Probabilistic damage stability verification of PYC motor ......Probabilistic damage stability verification on PYC motor yachts 7 “EMSHIP” Erasmus Mundus Master Course, period of

Probabilistic damage stability verification of PYC motor

yachts

Blanka Ascic

Master Thesis

presented in partial fulfillment

of the requirements for the double degree:

“Advanced Master in Naval Architecture” conferred by University of Liege

"Master of Sciences in Applied Mechanics, specialization in Hydrodynamics, Energetics and

Propulsion” conferred by Ecole Centrale de Nantes

developed at University of Genoa

in the framework of the

“EMSHIP”

Erasmus Mundus Master Course

in “Integrated Advanced Ship Design”

Ref. 159652-1-2009-1-BE-ERA MUNDUS-EMMC

Supervisor: Prof. Dario Boote, University of Genoa

Reviewer: Prof. Leonard Domnisoru, University of Galati

Genoa, February 2015

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Master Thesis developed at University of Genoa

Contents

DECLARATION OF AUTHORSHIP ....................................................................................... 4

ABSTRACT ............................................................................................................................... 5

1. INTRODUCTION .............................................................................................................. 6

2. BASICS OF SHIP STABILITY ........................................................................................ 7

2.1. Intact Stability .............................................................................................................. 7

2.2. Free Surface Effect ...................................................................................................... 9

2.3. Intact Stability Criterion ............................................................................................ 10

2.4. Damage Stability ....................................................................................................... 13

2.4.1. Deterministic Approach ..................................................................................... 13

2.4.2. Probabilistic Approach ....................................................................................... 15

3. CASE STUDY – 92 m MOTOR YACHT ....................................................................... 17

3.1. General Particulars .................................................................................................... 17

3.2. Capacity Plan ............................................................................................................. 18

3.3. Watertight Compartment Plan ................................................................................... 21

4. DETERMINISTIC CALCULATIONS ............................................................................ 24

4.1. Departure Condition – 100% Consumables .............................................................. 24

4.2. Half Load Condition – 50% Consumables ................................................................ 28

4.3. Arrival Condition – 10% Consumables ..................................................................... 32

4.4. KG Curve for Intact Stability .................................................................................... 36

4.5. Damage Stability Calculations .................................................................................. 37

4.5.1. Considered Damage Cases ................................................................................. 37

4.5.2. Analysis and the Results of Damage Conditions ............................................... 38

5. PROBABILISTIC APPROACH ...................................................................................... 51

5.1. PYC - Required Subdivision Index R ........................................................................ 51

5.2. PYC - Attained Subdivision Index A ........................................................................ 52

Probabilistic damage stability verification on PYC motor yachts 3

“EMSHIP” Erasmus Mundus Master Course, period of study September 2013 – February 2015

5.2.1. Calculation of the Factor pi ................................................................................ 54

5.2.2. Calculations of the Factor si ............................................................................... 63

5.2.3. Calculations of the Factor vm ............................................................................. 70

5.2.4. Final Results of the Attained Subdivision Index A ............................................ 73

6. COMPARISON OF RESULTS ....................................................................................... 75

7. CONCLUSIONS .............................................................................................................. 77

8. ACKNOWLEDGEMNTS ................................................................................................ 78

9. REFERENCES ................................................................................................................. 79

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DECLARATION OF AUTHORSHIP

I declare that this thesis and the work presented in it are my own and has been generated by

me as the result of my own original research.

Where I have consulted the published work of others, this is always clearly attributed.

Where I have quoted from the work of others, the source is always given. With the exception

of such quotations, this thesis is entirely my own work.

I have acknowledged all main sources of help.

Where the thesis is based on work done by myself jointly with others, I have made clear

exactly what was done by others and what I have contributed myself.

This thesis contains no material that has been submitted previously, in whole or in part, for

the award of any other academic degree or diploma.

I cede copyright of the thesis in favour of the University of Genoa.

Date: 12.01.2015 Signature:



ABSTRACT

Damage stability calculations are required in order to achieve a minimum degree of safety

after flooding. In order to assess the calculations, one has developed two approaches,

deterministic and probabilistic. Both methods have the same objective and that is to find the

most effective possible subdivision of the ship so that she remains afloat and stable in damage

conditions.

Taking into consideration operating purpose of a yacht and its risks, it has been recognized

that the international conventions have been disproportionally onerous in terms of design and

cost. Therefore the new Passenger Yacht Code was introduced aiming to provide a SOLAS

equivalent for yachts wishing to carry up to 36 passengers in order to provide additional

flexibility to the Naval Architects and Designers.

Deterministic method is based on the assumed damage scenarios i.e. one compartment or a

group of compartments is being flooded. SOLAS 90 two compartment standard is a

deterministic or rule-based approach which ensures the survivability of the ship in case of

flooding of up to two adjacent compartments.

The probabilistic method is based on statistical evidence concerning what actually happens

when ships collide, in terms of sea state and weather conditions, extent and location of

damage, speed and course of the ship and whether the ship survived or sank, therefore being a

more realistic approach.

The probabilistic approach implies the determination of characteristic safety factors:

- Attained subdivision index A, represents a measure for the probability of survival of

the ship in the damage case

- Required subdivision index R, represents a survival level imposed by the regulations,

given the size of the ship exposed to the damage and the number of people onboard.

It is required that the attained subdivision index, A is greater than the required subdivision

index, R.

Since general arrangement and lifesaving appliances are of high importance in the yacht

industry, it is valuable to introduce different sets of possibilities for it. Therefore both

deterministic and probabilistic calculations have been applied on a 92m motor yacht based on

PYC rules in order to compare the two and gain more insight into compartment definition of a

yacht.

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1. INTRODUCTION

The man has been sailing for thousands of years and the basic concept of hydrodynamics was

introduced by the ancient Archimedes in 300 BC. Archimedes' Principle states that when a

body is fully or partially immersed in fluid, it appears as if it has a loss in mass equal to the

mass of fluid it displaces. This is due to the buoyancy force which acts through the centre of

the immersed volume of the body and is opposite to gravity, a force which acts through the

centre of mass of the body.

However, the principles of modern ship stability were introduced and explained many

centuries later. In 1746 French Piere Bouguer published his work Traité du Navire and Swiss

Leonhard Euler with his Scientia Navalis in 1749, were the first to explain some specific

problems of ship theory based on Newtonian mechanics.

With the industrial revolution in nineteenth century, appeared the necessity for more practical

and systematic approach to ship stability. The classification societies established rules for

positioning bulkheads in merchant ships resulting with fore and aft peak tanks and separated

machinery and cargo space.

After the dramatic loss of Titanic on her maiden voyage from Southampton to New York, in

1914, the International Convention for the Safety of Life at Sea (SOLAS), was first

established and still governs the maritime safety in the world to this day.

However, it was only after the World War II that the first explicit requirements on damage

stability was introduced, in 1948 SOLAS, namely with the positive metacentric height in

damage conditions. It also laid the foundations for the International Maritime Organization

(IMO), the United Nations agency responsible for improving maritime safety and preventing

pollutions at sea. After the Andrea Doria accident, the 1960 SOLAS stated that the minimum

metacentric height of 0.05 m in damage conditions is mandatory, following with the 1974

SOLAS and an implicit requirement for a righting arm in damage conditions of at least 0.03

m. After the Herald of Free Enterprise accident in 1987, SOLAS introduced a complete

damage stability criterion known as SOLAS 90.



2. BASICS OF SHIP STABILITY

2.1. Intact Stability

Having a ship floating upright in still water, the centres of gravity and buoyancy are at G and

B respectively, as shown in Figure 1 (a).

Figure1.Stable equilibrium

After the ship is inclined by an external force to a small angle Θ, as shown in Figure 1(b), we

can observe that the centre of gravity stays in the same place since the mass hasn’t been

changed whereas the centre of buoyancy shifts since the shape of submerged volume has

changed, therefore changing the position of its centre, from original position B to new

position B1.

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The verticals trough the centres of buoyancy at two consecutive angels of heel intersect at a

point called the metacentre, M. For angels of heel up to around 15̊, the verticals trough the

centres of buoyancy intersect at the same point called the initial metacentre which depends on

the ship’s underwater form.

The metacentric height is the vertical distance between G and M and can be positive, having

the metacentre M above the centre of gravity G, or negative when M is below G.

Figure 1(c) shows the righting couple where the distance between G and Z is the righting arm.

(a) Unstable equilibrium (b) Neutral equilibrium

Figure 2.Unstable and neutral equilibrium

For a ship which is inclined with an angle and tends to heel over further, we say it’s an

unstable ship with a negative metacentric height as shown in Figure 2 (a). In order to have a

neutral position of the ship as shown on Figure 2 (b), the metacentre M and the centre of

gravity G must coincide thus creating no couple.



2.2. Free Surface Effect

Every ship contains tanks which are filled with different types of liquids. Depending on the

purpose of the tank, the liquid within can be fresh, grey or ballast water or more dens liquids

such as fuels and oils. When the tank is filled to the top, the fluid can’t move in the tank

therefore acts as a solid load having the centre of its mass placed in the centre of the tank.

The problem arises when the tank is not completely filled and the fluid can move around as

the ship moves.

Figure 3.Free Surface Effect

As the ship heels, the fluid moves to the heeled side shifting its own centre of gravity from g

to g1 as well as the centre of gravity of the entire ship from G to G1. As shown in the Figure 3,

this causes a virtual loss of metacentric height moving the centre of gravity G only virtually to

GV. In other words, the virtual loss of metacentric height is due to the free surface effect and

any loss of metacentric height is a loss in stability. Free surface effect in large dimensioned

tanks can be so high that it seriously damages ship’s stability causing the ship to capsize.

Therefore it is very important to take free surface effect into account while dimensioning

tanks. Reducing the size of the tanks, the free surface effect is being reduced as well.

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2.3. Intact Stability Criterion

Intact stability calculations are rather straightforward. One has to take into account every

individual centre of gravity regarding all the masses of the ship in order to determine the

centre of gravity of the ship as well as the centre of buoyancy of the hull. From there one can

proceed verifying if the given arrangement fulfils the requirements of the rules for intact

stability or not.

The IMO criterion for intact stability are:

1. The area under the righting lever curve (GZ curve) should not be less than 0.055 m.rad

up to 30o angle of heel as shown in Figure 4.

Figure 4.The IMO criterion for intact stability – area under the curve up to 30o

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

≥ 0,055



2. The area under the righting lever curve (GZ curve) should not be less than 0.09 m.rad

up to 40o angle of heel, or the angle of downflooding, as shown in Figure 5.

Figure 5.The IMO criterion for intact stability – area under the curve up to 40o

3. The area under the GZ curve between the angles of heel of 30o and 40

o or between 30

o

and the angle of downflooding if this is less than 40oshould not be less than 0.03 m.rad

as shown in Figure 6.

Figure 6.The IMO criterion for intact stability – area between the angles of 30o and 40

o

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

≥ 0,09

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

≥ 0,03

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4. The righting lever (GZ) should be at least 0.20 metres at an angle of heel equal to or

greater than 30o as shown in Figure 7.

Figure 7.The IMO criterion for intact stability for minimum GZ

5. The maximum GZ should occur at an angle of heel of preferably exceeding 30o but not

less than 25o as shown in Figure 8.

Figure 8.The IMO criterion for intact stability for maximum GZ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

Min 0,2 m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

GZmax

≥ 30o (not <25o)



6. After correction for free surface effects, the initial metacentric height (GM) should not

be less than 0.15 metres as shown in Figure 9.

Figure 9.The IMO criterion for intact stability for initial GM

2.4. Damage Stability


after flooding. The loss of stability from flooding may be due in part to the free surface effect

as well. In order to assess the calculations, one has developed two approaches, deterministic

and probabilistic. Both methods have the same objective and that is to find the most effective

possible subdivision of the ship so that she remains afloat and stable in damage conditions.

2.4.1. Deterministic Approach

Deterministic method is based on the assumed damage scenarios i.e. one compartment or a

group of compartments is being flooded. Different deterministic methods in damage stability

have been developed depending on ship’s type, freeboard reduction and the type of cargo

carried, some of which are: floodable length method, SOLAS90 damage stability criterion,

Stockholm Agreement, stability criteria for specific ship types.

Floodable length is defined as the maximum longitudinal extent of the flooded area centred in

any given point of the ship, without causing the immersion of the margin line as well as

maintaining positive metacentric height.

SOLAS 90 two compartment standard is a deterministic or rule-based approach which ensures

the survivability of the ship in case of flooding of up to two adjacent compartments.

00.10.20.30.40.50.60.70.8

0 10 20 30 40 50 60 70 80 90 100

GZ

[ m

]

Heeling Angle [ ̊]

≥ 0,15m

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The number of flooded compartments varies according to the ship’s length, from one for

smaller ships to 2+ for very large ships. The standard was partially empirical, based on

analysis of the stability data of damaged cases which led to capsizing or sinking of the ship.

