Joint Development of a Bow Height Formula by China and The Netherlands Based on Probabilistic Deck Wetness Analysis

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Joint Development of a Bow Height Formula

by China and the Netherlands

Based on Probabilistic Deck Wetness Analysis

by:

J.M.J. Journée 1),Zhu Yonge2), J.O. de Kat3) and H. Vermeer4)

Report No. 1270-P, DUT July 2001

Delft University of Technology, DUT

Shanghai Rules and Research Instititc, SRRI Maritime Research Institute Netherlands, MARIN Directorate General of Freight Transport, DGG

Prepared for: 1MO / SLF, Load Line Working Group,

September 2001 Meeting, London, U.K.

Commissioned by: Directoraat-Generaal Goederenvervoer,

P.O. Box 5817, 2280 HV Rijswijk. (Public Release)

Last revision: 06-07-2001

1 ¡J D E LFT

Faculty of Mechanical Engineering and Marine Technology

Ship Hydromechanics Laboratory Deift University of Technology

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Summary

On behalf of the "Sub-Committee on Stability and Load Lines and on Fishing Vessels Safety" of the "International Maritime Organization" studies, related to a revision of the technical regulations of the 1966 International Convention on Load Lines, have been carried in several countries. This joint study of China and the Netherlands concentrates

on bow heights.

Bow height calculations have been carried out in China for the "standard slender ship

form" with Ch (d) = 0.65 and Cb (di,) = 0.68, and the "standard full bodied ship form" with

Ch (d) = 0.80 and other 336 different ship forms linear scaling of length, breadth and draught of 13 parent ship fornis covering a wide range of slenderness parameters. In term

of polynomial form:

F

F(L/l00).G(Cb,Cbf,CW,C,L/d)

bow height formulas have been obtained from regression analyses for data calculated joint probability criteria on deck wetness at bow in the Winter North Atlantic of these

ship forms.

Bow height calculations have been carried out in the Netherlands for the "standard" 1966

ICLL Vermeer parent ship (Cb 0.68 at d = 0.85 D), 13 other parent ships (covering a

wide range of slenderness parameters) and a parent rectangular pontoon. Linear scaling of length, breadth and draught of these 15 parent hull forms resulted in 1980 different ships. Bow height formulas have been obtained from calculated long-term probabilities on bow deck wetness in the Winter North Atlantic of these ships, using a similar polynomial form

as proposed by China.

Finally, the results of both individual studies have been combined in a jointly proposed

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i

Introduction

5

2

Parent Hull Forms and ICLL 1966 Regulations

7

3

Probabilistic Method of China

11

3.1 Ships and Environment 11

3.2 Probabilistic Approach 13

3.3 Probabilistic Calculations 14

3.4 Bow Height Polynomials 15

3.4.1 Formula Based onDraughtd 16

3.4.2 Formula Based on Draught d1 17

4

Probabilistic Method of the Netherlands

19

4.1 Ships and Environment 19

4.2 Probabilistic Approach 21

4.3 Probabilistic Calculations 22

4.4 Bow Height Polynomials 24

4.4.1 Formula Based on Draught d 26

4.4.2 Formula Based on Draught d1 27

5

Joint Formulas of China and the Netherlands

29

5.1 Joint Formula Based on Draught d 29

5.2 Joint Formula Based on Draught d1 30

5.3 Comparison of Joint Formulas with 1966 ICLL Regulations 30

5.4 Comparison of Joint Formulas with Bow Heights of Existing Ships 38

6

Conclusions and Recommendations

41

7

References

43

8

Appendix A: Figures with Detailed Data of China

47

9

Appendix B: Figures with Detailed Data of the Netherlands

67

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i

Introduction

On behalf of the "Sub-Committee on Stability and Load Lines and on Fishing Vessels Safety' (SLF)" of the "International Maritime Organization (1MO)" studies, related to a revision of the technical regulations of the 1966 International Convention on Load Lines (1966 ICLL), are carried in several countries. The results of these studies were presented and discussed at Technical Progress Meetings, held at Wageningen in 1996, Shanghai in 1997, London in 1998, Gdansk in 1998, Washington in 2000, London in 2000 and

Alameda in 2001.

The contributions of China to this study have been given in technical reports of China Classification Society (CCS) and China Ship Scientific Research Center (CSSRC) by Zhu Yonge, Chen Guoquan, Zhou Zhengquan, Lu Deming and Zhang Gaofeng (1996, 1997,

1998, 2000 and 2001).

The Dutch contributions to this study have been given in technical reports by Journée, de Kat and Vermeer (1997a, 1997b, 1998, 2000a, 2000b, 2000c and 2001), obtainable from

web site hap ://shipmotions. nl or hap :Ildutw 189. wbmt.tudelft. nl/--johan.

This joint report of China and the Netherlands concentrates on bow height regulations

and probabilistic calculations on required minimum bow heights.

In the contributions of China to this study, a new program named JPCM-FBS of CCS was developed for reviewing freeboards of 1966 ICLL based on the linear strip-theory ship motion computer program SHIPMOTION. The results of vertical relative motions of this program were compared with other Members' results of research in LL Working Group of SLF Sub-Committee of 1MO and verified with data of seakeeping model test of

Flokstra ship carried out at CSSRC by Zhou, Zhou and Xie in 1996.

In the Dutch contributions to this study, the linear strip-theory ship motions computer program SEAWAY of the Delfi University of Technology was a basis for the creation of a new program, named SEAWAY-R. This program compares the results of research on load lines carried out in Japan, Germany, China and the Netherlands, respectively. Also, the rules of the 1966 International Convention on Load Lines (1966 ICLL) have been incorporated in this program. Journée (1997) has verified the program with experimental data on vertical relative motions of a Dutch container vessel, as determined by Zhou, Zhou and Xie (1996) in China.

Use has been made of the standard 1966 ICLL Vermeer ship, 13 parent ships made available by the Shanghai Rules and Research Institute in China and a rectangular pontoon. Linear scaling of length, breadth and draught of these 15 parent hull forms resulted in 1980 different ships, varying in length from 24 to 500 meters and sailing in head irregular seas defined by the Winter North Atlantic wave climate. Average length-depending long-term probabilities on deck wetness of the standard ICLL Vermeer ships

(Cb

0.68 at d

0.85.D), fulfilling the 1966 ICLL bow height regulations, have been

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other ship to calculate its bow height. Finally, a regression analysis has been used to obtain bow height formulas, taking some geometry parameters of the ship's hull form

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2

Parent Hull Forms and ICLL 1966 Regulations

Based on Vosser's study, it is clear that the influence of forebody section shape on the ship's behaviour in a seaway is great.

The following expression could be better to represent the U/V degree of section shape of the forebody for conventional ships:

n

85.7 C - 75.6 Cbf 9.0

where Cf and Cbj- are the water plane coefficient and block coefficient of the forebody at

the draught d. In absence of data for Cf and Cbf, the following approximate formulas

may be used:

= C+2.1 LcF

and Cbf = Ch + 2.1 LGB

Where C and Cb are the water plane area coefficient and block coefficient at the draught d, and LCF and LCB are the longitudinal centers of flotation and buoyancy forward of amidships at the draught din ratio of the length positive if forward of amidships and

negative if abaft of amidships.

The Shanghai Rules and Research Institute have 13 parent ships been made available. Offsets of these Chinese parent hull forms, those of the standard 1966 ICLL Vermeer

ship (with block coefficient 0.68 at a draught equal to 85 % of the depth) and a

rectangular pontoon have been used here.

For making the systematic calculations of bow heights, 13 parent ships were designed as

follows: Group A (5 ships): Ship Al and A2 Ship A3 and A4 Ship A5 Group B (8 ships): Ship Bl and B2 Ship B3 and B4 Ship B5 and B6 Ship B7 and B8

with Ch = 0.7, extreme U and extreme V

with C, 0.8, extreme U and extreme V

with Cb 0.9, extreme U

with Ch = 0.55, extreme U and extreme V with Ch = 0.65, extreme U and extreme V with Cb = 0.75, extreme U and extreme V with Ch = 0.85, extreme U and extreme V

The body plans of these parent hull forms are given in Figure 1. These ships cover a wide range of combinations of U and V shapes of the fore body and of block coefficients, Cb, as given in Figure 2.

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tIIIIL &W

_JJ U

V A wur

u.

&rva

w _JJi

w

viirni &w a

UIJ L!

Vermeer Ship Rectangular Pontoon

Figure 1 Body Plans of 15 Parent Hull Forms

AI Ship A2 Ship A3 Ship

A4 Ship A5 Ship

BI Ship B2 Ship B3 Ship

B4 Ship 85 Ship B6 Ship

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20 15 10 82 V-form B4 s A2 Vermeer' U Ship B6 A4 A3

.

B8 B7 A5 Rectangular Pontoon D 0.5 0.6 0.7 0.8 0.9 1.0 Block Coefficient Cb

Figure 2 U-v Parameters of 15 Parent Hull Forms

The required minimum bow height is given in Paragraph (1) of Regulation 39 of the

International Convention on Load Lines, 1966 as:

The minimum bow height,

defined as the vertical distance at the forward perpendicular between the waterline corresponding to the assigned summer freeboard and the designed trim and the top of the exposed deck at the side, shall not be less

than:

for ships below 250 meters in length:

Hb=0.056.L.1

L 1.36 meter

500) Cb+O.68

for ships of 250 meters and above in length: 1.36

Hh 7.0 meter

Cb + 0.68 where: L is the length of the ship in meters,

b is the block coefficient, which is to be taken as not less than 0.68 and

Hh as defined in Figure 3.

83 _Al _B5

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Depth D

Draft d

J

093

Freeboard Hd

Figure 3 Definition of Bow Height

For a "standard" 1966-ICLL ship (C8 = 0.68), called here the Vermeer ship, the ship

length dependency of the bow height is visualized in Figure 4.

