25)

18 16 14 12 10 18 16 14 12 10 8 6 4 2 o Cb = 0.8 prob. 0.05 deckf1.2m Cb = 0.8 prob. 0.15 deckfl. 2 m

18 16 14 12 10

-Cb = 0.8

prob.

0.1

deckfl.=2m

Froude numbers Fn, at a given maximum deck flooding DF = 2m and 3 short term probabilities of exceedence p, using deformed waves. Block coefficient Cb

0.8 2 4 6 8 10 12 14 16 18

6 8 10 12 14 16 18 4 6 10 12 14 16 18

- Ship "444' in head seas, deformed waves

(26)

16 14 12 10 Cb = 0.8 Hs = 13.1 _{Tz= 12.7}

ineid. waves _{incid. waves}

prob.= 0.15

deckfl. = 2 m for def. waves

;.t_

-:L.,, S.. ;5_ DYNBEL DYNBEL def. -aves PANEL.. PANEL 50 100 150 200 250 300 Length coordinate x [m] meld. waves DYNBEL S, ANEL 50 100 150 200 250 300 -0 50 100 150 200 250 300

Length coordinate x [ni]

Length coordinate x ml

Fibure 17 Maximum wave contours for knuckle'

configu-rations of the Fn=rO.087 lines in Figures 14, 15 and 16, at a given maximum deck flooding DF = 2m for a short term probability of exceedence p = 0.15, using deformed waves. Cb

0.6 Ship 444 in head seas, Fn = 0.087 16 14 12 10 , i Us = 11.2 Tz= 10.7 prob. = 0.15 _{deckfl. =2} ni Cb = 0.7

m s for def. waves

def. wav

Ship 444" in head seas, Fn

0.087 16 14 12 Cb = 0.6 Hs= 10.3 Tz= 10.1 prob. 0.15 ni s 10

deckfl. = 2 ni for def. waves

def. waves

(27)

17 16 15 14 13 12 11 10 9 8 i 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Vmax = 13.15 rn/s corresponding to

Cb=0.6, DF=2m, p=0.lS

significant wave height Hs [m]

Figure 18 Example of speed reduction due to increasing wave heights for different zero

Appendix B, 18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 i

relative ship speed V / Vmax

O 16 17 15 12 13 14 10 11 8 9

(28)

Appendix C

Lines plan of ship 444