Figure 10.Evolution of damage stability standards for passenger ships in SOLAS

The damage stability criterion SOLAS90 requires that the ship in damage condition meets the

following demands:

- Range of stability of at least 15º from the equilibrium angle.

- Minimum reserve of stability of 0.015 m.rad.

- Minimum metacentric height in damage condition of 0.05 m.

- Minimum righting arm of 0.10 m, including the effects of passengers crowded on one

side, launching of lifeboats and wind pressure.

- Maximum heeling angle before equalization should not exceed 15º.

Up to date there has been no SOLAS90 ship that sunk, but even so the deterministic approach

is being more and more replaced by probabilistic simply because the associated safety level of

deterministic requirements is unknown.



2.4.2. Probabilistic Approach

The probabilistic method is based on statistical evidence concerning what actually happens

when ships collide, in terms of sea state and weather conditions, extent and location of

damage, speed and course of the ship and whether the ship survived or sank. It is therefore

more realistic approach. The concept of probabilistic method was first introduced by Wendel

in the 1960's. The method recognized numerous uncertainties regarding damage location,

damage extent, loading condition as well as wave and wind condition. It was further

developed by Comstock and Robertson in 1961 and Volkov in 1963. It was adopted by the

International Maritime Organization in 1973 as an alternative to the deterministic regulations

for the assessment of the damage stability of ro-ro ferries and passenger ships but was very

rarely used due to its complexity. The probabilistic concept was modified in the 1992 revision

of SOLAS 74 taking part in the damage stability of all dry cargo ships of 100 m, which was

later reduced to 80 m, and above in length built after 1992.

When assessing the probability of ships survival in damage conditions, one has to include the

following:

- Probability of flooding each single compartment and each and every group of two or

more adjacent compartments

- Probability that buoyancy and stability after flooding is sufficient to prevent dangerous

heeling, sinking or capsizing of the ship

The probabilistic approach implies the determination of characteristic safety factors:

- Attained subdivision index A, represents a measure for the probability of survival of

the ship in the damage case

- Required subdivision index R, represents a survival level imposed by the regulations,

given the size of the ship exposed to the damage and the number of people onboard.

It is required that A ≥ R.

The general formula for the index A is:

𝐴 = pivisi

i

(1)

where:

- pi is the probability that the compartment or a group of compartments is flooded

- vi is the probability that the space above an existing horizontal boundary is not flooded

- si is the probability of survival after flooding the compartment or a group of

compartments

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Figure 11.Probability of a compartment being flooded

Figure 11 illustrates the damage location x and damage length y which are random variables.

Their distribution density function f(x, y) can be derived from statistics. Assuming that the

flooding exists, the total volume between the x-y plane and the f(x, y) equals to one. The

volume above a projected triangle onto x-y plane and under the distribution density function

represents the probability of a specific compartment being flooded.

The formula for required index R for passenger ships entered into force on 1st of January,

2009 and applies to all new build ships. According to SOLAS 2009, it is:

𝑅 = 1 −5000

𝐿𝑆 + 2,5𝑁 + 15252

(2)

where:

- LS is subdivision length

- N = N1 + 2N2

- N1 number of persons for whom lifeboats are provided

- N2 number of persons the ship is permitted to carry



3. CASE STUDY – 92 m MOTOR YACHT

3.1. General Particulars

The case study of the thesis is a 92 m motor yacht built at Benetti shipyard. General

information is presented in the following Table 1.

Table 1.General information – ZOZA motor yacht

Rule Length 88.6 m

Moulded Dimensions LOA 92 m, B 15.8 m, D 7.7 m

Max Displacement at Summer loaded draft 3178 t (preliminary)

Deadweight 528 t (preliminary)

Area of Operation Unrestricted

Standard of survivability Intact & Damage Stability

Number of crew 28

Number of passengers 34

FRAME OF REFERENCE

Aft Perpendicular 0 m

Midships 43.66 m

Fwd Perpendicular 87.33 m

Length Between Perpendiculars 87.36 m

Baseline 0 m

DatumWL 4.2 m

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3.2. Capacity Plan

Figure 12.Tank capacity plan of the motor yacht



The tanks are defined in Hydromax according to the tank capacity plan as shown in Figure 12.

Each tank was defined with its aftmost and foremost end as well as its starboard or portside

breadth and vertical height. The Table 2 below represents the tank definition details with its

dimensions as well as its containing fluid density.

Table 2. Tank definition details

Name

Intact

perm.

Damage

perm.

Specific

grav. Fluid type Aft Fore F.Port F.Stbd F.Top F.Bottom

Fuel 49C 98 95 0,84 Diesel 5,6 10,435 -1,5 1,5 3,5 1,782

Fuel 48PS 98 95 0,84 Diesel 10,435 17,6 -7,735 -4,2 3,85 1,016

Fuel 47SB 98 95 0,84 Diesel 10,435 17,6 4,2 7,735 3,85 1,016

Fuel 63 PS 98 95 0,84 Diesel 18,4 20,8 -4,2 -1,5 2,15 0

Fuel 63 PS 98 95 0,84 Diesel 20,8 26,4 -4,2 -1,5 1,9 0

Fuel 64 SB 98 95 0,84 Diesel 18,4 20,8 1,5 4,2 2,15 0

Fuel 64 SB 98 95 0,84 Diesel 20,8 26,4 1,5 4,2 1,9 0

Fuel 62 C 98 95 0,84 Diesel 19,5 20,8 -1,5 1,5 2,15 0,558

Fuel 62 C 98 95 0,84 Diesel 20,8 26,4 -1,5 1,5 1,9 0,231

Overflow 98 95 0,84 Diesel 29,6 32,8 -2,5 0 1,1 0,088

Fuel Settling 76 CL 98 95 0,84 Diesel 32,8 35,4 -2,5 2,5 1,1 0,049

Fuel 912 PS 98 95 0,84 Diesel 40 51,2 -6 -3,8 1,8 0

Fuel 913 SB 98 95 0,84 Diesel 40 51,2 3,8 6 1,8 0

Fuel 910 PS 98 95 0,84 Diesel 40 50,4 -3,8 -1,6 1,8 0

Fuel 911 SB 98 95 0,84 Diesel 40 50,4 1,6 3,8 1,8 0

Daly PS 98 95 0,84 Diesel 26,4 35 -7,89 -6,9 4,35 1,85

Daly SB 98 95 0,84 Diesel 26,4 35 6,9 7,89 4,35 1,85

Fresh Water 104 98 95 1 Fresh Water 53,8 59,4 -2,8 0 1,8 0

Fresh Water 103 98 95 1 Fresh Water 53,8 59,4 0 2,8 1,8 0

Fresh Water 105 98 95 1 Fresh Water 59,4 63,6 -2,1 2,1 1,8 0

Sewage Holding 98 95 1 Sewage 11,2 13,55 -1,5 1,5 2,75 1,391

Sewage Holding 98 95 1 Sewage 13,55 16 -1,5 1,5 2,65 1,152

Sewage 84 98 95 1 Sewage 48 50,4 -1,6 1,6 1,8 0

Heli Fuel S1 98 95 0,8203 JFA 16 17,6 -1,5 1,5 2,65 1,016

Pool Dump S2 98 95 1 Custom 3 -2,5 1,6 -2 2 4,74 2,892

Sanitary T2 98 95 1 Sewage 18,4 19,5 -1,5 1,5 2,15 0,686

Sanitary T1 98 95 1 Sewage 38,4 40 -2 2 1,1 0,021

Sanitary 95 PS 98 95 1 Sewage 51,2 53 0 3 1,8 0

Sanitary 107 98 95 1 Sewage 68,4 71,2 -0,8 0,8 1,8 0

Dirty Oil 98 95 0,92 Lube Oil 26,4 29,6 -2,5 0 1,1 0,148

Clean Oil 74 98 95 0,92 Lube Oil 26,4 32,8 0 2,5 1,1 0,088

Sludge 75 98 95 0,913 Slops 35,4 38,4 -2 -0,5 1,1 0,025

Bilge 76 98 95 1 Custom 6 35,4 38,4 -0,5 2 1,1 0,025

Sanitary 83 98 95 1 Sewage 46 48 -1,6 1,6 1,8 0

Laundry Water 96 98 95 1 Sewage 51,2 53 -3 0 1,8 0

Technical Water 87 98 95 1 Sewage 64,4 68,4 -1,4 1,4 1,8 0

Ballast 51PS 98 95 1,025 Sea Water 11,2 13,55 -4,2 -1,5 2,75 0

Ballast 52 SB 98 95 1,025 Sea Water 11,2 13,55 1,5 4,2 2,75 0

Ballast 51PS 98 95 1,025 Sea Water 13,55 17,6 -4,2 -1,5 2,65 0

Ballast 52 SB 98 95 1,025 Sea Water 11,2 13,55 1,5 4,2 2,65 0

Ballast 912 C 98 95 1,025 Sea Water 40 46 -1,6 1,6 1,8 0

Ballast 118 98 95 1,025 Sea Water 81,4 87,98 -0,3 0,3 3 0

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The following Figure 13 shows the 3D model of the hull with its placed tanks in Hydromax.

Figure 13.The hull of the yacht with the tanks



3.3. Watertight Compartment Plan

Figure 14.Watertight compartment plan

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Figure 14 shows how watertight compartments are placed inside the hull of the yacht. The

compartments are defined in Hydromax according to the general arrangement. Each

compartment was defined with its aftmost and foremost end as well as its vertical height. The

Table 3 below represents the compartment definition details with its dimensions.

Table 3.Compartment definition details

Name Intact perm. Damage perm. Aft Fore F.Port F.Stbd F.Top F.Bottom aft ULD 85 85 -4,673 3,6 -8 8 4,74 2,6

aft PS 85 85 -3,85 7,4 -8 -3,5 7,68 4,74

aft SB 85 85 -3,85 8 3,5 8 7,68 4,74

aft LD 95 95 -3,85 8 -3,5 3,5 7,68 4,74

aft LD 95 95 8 17,6 -8 8 7,68 4,74

aft LD 95 95 7,4 8 -8 -3,5 7,68 4,74

aft1 ULD 85 85 3,6 10,4 -8 8 4,74 1,8

aft2 ULD ext 95 95 10,4 11,2 -4,2 4,2 4,74 1,8

aft2 ULD ext 95 95 10,4 17,6 -8 -4,2 4,74 0

aft2 ULD ext 95 95 10,4 17,6 4,2 8 4,74 0

ABB room 85 85 17,6 26,4 -8 8 4,74 0,25

ABB room 95 95 17,6 26,4 -8 8 7,68 4,74

crew LD 2 95 95 26,4 31,2 -8 8 7,68 4,74

crew LD 2 95 95 31,2 40 -8 1,43 7,68 4,74

ER DB 95 95 26,4 40 -8 8 1,145 0

ER DB 85 85 26,4 40 -8 8 4,74 1,145

ER 85 85 31,2 40 1,43 8 7,68 4,74

Fins 85 85 40 51,2 -8 8 7,68 1,8

Fins DB 95 95 40 51,2 -8 8 1,8 0

crew fw1 DB 95 95 51,2 59,4 -8 8 1,8 0

crew fw1 95 95 51,2 59,4 -8 8 7,68 1,8



The following Figure 15 shows the top view of the hull with its placed compartments and the

Figure 16 represents the 3D view of the hull with the compartments defined in Hydromax.

Figure 15.Defined compartments – top view

Figure 16.The hull of the yacht with the compartments

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4. DETERMINISTIC CALCULATIONS

4.1. Departure Condition – 100% Consumables

Table 4.Loading condition for 100% consumables

Item name Quantity

Unit

Mass

Total

Mass

Unit

Volume

Total

Volume

Long.

Arm

Trans.

Arm

Vert.