8

7

50 100 150 200 250 Ship length L0850 (m)

Figure 4 Length Dependency of Required Minimum Bow Height of Standard Ship

300 350

Bow height Hb

waterline

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3

Probabilistic Method of China

This Chapter describes the probabilistic method, used by China, for determining the

required minimum bow heights of ships exceeding 24 meters in length. 3.1

Ships and Environment

Each of 5 parent ships of Group A has been transformed linearly to 16 ships with

parameters as follows:

L/T= L/B *B/T 6x250, 6x2.75, 6x325, 6x400

and

Lpp8Om, 150 m, 250 m, 350m

Each of 8 parent ships of Group B has been transformed linearly to 32 ships with

parameters as follows:

L/T= L/B *B/7'= 7x250, 7x2.75, 7x3.25, 7x400

and

= 24 m, 50 m, 75 m, 100 m, 150 m, 200 m, 300 m, 400 m

Using 13 parent ships 336 ship forms were resulted.

In addition, a "standard slender ship form" with Lpp = 150 m, Cb = 0.65, and n 6.6

(middle V shape) and a "standard full bodied ship form" with = 200 m, Cb = 0.80, and n = 2.1 (U shape) were designed for check and regression of data of bow height of

336 ships above.

12 ships from the "standard slender ship form" were resulted:

L/B= 5.5, 6.5,7.5, 8.5

and

B/T= 2,50, 2.75, 3.00

12 ships from the "standard full bodied ship form" were resulted:

= 5.0, 5.5, 6.0, 6.5

and

B/T= 2.50, 3.00, 3.50

For making the systematic calculation of bow height, the details of process are given as

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Wave Direction of Head Seas

Speed Corresponding to Fn = 0.1 Linear Strip Theory for

ITTC Wave Spectrum with Calculation

Two Parameters of Relative

Motions

North Atlantic Winter Wave

Statistics (Zone of No. 8,9,15,16) and

Probability Criteria Ps-Pc Joint

Pc=0.015, Ps0.4 Probability

Criteria

Hull Form Method

Height of Green Water above Deck: Hw = O m

Static Swell-up of Tasaki Formula No dynamic swell-up

Head irregular long-crested waves

Bow Height

where the wave statistics of North Atlantic Winter were obtained from combination of wave data of zones of No. 8, 9, 15, and 16 ( N. Hogben, 1986 ) as follows:

SUM = 100000 H113(m) Tz (s) 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 12.5

0000 0000 0000 0000 0000 0025 0050 0075 0000 0000 0000 0000

11.5

0000 0000 0000 0000 0000 0050 0100 0100 0075 0000 0000 0000

10.5

0000 0000 0000 0000 0025 0125 0175 0175 0100 0025 0000 0000

9.5

0000 0000 0000 0000 0100 0250 0325 0275 0125 0045 0020 0010

8.5

0000 0000 0000 0000 0200 0525 0625 0425 0175 0070 0025 0005

7.5

0000 0000 0000 0100 0475

1050

1150 0700 0275 0090 0010 0000

6.5

0000 0000 0000 0250 1100 2050 1875 0975 0300 0080 0020 0000

5.5

0000 0000 0050 0650 2425 3725 2800 1225 0350 0080 0020 0000

4.5

0000 0000 0175 1600 4725 5625 3350

1175 0275 0075 0000 0000

3.5

0000 0000 0525 3475 7400 6450 2875 0800 0150 0000 0000 0000

2.5 0000 0075 1350

5700 7725 4500 1400 0275 0025 0000 0000 0000

1.5

0000 0275 2375 4775 3425 1125 0225 0025 0000 0000 0000 0000

0.5

0025 0325 0825 0600 0150 0000 0000 0000 0000 0000 0000 0000

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3.2

Probabilistic Approach

The China Classification Society (CCS) has developed a typical methodology for the long-term prediction of the deck wetness of a ship, sailing in a seaway. Reference is given here to the 1MO documents SLF 37/8/1 and SLF 37/8/2, dated 28 September 1992.

This method is based on a joint Pc-Pg probability criterion.

In a sea state defined by (H113, T2), the short term probability on deck wetness Pg is

defined by:

pS = P

_{> Fb} }= exp

-(Fb

-hs)2

or:

Fb =-2m0 .hPs)+hs

in which Fb is the bow height and k is the bow wave.

An empirical formula of Tasaki (1963), based on model experiments,

is used for

determining the static swell-up (or bow wave) at the forward perpendicular:

h0.75.B

L

Fn2

Le

with:

L length of the ship B breadth of the ship

Le length of entrance of the water line

Fn Froude number

Use has been made of long-term ocean wave statistics, presented in a wave scatter diagram. Each number q,1 in this table represents the frequency of occurrence of a sea

state with the parameter combination (H1731, T2J).

With the expression for F,, and a given constant short-term probability criterion for Pg, a

minimum bow height F,,1,, can be obtained for each parameter combination H1/31, T21 in

plane q.

When assuming a minimum bow height Fba, the sum of all q,-values, satisfying the

condition F,,,1 >Fb, represents an encountering probability Pc. Opposite, when a criterion for this encountering probability has been set, for instance P = 0.015, the required

minimum bow height Fba can be found numerically from the expression:

N1 N1

ii

{F1/

> Fb

The short-term probability-criterion Ps and the encountering probability-criterion P for

bow deck wetness has been determined by China as:

Ps4O.O%

and

_Pc1.5%

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3.3

Probabilistic Calculations

For the Joint Ps-Pc Probability Criteria Method (JPCM) developed by CCS, the principal of determining probability criteria Ps and Pc is to make average level of bow height by JPCM for actual ships approximate those by the Regulation 39(1) of 1966 ICLL.

The encountering probability criterion Pc is taken as to equal the sum of probability of encountered heavy seas. And it is taken as 0.015 as an acceptable critical probability for

normal operation of ships at seaway referring to the relevant seakeeping criteria

suggested by ITTC Report.

The short-term probability Ps was determined based on variance analysis for data of bow height of actual ships by 1966 ICLL Regulation 39(1) and those by theory calculation

with the conditions given in 3.1.

The Probability-Criterion Ps has been defined by the investigation of bow height of

actual ships:

For 11 typical ships with:

Lpp34mto264m andCb=0.59to0.83

The sum of variance cf forPs = 0.2, 0.3, 0.4, and 0.5 are given as follows:

where: >c? = - Fb, )2

Fb66 is the bow height of the ship by 1966 ICLL Regulation 39(1), and

Fb is the bow height of the ship by theory calculation

From the above-mentioned table it is clear that the probability level of bow height by

Regulation 39(1) of 1966 ICLL approximates to joint probability criteria of Pc 0.0 15

and Ps = 0.4 at which a minimum is reached.

Therefore, the probabilistic method Ps-Pc Joint Probability Criteria Method for making analysis of bow height by theory calculation for all conventional ships has been decided

as follows:

Short-term Probability Criterion: Ps = 0.40

Encountering Probability Criterion: Pc = 0.0 15

Ps 0.2 0.3 0.4 0.5

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3.4

Bow Height Polynomials

Reference to the formula in Regulation 39(1) of 1966 ICLL, the bow height has been

decided to use a formula with a structure as follows:

where:

and:

F =F(L/lOO).G(Cb,Cbf,CW,Cflf,L/d)

F(L/100)=f .(L/100)+f .(L/loo)2 +f .(Liioo)3

G(C,Cf,CW,C,L/d)=g1+g2.Cb+g3.Cbf+g4.CW+g5.C+g6.(L/d)

and where the following definitions have been used:

F calculated bow height

L length between perpendiculars at Summer draught, d

B moulded breadth

d

Summer Load Line draught at even keel condition

D amidships depth

A water plane area at draught d

V volume of displacement at draught d

Ch block coefficient, determined by: Cb

''

B d)

Cbf block coefficient forward of / 2

C,

water plane area coefficient, defined by: C, = A, /(L B)

CWf water plane area coefficient forward of

/2

The procedure of analysis is given as follows:

Sensitive analyses of parameters including Cb, n ( combination of Gb/and Cwf)

and Lpp/d based on the results of bow height of the systematic calculation.

Primary regression analysis to establish the expression of bow height based on the

sensitive parameters of Ch, n and / d based on the results of systematic

calculation.

To define the basic expression F(Lpp) from the result of the primary regression

analysis for standard ships under the condition:

G ( Cb Cb/ Cq,Lpp/d) =

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and

G(Ch, Cbf C%ç,_{Lpp/d) = gi + g2}Cb + g3 Cbf+

g4 C+ gs L/d

G (Cb, Cwj,Lpp/d) = gj + g2 Ch + g4C+ g5Lpp/d

where the standard technique was employed for the multi-parameters regression analysis.

3.4.1 Formula Based on Draught d

Based on regression analyses (based on draught d) of calculated bow heights, China has found the next formula for required minimum bow heights of ships with a length of 24

meter or more:

with:

F, =F(LPP).G(Cb,C,LPP/d)

+0.200.(L/100

where in calculating F(L), is to be taken as 300 m for ships of 300 m and above in

length, and:

G(Cb,C,LPP/d)= 1.876+0.935Cb -l.663C -0.0115

where the following definitions have been used:

I,

calculated bow height

length between perpendiculars at Summer draught, d

B moulded breadth

d

V volume of displacement at Summer draught, d

water plane area forward of /2 at draught d

Ch block coefficient, defined by: Ch

v/(L

.B.d)

C water plane area coefficient forward of

/ 2: C = A,

/(L . BI 2)

Expression F(Lpp) presents the bow height of the standard ships with V shape of forebody section and the following parameters:

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and

G(Cb C,Lpp/d) =gj + g2Cb + g4C,+ g5Lpp/d

= 1.876 + 0.935x068 - 1.663 xO.7749-0.011Sx 19.4 = 1.0

and

n

85.7 C-- 75.6 Cbf 9

85.7 xO.7749-75.6x0.68 - 9.0 = 6.0 (see Figure 1)

3.4.2 Formula Based on Draught d1

Based on regression analyses (based on draught d1) of calculated bow heights, China has found the next formula for required minimum bow heights of ships with a length of 24 meter or more:

with:

F

_{F(L).G(Cb,C,L/dl)}

F(L)=6.075.(LI100)-1.875.(LI100)2 +o.200.(LIloo)3

where in calculating F(L), L is to be taken as 300 m for ships of 300 m and above in

length, and:

G(Cb,Cf Lid1) = 1.954+1.085 Cb 1.873 C

0.0146.(L/d1)

J,

L length at draught d1 = 85 % of the depth D

B moulded breadth

d

d1 draught at 85 % of the depth D

D amidships depth

V volume of displacement at draught d1

water plane area forward i 2 at draught d1

Cb block coefficient, defined by: Ch = V ¡(L B d1)

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ExpressionF(L) presents the bow height of the standard ships with V shape of forebody

section and the following parameters:

Cb=0.68, Cbf= 0.68, C-=0.7749,L/d1 = 16.5 and G= 1.0

The comparison of bow height of standard ships of 1966 ICLL and the expressionF(L)

is shown in Figure5. 8 7 6 E

U4

3 2 i 0

/

IOEL 66 Ps-Pc 50 lOO 150 200 250 L(nj

Figure 5 Length Dependency of Required Minimum Bow Height of Standard Ship

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4

Probabilistic Method of the Netherlands

This Chapter describes the probabilistic method, used by the Netherlands, for determining

the required minimum bow heights of ships exceeding 24 meters in length. 4.1

Ships and Environment

Each of these 15 parent hull forms has been transformed linearly to principal dimensions following from all 132 combinations of the dimensions given in Table i and Figure 6,

which resulted in 1980 different ships.

__ft

5L,

- Vr e-vv ç 4 . 3 100 200 L (m) pp

Table 1 Range of Ship Dimensions

V 300 400 500 o V D Bld = 3.75 Bl = 3.25 Bld = 2.75 Bld = 2.25 O 200 300 L (m) pp

Figure 6 Length-Breadth and Breadth-Draught Ratios

400 500

L(m)

24 38 50 75 100 150 200 250 300 400 500

low medium high

L/B(-)

3.50<L/B

5.00

4.75 <L/B

6.25

6.00 <L/B

7.50

B/d(-)

2.25 2.75 3.25 3.75 5 L /B high pp 4 A LlB = med. A 3 V L /B=Iow pp V 2

A Japanese ships A Japanese ships

V Norwegian ships V Norwegian ships

D Chinese ships D Chinese ships

O Russian ships O Russian ships

10

D

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When using the 1966 ICLL regulations, it is assumed here that: head waves play a significant role only,

the ships have no superstructures; they only have a forecastle with a length of 0.07L

with a standard height, see Figure 3, the ships have no sheer,

the length L of the waterline at 0.85D is equal to 1.0l5L (pontoon excepted) and

the freeboard is based on the summer draught.

The radius of inertia for pitch of the solid mass of each ship is fixed to 0.25L.

The linear (modified) strip theory has been used for relative motion computations. The 2-D potential coefficients have been determined by using the potential theory of Ursell and Tasai and a 10-parameter conformal mapping method. This theory has been described in detail in the theoretical manual of the strip theory program SEAWAY (see web site http://dutw189.wbmt.tudelft.nl/'-johan or http://shipmotions.nl for a link to this site) which was basis for the calculations here. Bow deck wetness will be calculated from the vertical relative motions at the forward perpendicular, consisting of heave and pitch motions in undisturbed waves. It has been assumed that the ships are sailing in severe weather conditions with long-crested irregular head waves defined by ideal Bretschneider wave spectra and the Winter North Atlantic sailing area. A previous study by Journée, de Kat and Vermeer (2000a) has showed that the required minimum bow height is governed

by head sea conditions.

Table 2 presents the winter (months 11-1) wave scatter data of the North Atlantic (areas

8, 9, 15 and 16) as Germanischer Lloyd has obtained it from Global Wave Statistics.

Table 2 Winter North Atlantic Wave Scatter Diagram Winter North Atlantic, Areas 8, 9, 15 and 16 from Global Wave Statistics (GL)

H,,3 T, 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 0 0 0 0 2 30 154 362 466 370 202 13.5 0 0 0 0 3 33 145 293 322 219 101 12.5 0 0 0 0 7 72 289 539 548 345 149 11.5 0 0 0 0 17 160 585 996 931 543 217 10.5 0 0 0 1 41 363 1200 1852 1579 843 310 9.5 0 0 0 4 109 845 2485 3443 2648 1283 432 8.5 0 0 0 12 295 1996 5157 6323 4333 1882 572 7.5 0 0 0 41 818 4723 10537 11242 6755 2594 703 6.5 0 0 1 138 2273 10967 20620 18718 9665 3222 767 5.5 0 0 7 471 6187 24075 36940 27702 11969 3387 694 4.5 0 0 31 1586 15757 47072 56347 33539 11710 2731 471 3.5 0 0 148 5017 34720 74007 64809 28964 7804 1444 202 2.5 0 4 681 13441 56847 77259 45013 13962 2725 381 41 1.5 0 40 2699 23284 47839 34532 11554 22(18 282 27 2 0.5 5 350 3314 8131 5858 1598 216 18 1 0 0

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The long-term probability level, PL, on bow deck wetness can be determined now from the short-term probability on deck wetness of the ship's bow at the forward perpendicular in head waves, a bow height according to the 1966 ICLL regulations and this wave

scatter diagram. This determination will be described in the next Section. 4.2

Probabilistic Approach

In a storm defined by a duration of 3 hours, a significant wave height H113 and an average

zero-uperossing wave period T2, the short-term probability on deck wetness P is given

by:

P8 =P{s0 >i}=exp

(Hb2"J

2m05 where:

PI..]

Sa Hb probability

vertical relative motion amplitude at the bow area of relative motion spectrum

bow height (above still water level)

This yields for the bow height: Hb j- 2m05 . in(R5)

The long-term probability, PLI, follows from a multiplication of the short-term probability Psi with the probability P, = P{H1131, T21} on the occurrence of this sea state or storm, i, in a wave scatter diagram of a certain sailing area:

It is obvious that for a wave scatter diagram with N sea states the sum of the N individual

probabilities becomes 1.0 because all data in the wave scatter diagram have been

divided by its total number of observations.

The total long-term probability, LTP, on deck wetness PL in this sailing area has been found here by using the wave scatter diagram and summing up these N individual

long-term probabilities on deck wetness:

W N

L 'Li "S,Wi

1=1

under the following conditions:

ships with a length between 24 and 500 meter,

forward ship speeds corresponding to Fn = 0.00 and Fn = 0.10,

no static swell-up at the bow (or bow wave), no dynamic swell-up,

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no "green water" on deck or a deck flooding height,

head irregular long-crested waves and

Winter North Atlantic wave scatter diagrams of Areas 8, 9, 15 and 16 of the North Atlantic Winter Season as Germanischer Lloyd has obtained it from Global Wave

Statistics.

The static and dynamic swell-up have been ignored here; these effects are supposed to be

included in PL, the selected value of the long-term probability level. This probability level

lias been determined from bow deck wetness calculations in head waves for ships

fulfilling the 1966 ICLL regulations for the summer season. 4.3

Probabilistic Calculations

All calculations have been carried here for Fn 0.00 and Fn 0.10 in head waves with

the Winter North Atlantic wave scatter diagram.

a FnOOO b Fn=000 15 lo 5 -s- Vermeer ships - - - - Average value 0 0 0 lOO 200 300 400 500 0 Ship Length L (m) pp

Figure 7 Long Term Probabilities of Vermeer Ships at Fn = 0.00

15 Io 5 u Average value of Vermeer ships S' a Ship Length L (m) 500 100 200 300 400

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15 * 4+ 10 + a Fn=OlO b Fn010 + Vermeer ships - - - - Average value

1

100 200 300 4(0 5(X) lOE) 200 3(X) 400 5(0

f 6.44 - 0.02540 L(m)

These long-term probabilities have been used to calculate the required minimum bow

heights of all ships at two forward ship speeds.

Figure 55 and Figure 56 show for all 1980 ships the bow heights obtained by this long-term probability (LTP) method (cross marks) compared with the 1966 ICLL bow heights

(solid line).

Figure 57 through Figure 71 show these LTP bow heights (solid line for Fn = 0.00 and a

dotted line for Fn 0.10) compared with the 1966 ICLL bow heights (circular marks) in

more detail. Fn = 0.00: = largest of

3.02 0.00356 L(m)

[13.10-0.05040 .L(m)

Fn = 0.10:

P(%)=largestof

6.48-0.01030.L(m)

Ship Length L (m) Ship Length L (m)

Figure 8 Long Term Probabilities of Vermeer Ships at Fn = 0.10

The long-term probabilities of exceeding the 1966 ICLL bow height by the vertical relative bow motions of all 132 Vermeer ships are presented in Figure 7-a and Figure 8-a

for two Froude numbers as a function of the ship length The mean value at each ship

length is given in the figure too (dotted line).

Figure 7-b and Figure 8-b shows these mean values as a function of the ship length Lp,,, separately. Based on these figures, it has been decided here to use for all ships a simple relation between the long-term probability PL and the ship length L:

(23)

4.4

Bow Height Polynomials

The average LTP bow height has been used to obtain a bow height formula with a

structure as proposed by China:

F, =F(LI1OO).G(Cb,Cbf,CH,C,L/d)

where:

F(L/100)=f1 .(L/100)+f2 (Libo)2 +j .(L/loo)3

and:

G(Cb, Cbf, C, Cf, L / d) g1 + g2 Ç + g3 Cbf + g4 C + g5 C + g6 (L / d) and where the following definitions have been used:

¡,

L = = length between perpendiculars at Summer draught, d

B moulded breadth

d

D amidships depth

A} water plane area at draught d

Cb block coefficient, determined by: Cb

vi(L

.B.d)

Cb! block coefficient forward of / 2

C water plane area coefficient, defined by: C = A,i(L B)

The coefficients have to be determined by a dedicated least square method. The sum, S, of the squares of the deviations of the polynomial freeboards, Fb,, from the object

freeboards, H,,,, has to be minimal:

1848

S = = minimal

i=1

This yields that the derivatives of S to each of the coefficients f, f, 13' g1, g2, g3,

g4, g5 and g6 has to be zero.