Arm

Total

FSM

Lightship 1 2650 2650 38,652 0 7 0

Provisions and stores 1 30 30 60 0 4,4 0 Spare 1 10 10 50 0 4,6 0

Pass and crew effects 1 11 11 42,465 0 11 0 Owner supplies 1 30 30 25 0 7,25 0

Helicopter 1 4 4 19,2 0 20,05 0 Automobile 1 6 6 26,4 0 19,55 0

Tender and jet ski 1 30 30 62,6 0 9,2 0

Diving equipment 1 1 1 4,6 0 5,6 0 Fuel 49C 98% 16,225 15,9 19,315 18,929 8,208 0 2,794 0

Fuel 48 SB 98% 28,316 27,75 33,71 33,036 14,296 -5,619 3,052 0 Fuel 47 PS 98% 28,316 27,75 33,71 33,036 14,296 5,619 3,052 0

Fuel 63 PS 98% 19,774 19,379 23,541 23,07 22,655 -2,753 1,387 0

Fuel 64 SB 98% 19,774 19,379 23,541 23,07 22,655 2,753 1,387 0 Fuel 62 C 98% 24,83 24,333 29,559 28,968 23,099 0 1,197 0

Overflow 98% 5,921 5,803 7,049 6,908 31,224 -1,196 0,639 0 Fuel Settling 76 CL 98% 10,271 10,066 12,228 11,983 34,11 0 0,609 0

Fuel 912 PS 98% 21,588 21,156 25,7 25,186 45,295 -4,767 1,228 0 Fuel 913 SB 98% 21,588 21,156 25,7 25,186 45,295 4,767 1,228 0

Fuel 910 PS 98% 28,965 28,386 34,482 33,792 45,143 -2,665 1,013 0

Fuel 911 SB 98% 28,965 28,386 34,482 33,792 45,143 2,665 1,013 0 Daly PS 98% 10,506 10,296 12,507 12,257 30,708 -7,223 3,285 0

Daly SB 98% 10,506 10,296 12,507 12,257 30,708 7,223 3,285 0 Fresh Water 104 98% 24,82 24,324 24,82 24,324 56,585 -1,335 0,971 0

Fresh Water 103 98% 24,82 24,324 24,82 24,324 56,585 1,335 0,971 0

Fresh Water 105 98% 32,199 31,555 32,199 31,555 61,405 0 0,979 0 Sanitary T2 10% 4,347 0,435 4,347 0,435 19,019 0 0,856 2,475

Sanitary T1 10% 6,437 0,644 6,437 0,644 39,205 0 0,117 8,533 Sanitary 95 PS 10% 8,651 0,865 8,651 0,865 52,092 0,93 0,208 4,05

Sanitary 107 10% 10,016 1,002 10,016 1,002 69,747 0 0,191 2,674 Sanitary 83 10% 10,908 1,091 10,908 1,091 46,995 0 0,143 5,461

Sewage Holding 10% 17,879 1,788 17,879 1,788 14,867 0 1,402 10,8

Sewage 84 10% 13,049 1,305 13,049 1,305 49,193 0 0,147 6,554 Heli Fuel S1 98% 6,016 5,895 7,334 7,187 16,813 0 1,854 0

Pool Dump S2 98% 26,359 25,832 26,359 25,832 -0,395 0 3,9 0 Dirty Oil 10% 5,8 0,58 6,304 0,63 28,257 -0,684 0,294 3,833

Clean Oil 74 98% 12,264 12,019 13,331 13,064 29,722 1,188 0,661 0

Sludge 75 10% 4,633 0,463 5,074 0,507 36,954 -1,162 0,154 1,274 Bilge 76 10% 8,193 0,819 8,193 0,819 36,961 0,515 0,125 5,287

Laundry Water 96 10% 8,651 0,865 8,651 0,865 52,092 -0,93 0,208 4,05 Technical Water 87 10% 21,03 2,103 21,03 2,103 66,317 0 0,21 12,26

Ballast 51 PS 0% 17,946 0 17,508 0 17,577 -1,5 1,052 0 Ballast 52 SB 0% 17,946 0 17,508 0 17,577 1,5 1,052 0

Ballast 912 C 0% 33,681 0 32,86 0 43 0 0 0

Ballast 118 0% 12,513 0 12,208 0 81,68 0 0,26 0

Total Loadcase 3177,944 657,519 459,811 38,307 0,002 6,366 67,251

FS correction 0,021

VCG fluid 6,387



Table 4 represents the details of the loading condition on departure where the yacht has its

fuel tanks full as well as its total fresh water supplies. After performing calculations in

Hydromax, the following results have been obtained regarding the equilibrium condition

which is shown in Table 5, GZ curve diagram in Figure 17 and whether or not the demanded

rules have been satisfied which is showed in Table 6.

Table 5.Equilibrium condition for Loadcase - 100% consumables

Draft Amidships m 4,099

Displacement t 3178

Heel deg 0

Draft at FP m 3,91

Draft at AP m 4,288

Draft at LCF m 4,141

Trim (+ve by stern) m 0,378

WL Length m 91,947

Beam max extents on WL m 15,401

Wetted Area m^2 1585,649

Waterpl. Area m^2 1133,564

Prismatic coeff. (Cp) 0,631

Block coeff. (Cb) 0,484

Max Sect. area coeff. (Cm) 0,798

Waterpl. areacoeff. (Cwp) 0,8

LCB from zero pt. (+vefwd) m 38,296

LCF from zero pt. (+vefwd) m 34,081

KB m 2,527

KG fluid m 6,387

BMt m 5,95

BML m 194,131

GMt corrected m 2,089

GML m 190,27

KMt m 8,477

KML m 196,656

Immersion (TPc) tonne/cm 11,619

MTctonne.m 69,243

RM at 1deg = GMt.Disp.sin(1) tonne.m 115,878

Max deck inclination deg 0,248

Trim angle (+ve by stern) deg 0,248

P 26 Blanka Ascic


Figure 17.GZ curve for loading condition – 100 % consumables

Table 6.Margin line and deck edge key points at given immersion angles

Key point Immersion angle deg

Margin Line (immersion pos = 36,447 m) 25,6

Deck Edge (immersion pos = 37,381 m) 26,1

After the analysis it is concluded that the requirements have been met and all the criteria

satisfied as shown in Table 7. The criteria are chosen according to previously explained IMO

requirements and are automatically verified by the software during the calculations. The

expression “Pass” or “Failed” in the status column of Table 7 provides information whether

the given criterion has been satisfied or not. The last column of the Table 7 shows the margin

between the actual and required state and is expressed in percentage.



Table 7.Verification of the criteria

CODE Criteria Value Units Actual Status

Margin

%

11.2.1.1 Monohulls 11.2.1.1.1a Area 0 to 30 Pass

from the greater of

spec. heel angle 0 deg 0

to the lesser of


angle of vanishing stability 55,8 deg

shall not be less than (>=) 3,1513 m.deg 14,4122 Pass 357,34

11.2.1.1 Monohulls 11.2.1.1.1b Area 0 to 40 Pass

from the greater of


to the lesser of


first downflooding angle n/a deg


shall be greater than (>) 5,1566 m.deg 22,1786 Pass 330,1

11.2.1.1 Monohulls 11.2.1.1.2 Area 30 to 40 Pass

from the greater of


to the lesser of





11.2.1.1 Monohulls 11.2.1.1.3 Max GZ at 30 or greater Pass

in the range from the greater of


to the lesser of

angle of max. GZ 30,9 deg 30,9


shall be greater than (>) 0,2 m 0,829 Pass 314,5

Intermediate values

angle at which this GZ occurs deg 30,9

11.2.1.1 Monohulls 11.2.1.1.4 Angle of maximum GZ Pass

shall not be less than (>=) 25 deg 30,9 Pass 23,64

11.2.1.1 Monohulls 11.2.1.1.5 Initial GMt Pass

spec. heel angle 0 deg

shall not be less than (>=) 0,15 m 2,089 Pass 1292,67

P 28 Blanka Ascic


4.2. Half Load Condition – 50% Consumables

Table 8.Loading condition for 50 % consumables

Item name Quantity

Unit

Mass

Total

Mass

Unit

Volume

Total

Volume

Long.

Arm

Trans.

Arm

Vert.

Arm

Total

FSM

Lightship 1 2650 2650 38,652 0 7 0

Provisions and stores 0,5 30 15 60 0 4,4 0

Spare 1 10 10 50 0 4,6 0 Pass and crew effects 1 11 11 42,465 0 11 0

Owner supplies 1 30 30 25 0 7,25 0 Helicopter 1 4 4 19,2 0 20,05 0

Automobile 1 6 6 26,4 0 19,55 0 Tender and jet ski 1 30 30 62,6 0 9,2 0

Diving equipment 1 1 1 4,6 0 5,6 0

Fuel 49C 50% 16,225 8,112 19,315 9,658 8,378 0 2,455 9,138 Fuel 48 SB 50% 28,316 14,158 33,71 16,855 14,496 -5,412 2,648 19,236

Fuel 47 PS 50% 28,316 14,158 33,71 16,855 14,496 5,412 2,648 19,236 Fuel 63 PS 50% 19,774 9,887 23,541 11,77 23,124 -2,66 1,094 11,022

Fuel 64 SB 50% 19,774 9,887 23,541 11,77 23,124 2,66 1,094 11,022

Fuel 62 C 50% 24,83 12,415 29,559 14,78 23,287 0 0,84 13,041 Overflow 50% 5,921 2,961 7,049 3,525 31,238 -1,144 0,42 3,5

Fuel Settling 76 CL 50% 10,271 5,136 12,228 6,114 34,115 0 0,377 22,75 Fuel 912 PS 50% 21,588 10,794 25,7 12,85 44,962 -4,648 0,945 8,348

Fuel 913 SB 50% 21,588 10,794 25,7 12,85 44,962 4,648 0,945 8,348 Fuel 910 PS 50% 28,965 14,482 34,482 17,241 45,037 -2,632 0,642 7,752

Fuel 911 SB 50% 28,965 14,482 34,482 17,241 45,037 2,632 0,642 7,752

Daly PS 50% 10,506 5,253 12,507 6,254 30,726 -7,173 2,745 0,308 Daly SB 50% 10,506 5,253 12,507 6,254 30,726 7,173 2,745 0,308

Fresh Water 104 50% 24,82 12,41 24,82 12,41 56,556 -1,273 0,578 10,244 Fresh Water 103 50% 24,82 12,41 24,82 12,41 56,556 1,273 0,578 10,244

Fresh Water 105 50% 32,199 16,099 32,199 16,099 61,401 0 0,59 42,037

Sanitary T2 50% 4,347 2,174 4,347 2,174 18,963 0 1,138 2,475 Sanitary T1 50% 6,437 3,218 6,437 3,218 39,199 0 0,329 8,533

Sanitary 95 PS 50% 8,651 4,326 8,651 4,326 52,096 1,38 0,566 4,05 Sanitary 107 50% 10,016 5,008 10,016 5,008 69,686 0 0,549 2,674

Sanitary 83 50% 10,908 5,454 10,908 5,454 46,997 0 0,495 5,461 Sewage Holding 50% 17,879 8,939 17,879 8,939 13,937 0 1,727 10,8

Sewage 84 50% 13,049 6,525 13,049 6,525 49,196 0 0,498 6,554

Heli Fuel S1 50% 6,016 3,008 7,334 3,667 16,824 0 1,479 2,953 Pool Dump S2 50% 26,359 13,18 26,359 13,18 -0,35 0 3,503 21,867

Dirty Oil 50% 5,8 2,9 6,304 3,152 28,065 -1,106 0,487 3,833 Clean Oil 74 50% 12,264 6,132 13,331 6,665 29,804 1,129 0,453 7,667

Sludge 75 50% 4,633 2,316 5,074 2,537 36,847 -1,338 0,358 1,274

Bilge 76 50% 8,193 4,096 8,193 4,096 36,871 0,805 0,338 5,287 Laundry Water 96 50% 8,651 4,326 8,651 4,326 52,096 -1,38 0,566 4,05

Technical Water 87 50% 21,03 10,515 21,03 10,515 66,297 0 0,571 12,26 Ballast 51 PS 0% 17,946 0 17,508 0 17,577 -1,5 1,052 0

Ballast 52 SB 0% 17,946 0 17,508 0 17,577 1,5 1,052 0 Ballast 912 C 0% 33,681 0 32,86 0 40,034 0 0 0

Ballast 118 0% 12,513 0 12,208 0 81,68 0 0,26 0

Total Loadcase 3017,81 657,519 288,717 38,623 0 6,56 304,027

FS correction 0,101

VCG fluid 6,661








Table 9.Equilibrium condition for Loadcase - 50% consumables

Draft Amidships m 3,966

Displacement t 3018

Heel deg 0

Draft at FP m 3,797

Draft at AP m 4,135



WL Length m 91,924










KB m 2,445

KG fluid m 6,661

BMt m 6,198

BML m 202,855


GML m 198,639

KMt m 8,643

KML m 205,298


MTctonne.m 68,646




P 30 Blanka Ascic






Deck Edge (immersion pos = 37,381 m) 27,3


satisfied as shown in Table 11 where the margin between the actual and required condition is

shown in percentage.





Margin

%


from the greater of


to the lesser of





from the greater of


to the lesser of






from the greater of


to the lesser of








to the lesser of

angle of max. GZ 30,9 deg 30



Intermediate values

angle at which this GZ occurs deg 30


shall not be less than (>=) 25 deg 30 Pass 20




P 32 Blanka Ascic


4.3. Arrival Condition – 10% Consumables

Table 12.Loading condition for 10 % consumables

Item name Quantity

Unit

Mass

Total

Mass

Unit

Volume

Total

Volume

Long.