The polynomial expression for the bow height has 3 + 6 = 9 coefficients (1' 12' .f g1,

g.,, g3, g4, g5 and g6), but a straight-forward least square method will solve 3 *6 = 18

coefficient-combinations (fg1, fg2, fg3, fg4, fg5, Jg6, f2g1, f2g2, f2g3,

(24)

The procedure used here is as follows. Set as starting values:

Gl(CbI,Cbfi,C,C,L,/d,)1.O

Then the sum of the squares of the deviations is:

1848

s=jJf,

.(L/1oo)+f2 .(L/100)2

_+f

.(L,/lOO)].G, _[Hbß]}2

= minimal

The derivative of this sum, S, to each of the coefficients f1, f2 and_f3 has to be zero:

2/(L /1oo)+f2(L /100)2

+f3(L1

_{/100)].G, [Hb]}.(L,}

¡ioo)=

i=1

=

2j(L /loo)+f2(L,

/100)2 +f3(L, iiO0)]. G

-

[Hb]}. (L, /100)2

1=I

as

=

2'j/(L1 ¡Ioo)+f2(L

/100)2 +f3(L1

Il00)}.G, [Hb,]}(L, iiOü)

The coefficients J, f2 and

f

can be solved from these 3 equations.

Now, the equations can be written as:

=_F1 1g1 + g2 CbI + g3 Cbfi + g4 C +

g5 C + g6

(L Id1 ¡lo)]

in which F is known.

Then the sum of the squares of the deviations is:

1848

s {i [g + g2 Ch, + g3 Cbfi + g4 C + g5 C + g6 (L, / d, )] - [Hb, ]

= minimal

The derivative of this sum, S, to each of the coefficients g1, g2, g3, g4, g5 and g6 has

(25)

1848

2{I.g1

1848

2(/.g

1848

2{1

jg1 1848

2{/.g

os

1848

2{.[g

0g3 ¡=1 1848 0g6 The coefficients g1, +g2C1 +g3Cbfi +g4C +g5C +g6(L1/d1)]_[Hj}.1.0 = o

+ g2C1 + g3Cbfi + g4C + g5C + g6(L1 Id1)] [HbÌ]}.CbI O

+ g2C1 + g3Cbfi + g4C + g5C + g6(L1 Id1)] EHb, ]}. = O

+g2C1 +g3Cfi +g4C1 +g5Cfl +g6(L1/d1)]_[Hb1]}.0 o

+g2C1 +g3Cbfi +g4C1,, +g5C

+g6(LÌId,)][H1]}.0

o

+g2C1 +g3Cbfi +g4C,, +g5C +g6(LId1)]_[Hb1]}.(L1/d,)= O g2, g3, g4, g5 and g6 can be solved from these 6 equations. Then, this procedure will be repeated by a new determination of the coefficients J, f2

and f3 with the value G

g1 + g2 ChI + g3 Cbfi + g4 C + g3 C + g6 (L1 id), etc.

The coefficients become constant in a few steps.

Coefficients J, f2 , f3, g1, g5 and g6 have a very significant contribution into the bow

height function, the contribution of g2 is doubtful and the contributions of g3 and g4

appeared to be insignificant.

4.4.1 Formula Based on Draught d

The LPT bow heights at the two forward ship speeds (Fn

0.00 and Fn = 0.10), for

required minimum bow heights of all ships with a length of 24 meter or more is found by

regression analysis as:

with:

Fb =F(LPP).G(Cb,CWJ,LPP/d)

length, and:

G(Cb,C,LPPid)=2.143+0.499.Cb-1.613.C-0.0093.(LPPId)

OS 3g1

os

0g2 OS 0g3 OS 0g4

(26)

Fb calculated bow height

B moulded breadth

d

V volume of displacement at Summer draught, d

A.. water plane area forward of /2 at draught d

Cb block coefficient, defined by: Cb y /(L

B d)

/ 2: C = A /(L

B / 2)

Figure 72 through Figure 86 show a comparison of this polynomial expression, based on draught d, with the LTP bow heights.

4.4.2 Formula Based on Draught d1

The average LTP bow heights at the two forward ship speeds (Fn = 0.00 and Fn = 0.10) has been used to obtain a bow height formula based on the draught d1 at 85 % of the

depth too:

with:

F =F(L).G(Cb,C,L/dl)

F(L)=6.087.(L/100)-2.041.(L/100)2 +O.245.(L/100)3

length,

and:

G(Cb,C,L/dl)= 2.2O6+O.l32Cb

- 1.332C

o.oIll.(L/d1)

F, calculated bow height

B moulded breadth

d

(27)

A water plane area forward / 2 at draught d1

Cb block coefficient, defined by: Ch = V ¡(L B d1)

(28)

5

Joint Formulas of China and the Netherlands

The previous new formulas of China and the Netherlands result in relatively small mutual differences in calculated required minimum bow heights. Therefore, it was decided at the IMO/SLF Correspondence Group Meeting in April 2001 in Alameda (California, USA) by the authors of this report to take the average of their individually derived formulas as a jointly proposed new formula on required minimum bow heights.

5.1

Joint Formula Based on Draught d

China and the Netherlands propose the next joint formula (based on draught d) for

required minimum bow heights of ships with a length of 24 meter or more:

with:

Fb =FÇLPP).G(Cb,C,LPP/d)

+0.227.(L/100)

length, and:

G(Cb,C,LPPId)

2.010+ 0.717.Cb 1.638C. - 0.0104.(L/d)

13, calculated bow height

B moulded breadth

d

A water plane area forward of /2 at Summer draught, d

Cb block coefficient, defined by: Cb = v/(L

.B.d)

C14. water plane area coefficient forward of

/2: C = A /(L

B / 2)

In Figure 87 through Figure 101, the bow heights obtained by the new formulas (based on the draught d) of China and the Netherlands have been compared mutually and with the

(29)

5.2

Joint Formula Based on Draught d1

China and the Netherlands propose the next joint formula (based on draught d1) for

required minimum bow heights of ships with a length of 24 meter or more:

with:

F,, =F(L).G(Cb,C,L/d,)

F(L)=6.081.(L/l00)-1.958.(L/100)2 +0.223.(LI100)3

length, and:

B moulded breadth

d

d, draught at 85 % of the depth D

D amidships depth

V volume of displacement at draught d,

water plane area forward /2 at draught d1

C,, block coefficient, defined by: Ch

V/(L.B.d1)

/ 2: C = A,

/(L B /2)

5.3

Comparison of Joint Formulas with 1966 ICLL Regulations

in Figure 9 through Figure 23, the bow heights obtained by the new formulas (based on d as well as on d,) have been compared for the 1980 ships with the bow heights of the

1966 ICLL.

(30)

r

2' 50 a)

I

2.5 cC o 10.0 7.5 o 10.0 7.5

r

2' 50 a)

I

2.5 cc o . o b 'a . Al Ship LIB = low Bld = 2 25 0 100200300400500 Al Ship LIB medium B/d = 2.25 100200300400500 a a

a..

Al Ship LIB = high Bld = 2.25 0 100200300400500

Figure 9 Final Bow Height Results of Vermeer Ships

100 7.5 100 7.5 5.0 2.5 Al Ship LIB = low B/d = 2.75 0 100200300400500 J 5 s Al Ship L/B medium B/d = 2.75 O 0 100200300400500 O 0 100200300400500

Ship Length (m) Ship Length (m)

Figure 10 Final Bow Height Results of Al Ships

2.5 - - - - Formula based ort d Al Ship L/B = medium Bld = 3.25 o 0 100200300400500 'a '3 e e Al Ship L/B = high Bld = 3.25 O 0 100200300400500 Ship Length (m) 2.5 10.0 7.5

.

loo 75 5.0 s Al Ship LIB = low B/d = 3.75 o o 100200300400500 Al Ship L/B = medium B/d = 3.75 o O 100200300400500 2.5 O O 100200300400500 Ship Length (m) lo-o 10.0 Formula lo o 10.0 E

r

75 0 1966 ICLL 7.5 75 Formula based on d ₇₅

b-..

.' 000

o 00 0 0 s s I J C) a) 5.0 50 o 5.0 5.0

I

S o cC 2.5 o Vermeer Ship L/B = low Bld = 2.25 2.5 O I Vermeer Ship 'I L/B r low . Bld r 2 75 2.5 O Vermeer Ship L/B s low Bld = 325 2.5 o Vermeer Ship L/B = low Bld = 3.75 0 100200300400500 0 100200300400500 0 100200300400500 0 100200300400500 10.0 10.0 lo-o 100

r

7.5 7.5 b 7.5 _J _{J- j} 75

000

. 2' a) 50 5.0 a 5.0 a 5.0

I

et 2.5 o Vermeer Ship LIB = medium Bld = 2.25 2.5 O Vermeer Ship L/B r medium s Bld = 2 75 2.5 o Vermeer Ship L/B = medium B/d = 3.25 2.5 o 'a Vermeer Ship L/B = medium Bld = 3.75 0 100200300400500 0 100200300400500 0 100200300400500 0 100200300400500 10.0 100 10.0 10.0 2' a) 7.5 50 e a a 7.5 50 7,5 5.0 e 7.5 5.0 s _._f r, s

I

cc 2.5 o Vermeer Ship 'I UB = high s Bld = 2.25 2.5 o Vermeer Ship L/B= high B/ds 2.75 2.5 o Vermeer Ship L/B = high Bld = 3.25 2.5 o Vermeer Ship 'I _{L/B = high} B/d = 3.75 0 100200300400500 O 100200300400500 0 100200300400500 o 100200300400500

Ship Length (m) Ship Length (m) Ship Length (m) Ship Length (m)

10.0 0 1966 ICLL 7.5 s 00 0 0 100 Formula 7,5 based on d e 00 0 0 50 _o I 2.5 a s o o o s 5.0 2.5 Al Ship LIB = low o B/d = 3.25 0 100200300400500 10.0 7,5 I 5,0 a 50 .3 'j 2.5 10.0 7.5 5.0 a a 10.0 7.5 50 2.5 loo 7,5 5.0 2.5

(31)

10.0 7.5 -c

)

50 Q)

I

2.5 co o 10.0 7.5 -C .0' 50 Q)

I

2.5 co O 10,0 7.5 10.0 7.5 .2) 50 Q)

I

2.5 co o 10.0 7-5 n .2) 50 Q)

I

2.5 1:0 0 100200300400500 0 100200300400500 10,0 7.5 n .0' 50 Q)

I

2.5 co o 0 100200300400500 Ship Length (m) 0O O O s A2 Ship LIB = high Bld = 2.25 o 0 100200300400500 100200300400500 A3 Ship LIB = high B/d = 2.25 o 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 2.5 10.0 7.5 50 A2 Ship 25 .) LIB=mediuni Bld = 2.75 O 100 75 5.0 2.5 O 0 100200300400500 Ship Length (m) 10.0 o 0 100200300400500 7.5 5.0 25 10.0 7.5 5.0 25 o °2 O o 100200300400500 Formula based on d d A3 Ship LIB = tow B/d = 2.75 O 0 100200300400500 '-4 î) -A3 Ship L/B = medium Bld 2.75 o 0 100200300400500 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 2.5 O 10,0 7.5 5.0 2.5 10,0 7.5 50 2.5 o 0 100200300400500 Ship Length (m) 10.0 75 5.0 2.5 10.0 7.5 50 2.5 10.0 7.5 50 2. 0 100200300400500 O 0 100200300400500 00 O O o A2 Ship L/B = high B/d = 3.25 o 0 100200300400500 A3 Ship L/B = medium Bld = 3.25 O 0 100200300400500 Ship Length (m) 10.0 75 50

25 j'

A2ShipL/B = medium B/d = 3.75 O 10.0 7.5 5.0

Figure 11 Final Bow Height Results of A2 Ships

2.5 o 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 25 10,0 7.5 5.0 25 0 100200300400500 o

000 0 0

100200300400500 00 O O o A2 Ship L/B = high Bld = 3.75 A3 Ship LIB = low B/d = 375 O o 100200300400500 o o 100200300400500 5 o o o 100200300400500 0 100200300400500 Ship Length (m) - - - - Formuta based on d1 000 0 0 10.0 7.5 50 25 o f. fi fi 000 0 0 s A2 Ship LIB = low Bld = 3 25 o A2 Ship L/B = low Bld = 3.75 100 oOO O O 75 S ₅₀ 'i Ii A3Ship_{L/B = high} 25 4. B/d = 3.25 10.0 7.5 S 5.0 o 2.5 (j A3 Ship LIB = high B/d = 2.75 O

(32)

10.0 50 o 10.0 7.5 2.5 10.0 7.5 -C 2' 50 a>

I

S o ro 100 5.0 10,0 7.5 10.0 - 7.5 -C o) a) :i: 2.5 co 5.0 0 100200300400500 O 0 100200300400500 .000 0 0 A4 Ship L/B = high B/d = 2.25 2.5 o 0 100200300400500 Ship Length (m) O 0 100200300400500 o 0 100200300400500 I 'I 'a AS Ship UB = high B/d 2.25 O 0 100200300400500 100 7.5 5.0 2.5 O 10.0 7,5 5.0 2.5 10.0 7,5 5.0 2.5 o 0 100200300400500 Ship Length (w) 0 100200300400500 'j AS Ship L/B = medium B/d = 2.75 O 0 100200300400500 0 100200300400500

0 100200300400500

Ship Length (m)

0 100200300400500

Ship Length (m)

0 100200300400S00

Ship Length (m)

O 100200300400500 Ship Length (w) 100 Formula 10,0 10.0 7.5 7.5 Formula based on o00 0 0 7,5 000 0 0 based on d o o I S S'O 5.0 . SO 2.5 A4 Ship LIB = low 25 A4 Ship LIB = low 2.5 A4 Ship LiB = low Bld 2.75 B/d = 3.25 B/d = 3.75 O O o 100200300400500 0 0 100200300400500 O 100200300400500 10.0 100 10.0 7,5 75 75 S'o 000 0 0 So 000 0 0 S.0 000 0 0 o I 2.5 A4 Ship LIB medium 2.5 A4 Ship L/B = medium 2.5 A4 Ship L/B = medium Bld = 2,75 B/d = 3.25 B/d = 3.75 O o o 0 100200300400500 0 100200300400500 o 100200300400500 10.0 100 10.0 7,5 7,5 7.5 000 0 0 000 0 0 00 O O So o So o S'O o o

25 A4 Ship_{L/B = high} 2.5 A4 Ship_{LIB = high} 2.5 A4 Ship_L/B _high Bld = 2.75 B/d = 325 B/d = 3.75 O O o 7.5 SO 100 Formula based on e 7,5 S.0 100 e 25 'i AS Ship _2.5 AS Ship L/B = low LIB = low

O Bld = 325 O B/d = 37 0 100200300400500 O 100200300400500 100 10.0 75 7.5

SS I 5

000 . S 5.0 50 S 25 A5 Ship L/B = medium 2.5 A5 Ship L/B = medium Bld = 3.25 B/d = 375 O O 100200300400500 0 o 100200300400500 10.0 10,0 7.5 7.5 000 0 0 000 0 0 5.0 . S'o O 2.5 AS Ship L/B = high 2.5 A5 Ship LIB = high B/d = 3.25 B/d = 375 o o 0 1966 ICLL . . AS Ship UB = low Bld 2.25 e e e Formula based on d e e _{AS Ship} LIB low B/d = 2.75

(33)

Ship Length (m) Ship Length (ni)

Figure 15 Final Bow Height Results of Bi Ships

0 100200300400500 Ship Length (m) 'a 'a 'a Formula based on d 3 B2 Ship L/B = low B/d = 2 75 'a 'a

. I

B2 Ship L/B = medium B/d = 2.75 0 100200300400500 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 2.5 100

-- Formula based on d -- _Ì B2 Ship L/B = low B/d = 3.25 o o 000 O O I B2 Ship L/B = medium B/d = 3.25 o 100200300400500 10.0 7,5 5.0 2.5

Figure 16 Final Bow Height Results ofB2 Ships

QOO O O B2 Ship LIB = medium B/d = 3 75 O O 100200300400500 loo 10.0 7,5 000 0 0 o -50

, -

5.0 V B2 Ship 2.5 _¿' _{LIB = high} 2.5 B/d = 3.25 o o O 100200300400500 0 100200300400500

Ship Length (ni) Ship Length (m) E -c 10,0 7,5 o 1966 ICLL 10.0 7,5 Form cia 10.0 7,5 - - - - Formula o00 0 0 10.0 7.5 O O 0 O0 O O s 00 O O I D, a)

I

el 50 2.5 O Bi Ship LIB = low B/d = 2.25 5.0 2.5 o I I _{Bi Ship} b a _{L/B = low} I _{B/d = 2.75} 5.0 2.5 o a BI Ship L/B = low I _{B/d = 3.25} 50 25 o I a Bi Ship LIB = low s B/d 3.75 0 100200300400500 0 100200300400500 0 100200300400500 o 100200300400500 10.0 10.0 100 i 0.0 -C 75 _{OO O O} o 7.5 _{oOO O O} I 75 _{I 00 0} ₀ 75

000

e C, 'D 5,0 I 5.0 50 5.0

I

w 2.5 O Bi Ship

i

LIB = medium . _{B/d = 2.25} 2.5 O Bi Ship L/B = medium B/d = 2.75 2.5 o Bi Ship L/B = medium B/d = 3.25 2.5 o Bi Ship LIB = medium B/d = 3.75 0 100200300400500 0 100200300400500 0 100200300400500 o 100200300400500 100 100 10.0 10.0 7.5 _{öOO O O} 7,5 _{. 00 0 0} 7,5

II 00

7.5 _{_.} ₄ -c I C, a) w 50 2.5 0 Bi Ship LIB = high Bld = 2 25 5.0 25 o a a a Bi Ship 'a LiB = high I _B/d _{2 75} 5,0 2.5 o a a Bi Ship LIB = high B/d = 3.25 5.0 25 o a Bi Ship LIB = high B/d = 3.75 E -C 10.0 7.5 10.0 7.5 o 1966 ICLL D, a) 5.0 5.0

I

S o 01

2.5 _'3 B2 Ship_{LIB = low} 2.5 B/d = 2.25 O O 0 100200300400500 100 10.0 7.5 _.. 7.5 -c B) a) 50 50

I

S o el 25 'a w 02 Ship L/B = medium Bld = 2.25 2.5 O O 0 100200300400500 10.0 10.0 7.5

S

_{¶_I} 7.5 -c .2' a) 50 50

I

OEl 25 ₎₃'i w B2 Ship LIB = high B/d = 2.25 2.5 o o 0 100200300400500 0 100200300400500 0 100200300400500 0 100200300400500 0 100200300400500 o 100200300400500 0 100200300400500 7.5 5.0 2.5 o i O. O 7.5 50 2.5 000 0 0 I B2 Ship L/B = high B/d = 2 75 QOO O O o B2 Ship LIB = high B/d = 3.75

(34)

10.0 7.5 5.0 2.5 100 75 -c 2' 50 o)

-I

2.5 cil o 10.0 75 10.0 7.5 -C .0 50 Q)

I

25 10.0 7.5 -c 2' 50 Q) 2.5 ce 100 7.5 -c 2' 50 a)