Arm

Trans.

Arm

Vert.

Arm

Total

FSM

Lightship 1 2650 2650 38,652 0 7 0

Provisions and stores 0,1 30 3 60 0 4,4 0

Spare 1 10 10 50 0 4,6 0 Pass and crew effects 1 11 11 42,465 0 11 0

Owner supplies 1 30 30 25 0 7,25 0 Helicopter 1 4 4 19,2 0 20,05 0

Automobile 1 6 6 26,4 0 19,55 0 Tender and jet ski 1 30 30 62,6 0 9,2 0

Diving equipment 1 1 1 4,6 0 5,6 0

Fuel 49C 10% 16,225 1,622 19,315 1,932 9,332 0 2,096 9,138 Fuel 48 SB 10% 28,316 2,832 33,71 3,371 15,486 -4,937 2,147 19,236

Fuel 47 PS 10% 28,316 2,832 33,71 3,371 15,486 4,937 2,147 19,236 Fuel 63 PS 10% 19,774 1,977 23,541 2,354 24,373 -2,32 0,754 11,022

Fuel 64 SB 10% 19,774 1,977 23,541 2,354 24,373 2,32 0,754 11,022

Fuel 62 C 10% 24,83 2,483 29,559 2,956 24,363 0 0,499 13,041 Overflow 10% 5,921 0,592 7,049 0,705 31,355 -0,768 0,219 3,5

Fuel Settling 76 CL 10% 10,271 1,027 12,228 1,223 34,168 0 0,171 22,75 Fuel 912 PS 10% 21,588 2,159 25,7 2,57 44,159 -4,297 0,627 8,348

Fuel 913 SB 10% 21,588 2,159 25,7 2,57 44,159 4,297 0,627 8,348 Fuel 910 PS 10% 28,965 2,896 34,482 3,448 44,456 -2,376 0,314 7,752

Fuel 911 SB 10% 28,965 2,896 34,482 3,448 44,456 2,376 0,314 7,752

Daly PS 10% 10,506 1,051 12,507 1,251 30,959 -7,066 2,153 0,308 Daly SB 10% 10,506 1,051 12,507 1,251 30,959 7,066 2,153 0,308

Fresh Water 104 10% 24,82 2,482 24,82 2,482 56,444 -0,829 0,216 10,244 Fresh Water 103 10% 24,82 2,482 24,82 2,482 56,444 0,829 0,216 10,244

Fresh Water 105 10% 32,199 3,22 32,199 3,22 61,394 0 0,224 42,036

Sanitary T2 98% 4,347 4,26 4,347 4,26 18,957 0 1,463 0 Sanitary T1 98% 6,437 6,308 6,437 6,308 39,2 0 0,576 0

Sanitary 95 PS 98% 8,651 8,478 8,651 8,478 52,098 1,439 0,962 0 Sanitary 107 98% 10,016 9,816 10,016 9,816 69,68 0 0,95 0

Sanitary 83 98% 10,908 10,69 10,908 10,69 46,999 0 0,912 0 Sewage Holding 98% 17,879 17,521 17,879 17,521 13,755 0 2,042 0

Sewage 84 50% 13,049 6,525 13,049 6,525 49,196 0 0,498 6,554

Heli Fuel S1 10% 6,016 0,602 7,334 0,733 16,921 0 1,162 2,953 Pool Dump S2 98% 26,359 25,832 26,359 25,832 -0,399 0 3,9 0

Dirty Oil 98% 5,8 5,684 6,304 6,178 28,033 -1,176 0,685 0 Clean Oil 74 10% 12,264 1,226 13,331 1,333 30,34 0,777 0,25 7,667

Sludge 75 98% 4,633 4,54 5,074 4,973 36,838 -1,359 0,596 0

Bilge 76 98% 8,193 8,029 8,193 8,029 36,863 0,841 0,582 0 Laundry Water 96 98% 8,651 8,478 8,651 8,478 52,098 -1,439 0,962 0

Technical Water 87 98% 21,03 20,609 21,03 20,609 66,298 0 0,966 0 Ballast 51 PS 0% 17,946 0 17,508 0 17,577 -1,5 1,052 0

Ballast 52 SB 0% 17,946 0 17,508 0 17,577 1,5 1,052 0 Ballast 912 C 0% 33,681 0 32,86 0 40,034 0 0 0

Ballast 118 0% 12,513 0 12,208 0 81,68 0 0,26 0

Total Loadcase 2919,338 657,519 180,751 38,616 -0,002 6,74 221,46

FS correction 0,076

VCG fluid 6,815








Table 13.Equilibrium condition for Loadcase – 10% consumables

Displacement t 2919

Heel deg 0

Draft at FP m 3,667

Draft at AP m 4,078



WL Length m 91,897










KB m 2,394

KG fluid m 6,815

BMt m 6,361

BML m 208,325


GML m 203,903

KMt m 8,755

KML m 210,716


MTctonne.m 68,166




P 34 Blanka Ascic






Deck Edge (immersion pos = 37,381 m) 28


satisfied as shown in Table 15 where the margin between the actual and required condition is

shown in percentage.





Margin

%


from the greater of


to the lesser of





from the greater of


to the lesser of






from the greater of


to the lesser of








to the lesser of

angle of max. GZ 30,9 deg 30



Intermediate values

angle at which this GZ occurs deg 30


shall not be less than (>=) 25 deg 30 Pass 20




P 36 Blanka Ascic


4.4. KG Curve for Intact Stability

In Table 16 the values of maximum KG are given for different displacement values from 2980

tonnes to 3260 tonnes with a step of 20 tonnes and for different trim conditions.

Table 16.Values for max KG for different trim conditions

Trim -0,2 Trim -0,1 Trim 0 Trim 0,1 Trim 0,2

Displacement Max KG Max KG Max KG Max KG Max KG

2980 6,69 6,246 6,266 6,288 6,31

3000 6,684 6,254 6,276 6,298 6,32 3020 6,677 6,264 6,285 6,307 6,329

3040 6,67 6,272 6,294 6,316 6,338 3060 6,662 6,28 6,302 6,323 6,346

3080 6,655 6,288 6,309 6,331 6,353

3100 6,648 6,295 6,316 6,338 6,359 3120 6,655 6,301 6,323 6,346 6,366

3140 6,676 6,308 6,329 6,351 6,372 3160 6,699 6,313 6,335 6,356 6,377

3180 1,878 6,318 6,34 6,36 6,381 3200 7,149 6,323 6,343 6,365 6,384

3220 7,099 6,327 6,348 6,368 6,387

3240 7,051 6,33 6,35 6,371 6,39 3260 7,004 6,333 6,354 6,373 6,392

The values are illustrated with a graph in Figure 20 where it's shown how KG increases with

the increment of displacement as well as how it is higher for positive trim and decreases

towards the negative one.

Figure 20.Max KG for different trim and displacement values

6

6.07

6.14

6.21

6.28

6.35

6.42

6.49

6.56

2960 3000 3040 3080 3120 3160 3200 3240 3280

KG

[m

]

Displacement [t]

trim -0,2

trim -0,1

trim 0

trim 0,1

trim 0,2



4.5. Damage Stability Calculations


after flooding. Deterministic method is based on the assumed damage scenarios i.e. one

compartment or a group of compartments is being flooded. Based on deterministic

calculations, the maximum permissible length of the compartment is obtained, which should

ensure the ship remains afloat and stable in damage condition.

4.5.1. Considered Damage Cases

Table 17 illustrates with red colour which room is considered damaged. There are twelve

different damage case scenarios for analysis.

Table 17.Considered Damage Cases

Room DCase

1

DCase

2

DCase

3

DCase

4

DCase

5

DCase

6

DCase

7

Dcase

8

DCase

9

DCase

10

DCase

11

DCase

12

Fuel

49C

Fuel 48

SB

Fuel 47

PS

Fuel 63

PS

Fuel 64

SB

Fuel 62

C

Overflo

w

Fuel

Settling

76 CL

Fuel 912

PS

Fuel 913

SB

Fuel 910

PS

Fuel 911

SB

Daly PS

Daly SB

Ballast

118

aft ULD

aft PS

aft SB

aft LD

aft1

ULD

aft2

ULD ext

ABB

room

crew LD

1

crew LD

2

ER DB

ER

Fins

ULD

Fins LD

Fins DB

crew

fw1 DB

crew

fw1

ULD

crew

fw1 LD

crew

fw2 DB

crew

fw2

ULD

crew

fw2 LD

crew

fw3 DB

crew

fw3

ULD

crew

fw3 LD

fwd

P 38 Blanka Ascic


4.5.2. Analysis and the Results of Damage Conditions

With the required two compartment damaged deterministic criteria it was mandatory to satisfy

enhanced survivability according to the Chapter 4, part VII of the Passenger Yacht Code

which refers to Additional Provisions for vessels permitted to carry davit launched liferafts

and marine evacuation systems in lieu of lifeboats.

Figure 21.Table summarising categories of Passenger Yacht and Standards of Stability

Davit launched liferafts are supplements to slide and chute systems and are ideal due to the

fact they facilitate the usage to injured persons.

The following Figures 22-33 show the damaged compartments and tanks considered in twelve

different damage scenarios and the Tables 18-29 represent the results that satisfy the required

criteria for each damage scenario.



Figure 22.Damaged compartments and tanks in Damage case 1

Table 18.Results of the required Criteria – Damage case 1


Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 2,006 Pass 2574,67

11.3 Damage

Stability

11.3.1.4 Equilibrium angle Pass

shall not be greater than (<=) 7 deg 1,9 Pass 73,19

11.3 Damage

Stability

11.3.1.4 Range of positive stability Pass


11.3 Damage

Stability

11.3.1.4 Value of max. GZ Pass shall not be less than (>=) 0,1 m 0,381 Pass 281

11.3 Damage

Stability

11.3.1.4 GZ area under curve Pass shall not be less than (>=) 0,8594 m.deg 9,3581 Pass 988,91

Enhanced

Survivability

4.30(1)(a)(i) Angle of equilibrium Pass

shall be less than (<) 7 deg 1,9 Pass 73,19

Enhanced

Survivability

4.30(1)(a)(i) Range of residual positive

stability

Pass


Enhanced

Survivability

4.30(1)(a)(ii) Maximum residual GZ Pass shall not be less than (>=) 0,05 m 0,381 Pass 662

Enhanced

Survivability

4.30(1)(a)(ii) Residual GM Pass shall not be less than (>=) 0,05 m 0,832 Pass 1564

Enhanced

Survivability

4.30(1)(a)(iii) Margin line immersion - GZ

based

Pass

shall be less than (<) 100 % 12,34 Pass 87,66

P 40 Blanka Ascic





Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 2,826 Pass +3668,00 11.3 Damage

Stability

11.3.1.4 Equilibrium angle Pass shall not be greater than (<=) 7 deg 0,3 Pass 95,43 11.3 Damage

Stability

11.3.1.4 Range of positive stability Pass shall not be less than (>=) 15 deg 42,9 Pass 186,12 11.3 Damage

Stability

11.3.1.4 Value of max. GZ Pass shall not be less than (>=) 0,1 m 0,369 Pass 269 11.3 Damage

Stability

11.3.1.4 GZ area under curve Pass shall not be less than (>=) 0,8594 m.deg 9,1129 Pass 960,38 Enhanced

Survivability

4.30(1)(a)(i) Angle of equilibrium Pass shall be less than (<) 7 deg 0,3 Pass 95,43 Enhanced

Survivability


stability

Pass shall not be less than (>=) 7 deg 18,2 Pass 160,06 Enhanced

Survivability

4.30(1)(a)(ii) Maximum residual GZ Pass shall not be less than (>=) 0,05 m 0,369 Pass 638 Enhanced

Survivability

4.30(1)(a)(ii) Residual GM Pass shall not be less than (>=) 0,05 m 0,875 Pass 1650 Enhanced

Survivability


based

Pass shall be less than (<) 100 % 1,73 Pass 98,27






Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass

shall not be less than (>=) 0,075 m 2,617 Pass +3389,33 11.3 Damage

Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based


P 42 Blanka Ascic





Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 1,991 Pass 2554,67 11.3 Damage

Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based







Margin

%

11.3 Damage

Stability


Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based


P 44 Blanka Ascic





Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 3 Pass 3900 11.3 Damage

Stability


Stability

11.3.1.4 Range of positive stability Pass shall not be less than (>=) 15 deg 51 Pass 239,81 11.3 Damage

Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based







Margin

%

11.3 Damage

Stability


Stability


Stability


Stability


Stability


Survivability


Survivability


stability

Pass shall not be less than (>=) 7 deg 22 Pass 213,66 Enhanced

Survivability


Survivability


Survivability


based


P 46 Blanka Ascic





Margin

%

11.3 Damage

Stability


Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based







Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 1,917 Pass 2456 11.3 Damage

Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based


P 48 Blanka Ascic





Margin

%

11.3 Damage

Stability


Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based







Margin

%

11.3 Damage

Stability

11.3.1.1 Equilibrium waterline Pass shall not be less than (>=) 0,075 m 2,571 Pass 3328 11.3 Damage

Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based


P 50 Blanka Ascic





Margin

%

11.3 Damage

Stability


Stability


Stability


Stability


Stability


Survivability


Survivability


stability


Survivability


Survivability


Survivability


based




5. PROBABILISTIC APPROACH

5.1. PYC - Required Subdivision Index R

Calculation of the required subdivision index R is very simple and according to the following

formula:

𝑅 = 1 −5000

𝐿𝑆 + 2,5𝑁 + 15252

(3)

Where:

- LS is subdivision length

- N = N1 + 2N2

- N1 number of persons for whom lifeboats are provided

- N2 number of persons the ship is permitted to carry

-

The required subdivision index R was calculated as follows:

Ls = 92.65 meters

N1 = 0

N2 = 62 (Passenger and crew)

N = 124

Final result for the required subdivision index R is:

R = 0.680054

P 52 Blanka Ascic


5.2. PYC - Attained Subdivision Index A

Calculation of the attained subdivision index A is based on three drafts as shown in Figure 34:

- Deepest subdivision draft, ds

- Light service draft, dl

- Partial subdivision draft, dp

Figure 34. The three drafts for the attained subdivision index A

Summation of the attained subdivision index A is determined by the following expression:

A = 0.4As + 0.4Ap + 0.2Al (4)

This is due to an assumption that a ship will spend 40% of the time at the deepest subdivision

draft, 40% of the time at the partial subdivision draught and 20% of the time at the lightest

service draft condition.