I

2.5 ce 0 1966 ICLL

000

63 Ship LIB = low B/d = 2.25 O 0 100200300400500 0 0 03 Ship LIB = medium B/d = 2.25 0 100200300400500 00 0 0 63 Ship LIB = high Bld = 2.25 o 0 100200300400500 0 1966 ICLL r B4 Ship LIB = ow B/d = 2 25 o 0 100200300400500 -B4 Ship LIB = medium B/d = 2.25 o 0 100200300400500 o 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 2.5 o 10.0 75 50 2.5 O 10.0 7.5 5.0 2.5

Ship Length (ni) Ship Length (ni)

10.0 7.5 5.0 10,0 75 5.0 2.5 O 0 100200300400500 Formula based on d '-J e lOA hir, Lili OW B/d = 275 O 0 100200300400500 00 O O 0_ q' 64 Ship L/D = high B/d = 2.75 2.5 o 0 100200300400500

Ship Length (ni) 2.5 o 0 100200300400500 Ship Length (m) 10.0 75 5.0 2 5 'a " 2 5 B4 Ship L/B = low - o B/d=3.25 0 100200300400500 0 100200300400500 100 75 50 2.5 - - - - Formula based on d o000 0 0 B4 Ship L/B = medium B/d = 3.25 o 0 100200300400500 2.5 o 0 100200300400500

Ship Length (ni)

Figure 17 Final Bow Height Results of B3 Ships

100 7.5 50 2.5 10.0 7,5 5.0 2.5 100 7.5 5.0 2.5 o O 100200300400500 'I 'a 'J 'J e a) B3 Ship LIB = high B/d = 3.75 O 100200300400500

Ship Length (ni)

00 0 0 64 Ship LIB = low B/d = 3.75 o o 100200300400500 o000 0 0 B4 Ship LIB = medium B/d = 3.75 o o 100200300400500 O O 100200300400500

Ship Length (ni) Form ula 10.0 Formula 10.0

000 0 0 7,5 _{s 00 0 0} 7-5 _{O O O} . 5.0 5.0 63 Ship L/B = low 2.5 B3 Ship L/B = low 2.5 B3 Ship LIB = low B/d = 2.75 O B/d = 3.25 o B/d = 3.75 0 100200300400500 0 100200300400500 O 100200300400500 10.0 10.0 7,5 75 . 00 0 0

000 o-.

5.0 5.0 63 Ship L/B = medium 2.5 63 Ship L/B = medium 2.5 B3 Ship LIB = medium Bld = 2.75 B/d = 3.25 B/d = 3.75

o 0 100200300400500 0 100200300400500

000

4

63 Ship L/B = high B/d = 2.75 S

--s

a B3 Ship LIB = high B/d 3.25 s 10.0 7,5 5.0 10.0 7-5 5.0 2.5 O . . . . 64 Ship LIB = high B/d = 2.25 10.0 75 5.0 100 7-5 5.0 000 0 0 B4 Ship LIB = high B/d = 3 25 000 O O B4 Ship LIB = high B/d = 3.75

(35)

10.0 7.5 9) 50 e

I

2.5 co o 100 7.5 9) 50 a 2.5 ro 10.0 7.5 4: E = o) a

I

E o co o o 0 0 100200300400500 I e B5 Ship L/B = medium Bld = 2.25 100200300400500 B5 Ship LIB = high Bld = 2.25 100200300400500 Ship Length (m) . e 86 Ship L/B = medium Bld = 2.25 0 100200300400500 10.0 7.5 4: .9' 50 e

I

2.5 co o 0 100200300400500 Ship Length (m) 50 25 100 7.5 5.0 100 0 100200300400500 Ship Length (m) o 2.5 7.5 50 2.5 06 Ship L/B low B/d = 2.75 100200300400500 B6 Ship L/B = medium B/d = 2,75 o 0 100200300400500 000 0 0 86 Ship L/B = high B/d = 2.75 O 0 100200300400500 Ship Length (w) 0 100200300400500 0 100200300400500

85 Shìp LIB = low Bld = 3 75 (I 'a w B5 Ship L/B = medium B/d = 3.75 B5 Ship LIB = high B/d = 3.75 loo 200 300 400 500 Ship Length (m) 10.0 7.5 5.0 Form ula 10.0 7,5 5.0 I Formula based on d1 10.0 7.5 5.0 J based on d

I.e o

e_e 4 2.5 O I e 05 Ship L/B = low B/d = 2.75 2.5 O 'a s B5 Ship L/B = low B/d = 3.25 25 o D 100200300400500 0 100200300400500 10,0 10.0 10.0 7.5 7.5 7.5 t 50 a 5.0 50 2.5 e 85 Ship L/B = medium B/d = 2.75 2.5 'I (j w 05 Ship LIB = medium B/d = 3.25 2.5 o o O 0 100200300400500 0 100200300400500 10.0 10.0 10.0 7.5 7.5 7.5 e

.e

IC

S S 5.0 5.0 p 5.0 2.5 (g(I'I B5 Ship LIB = high Bld = 2.75 2.5 'I 'a 'a w B5 Ship LIB = high B/d = 3.25 2.5 o o O 100 _{- - - - Formula} 100 based on d1 7.5 75 5,0 00 s 5.0 000 0 0 s p

2.5 B6 Ship_{L/B = low} 2.5 B6 Ship_{LIB = low}

B/d = 3,25 B/d = 3.75 o O 100200300400500 0 o 100200300400500 100 10.0 7.5 7.5 00 Q O 000 0 O 5.0 5.0 O

25 06 Ship_{L/B = medium} 2.5 B6 Ship_{LIB = medium}

Bld = 3.25 B/d = 3.75 O o 0 100200300400500 o 100200300400500 10.0 10.0 75 75 50 000 0 0 50 000 0 0 o o 86 Ship B6 Ship

25 _{LIB = high} 2.5 _{LIB = high} B/d = 3.25 B/d = 3 75

o O

0 100200300400500 o 100200300400500

loo 0 1966 ICLL 7.5 5.0 2.5 B6 Ship LIB = ow Bld = 2.25 o 0 100200300400500 0 1966 ICLL

000

4 05 Ship LIB = low Bld = 2.25 100200300400500 Ship Length (m) o 100 75 Formula based on d e

I

10.0 7.5 -c 5.0 'I 25 co e 86 Ship LIB = high B/d = 2.25

(36)

10.0 g 7.5 100 g -c 9' 50 a)

I

2.5 co o -'--10.0 g 9) 50 a,

I

2.5 co o 1966 ICLL 1 'I B8 Ship LIB = low B/d = 2 25 o 0 100200300400500 O 0 100200300400500 Ship Length (m) 0 100200300400500 0 100200300400500 Ship Length (m) 0 100200300400500 Ship Length (m)

Figure 21 Final Bow Height Results ofB7 Ships

o 100200300400500 00 O O

t-

B8 Ship LIB = medium B/d = 3.75 o 100200300400500 oQOO O O 98 Ship UB = high B/d = 3.75 o 100200300400500 Ship Length (m) E -c o, a)

I

10.0 7.5 5.0 2.5 10.0 7,5 5.0 2.5 100 7.5 5.0 2.5 10.0 7,5 5.0 2.5

o 1966 ICLL Formula - - - - Formula

based on d, a a _{B7 Ship} 'I r, LIB = low B/d = 3.25

.

-'a _{B7 Ship} 'I 'I LIB = low w _{B/d = 3.75} based on d s 97 Ship LIB = low B/d = 2.25 e e j B7 Ship LIB = low B/d = 2 75 o o o O 0 100200300400500 0 100200300400500 D 100200300400500 o 100200300400500 10,0 100 100 10.0 g .B'

I

7,5 50 25 o 7.5 5.0 25 O 7.5 5.0 2.5 O e 87 Ship L/B medium B/d 3.25 75 5.0 2.5 o s s s p 97 Ship LIB = medium B/d = 3.75 e w a B7 Ship 'i L/B = medium w Bld = 2.25 'I B7 Ship 'I _{L/B = medium} w _{B/d = 2 75} 0 100200300400500 0 100200300400500 0 100200300400500 o 100200300400500 10,0 10.0 10.0 10.0 -c 2' a)

I

co 7.5 50

2.5 97 Ship_{LIB = high} B/d = 2.25 7,5 5.0 2.5

. e,

B7 Ship LIB = high B/d = 2.75 7,5 So 2.5

s..

7.5 50 25 000 O O s B7 Ship LiB = high B/d = 3,25 Q B7 Ship LIB = high B/d = 3.75 o o o O 0 100200300400500 0 100200300400500 0 100200300400500 O 100200300400500

Ship Length (m) Ship Length (m) Ship Length (m) Ship Length (m)

10.0 10.0 10.0 Formula Formula based on

s..

7,5 based on d 7,5 7_5 -5.0 50 s 5.0

2.5 _f,'I B8 Ship_{L/B = low} 2.5 138 Ship

V, LIB = low 2.5 B/d = 2.75 B/d = 325 o O o 0 100200300400500 0 100200300400500 10.0 100 100 7,5 s s s 7.5 000 0 0 7,5 5.0 e 5.0 5.0

2.5 B8 Ship_{LIB = medium} 2.5 88 Ship_{L/B = medium} 25

B/d = 2.75 B/d = 3.25 O o o 0 100200300400500 0 100200300400500 10.0 10.0 10.0 7,5 o00 O O 7.5 00 O O 7.5 5.0 s 5.0

0_-

- 5.0

2.5 _VI 98 Ship_{L/B = high} 2.5 B8 Ship_{L/B = high} 25

B/d = 2.75 B/d = 3.25 o o o s 000 s B8 Ship LIB = low B/d = 3.75

(37)

0 100200300400500 Ship Length (m) 8 7 6 5 4 3 2 O o 4

...

e s Pontoon L/B = medium B/d = 2.75 0 100200300400500 100200300400500 Ship Length (m) Pontoon L/B = high B/d = 2.75 10.0 7.5 50 2.5 10.0 7.5 50 2.5 Ship Length L (m) pp

Figure 24 Final Bow Height Results of 30 Existing Chinese Ships

o 0 100200300400500 ase e Pontoon L/B high Bld = 3.25 o 0 100200300400500 Ship Length (m) 10.0 7.5 5.0 2.5 o 9qc o

¿

o «3 o 5v, 9 0 1966 ICLL y New formula 'i a S S Pontoon L/B = high B/d = 3.75 o 0 100200300400500 Ship Length (m)

Figure 23 Final Bow Height Results of Rectangular Pontoons

5.4

Comparison of Joint Formulas with Bow Heights of Existing Ships

Figure 24, Figure 25 and Figure 26 give the final bow height results of 30 existing

Chinese ships, 60 existing Japanese ships and 17 existing Norwegian ships.