Partial subdivision draft, dp is determined by adding 60% of difference between the two drafts

to the light service draft, dl.

Also, a minimum attained index should be reached on each draft so that each of the partial

indices As, Ap and Al are not to be less than 0.9R.



The formula for the index A is:

𝐴 = pivirisi

i

(5)

Where:

- pi is the probability of the damage situation or that the compartment or a group of

compartments is flooded

- vi is the probability of vertical extend of damage or that the space above an existing

horizontal boundary is not flooded

- ri is the probability of transversal extend of damage or that the longitudinal bulkhead

will not be breached by the damage

- si the probability of survival after flooding the compartment or a group of

compartments

Figure 35 illustrates how to determine factors pi , ri and vi based on the dimensions of the

damage. Since the 92 m yacht has no longitudinal bulkheads, the factor ri shall not be

calculated.

Figure 35.Probability factors for Attained Subdivision Index, A

P 54 Blanka Ascic


5.2.1. Calculation of the Factor pi

The factor pi is the probability that the compartment or a group of compartments is flooded

and is illustrated in Figures 36 and 37 where the red coloured triangle represents the

probability of one compartment, in this case compartment number six and number nine

respectively, being flooded.

Figure 36.Probability of a compartment number 6 being flooded

Figure 37. Probability of a compartment number 9 being flooded



In order to calculate the probability of more compartments being flooded, one first has to

determine the probability of each single compartment being flooded, then the probability of

two adjacent compartments being flooded and so on.

Figure 38 illustrates the probability of two adjacent compartments being flooded, in this case

compartments number four and five, where the red rectangle represents that probability and

can be calculated applying the following principle:

- for compartments taken by pairs:

pi = p12-p1-p2, etc.

This is why it was necessary to calculate the probability of each individual compartment

being flooded.

Figure 38.Probability of two adjacent compartments being flooded

P 56 Blanka Ascic


Knowing the probabilities of one and two adjacent compartments being flooded, one can

determine the probability of three adjacent compartments being flooded as follows:

- for compartments taken by groups of three

pi = p123-p12-p23+p2, etc.

Figure 39 illustrates the probability of three adjacent compartments being flooded with a red

rectangle, in this case compartments number four, five and six.

Figure 39.Probability of three adjacent compartments being flooded



Following the same principle, one can determine the probability of four adjacent

compartments being flooded:

- for compartments taken by groups of four

pi = p1234-p123-p234+p23, etc.

Figure 40 illustrates the probability of four adjacent compartments, in this case compartments

number four, five, six and seven, being flooded and is presented with a red rectangle.

Figure 40.Probability of four adjacent compartments being flooded

This principle is applied until the maximum permissible damage length of 60 m is reached.

After that length, it is considered that the probability of adjacent compartments being flooded

is zero.

P 58 Blanka Ascic


The factor p(x1, x2) is to be calculated according to the following formulae:

x1................................................................... from the aft terminal Ls to the aft end of the zone

x2.................................................................from the aft terminal Ls to the fore end of the zone

Jmax.................................................................. overall normalised damage length, Jmax=10/33

Jmax=0.33333

Jkn............................................................................ knuckle point in the distribution, Jkn=5/33

Jkn=0.151515

pk............................................................................... cumulative probability at Jkn, pk=11/12

pk=0.916667

lmax...................................................................................... maximum absolute damage length

lmax=60 meters

L*.............................................................................length where normalised distribution ends

L*=260 meters

After determination of Ls≤ L*, one can proceed with the following formulae:

𝐽𝑚 = 𝑚𝑖𝑛 𝐽𝑚𝑎𝑥 ,𝑙𝑚𝑎𝑥

𝐿𝑠

(6)

Result:

Jm= 0.333

𝐽𝑘 = 𝐽𝑚2

+1 − 1 − 1 − 2𝑝𝑘 𝑏0𝐽𝑚 +

1

4𝑏0

2𝐽𝑚2

𝑏0

(7)

Result:

Jk = 0.1515



Probability density at J=0:

𝑏0 = 2(𝑝𝑘

𝐽𝑘𝑛−

1 − 𝑝𝑘

𝐽𝑚𝑎𝑥 − 𝐽𝑘𝑛)

(8)

Result:

b0 = 11.18

𝑏12 = 𝑏0 (9)

Result:

b12 = 11.18

𝑏11 = 41 − 𝑝𝑘

(𝐽𝑚 − 𝐽𝑘)𝐽𝑘− 2

𝑝𝑝

𝐽𝑘2

(10)

Result:

b11 = -67.76

𝑏21 = −21 − 𝑝𝑘

(𝐽𝑚 − 𝐽𝑘)2

(11)

Result:

b21 = -5.041

𝑏22 = −𝑏21𝐽𝑚 (12)

Result:

b22 =1.681

P 60 Blanka Ascic


The non-dimensional damage length shall be calculated for each compartment or a group of

compartments under consideration according to the following formulae:

𝐽 =(𝑥2 − 𝑥1)

𝐿𝑠

(13)

If neither limit of the compartment or a group of compartments under consideration coincides

with the aft or forward terminals, one uses the following formulae to calculate p(x1, x2):

For

J≤Jk

𝑝 𝑥1,𝑥2 = 𝑝1 =1

6𝐽2(𝑏11𝐽 + 3𝑏12)

(14)

For

J>Jk

𝑝 𝑥1, 𝑥2 = 𝑝2 = −1

3𝑏11𝐽𝑘

3 +1

2 𝑏11𝐽 − 𝑏12 𝐽𝑘

2 + 𝑏12𝐽𝐽𝑘 −1

3𝑏12 𝐽𝑛

3 − 𝐽𝑘3

+1

2 𝑏21𝐽 − 𝑏22 𝐽𝑛

2 − 𝐽𝑘2 + 𝑏22𝐽(𝐽𝑛 − 𝐽𝑘)

(15)



When aft or fore part of the compartment or a group of compartments under consideration

coincides with the aft or fore terminal, one proceeds with the following formulae to calculate

p(x1, x2):

For

J≤Jk

𝑝 𝑥1,𝑥2 =1

2 𝑝1 + 𝐽

(16)

For

J>Jk

𝑝 𝑥1,𝑥2 =1

2(𝑝2 + 𝐽)

(17)

The process of calculations was to determine all possible factors p(x1, x2) for one, two, three,

four, five and six adjacent compartments being flooded and later on determine the correct one

whether or not there is coincidence with the fore or aft part regarding the factor J, as indicated

with the rules. The final results for factor p(x1, x2) for all possible damage conditions are

given in the Table 30.below. The values x1 and x2 in Table 30 represent the aft and fore part

longitudinally in meters of one compartment or a group of adjacent compartments

determining the damage length. The last column of Table 30 represents the final obtained

result of the factor pi for a given compartment or a group of compartments under

consideration.

The result can be verified summing all the partial solutions of factor pi for each compartment

or a group of compartments considered and the value can’t be more than 1, since the

probability of the event can’t be more than 1 or less than zero. The maximum damage length

is exceeded after first two combinations of six adjacent compartments being flooded so it was

no longer required to perform the calculations since the probability for them being flooded is

zero.

P 62 Blanka Ascic


Table 30.Calculations of factor pi

No coincidation A/F coincidation

J<=Jk J>Jk J<=Jk J>Jk FINAL

RESULT Compartment x1 x2 Damage

length J Jn p(x1,x2) p(x1,x2) p(x1,x2) p(x1,x2) p(x1,x2)

1 cmp flooded [ m ] pi

1 0 8,29 8,29 0,0895 0,0895 0,0367 0,0342 0,0631 0,0618 0,0631

2 8,29 15,11 6,82 0,0736 0,0736 0,0258 0,0209 0,0497 0,0472 0,0258

3 15,11 22,27 7,16 0,0773 0,0773 0,0282 0,0239 0,0527 0,0506 0,0282

4 22,27 31,07 8,8 0,0950 0,0950 0,0408 0,0389 0,0679 0,0669 0,0408

5 31,07 44,67 13,6 0,1468 0,1468 0,0848 0,0848 0,1158 0,1158 0,0848

6 44,67 55,87 11,2 0,1209 0,1209 0,0618 0,0615 0,0913 0,0912 0,0618

7 55,87 64,08 8,21 0,0886 0,0886 0,0360 0,0334 0,0623 0,0610 0,0360

8 64,08 75,87 11,79 0,1273 0,1273 0,0673 0,0671 0,0973 0,0972 0,0673

9 75,87 86,07 10,2 0,1101 0,1101 0,0527 0,0520 0,0814 0,0810 0,0527

10 86,07 92,65 6,58 0,0710 0,0710 0,0242 0,0187 0,0476 0,0449 0,0476

2 cmps flooded pi

1 and 2 0 15,11 15,11 0,1631 0,1631 0,0997 0,0998 0,1314 0,1314 0,0425

2 and 3 8,29 22,27 13,98 0,1509 0,1509 0,0885 0,0885 0,1197 0,1197 0,0345

3 and 4 15,11 31,07 15,96 0,1723 0,1723 0,1082 0,1083 0,1402 0,1403 0,0393

4 and 5 22,27 44,67 22,4 0,2418 0,2418 0,1672 0,1749 0,2045 0,2084 0,0494

5 and 6 31,07 55,87 24,8 0,2677 0,2677 0,1840 0,2004 0,2259 0,2341 0,0539

6 and 7 44,67 64,08 19,41 0,2095 0,2095 0,1416 0,1436 0,1755 0,1766 0,0458

7 and 8 55,87 75,87 20 0,2159 0,2159 0,1470 0,1497 0,1814 0,1828 0,0464

8 and 9 64,08 86,07 21,99 0,2373 0,2373 0,1640 0,1706 0,2007 0,2040 0,0506

9 and 10 75,87 92,65 16,78 0,1811 0,1811 0,1163 0,1166 0,1487 0,1489 0,0486

3 cmps flooded pi

1, 2 and 3 0 22,27 22,27 0,2404 0,2404 0,1662 0,1736 0,2033 0,2070 0,0128

2, 3 and 4 8,29 31,07 22,78 0,2459 0,2459 0,1702 0,1790 0,2080 0,2124 0,0103

3, 4 and 5 15,11 44,67 29,56 0,3191 0,3191 0,2024 0,2516 0,2607 0,2853 0,0091

4, 5 and 6 22,27 55,87 33,6 0,3627 0,3333 0,1968 0,2952 0,2797 0,3289 0,0046

5, 6 and 7 31,07 64,08 33,01 0,3563 0,3333 0,1990 0,2888 0,2777 0,3225 0,0065

6, 7 and 8 44,67 75,87 31,2 0,3368 0,3333 0,2028 0,2693 0,2698 0,3030 0,0120

7, 8 and 9 55,87 86,07 30,2 0,3260 0,3260 0,2030 0,2585 0,2645 0,2922 0,0054

8, 9 and 10 64,08 92,65 28,57 0,3084 0,3084 0,2006 0,2409 0,2545 0,2746 0,0079

4 cmps flooded pi

1, 2, 3 and 4 0 31,07 31,07 0,3353 0,3333 0,2029 0,2679 0,2691 0,3016 0,0042

2, 3, 4 and 5 8,29 44,67 36,38 0,3927 0,3333 0,1784 0,3252 0,2855 0,3589 0,0029

3, 4, 5 and 6 15,11 55,87 40,76 0,4399 0,3333 0,1206 0,3725 0,2803 0,4062 0,0006

4, 5, 6 and 7 22,27 64,08 41,81 0,4513 0,3333 0,1009 0,3838 0,2761 0,4175 0,0002

5, 6, 7 and 8 31,07 75,87 44,8 0,4835 0,3333 0,0306 0,4161 0,2571 0,4498 0,0016

6, 7, 8 and 9 44,67 86,07 41,4 0,4468 0,3333 0,1089 0,3794 0,2779 0,4131 0,0014

7, 8, 9 and 10 55,87 92,65 36,78 0,3970 0,3333 0,1747 0,3295 0,2858 0,3632 0,0007

5 cmps flooded pi

1, 2, 3, 4 and 5 0 44,67 44,67 0,4821 0,3333 0,0341 0,4147 0,2581 0,4484 0,0005622

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,5135 0,3333 -0,0548 0,4461 0,2293 0,4798 0

3, 4, 5, 6 and 7 15,11 64,08 48,97 0,5285 0,3333 -0,1054 0,4611 0,2116 0,4948 0

4, 5, 6 , 7 and 8 22,27 75,87 53,6 0,5785 0,3333 -0,3152 0,5110 0,1317 0,5448 0

5, 6, 7, 8 and 9 31,07 86,07 55 0,5936 0,3333 -0,3920 0,5262 0,1008 0,5599 0

6, 7, 8, 9 and 10 44,67 92,65 47,98 0,5179 0,3333 -0,0689 0,4504 0,2245 0,4841 0

6 cmps flooded pi

1, 2, 3, 4, 5 and

6

0 55,87 55,87 0,6030 0,3333 -0,4431 0,5355 0,0800 0,5693 0

2, 3, 4, 5, 6 and

7

8,29 64,08 55,79 0,6022 0,3333 -0,4383 0,5347 0,0819 0,5684 0

3, 4, 5, 6, 7 and

8

15,11 75,87 60,76 0,6558 0,3333 -0,7804 0,5883 -0,0623 0,6221 0

4, 5, 6 , 7, 8 and

9

22,27 86,07 63,8 0,6886 0,3333 -1,0361 0,6211 -0,1738 0,6549 0

5, 6, 7, 8, 9 and

10

31,07 92,65 61,58 0,6647 0,3333 -0,8457 0,5972 -0,0905 0,6309 0

SUM= 1



5.2.2. Calculations of the Factor si

The factor si accounts for the probability of survival after flooding the compartment or a

group of compartments under consideration and is obtained from the following formulae:

𝑠𝑖 = 𝑚𝑖𝑚𝑖𝑛𝑢𝑚 𝑠𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 ,𝑖 𝑜𝑟 𝑠𝑓𝑖𝑛𝑎𝑙 ,𝑖 ∗ 𝑠𝑚𝑜𝑚 ,𝑖 (18)

where

- sintermediate,i is the probability to survive all intermediate floodingstages until the final

equilibrium stageand is obtained from the formulae:

𝑠𝑖𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 ,𝑖 = 𝐺𝑍𝑚𝑎𝑥

0,05∗𝑅𝑎𝑛𝑔𝑒

7

1

4

(19)

where GZmax is not more than 0,05 m and Range is not more than 7 ̊

- sfinal,i is the probability to survive in the final equilibrium stage of flooding and it is

obtained from the formulae:

𝑠𝑓𝑖𝑛𝑎𝑙 ,𝑖 = 𝐾 𝐺𝑍𝑚𝑎𝑥

0,012∗𝑅𝑎𝑛𝑔𝑒

16

1

4

(20)

where GZmax is not more than 0,12 m and Range is not more than 16 ̊

Figure 41.Heeling angle and Range values for calculations of factor si

P 64 Blanka Ascic


- smom,i is the probability to survive heeling moments and it is obtained from the

formulae:

𝑠𝑚𝑜𝑚 ,𝑖 = 𝐺𝑍𝑚𝑎𝑥 − 0,04 ∗ 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑀𝑕𝑒𝑒𝑙

(21)

The heeling moment is taken as the highest one from the possible ones, either the heeling

moment due to the passengers, wind or launching of all fully loaded davit-launched survival

craft.

The heeling moments are obtained from the following formulae:

- Mpassenger

𝑀𝑝𝑎𝑠𝑠𝑒𝑛𝑔𝑒𝑟 = 0,075 ∗ 𝑁𝑝 ∗ 0,45 ∗ 𝐵 (𝑡𝑚) (22)

- Mwind

𝑀𝑤𝑖𝑛𝑑 =𝑃 ∗ 𝐴 ∗ 𝑍

9,806(𝑡𝑚)

(23)

- MSurvivalcraft

Each si factor shall be calculated for the three different draft values and the results for the

heeling moment are presented in the Table 31. In each case the heeling moment due to the

passengers was the highest one.

Table 31.Heeling moment for three different conditions

Initial condition T Min GM A Z Mwind Mheel

dl 3,985 1,5 364,4 4,038 18,004 33,062

dp 4,114 1,5 352,5 4,033 17,397 33,062

ds 4,2 1,5 344,4 4,010 16,900 33,062

In order to obtain si, for each individual damage case it was required to determine GZmax and

Range values. Since the calculations were done without software for probabilistic analysis, it

was necessary to determine required data in Hydromax for each considered damage case and

obtain the two values. There are 42 different damage cases for each of the three possible

drafts so in total 126 different damage cases were defined in Hydromax for which the large

angle stability and equilibrium conditions were calculated in order to obtain determine GZmax



and Range values. It was then possible to proceed with the calculations of factor si as shown

below in Tables 32-34.

Table 32.Calculations of factor si for lightest service draft, dl

Compartment x1 x2 Damage

length

Heel

angle GZmax Range s(intmd) s(final) s(mom) si

1 cmp flooded [ m ]

1 0 8,29 8,29 0 0,641 55 1 1 0,9083 0,9083

2 8,29 15,11 6,82 0 0,637 55 1 1 0,9083 0,9083

3 15,11 22,27 7,16 0 0,636 55 1 1 0,9083 0,9083

4 22,27 31,07 8,8 0 0,624 55 1 1 0,9083 0,9083

5 31,07 44,67 13,6 0 0,532 50 1 1 0,9083 0,9083

6 44,67 55,87 11,2 0 0,589 55 1 1 0,9083 0,9083

7 55,87 64,08 8,21 0 0,614 55 1 1 0,9083 0,9083

8 64,08 75,87 11,79 0 0,643 55 1 1 0,9083 0,9083

9 75,87 86,07 10,2 0 0,664 55 1 1 0,9083 0,9083

10 86,07 92,65 6,58 0 0,658 55 1 1 0,9083 0,9083

2 cmps flooded

1 and 2 0 15,11 15,11 0 0,626 55 1 1 0,9083 0,9083

2 and 3 8,29 22,27 13,98 0 0,62 55 1 1 0,9083 0,9083

3 and 4 15,11 31,07 15,96 0 0,607 55 1 1 0,9083 0,9083

4 and 5 22,27 44,67 22,4 0 0,513 50 1 1 0,9083 0,9083

5 and 6 31,07 55,87 24,8 0 0,483 50 1 1 0,9083 0,9083

6 and 7 44,67 64,08 19,41 0 0,566 55 1 1 0,9083 0,9083

7 and 8 55,87 75,87 20 0 0,636 55 1 1 0,9083 0,9083

8 and 9 64,08 86,07 21,99 0 0,682 55 1 1 0,9083 0,9083

9 and 10 75,87 92,65 16,78 0 0,665 55 1 1 0,9083 0,9083

3 cmps flooded

1, 2 and 3 0 22,27 22,27 0 0,608 55 1 1 0,9083 0,9083

2, 3 and 4 8,29 31,07 22,78 0 0,593 55 1 1 0,9083 0,9083

3, 4 and 5 15,11 44,67 29,56 0 0,494 50 1 1 0,9083 0,9083

4, 5 and 6 22,27 55,87 33,6 0,4 0,503 50 1 1 0,9083 0,9083

5, 6 and 7 31,07 64,08 33,01 0,4 0,517 50 1 1 0,9083 0,9083

6, 7 and 8 44,67 75,87 31,2 0 0,639 55 1 1 0,9083 0,9083

7, 8 and 9 55,87 86,07 30,2 0 0,699 55 1 1 0,9083 0,9083

8, 9 and 10 64,08 92,65 28,57 0 0,685 55 1 1 0,9083 0,9083

4 cmps flooded

1, 2, 3 and 4 0 31,07 31,07 0 0,582 55 1 1 0,9083 0,9083

2, 3, 4 and 5 8,29 44,67 36,38 0,3 0,491 50 1 1 0,9083 0,9083

3, 4, 5 and 6 15,11 55,87 40,76 0,5 0,484 50 1 1 0,9083 0,9083

4, 5, 6 and 7 22,27 64,08 41,81 0,7 0,579 50 1 1 0,9083 0,9083

5, 6, 7 and 8 31,07 75,87 44,8 0,7 0,683 50 1 1 0,9083 0,9083

6, 7, 8 and 9 44,67 86,07 41,4 0 0,73 55 1 1 0,9083 0,9083

7, 8, 9 and 10 55,87 92,65 36,78 0 0,703 55 1 1 0,9083 0,9083

5 cmps flooded

1, 2, 3, 4 and 5 0 44,67 44,67 0,5 0,488 50 1 1 0,9083 0,9083

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,6 0,492 50 1 1 0,9083 0,9083

3, 4, 5, 6 and 7 15,11 64,08 48,97 0,9 0,56 50 1 1 0,9083 0,9083

4, 5, 6 , 7 and 8 22,27 75,87 53,6 1,1 0,746 50 1 1 0,9083 0,9083

5, 6, 7, 8 and 9 31,07 86,07 55 0,9 0,746 50 1 1 0,9083 0,9083

6, 7, 8, 9 and 10 44,67 92,65 47,98 0 0,735 55 1 1 0,9083 0,9083

6 cmps flooded

1, 2, 3, 4, 5 and 6 0 55,87 55,87 0,9 0,503 40 1 1 0,9083 0,9083

2, 3, 4, 5, 6 and 7 8,29 64,08 55,79 1,1 0,573 45 1 1 0,9083 0,9083

3, 4, 5, 6, 7 and 8 15,11 75,87 60,76 / / / / / / /

4, 5, 6 , 7, 8 and 9 22,27 86,07 63,8 / / / / / / /

5, 6, 7, 8, 9 and 10 31,07 92,65 61,58 / / / / / / /

P 66 Blanka Ascic


Table 33.Calculations of factor si for the middle service draft, dp


length

Heel


1 cmp flooded [ m ]