30 Existing Chinese Ships 10.0 7.5 10.0 7.5

. 000

.0) a) 50 . 5.0 25 Pontoon 2.5 (n UB = medium O B/d = 2 25 O 0 100200300400500 10,0 10.0 75 75 L:

.5.

.9, a) 50 5.0 3: 2.5 Pontoon 2.5 (n L/B= high o Bld = 2.25 O E = D) a) :i: (n 7.5 5.0 2.5 100 o 0 1966 ICLL a 00 0 Pontoon LIB = low Bld = 2.25 0 75 50 2.5 o 10.0 Formula I I I based on d

000

Pontoon LIB = low B/d = 2 75 - - - - Formula based on d1

dli

S a Pontoon L/B = low Bld = 3 25 10.0 7.5 50 2.5 o 4 I Pontoon L/B = low B/d = 375 0 100200300400500 0 100200300400500 0 100200300400500 0 100200300400500 100 200 300 400 10.0 7.5 5.0 2.5 O 10.0 7.5 a 5.0 q 2.5 Pontoon LIB = medium B/d = 3.75 O 0 100200300400500

(38)

8 7 6 5 2 o o 6 5 2 0 o V

60 Existing Japanese Ships

w aSP o - b)010 o V o o Ship Length L (m) pp

Figure 25 Final Bow Height Results of 60 Existing Japanese Ships

17 Existing Norwegian Ships

o 1966 CLL y New formula 100 200 300 400 y V V eiQ O 00V V V o V o V o 0 1966 ICLL y New formula Ship Length L (m) pp

Figure 26 Final Bow Height Results of 17 Existing Norwegian Ships

8

7

300

(39)

6

Conclusions and Recommendations

Extensive studies on probabilistic deck wetness analysis has been carried out in China and in the Netherlands with respect to required minimum bow height of ships exceeding

24 m in length.

The following conclusions may be drawn from the results of these studies:

1. The present 1966 ICLL bow height formula accounts for ship length and block

coefficient only. These parameters govern to a large extent the heave motions of the

ship

A revised bow height formula should in addition account for the water plane area coefficient of the fore ship and the ship's (Summer) draft. These parameters have an important influence on the pitch motions of the ship and hence govern the relative

motions (as well as shipping water) at the bow.

3. From a scientific point of view China and the Netherlands propose the following

formula, based on the (Summer) draught d, for the required minimum bow height of

ships with a length of 24 meter or more:

with:

F(L). G(Cb,C,L

_PP

Id)

+O.227.(L/1O0

where in calculating F(L),

is to be taken as 300 m for ships of 300 m and

above in length, and:

G(Cb,C,LId)= 2.010+ 0.717 'Cb - 1.638 Cf - 0.0104

(LId)

length between perpendiculars at Summer draught, d B moulded breadth

d

A,4,. water plane area forward of /2 at Summer draught, d

Cb block coefficient, determined by: Gb = y

B d)

(40)

4. A more or less equivalent but less scientifically based formula, based on moulded

draught d1, is given by:

with:

F,, =F(L)G(C,,,C,L/d)

F(L)6.O81.(L/10O)-1.958.(L/l00)2+O.223.(L/l0O)3

where in calculating F(L), L is to be taken as 300m for ships of 300 m and above in

length, and:

where the following definitions have been used: calculated bow height

B moulded breadth

d

D amidships depth

water plane area forward /2 at draught d1

Cb block coefficient, defined by: C,, = V/(L B d1)

(41)

7

References

Journée (1997)

J.M.J. Journée, "Comparative Motion Calculations of Flokstra Container Ship Model", Technical Report 1093-P, 1997, DeIft University of Technology, Ship Hydromechanics Laboratory, the Netherlands.

Journée, de Kat and Vermeer (1997a)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part Technical Report 1078-P, January 1997, DeIft University of Technology, Ship

1-lydromechanics Laboratory, the Netherlands.

Journée, de Kat and Vermeer (1997b)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part Technical Report 1099-P, August 1997, DeIft University of Technology, Ship

Hydromechanics Laboratory, the Netherlands.

Journée, de Kat and Vermeer (1998)

J. M.J. Journée, J .0. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part IlL Bow Height Determination Based on Deck Wetness Considerations", Technical Report 1159-P, September 1998, DeIft University of Technology, Ship Hydromechanics

Laboratory, the Netherlands.

Journée, de Kat and Vermeer (2000a)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part Effect of Heading on Deck Wetness", Technical Report 1222-P, March 2000, DeIft

University of Technology, Ship Hydromechanics Laboratory, the Netherlands.

Journée, de Kat and Vermeer (2000b)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part Bow Height as a Function of Hull Form by Means of Probabilistic Deck Wetness Calculations", Technical Report 1226-P, May 2000, DeIft University of Technology,

Ship Hydromechanics Laboratory, The Netherlands.

Journée, de Kat and Vermeer (2000e)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line Calculations, Part VJ Probabilistic Freeboard Calculations", Technical Report 1227-P, June 2000, DeIft University of Technology, Ship Hydromechanics Laboratory, the Netherlands.

Journée, de Kat and Vermeer (2001)

J.M.J. Journée, JO. de Kat and H. Vermeer, "Comparative Load Line calculations, Part VII, Development of Bow Height Formula Based on Probabilistic Deck Wetness Analysis", Technical Report 1263-P, March 2001, DeIft University of Technology, Ship

(42)

G.Vossers (1962)

G. Vossers, "PART V. Various Aspects of the Behaviour of a Ship in Waves ", Tnt.

Shipbuilding Progress, Vol. 9. No. 92, April 1962.

"Report of the Seakeeping Committee ", 18 TTTC, 1987.

Zhu Yonge, Chen Guoquan and Lu fleming (1996)

Zhu Yonge, Chen Guoquan and Lu Deming, "The Principle Method for Calculation of Freeboard Distribution ", Technical Report 1 of Study on Reviewing Freeboards of ICLL

1966, China Classification Society, Shanghai Rules and Research Institute Shanghai,

China.

Zhu Yonge, Chen Guoquan and Lu Deming, "Probability Criteria for Determination qf Freeboard Distribution and Analysis on Practical Ships ", Technical Report 2 of Study

on Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules

and Research institute Shanghai, China.

Zhu Yonge, Chen Guoquan and Lu Deming, "computations of Freeboard Distribution for Reference Ships and Typical Ships ", Technical Report 3 of Study on Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and Research

Institute Shanghai, China.

Zhou, Zhou and Xie (1996)

Z. Zhou, D., Zhou and N. Xie, "A Seakeeping Experiment Research on Flokstra

Container Ship Model", Technical Report 4 of Study on Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and Research Institute Shanghai,

China.

Zhu Yonge, Chen Guoquan and Lu Deming, "Series Ship Forms for Calculation of Freeboard Distri bution ", Technical Report 5 of Study on Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and Research Institute Shanghai,

China.

Zhu Yonge, Chen Guoquan and Lu Deming, "Freeboard Distribution of Series Ship Forms by J'alcuiation of Deck Wetness", Technical Report 6 of Study on Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and Research

(43)

Zhu Yonge, Chen Guoquan and Lu Deming, "Regression Analyses of Freeboard

Distribution for Series Ship Forms ",

Technical Report 7 of Study on Reviewing

Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and Research Institute Shanghai, China.

Zhu Yonge, Chen Guoquan and Lu Deming,

"Supplementary Calculation and

Regression Analyses of Freeboard Distribution ",

Technical Report 9 of Study on

Reviewing Freeboards of ICLL 1966, China Classification Society, Shanghai Rules and

Research Institute Shanghai, China.

Zhu Yonge, Chen Guoquan and Zliang Gaofeng (2000)

Zhu Yonge, Chen Guoquan and Zhang Gaofeng, "Consideration on Structure c?f Bow Height Formula", Technical Report 11 of Study on Reviewing Freeboards of ICLL 1966,

China Classification Society, Shanghai Rules and Research Institute Shanghai, China.

Zhu Yoiige (2001)

Zhu Yonge, "Comparison of Available Options of Bow Height Formula ", Technical Report 12 of Study on Reviewing Freeboards of ICLL 1966, China Classification

(44)

8

Appendix A: Figures with Detailed Data of China

7.5 o 2,5 7,5 10 o 2.5 ol I I 100 200 300 Lpp(m) L/d=I5.0 IO 7,5 2. 73 -5.-, I I I

ol

I I lOO 200 300 lOO 200 300 Lpp (m) L/d16.5 Lpp (as) L1d19.5

- PsPe - - -Polynomial o 1966 ICLL

Figure 27 Bow Height Results of Al Ships

IO 2.5 7.5 2.0 - I I lOO 200 300 Lpp(m) L/di95 - PsPc - - -Polynomial o 1966 ICLL

Figure 29 Bow Height Results of A3 Ships

2. lo 75 7_5 -2.3 7.5 23 s-lOO 200 300 Lpp (m) LId24.O 01 I I lo lOO 200 300 Lpp (m) L/d24.O Lpp (as) Lfd=24.O 2.5 -I I 0 I I lOO 200 300 lOO 200 300 Lpp(m) L/dI5O Lpp(m) IJdIóS IO 73 10 o 25 IO Io 2.5 Io lo 7.3 20 nornial IO o O 5-01 I I 01 I 100 200 Lpp(m) 300 L/d150 Figure lOO 200 300 Lpp(m) L/d=16.S - PsPc - - -Poly

28 Bow Height Results

lOO 200 300 Lpp(m) L/d=19.5 o 1966 ICLL of A2 Ships lo 10 300 lOO 200

(45)

a lo lo a 73 o P2 2.5 5

lOO 200 300 lOO 200 300 lOO 200 300 Lpp(m) LId5.O Lpp(m) L/d16.5 Lpp(m) 1JdI9.5 PsPc - --Polynomial o 1966 ICLL I I I lOO 200 300 Lpp(m) IJdI5.O lOO 200 300 400 Lpp(m) L/d=I7,5 Io 7.5

IO

I I 0 IO 7.5 2.5 o 2,5 25 100 200 300 Lpp(m) Ud=16.5 - PsPc - - -Polynomial 73 2.5 lOO 200 300 Lpp(m) IJd'19.S o 1966 ICLL lOO 200 300 400 0 100 200 300 400 Lpp(m) Ud19.25 Lpp(m) Ud22.75 - PsPc - - -Polynomial o 1966 ICLL

Figure 32 Bow Height Results of Bi Ships

IO 7.5 23 IO 73 2.5 lOO 200 300 Lpp (m) L/d24.O IO 7.5 2.5 lOO 200 300 Lpp (m) IJd24.O 0 100 200 300 400 Lpp (m) LId28.O o 2.5- 25 IO 73

7.5-l5

P2 2.5 2.

(46)

10 7.5 o 0 2.5 Io 7.5 o 02 2.5 0 100 200 300 400 Lpp(m) Lfd17.5 O lOO 200 300 400 Lpp(m) L/d17.5 IO 25 Io 7.5 25 0 105 200 300 400 0 lOO 200 300 400 Lpp (m) L/d19.25 Lpp m) IJd22 75 - PsPc - - -Polynomial o 1966 ICLL

Figure 33 Bow Height Results of B2 Ships

10 7.5 23 7 10 25 o lOO 200 300 400 0 100 200 300 400 Lpp(m) L/d=1925 Lpp(m) Ud2275 - PsPc - - -Polynomial o 1966 ICLL

I I I

lOO 200 300 400 0 ISO 200 300 400 Lpp (m) Ltd19,25 Lpp (m) Ud22.75

PsPc - - -Polynomial o 1966 ICLL

lOO 200 300 400 Lpp(m) L/d=28.O Io 7. 2,5 .1 I I lOO 200 300 400 Lpp(m) L1d280 IO lOO 200 300 400 Lpp(m) IJd2S.O 7.5 o o

-

O 25 10 lo 7. 7.5 o 2.5 - 25 Io 7, o O o 2.5 I I I Io 7.5 o 2.5 0 100 200 300 400 Lpp(m) L/d17.5

(47)

lo o O lOO 200 300 400 Lpp(ni) IJdll.5 0 100 200 300 400 Lpp(m) L/dS17.5 I I lOO 200 300 400 Lpp(m) 11d175

lo 7.5 2.5 IO 7.5 2.5 lOO 200 300 400 0 100 200 300 400 Lpp (m LidI9.25 Lpp IJd=22.75 - PsPc - - -Polynomial o 1966 ICLL o O o 2.0 I I o lOO 200 300 400 0 lOO 200 300 400 Lpp(m) L1d19.25 Lpp(m) L1d22.75 - PsPc - - -Polynomial o 1966 ICLL

7.5

2.3

lOO 200 300 400 0 lOO 200 300 400

Lpp (m) L/d19.25 Lpp (m) LIdS22.75

- PsPc - - -Polynomial o 1966 ICLL

7.0 25 10

li

o O I o ._-_____ 2.5 lo 7.5 2.5 0 lOO 200 300 400 Lpp(m) IJd28.O 100 200 300 400 Lpp Cm) L/d28.O

O'

lOO 200 300 400 Lpp (m) L/d28 O 10 lo a 7.5 X o 2.5 lo 7.5 X o 00 2.5

(48)

7.5-z o 122 2.5-IO 2.5 5-Io 7.5 23 IO 7.5 2.5

100 200 300 400 0 loo 200 300 400 0 lOO 200 300 400 0 lOO 200 300 400 Lpp(m) Uo117.5 Lpp (m) Ud19.25 Lpp (m) L1d22.75 Lpp (m) L/d28.O

- PsPc - - -Polynomial o 1966 ICLL

(49)

7.5 .15

z

o

0 2.5

8.2 Figures with Detailed Data for the Netherlands Series

0 100 200 300 400 500 Lpp (m) 0 100 . 200 300 400 500 Lpp (m) 0 OC o 10 73 2.5 lo 7.5 2.5 O lOO 200 300 400 500 Lpp (m) lOO 200 300 400 500 Lpp (m) 10 7.5 2.5 L/B=low 7.5 2.5 L/B=medium io 7.5 2.5 L/B =hig h

- China o 1966 ICLL B/d low to high

Figure 40 Bow Height ResuLts of Vermeer Ships

o o 0 100 200 500 400 500 0 100 200 300 400 500 Lpp (m) Lpp (m) lOO 200 300 400 500 Lpp (m) 0 100 200 300 400 500 IO 7.5 2.5 2. lo

5

i i i lOO 200 300 400 500 Lpp (m) Lpp (m) Lpp (m)

020 0

i r i lOO 200 300 400 500 o o lOO 200 300 400 500 Lpp (m) 7.5 ₀₀ ₀ C . o 2.5 I t O O lOO 200 300 400 500 Lpp (m) IO 7. 2.5 10 7.5

(50)

-I I lOO 200 300 400 500 Lpp (m) L/B=medium lo 75 lo 7.5 I I lOO 200 300 400 500 Lpp (os) L/B=high

- China o 1966 ICLL BId= low to high

Figure 41 Bow Height Results of Al Ships

2.5 7.5 2.5 IO 7,5 2.5 o o I j lOO 200 300 400 500 Lpp(m) 0 100 200 300 400 500 Lpp (os) lOO 200 300 400 500 Lpp (os) o I I I O 100 200 300 400 500 Lpp (m) IO 7.5 7.3 000 0 O o 0 2.5 2. lOO 200 300 400 500 Lpp (m) lo

7.5-boo o

o o 0 2,5 2.5 I I lOO 200 300 400 500 Lpp (m) I I I I lOO 200 Lpp 300 400 500 L/B=low Io 7,5 2.5 500 lOO 200 000 Lpp (m) 400 500 I o I o I o C 00 0 lOO 200 300 400 0 lOO 200 300 400 500 I0 7. 2. o o c o o 0 2.3 o000

0 2

Lpp (m) Lpp (m) Io 7,5

(51)

o 25 O lOO 200 300 400 500 Lpp (m) IO o o 0 lOO 200 300 400 500 Lpp (m) lOO 200 300 400 000 Lpp (m) IO 7. 2 lo 7.5 2.5 10 2.5 lOO 200 300 400 500 Lpp (m) o o o lOO 200 300 400 500 Lpp (m) 10 7.5 2.5 L/B=Iow 7,5 2.5 lo 7.5 23 lo L/B=medium LfBrhigh

- China o 1966 ICLL BId= low to high Figure 42 Bow Height Results of A2 Ships

o o I I 100 200 300 400 500 Lpp (m) O lOO 200 300 400 500 Lpp (m) IO 7.5 - 23 IO 7.5 2.5 IO 7,5 25 o I I 100 200 300 400 300 Lpp (m) O lOO 200 300 400 500 Lpp (m) O O O lOO 200 300 400 500 0 lOO 200 300 400 500 Lpp (m) Lpp (m) o lOO 200 300 400 500 Lpp (m) lo

(52)

10 7,5 o 0 2.5 10 7.5 O J I 0 lOO 200 300 Lpp (m) o 0 00 0 I I 0 100 200 300 400 500 Lpp (m) 1 L/B=low O I I I 100 200 300 400 500 Lpp (m) 10 2. lo 75 2.5 5-L/B=medium 10 7,3 2.5 o

o00 0

I I I oOO O lOO 200 500 400 500 Lpp (m) 00 200 300 400 500 Lpp (m) L/B=high

- China o 1966 ICLL B/d= low to high Figure 43 Bow Height Results of A3 Ships

7. 2.5 75 2 10 lo 7.5 2. 5-oOO O -I I I lOO 200 300 400 500 Lpp (m) oOO O o 00 O O 10 0 C

o00

2.5 I I 400 300 lOO 200 300 400 Lpp (m) IO 7. 0 C

o00 0

2. O o 0 2.5 lo 7. 2,3 I I lOO 200 300 Lpp (m) 400 000 o lOO 200 300 Lpp (m) 00 0 C oOO 7. -200 300 400 500 Lpp (m) 500 lOO 400 300 lOO 200 300 400 500 Lpp (m) o I I lOO 200 300 400 500 Lpp (m)

(53)

i 2.5 lo 7.5 o m 2.5 o o ( lOO 200 300 400 500 Lpp (m) 2.5 Io 7.5 5 25 IO i i Io o lOO 200 300 400 000 Lpp (m) o O O lOO 200 300 400 500 0 lOO 200 000 400 500 Lpp (m) Lpp (m) lo 7.5 2.5 LLB=low O O lOO 200 300 400 500 0 lOO 200 300 400 500 Lpp (m) Lpp (m) IO 7.5 2.5 LtB ed iu m 2.5 100 200 300 400 500 Lpp (m) IO 7.5 2.5 10 2.5 I I 00 200 300 400 500 Lpp (m) 00 7.5 - 7.5 - 5 il 2.5t - 2.5 O O

lOO 200 300 400 500 0 lOO 200 000 400 500 100 200 300 400 500 lOO 200 300 400 500

Lpp (m) Lpp (m) Lpp (in) Lpp (m)

L/B=high

China o 1966 ICLL B/d= low to high Figure 44 Bow Height Results of A4 Ships

75 75

Io

Joint Development of a Bow Height Formula by China and The Netherlands Based on Probabilistic Deck Wetness Analysis