1 0 8,29 8,29 0,00 0,699 50 1 1 0,9525 0,9525

2 8,29 15,11 6,82 0,00 0,695 50 1 1 0,9525 0,9525

3 15,11 22,27 7,16 0,00 0,696 50 1 1 0,9525 0,9525

4 22,27 31,07 8,8 0,00 0,682 50 1 1 0,9525 0,9525

5 31,07 44,67 13,6 0,00 0,584 50 1 1 0,9525 0,9525

6 44,67 55,87 11,2 0,00 0,651 50 1 1 0,9525 0,9525

7 55,87 64,08 8,21 0,00 0,676 50 1 1 0,9525 0,9525

8 64,08 75,87 11,79 0,00 0,705 50 1 1 0,9525 0,9525

9 75,87 86,07 10,2 0,00 0,724 50 1 1 0,9525 0,9525

10 86,07 92,65 6,58 0,00 0,713 50 1 1 0,9525 0,9525

2 cmps flooded

1 and 2 0 15,11 15,11 0,00 0,684 50 1 1 0,9525 0,9525

2 and 3 8,29 22,27 13,98 0,00 0,678 50 1 1 0,9525 0,9525

3 and 4 15,11 31,07 15,96 0,00 0,664 50 1 1 0,9525 0,9525

4 and 5 22,27 44,67 22,4 0,10 0,564 45 1 1 0,9525 0,9525

5 and 6 31,07 55,87 24,8 0,30 0,539 45 1 1 0,9525 0,9525

6 and 7 44,67 64,08 19,41 0,00 0,628 50 1 1 0,9525 0,9525

7 and 8 55,87 75,87 20 0,00 0,699 50 1 1 0,9525 0,9525

8 and 9 64,08 86,07 21,99 0,00 0,741 50 1 1 0,9525 0,9525

9 and 10 75,87 92,65 16,78 0,00 0,725 50 1 1 0,9525 0,9525

3 cmps flooded

1, 2 and 3 0 22,27 22,27 0,00 0,633 50 1 1 0,9525 0,9525

2, 3 and 4 8,29 31,07 22,78 0,00 0,648 50 1 1 0,9525 0,9525

3, 4 and 5 15,11 44,67 29,56 0,10 0,544 45 1 1 0,9525 0,9525

4, 5 and 6 22,27 55,87 33,6 0,60 0,560 45 1 1 0,9525 0,9525

5, 6 and 7 31,07 64,08 33,01 0,70 0,579 45 1 1 0,9525 0,9525

6, 7 and 8 44,67 75,87 31,2 0,00 0,704 50 1 1 0,9525 0,9525

7, 8 and 9 55,87 86,07 30,2 0,00 0,756 50 1 1 0,9525 0,9525

8, 9 and 10 64,08 92,65 28,57 0,00 0,743 50 1 1 0,9525 0,9525

4 cmps flooded

1, 2, 3 and 4 0 31,07 31,07 0,00 0,634 50 1 1 0,9525 0,9525

2, 3, 4 and 5 8,29 44,67 36,38 0,50 0,537 40 1 1 0,9525 0,9525

3, 4, 5 and 6 15,11 55,87 40,76 0,60 0,539 40 1 1 0,9525 0,9525

4, 5, 6 and 7 22,27 64,08 41,81 1,00 0,636 45 1 1 0,9525 0,9525

5, 6, 7 and 8 31,07 75,87 44,8 0,80 0,730 45 1 1 0,9525 0,9525

6, 7, 8 and 9 44,67 86,07 41,4 0,00 0,783 50 1 1 0,9525 0,9525

7, 8, 9 and 10 55,87 92,65 36,78 0,00 0,758 50 1 1 0,9525 0,9525

5 cmps flooded

1, 2, 3, 4 and 5 0 44,67 44,67 0,70 0,529 40 1 1 0,9525 0,9525

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,90 0,541 40 1 1 0,9525 0,9525

3, 4, 5, 6 and 7 15,11 64,08 48,97 1,10 0,614 40 1 1 0,9525 0,9525

4, 5, 6 , 7 and 8 22,27 75,87 53,6 1,10 0,784 45 1 1 0,9525 0,9525

5, 6, 7, 8 and 9 31,07 86,07 55 0,90 0,788 50 1 1 0,9525 0,9525

6, 7, 8, 9 and 10 44,67 92,65 47,98 0,00 0,782 50 1 1 0,9525 0,9525

6 cmps flooded

1, 2, 3, 4, 5 and 6 0 55,87 55,87 1,00 0,546 40 1 1 0,9525 0,9525

2, 3, 4, 5, 6 and 7 8,29 64,08 55,79 1,10 0,620 40 1 1 0,9525 0,9525

3, 4, 5, 6, 7 and 8 15,11 75,87 60,76 / / / / / / /

4, 5, 6 , 7, 8 and 9 22,27 86,07 63,8 / / / / / / /

5, 6, 7, 8, 9 and 10 31,07 92,65 61,58 / / / / / / /



Table 34.Calculation of factor si for deepest subdivision draft, ds


length

Heel


1 cmp flooded [ m ]

1 0 8,29 8,29 0,00 0,811 55 1 1 0,9824 0,9824

2 8,29 15,11 6,82 0,00 0,807 55 1 1 0,9824 0,9824

3 15,11 22,27 7,16 0,00 0,810 55 1 1 0,9824 0,9824

4 22,27 31,07 8,8 0,00 0,792 55 1 1 0,9824 0,9824

5 31,07 44,67 13,6 0,00 0,683 50 1 1 0,9824 0,9824

6 44,67 55,87 11,2 0,00 0,766 55 1 1 0,9824 0,9824

7 55,87 64,08 8,21 0,00 0,792 55 1 1 0,9824 0,9824

8 64,08 75,87 11,79 0,00 0,822 55 1 1 0,9824 0,9824

9 75,87 86,07 10,2 0,00 0,840 55 1 1 0,9824 0,9824

10 86,07 92,65 6,58 0,00 0,829 55 1 1 0,9824 0,9824

2 cmps flooded

1 and 2 0 15,11 15,11 0,00 0,788 55 1 1 0,9824 0,9824

2 and 3 8,29 22,27 13,98 0,00 0,788 55 1 1 0,9824 0,9824

3 and 4 15,11 31,07 15,96 0,00 0,773 55 1 1 0,9824 0,9824

4 and 5 22,27 44,67 22,4 0,30 0,660 50 1 1 0,9824 0,9824

5 and 6 31,07 55,87 24,8 0,40 0,640 50 1 1 0,9824 0,9824

6 and 7 44,67 64,08 19,41 0,00 0,744 55 1 1 0,9824 0,9824

7 and 8 55,87 75,87 20 0,00 0,814 55 1 1 0,9824 0,9824

8 and 9 64,08 86,07 21,99 0,00 0,854 55 1 1 0,9824 0,9824

9 and 10 75,87 92,65 16,78 0,00 0,840 55 1 1 0,9824 0,9824

3 cmps flooded

1, 2 and 3 0 22,27 22,27 0,00 0,768 55 1 1 0,9824 0,9824

2, 3 and 4 8,29 31,07 22,78 0,00 0,758 55 1 1 0,9824 0,9824

3, 4 and 5 15,11 44,67 29,56 0,30 0,636 50 1 1 0,9824 0,9824

4, 5 and 6 22,27 55,87 33,6 0,80 0,655 50 1 1 0,9824 0,9824

5, 6 and 7 31,07 64,08 33,01 0,70 0,682 50 1 1 0,9824 0,9824

6, 7 and 8 44,67 75,87 31,2 0,00 0,816 55 1 1 0,9824 0,9824

7, 8 and 9 55,87 86,07 30,2 0,00 0,863 55 1 1 0,9824 0,9824

8, 9 and 10 64,08 92,65 28,57 0,00 0,852 55 1 1 0,9824 0,9824

4 cmps flooded

1, 2, 3 and 4 0 31,07 31,07 0,00 0,734 55 1 1 0,9824 0,9824

2, 3, 4 and 5 8,29 44,67 36,38 0,70 0,618 50 1 1 0,9824 0,9824

3, 4, 5 and 6 15,11 55,87 40,76 0,80 0,629 50 1 1 0,9824 0,9824

4, 5, 6 and 7 22,27 64,08 41,81 1,20 0,723 50 1 1 0,9824 0,9824

5, 6, 7 and 8 31,07 75,87 44,8 1,00 0,809 50 1 1 0,9824 0,9824

6, 7, 8 and 9 44,67 86,07 41,4 0,00 0,880 55 1 1 0,9824 0,9824

7, 8, 9 and 10 55,87 92,65 36,78 0,00 0,859 55 1 1 0,9824 0,9824

5 cmps flooded

1, 2, 3, 4 and 5 0 44,67 44,67 0,70 0,604 50 1 1 0,9824 0,9824

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,90 0,620 50 1 1 0,9824 0,9824

3, 4, 5, 6 and 7 15,11 64,08 48,97 1,10 0,697 50 1 1 0,9824 0,9824

4, 5, 6 , 7 and 8 22,27 75,87 53,6 1,30 0,847 50 1 1 0,9824 0,9824

5, 6, 7, 8 and 9 31,07 86,07 55 1,10 0,841 50 1 1 0,9824 0,9824

6, 7, 8, 9 and 10 44,67 92,65 47,98 0,00 0,872 55 1 1 0,9824 0,9824

6 cmps flooded

1, 2, 3, 4, 5 and 6 0 55,87 55,87 1,10 0,615 40 1 1 0,9824 0,9824

2, 3, 4, 5, 6 and 7 8,29 64,08 55,79 1,30 0,690 45 1 1 0,9824 0,9824

3, 4, 5, 6, 7 and 8 15,11 75,87 60,76 / / / / / / /

4, 5, 6 , 7, 8 and 9 22,27 86,07 63,8 / / / / / / /

5, 6, 7, 8, 9 and 10 31,07 92,65 61,58 / / / / / / /

P 68 Blanka Ascic


It is important to note that wherever the escape routes are flooded, the si factor is 0 meaning

the compartment is considered to be lost in case of a flooded vertical escape route. Figure 42

illustrates a situation in which the vertical escapes are not flooded therefore it would be

required to calculate factor si which is greater than zero.

Figure 42.The vertical escapes are not flooded

In Figure 43 it is illustrated that the vertical escapes are flooded, therefore in this case the

factor of survival si would be equal to zero.

Figure 43.The vertical escapes are flooded



On the other hand, flooding angle of relative openings limits the Range values as shown in

Figure 44. One should take into account location of the openings and hatches in order to

obtain more precise results.

Figure 44.Limitation of Range by openings

Opening

P 70 Blanka Ascic


5.2.3. Calculations of the Factor vm

The vm factor is the reduction factor which represents the probability that the spaces above the

horizontal subdivision will not be flooded. Figure 42 illustrates how watertight decks can

limit the damage vertically. If the damage is limited by H1 and H3 decks, the flooded

compartments will be R11, R12, R21 and R22.

Figure 45.Vertical subdivision of the ship

In this study case, the 92 m yacht is vertically divided by a watertight deck at 4.74 m

illustrated in Figure 43. The calculated factor vm represents the probability that the spaces

above this deck will remain intact, up to the main deck of the yacht.

Figure 46.The watertight deck of the 92 m yacht



The factor vm is obtained from the following formulae:

𝑣𝑚 = 𝑣 𝐻𝑗 , 𝑛 , 𝑚 ,𝑑 − 𝑣(𝐻𝑗 , 𝑛 , 𝑚−1 ,𝑑) (24)

Where

- Hj, n, m is the least height above the baseline within the longitudinal range of the mth

horizontal boundary

- Hj, n, m-1 is the least height above the baseline within the longitudinal range of the

(m-1)th

horizontal boundary

The two required factor shall be obtained from the following formulae:

𝑣 𝐻, 𝑑 = 0,8(𝐻 − 𝑑)

7,8

(25)

In case the Hm coincides with the uppermost watertight deck, the v (Hj, n, m) is considered to

be 1.

Factor vm was calculated for three different draft conditions according to the formulae and the

obtained results are given in the Table 35.

P 72 Blanka Ascic


Table 35.Calculation of factor vm for three different draft conditions

T=3,985 T=4,114 T=4,2

Compartment x1 x2 Damage length vm vm vm

1 compartment flooded [ m ]

1 0 8,29 8,29 0,9418 0,8245 0,8448

2 8,29 15,11 6,82 0,9418 0,8245 0,8448

3 15,11 22,27 7,16 0,9418 0,8245 0,8448

4 22,27 31,07 8,8 0,9418 0,8245 0,8448

5 31,07 44,67 13,6 0,9418 0,8245 0,8448

6 44,67 55,87 11,2 0,9418 0,8245 0,8448

7 55,87 64,08 8,21 0,9418 0,8245 0,8448

8 64,08 75,87 11,79 0,9418 0,8245 0,8448

9 75,87 86,07 10,2 0,9418 0,8245 0,8448

10 86,07 92,65 6,58 0,9418 0,8245 0,8448

2 compartments flooded

1 and 2 0 15,11 15,11 0,9418 0,8245 0,8448

2 and 3 8,29 22,27 13,98 0,9418 0,8245 0,8448

3 and 4 15,11 31,07 15,96 0,9418 0,8245 0,8448

4 and 5 22,27 44,67 22,4 0,9418 0,8245 0,8448

5 and 6 31,07 55,87 24,8 0,9418 0,8245 0,8448

6 and 7 44,67 64,08 19,41 0,9418 0,8245 0,8448

7 and 8 55,87 75,87 20 0,9418 0,8245 0,8448

8 and 9 64,08 86,07 21,99 0,9418 0,8245 0,8448

9 and 10 75,87 92,65 16,78 0,9418 0,8245 0,8448


1, 2 and 3 0 22,27 22,27 0,7957 0,8245 0,8448

2, 3 and 4 8,29 31,07 22,78 0,7957 0,8245 0,8448

3, 4 and 5 15,11 44,67 29,56 0,7957 0,8245 0,8448

4, 5 and 6 22,27 55,87 33,6 0,7957 0,8245 0,8448

5, 6 and 7 31,07 64,08 33,01 0,7957 0,8245 0,8448

6, 7 and 8 44,67 75,87 31,2 0,7957 0,8245 0,8448

7, 8 and 9 55,87 86,07 30,2 0,7957 0,8245 0,8448

8, 9 and 10 64,08 92,65 28,57 0,7957 0,8245 0,8448


1, 2, 3 and 4 0 31,07 31,07 0,7957 0,8245 0,8448

2, 3, 4 and 5 8,29 44,67 36,38 0,7957 0,8245 0,8448

3, 4, 5 and 6 15,11 55,87 40,76 0,7957 0,8245 0,8448

4, 5, 6 and 7 22,27 64,08 41,81 0,7957 0,8245 0,8448

5, 6, 7 and 8 31,07 75,87 44,8 0,7957 0,8245 0,8448

6, 7, 8 and 9 44,67 86,07 41,4 0,7957 0,8245 0,8448

7, 8, 9 and 10 55,87 92,65 36,78 0,7957 0,8245 0,8448


1, 2, 3, 4 and 5 0 44,67 44,67 0,7957 0,8245 0,8448

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,7957 0,8245 0,8448

3, 4, 5, 6 and 7 15,11 64,08 48,97 0,7957 0,8245 0,8448

4, 5, 6 , 7 and 8 22,27 75,87 53,6 0,7957 0,8245 0,8448

5, 6, 7, 8 and 9 31,07 86,07 55 0,7957 0,8245 0,8448

6, 7, 8, 9 and 10 44,67 92,65 47,98 0,7957 0,8245 0,8448


1, 2, 3, 4, 5 and 6 0 55,87 55,87 0,7957 0,8245 0,8448

2, 3, 4, 5, 6 and 7 8,29 64,08 55,79 0,7957 0,8245 0,8448

3, 4, 5, 6, 7 and 8 15,11 75,87 60,76 0,7957 0,8245 0,8448

4, 5, 6 , 7, 8 and 9 22,27 86,07 63,8 0,7957 0,8245 0,8448

5, 6, 7, 8, 9 and 10 31,07 92,65 61,58 0,7957 0,8245 0,8448



5.2.4. Final Results of the Attained Subdivision Index A

With all the individual factors determined, it is possible to obtain the final result for the partial

attained index Al, Ap and As and the results are presented in the Table 36.

Table 36.Final calculations of the partial attained subdivision index Al, Ap and As

Compartment x1 x2 Damage length T=3,985 T=4,114 T=4,2

1 compartment flooded [ m ]

1 0 8,29 8,29 0,0540 0,0495 0,0524

2 8,29 15,11 6,82 0,0221 0,0203 0,0214

3 15,11 22,27 7,16 0,0241 0,0221 0,0234

4 22,27 31,07 8,8 0,0349 0,0320 0,0338

5 31,07 44,67 13,6 0,0725 0,0666 0,0704

6 44,67 55,87 11,2 0,0528 0,0485 0,0513

7 55,87 64,08 8,21 0,0308 0,0283 0,0299

8 64,08 75,87 11,79 0,0576 0,0528 0,0558

9 75,87 86,07 10,2 0,0451 0,0414 0,0437

10 86,07 92,65 6,58 0,0407 0,0374 0,0395


1 and 2 0 15,11 15,11 0,0364 0,0334 0,0353

2 and 3 8,29 22,27 13,98 0,0295 0,0271 0,0287

3 and 4 15,11 31,07 15,96 0,0337 0,0309 0,0327

4 and 5 22,27 44,67 22,4 0,0423 0,0388 0,0410

5 and 6 31,07 55,87 24,8 0,0461 0,0423 0,0447

6 and 7 44,67 64,08 19,41 0,0392 0,0360 0,0380

7 and 8 55,87 75,87 20 0,0397 0,0365 0,0385

8 and 9 64,08 86,07 21,99 0,0433 0,0398 0,0420

9 and 10 75,87 92,65 16,78 0,0415 0,0381 0,0403


1, 2 and 3 0 22,27 22,27 0,0093 0,0101 0,0106

2, 3 and 4 8,29 31,07 22,78 0,0075 0,0081 0,0086

3, 4 and 5 15,11 44,67 29,56 0,0066 0,0072 0,0076

4, 5 and 6 22,27 55,87 33,6 0,0033 0,0036 0,0038

5, 6 and 7 31,07 64,08 33,01 0,0047 0,0051 0,0054

6, 7 and 8 44,67 75,87 31,2 0,0086 0,0094 0,0099

7, 8 and 9 55,87 86,07 30,2 0,0039 0,0042 0,0045

8, 9 and 10 64,08 92,65 28,57 0,0057 0,0062 0,0065


1, 2, 3 and 4 0 31,07 31,07 0,0030 0,0033 0,0035

2, 3, 4 and 5 8,29 44,67 36,38 0,0021 0,0023 0,0024

3, 4, 5 and 6 15,11 55,87 40,76 0,0005 0,0005 0,0005

4, 5, 6 and 7 22,27 64,08 41,81 0,0002 0,0002 0,0002

5, 6, 7 and 8 31,07 75,87 44,8 0,0012 0,0013 0,0013

6, 7, 8 and 9 44,67 86,07 41,4 0,0010 0,0011 0,0011

7, 8, 9 and 10 55,87 92,65 36,78 0,0005 0,0006 0,0006


1, 2, 3, 4 and 5 0 44,67 44,67 0,0004 0,0004 0,0005

2, 3, 4, 5 and 6 8,29 55,87 47,58 0,0000 0,0000 0,0000

3, 4, 5, 6 and 7 15,11 64,08 48,97 0,0000 0,0000 0,0000

4, 5, 6 , 7 and 8 22,27 75,87 53,6 0,0000 0,0000 0,0000

5, 6, 7, 8 and 9 31,07 86,07 55 0,0000 0,0000 0,0000

6, 7, 8, 9 and 10 44,67 92,65 47,98 0,0000 0,0000 0,0000


1, 2, 3, 4, 5 and 6 0 55,87 55,87 0,0000 0,0000 0,0000

2, 3, 4, 5, 6 and 7 8,29 64,08 55,79 0,0000 0,0000 0,0000

3, 4, 5, 6, 7 and 8 15,11 75,87 60,76 0,0000 0,0000 0,0000

Al Ap As

0,8447 0,7853 0,8300

P 74 Blanka Ascic


It is verified that each partial attained index Al, Ap and Ad is greater than 0.9R value, as

required and presented below:

0,9R Al Ap Ad

0,6120 0,8447 0,7853 0,8300

The final value is determined according to equation (4).

Final result of the attained subdivision index A is:

A=0.815037

Comparing the two obtained results, it is clear that the attained index A is greater than the

required index R by a margin of 16.56%.

A (0.815037) > R (0.680054)



6. COMPARISON OF RESULTS

The results, assumptions and remarks on PYC damage stability are the following:

1. The following GM values were used in determining compliance with Chapter 4, Part

II, Para 4.5 and 4.6 (SOLAS Regulation 6 and 7 respectively):

Initial Condition Draught Trim Min GM

dl 3.985 0.0 1.50

dp 4.114 0.0 1.50

ds 4.2 0.0 1.50

2. Using the above values an Attained Index “A” value of 0.815037 was achieved against

an estimated Required Index “R” value of 0.680054.

3. In addition the partial indices Al, Ap and As were confirmed as being greater than

0.9R

4. Given the above it is considered that the vessel’s subdivision is sufficient to meet the

requirements of Chapter 4, Part II, Para 4.5.

5. The following assumptions were made in the calculations:

- Information regarding the opening was taken from the GA – considered openings were

the vertical escapes which were assumed to be 0.6 m above the main deck

- Air pipes and ventilators which are weathertight were not considered

- Cross – flooding was not considered

6. If other information is provided regarding openings, controls and piping systems it

may be prudent to assess the impact on the “s” values.

7. It was assumed that a double bottom with a height greater than b/20 is fitted through

the vessel. There should be some clarifications regarding the part of the double bottom

below the engine room, laundry and cold stores in order to be sure of that assumption.

P 76 Blanka Ascic


The calculations of probabilistic damage stability were performed by Classification Society

“Lloyd’s Register” according to their rules. Using the same assumptions and initial conditions,

the reached result regarding the Attained Index “A” and the Required Index “R” was

following:

1. The following GM values were used in determining compliance with Chapter 4, Part

II, Para 4.5 and 4.6 (SOLAS Regulation 6 and 7 respectively):

Initial Condition Draught Trim Min GM

dl 3.985 0.0 1.50

dp 4.114 0.0 1.50

ds 4.2 0.0 1.50

2. Using the above values an Attained Index “A” value of 0.82163 was achieved against

an estimated Required Index “R” value of 0.68.

Since the assumptions and initial conditions were the same, it is possible to compare the two

obtained results. High similitude was accomplished as expected and shown in the Table 37.

Table 37.Comparison of the LR's and PYC results

Lloyd's Register Passenger Yacht Code

R A R A

Obtained values 0,68 0,82163 0,68005 0,81504

Required Index "R" Attained Index "A"

Difference in % between the

results 0,00798 0,80243

It is notable that the calculation of Attained Index “A” and Required Index “R” using the rules

of the Passenger Yacht Code in Excel managed to reach lower than 1% difference in

comparison with the results obtained by Lloyd’s Register. It is therefore possible and safe to

use this approximation for a rough estimation of the Attained Index “A” and Required Index

“R” regarding the probabilistic damage stability calculations.



7. CONCLUSIONS


after flooding. Both deterministic and probabilistic methods have the same objective to find

the most effective possible subdivision of the ship.

Deterministic method is based on the assumed damage scenarios.SOLAS90 two compartment

standard is a deterministic approach which ensures the survivability of the ship in case of

flooding of up to two adjacent compartments and up to date there has been no SOLAS90 ship

that sunk.

Even so, the deterministic approach is being often replaced by probabilistic one which is

based on the statistical evidence making it therefore a more realistic approach and is now

mandatory for cargo and passenger ships above 80 m.

The new Passenger Yacht Code was introduced aiming to provide a SOLAS equivalent for

yachts wishing to carry up to 36 passengers taking into consideration operating purpose of a

yacht since it has been recognized that the international conventions have been onerous in

terms of design and cost.

Within this Master Thesis, after achieving satisfying subdivision of the 92 m yacht with a

deterministic approach, the probabilistic verification has been performed in Excel based on

Passenger Yacht Code rules and the results have been compared with the ones reached by

Lloyd’s Register. The results of the attained index A and the required index R are highly

similar, with less than 1% difference. It is therefore possible to use this sort of approach to

probabilistic calculations for a rough estimation of the ships subdivision.

Deterministic approach still remains the most reliable way of determining compartments

definition in a ship given its unsinkable history, but can be reassessed when it becomes too

onerous with the demands as it can happen while taking into account the purpose of the yacht.

Probabilistic method considers a large number of damage cases in the calculations which

requires more work but can result with a more flexible bulkhead arrangement in the end. The

Passenger Yacht Code and the probabilistic approach to damage stability have been therefore

well received giving more flexibility regarding general arrangement and lifesaving appliances

which are of high importance in the yacht industry.

P 78 Blanka Ascic


8. ACKNOWLEDGEMNTS

This thesis was developed in the frame of the European Master Course in “Integrated

Advanced Ship Design” named “EMSHIP” for “European Education in Advanced Ship

Design”, Ref.: 159652-1-2009-1-BE-ERA MUNDUS-EMMC.

Acknowledgments to:

- Mr. Emanuele Camporese, Benetti Shipyard, Italy

- Mr. Massimiliano Caviglia, RINA Services, S.p.A., Italy

- Mrs. Maria Acanfora, PhD, Aalto University, Finland



9. REFERENCES

Publication

Hardy, A.M., Barrie, R., Julien, S., Evans, G., Roy, R., The New

Generation of Passenger Superyachts – SOLAS or PYC?. Technical

Paper BMT Yachts, paper 61

Santos, T.A. and Guedes Soares, C., Probabilistic approach to

damage stability, Taylor & Francis Group, London, UK, pp. 227-

242.

Francescutto, A. and Papanikolaou, A.D., Buoyancy, stability, and

subdivision: from Archimedes to SOLAS 2009 and the way ahead,

International Journal of Engineering for the Maritime Environment

Book

The Red Ensign Group, The Passenger Yacht Code, Fourth Edition –

January 2014

SOLAS, Consolidated Edition, 2002

Captain D. R. Derrett, Ship Stability for Masters and Mates, Fifth

Edition - 1999, Butterworth -Heinemann

Pishro-Nik, H., Introduction to Probability, Statistics, and Random

Processes, Kappa Research, LLC 2014

Internet document

Ruponen, P., Probabilistic Damage Stability SOLAS 2009,

November 2014, Available from: http://stab2012.ntua.gr

Baltsersen, J.P., Erichsen, H., Presentation of Probabilistic Damage

Stability regulations, New SPS Code and MARPOL Regulation 12A,

Available from: http://www.skibstehniskselskab.dk

Strachan, J., Probabilistic versus Deterministic Damage Stability,

Available from: http://www.bctq.com

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